Abstract

The THz and infrared photonic dispersion relations of superlattices composed of polaritonic material and bismuth (Bi) layers are theoretically investigated. The semimetal Bi presents a far-infrared response described by a Drude-like formula with a large high-frequency background dielectric constant. We have considered three different polaritonic materials: NaBr, LiCl and LiH, such that the Bi plasma frequency lies above, in-between and below the characteristic frequencies of the polaritonic materials, respectively. Investigating the photonic band structure of each superlattice, we have found that when the Bi plasma frequency lies below the polaritonic gap, appears a photonic pass band of negative dispersion for TM modes just above the longitudinal-optical phonon frequency, attributed to the frequency dependence of the permittivity for the polaritonic material and the large high-frequency background dielectric constant for Bi, that can be relevant to the metamaterials community.

© 2015 Optical Society of America

1. Introduction

The study of the interaction of electromagnetic waves with periodic multilayer systems goes back at least a couple of centuries ago, with the pioneering results of Lord Rayleigh in 1888, showing the existence of a photonic band-gap in one dimensional multilayer dielectric stacks. In recent years, the interest in the field has grown with the seminal works of Yablonovitch [1] and John [2] both published in 1987, extending the study not only to one dimensional systems. Yablonovitch showed that it is possible to inhibit totally the spontaneous emission of atoms by modifying its environment, opening the possibility of wide technological applications that we appreciate nowadays. On the other hand, John showed that for specific disordered dielectric superlattices it is possible to strongly localize light, which is known as Anderson localization [3]. The applications of such periodic systems, named presently as photonic crystals, are focused mainly on one dimensional periodic systems in the thin-films field, used to eliminate undesired reflections in mirrors and lenses, as well as coatings in paint and ink industries. The fabrication of one dimensional systems can be as easy as simply stacking layers onto a substrate. Drilling holes in a suitable substrate can be a way of fabricating two dimensional photonic crystals, and in fact holey fibers are commercially available at present. However, the situation is remarkable different for three dimensional structures, being still far from commercial applications. Among the variety of fabrication techniques highlights photolithography [4], interfering two pulsed lasers, and self-assembly colloidal crystals, such as inverse opals [5, 6].

In the last fifteen years, the interest in the field of photonic crystals has been renewed with the appearance of the photonic metamaterials or simply called metamaterials, obtaining the first experimental realization in 2000 by Smith et. al. [7], showing the existance of a band where both the dielectric permittivity and the magnetic permeability become negative at GHz frequencies. The main properties of such a system were first studied by the pioneering work of Veselago in 1968 [8], and since then, the topic has attracted the attention of a large number of researchers. The potential applications of such systems, not only in electromagnetism but also in acoustic [9] and seismic [10] fields, and recently in medicine [11], exploit their properties such as perfect lensing [12] and invisibility [13–16].

As it is well known, metal is the main functional component of most of today’s metamaterials, basing their fascinating properties and possible applications mostly on the negative permittivity response of the metal, resulting from the resonant free electron currents [7,17]. In order to reduce losses, it has been proposed the use of high-index dielectrics instead of metals achieving both negative permeability (like artificial magnetism) and negative permittivity [18–20]. A suitable alternative can be the use of polaritonic materials, which combine the advantages of both metallic and high-index dielectric materials. Polaritonic materials are polar crystals where an incident electromagnetic wave can excite optical phonons (lattice vibrations) within the crystal, occurring this coupling typically in the THz regime [21]. The electromagnetic response of this type of materials can be described by a Lorentzian resonant electric permittivity response function, characterized by both strong positive and negative permittivity regimes, making polaritonic materials a perfect replacement of metals in metamaterials working at THz frequencies. By tailoring properly such polaritonic inclusions, it is possible to achieve metamaterial properties like negative effective permeability [20] or negative refractive index [19, 22].

With the recent developing technology of THz sources, such as Quantum Cascade Lasers (QCL) [23], the interest in exploring and exploiting the THz regime becomes more appealing, due to the huge technological applications, ranging from telecommunications [24], security and sensing [25], tissue imaging [26], and even in astronomy [27]. Since the conventional optical devices are not suitable in general to manipulate THz beams, there is the need to develop new kind of materials to be used as lenses, beam splitters, polarizers, collimators, etc. A good candidate to fulfill the requirements are the so-called THz metamaterials, that is, metamaterials with polaritonic inclusions showing resonances at THz regime, a topic that has attracted the attention of a growing scientific community (see, for example, [28–33] and references therein). Indeed, as shown in previous works [29,30], two-dimensional photonic crystals composed of dielectric-polaritonic or polaritonic-polaritonic material constituents behave as THz uniaxial metamaterials with hyperbolic dispersion relation. Moreover, the THz photonic band structure for superlattices of metal and polar material is characterized by flat Fabry-Perot resonance bands outside the polaritonic gap [33]. Such Fabry-Perot resonance bands turn out to be noticeably altered by the metal spatial dispersion, which is well manifested in the THz range [34, 35]. Another interesting conducting material to be used in THz metamaterials is the semimetal bismuth (Bi), since its frequency-dependent permittivity is well described by the local Drude model with an infrared plasma frequency and a large high-frequency background dielectric constant [36, 37]. The use of Bi as one of the material constituents in polaritonic superlattices might lead to a strong plasma-phonon polariton coupling, which could manifest itself in the photonic dispersion, as well as optical spectra.

In this paper, we present a study of a one-dimensional periodic stack-slab system, using a polaritonic slab material inserted in between bismuth slabs. We explore the consequences in the THz spectrum of the whole system by changing the position of the polaritonic gap of the polaritonic material with respect to the Bi plasma frequency, showing the appearance of frequency bands with negative dispersion. In Sec. 2, we present the general analytical formulas for the photonic dispersion relation for transverse-electric (TE) and transverse-magnetic (TM) modes in a superlattice composed of alternating layers of polaritonic material and Bi. In Sec. 3, explicit formulas for the calculation of the principal values of the macroscopic permittivity tensor are applied in order to analyze the photonic dispersion relation at long wavelengths for polaritonic-material/Bi superlattices, as well as their optical characterization, named reflection and transmission spectra. Finally, the size quantization of polaritons in superlattices, having relatively thick layers of both polaritonic material and Bi (i.e. when the long wavelength approach does not hold in the THz range), are studied in Sec. 4. Our findings are summarized in Sec. 5.

2. Photonic dispersion

We consider a binary superlattice composed of metallic and resonant-dielectric layers, which are alternated along the z-axis (Fig. 1), both materials being non-magnetic materials. The infrared response of the polaritonic material (a-layer) is described with a resonant permittivity of the form

εa=εa,(ω2ωLO2+iωνa)/(ω2ωTO2+iωνa),
while the metallic (b-layer) is characterized by a frequency-dependent permittivity modeled with the local Drude model
εb=εb,[1ωP2/(ω2+iνbω)],
where ω is the frequency of the electromagnetic field; ωP is the plasma frequency of the metallic layer; εa, and εb, correspond to the high-frequency limit dielectric constant for each material, determining the contribution of bounded electrons in completely-filled bands to the dielectric function; ωLO and ωTO are respectively the frequencies of the longitudinal and transverse optical phonon modes at the center of the Brillouin zone; and νa and νb are the damping constants for each material, resp. The thickness of the resonant-dielectric layer is da while for the metallic layer is db = Λ − da (Λ is the superlattice period).

 figure: Fig. 1

Fig. 1 Scheme of a superlattice with two alternating non-magnetic polaritonic-material/bismuth layers. The system represents a uniaxial crystal with the c-axis parallel to the z direction.

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Using the permittivities (1) and (2), Maxwell equations, the boundary conditions for the electric and magnetic fields (i.e. the continuity of their tangential components at the interfaces of the superlattice layers), and the Bloch theorem, one can derive the dispersion equation for the plasma-phonon polaritonic modes as [38–41]

cos(kzΛ)=cos(kzada)cos(kzbdb)αsin(kzada)sin(kzbdb),
where
α={12[(kza/kzb)+(kzb/kza)],for TE modes,12[(εbkza/εakzb)+(εakzb/εbkza)],for TM modes.

Here, kz is the Bloch wave vector, kza=εaω2/c2kx2, kzb=εbω2/c2kx2, and kx is given by the x-component of the wave vector of incident light on the superlattice (in practice, a multilayer periodic stack of finite size L ≫ Λ), and c is the velocity of light in vacuum.

3. Effective medium approach

In the case of wavelengths much larger than the superlattice period Λ, |kz|Λ ≪ 1, the optical response of a binary superlattice can be described by using an effective permittivity tensor εij = εiδij (i, j = x,y,z) with diagonal components given by [42]

εx=εy=(εada+εbdb)/Λandεz1=Λ1[(da/εa)+(db/εb)].

Bi is characterized by a dielectric tensor corresponding to a uniaxial crystal, which has two basic dielectric tensor components corresponding to the ordinary and extraordinary axes. Here εb corresponds to the ordinary axis since the z-axis is oriented parallel to the growth direction of the superlattice. Thus, in the case of s-polarization the Bi optical axis should be oriented along the x-axis, whereas for p-polarization should be oriented along y-axis.

The use of Rytov formulas (5) for superlattices of metal components can be questioned [43–46], because they were derived by assuming smooth variations of the electromagnetic field inside each layer,

kzada1,kzbdb1,
besides the condition |kz|Λ ≪ 1. A more accurate expression for the εx and εy components of the frequency-dependent effective permittivity tensor of a binary superlattice have been derived previously [46]:
εx=εy=εb(1[1(ωΛ/2c)εbtan[(ωΛ/2c)εb]Λεbda(εaεb)]1),
which holds when the magnitude of the parameter |εb|ωda/c is much smaller than 1, that can be rewritten as
|εb|ωΛcdaΛ1,
that is, the wavelength in the b-medium should be much larger than the superlattice period and the filling fraction of the a-medium should be small enough.

In the general case (|kz≤ π), the effective optical response of the supperlattice is nonlocal since the permittivity depends not only on the frequency, but also on the wave number kz [47, 48].

Using the diagonal effective permittivity tensor, εiδij (i = x,y,z), the dispersion relation for TE and TM electromagnetic modes with zero y-component of the wave vector (ky = 0) can be written as

kz={(εyω2/c2)kx2,for TE modes,εx[(ω2/c2)(kx2/εz)],for TM modes.

We equate kx with the x-component of the wave vector of the incident light on the superlattice: kx = (ω/c)sin θ, where θ is the incidence angle. Then, the dispersion relations (9) can be rewritten as

kz=ωcη1,η1=εysin2θ;for TE modes,
kz=ωcη2,η2=εx[1(sin2θ/εz)];for TM modes.

In the next subsections, the dispersion curves for TE and TM modes in NaBr/Bi, LiCl/Bi, and LiH/Bi superlattices, for an incidence angle θ = 45°, will be calculated by using the exact expressions (3) and (4). Such superlattices are interesting because the plasma frequency for Bi is in the THz range (ωP = 60.77 × 1012rad/s (0.04 eV), taken from [36]) and close to the frequencies of the longitudinal and transverse optical phonon modes (at Γ point) of the polaritonic materials (see Table 1 where the high-frequency permittivity ε values are also indicated). Other Bi parameters used here are [36, 37]: its relatively-large background permittivity εb, = 102 and a damping parameter ħνb = 9 × 103eV. The chosen damping constant for a polaritonic material is νa = 102ωTO. Besides, the thicknesses of the superlattice layers are: da = 0.3Λ and db = 0.7Λ (Λ = da + db = 0.15µm). Consequently, at THz frequencies, the photonic band structures for such superlattices can also be obtained by applying the effective medium approaches discussed above. According to the chosen parameters, the conditions for applying Rytov formulas (5), i.e. the smooth variation of the “microscopic” field inside the layers (6), are well satisfied at frequencies ω of the order of the Bi plasma frequency ωP except, perhaps, near the resonance frequency ωTO for the polaritonic material. In addition, in using the other formula for the effective permittivity components εx = εy [i.e. Eq. (7)], the condition of smallness of the parameter |εb|ωda/c|, Eq. (8), is fulfilled within a wide frequency interval (see Fig. 2). Notice that the quantity |εb|ωda/c is independent of the resonant THz response of the a-layers.

Tables Icon

Table 1. Parameters of the polaritonic materials

 figure: Fig. 2

Fig. 2 Frequency dependence of the real (solid line, 1) and imaginary (dashed line, 2) parts of the parameter εb(ω)ωda/c calculated for a superlattice composed of alternating Bi and polaritonic layers.

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Below, we will also show s- and p-polarization reflectivity and transmissivity spectra for NaBr/Bi, LiCl/Bi, and LiH/Bi multilayer stacks, having 50 bilayers and being embedded in air. The optical spectra are calculated by applying the transfer matrix method [40] and compared with the photonic dispersion curves for polaritonic-material/Bi superlattices.

3.1. NaBr/Bi superlattice (ωLO < ωP)

In the case of NaBr/Bi superlattice, the plasma frequency ωP of Bi is above the reststrahlen band for NaBr. In panels (a) and (c) of Fig. 3, we present the frequency dependences of the quantities η1 and η2, whose square root determines the wave vector kz for TE and TM modes according to Eqs. (10) and (11). The curves η1(ω) and η2(ω) were calculated with applying both Eq. (5) and Eq. (7). However, the difference between their predictions is not discernible in the panels. Below ωP, both η1 and η2 have a negative real part, as well as a large imaginary one. For this reason, the values of kz for TE and TM modes are complex numbers with relatively-large imaginary parts at ω < ωP, whereas they become positive real numbers at ω > ωP. So, there is a low-frequency stop band, whose width Δ is determined by an effective plasma frequency ωP,eff≡ ωP,eff), which can be estimated by using Rytov formulas. Indeed, employing Eqs. (2) and (5), we can write the effective permittivity components εx and εy as

εx=εy=ε¯(1ωP2,effω(ω+iνb)),
where
ωP,eff=dbΛεb,ε¯ωP,
ε¯=(εa,da+εb,db)/Λ.

 figure: Fig. 3

Fig. 3 Left panels: Curves of frequency ω versus η1 (10) [η2 (11)] for TE [TM] modes in a NaBr/Bi superlattice at θ = 45°. Right panels: s– and p–polarization reflectivity and transmissivity spectra for a stack of 50 NaBr/Bi bilayers in air.

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In deriving Eq. (12), we have used εa = εa, which is valid at frequencies ωωP > ωLO. From Eqs. (10)(14), it follows that ℜη1 [ℜη2] vanishes at ω ≈ ωP,eff ≈ ωP in good agreement with the results shown in panel (a) [(c)] of Fig. 3.

