Abstract

We use a homogenization technique to estimate the efficiency of the real part of the effective permittivity nulling for suspensions of randomly oriented metal spheroids in terms of bandwidth and dielectric losses. The design of broadband epsilon-near-zero metamaterials have been demonstrated through the solution of an inverse problem. Manyfold solution branches for extracted geometrical parameters have been predicted, their origin has been explained, and the behavior of losses has been briefly considered. Realizability of metamaterials with the extracted parameters has been discussed in terms of aspect ratio and size of spheroids, and their promise for high broadband absorption has been demonstrated.

© 2014 Optical Society of America

1. Introduction

Nanocomposite metamaterials (MMs) with the effective permittivity close to zero (so-called epsilon-near-zero, or ENZ MMs) have attracted a lot of interest in recent years. Such materials, when properly designed, can potentially be utilized in multiple technologically important applications. Furtheremore, they can potentially advance a number of optical and electronic components. So far, most studies on the subject, both the experimental [13] and theoretical ones (see, e.g., [4] and references therein), have focused on narrowband ENZ MMs, when the condition Reεeff ≈ 0 is fulfilled in the vicinity of one frequency only. At the same time, extended bandwidth may be a critical issue for many optical applications, such as, e.g., multi-color and hyperspectral imaging with high resolution [4, 5], cloaking devices [6], or perfect absorption [7]. Very recently, consideration has been given to broadband ENZ MMs [813], but the most papers were restricted to one-dimensional (1d) and quasi-1d nanocomposites. The only exception is the paper [10], where an assembly of spherical metal alloy particles embedded in a dielectric host has been suggested to null the real part of the effective permittivity over a frequency range. Thus, in spite of its importance, the problem of designing broadband 3d ENZ MMs has not been addressed so far. The present study was undertaken to partially fill this gap.

In the 3d case, dealing with accurate ab initio numerical simulation is prohibitively time and memory consuming. Because of this and also seeing the present study as a preliminary to a more detailed and complicated analysis, in what follows we restrict ourselves to consideration of very simple approach based on classical homogenization theory. The basics of this theory were laid down by Maxwell Garnett in 1904 [14]. Maxwell Garnett theory (MGT), based on the concept of the local Lorentz field, dealt with a dilute suspension of homogeneous spherical particles embedded in a host medium. Using a plane-wave-expansion method, Datta et al. obtained a good agreement of the MGT with their results for dielectric spheres arrayed in face-centered cubic, simple cubic, and diamond lattices [15]. For random suspensions of spherical particles, it was shown that the MGT predicts the effective response very well when the contrast ratio is not too high and the spheres are more or less separated [16]. The MGT withstands the most stringent test for superconducting inclusions (the infinite contrast ratio) for inclusion volume fraction up to 0.3 when compared with the strong-contrast expansion in terms of three-point correlation function [17]. Generally, for disordered systems, a red shift and broadening of absorption peaks occur as compared to the MGT; these effects are largest when the filling factor is about 10 – 20%.

We use more sophisticated homogenization technique dealing with spheroidal shapes. The necessity of such a complication stems from the fact that to design a composite with desired optical properties over a frequency band, it should have a sufficient number of degrees of freedom. This can be achieved by two means. Because the effective permittivity depends on both the material parameters (constituents’ permittivities) and geometrical parameters, we could change either latter or former. So, dealing with metal alloy spheres allows one to vary the particles’ composition and, hence, to change their polarizabilities and tune the effective permittivity [10]. Here, we propose to control the effective permittivity of the composite through designing its geometry. More specifically, we deal with such geometry as a dilute random suspension of metal nanoparticles of spheroidal shape. To have the nesessary number of degrees of freedom, polydisperse suspensions have been considered.

Formally, our technique can be used in the visible as well as in the IR spectral regions. However, its practical implementation can cause some technical issues. For example, one of the major issues with the implementation of the technique in the visible spectral range is that because our composite must be macroscopically homogeneous, many particles of different kind must be placed and randomly oriented inside a relatively small volume. At the same time, in the mid-IR and far-IR, our basic geometry includes extremely sharp needles and/or very flat disks. That is why the fabrication of such composites micht be a challenging task.

2. Nulling technique and basic approximations

In our consideration, the problem of broadband permittivity nulling on the band [ω1, ω2] can be formulated as finding a minimum of the function

η(χi)=ω1ω2|Reεeff(χi,ω)|2dω,
where εeff is the scalar (isotropic) effective permittivity and χi are unknown geometrical parameters. To assess the nulling efficiency, we introduce a dimensionless bandwidth Δ (the bandwidth, normalized to the central frequency of the actual band ω0, Δ = (ω2ω1)/ω0 with ω0 = (ω2 + ω1)/2), and the root mean square (rms) which can be defined as rms=η/(ω2ω1). Thus, within the framework of our approach, the problem reduces to the proper choice of the composite constituents and geometry.

We focus on geometry which allows an analytical solution for the effective permittivity. This solution may be considered as a Maxwell-Garnett type approximation. It applies to composites where some particles (inclusions) are embedded in a dielectric host (matrix). If the inclusions are of spheroidal shape (see Fig. 1), an analytical solution is available. As it is well known, the Maxwell-Garnett type approximation works the best for dilute suspensions, when the total filling factor of inclusions is much less than unity. On the other hand, if the total filling factor is too small, efficient nulling becomes hardly possible (rms becomes too large). Because of this, in what follows we fix an intermediate value of the total filling factor (f = 0.08) and consider rms as a function of the central wavelength λ0 = 2πc/ω0 for different values of the dimensionless bandwidth. In fact, the required permittivity nulling may also be accomplished for more concentrated suspensions of spheroidal particles. As an example of such homogenization technique we could use, e.g., asymmetric Bruggeman approximation for spheroids [18]. However, it is nesessary to keep in mind that an increase of the metal filling factor can result in undesired increase of the electromagnetic losses.

 

Fig. 1 Geometry of the composite under consideration: suspension of randomly oriented and variously shaped metal spheroids with the permittivity ε1 embedded in a dielectric host with the permittivity ε0.

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The homogenization of such an assembly was considered by Nan et al. in terms of the T-matrix formalism [19] and independently by Gao et al. [20,21] who considered nonlinear optical properties of metal-dielectric composites. Although they only considered spheroids of one kind (fixed shape), the generalization of their results to the case of variously shaped spheroids is straightforward. Indeed, within the framework of the MGT, the effective permittivity can be written as [20, 21]

εeff=D¯E=i=1Nfiε1E¯i+(1f)ε0ELi=1NfiE¯i+(1f)EL,
where and Ē are the spatially averaged electric displacement and electric field, respectively, EL is the Lorentz local field, ε0 and ε1 are the permittivities of the host medium and of the spheroids, and the superscript i refers to the spheroids of the ith kind. Furthermore, the average electric field for the spheroids of certain kind is
E¯i=13[ε1L(i)ε0+(1L(i))ε1+2ε1L(i)ε0+(1L(i))ε1]EL=13ELε1ε0[β(i)+2β(i)],
where β(i) and β(i) are the Clausius-Mossotti factors of the corresponding spheroids,
β(i)=ε1ε0ε0+L(i)(ε1ε0),β(i)=ε1ε0ε0+L(i)(ε1ε0),
L(i) and L(i) are their depolarization factors for the electric field oriented parallel and perpendicular to the spheroid symmetry axis, respectively. The depolarization factors are known to satisfy the sum rule
L(i)+2L(i)=1.
As is known, L < 1/3(L > 1/3) corresponds to prolate spheroids, while L > 1/3(L < 1/3) corresponds to oblate spheroids. As L = L = 1/3, the spheroid degenerates into a sphere. After substituting Eq. (3) into Eq. (2) and some algebra, one has
εeff=ε01+i=1Nfi[β(i)(1L(i))+2β(1L(i))]/31i=1Nfi[β(i)L(i)+2βL(i)]/3.
At N = 1 this equation coincides with that given in [19,20]. It should be also noted that Eq. (6) can be derived by generalizing the expression for the spectral density function of composites made of randomly oriented spheroidal particles [22].