Subfigures 3(b) and 3(d) respectively show the s– and p–polarization reflectivity and transmissivity spectra for a stack of 50 NaBr/Bi bilayers in air. The angle of the incident light is θ = 45°. These results confirm the existence of a stop band below the effective plasma frequency ωP,eff (13). Indeed, at ω < ωP,eff ≈ ωP, the transmissivities Ts and Tp are extremely small. The fact that the reflectivity spectra (Rs and Rp) are smaller than the unity, implies that the absorption (A = 1−R−T) inside the multilayer system is considerable. Unlike the Rs spectrum, having only one resonance at ω = ωTO < ωP, the reflectivity Rp exhibits an additional resonance at ω = ωLO < ωP. Above the effective plasma frequency ωP,eff, there is a pass band where both transmissivity and reflectivity spectra have oscillations associated with Fabry-Perot resonances occurring within the whole multilayer stack.

3.2. LiCl/Bi superlattice (ωTO < ωP < ωLO)

In Fig. 4 (panels (a) and (c)), the frequency dependence of η1 (10) [η2 (11)] for TE [TM] modes in a LiCl/Bi superlattice at θ = 45° is presented. The curves η1(ω) and η2(ω) were calculated by using both effective-medium approaches, namely Eqs. (5) and (7). However, their difference is almost undistinguishable. In the case of the LiCl/Bi superlattice, the Bi plasma frequency ωP is between the frequencies of the transverse (ωTO) and longitudinal (ωLO) optical phonons for LiCl. Since the wave vector kz is given by the square root of η1 and η2 for TE and TM photonic modes, respectively, a low-frequency stop band should appear below the Bi plasma frequency ωP where both η1 and η2 have negative real parts together with large imaginary parts. Our numerical results for the s- and p-polarizaion reflectivity and transmissivity spectra (see panels (b) and (d) of Fig. 4) confirm the presence of the low-frequency gap at ω < ωP. So, the bottom of the first pass band for both TE and TM modes is below ωLO, i.e. inside the LiCl polaritonic gap. As in NaBr/Bi superlattice system, we can introduce an effective plasma frequency ωP,eff, which limits the low-frequency stop band. Using Rytov formulas (2) and considering the relatively-large Bi background permittivity (εb, ≫ |εa(ω)| at ωωP > ωTO), the components εx and εy of the effective permittivity tensor can be written as

εx=εyεb,dbΛ(1ωP,eff2ω(ω+iνb)),
with ωP,eff = ωP. Hence, the real parts of both η1(ω) (10) and η2(ω) (11) should vanish at frequencies close to ωP (see panels (a) and (c) of Fig. 4). The photonic dispersion for TM modes also exhibits a narrow stop band near ωLO (compare subfigures 4(c) and 4(d)) and at the bottom of their second pass band (at ω = ωU), the real part of the factor (1sin2θεz) in η2 (11) vanishes.

 figure: Fig. 4

Fig. 4 Left panels: Curves of frequency ω versus η1 (10) [η2 (11)] for TE [TM] modes in a LiCl/Bi superlattice at θ = 45°. Right panels: s– and p–polarization reflectivity and transmissivity spectra for a stack of 50 LiCl/Bi bilayers in air.

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3.3. LiH/Bi superlattice (ωP < ωTO)

For the LiH/Bi superlattice, the LiH reststrahlen band is above the Bi plasma frequency ωP and, consequently, the dispersion curves for both TE and TM modes have a low-frequency band gap at ω < ωP where η1 (10) [η2 (11)] have negative real parts and large imaginary parts (see subfigures 5(a) and 5(c)). It should be commented that the frequency dependences η1(ω) and η2(ω) were calculated by using formulas (5) and (7) for the principal values of the effective permittivity tensor. As above (panels (a) and (c) in Figs. 3 and 4), there is no visible difference between the predictions of Rytov formula (5) and those of (7) since the superlattice layers are rather thin. The low-frequency band gap is well seen in both reflectivity an transmissivity spectra shown in panels (b) and (d) of Fig. 5. The first two pass bands for TE modes are separated by a narrow gap near the frequency of transverse optical phonons (ωTO). On the other hand, the band structure for the TM photonic modes has an additional narrow gap around ωLO. These results are interesting because the propagation of photonic modes in the superlattice can occur within the LiH polaritonic gap despite the fact that the photon modes in the polaritonic material a-layers are evanescent waves.

 figure: Fig. 5

Fig. 5 Left panels: Curves of frequency ω versus η1 (10) [η2 (11)] for TE [TM] modes in a LiH/Bi superlattice at θ = 45°. Right panels: s– and p–polarization reflectivity and transmissivity spectra for a stack of 50 LiH/Bi bilayers in air.

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The effective plasma frequency, determining the width of the low-frequency photonic gap, can be analytically calculated with the Rytov formula (5). The frequency dependence of the components εx and εy at low frequencies (ω < ωTO) is given by

εx=εyε˜(1ωP,eff2ω(ω+iνb)),
where
ωP,eff=dbΛεb,ε˜ωPωP,
ε˜=(εa(0)da+εb,db)/Λ.

Using Eqs. (10), (11), (5) (this last for εz) and the approximate formula (16), it follows that the real parts of the quantities η1 and η2 vanish at frequencies very close to ωP,eff (17), in good agreement with the curves shown in the panels (a) and (c) of Fig. 5.

To determine the zeros ω1 and ω2 of η1(ω) and η2(ω), respectively, within the polaritonic gap (ωP < ωTOω < ωLO), it is convenient to write the effective components εx and εy [Eq. (5)] as

εx=εyεa.ωLO2ωTO2ω2ωTO2daΛ+εb,dbΛ.

Since the Bi background dielectric permittivity is large in comparison with that of LiH (εb,εa,), the zeros of the real parts of η1(ω) (i.e εy sin2 θ) and η2(ω) (i.e. εx) in the polaritonic gap are close to ωTO:

ω12=ωTO2+εa,da(εb,dbΛsin2θ)(ωLO2ωTO2),
ω22=ωTO2+εa,daεb,db(ωLO2ωTO2),

Substituting the parameters for LiH and Bi into Eqs. (20) and (21), we get ω1 ≈ ω2 = 1.02ωTO. The quantity ℜ[η2] for TM modes has another zero at ω = ωU (the bottom of the third TM pass band, see subfigures 5(c)) because of the vanishing of the factor (1sin2θεz) in (11) at that frequency.

4. Size-quantized polaritons

Let us calculate the photonic band structure of a LiH/Bi superlattice (ωP < ωTO) with layers thicker than those considered in Subsec. 3.3, such that the conditions (6) and (8) for the applicability of the effective medium approaches are not satisfied in the THz and far-infrared ranges. In Fig. 6, we present the photonic dispersion for both TE and TM modes calculated by using the general expressions (3) and (4). The thicknesses of LiH and Bi layers are, respectively, da = 0.9Λ and db = 0.1Λ, where Λ = 5.914µm (the reason for choosing such a Λ value is explained below) and the incidence angle is set to θ = 45°. Fig. 6 exhibits dispersion curves, kz(ω), corresponding to the solutions of Eqs. (3) and (4), whose imaginary part ℑ[kz] is positive. As it is seen in Fig. 6, the band structures for both TE and TM modes below the polaritonic gap (ω < ωTO) are characterized by narrow pass bands, associated with Fabry-Perot resonances arising in the polaritonic layer because of the high contrast between LiH and Bi impedances (|α| ≫ 1). In such a case, the dispersion equation (3) for the electromagnetic modes has solutions for the Bloch wave number kz with |ℜ[kz]| < π/Λ and 0 < ℑ[kz] < |ℜ[kz]| in slightly-dispersive bands, including the frequencies ωj (j = 1,2,3,…) where the condition

[kza]da=jπ,j=1,2,3,,
is fulfilled. In Fig. 7, the blue circles indicate the frequencies where the value of [kza]da/π is precisely an integer. In fact, Eq. (22) was used to choose the thickness da of LiH layer such that the first Fabry-Perot resonance band appear at ħωj=1 = 0.03eV which is smaller than ωP (ω1 < ωP). The thickness db of the Bi layer was assumed to be equal to da/9 and, consequently, Λ = da + db = 5.914µm. At the frequency ω1 < ωP, Bi has a negative permittivity with large absolute value (εbεb,ωP2/ω12). On the other hand, at frequencies ωj > ωP (j > 1), the Bi layers possess a large positive permittivity (εb ≈ εb,). According to Figs. 6 and 7, the Fabry-Perot resonance bands are highly concentrated just below the polaritonic gap.

 figure: Fig. 6

Fig. 6 Curves of ω versus the real (left column) and imaginary (right column) parts of the Bloch wave number kz for a LiH/Bi superlattice at θ = 45°, for both polarizations. The indices j and j′ correspond to the Fabry-Perot resonances in the polaritonic material and m in the Bi medium.

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 figure: Fig. 7

Fig. 7 Bulk dispersion curves for the phonon-polariton (photon) modes in LiH, blue lines (Bi, red lines). The A and C solid lines (B and D dashed curves) correspond to the real (imaginary) parts of the wave vectors kza and kzb for the electromagnetic modes in the LiH and Bi layers of the superlattice, as in Fig. 6. The indices j and j′ correspond to the Fabry-Perot resonances in the polaritonic material and m in the Bi medium.

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Because of the frequency dependence of the LiH permittivity, εa(ω) (1), the Fabry-Perot resonance condition (22) is also satisfied at frequencies ωj (j′ = 1,2,3,…), being above the polaritonic gap (ωj > ωLO) (see Figs. 6 and 7). It should be noted that at such frequencies the contrast between the impedances of the a- and b-layers is rather large and, therefore, the Fabry-Perot resonance bands are very narrow. The photonic band structures for both TE and TM modes also exhibit an almost-flat pass band inside the polaritonic gap (Fig. 6). The band corresponds to the lowest Fabry-Perot resonance in the Bi layer, at the frequency ωm=1, where the condition

[kzb]db=π
is met (see the red square in Fig. 7).

In the case of TM modes, there is another pass band at ω = ω* > ωLO (see panel (c) of Fig. 6). This peculiar band does not correspond to any size-quantized polariton (photon) mode in the LiH (Bi) layers. Its origin is related with the frequency dependence of the parameter α(ω) in Eqs. (3) and (4). In general, the absolute value of α is large because of the high contrast between the impedances of the LiH and Bi layers. However, the function α(ω) has a zero at ω = ω*, where the solution kz for the dispersion equation (3) may be a real number. Within the leading approximation in the parameter εa,b, ≪1, the frequency ω* can be calculated by using the formula

ω*=ωLO(1ωTO2sin2θ/ωLO2εa,1sin2θ/εa,)1/2.

Substituting the LiH parameters into Eq. (24), we obtain ω* = 1.057ωLO.

The photonic band structure shown in Fig. 6 corresponds to modes whose wave vector has a positive imaginary part (ℑ[kz] > 0), i.e. modes decaying along the positive direction of the z-axis. The pass bands of negative dispersion are those where ℜ[kz] [|ℜ[kz]| ≫ℑ[kz]] and the derivative dω/dkz have opposite sign. Interestingly, the Fabry-Perot resonance band (m = 1) inside the polaritonic gap and the photonic band just above ωLO (at ω = ω*) possess negative dispersion.

Panels (a) and (b) of Fig. 8 show the s- and p-polarization reflectivity and transmissivity spectra for a multilayer stack of 50 LiH/Bi bilayers. The thicknesses of LiH and Bi layers are equal to those of the superlattice analyzed in previous paragraphs. The calculated optical spectra agree with the predicted photonic band structure for the LiH/Bi superlattice (Fig. 6). Indeed, both s- and p-polarization reflectivities exhibit resonances at frequencies corresponding to the pass bands associated with size-quantized polariton and photon modes in LiH and Bi layers, respectively (compare Figs. 6 and 8). As can be seen, the transmissivity is rather small implying considerable absorption in the superlattice.

 figure: Fig. 8

Fig. 8 s– and p–polarization reflectivity and transmissivity spectra at θ = 45° for a stack of 50 LiH/Bi bilayers in air. The thicknesses of the LiH and Bi layers are the same as those of the superlattice in Figs. 6 and 7.

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5. Conclusion

We have studied the effect of the plasma-phonon polariton coupling upon the photonic band structure of superlattices composed of Bi and polaritonic material layers. We have analyzed the photonic dispersions for TE and TM plasma-phonon polaritons in three cases: i) the Bi plasma frequency is above the LO phonon frequency (ωLO < ωP) as for NaBr/Bi superlattices; ii) the Bi plasma frequency is inside the polaritonic gap (ωTO < ωP < ωLO) as for LiCl/Bi heterostructures; and iii) the Bi plasma frequency is below the TO phonon frequency (ωP < ωTO) as for LiH/Bi superlattices. Due to the plasma-like behavior of the semimetal Bi in the infrared, in the three cases investigated there is a low-frequency band gap similar to that observed in metal-dielectric superlattices [35, 44, 46]. We have generated reflectivity and transmissivity spectra for each of the three cases investigated to help experimentalists to compare results with our theoretical predictions.

In the long wavelength limit, we have calculated the effective permittivity tensor for homogenized polaritonic-material/Bi superlattices, which behave as uniaxial crystals. The frequency dependence for the transverse components of the effective permittivity tensor is described by a Drude-like formula, but with an effective plasma frequency, ωP,eff. Thanks to the high-frequency background dielectric constant of Bi, ωP,eff is very close to the Bi plasma frequency ωP in all the cases. We have shown that the effective medium theory developed by Rytov [42] and a more accurate theory [46] coincides for the three cases investigated, thus enabling the use of the simpler theory to model these kind of superlattice systems.

For superlattices with relatively thick layers, their infrared photonic band structures exhibit narrow pass bands associated to Fabry-Perot resonances either in the polaritonic layers or in the Bi ones. These resonance bands are owing to the high-dielectric contrast between the polar material and the semimetal Bi. In the photonic dispersion for both TE and TM modes propagating in a LiH/Bi superlattice, we have observed a Fabry-Perot resonance band inside the polaritonic gap of the polaritonic material. Interestingly, for TM modes there is, additionally, a pass band just above the LO phonon frequency that presents a negative dispersion, attributed to the frequency dependence of the permittivity for the polaritonic material and the large high-frequency background dielectric constant for Bi, that can be relevant to the metamaterials community.

Acknowledgments

This work was partially supported by SEP-CONACyT (grant CB-2011-01-166382), VIEP-BUAP (grants 71-EXC13-I and ZEMB-ING13-I), PIFI 2012, and PIFCA 2013. A.R.-C. thanks the financial support from PROMEP (grant 103.5/12/4367) and PAPIIT-UNAM (grant IA105015).

References and links

1. E. Yablonovitch, “Inhibited Spontaneous Emission in Solid-State Physics and Electronics,” Phys. Rev. Lett. 58 (20) 2059–2062 (1987). [CrossRef]   [PubMed]  

2. S. John, “Strong Localization of Photons in Certain Disordered Dielectric Superlattices,” Phys. Rev. Lett. 58 (23) 2486–2489 (1987). [CrossRef]   [PubMed]  

3. P. W. Anderson, “Absence of Diffusion in Certain Random Lattices,” Phys. Rev. 109 (5) 1492–1505 (1958). [CrossRef]  

4. G. Bickauskaite, M. Manousidaki, K. Terzaki, E. Kambouraki, I. Sakellari, N. Vasilantonakis, D. Gray, C. M. Soukoulis, C. Fotakis, M. Vamvakaki, M. Kafesaki, M. Farsari, A. Pikulin, and N. Bityurin, “3D Photonic Nanostructures via Diffusion-Assisted Direct fs Laser Writing,” P. Soc. Photo-Opt. Ins. 20129279311–6 (2012).

5. E. Sánchez-Mora, M. Fernández-Candelario, E. Gómez-Barojas, and F. Pérez-Rodríguez, “Influence of Fe Ions on the Optical Properties of Fe-ZnO Inverse Opals,” J. Supercond. Nov. Magn. 26, 2447–2449 (2013). [CrossRef]  

6. S. Kim, A. N. Mitropoulos, J. D. Spitzberg, H. Tao, D. L. Kaplan, and F. G. Omenetto, “Silk inverse opals,” Nature Photonics 6, 818–823 (2012). [CrossRef]  

7. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000). [CrossRef]   [PubMed]  

8. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and µ,” Sov. Phys. Uspekhi 10, 509–514 (1968). [CrossRef]  

9. S. Guenneau, A. Movchan, G. Pétursson, and S. A. Ramakrishna, “Acoustic metamaterials for sound focusing and confinement,” New J. Phys. 9, 399 (2007). [CrossRef]  

10. M. Brun, S. Guenneau, and A. B. Movchan, “Achieving control of in-plane elastic waves,” Appl. Phys. Lett. 94, 61903 (2009). [CrossRef]  

11. A. Tuniz, K. J. Kaltenecker, B. M. Fischer, M. Walther, S. C. Fleming, A. Argyros, and B. T. Kuhlmey, “Metamaterial fibres for subdiffraction imaging and focusing at terahertz frequencies over optically long distances,” Nat. Commun. 4, 2706 (2013). [CrossRef]   [PubMed]  

12. J. B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett. 85, 3966–3969 (2000). [CrossRef]   [PubMed]  

13. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial Electromagnetic Cloak at Microwave Frequencies,” Science 314, 977–980 (2006). [CrossRef]   [PubMed]  

14. T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-Dimensional Invisibility Cloak at Optical Wavelengths,” Science 328, 337–339 (2010). [CrossRef]   [PubMed]  

15. H. Chen and C. T. Chan, “Acoustic cloaking in three dimensions using acoustic metamaterials,” App. Phys. Lett. 91, 183518 (2007). [CrossRef]  

16. W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat Photonics 1, 224–227 (2007). [CrossRef]  

17. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Low frequency plasmons in thin-wire structures,” J. Phys.: Condens. Matter 10, 4785–4809 (1998).

18. S. O’Brien and J. B. Pendry, “Photonic band-gap effects and magnetic activity in dielectric composites,” J. Phys.: Condens. Matter 14, 4035–4044 (2002).

19. J. A. Schuller, R. Zia, T. Taubner, and M. L. Brongersma, “Dielectric metamaterials based on electric and magnetic resonances of silicon carbide particles,” Phys. Rev. Lett. 99, 107401 (2007). [CrossRef]   [PubMed]  

20. L. Jylhä, I. Kolmakov, S. Maslovski, and S. Tretyakov, “Modeling of isotropic backward-wave materials composed of resonant spheres,” J. Appl. Phys. 99, 043102 (2006). [CrossRef]  

21. C. Kittel, Introduction to Solid State Physics (John Wiley & Sons, 2005).

22. V. Yannopapas and A. Moroz, “Negative refractive index metamaterials from inherently non-magnetic materials for deep infrared to terahertz frequency ranges,” J. Phys.: Condens. Matter 17, 3717–3734 (2005).

23. R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417, 156–159 (2002). [CrossRef]   [PubMed]  

24. T. Edwards, Gigahertz and Terahertz Technologies for Broadband Communications (Artech House Inc., 2000).

25. D. L. Woolard, J. O. Jensen, R. J. Hwu, and M. S. Shur, Terahertz Science and Technology for Military and Security Applications (World Scientific Publishing Co. Pte. Ltd., 2007).

26. S. W. Smye, J. M. Chamberlain, A. J. Fitzgerald, and E. Berry, “The interaction between Terahertz radiation and biological tissue,” Phys. Med. Biol. 46, R101–R112 (2001). [CrossRef]   [PubMed]  

27. V. Minier, G. Durand, P.-O. Lagage, M. Talvard, T. Travouillon, M. Busso, and G. Tosti, “Submillimetre/terahertz astronomy at dome C with CEA filled bolometer array,” EAS Publications Series 25, 321–326 (2007). [CrossRef]  

28. A. Reyes-Coronado, M. F. Acosta, R. I. Merino, V. M. Orera, G. Kenanakis, N. Katsarakis, M. Kafesaki, and C. M. Soukoulis, “Electromagnetic response of anisotropic eutectic metamaterials in THz range,” AIP Conf. Proc. 1291, 148–150 (2010). [CrossRef]  

29. S. Foteinopoulou, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Two-dimensional polaritonic photonic crystals as terahertz uniaxial metamaterials,” Phys. Rev. B 84, 035128 (2011). [CrossRef]  

30. A. Reyes-Coronado, M. F. Acosta, R. I. Merino, V. M. Orera, G. Kenanakis, N. Katsarakis, M. Kafesaki, Ch. Mavidis, J. García de Abajo, E. N. Economou, and C. M. Soukoulis, “Self-organization approach for THz polaritonic metamaterials,” Opt. Express 20, 14663–14682 (2012). [CrossRef]   [PubMed]  

31. A. A. Basharin, C. Mavidis, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Epsilon near zero based phenomena in metamaterials,” Phys. Rev. B 87, 155130 (2013). [CrossRef]  

32. M. Massaouti, A. A. Basharin, M. Kafesaki, M. F. Acosta, R. I. Merino, V. M. Orera, E. N. Economou, C. M. Soukoulis, and S. Tzortzakis, “Eutectic epsilon-near-zero metamaterial terahertz waveguides,” Opt. Lett. 38, 1140–1142 (2013). [CrossRef]   [PubMed]  

33. F. Díaz-Monge, A. Paredes-Juárez, D. A. Iakushev, N. M. Makarov, and F. Pérez-Rodríguez, “THz photonic bands of periodic stacks composed of resonant dielectric and nonlocal metal,” Opt. Mater. Express , 5, 361–372 (2015). [CrossRef]  

34. A. Paredes-Juárez, F. Díaz-Monge, N. M. Makarov, and F. Pérez-Rodríguez, “Nonlocal effects in the electrodynamics of metallic slabs,” JETP Letters 90, 623–627 (2009). [CrossRef]  

35. A. Paredes-Juárez, D. A. Iakushev, B. Flores-Desirena, N. M. Makarov, and F. Pérez-Rodríguez, “Nonlocal Effect on Optic Spectrum of a Periodic Dielectric-Metal Stack,” Opt. Express 22, 7581–7586 (2014). [CrossRef]   [PubMed]  

36. M. Shahzad, “Infrared surface plasmon polaritons on semiconductor, semimetal and conducting polymer,” Ph.D. thesis (University of Central Florida, Orlando, Florida, 2012).

37. F. Khalilzadeh-Rezaie, C. W. Smith, J. Nath, N. Nader, M. Shahzad, J. W. Cleary, I. Avrutsky, and R. E. Peale, “Infrared surface polaritons on bismuth,” J. Nanophoton. 9, 093792 (2015). [CrossRef]  

38. A. Yariv and P. Yeh, Optical Waves in Crystals. Propagation and Control of Laser Radiation (Wiley, 1984).

39. A. S. Sánchez and P. Halevi, “Spontaneous emission in one-dimensional photonic crystals,” Phys. Rev. E 72, 056609 (2005). [CrossRef]  

40. P. Markoš and C. M. Soukoulis, Wave Propagation. From Electrons to Photonic Crystals and Left-Handed Materials (Princeton University Press, Princeton, 2008).

41. A. Orlov, I. Iorsh, P. Belov, and Y. Kivshar, “Complex band structure of nanostructured metal-dielectric metamaterials,” Opt. Express 21, 1593–1598 (2013). [CrossRef]   [PubMed]  

42. S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

43. B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74, 115116 (2006). [CrossRef]  

44. X. Xu, Y. Xi, D. Han, X. Liu, J. Zi, and Z. Zhu, “Effective plasma frequency in one-dimensional metallic-dielectric photonic crystals,” Appl. Phys. Lett. 86, 091112 (2005). [CrossRef]  

45. J. Manzanares-Martínez, “Analytic expression for the effective plasma frequency in one-dimensional metallic-dielectric photonic crystal,” Progress In Electromagnetics Research M , 13, 189–202 (2010). [CrossRef]  

46. B. Zenteno-Mateo, V. Cerdán-Ramírez, B. Flores-Desirena, M. P. Sampedro, E. Juárez-Ruiz, and F. Pérez-Rodríguez, “Effective permittivity tensor for a metal-dielectric superlattice,” Progress in Electromagnetics Research Letters 22, 165–174 (2011).

47. J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett. 90, 191109 (2007). [CrossRef]  

48. V. Cerdán-Ramírez, B. Zenteno-Mateo, M. P. Sampedro, M. A. Palomino-Ovando, B. Flores-Desirena, and F. Pérez-Rodríguez, “Anisotropy effects in homogenized magnetodielectric photonic crystals,” J. Appl. Phys. 106, 103520 (2009). [CrossRef]  

References

  • View by:

  1. E. Yablonovitch, “Inhibited Spontaneous Emission in Solid-State Physics and Electronics,” Phys. Rev. Lett. 58 (20) 2059–2062 (1987).
    [Crossref] [PubMed]
  2. S. John, “Strong Localization of Photons in Certain Disordered Dielectric Superlattices,” Phys. Rev. Lett. 58 (23) 2486–2489 (1987).
    [Crossref] [PubMed]
  3. P. W. Anderson, “Absence of Diffusion in Certain Random Lattices,” Phys. Rev. 109 (5) 1492–1505 (1958).
    [Crossref]
  4. G. Bickauskaite, M. Manousidaki, K. Terzaki, E. Kambouraki, I. Sakellari, N. Vasilantonakis, D. Gray, C. M. Soukoulis, C. Fotakis, M. Vamvakaki, M. Kafesaki, M. Farsari, A. Pikulin, and N. Bityurin, “3D Photonic Nanostructures via Diffusion-Assisted Direct fs Laser Writing,” P. Soc. Photo-Opt. Ins. 20129279311–6 (2012).
  5. E. Sánchez-Mora, M. Fernández-Candelario, E. Gómez-Barojas, and F. Pérez-Rodríguez, “Influence of Fe Ions on the Optical Properties of Fe-ZnO Inverse Opals,” J. Supercond. Nov. Magn. 26, 2447–2449 (2013).
    [Crossref]
  6. S. Kim, A. N. Mitropoulos, J. D. Spitzberg, H. Tao, D. L. Kaplan, and F. G. Omenetto, “Silk inverse opals,” Nature Photonics 6, 818–823 (2012).
    [Crossref]
  7. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
    [Crossref] [PubMed]
  8. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and µ,” Sov. Phys. Uspekhi 10, 509–514 (1968).
    [Crossref]
  9. S. Guenneau, A. Movchan, G. Pétursson, and S. A. Ramakrishna, “Acoustic metamaterials for sound focusing and confinement,” New J. Phys. 9, 399 (2007).
    [Crossref]
  10. M. Brun, S. Guenneau, and A. B. Movchan, “Achieving control of in-plane elastic waves,” Appl. Phys. Lett. 94, 61903 (2009).
    [Crossref]
  11. A. Tuniz, K. J. Kaltenecker, B. M. Fischer, M. Walther, S. C. Fleming, A. Argyros, and B. T. Kuhlmey, “Metamaterial fibres for subdiffraction imaging and focusing at terahertz frequencies over optically long distances,” Nat. Commun. 4, 2706 (2013).
    [Crossref] [PubMed]
  12. J. B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
    [Crossref] [PubMed]
  13. D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial Electromagnetic Cloak at Microwave Frequencies,” Science 314, 977–980 (2006).
    [Crossref] [PubMed]
  14. T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-Dimensional Invisibility Cloak at Optical Wavelengths,” Science 328, 337–339 (2010).
    [Crossref] [PubMed]
  15. H. Chen and C. T. Chan, “Acoustic cloaking in three dimensions using acoustic metamaterials,” App. Phys. Lett. 91, 183518 (2007).
    [Crossref]
  16. W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat Photonics 1, 224–227 (2007).
    [Crossref]
  17. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Low frequency plasmons in thin-wire structures,” J. Phys.: Condens. Matter 10, 4785–4809 (1998).
  18. S. O’Brien and J. B. Pendry, “Photonic band-gap effects and magnetic activity in dielectric composites,” J. Phys.: Condens. Matter 14, 4035–4044 (2002).
  19. J. A. Schuller, R. Zia, T. Taubner, and M. L. Brongersma, “Dielectric metamaterials based on electric and magnetic resonances of silicon carbide particles,” Phys. Rev. Lett. 99, 107401 (2007).
    [Crossref] [PubMed]
  20. L. Jylhä, I. Kolmakov, S. Maslovski, and S. Tretyakov, “Modeling of isotropic backward-wave materials composed of resonant spheres,” J. Appl. Phys. 99, 043102 (2006).
    [Crossref]
  21. C. Kittel, Introduction to Solid State Physics (John Wiley & Sons, 2005).
  22. V. Yannopapas and A. Moroz, “Negative refractive index metamaterials from inherently non-magnetic materials for deep infrared to terahertz frequency ranges,” J. Phys.: Condens. Matter 17, 3717–3734 (2005).
  23. R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417, 156–159 (2002).
    [Crossref] [PubMed]
  24. T. Edwards, Gigahertz and Terahertz Technologies for Broadband Communications (Artech House Inc., 2000).
  25. D. L. Woolard, J. O. Jensen, R. J. Hwu, and M. S. Shur, Terahertz Science and Technology for Military and Security Applications (World Scientific Publishing Co. Pte. Ltd., 2007).
  26. S. W. Smye, J. M. Chamberlain, A. J. Fitzgerald, and E. Berry, “The interaction between Terahertz radiation and biological tissue,” Phys. Med. Biol. 46, R101–R112 (2001).
    [Crossref] [PubMed]
  27. V. Minier, G. Durand, P.-O. Lagage, M. Talvard, T. Travouillon, M. Busso, and G. Tosti, “Submillimetre/terahertz astronomy at dome C with CEA filled bolometer array,” EAS Publications Series 25, 321–326 (2007).
    [Crossref]
  28. A. Reyes-Coronado, M. F. Acosta, R. I. Merino, V. M. Orera, G. Kenanakis, N. Katsarakis, M. Kafesaki, and C. M. Soukoulis, “Electromagnetic response of anisotropic eutectic metamaterials in THz range,” AIP Conf. Proc. 1291, 148–150 (2010).
    [Crossref]
  29. S. Foteinopoulou, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Two-dimensional polaritonic photonic crystals as terahertz uniaxial metamaterials,” Phys. Rev. B 84, 035128 (2011).
    [Crossref]
  30. A. Reyes-Coronado, M. F. Acosta, R. I. Merino, V. M. Orera, G. Kenanakis, N. Katsarakis, M. Kafesaki, Ch. Mavidis, J. García de Abajo, E. N. Economou, and C. M. Soukoulis, “Self-organization approach for THz polaritonic metamaterials,” Opt. Express 20, 14663–14682 (2012).
    [Crossref] [PubMed]
  31. A. A. Basharin, C. Mavidis, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Epsilon near zero based phenomena in metamaterials,” Phys. Rev. B 87, 155130 (2013).
    [Crossref]
  32. M. Massaouti, A. A. Basharin, M. Kafesaki, M. F. Acosta, R. I. Merino, V. M. Orera, E. N. Economou, C. M. Soukoulis, and S. Tzortzakis, “Eutectic epsilon-near-zero metamaterial terahertz waveguides,” Opt. Lett. 38, 1140–1142 (2013).
    [Crossref] [PubMed]
  33. F. Díaz-Monge, A. Paredes-Juárez, D. A. Iakushev, N. M. Makarov, and F. Pérez-Rodríguez, “THz photonic bands of periodic stacks composed of resonant dielectric and nonlocal metal,” Opt. Mater. Express,  5, 361–372 (2015).
    [Crossref]
  34. A. Paredes-Juárez, F. Díaz-Monge, N. M. Makarov, and F. Pérez-Rodríguez, “Nonlocal effects in the electrodynamics of metallic slabs,” JETP Letters 90, 623–627 (2009).
    [Crossref]
  35. A. Paredes-Juárez, D. A. Iakushev, B. Flores-Desirena, N. M. Makarov, and F. Pérez-Rodríguez, “Nonlocal Effect on Optic Spectrum of a Periodic Dielectric-Metal Stack,” Opt. Express 22, 7581–7586 (2014).
    [Crossref] [PubMed]
  36. M. Shahzad, “Infrared surface plasmon polaritons on semiconductor, semimetal and conducting polymer,” Ph.D. thesis (University of Central Florida, Orlando, Florida, 2012).
  37. F. Khalilzadeh-Rezaie, C. W. Smith, J. Nath, N. Nader, M. Shahzad, J. W. Cleary, I. Avrutsky, and R. E. Peale, “Infrared surface polaritons on bismuth,” J. Nanophoton. 9, 093792 (2015).
    [Crossref]
  38. A. Yariv and P. Yeh, Optical Waves in Crystals. Propagation and Control of Laser Radiation (Wiley, 1984).
  39. A. S. Sánchez and P. Halevi, “Spontaneous emission in one-dimensional photonic crystals,” Phys. Rev. E 72, 056609 (2005).
    [Crossref]
  40. P. Markoš and C. M. Soukoulis, Wave Propagation. From Electrons to Photonic Crystals and Left-Handed Materials (Princeton University Press, Princeton, 2008).
  41. A. Orlov, I. Iorsh, P. Belov, and Y. Kivshar, “Complex band structure of nanostructured metal-dielectric metamaterials,” Opt. Express 21, 1593–1598 (2013).
    [Crossref] [PubMed]
  42. S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).
  43. B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74, 115116 (2006).
    [Crossref]
  44. X. Xu, Y. Xi, D. Han, X. Liu, J. Zi, and Z. Zhu, “Effective plasma frequency in one-dimensional metallic-dielectric photonic crystals,” Appl. Phys. Lett. 86, 091112 (2005).
    [Crossref]
  45. J. Manzanares-Martínez, “Analytic expression for the effective plasma frequency in one-dimensional metallic-dielectric photonic crystal,” Progress In Electromagnetics Research M,  13, 189–202 (2010).
    [Crossref]
  46. B. Zenteno-Mateo, V. Cerdán-Ramírez, B. Flores-Desirena, M. P. Sampedro, E. Juárez-Ruiz, and F. Pérez-Rodríguez, “Effective permittivity tensor for a metal-dielectric superlattice,” Progress in Electromagnetics Research Letters 22, 165–174 (2011).
  47. J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett. 90, 191109 (2007).
    [Crossref]
  48. V. Cerdán-Ramírez, B. Zenteno-Mateo, M. P. Sampedro, M. A. Palomino-Ovando, B. Flores-Desirena, and F. Pérez-Rodríguez, “Anisotropy effects in homogenized magnetodielectric photonic crystals,” J. Appl. Phys. 106, 103520 (2009).
    [Crossref]

2015 (2)

F. Díaz-Monge, A. Paredes-Juárez, D. A. Iakushev, N. M. Makarov, and F. Pérez-Rodríguez, “THz photonic bands of periodic stacks composed of resonant dielectric and nonlocal metal,” Opt. Mater. Express,  5, 361–372 (2015).
[Crossref]

F. Khalilzadeh-Rezaie, C. W. Smith, J. Nath, N. Nader, M. Shahzad, J. W. Cleary, I. Avrutsky, and R. E. Peale, “Infrared surface polaritons on bismuth,” J. Nanophoton. 9, 093792 (2015).
[Crossref]

2014 (1)

2013 (5)

A. A. Basharin, C. Mavidis, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Epsilon near zero based phenomena in metamaterials,” Phys. Rev. B 87, 155130 (2013).
[Crossref]

M. Massaouti, A. A. Basharin, M. Kafesaki, M. F. Acosta, R. I. Merino, V. M. Orera, E. N. Economou, C. M. Soukoulis, and S. Tzortzakis, “Eutectic epsilon-near-zero metamaterial terahertz waveguides,” Opt. Lett. 38, 1140–1142 (2013).
[Crossref] [PubMed]

E. Sánchez-Mora, M. Fernández-Candelario, E. Gómez-Barojas, and F. Pérez-Rodríguez, “Influence of Fe Ions on the Optical Properties of Fe-ZnO Inverse Opals,” J. Supercond. Nov. Magn. 26, 2447–2449 (2013).
[Crossref]

A. Tuniz, K. J. Kaltenecker, B. M. Fischer, M. Walther, S. C. Fleming, A. Argyros, and B. T. Kuhlmey, “Metamaterial fibres for subdiffraction imaging and focusing at terahertz frequencies over optically long distances,” Nat. Commun. 4, 2706 (2013).
[Crossref] [PubMed]

A. Orlov, I. Iorsh, P. Belov, and Y. Kivshar, “Complex band structure of nanostructured metal-dielectric metamaterials,” Opt. Express 21, 1593–1598 (2013).
[Crossref] [PubMed]

2012 (3)

S. Kim, A. N. Mitropoulos, J. D. Spitzberg, H. Tao, D. L. Kaplan, and F. G. Omenetto, “Silk inverse opals,” Nature Photonics 6, 818–823 (2012).
[Crossref]

G. Bickauskaite, M. Manousidaki, K. Terzaki, E. Kambouraki, I. Sakellari, N. Vasilantonakis, D. Gray, C. M. Soukoulis, C. Fotakis, M. Vamvakaki, M. Kafesaki, M. Farsari, A. Pikulin, and N. Bityurin, “3D Photonic Nanostructures via Diffusion-Assisted Direct fs Laser Writing,” P. Soc. Photo-Opt. Ins. 20129279311–6 (2012).

A. Reyes-Coronado, M. F. Acosta, R. I. Merino, V. M. Orera, G. Kenanakis, N. Katsarakis, M. Kafesaki, Ch. Mavidis, J. García de Abajo, E. N. Economou, and C. M. Soukoulis, “Self-organization approach for THz polaritonic metamaterials,” Opt. Express 20, 14663–14682 (2012).
[Crossref] [PubMed]

2011 (2)

S. Foteinopoulou, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Two-dimensional polaritonic photonic crystals as terahertz uniaxial metamaterials,” Phys. Rev. B 84, 035128 (2011).
[Crossref]

B. Zenteno-Mateo, V. Cerdán-Ramírez, B. Flores-Desirena, M. P. Sampedro, E. Juárez-Ruiz, and F. Pérez-Rodríguez, “Effective permittivity tensor for a metal-dielectric superlattice,” Progress in Electromagnetics Research Letters 22, 165–174 (2011).

2010 (3)

J. Manzanares-Martínez, “Analytic expression for the effective plasma frequency in one-dimensional metallic-dielectric photonic crystal,” Progress In Electromagnetics Research M,  13, 189–202 (2010).
[Crossref]

A. Reyes-Coronado, M. F. Acosta, R. I. Merino, V. M. Orera, G. Kenanakis, N. Katsarakis, M. Kafesaki, and C. M. Soukoulis, “Electromagnetic response of anisotropic eutectic metamaterials in THz range,” AIP Conf. Proc. 1291, 148–150 (2010).
[Crossref]

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-Dimensional Invisibility Cloak at Optical Wavelengths,” Science 328, 337–339 (2010).
[Crossref] [PubMed]

2009 (3)

M. Brun, S. Guenneau, and A. B. Movchan, “Achieving control of in-plane elastic waves,” Appl. Phys. Lett. 94, 61903 (2009).
[Crossref]

A. Paredes-Juárez, F. Díaz-Monge, N. M. Makarov, and F. Pérez-Rodríguez, “Nonlocal effects in the electrodynamics of metallic slabs,” JETP Letters 90, 623–627 (2009).
[Crossref]

V. Cerdán-Ramírez, B. Zenteno-Mateo, M. P. Sampedro, M. A. Palomino-Ovando, B. Flores-Desirena, and F. Pérez-Rodríguez, “Anisotropy effects in homogenized magnetodielectric photonic crystals,” J. Appl. Phys. 106, 103520 (2009).
[Crossref]

2007 (6)

J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett. 90, 191109 (2007).
[Crossref]

V. Minier, G. Durand, P.-O. Lagage, M. Talvard, T. Travouillon, M. Busso, and G. Tosti, “Submillimetre/terahertz astronomy at dome C with CEA filled bolometer array,” EAS Publications Series 25, 321–326 (2007).
[Crossref]

J. A. Schuller, R. Zia, T. Taubner, and M. L. Brongersma, “Dielectric metamaterials based on electric and magnetic resonances of silicon carbide particles,” Phys. Rev. Lett. 99, 107401 (2007).
[Crossref] [PubMed]

H. Chen and C. T. Chan, “Acoustic cloaking in three dimensions using acoustic metamaterials,” App. Phys. Lett. 91, 183518 (2007).
[Crossref]

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat Photonics 1, 224–227 (2007).
[Crossref]

S. Guenneau, A. Movchan, G. Pétursson, and S. A. Ramakrishna, “Acoustic metamaterials for sound focusing and confinement,” New J. Phys. 9, 399 (2007).
[Crossref]

2006 (3)

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial Electromagnetic Cloak at Microwave Frequencies,” Science 314, 977–980 (2006).
[Crossref] [PubMed]

L. Jylhä, I. Kolmakov, S. Maslovski, and S. Tretyakov, “Modeling of isotropic backward-wave materials composed of resonant spheres,” J. Appl. Phys. 99, 043102 (2006).
[Crossref]

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74, 115116 (2006).
[Crossref]

2005 (3)

X. Xu, Y. Xi, D. Han, X. Liu, J. Zi, and Z. Zhu, “Effective plasma frequency in one-dimensional metallic-dielectric photonic crystals,” Appl. Phys. Lett. 86, 091112 (2005).
[Crossref]

V. Yannopapas and A. Moroz, “Negative refractive index metamaterials from inherently non-magnetic materials for deep infrared to terahertz frequency ranges,” J. Phys.: Condens. Matter 17, 3717–3734 (2005).

A. S. Sánchez and P. Halevi, “Spontaneous emission in one-dimensional photonic crystals,” Phys. Rev. E 72, 056609 (2005).
[Crossref]

2002 (2)

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417, 156–159 (2002).
[Crossref] [PubMed]

S. O’Brien and J. B. Pendry, “Photonic band-gap effects and magnetic activity in dielectric composites,” J. Phys.: Condens. Matter 14, 4035–4044 (2002).

2001 (1)

S. W. Smye, J. M. Chamberlain, A. J. Fitzgerald, and E. Berry, “The interaction between Terahertz radiation and biological tissue,” Phys. Med. Biol. 46, R101–R112 (2001).
[Crossref] [PubMed]

2000 (2)

J. B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[Crossref] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[Crossref] [PubMed]

1998 (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Low frequency plasmons in thin-wire structures,” J. Phys.: Condens. Matter 10, 4785–4809 (1998).

1987 (2)

E. Yablonovitch, “Inhibited Spontaneous Emission in Solid-State Physics and Electronics,” Phys. Rev. Lett. 58 (20) 2059–2062 (1987).
[Crossref] [PubMed]

S. John, “Strong Localization of Photons in Certain Disordered Dielectric Superlattices,” Phys. Rev. Lett. 58 (23) 2486–2489 (1987).
[Crossref] [PubMed]

1968 (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and µ,” Sov. Phys. Uspekhi 10, 509–514 (1968).
[Crossref]

1958 (1)

P. W. Anderson, “Absence of Diffusion in Certain Random Lattices,” Phys. Rev. 109 (5) 1492–1505 (1958).
[Crossref]

1956 (1)

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Acosta, M. F.

Anderson, P. W.

P. W. Anderson, “Absence of Diffusion in Certain Random Lattices,” Phys. Rev. 109 (5) 1492–1505 (1958).
[Crossref]

Argyros, A.