In real nanoparticle suspensions, nanoparticles are usually shape-distributed. The question arizes how to accurately take into account their depolarization factor or aspect ratio distribution. In order to do that, we invoke earlier obtained results [23], properly adopted for polydisperse spheroid suspensions. In this case, the effective permittivity reads

εeff=ε0(1+i=1Nfiαi1f+si=1Nfiαi),
where s = ε0/(ε1ε0), αi=(2γ(i)+γ(i))/3, f = ∑fi,
γ(i)=01(s+L)1Pi(L)dL,γ(i)=01[s+(1L)/2]1Pi(L)dL,
LL, and Pi(L) is the shape distribution function for the spheroids of the ith kind.

When dealing with metal nanospheroids, it is necessary to keep in mind that if at least one of their dimensions is too small, one cannot use the bulk values of the metal permittivity (due to surface scattering, the limitation of the electron mean free path must be taken into account). If so, Eq. (6) must be modified in such a way that ε1=ε1(i) when calculating β(i), and ε1=ε1(i) when calculating β(i), where ε1(i) and ε1(i) take into account corresponding corrections for surface scattering.

3. Numerical results

In what follows, we assume gold as the metal constituent in the composite. Its permittivity has been taken by using the Drude-critical points model which is shown to be rather accurate at wavelengths above 200 nm [24]. Teflon (εd = 1.823) has been considered as host medium (εdε0).

As is easy to see, if the total volume fraction of spheroids is specified, the minimization procedure (1) involves 2N − 1 fitting parameters. Generally, enlarging N for a given bandwidth, it becomes possible to obtain rms as small as desired. However, the fabrication of similar MMs becomes more and more challenging as N rises. Here, we take the moderate value of this parameter, N = 3, and the bandwidths of 10 and 15%.

A feature of any minimization procedure applied to the function η with the use of Eq. (6) is that several solutions for extracted geometrical parameters can occur. As an example, in Fig. 2 we show the results for εeff when Reεeff has been fitted to zero with 10% bandwidth at λ0 = 875 nm. For the first solution (solid line) rms = 0.043, while for the other (dashed curve) rms = 0.019. We also note that Imεeff essentially depends on the choice of the solution; so, in our case it can differ from each other by as much as a factor of 2.5 within the actual band.

 

Fig. 2 The effective permittivity of a suspension of gold spheroids in a Teflon host with Reεeff fitted to zero with 10% bandwidth at λ0 = 875 nm. The parameters of the spheroids are L1 = 0.0325, L2 = 0.883, L3 = 0.8945, f1 = 0.077, f2 = 0.0014, f3 = 0.0016 (solid curves) and L1 = 0.053, L2 = 0.882, L3 = 0.9907, f1 = 0.0013, f2 = 0.00068, f3 = 0.078 (dashed curves) (here and below LiL(i)).

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The different solution branches in the near-IR range are clearly seen in Fig. 3, where we show rms(λ0) for the bandwidths Δ = 10% and 15%. In particular, two threefold branches occur in the range under consideration (for Δ = 15% we show only one curve for every branch). Moving to the visible range, rms (not shown here) rises rapidly. Two minima (at λ0 ≈ 900 and λ0 ≈ 1260 nm) are caused by the fact that the depolarization factor L(i) of spheroids, comprising the dominant fraction in the suspension, takes its limiting value 1 (or 0) at these wavelengths after its monotonic increasing (decreasing). We note that the positions of these minima can be changed, if necessary, by replacing either inclusion or host material. For example, for copper in the near-IR range the real part of the permittivity is less negative than that for gold, and the above minima occur at longer wavelengths.

 

Fig. 3 The rms vs λ0 for a suspension of gold spheroids in a Teflon host with Reεeff fitted to zero with 10% and 15% bandwidths.

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As is well known, for many optical applications the dielectric losses play a critical role. To analyse the behavior of Imεeff at different λ0, in Fig. 4 we show the spectra of Imεeff (λ) for Δ = 10% and several values of λ0 up to those at which rms takes its minimum values. Only one of three solutions is shown for two solution branches (other solutions yield almost the same values of Imεeff, as well as of Reεeff). The results point to a decrease of dielectric losses as the central wavelength λ0 rises.

 

Fig. 4 The imaginary part of the effective permittivity of a suspension of gold spheroids in a Teflon host with Reεeff fitted to zero with 10% bandwidth. Solid curves and dashed curves correspond to two different branches. The respective values of λ0 are shown in the inset.

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4. Discussion

Our further analysis involves dealing with strongly prolate and oblate spheroids. For convenience, let us denote strongly prolate spheroids (L ≈ 0) by ’p’, and strongly oblate spheroids (L ≈ 1) by ’o’. Close inspection shows that the curves 1, 2, and 3 in Fig. 3 correspond to (p-o-o), (p-p-o), and (p-p-p) arrays, respectively, while the curves 4, 5, and 6 correspond to (p-o-o), (p-p-o), and (o-o-o) arrays. Why such threefold branches occur? This issue looks interesting, and we address it in more detail.

For simplicity, we consider the problem in terms of real variables. Althougn we have performed our computations using complex values of the metal permittivity, the availability of the imaginary part (which is small as compared to the real part in this range) does not affect our reasoning significantly. Let us first take a look at the behavior of the Clausius-Mossotti factors for strongly prolate and strongly oblate spheroids. Because the permittivity of metal in the considered range is negative and large as compared to the permittivity of dielectric, it is easy to see that β is large and negative, while β ≈ 2 when L is close to zero. This means that β can be neglected when compared with β in this case. In contrast, when L is close to unity, β is large and negative, while β ≈ 1. Thus, then β can be neglected when compared with β. Using this reasoning, one can see that the effective permittivity, represented by Eq. (6), for (o-o-o) arrays takes the form

εeff(ooo)ε01+2fβ¯1fβ.
with f = ∑ifi, β¯=iβ(i)/3, and β¯=iβ(i)/3. At the same time, for (p-o-o) arrays one has
εeff(poo)ε01+[f1β(1)+2f2β(2)+2f3β(3)]/31[f1β(1)+f2β(2)+f3β(3)]/3,
and for (p-p-o) arrays
εeff(ppo)ε01+[f1β(1)+f2β(2)+2f3β(3)]/31[f1β(1)+f2β(2)+f3β(3)]/3.
As is easy to see, Eq. (10) takes the form of Eq. (9) when f1 → 0, and Eq. (11) takes the form of Eq. (9) when f1, f2 → 0. Thus, if there is a set of parameters that provides a local minimum of the objective function η, Eq. (1), for a (o-o-o) array, there are also sets of the parameters that provide very close values of εeff (and, hence, local minima of the function η) for (p-o-o) and (p-p-o) arrays. We note also that, generally, these minima are achieved for nontrivial (nonzero) values of the vulume fractions fi. Besides, although the above arrays contain spheroids of different kind, the strongly oblate ones are predominating for this solution branch.

In a similar fashion, Eq. (6) for (p-p-p) arrays takes the form

εeff(ppp)ε01+2fβ¯1fβ,
and Eq. (11) takes now the form of Eq. (12) when f3 → 0, while Eq. (10) takes the form of Eq. (12) when f2, f3 → 0. We note that the strongly prolate spheroids are predominating for this solution branch.

Here, we have taken N = 3 and have obtained two threefold branches. Similar reasoning shows that each branch becomes N-fold for an arbitrary number N. The above analysis shows that if the needed optical properties can be achieved for arrays of strongly oblate or strongly prolate spheroids, the same can be also achieved for mixtures of prolate and oblate spheroidal shapes. This leads to multiplicating solutions of the inverse problem.

It is interesting that Imεeff correlates with rms, because Imεeff within the actual band tends to decrease when λ0λ0min ( λ0min900nm and 1260 nm for the two branches), see Figs. 2 and 3. Besides, we note that the function Imεeff (λ) for various λ0 is nonmonotonic within the actual band (see Figs. 2 and 4).

The presence of several solutions poses a question which one is most preferable. From a conceptual point of view, it makes sense to choose a solution for which rms is minimal. However, in practice this is not exactly so. The matter is that when λ0=λ0min, the depolarization factor L reaches its limiting value (0 or 1). This means that the basic geometry must include either infinitely long cylinders or thin sheets that seems to be impractical. Moreover, if L is too close to 0 (1), the spheroid aspect ratio becomes too large (small). Because the larger semiaxis of the spheroid must be much less than wavelength, this means that the spheroid (sharp needle or flat disk) becomes very thin. This, in turn, can present a considerable challenge to experimentalists. In addition, as one of the spheroid semiaxes is too small, due to electron scattering at boundaries, bulk value of the metal permittivity cannot be used when the electric field is applied along this axis. To take into account this effect, a more sophisticated homogenization technique must be developed.