A. Tuniz, K. J. Kaltenecker, B. M. Fischer, M. Walther, S. C. Fleming, A. Argyros, and B. T. Kuhlmey, “Metamaterial fibres for subdiffraction imaging and focusing at terahertz frequencies over optically long distances,” Nat. Commun. 4, 2706 (2013).
[Crossref] [PubMed]

Avrutsky, I.

F. Khalilzadeh-Rezaie, C. W. Smith, J. Nath, N. Nader, M. Shahzad, J. W. Cleary, I. Avrutsky, and R. E. Peale, “Infrared surface polaritons on bismuth,” J. Nanophoton. 9, 093792 (2015).
[Crossref]

J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett. 90, 191109 (2007).
[Crossref]

Basharin, A. A.

Beere, H. E.

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417, 156–159 (2002).
[Crossref] [PubMed]

Belov, P.

Beltram, F.

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417, 156–159 (2002).
[Crossref] [PubMed]

Berry, E.

S. W. Smye, J. M. Chamberlain, A. J. Fitzgerald, and E. Berry, “The interaction between Terahertz radiation and biological tissue,” Phys. Med. Biol. 46, R101–R112 (2001).
[Crossref] [PubMed]

Bickauskaite, G.

G. Bickauskaite, M. Manousidaki, K. Terzaki, E. Kambouraki, I. Sakellari, N. Vasilantonakis, D. Gray, C. M. Soukoulis, C. Fotakis, M. Vamvakaki, M. Kafesaki, M. Farsari, A. Pikulin, and N. Bityurin, “3D Photonic Nanostructures via Diffusion-Assisted Direct fs Laser Writing,” P. Soc. Photo-Opt. Ins. 20129279311–6 (2012).

Bityurin, N.

G. Bickauskaite, M. Manousidaki, K. Terzaki, E. Kambouraki, I. Sakellari, N. Vasilantonakis, D. Gray, C. M. Soukoulis, C. Fotakis, M. Vamvakaki, M. Kafesaki, M. Farsari, A. Pikulin, and N. Bityurin, “3D Photonic Nanostructures via Diffusion-Assisted Direct fs Laser Writing,” P. Soc. Photo-Opt. Ins. 20129279311–6 (2012).

Brenner, P.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-Dimensional Invisibility Cloak at Optical Wavelengths,” Science 328, 337–339 (2010).
[Crossref] [PubMed]

Brongersma, M. L.

J. A. Schuller, R. Zia, T. Taubner, and M. L. Brongersma, “Dielectric metamaterials based on electric and magnetic resonances of silicon carbide particles,” Phys. Rev. Lett. 99, 107401 (2007).
[Crossref] [PubMed]

Brun, M.

M. Brun, S. Guenneau, and A. B. Movchan, “Achieving control of in-plane elastic waves,” Appl. Phys. Lett. 94, 61903 (2009).
[Crossref]

Busso, M.

V. Minier, G. Durand, P.-O. Lagage, M. Talvard, T. Travouillon, M. Busso, and G. Tosti, “Submillimetre/terahertz astronomy at dome C with CEA filled bolometer array,” EAS Publications Series 25, 321–326 (2007).
[Crossref]

Cai, W.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat Photonics 1, 224–227 (2007).
[Crossref]

Cerdán-Ramírez, V.

B. Zenteno-Mateo, V. Cerdán-Ramírez, B. Flores-Desirena, M. P. Sampedro, E. Juárez-Ruiz, and F. Pérez-Rodríguez, “Effective permittivity tensor for a metal-dielectric superlattice,” Progress in Electromagnetics Research Letters 22, 165–174 (2011).

V. Cerdán-Ramírez, B. Zenteno-Mateo, M. P. Sampedro, M. A. Palomino-Ovando, B. Flores-Desirena, and F. Pérez-Rodríguez, “Anisotropy effects in homogenized magnetodielectric photonic crystals,” J. Appl. Phys. 106, 103520 (2009).
[Crossref]

Chamberlain, J. M.

S. W. Smye, J. M. Chamberlain, A. J. Fitzgerald, and E. Berry, “The interaction between Terahertz radiation and biological tissue,” Phys. Med. Biol. 46, R101–R112 (2001).
[Crossref] [PubMed]

Chan, C. T.

H. Chen and C. T. Chan, “Acoustic cloaking in three dimensions using acoustic metamaterials,” App. Phys. Lett. 91, 183518 (2007).
[Crossref]

Chen, H.

H. Chen and C. T. Chan, “Acoustic cloaking in three dimensions using acoustic metamaterials,” App. Phys. Lett. 91, 183518 (2007).
[Crossref]

Chettiar, U. K.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat Photonics 1, 224–227 (2007).
[Crossref]

Cleary, J. W.

F. Khalilzadeh-Rezaie, C. W. Smith, J. Nath, N. Nader, M. Shahzad, J. W. Cleary, I. Avrutsky, and R. E. Peale, “Infrared surface polaritons on bismuth,” J. Nanophoton. 9, 093792 (2015).
[Crossref]

Cummer, S. A.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial Electromagnetic Cloak at Microwave Frequencies,” Science 314, 977–980 (2006).
[Crossref] [PubMed]

Davies, A. G.

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417, 156–159 (2002).
[Crossref] [PubMed]

de Abajo, J. García

Díaz-Monge, F.

F. Díaz-Monge, A. Paredes-Juárez, D. A. Iakushev, N. M. Makarov, and F. Pérez-Rodríguez, “THz photonic bands of periodic stacks composed of resonant dielectric and nonlocal metal,” Opt. Mater. Express,  5, 361–372 (2015).
[Crossref]

A. Paredes-Juárez, F. Díaz-Monge, N. M. Makarov, and F. Pérez-Rodríguez, “Nonlocal effects in the electrodynamics of metallic slabs,” JETP Letters 90, 623–627 (2009).
[Crossref]

Durand, G.

V. Minier, G. Durand, P.-O. Lagage, M. Talvard, T. Travouillon, M. Busso, and G. Tosti, “Submillimetre/terahertz astronomy at dome C with CEA filled bolometer array,” EAS Publications Series 25, 321–326 (2007).
[Crossref]

Economou, E. N.

Edwards, T.

T. Edwards, Gigahertz and Terahertz Technologies for Broadband Communications (Artech House Inc., 2000).

Elser, J.

J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett. 90, 191109 (2007).
[Crossref]

Ergin, T.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-Dimensional Invisibility Cloak at Optical Wavelengths,” Science 328, 337–339 (2010).
[Crossref] [PubMed]

Farsari, M.

G. Bickauskaite, M. Manousidaki, K. Terzaki, E. Kambouraki, I. Sakellari, N. Vasilantonakis, D. Gray, C. M. Soukoulis, C. Fotakis, M. Vamvakaki, M. Kafesaki, M. Farsari, A. Pikulin, and N. Bityurin, “3D Photonic Nanostructures via Diffusion-Assisted Direct fs Laser Writing,” P. Soc. Photo-Opt. Ins. 20129279311–6 (2012).

Fernández-Candelario, M.

E. Sánchez-Mora, M. Fernández-Candelario, E. Gómez-Barojas, and F. Pérez-Rodríguez, “Influence of Fe Ions on the Optical Properties of Fe-ZnO Inverse Opals,” J. Supercond. Nov. Magn. 26, 2447–2449 (2013).
[Crossref]

Fischer, B. M.

A. Tuniz, K. J. Kaltenecker, B. M. Fischer, M. Walther, S. C. Fleming, A. Argyros, and B. T. Kuhlmey, “Metamaterial fibres for subdiffraction imaging and focusing at terahertz frequencies over optically long distances,” Nat. Commun. 4, 2706 (2013).
[Crossref] [PubMed]

Fitzgerald, A. J.

S. W. Smye, J. M. Chamberlain, A. J. Fitzgerald, and E. Berry, “The interaction between Terahertz radiation and biological tissue,” Phys. Med. Biol. 46, R101–R112 (2001).
[Crossref] [PubMed]

Fleming, S. C.

A. Tuniz, K. J. Kaltenecker, B. M. Fischer, M. Walther, S. C. Fleming, A. Argyros, and B. T. Kuhlmey, “Metamaterial fibres for subdiffraction imaging and focusing at terahertz frequencies over optically long distances,” Nat. Commun. 4, 2706 (2013).
[Crossref] [PubMed]

Flores-Desirena, B.

A. Paredes-Juárez, D. A. Iakushev, B. Flores-Desirena, N. M. Makarov, and F. Pérez-Rodríguez, “Nonlocal Effect on Optic Spectrum of a Periodic Dielectric-Metal Stack,” Opt. Express 22, 7581–7586 (2014).
[Crossref] [PubMed]

B. Zenteno-Mateo, V. Cerdán-Ramírez, B. Flores-Desirena, M. P. Sampedro, E. Juárez-Ruiz, and F. Pérez-Rodríguez, “Effective permittivity tensor for a metal-dielectric superlattice,” Progress in Electromagnetics Research Letters 22, 165–174 (2011).

V. Cerdán-Ramírez, B. Zenteno-Mateo, M. P. Sampedro, M. A. Palomino-Ovando, B. Flores-Desirena, and F. Pérez-Rodríguez, “Anisotropy effects in homogenized magnetodielectric photonic crystals,” J. Appl. Phys. 106, 103520 (2009).
[Crossref]

Fotakis, C.

G. Bickauskaite, M. Manousidaki, K. Terzaki, E. Kambouraki, I. Sakellari, N. Vasilantonakis, D. Gray, C. M. Soukoulis, C. Fotakis, M. Vamvakaki, M. Kafesaki, M. Farsari, A. Pikulin, and N. Bityurin, “3D Photonic Nanostructures via Diffusion-Assisted Direct fs Laser Writing,” P. Soc. Photo-Opt. Ins. 20129279311–6 (2012).

Foteinopoulou, S.

S. Foteinopoulou, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Two-dimensional polaritonic photonic crystals as terahertz uniaxial metamaterials,” Phys. Rev. B 84, 035128 (2011).
[Crossref]

Gómez-Barojas, E.

E. Sánchez-Mora, M. Fernández-Candelario, E. Gómez-Barojas, and F. Pérez-Rodríguez, “Influence of Fe Ions on the Optical Properties of Fe-ZnO Inverse Opals,” J. Supercond. Nov. Magn. 26, 2447–2449 (2013).
[Crossref]

Gray, D.

G. Bickauskaite, M. Manousidaki, K. Terzaki, E. Kambouraki, I. Sakellari, N. Vasilantonakis, D. Gray, C. M. Soukoulis, C. Fotakis, M. Vamvakaki, M. Kafesaki, M. Farsari, A. Pikulin, and N. Bityurin, “3D Photonic Nanostructures via Diffusion-Assisted Direct fs Laser Writing,” P. Soc. Photo-Opt. Ins. 20129279311–6 (2012).

Guenneau, S.

M. Brun, S. Guenneau, and A. B. Movchan, “Achieving control of in-plane elastic waves,” Appl. Phys. Lett. 94, 61903 (2009).
[Crossref]

S. Guenneau, A. Movchan, G. Pétursson, and S. A. Ramakrishna, “Acoustic metamaterials for sound focusing and confinement,” New J. Phys. 9, 399 (2007).
[Crossref]

Halevi, P.

A. S. Sánchez and P. Halevi, “Spontaneous emission in one-dimensional photonic crystals,” Phys. Rev. E 72, 056609 (2005).
[Crossref]

Han, D.

X. Xu, Y. Xi, D. Han, X. Liu, J. Zi, and Z. Zhu, “Effective plasma frequency in one-dimensional metallic-dielectric photonic crystals,” Appl. Phys. Lett. 86, 091112 (2005).
[Crossref]

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Low frequency plasmons in thin-wire structures,” J. Phys.: Condens. Matter 10, 4785–4809 (1998).

Hwu, R. J.

D. L. Woolard, J. O. Jensen, R. J. Hwu, and M. S. Shur, Terahertz Science and Technology for Military and Security Applications (World Scientific Publishing Co. Pte. Ltd., 2007).

Iakushev, D. A.

Iorsh, I.

Iotti, R. C.

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417, 156–159 (2002).
[Crossref] [PubMed]

Jensen, J. O.

D. L. Woolard, J. O. Jensen, R. J. Hwu, and M. S. Shur, Terahertz Science and Technology for Military and Security Applications (World Scientific Publishing Co. Pte. Ltd., 2007).

John, S.

S. John, “Strong Localization of Photons in Certain Disordered Dielectric Superlattices,” Phys. Rev. Lett. 58 (23) 2486–2489 (1987).
[Crossref] [PubMed]

Juárez-Ruiz, E.

B. Zenteno-Mateo, V. Cerdán-Ramírez, B. Flores-Desirena, M. P. Sampedro, E. Juárez-Ruiz, and F. Pérez-Rodríguez, “Effective permittivity tensor for a metal-dielectric superlattice,” Progress in Electromagnetics Research Letters 22, 165–174 (2011).

Justice, B. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial Electromagnetic Cloak at Microwave Frequencies,” Science 314, 977–980 (2006).
[Crossref] [PubMed]

Jylhä, L.

L. Jylhä, I. Kolmakov, S. Maslovski, and S. Tretyakov, “Modeling of isotropic backward-wave materials composed of resonant spheres,” J. Appl. Phys. 99, 043102 (2006).
[Crossref]

Kafesaki, M.

A. A. Basharin, C. Mavidis, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Epsilon near zero based phenomena in metamaterials,” Phys. Rev. B 87, 155130 (2013).
[Crossref]

M. Massaouti, A. A. Basharin, M. Kafesaki, M. F. Acosta, R. I. Merino, V. M. Orera, E. N. Economou, C. M. Soukoulis, and S. Tzortzakis, “Eutectic epsilon-near-zero metamaterial terahertz waveguides,” Opt. Lett. 38, 1140–1142 (2013).
[Crossref] [PubMed]

A. Reyes-Coronado, M. F. Acosta, R. I. Merino, V. M. Orera, G. Kenanakis, N. Katsarakis, M. Kafesaki, Ch. Mavidis, J. García de Abajo, E. N. Economou, and C. M. Soukoulis, “Self-organization approach for THz polaritonic metamaterials,” Opt. Express 20, 14663–14682 (2012).
[Crossref] [PubMed]

G. Bickauskaite, M. Manousidaki, K. Terzaki, E. Kambouraki, I. Sakellari, N. Vasilantonakis, D. Gray, C. M. Soukoulis, C. Fotakis, M. Vamvakaki, M. Kafesaki, M. Farsari, A. Pikulin, and N. Bityurin, “3D Photonic Nanostructures via Diffusion-Assisted Direct fs Laser Writing,” P. Soc. Photo-Opt. Ins. 20129279311–6 (2012).