By way of illustration, let us now consider specific examples. Assume that we are interested in designing ENZ MM with λ0 = 875 nm and 10% bandwidth. Admitting that the maximum allowable size of the spheroids is 0.2λ, we evaluate it as 175 nm. Then, our calculations yield the following three solutions for the branch with predominating oblate spheroids: L1 = 0.882, L2 = 0.894, L3 = 0.992, f1 = 0.00067, f2 = 0.00065, f3 = 0.07868 for (o-o-o) array, L1 = 0.053, L2 = 0.882, L3 = 0.9907, f1 = 0.0013, f2 = 0.00068, f3 = 0.078 for (p-o-o) array, and L1 = 0.053, L2 = 0.0588, L3 = 0.9896, f1 = 0.0013, f2 = 0.0014, f3 = 0.077 for (p-p-o) array. For the branch with predominating prolate spheroids, we have: L1 = 0.0336, L2 = 0.053, L3 = 0.0584, f1 = 0.0736, f2 = 0.00336, f3 = 0.003 for (p-p-p) array, L1 = 0.033, L2 = 0.0584, L3 = 0.8945, f1 = 0.075, f2 = 0.0029, f3 = 0.0016 for (p-p-o) array, and L1 = 0.0325, L2 = 0.883, L3 = 0.8945, f1 = 0.077, f2 = 0.0014, f3 = 0.0016 for (p-o-o) array. Using the well known relationships between the depolarization factors of spheroids and their aspect ratios (see, e.g., [20]), we estimate the minimum size of the spheroids as 0.9 nm, 1 nm, and 1.2 nm in the former case and 25 nm, 13 nm, and 13 nm in the latter case, respectively. This obviously means that, due to existing manufacturing tolerances, composites with oblate spheroids predominating, although providing small rms and dielectric losses, are unfeasible for designing ENZ MMs with given λ0 and bandwidth because they involve very thin spheroids (extremely flat disks). It should be noted that after decreasing λ0, requirements for spheroid sizes become less stringent, while rms rises. So, at λ0 = 750 nm, the solution for (o-o-o) array is L1 = 0.827, L2 = 0.845, L3 = 0.932, f1 = 0.0019, f2 = 0.0018, f3 = 0.076, while rms = 0.035, and the minimum size of the oblate spheroids is about 7 nm.

It is also of interest, from the point of view of realizability of designed composites, to assess the sensitivity of the obtained solutions to distribution of aspect ratios which is, obviously, always present in real composites. With this aim, we take the simplest (uniform) distribution of the form

Pi(L)=Δi1χ(LLi+ΔiLi)χ[L+Li+Δi(1Li)],
where χ (...) is the Dirac delta function and Δi is the width of the distribution in terms of the depolarization factor L of the spheroids of the ith kind; in essence, this is the one-dimensional analog of the two-dimensional uniform distribution [25], centered around the depolarization factor Li. After substituting this into Eq. (8), one has
γ(i)=1Δilns+Li(1Δi)+Δis+Li(1Δi),γ(i)=2Δiln2s+1Li(1Δi)Δi2s+1Li(1Δi).
Then the sensitivity of rms to the aspect ratio distribution for small Δi can be estimated as
δ(rms)Δi(r)=δ(rms)ΔidLdr,
where Δi(r) is the width of the distribution in terms of the aspect ratio r. Considering the case shown in Fig. 2, we have obtained, for example, that the above sensitivity comprises about 0.13 for composites with prolate spheroids predominating and about 3.4 for those with oblate spheroids predominating. This means that rms for oblate spheroids is more sensitive to their aspect ratio distribution than that for prolate ones (one can show that this happens because the dL/dr derivative is a monotonically decreasing function of r, and it approaches 0 as r → ∞, i.e., for strongly prolate spheroids).

As can be seen from Fig. 4, high losses can occur at least for one of the solution branches. It has been recently shown that ENZ hyperbolic MMs hold promise for realizing near-perfect absorption over a range of frequencies and subwavelength thicknesses [26]. In our case, high broadband absorption can be also achieved for subwavelength thicknesses (see Fig. 5).

 

Fig. 5 The intensity absorption for composite films of different thickness t made of gold spheroids in a Teflon host with Reεeff fitted to zero with λ0 = 900 nm and 10% bandwidth.

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Because here we do not tailor the magnetic response, impedance mismatching with free space causes the inevitable reflection at the vacuum-slab interface. This, in turn, limits the absorption by the slab. Losses reduce the transmission, but they also increase reflection (it is epecially high at long wavelengths, that results in an absorption decrease, as can be seen from Fig. 5). The high absorption within the band can be considered as a trade-off between the low reflection, which rises with losses, and low transmission, which drops with losses.

In some cases, losses have only a moderate impact on the performance of ENZ MMs, as it takes place, e.g., for tailoring the radiation phase pattern [27]. At the same time, it is well known that losses can substantially hinder the practical implementation of unique optical properties of many MMs and strongly limit the performance of corresponding devices. Dealing with metal constituents involves Ohmic losses related to undesirable conversion of electromagnetic energy into heat. And even nanostructures made of nearly lossless dielectrics suffer from transmission losses resulted from scattering and out-of-plane diffraction. Although overcoming the losses is, generally, a challenging task, there is a plenty of rooms to reduce or compensate them.

First of all, the negative impact of losses can be reduced by dealing with very thin films made of actual MMs (see, e.g., [28]). Another way is to use metals (or metal alloys) possessing lower intrinsic losses, e.g., silver instead of gold in the visible range. The use of superconducting materials with ultralow losses can be benefited at very low frequencies [29]. Furthermore, as has been recently suggested by Khurgin and Sun, in some synthetic structures the transition to the lossless mode can occur in the mid-IR range if the interatomic distances exceed certain values [30]. Finally, conceptually different solution could consist in using loss-compensating techniques involving dissipated structures combined with gain (optically active) media [31,32] or using parametric optical amplification [33].

Although the fabrication of MMs like those considered here is challenging, at present there exists a number of various techniques which allow to synthesize metal nanodisks [34, 35] and especially nanorods (see, e.g., [36,37] and references therein) with very reproducible sizes and shapes. Moreover, gold nanorods are commercially available with diameters from 10 to 50 nm, aspect ratios up to 20, and typical aspect ratio variation within 5% [38]. This allows us to hope that above MMs can be synthesized in the future.

5. Conclusion

In this paper we have considered the use of polydisperse suspensions of metal spheroidal particles for the purpose of designing broadband ENZ MMs. We introduced an efficiency of the permittivity nulling over a band (rms) and solved an inverse problem to extract the depolarization factors and partial volume fractions of the spheroids of different kind comprising designed MM. Considering gold nanospheroids in the Teflon host as an example, we have shown that the solutions of this problem form N-fold branches in the coordinates rmsλ0, where λ0 is defined as the centre of the actual band. For each branch, minima of the function rms(λ0) can occur. Although the regime of operation close to the minima is best matched to the problem at hand, it is hardly feasible due to existing fabrication tolerances. In some cases, and especially for strongly oblate spheroids, aspect ratio distribution should be taken into account. In practice the parameters of suspensions must be chosen as a trade-off between small rms and dielectric losses, on the one hand, and practical realizability of designed MMs, on the other hand. As shown, the effect of high broadband absorption can be achieved with the use of subwavelength films made of designed ENZ MMs.

Acknowledgments

A.P acknowledges partial support from Biofrontiers Institue, UCCS, and CRDF ( UKC2-7071-CH-12).

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22. L. Gao, L.P. Gu, and Z.Y. Li, “Optical bistabity and tristability in nonlinear metal/dielectric composite media of nonspherical particles,” Phys. Rev. E 68, 066601 (2003). [CrossRef]  

23. A.V. Goncharenko, V.Z. Lozovskii, and E.F. Venger, “Effective dielectric response of a shape-distributed particle system,” J. Phys.: Condens. Matter 13, 8217–8234 (2001).

24. A. Vial and T. Laroche, “Comparison of gold and silver dispersion laws suitable for FDTD simulations,” Appl. Phys. B 93, 139–143 (2008). [CrossRef]  

25. A.V. Goncharenko, Yu.V. Semenov, and E.F. Venger, “Effective scattering cross section of an assembly of small ellipsoidal particles,” J. Opt. Soc. Am. A 16, 517–522 (1999). [CrossRef]  

26. L. Halterman and J.M. Elsen, “Near-perfect absorption in epsilon-near-zero structures with hyperbolic dispersion,” Opt. Express 22, 7337–7348 (2014). [CrossRef]   [PubMed]  

27. A. Alu, M.G. Silveirinha, A. Salandrino, and N. Engheta, “Epsiolon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75, 155410 (2007). [CrossRef]  

28. A.N. Lagarkov, A.K. Sarychev, V.N. Kissel, and G. Tartakovsky, “Superresolution and enhancement in metamaterials,” Physics-Uspekhi 52, 959–967 (2009). [CrossRef]  

29. C. Kurter, J. Abrahams, G. Shvets, and S.M. Anlage, “Plasmonic scaling of superconducting metamaterials,” Phys. Rev. B 88, 180510(R) (2013). [CrossRef]  

30. J.B. Khurgin and G. Sun, “In search of the elusive lossless metal,” Appl. Phys. Lett. 96, 181102 (2010). [CrossRef]  

31. M.A. Noginov, G. Zhu, M. Mayy, B.A. Ritzo, N. Noginova, and V.A. Podolskiy, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101, 226806 (2008). [CrossRef]   [PubMed]  

32. S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials, Nature 466, 735–738 (2010). [CrossRef]   [PubMed]  

33. A.K. Popov and S.A. Myslivets, “Transformable broad-band transparency and amplification in negative-index films,” Appl. Phys. Lett. 93, 191117 (2008). [CrossRef]  

34. P. Hanarp, M. Käll, and D.S. Sutherland, “Optical properties of short range ordered arrays of nanometer gold disks prepared by colloidal lithography,” J. Phys. Chem. B 107, 5768–5772 (2003). [CrossRef]  

35. C. Langhammer, B. Kasemo, and I. Zorić, “Absorption and scattering of light by Pt, Pd, Ag, and Au nanodisks: Absolute cross sections and branching ratios,” J. Chem. Phys. 126, 194702 (2007). [CrossRef]   [PubMed]  

36. X. Huang, S. Neretina, and M.A. El-Sayed, “Gold nanorods: From synthesis and properties to biological and biomedical applications,” Adv. Mater. 21, 4880–4910 (2009). [CrossRef]  

37. H. Chen, L. Shao, Q. Li, and J. Wang, “Gold nanorods and their plasmonic properties,” Chem. Soc. Rev. 42, 2679–2724 (2013). [CrossRef]  

38. www.nanopartz.com.

References

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  1. M.J. Roberts, S. Feng, M. Moran, and L. Johnson, “Effective permittivity near zero in nanolaminates of silver and amorphous polycarbonate,” J. Nanophoton. 4, 043511 (2010).
    [Crossref]
  2. P. Moitra, Y. Yang, Z. Anderson, I.I. Kravchenko, D.P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nature Photon. 7, 791–795 (2013).
    [Crossref]
  3. R. Maas, J. Parsons, N. Engheta, and A. Polman, “Experimental realization of an epsilon-near-zero metamaterial at visible wavelengths,” Nature Photon. 7, 907–912 (2013).
    [Crossref]
  4. G. Castaldi, S. Savoia, V. Galdi, A. Alu, and N. Engheta, “Analytical study of subwavelength imaging by uniaxial epsilon-near-zero metamaterial slabs,” Phys. Rev. B 86, 115123 (2012).
    [Crossref]
  5. S. Yokogava, S.P. Burgos, and H.A. Atwater, “Plasmonic color filters for CMOS image sensor applications,” Nano Lett. 12, 4349–4354 (2012).
    [Crossref]
  6. E.O. Liznev, A.V. Dorofeenko, L. Huizhe, A.P. Vinogradov, and S. Zouhdi, “Epsilon-near-zero material as a unique solution to three different approaches to cloaking,” Appl. Phys. A 100, 321–325 (2010).
    [Crossref]
  7. S. Feng and K. Halterman, “Coherent perfect absorption in epsilon-near-zero metamaterials,” Phys. Rev. B 86, 165103 (2012).
    [Crossref]
  8. A.V. Goncharenko and K.R. Chen, “Strategy for designing epsilon-near-zero nanostructured metamaterials over a frequency range,” J. Nanophoton. 4, 041530 (2010).
    [Crossref]
  9. A.V. Goncharenko, V.U. Nazarov, and K.R. Chen, “Development of metamaterials with desired broadband optical properties,” Appl. Phys. Lett. 101, 071907 (2012).
    [Crossref]
  10. A.V. Goncharenko, V.U. Nazarov, and K.R. Chen, “Nanostructured metamaterials with broadband optical properties,” Opt. Mater. Express 3, 143–156 (2013).
    [Crossref]
  11. L. Sun and K.W. Yu, “Strategy for designing broadband epsilon-near-zero metamaterials,” J. Opt. Soc. Am. B 29, 984–989 (2012).
    [Crossref]
  12. L. Sun, K.W. Yu, and X. Yang, “Integrated optical devices based on broadband epsilon-near-zero meta-atoms,” Opt. Lett. 37, 3096–3098 (2012).
    [Crossref] [PubMed]
  13. A.V. Goncharenko, E.F. Venger, and A.O. Pinchuk, “Homogenization of quasi-1d metamaterials and the problem of extended bandwidth,” Opt. Express 22, 2429–2442 (2014).
    [Crossref]
  14. J.C. Maxwell Garnett, “Colours in metal glasses and in metallic films,” Phil. Trans. Roy. Soc. A 203, 385–420 (1904).
    [Crossref]
  15. S. Datta, C.T. Chan, K.M. Ho, and C.M. Soukoulis, “Effective dielectric constant of periodic composite structures,” Phys. Rev. B 48, 14936–14943 (1993).
    [Crossref]
  16. R.T. Bonnecaze and J.F. Brady, “The effective conductivity of random suspensions of spherical particles,” Roc. R. Soc. Lond. A 432, 445–465 (1991).
    [Crossref]
  17. D.C. Pham and S. Torquato, “Strong-contrast expansions and approximations for the effective conductivity of isotropic multiphase composites,” J. Appl. Phys. 94, 6591–6602 (2003).
    [Crossref]
  18. S. Giordano, “Effective medium theory for dispersions of dielectric ellipsoids,” J. Electrostat. 58, 59–76 (2003).
    [Crossref]
  19. C. W. Nan, R. Birringer, D.R. Clarke, and H. Gleiter, “Effective thermal conductivity of particulate composites with interfacial thermal resistance,” J. Appl. Phys. 81, 6692–6699 (1997).
    [Crossref]
  20. L. Gao, J.T.K. Wan, K.W. Yu, and Z.Y. Li, “Effective non-linear optical properties of metal-dielectric composites of spheroidal particles,” J. Phys.: Condens. Matter 12, 6825–6836 (2000).
  21. L. Gao, Z.Y. Li, and K.W. Yu, “Enhancement of optical nonlinearity through shape distribution,” J. Phys.: Condens. Matter 13, 7271–7282 (2001).
  22. L. Gao, L.P. Gu, and Z.Y. Li, “Optical bistabity and tristability in nonlinear metal/dielectric composite media of nonspherical particles,” Phys. Rev. E 68, 066601 (2003).
    [Crossref]
  23. A.V. Goncharenko, V.Z. Lozovskii, and E.F. Venger, “Effective dielectric response of a shape-distributed particle system,” J. Phys.: Condens. Matter 13, 8217–8234 (2001).
  24. A. Vial and T. Laroche, “Comparison of gold and silver dispersion laws suitable for FDTD simulations,” Appl. Phys. B 93, 139–143 (2008).
    [Crossref]
  25. A.V. Goncharenko, Yu.V. Semenov, and E.F. Venger, “Effective scattering cross section of an assembly of small ellipsoidal particles,” J. Opt. Soc. Am. A 16, 517–522 (1999).
    [Crossref]
  26. L. Halterman and J.M. Elsen, “Near-perfect absorption in epsilon-near-zero structures with hyperbolic dispersion,” Opt. Express 22, 7337–7348 (2014).
    [Crossref] [PubMed]
  27. A. Alu, M.G. Silveirinha, A. Salandrino, and N. Engheta, “Epsiolon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75, 155410 (2007).
    [Crossref]
  28. A.N. Lagarkov, A.K. Sarychev, V.N. Kissel, and G. Tartakovsky, “Superresolution and enhancement in metamaterials,” Physics-Uspekhi 52, 959–967 (2009).
    [Crossref]
  29. C. Kurter, J. Abrahams, G. Shvets, and S.M. Anlage, “Plasmonic scaling of superconducting metamaterials,” Phys. Rev. B 88, 180510(R) (2013).
    [Crossref]
  30. J.B. Khurgin and G. Sun, “In search of the elusive lossless metal,” Appl. Phys. Lett. 96, 181102 (2010).
    [Crossref]
  31. M.A. Noginov, G. Zhu, M. Mayy, B.A. Ritzo, N. Noginova, and V.A. Podolskiy, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101, 226806 (2008).
    [Crossref] [PubMed]
  32. S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials, Nature 466, 735–738 (2010).
    [Crossref] [PubMed]
  33. A.K. Popov and S.A. Myslivets, “Transformable broad-band transparency and amplification in negative-index films,” Appl. Phys. Lett. 93, 191117 (2008).
    [Crossref]
  34. P. Hanarp, M. Käll, and D.S. Sutherland, “Optical properties of short range ordered arrays of nanometer gold disks prepared by colloidal lithography,” J. Phys. Chem. B 107, 5768–5772 (2003).
    [Crossref]
  35. C. Langhammer, B. Kasemo, and I. Zorić, “Absorption and scattering of light by Pt, Pd, Ag, and Au nanodisks: Absolute cross sections and branching ratios,” J. Chem. Phys. 126, 194702 (2007).
    [Crossref] [PubMed]
  36. X. Huang, S. Neretina, and M.A. El-Sayed, “Gold nanorods: From synthesis and properties to biological and biomedical applications,” Adv. Mater. 21, 4880–4910 (2009).
    [Crossref]
  37. H. Chen, L. Shao, Q. Li, and J. Wang, “Gold nanorods and their plasmonic properties,” Chem. Soc. Rev. 42, 2679–2724 (2013).
    [Crossref]
  38. www.nanopartz.com .