S. Foteinopoulou, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Two-dimensional polaritonic photonic crystals as terahertz uniaxial metamaterials,” Phys. Rev. B 84, 035128 (2011).
[Crossref]

A. Reyes-Coronado, M. F. Acosta, R. I. Merino, V. M. Orera, G. Kenanakis, N. Katsarakis, M. Kafesaki, and C. M. Soukoulis, “Electromagnetic response of anisotropic eutectic metamaterials in THz range,” AIP Conf. Proc. 1291, 148–150 (2010).
[Crossref]

Kaltenecker, K. J.

A. Tuniz, K. J. Kaltenecker, B. M. Fischer, M. Walther, S. C. Fleming, A. Argyros, and B. T. Kuhlmey, “Metamaterial fibres for subdiffraction imaging and focusing at terahertz frequencies over optically long distances,” Nat. Commun. 4, 2706 (2013).
[Crossref] [PubMed]

Kambouraki, E.

G. Bickauskaite, M. Manousidaki, K. Terzaki, E. Kambouraki, I. Sakellari, N. Vasilantonakis, D. Gray, C. M. Soukoulis, C. Fotakis, M. Vamvakaki, M. Kafesaki, M. Farsari, A. Pikulin, and N. Bityurin, “3D Photonic Nanostructures via Diffusion-Assisted Direct fs Laser Writing,” P. Soc. Photo-Opt. Ins. 20129279311–6 (2012).

Kaplan, D. L.

S. Kim, A. N. Mitropoulos, J. D. Spitzberg, H. Tao, D. L. Kaplan, and F. G. Omenetto, “Silk inverse opals,” Nature Photonics 6, 818–823 (2012).
[Crossref]

Katsarakis, N.

A. Reyes-Coronado, M. F. Acosta, R. I. Merino, V. M. Orera, G. Kenanakis, N. Katsarakis, M. Kafesaki, Ch. Mavidis, J. García de Abajo, E. N. Economou, and C. M. Soukoulis, “Self-organization approach for THz polaritonic metamaterials,” Opt. Express 20, 14663–14682 (2012).
[Crossref] [PubMed]

A. Reyes-Coronado, M. F. Acosta, R. I. Merino, V. M. Orera, G. Kenanakis, N. Katsarakis, M. Kafesaki, and C. M. Soukoulis, “Electromagnetic response of anisotropic eutectic metamaterials in THz range,” AIP Conf. Proc. 1291, 148–150 (2010).
[Crossref]

Kenanakis, G.

A. Reyes-Coronado, M. F. Acosta, R. I. Merino, V. M. Orera, G. Kenanakis, N. Katsarakis, M. Kafesaki, Ch. Mavidis, J. García de Abajo, E. N. Economou, and C. M. Soukoulis, “Self-organization approach for THz polaritonic metamaterials,” Opt. Express 20, 14663–14682 (2012).
[Crossref] [PubMed]

A. Reyes-Coronado, M. F. Acosta, R. I. Merino, V. M. Orera, G. Kenanakis, N. Katsarakis, M. Kafesaki, and C. M. Soukoulis, “Electromagnetic response of anisotropic eutectic metamaterials in THz range,” AIP Conf. Proc. 1291, 148–150 (2010).
[Crossref]

Khalilzadeh-Rezaie, F.

F. Khalilzadeh-Rezaie, C. W. Smith, J. Nath, N. Nader, M. Shahzad, J. W. Cleary, I. Avrutsky, and R. E. Peale, “Infrared surface polaritons on bismuth,” J. Nanophoton. 9, 093792 (2015).
[Crossref]

Kildishev, A. V.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat Photonics 1, 224–227 (2007).
[Crossref]

Kim, S.

S. Kim, A. N. Mitropoulos, J. D. Spitzberg, H. Tao, D. L. Kaplan, and F. G. Omenetto, “Silk inverse opals,” Nature Photonics 6, 818–823 (2012).
[Crossref]

Kittel, C.

C. Kittel, Introduction to Solid State Physics (John Wiley & Sons, 2005).

Kivshar, Y.

Köhler, R.

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417, 156–159 (2002).
[Crossref] [PubMed]

Kolmakov, I.

L. Jylhä, I. Kolmakov, S. Maslovski, and S. Tretyakov, “Modeling of isotropic backward-wave materials composed of resonant spheres,” J. Appl. Phys. 99, 043102 (2006).
[Crossref]

Kuhlmey, B. T.

A. Tuniz, K. J. Kaltenecker, B. M. Fischer, M. Walther, S. C. Fleming, A. Argyros, and B. T. Kuhlmey, “Metamaterial fibres for subdiffraction imaging and focusing at terahertz frequencies over optically long distances,” Nat. Commun. 4, 2706 (2013).
[Crossref] [PubMed]

Lagage, P.-O.

V. Minier, G. Durand, P.-O. Lagage, M. Talvard, T. Travouillon, M. Busso, and G. Tosti, “Submillimetre/terahertz astronomy at dome C with CEA filled bolometer array,” EAS Publications Series 25, 321–326 (2007).
[Crossref]

Linfield, E. H.

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417, 156–159 (2002).
[Crossref] [PubMed]

Liu, X.

X. Xu, Y. Xi, D. Han, X. Liu, J. Zi, and Z. Zhu, “Effective plasma frequency in one-dimensional metallic-dielectric photonic crystals,” Appl. Phys. Lett. 86, 091112 (2005).
[Crossref]

Makarov, N. M.

Manousidaki, M.

G. Bickauskaite, M. Manousidaki, K. Terzaki, E. Kambouraki, I. Sakellari, N. Vasilantonakis, D. Gray, C. M. Soukoulis, C. Fotakis, M. Vamvakaki, M. Kafesaki, M. Farsari, A. Pikulin, and N. Bityurin, “3D Photonic Nanostructures via Diffusion-Assisted Direct fs Laser Writing,” P. Soc. Photo-Opt. Ins. 20129279311–6 (2012).

Manzanares-Martínez, J.

J. Manzanares-Martínez, “Analytic expression for the effective plasma frequency in one-dimensional metallic-dielectric photonic crystal,” Progress In Electromagnetics Research M,  13, 189–202 (2010).
[Crossref]

Markoš, P.

P. Markoš and C. M. Soukoulis, Wave Propagation. From Electrons to Photonic Crystals and Left-Handed Materials (Princeton University Press, Princeton, 2008).

Maslovski, S.

L. Jylhä, I. Kolmakov, S. Maslovski, and S. Tretyakov, “Modeling of isotropic backward-wave materials composed of resonant spheres,” J. Appl. Phys. 99, 043102 (2006).
[Crossref]

Massaouti, M.

Mavidis, C.

A. A. Basharin, C. Mavidis, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Epsilon near zero based phenomena in metamaterials,” Phys. Rev. B 87, 155130 (2013).
[Crossref]

Mavidis, Ch.

Merino, R. I.

Minier, V.

V. Minier, G. Durand, P.-O. Lagage, M. Talvard, T. Travouillon, M. Busso, and G. Tosti, “Submillimetre/terahertz astronomy at dome C with CEA filled bolometer array,” EAS Publications Series 25, 321–326 (2007).
[Crossref]

Mitropoulos, A. N.

S. Kim, A. N. Mitropoulos, J. D. Spitzberg, H. Tao, D. L. Kaplan, and F. G. Omenetto, “Silk inverse opals,” Nature Photonics 6, 818–823 (2012).
[Crossref]

Mock, J. J.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial Electromagnetic Cloak at Microwave Frequencies,” Science 314, 977–980 (2006).
[Crossref] [PubMed]

Moroz, A.

V. Yannopapas and A. Moroz, “Negative refractive index metamaterials from inherently non-magnetic materials for deep infrared to terahertz frequency ranges,” J. Phys.: Condens. Matter 17, 3717–3734 (2005).

Movchan, A.

S. Guenneau, A. Movchan, G. Pétursson, and S. A. Ramakrishna, “Acoustic metamaterials for sound focusing and confinement,” New J. Phys. 9, 399 (2007).
[Crossref]

Movchan, A. B.

M. Brun, S. Guenneau, and A. B. Movchan, “Achieving control of in-plane elastic waves,” Appl. Phys. Lett. 94, 61903 (2009).
[Crossref]

Nader, N.

F. Khalilzadeh-Rezaie, C. W. Smith, J. Nath, N. Nader, M. Shahzad, J. W. Cleary, I. Avrutsky, and R. E. Peale, “Infrared surface polaritons on bismuth,” J. Nanophoton. 9, 093792 (2015).
[Crossref]

Nath, J.

F. Khalilzadeh-Rezaie, C. W. Smith, J. Nath, N. Nader, M. Shahzad, J. W. Cleary, I. Avrutsky, and R. E. Peale, “Infrared surface polaritons on bismuth,” J. Nanophoton. 9, 093792 (2015).
[Crossref]

Nemat-Nasser, S. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[Crossref] [PubMed]

O’Brien, S.

S. O’Brien and J. B. Pendry, “Photonic band-gap effects and magnetic activity in dielectric composites,” J. Phys.: Condens. Matter 14, 4035–4044 (2002).

Omenetto, F. G.

S. Kim, A. N. Mitropoulos, J. D. Spitzberg, H. Tao, D. L. Kaplan, and F. G. Omenetto, “Silk inverse opals,” Nature Photonics 6, 818–823 (2012).
[Crossref]

Orera, V. M.

Orlov, A.

Padilla, W. J.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[Crossref] [PubMed]

Palomino-Ovando, M. A.

V. Cerdán-Ramírez, B. Zenteno-Mateo, M. P. Sampedro, M. A. Palomino-Ovando, B. Flores-Desirena, and F. Pérez-Rodríguez, “Anisotropy effects in homogenized magnetodielectric photonic crystals,” J. Appl. Phys. 106, 103520 (2009).
[Crossref]

Paredes-Juárez, A.

Peale, R. E.

F. Khalilzadeh-Rezaie, C. W. Smith, J. Nath, N. Nader, M. Shahzad, J. W. Cleary, I. Avrutsky, and R. E. Peale, “Infrared surface polaritons on bismuth,” J. Nanophoton. 9, 093792 (2015).
[Crossref]

Pendry, J. B.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-Dimensional Invisibility Cloak at Optical Wavelengths,” Science 328, 337–339 (2010).
[Crossref] [PubMed]

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial Electromagnetic Cloak at Microwave Frequencies,” Science 314, 977–980 (2006).
[Crossref] [PubMed]

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74, 115116 (2006).
[Crossref]

S. O’Brien and J. B. Pendry, “Photonic band-gap effects and magnetic activity in dielectric composites,” J. Phys.: Condens. Matter 14, 4035–4044 (2002).

J. B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[Crossref] [PubMed]

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Low frequency plasmons in thin-wire structures,” J. Phys.: Condens. Matter 10, 4785–4809 (1998).

Pérez-Rodríguez, F.

F. Díaz-Monge, A. Paredes-Juárez, D. A. Iakushev, N. M. Makarov, and F. Pérez-Rodríguez, “THz photonic bands of periodic stacks composed of resonant dielectric and nonlocal metal,” Opt. Mater. Express,  5, 361–372 (2015).
[Crossref]

A. Paredes-Juárez, D. A. Iakushev, B. Flores-Desirena, N. M. Makarov, and F. Pérez-Rodríguez, “Nonlocal Effect on Optic Spectrum of a Periodic Dielectric-Metal Stack,” Opt. Express 22, 7581–7586 (2014).
[Crossref] [PubMed]

E. Sánchez-Mora, M. Fernández-Candelario, E. Gómez-Barojas, and F. Pérez-Rodríguez, “Influence of Fe Ions on the Optical Properties of Fe-ZnO Inverse Opals,” J. Supercond. Nov. Magn. 26, 2447–2449 (2013).
[Crossref]

B. Zenteno-Mateo, V. Cerdán-Ramírez, B. Flores-Desirena, M. P. Sampedro, E. Juárez-Ruiz, and F. Pérez-Rodríguez, “Effective permittivity tensor for a metal-dielectric superlattice,” Progress in Electromagnetics Research Letters 22, 165–174 (2011).

V. Cerdán-Ramírez, B. Zenteno-Mateo, M. P. Sampedro, M. A. Palomino-Ovando, B. Flores-Desirena, and F. Pérez-Rodríguez, “Anisotropy effects in homogenized magnetodielectric photonic crystals,” J. Appl. Phys. 106, 103520 (2009).
[Crossref]

A. Paredes-Juárez, F. Díaz-Monge, N. M. Makarov, and F. Pérez-Rodríguez, “Nonlocal effects in the electrodynamics of metallic slabs,” JETP Letters 90, 623–627 (2009).
[Crossref]

Pétursson, G.

S. Guenneau, A. Movchan, G. Pétursson, and S. A. Ramakrishna, “Acoustic metamaterials for sound focusing and confinement,” New J. Phys. 9, 399 (2007).
[Crossref]

Pikulin, A.

G. Bickauskaite, M. Manousidaki, K. Terzaki, E. Kambouraki, I. Sakellari, N. Vasilantonakis, D. Gray, C. M. Soukoulis, C. Fotakis, M. Vamvakaki, M. Kafesaki, M. Farsari, A. Pikulin, and N. Bityurin, “3D Photonic Nanostructures via Diffusion-Assisted Direct fs Laser Writing,” P. Soc. Photo-Opt. Ins. 20129279311–6 (2012).

Podolskiy, V. A.

J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett. 90, 191109 (2007).
[Crossref]

Ramakrishna, S. A.

S. Guenneau, A. Movchan, G. Pétursson, and S. A. Ramakrishna, “Acoustic metamaterials for sound focusing and confinement,” New J. Phys. 9, 399 (2007).
[Crossref]

Reyes-Coronado, A.

A. Reyes-Coronado, M. F. Acosta, R. I. Merino, V. M. Orera, G. Kenanakis, N. Katsarakis, M. Kafesaki, Ch. Mavidis, J. García de Abajo, E. N. Economou, and C. M. Soukoulis, “Self-organization approach for THz polaritonic metamaterials,” Opt. Express 20, 14663–14682 (2012).
[Crossref] [PubMed]

A. Reyes-Coronado, M. F. Acosta, R. I. Merino, V. M. Orera, G. Kenanakis, N. Katsarakis, M. Kafesaki, and C. M. Soukoulis, “Electromagnetic response of anisotropic eutectic metamaterials in THz range,” AIP Conf. Proc. 1291, 148–150 (2010).
[Crossref]

Ritchie, D. A.

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417, 156–159 (2002).
[Crossref] [PubMed]

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Low frequency plasmons in thin-wire structures,” J. Phys.: Condens. Matter 10, 4785–4809 (1998).