2014 (2)

2013 (5)

C. Kurter, J. Abrahams, G. Shvets, and S.M. Anlage, “Plasmonic scaling of superconducting metamaterials,” Phys. Rev. B 88, 180510(R) (2013).
[Crossref]

H. Chen, L. Shao, Q. Li, and J. Wang, “Gold nanorods and their plasmonic properties,” Chem. Soc. Rev. 42, 2679–2724 (2013).
[Crossref]

A.V. Goncharenko, V.U. Nazarov, and K.R. Chen, “Nanostructured metamaterials with broadband optical properties,” Opt. Mater. Express 3, 143–156 (2013).
[Crossref]

P. Moitra, Y. Yang, Z. Anderson, I.I. Kravchenko, D.P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nature Photon. 7, 791–795 (2013).
[Crossref]

R. Maas, J. Parsons, N. Engheta, and A. Polman, “Experimental realization of an epsilon-near-zero metamaterial at visible wavelengths,” Nature Photon. 7, 907–912 (2013).
[Crossref]

2012 (6)

G. Castaldi, S. Savoia, V. Galdi, A. Alu, and N. Engheta, “Analytical study of subwavelength imaging by uniaxial epsilon-near-zero metamaterial slabs,” Phys. Rev. B 86, 115123 (2012).
[Crossref]

S. Yokogava, S.P. Burgos, and H.A. Atwater, “Plasmonic color filters for CMOS image sensor applications,” Nano Lett. 12, 4349–4354 (2012).
[Crossref]

S. Feng and K. Halterman, “Coherent perfect absorption in epsilon-near-zero metamaterials,” Phys. Rev. B 86, 165103 (2012).
[Crossref]

A.V. Goncharenko, V.U. Nazarov, and K.R. Chen, “Development of metamaterials with desired broadband optical properties,” Appl. Phys. Lett. 101, 071907 (2012).
[Crossref]

L. Sun and K.W. Yu, “Strategy for designing broadband epsilon-near-zero metamaterials,” J. Opt. Soc. Am. B 29, 984–989 (2012).
[Crossref]

L. Sun, K.W. Yu, and X. Yang, “Integrated optical devices based on broadband epsilon-near-zero meta-atoms,” Opt. Lett. 37, 3096–3098 (2012).
[Crossref] [PubMed]

2010 (5)

M.J. Roberts, S. Feng, M. Moran, and L. Johnson, “Effective permittivity near zero in nanolaminates of silver and amorphous polycarbonate,” J. Nanophoton. 4, 043511 (2010).
[Crossref]

A.V. Goncharenko and K.R. Chen, “Strategy for designing epsilon-near-zero nanostructured metamaterials over a frequency range,” J. Nanophoton. 4, 041530 (2010).
[Crossref]

E.O. Liznev, A.V. Dorofeenko, L. Huizhe, A.P. Vinogradov, and S. Zouhdi, “Epsilon-near-zero material as a unique solution to three different approaches to cloaking,” Appl. Phys. A 100, 321–325 (2010).
[Crossref]

J.B. Khurgin and G. Sun, “In search of the elusive lossless metal,” Appl. Phys. Lett. 96, 181102 (2010).
[Crossref]

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials, Nature 466, 735–738 (2010).
[Crossref] [PubMed]

2009 (2)

X. Huang, S. Neretina, and M.A. El-Sayed, “Gold nanorods: From synthesis and properties to biological and biomedical applications,” Adv. Mater. 21, 4880–4910 (2009).
[Crossref]

A.N. Lagarkov, A.K. Sarychev, V.N. Kissel, and G. Tartakovsky, “Superresolution and enhancement in metamaterials,” Physics-Uspekhi 52, 959–967 (2009).
[Crossref]

2008 (3)

A.K. Popov and S.A. Myslivets, “Transformable broad-band transparency and amplification in negative-index films,” Appl. Phys. Lett. 93, 191117 (2008).
[Crossref]

M.A. Noginov, G. Zhu, M. Mayy, B.A. Ritzo, N. Noginova, and V.A. Podolskiy, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101, 226806 (2008).
[Crossref] [PubMed]

A. Vial and T. Laroche, “Comparison of gold and silver dispersion laws suitable for FDTD simulations,” Appl. Phys. B 93, 139–143 (2008).
[Crossref]

2007 (2)

A. Alu, M.G. Silveirinha, A. Salandrino, and N. Engheta, “Epsiolon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75, 155410 (2007).
[Crossref]

C. Langhammer, B. Kasemo, and I. Zorić, “Absorption and scattering of light by Pt, Pd, Ag, and Au nanodisks: Absolute cross sections and branching ratios,” J. Chem. Phys. 126, 194702 (2007).
[Crossref] [PubMed]

2003 (4)

P. Hanarp, M. Käll, and D.S. Sutherland, “Optical properties of short range ordered arrays of nanometer gold disks prepared by colloidal lithography,” J. Phys. Chem. B 107, 5768–5772 (2003).
[Crossref]

L. Gao, L.P. Gu, and Z.Y. Li, “Optical bistabity and tristability in nonlinear metal/dielectric composite media of nonspherical particles,” Phys. Rev. E 68, 066601 (2003).
[Crossref]

D.C. Pham and S. Torquato, “Strong-contrast expansions and approximations for the effective conductivity of isotropic multiphase composites,” J. Appl. Phys. 94, 6591–6602 (2003).
[Crossref]

S. Giordano, “Effective medium theory for dispersions of dielectric ellipsoids,” J. Electrostat. 58, 59–76 (2003).
[Crossref]

2001 (2)

A.V. Goncharenko, V.Z. Lozovskii, and E.F. Venger, “Effective dielectric response of a shape-distributed particle system,” J. Phys.: Condens. Matter 13, 8217–8234 (2001).

L. Gao, Z.Y. Li, and K.W. Yu, “Enhancement of optical nonlinearity through shape distribution,” J. Phys.: Condens. Matter 13, 7271–7282 (2001).

2000 (1)

L. Gao, J.T.K. Wan, K.W. Yu, and Z.Y. Li, “Effective non-linear optical properties of metal-dielectric composites of spheroidal particles,” J. Phys.: Condens. Matter 12, 6825–6836 (2000).

1999 (1)

1997 (1)

C. W. Nan, R. Birringer, D.R. Clarke, and H. Gleiter, “Effective thermal conductivity of particulate composites with interfacial thermal resistance,” J. Appl. Phys. 81, 6692–6699 (1997).
[Crossref]

1993 (1)

S. Datta, C.T. Chan, K.M. Ho, and C.M. Soukoulis, “Effective dielectric constant of periodic composite structures,” Phys. Rev. B 48, 14936–14943 (1993).
[Crossref]

1991 (1)

R.T. Bonnecaze and J.F. Brady, “The effective conductivity of random suspensions of spherical particles,” Roc. R. Soc. Lond. A 432, 445–465 (1991).
[Crossref]

1904 (1)

J.C. Maxwell Garnett, “Colours in metal glasses and in metallic films,” Phil. Trans. Roy. Soc. A 203, 385–420 (1904).
[Crossref]

Abrahams, J.

C. Kurter, J. Abrahams, G. Shvets, and S.M. Anlage, “Plasmonic scaling of superconducting metamaterials,” Phys. Rev. B 88, 180510(R) (2013).
[Crossref]

Alu, A.

G. Castaldi, S. Savoia, V. Galdi, A. Alu, and N. Engheta, “Analytical study of subwavelength imaging by uniaxial epsilon-near-zero metamaterial slabs,” Phys. Rev. B 86, 115123 (2012).
[Crossref]

A. Alu, M.G. Silveirinha, A. Salandrino, and N. Engheta, “Epsiolon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75, 155410 (2007).
[Crossref]

Anderson, Z.

P. Moitra, Y. Yang, Z. Anderson, I.I. Kravchenko, D.P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nature Photon. 7, 791–795 (2013).
[Crossref]

Anlage, S.M.

C. Kurter, J. Abrahams, G. Shvets, and S.M. Anlage, “Plasmonic scaling of superconducting metamaterials,” Phys. Rev. B 88, 180510(R) (2013).
[Crossref]

Atwater, H.A.

S. Yokogava, S.P. Burgos, and H.A. Atwater, “Plasmonic color filters for CMOS image sensor applications,” Nano Lett. 12, 4349–4354 (2012).
[Crossref]

Birringer, R.

C. W. Nan, R. Birringer, D.R. Clarke, and H. Gleiter, “Effective thermal conductivity of particulate composites with interfacial thermal resistance,” J. Appl. Phys. 81, 6692–6699 (1997).
[Crossref]

Bonnecaze, R.T.

R.T. Bonnecaze and J.F. Brady, “The effective conductivity of random suspensions of spherical particles,” Roc. R. Soc. Lond. A 432, 445–465 (1991).
[Crossref]

Brady, J.F.

R.T. Bonnecaze and J.F. Brady, “The effective conductivity of random suspensions of spherical particles,” Roc. R. Soc. Lond. A 432, 445–465 (1991).
[Crossref]

Briggs, D.P.

P. Moitra, Y. Yang, Z. Anderson, I.I. Kravchenko, D.P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nature Photon. 7, 791–795 (2013).
[Crossref]

Burgos, S.P.

S. Yokogava, S.P. Burgos, and H.A. Atwater, “Plasmonic color filters for CMOS image sensor applications,” Nano Lett. 12, 4349–4354 (2012).
[Crossref]

Castaldi, G.

G. Castaldi, S. Savoia, V. Galdi, A. Alu, and N. Engheta, “Analytical study of subwavelength imaging by uniaxial epsilon-near-zero metamaterial slabs,” Phys. Rev. B 86, 115123 (2012).
[Crossref]

Chan, C.T.

S. Datta, C.T. Chan, K.M. Ho, and C.M. Soukoulis, “Effective dielectric constant of periodic composite structures,” Phys. Rev. B 48, 14936–14943 (1993).
[Crossref]

Chen, H.

H. Chen, L. Shao, Q. Li, and J. Wang, “Gold nanorods and their plasmonic properties,” Chem. Soc. Rev. 42, 2679–2724 (2013).
[Crossref]

Chen, K.R.

A.V. Goncharenko, V.U. Nazarov, and K.R. Chen, “Nanostructured metamaterials with broadband optical properties,” Opt. Mater. Express 3, 143–156 (2013).
[Crossref]

A.V. Goncharenko, V.U. Nazarov, and K.R. Chen, “Development of metamaterials with desired broadband optical properties,” Appl. Phys. Lett. 101, 071907 (2012).
[Crossref]

A.V. Goncharenko and K.R. Chen, “Strategy for designing epsilon-near-zero nanostructured metamaterials over a frequency range,” J. Nanophoton. 4, 041530 (2010).
[Crossref]

Chettiar, U. K.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials, Nature 466, 735–738 (2010).
[Crossref] [PubMed]

Clarke, D.R.

C. W. Nan, R. Birringer, D.R. Clarke, and H. Gleiter, “Effective thermal conductivity of particulate composites with interfacial thermal resistance,” J. Appl. Phys. 81, 6692–6699 (1997).
[Crossref]

Datta, S.

S. Datta, C.T. Chan, K.M. Ho, and C.M. Soukoulis, “Effective dielectric constant of periodic composite structures,” Phys. Rev. B 48, 14936–14943 (1993).
[Crossref]

Dorofeenko, A.V.

E.O. Liznev, A.V. Dorofeenko, L. Huizhe, A.P. Vinogradov, and S. Zouhdi, “Epsilon-near-zero material as a unique solution to three different approaches to cloaking,” Appl. Phys. A 100, 321–325 (2010).
[Crossref]

Drachev, V. P.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials, Nature 466, 735–738 (2010).
[Crossref] [PubMed]

El-Sayed, M.A.

X. Huang, S. Neretina, and M.A. El-Sayed, “Gold nanorods: From synthesis and properties to biological and biomedical applications,” Adv. Mater. 21, 4880–4910 (2009).
[Crossref]

Elsen, J.M.

Engheta, N.

R. Maas, J. Parsons, N. Engheta, and A. Polman, “Experimental realization of an epsilon-near-zero metamaterial at visible wavelengths,” Nature Photon. 7, 907–912 (2013).
[Crossref]

G. Castaldi, S. Savoia, V. Galdi, A. Alu, and N. Engheta, “Analytical study of subwavelength imaging by uniaxial epsilon-near-zero metamaterial slabs,” Phys. Rev. B 86, 115123 (2012).
[Crossref]

A. Alu, M.G. Silveirinha, A. Salandrino, and N. Engheta, “Epsiolon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75, 155410 (2007).
[Crossref]

Feng, S.

S. Feng and K. Halterman, “Coherent perfect absorption in epsilon-near-zero metamaterials,” Phys. Rev. B 86, 165103 (2012).
[Crossref]

M.J. Roberts, S. Feng, M. Moran, and L. Johnson, “Effective permittivity near zero in nanolaminates of silver and amorphous polycarbonate,” J. Nanophoton. 4, 043511 (2010).
[Crossref]

Galdi, V.

G. Castaldi, S. Savoia, V. Galdi, A. Alu, and N. Engheta, “Analytical study of subwavelength imaging by uniaxial epsilon-near-zero metamaterial slabs,” Phys. Rev. B 86, 115123 (2012).
[Crossref]

Gao, L.

L. Gao, L.P. Gu, and Z.Y. Li, “Optical bistabity and tristability in nonlinear metal/dielectric composite media of nonspherical particles,” Phys. Rev. E 68, 066601 (2003).
[Crossref]

L. Gao, Z.Y. Li, and K.W. Yu, “Enhancement of optical nonlinearity through shape distribution,” J. Phys.: Condens. Matter 13, 7271–7282 (2001).

L. Gao, J.T.K. Wan, K.W. Yu, and Z.Y. Li, “Effective non-linear optical properties of metal-dielectric composites of spheroidal particles,” J. Phys.: Condens. Matter 12, 6825–6836 (2000).

Giordano, S.

S. Giordano, “Effective medium theory for dispersions of dielectric ellipsoids,” J. Electrostat. 58, 59–76 (2003).
[Crossref]

Gleiter, H.

C. W. Nan, R. Birringer, D.R. Clarke, and H. Gleiter, “Effective thermal conductivity of particulate composites with interfacial thermal resistance,” J. Appl. Phys. 81, 6692–6699 (1997).
[Crossref]

Goncharenko, A.V.