Rossi, F.

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417, 156–159 (2002).
[Crossref] [PubMed]

Rytov, S. M.

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Sakellari, I.

G. Bickauskaite, M. Manousidaki, K. Terzaki, E. Kambouraki, I. Sakellari, N. Vasilantonakis, D. Gray, C. M. Soukoulis, C. Fotakis, M. Vamvakaki, M. Kafesaki, M. Farsari, A. Pikulin, and N. Bityurin, “3D Photonic Nanostructures via Diffusion-Assisted Direct fs Laser Writing,” P. Soc. Photo-Opt. Ins. 20129279311–6 (2012).

Salakhutdinov, I.

J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett. 90, 191109 (2007).
[Crossref]

Sampedro, M. P.

B. Zenteno-Mateo, V. Cerdán-Ramírez, B. Flores-Desirena, M. P. Sampedro, E. Juárez-Ruiz, and F. Pérez-Rodríguez, “Effective permittivity tensor for a metal-dielectric superlattice,” Progress in Electromagnetics Research Letters 22, 165–174 (2011).

V. Cerdán-Ramírez, B. Zenteno-Mateo, M. P. Sampedro, M. A. Palomino-Ovando, B. Flores-Desirena, and F. Pérez-Rodríguez, “Anisotropy effects in homogenized magnetodielectric photonic crystals,” J. Appl. Phys. 106, 103520 (2009).
[Crossref]

Sánchez, A. S.

A. S. Sánchez and P. Halevi, “Spontaneous emission in one-dimensional photonic crystals,” Phys. Rev. E 72, 056609 (2005).
[Crossref]

Sánchez-Mora, E.

E. Sánchez-Mora, M. Fernández-Candelario, E. Gómez-Barojas, and F. Pérez-Rodríguez, “Influence of Fe Ions on the Optical Properties of Fe-ZnO Inverse Opals,” J. Supercond. Nov. Magn. 26, 2447–2449 (2013).
[Crossref]

Schuller, J. A.

J. A. Schuller, R. Zia, T. Taubner, and M. L. Brongersma, “Dielectric metamaterials based on electric and magnetic resonances of silicon carbide particles,” Phys. Rev. Lett. 99, 107401 (2007).
[Crossref] [PubMed]

Schultz, S.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[Crossref] [PubMed]

Schurig, D.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial Electromagnetic Cloak at Microwave Frequencies,” Science 314, 977–980 (2006).
[Crossref] [PubMed]

Shahzad, M.

F. Khalilzadeh-Rezaie, C. W. Smith, J. Nath, N. Nader, M. Shahzad, J. W. Cleary, I. Avrutsky, and R. E. Peale, “Infrared surface polaritons on bismuth,” J. Nanophoton. 9, 093792 (2015).
[Crossref]

M. Shahzad, “Infrared surface plasmon polaritons on semiconductor, semimetal and conducting polymer,” Ph.D. thesis (University of Central Florida, Orlando, Florida, 2012).

Shalaev, V. M.

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat Photonics 1, 224–227 (2007).
[Crossref]

Shur, M. S.

D. L. Woolard, J. O. Jensen, R. J. Hwu, and M. S. Shur, Terahertz Science and Technology for Military and Security Applications (World Scientific Publishing Co. Pte. Ltd., 2007).

Smith, C. W.

F. Khalilzadeh-Rezaie, C. W. Smith, J. Nath, N. Nader, M. Shahzad, J. W. Cleary, I. Avrutsky, and R. E. Peale, “Infrared surface polaritons on bismuth,” J. Nanophoton. 9, 093792 (2015).
[Crossref]

Smith, D. R.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial Electromagnetic Cloak at Microwave Frequencies,” Science 314, 977–980 (2006).
[Crossref] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[Crossref] [PubMed]

Smye, S. W.

S. W. Smye, J. M. Chamberlain, A. J. Fitzgerald, and E. Berry, “The interaction between Terahertz radiation and biological tissue,” Phys. Med. Biol. 46, R101–R112 (2001).
[Crossref] [PubMed]

Soukoulis, C. M.

A. A. Basharin, C. Mavidis, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Epsilon near zero based phenomena in metamaterials,” Phys. Rev. B 87, 155130 (2013).
[Crossref]

M. Massaouti, A. A. Basharin, M. Kafesaki, M. F. Acosta, R. I. Merino, V. M. Orera, E. N. Economou, C. M. Soukoulis, and S. Tzortzakis, “Eutectic epsilon-near-zero metamaterial terahertz waveguides,” Opt. Lett. 38, 1140–1142 (2013).
[Crossref] [PubMed]

A. Reyes-Coronado, M. F. Acosta, R. I. Merino, V. M. Orera, G. Kenanakis, N. Katsarakis, M. Kafesaki, Ch. Mavidis, J. García de Abajo, E. N. Economou, and C. M. Soukoulis, “Self-organization approach for THz polaritonic metamaterials,” Opt. Express 20, 14663–14682 (2012).
[Crossref] [PubMed]

G. Bickauskaite, M. Manousidaki, K. Terzaki, E. Kambouraki, I. Sakellari, N. Vasilantonakis, D. Gray, C. M. Soukoulis, C. Fotakis, M. Vamvakaki, M. Kafesaki, M. Farsari, A. Pikulin, and N. Bityurin, “3D Photonic Nanostructures via Diffusion-Assisted Direct fs Laser Writing,” P. Soc. Photo-Opt. Ins. 20129279311–6 (2012).

S. Foteinopoulou, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Two-dimensional polaritonic photonic crystals as terahertz uniaxial metamaterials,” Phys. Rev. B 84, 035128 (2011).
[Crossref]

A. Reyes-Coronado, M. F. Acosta, R. I. Merino, V. M. Orera, G. Kenanakis, N. Katsarakis, M. Kafesaki, and C. M. Soukoulis, “Electromagnetic response of anisotropic eutectic metamaterials in THz range,” AIP Conf. Proc. 1291, 148–150 (2010).
[Crossref]

P. Markoš and C. M. Soukoulis, Wave Propagation. From Electrons to Photonic Crystals and Left-Handed Materials (Princeton University Press, Princeton, 2008).

Spitzberg, J. D.

S. Kim, A. N. Mitropoulos, J. D. Spitzberg, H. Tao, D. L. Kaplan, and F. G. Omenetto, “Silk inverse opals,” Nature Photonics 6, 818–823 (2012).
[Crossref]

Starr, A. F.

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial Electromagnetic Cloak at Microwave Frequencies,” Science 314, 977–980 (2006).
[Crossref] [PubMed]

Stenger, N.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-Dimensional Invisibility Cloak at Optical Wavelengths,” Science 328, 337–339 (2010).
[Crossref] [PubMed]

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Low frequency plasmons in thin-wire structures,” J. Phys.: Condens. Matter 10, 4785–4809 (1998).

Talvard, M.

V. Minier, G. Durand, P.-O. Lagage, M. Talvard, T. Travouillon, M. Busso, and G. Tosti, “Submillimetre/terahertz astronomy at dome C with CEA filled bolometer array,” EAS Publications Series 25, 321–326 (2007).
[Crossref]

Tao, H.

S. Kim, A. N. Mitropoulos, J. D. Spitzberg, H. Tao, D. L. Kaplan, and F. G. Omenetto, “Silk inverse opals,” Nature Photonics 6, 818–823 (2012).
[Crossref]

Taubner, T.

J. A. Schuller, R. Zia, T. Taubner, and M. L. Brongersma, “Dielectric metamaterials based on electric and magnetic resonances of silicon carbide particles,” Phys. Rev. Lett. 99, 107401 (2007).
[Crossref] [PubMed]

Terzaki, K.

G. Bickauskaite, M. Manousidaki, K. Terzaki, E. Kambouraki, I. Sakellari, N. Vasilantonakis, D. Gray, C. M. Soukoulis, C. Fotakis, M. Vamvakaki, M. Kafesaki, M. Farsari, A. Pikulin, and N. Bityurin, “3D Photonic Nanostructures via Diffusion-Assisted Direct fs Laser Writing,” P. Soc. Photo-Opt. Ins. 20129279311–6 (2012).

Tosti, G.

V. Minier, G. Durand, P.-O. Lagage, M. Talvard, T. Travouillon, M. Busso, and G. Tosti, “Submillimetre/terahertz astronomy at dome C with CEA filled bolometer array,” EAS Publications Series 25, 321–326 (2007).
[Crossref]

Travouillon, T.

V. Minier, G. Durand, P.-O. Lagage, M. Talvard, T. Travouillon, M. Busso, and G. Tosti, “Submillimetre/terahertz astronomy at dome C with CEA filled bolometer array,” EAS Publications Series 25, 321–326 (2007).
[Crossref]

Tredicucci, A.

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417, 156–159 (2002).
[Crossref] [PubMed]

Tretyakov, S.

L. Jylhä, I. Kolmakov, S. Maslovski, and S. Tretyakov, “Modeling of isotropic backward-wave materials composed of resonant spheres,” J. Appl. Phys. 99, 043102 (2006).
[Crossref]

Tsai, D. P.

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74, 115116 (2006).
[Crossref]

Tuniz, A.

A. Tuniz, K. J. Kaltenecker, B. M. Fischer, M. Walther, S. C. Fleming, A. Argyros, and B. T. Kuhlmey, “Metamaterial fibres for subdiffraction imaging and focusing at terahertz frequencies over optically long distances,” Nat. Commun. 4, 2706 (2013).
[Crossref] [PubMed]

Tzortzakis, S.

Vamvakaki, M.

G. Bickauskaite, M. Manousidaki, K. Terzaki, E. Kambouraki, I. Sakellari, N. Vasilantonakis, D. Gray, C. M. Soukoulis, C. Fotakis, M. Vamvakaki, M. Kafesaki, M. Farsari, A. Pikulin, and N. Bityurin, “3D Photonic Nanostructures via Diffusion-Assisted Direct fs Laser Writing,” P. Soc. Photo-Opt. Ins. 20129279311–6 (2012).

Vasilantonakis, N.

G. Bickauskaite, M. Manousidaki, K. Terzaki, E. Kambouraki, I. Sakellari, N. Vasilantonakis, D. Gray, C. M. Soukoulis, C. Fotakis, M. Vamvakaki, M. Kafesaki, M. Farsari, A. Pikulin, and N. Bityurin, “3D Photonic Nanostructures via Diffusion-Assisted Direct fs Laser Writing,” P. Soc. Photo-Opt. Ins. 20129279311–6 (2012).

Veselago, V. G.

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and µ,” Sov. Phys. Uspekhi 10, 509–514 (1968).
[Crossref]

Vier, D. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[Crossref] [PubMed]

Walther, M.

A. Tuniz, K. J. Kaltenecker, B. M. Fischer, M. Walther, S. C. Fleming, A. Argyros, and B. T. Kuhlmey, “Metamaterial fibres for subdiffraction imaging and focusing at terahertz frequencies over optically long distances,” Nat. Commun. 4, 2706 (2013).
[Crossref] [PubMed]

Wegener, M.

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-Dimensional Invisibility Cloak at Optical Wavelengths,” Science 328, 337–339 (2010).
[Crossref] [PubMed]

Wood, B.

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74, 115116 (2006).
[Crossref]

Woolard, D. L.

D. L. Woolard, J. O. Jensen, R. J. Hwu, and M. S. Shur, Terahertz Science and Technology for Military and Security Applications (World Scientific Publishing Co. Pte. Ltd., 2007).

Xi, Y.

X. Xu, Y. Xi, D. Han, X. Liu, J. Zi, and Z. Zhu, “Effective plasma frequency in one-dimensional metallic-dielectric photonic crystals,” Appl. Phys. Lett. 86, 091112 (2005).
[Crossref]

Xu, X.

X. Xu, Y. Xi, D. Han, X. Liu, J. Zi, and Z. Zhu, “Effective plasma frequency in one-dimensional metallic-dielectric photonic crystals,” Appl. Phys. Lett. 86, 091112 (2005).
[Crossref]

Yablonovitch, E.

E. Yablonovitch, “Inhibited Spontaneous Emission in Solid-State Physics and Electronics,” Phys. Rev. Lett. 58 (20) 2059–2062 (1987).
[Crossref] [PubMed]

Yannopapas, V.

V. Yannopapas and A. Moroz, “Negative refractive index metamaterials from inherently non-magnetic materials for deep infrared to terahertz frequency ranges,” J. Phys.: Condens. Matter 17, 3717–3734 (2005).

Yariv, A.

A. Yariv and P. Yeh, Optical Waves in Crystals. Propagation and Control of Laser Radiation (Wiley, 1984).

Yeh, P.

A. Yariv and P. Yeh, Optical Waves in Crystals. Propagation and Control of Laser Radiation (Wiley, 1984).

Zenteno-Mateo, B.

B. Zenteno-Mateo, V. Cerdán-Ramírez, B. Flores-Desirena, M. P. Sampedro, E. Juárez-Ruiz, and F. Pérez-Rodríguez, “Effective permittivity tensor for a metal-dielectric superlattice,” Progress in Electromagnetics Research Letters 22, 165–174 (2011).

V. Cerdán-Ramírez, B. Zenteno-Mateo, M. P. Sampedro, M. A. Palomino-Ovando, B. Flores-Desirena, and F. Pérez-Rodríguez, “Anisotropy effects in homogenized magnetodielectric photonic crystals,” J. Appl. Phys. 106, 103520 (2009).
[Crossref]

Zhu, Z.

X. Xu, Y. Xi, D. Han, X. Liu, J. Zi, and Z. Zhu, “Effective plasma frequency in one-dimensional metallic-dielectric photonic crystals,” Appl. Phys. Lett. 86, 091112 (2005).
[Crossref]

Zi, J.

X. Xu, Y. Xi, D. Han, X. Liu, J. Zi, and Z. Zhu, “Effective plasma frequency in one-dimensional metallic-dielectric photonic crystals,” Appl. Phys. Lett. 86, 091112 (2005).
[Crossref]

Zia, R.