A.V. Goncharenko, E.F. Venger, and A.O. Pinchuk, “Homogenization of quasi-1d metamaterials and the problem of extended bandwidth,” Opt. Express 22, 2429–2442 (2014).
[Crossref]

A.V. Goncharenko, V.U. Nazarov, and K.R. Chen, “Nanostructured metamaterials with broadband optical properties,” Opt. Mater. Express 3, 143–156 (2013).
[Crossref]

A.V. Goncharenko, V.U. Nazarov, and K.R. Chen, “Development of metamaterials with desired broadband optical properties,” Appl. Phys. Lett. 101, 071907 (2012).
[Crossref]

A.V. Goncharenko and K.R. Chen, “Strategy for designing epsilon-near-zero nanostructured metamaterials over a frequency range,” J. Nanophoton. 4, 041530 (2010).
[Crossref]

A.V. Goncharenko, V.Z. Lozovskii, and E.F. Venger, “Effective dielectric response of a shape-distributed particle system,” J. Phys.: Condens. Matter 13, 8217–8234 (2001).

A.V. Goncharenko, Yu.V. Semenov, and E.F. Venger, “Effective scattering cross section of an assembly of small ellipsoidal particles,” J. Opt. Soc. Am. A 16, 517–522 (1999).
[Crossref]

Gu, L.P.

L. Gao, L.P. Gu, and Z.Y. Li, “Optical bistabity and tristability in nonlinear metal/dielectric composite media of nonspherical particles,” Phys. Rev. E 68, 066601 (2003).
[Crossref]

Halterman, K.

S. Feng and K. Halterman, “Coherent perfect absorption in epsilon-near-zero metamaterials,” Phys. Rev. B 86, 165103 (2012).
[Crossref]

Halterman, L.

Hanarp, P.

P. Hanarp, M. Käll, and D.S. Sutherland, “Optical properties of short range ordered arrays of nanometer gold disks prepared by colloidal lithography,” J. Phys. Chem. B 107, 5768–5772 (2003).
[Crossref]

Ho, K.M.

S. Datta, C.T. Chan, K.M. Ho, and C.M. Soukoulis, “Effective dielectric constant of periodic composite structures,” Phys. Rev. B 48, 14936–14943 (1993).
[Crossref]

Huang, X.

X. Huang, S. Neretina, and M.A. El-Sayed, “Gold nanorods: From synthesis and properties to biological and biomedical applications,” Adv. Mater. 21, 4880–4910 (2009).
[Crossref]

Huizhe, L.

E.O. Liznev, A.V. Dorofeenko, L. Huizhe, A.P. Vinogradov, and S. Zouhdi, “Epsilon-near-zero material as a unique solution to three different approaches to cloaking,” Appl. Phys. A 100, 321–325 (2010).
[Crossref]

Johnson, L.

M.J. Roberts, S. Feng, M. Moran, and L. Johnson, “Effective permittivity near zero in nanolaminates of silver and amorphous polycarbonate,” J. Nanophoton. 4, 043511 (2010).
[Crossref]

Käll, M.

P. Hanarp, M. Käll, and D.S. Sutherland, “Optical properties of short range ordered arrays of nanometer gold disks prepared by colloidal lithography,” J. Phys. Chem. B 107, 5768–5772 (2003).
[Crossref]

Kasemo, B.

C. Langhammer, B. Kasemo, and I. Zorić, “Absorption and scattering of light by Pt, Pd, Ag, and Au nanodisks: Absolute cross sections and branching ratios,” J. Chem. Phys. 126, 194702 (2007).
[Crossref] [PubMed]

Khurgin, J.B.

J.B. Khurgin and G. Sun, “In search of the elusive lossless metal,” Appl. Phys. Lett. 96, 181102 (2010).
[Crossref]

Kildishev, A. V.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials, Nature 466, 735–738 (2010).
[Crossref] [PubMed]

Kissel, V.N.

A.N. Lagarkov, A.K. Sarychev, V.N. Kissel, and G. Tartakovsky, “Superresolution and enhancement in metamaterials,” Physics-Uspekhi 52, 959–967 (2009).
[Crossref]

Kravchenko, I.I.

P. Moitra, Y. Yang, Z. Anderson, I.I. Kravchenko, D.P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nature Photon. 7, 791–795 (2013).
[Crossref]

Kurter, C.

C. Kurter, J. Abrahams, G. Shvets, and S.M. Anlage, “Plasmonic scaling of superconducting metamaterials,” Phys. Rev. B 88, 180510(R) (2013).
[Crossref]

Lagarkov, A.N.

A.N. Lagarkov, A.K. Sarychev, V.N. Kissel, and G. Tartakovsky, “Superresolution and enhancement in metamaterials,” Physics-Uspekhi 52, 959–967 (2009).
[Crossref]

Langhammer, C.

C. Langhammer, B. Kasemo, and I. Zorić, “Absorption and scattering of light by Pt, Pd, Ag, and Au nanodisks: Absolute cross sections and branching ratios,” J. Chem. Phys. 126, 194702 (2007).
[Crossref] [PubMed]

Laroche, T.

A. Vial and T. Laroche, “Comparison of gold and silver dispersion laws suitable for FDTD simulations,” Appl. Phys. B 93, 139–143 (2008).
[Crossref]

Li, Q.

H. Chen, L. Shao, Q. Li, and J. Wang, “Gold nanorods and their plasmonic properties,” Chem. Soc. Rev. 42, 2679–2724 (2013).
[Crossref]

Li, Z.Y.

L. Gao, L.P. Gu, and Z.Y. Li, “Optical bistabity and tristability in nonlinear metal/dielectric composite media of nonspherical particles,” Phys. Rev. E 68, 066601 (2003).
[Crossref]

L. Gao, Z.Y. Li, and K.W. Yu, “Enhancement of optical nonlinearity through shape distribution,” J. Phys.: Condens. Matter 13, 7271–7282 (2001).

L. Gao, J.T.K. Wan, K.W. Yu, and Z.Y. Li, “Effective non-linear optical properties of metal-dielectric composites of spheroidal particles,” J. Phys.: Condens. Matter 12, 6825–6836 (2000).

Liznev, E.O.

E.O. Liznev, A.V. Dorofeenko, L. Huizhe, A.P. Vinogradov, and S. Zouhdi, “Epsilon-near-zero material as a unique solution to three different approaches to cloaking,” Appl. Phys. A 100, 321–325 (2010).
[Crossref]

Lozovskii, V.Z.

A.V. Goncharenko, V.Z. Lozovskii, and E.F. Venger, “Effective dielectric response of a shape-distributed particle system,” J. Phys.: Condens. Matter 13, 8217–8234 (2001).

Maas, R.

R. Maas, J. Parsons, N. Engheta, and A. Polman, “Experimental realization of an epsilon-near-zero metamaterial at visible wavelengths,” Nature Photon. 7, 907–912 (2013).
[Crossref]

Maxwell Garnett, J.C.

J.C. Maxwell Garnett, “Colours in metal glasses and in metallic films,” Phil. Trans. Roy. Soc. A 203, 385–420 (1904).
[Crossref]

Mayy, M.

M.A. Noginov, G. Zhu, M. Mayy, B.A. Ritzo, N. Noginova, and V.A. Podolskiy, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101, 226806 (2008).
[Crossref] [PubMed]

Moitra, P.

P. Moitra, Y. Yang, Z. Anderson, I.I. Kravchenko, D.P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nature Photon. 7, 791–795 (2013).
[Crossref]

Moran, M.

M.J. Roberts, S. Feng, M. Moran, and L. Johnson, “Effective permittivity near zero in nanolaminates of silver and amorphous polycarbonate,” J. Nanophoton. 4, 043511 (2010).
[Crossref]

Myslivets, S.A.

A.K. Popov and S.A. Myslivets, “Transformable broad-band transparency and amplification in negative-index films,” Appl. Phys. Lett. 93, 191117 (2008).
[Crossref]

Nan, C. W.

C. W. Nan, R. Birringer, D.R. Clarke, and H. Gleiter, “Effective thermal conductivity of particulate composites with interfacial thermal resistance,” J. Appl. Phys. 81, 6692–6699 (1997).
[Crossref]

Nazarov, V.U.