J. A. Schuller, R. Zia, T. Taubner, and M. L. Brongersma, “Dielectric metamaterials based on electric and magnetic resonances of silicon carbide particles,” Phys. Rev. Lett. 99, 107401 (2007).
[Crossref] [PubMed]

AIP Conf. Proc. (1)

A. Reyes-Coronado, M. F. Acosta, R. I. Merino, V. M. Orera, G. Kenanakis, N. Katsarakis, M. Kafesaki, and C. M. Soukoulis, “Electromagnetic response of anisotropic eutectic metamaterials in THz range,” AIP Conf. Proc. 1291, 148–150 (2010).
[Crossref]

App. Phys. Lett. (1)

H. Chen and C. T. Chan, “Acoustic cloaking in three dimensions using acoustic metamaterials,” App. Phys. Lett. 91, 183518 (2007).
[Crossref]

Appl. Phys. Lett. (3)

M. Brun, S. Guenneau, and A. B. Movchan, “Achieving control of in-plane elastic waves,” Appl. Phys. Lett. 94, 61903 (2009).
[Crossref]

X. Xu, Y. Xi, D. Han, X. Liu, J. Zi, and Z. Zhu, “Effective plasma frequency in one-dimensional metallic-dielectric photonic crystals,” Appl. Phys. Lett. 86, 091112 (2005).
[Crossref]

J. Elser, V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, “Nonlocal effects in effective-medium response of nanolayered metamaterials,” Appl. Phys. Lett. 90, 191109 (2007).
[Crossref]

EAS Publications Series (1)

V. Minier, G. Durand, P.-O. Lagage, M. Talvard, T. Travouillon, M. Busso, and G. Tosti, “Submillimetre/terahertz astronomy at dome C with CEA filled bolometer array,” EAS Publications Series 25, 321–326 (2007).
[Crossref]

J. Appl. Phys. (2)

V. Cerdán-Ramírez, B. Zenteno-Mateo, M. P. Sampedro, M. A. Palomino-Ovando, B. Flores-Desirena, and F. Pérez-Rodríguez, “Anisotropy effects in homogenized magnetodielectric photonic crystals,” J. Appl. Phys. 106, 103520 (2009).
[Crossref]

L. Jylhä, I. Kolmakov, S. Maslovski, and S. Tretyakov, “Modeling of isotropic backward-wave materials composed of resonant spheres,” J. Appl. Phys. 99, 043102 (2006).
[Crossref]

J. Nanophoton. (1)

F. Khalilzadeh-Rezaie, C. W. Smith, J. Nath, N. Nader, M. Shahzad, J. W. Cleary, I. Avrutsky, and R. E. Peale, “Infrared surface polaritons on bismuth,” J. Nanophoton. 9, 093792 (2015).
[Crossref]

J. Phys.: Condens. Matter (3)

V. Yannopapas and A. Moroz, “Negative refractive index metamaterials from inherently non-magnetic materials for deep infrared to terahertz frequency ranges,” J. Phys.: Condens. Matter 17, 3717–3734 (2005).

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Low frequency plasmons in thin-wire structures,” J. Phys.: Condens. Matter 10, 4785–4809 (1998).

S. O’Brien and J. B. Pendry, “Photonic band-gap effects and magnetic activity in dielectric composites,” J. Phys.: Condens. Matter 14, 4035–4044 (2002).

J. Supercond. Nov. Magn. (1)

E. Sánchez-Mora, M. Fernández-Candelario, E. Gómez-Barojas, and F. Pérez-Rodríguez, “Influence of Fe Ions on the Optical Properties of Fe-ZnO Inverse Opals,” J. Supercond. Nov. Magn. 26, 2447–2449 (2013).
[Crossref]

JETP Letters (1)

A. Paredes-Juárez, F. Díaz-Monge, N. M. Makarov, and F. Pérez-Rodríguez, “Nonlocal effects in the electrodynamics of metallic slabs,” JETP Letters 90, 623–627 (2009).
[Crossref]

Nat Photonics (1)

W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloaking with metamaterials,” Nat Photonics 1, 224–227 (2007).
[Crossref]

Nat. Commun. (1)

A. Tuniz, K. J. Kaltenecker, B. M. Fischer, M. Walther, S. C. Fleming, A. Argyros, and B. T. Kuhlmey, “Metamaterial fibres for subdiffraction imaging and focusing at terahertz frequencies over optically long distances,” Nat. Commun. 4, 2706 (2013).
[Crossref] [PubMed]

Nature (1)

R. Köhler, A. Tredicucci, F. Beltram, H. E. Beere, E. H. Linfield, A. G. Davies, D. A. Ritchie, R. C. Iotti, and F. Rossi, “Terahertz semiconductor-heterostructure laser,” Nature 417, 156–159 (2002).
[Crossref] [PubMed]

Nature Photonics (1)

S. Kim, A. N. Mitropoulos, J. D. Spitzberg, H. Tao, D. L. Kaplan, and F. G. Omenetto, “Silk inverse opals,” Nature Photonics 6, 818–823 (2012).
[Crossref]

New J. Phys. (1)

S. Guenneau, A. Movchan, G. Pétursson, and S. A. Ramakrishna, “Acoustic metamaterials for sound focusing and confinement,” New J. Phys. 9, 399 (2007).
[Crossref]

Opt. Express (3)

Opt. Lett. (1)

Opt. Mater. Express (1)

P. Soc. Photo-Opt. Ins. (1)

G. Bickauskaite, M. Manousidaki, K. Terzaki, E. Kambouraki, I. Sakellari, N. Vasilantonakis, D. Gray, C. M. Soukoulis, C. Fotakis, M. Vamvakaki, M. Kafesaki, M. Farsari, A. Pikulin, and N. Bityurin, “3D Photonic Nanostructures via Diffusion-Assisted Direct fs Laser Writing,” P. Soc. Photo-Opt. Ins. 20129279311–6 (2012).

Phys. Med. Biol. (1)

S. W. Smye, J. M. Chamberlain, A. J. Fitzgerald, and E. Berry, “The interaction between Terahertz radiation and biological tissue,” Phys. Med. Biol. 46, R101–R112 (2001).
[Crossref] [PubMed]

Phys. Rev. (1)

P. W. Anderson, “Absence of Diffusion in Certain Random Lattices,” Phys. Rev. 109 (5) 1492–1505 (1958).
[Crossref]

Phys. Rev. B (3)

A. A. Basharin, C. Mavidis, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Epsilon near zero based phenomena in metamaterials,” Phys. Rev. B 87, 155130 (2013).
[Crossref]

S. Foteinopoulou, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Two-dimensional polaritonic photonic crystals as terahertz uniaxial metamaterials,” Phys. Rev. B 84, 035128 (2011).
[Crossref]

B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74, 115116 (2006).
[Crossref]

Phys. Rev. E (1)

A. S. Sánchez and P. Halevi, “Spontaneous emission in one-dimensional photonic crystals,” Phys. Rev. E 72, 056609 (2005).
[Crossref]

Phys. Rev. Lett. (5)

E. Yablonovitch, “Inhibited Spontaneous Emission in Solid-State Physics and Electronics,” Phys. Rev. Lett. 58 (20) 2059–2062 (1987).
[Crossref] [PubMed]

S. John, “Strong Localization of Photons in Certain Disordered Dielectric Superlattices,” Phys. Rev. Lett. 58 (23) 2486–2489 (1987).
[Crossref] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
[Crossref] [PubMed]

J. B. Pendry, “Negative Refraction Makes a Perfect Lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
[Crossref] [PubMed]

J. A. Schuller, R. Zia, T. Taubner, and M. L. Brongersma, “Dielectric metamaterials based on electric and magnetic resonances of silicon carbide particles,” Phys. Rev. Lett. 99, 107401 (2007).
[Crossref] [PubMed]

Progress in Electromagnetics Research Letters (1)

B. Zenteno-Mateo, V. Cerdán-Ramírez, B. Flores-Desirena, M. P. Sampedro, E. Juárez-Ruiz, and F. Pérez-Rodríguez, “Effective permittivity tensor for a metal-dielectric superlattice,” Progress in Electromagnetics Research Letters 22, 165–174 (2011).

Progress In Electromagnetics Research M (1)

J. Manzanares-Martínez, “Analytic expression for the effective plasma frequency in one-dimensional metallic-dielectric photonic crystal,” Progress In Electromagnetics Research M,  13, 189–202 (2010).
[Crossref]

Science (2)

D. Schurig, J. J. Mock, B. J. Justice, S. A. Cummer, J. B. Pendry, A. F. Starr, and D. R. Smith, “Metamaterial Electromagnetic Cloak at Microwave Frequencies,” Science 314, 977–980 (2006).
[Crossref] [PubMed]

T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-Dimensional Invisibility Cloak at Optical Wavelengths,” Science 328, 337–339 (2010).
[Crossref] [PubMed]

Sov. Phys. JETP (1)

S. M. Rytov, “Electromagnetic properties of a finely stratified medium,” Sov. Phys. JETP 2, 466–475 (1956).

Sov. Phys. Uspekhi (1)

V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and µ,” Sov. Phys. Uspekhi 10, 509–514 (1968).
[Crossref]

Other (6)

M. Shahzad, “Infrared surface plasmon polaritons on semiconductor, semimetal and conducting polymer,” Ph.D. thesis (University of Central Florida, Orlando, Florida, 2012).

C. Kittel, Introduction to Solid State Physics (John Wiley & Sons, 2005).

T. Edwards, Gigahertz and Terahertz Technologies for Broadband Communications (Artech House Inc., 2000).

D. L. Woolard, J. O. Jensen, R. J. Hwu, and M. S. Shur, Terahertz Science and Technology for Military and Security Applications (World Scientific Publishing Co. Pte. Ltd., 2007).

P. Markoš and C. M. Soukoulis, Wave Propagation. From Electrons to Photonic Crystals and Left-Handed Materials (Princeton University Press, Princeton, 2008).

A. Yariv and P. Yeh, Optical Waves in Crystals. Propagation and Control of Laser Radiation (Wiley, 1984).

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Figures (8)

Fig. 1
Fig. 1 Scheme of a superlattice with two alternating non-magnetic polaritonic-material/bismuth layers. The system represents a uniaxial crystal with the c-axis parallel to the z direction.
Fig. 2
Fig. 2 Frequency dependence of the real (solid line, 1) and imaginary (dashed line, 2) parts of the parameter ε b ( ω ) ω d a / c calculated for a superlattice composed of alternating Bi and polaritonic layers.
Fig. 3
Fig. 3 Left panels: Curves of frequency ω versus η1 (10) [η2 (11)] for TE [TM] modes in a NaBr/Bi superlattice at θ = 45°. Right panels: s– and p–polarization reflectivity and transmissivity spectra for a stack of 50 NaBr/Bi bilayers in air.
Fig. 4
Fig. 4 Left panels: Curves of frequency ω versus η1 (10) [η2 (11)] for TE [TM] modes in a LiCl/Bi superlattice at θ = 45°. Right panels: s– and p–polarization reflectivity and transmissivity spectra for a stack of 50 LiCl/Bi bilayers in air.
Fig. 5
Fig. 5 Left panels: Curves of frequency ω versus η1 (10) [η2 (11)] for TE [TM] modes in a LiH/Bi superlattice at θ = 45°. Right panels: s– and p–polarization reflectivity and transmissivity spectra for a stack of 50 LiH/Bi bilayers in air.
Fig. 6
Fig. 6 Curves of ω versus the real (left column) and imaginary (right column) parts of the Bloch wave number kz for a LiH/Bi superlattice at θ = 45°, for both polarizations. The indices j and j′ correspond to the Fabry-Perot resonances in the polaritonic material and m in the Bi medium.
Fig. 7
Fig. 7 Bulk dispersion curves for the phonon-polariton (photon) modes in LiH, blue lines (Bi, red lines). The A and C solid lines (B and D dashed curves) correspond to the real (imaginary) parts of the wave vectors k z a and k z b for the electromagnetic modes in the LiH and Bi layers of the superlattice, as in Fig. 6. The indices j and j′ correspond to the Fabry-Perot resonances in the polaritonic material and m in the Bi medium.
Fig. 8
Fig. 8 s– and p–polarization reflectivity and transmissivity spectra at θ = 45° for a stack of 50 LiH/Bi bilayers in air. The thicknesses of the LiH and Bi layers are the same as those of the superlattice in Figs. 6 and 7.

Tables (1)

Tables Icon

Table 1 Parameters of the polaritonic materials

Equations (24)

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ε a = ε a , ( ω 2 ω LO 2 + i ω ν a ) / ( ω 2 ω TO 2 + i ω ν a ) ,
ε b = ε b , [ 1 ω P 2 / ( ω 2 + i ν b ω ) ] ,
cos ( k z Λ ) = cos ( k z a d a ) cos ( k z b d b ) α sin ( k z a d a ) sin ( k z b d b ) ,
α = { 1 2 [ ( k z a / k z b ) + ( k z b / k z a ) ] , for TE modes , 1 2 [ ( ε b k z a / ε a k z b ) + ( ε a k z b / ε b k z a ) ] , for TM modes .
ε x = ε y = ( ε a d a + ε b d b ) / Λ and ε z 1 = Λ 1 [ ( d a / ε a ) + ( d b / ε b ) ] .
k z a d a 1 , k z b d b 1 ,
ε x = ε y = ε b ( 1 [ 1 ( ω Λ / 2 c ) ε b tan [ ( ω Λ / 2 c ) ε b ] Λ ε b d a ( ε a ε b ) ] 1 ) ,
| ε b | ω Λ c d a Λ 1 ,
k z = { ( ε y ω 2 / c 2 ) k x 2 , for TE modes , ε x [ ( ω 2 / c 2 ) ( k x 2 / ε z ) ] , for TM modes .
k z = ω c η 1 , η 1 = ε y sin 2 θ ; for TE modes ,
k z = ω c η 2 , η 2 = ε x [ 1 ( sin 2 θ / ε z ) ] ; for TM modes .
ε x = ε y = ε ¯ ( 1 ω P 2 , eff ω ( ω + i ν b ) ) ,
ω P , eff = d b Λ ε b , ε ¯ ω P ,
ε ¯ = ( ε a , d a + ε b , d b ) / Λ .
ε x = ε y ε b , d b Λ ( 1 ω P , eff 2 ω ( ω + i ν b ) ) ,
ε x = ε y ε ˜ ( 1 ω P , eff 2 ω ( ω + i ν b ) ) ,
ω P , eff = d b Λ ε b , ε ˜ ω P ω P ,
ε ˜ = ( ε a ( 0 ) d a + ε b , d b ) / Λ .
ε x = ε y ε a . ω LO 2 ω TO 2 ω 2 ω TO 2 d a Λ + ε b , d b Λ .
ω 1 2 = ω TO 2 + ε a , d a ( ε b , d b Λ sin 2 θ ) ( ω LO 2 ω TO 2 ) ,
ω 2 2 = ω TO 2 + ε a , d a ε b , d b ( ω LO 2 ω TO 2 ) ,
[ k z a ] d a = j π , j = 1 , 2 , 3 , ,
[ k z b ] d b = π
ω * = ω LO ( 1 ω TO 2 sin 2 θ / ω LO 2 ε a , 1 sin 2 θ / ε a , ) 1 / 2 .

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