A.V. Goncharenko, V.U. Nazarov, and K.R. Chen, “Nanostructured metamaterials with broadband optical properties,” Opt. Mater. Express 3, 143–156 (2013).
[Crossref]

A.V. Goncharenko, V.U. Nazarov, and K.R. Chen, “Development of metamaterials with desired broadband optical properties,” Appl. Phys. Lett. 101, 071907 (2012).
[Crossref]

Neretina, S.

X. Huang, S. Neretina, and M.A. El-Sayed, “Gold nanorods: From synthesis and properties to biological and biomedical applications,” Adv. Mater. 21, 4880–4910 (2009).
[Crossref]

Ni, X.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials, Nature 466, 735–738 (2010).
[Crossref] [PubMed]

Noginov, M.A.

M.A. Noginov, G. Zhu, M. Mayy, B.A. Ritzo, N. Noginova, and V.A. Podolskiy, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101, 226806 (2008).
[Crossref] [PubMed]

Noginova, N.

M.A. Noginov, G. Zhu, M. Mayy, B.A. Ritzo, N. Noginova, and V.A. Podolskiy, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101, 226806 (2008).
[Crossref] [PubMed]

Parsons, J.

R. Maas, J. Parsons, N. Engheta, and A. Polman, “Experimental realization of an epsilon-near-zero metamaterial at visible wavelengths,” Nature Photon. 7, 907–912 (2013).
[Crossref]

Pham, D.C.

D.C. Pham and S. Torquato, “Strong-contrast expansions and approximations for the effective conductivity of isotropic multiphase composites,” J. Appl. Phys. 94, 6591–6602 (2003).
[Crossref]

Pinchuk, A.O.

Podolskiy, V.A.

M.A. Noginov, G. Zhu, M. Mayy, B.A. Ritzo, N. Noginova, and V.A. Podolskiy, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101, 226806 (2008).
[Crossref] [PubMed]

Polman, A.

R. Maas, J. Parsons, N. Engheta, and A. Polman, “Experimental realization of an epsilon-near-zero metamaterial at visible wavelengths,” Nature Photon. 7, 907–912 (2013).
[Crossref]

Popov, A.K.

A.K. Popov and S.A. Myslivets, “Transformable broad-band transparency and amplification in negative-index films,” Appl. Phys. Lett. 93, 191117 (2008).
[Crossref]

Ritzo, B.A.

M.A. Noginov, G. Zhu, M. Mayy, B.A. Ritzo, N. Noginova, and V.A. Podolskiy, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101, 226806 (2008).
[Crossref] [PubMed]

Roberts, M.J.

M.J. Roberts, S. Feng, M. Moran, and L. Johnson, “Effective permittivity near zero in nanolaminates of silver and amorphous polycarbonate,” J. Nanophoton. 4, 043511 (2010).
[Crossref]

Salandrino, A.

A. Alu, M.G. Silveirinha, A. Salandrino, and N. Engheta, “Epsiolon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75, 155410 (2007).
[Crossref]

Sarychev, A.K.

A.N. Lagarkov, A.K. Sarychev, V.N. Kissel, and G. Tartakovsky, “Superresolution and enhancement in metamaterials,” Physics-Uspekhi 52, 959–967 (2009).
[Crossref]

Savoia, S.

G. Castaldi, S. Savoia, V. Galdi, A. Alu, and N. Engheta, “Analytical study of subwavelength imaging by uniaxial epsilon-near-zero metamaterial slabs,” Phys. Rev. B 86, 115123 (2012).
[Crossref]

Semenov, Yu.V.

Shalaev, V. M.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials, Nature 466, 735–738 (2010).
[Crossref] [PubMed]

Shao, L.

H. Chen, L. Shao, Q. Li, and J. Wang, “Gold nanorods and their plasmonic properties,” Chem. Soc. Rev. 42, 2679–2724 (2013).
[Crossref]

Shvets, G.

C. Kurter, J. Abrahams, G. Shvets, and S.M. Anlage, “Plasmonic scaling of superconducting metamaterials,” Phys. Rev. B 88, 180510(R) (2013).
[Crossref]

Silveirinha, M.G.

A. Alu, M.G. Silveirinha, A. Salandrino, and N. Engheta, “Epsiolon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75, 155410 (2007).
[Crossref]

Soukoulis, C.M.

S. Datta, C.T. Chan, K.M. Ho, and C.M. Soukoulis, “Effective dielectric constant of periodic composite structures,” Phys. Rev. B 48, 14936–14943 (1993).
[Crossref]

Sun, G.

J.B. Khurgin and G. Sun, “In search of the elusive lossless metal,” Appl. Phys. Lett. 96, 181102 (2010).
[Crossref]

Sun, L.

Sutherland, D.S.

P. Hanarp, M. Käll, and D.S. Sutherland, “Optical properties of short range ordered arrays of nanometer gold disks prepared by colloidal lithography,” J. Phys. Chem. B 107, 5768–5772 (2003).
[Crossref]

Tartakovsky, G.

A.N. Lagarkov, A.K. Sarychev, V.N. Kissel, and G. Tartakovsky, “Superresolution and enhancement in metamaterials,” Physics-Uspekhi 52, 959–967 (2009).
[Crossref]

Torquato, S.

D.C. Pham and S. Torquato, “Strong-contrast expansions and approximations for the effective conductivity of isotropic multiphase composites,” J. Appl. Phys. 94, 6591–6602 (2003).
[Crossref]

Valentine, J.

P. Moitra, Y. Yang, Z. Anderson, I.I. Kravchenko, D.P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nature Photon. 7, 791–795 (2013).
[Crossref]

Venger, E.F.

Vial, A.

A. Vial and T. Laroche, “Comparison of gold and silver dispersion laws suitable for FDTD simulations,” Appl. Phys. B 93, 139–143 (2008).
[Crossref]

Vinogradov, A.P.

E.O. Liznev, A.V. Dorofeenko, L. Huizhe, A.P. Vinogradov, and S. Zouhdi, “Epsilon-near-zero material as a unique solution to three different approaches to cloaking,” Appl. Phys. A 100, 321–325 (2010).
[Crossref]

Wan, J.T.K.

L. Gao, J.T.K. Wan, K.W. Yu, and Z.Y. Li, “Effective non-linear optical properties of metal-dielectric composites of spheroidal particles,” J. Phys.: Condens. Matter 12, 6825–6836 (2000).

Wang, J.

H. Chen, L. Shao, Q. Li, and J. Wang, “Gold nanorods and their plasmonic properties,” Chem. Soc. Rev. 42, 2679–2724 (2013).
[Crossref]

Xiao, S.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials, Nature 466, 735–738 (2010).
[Crossref] [PubMed]

Yang, X.

Yang, Y.

P. Moitra, Y. Yang, Z. Anderson, I.I. Kravchenko, D.P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nature Photon. 7, 791–795 (2013).
[Crossref]

Yokogava, S.

S. Yokogava, S.P. Burgos, and H.A. Atwater, “Plasmonic color filters for CMOS image sensor applications,” Nano Lett. 12, 4349–4354 (2012).
[Crossref]

Yu, K.W.

L. Sun, K.W. Yu, and X. Yang, “Integrated optical devices based on broadband epsilon-near-zero meta-atoms,” Opt. Lett. 37, 3096–3098 (2012).
[Crossref] [PubMed]

L. Sun and K.W. Yu, “Strategy for designing broadband epsilon-near-zero metamaterials,” J. Opt. Soc. Am. B 29, 984–989 (2012).
[Crossref]

L. Gao, Z.Y. Li, and K.W. Yu, “Enhancement of optical nonlinearity through shape distribution,” J. Phys.: Condens. Matter 13, 7271–7282 (2001).

L. Gao, J.T.K. Wan, K.W. Yu, and Z.Y. Li, “Effective non-linear optical properties of metal-dielectric composites of spheroidal particles,” J. Phys.: Condens. Matter 12, 6825–6836 (2000).

Yuan, H. K.

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials, Nature 466, 735–738 (2010).
[Crossref] [PubMed]

Zhu, G.

M.A. Noginov, G. Zhu, M. Mayy, B.A. Ritzo, N. Noginova, and V.A. Podolskiy, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101, 226806 (2008).
[Crossref] [PubMed]

Zoric, I.

C. Langhammer, B. Kasemo, and I. Zorić, “Absorption and scattering of light by Pt, Pd, Ag, and Au nanodisks: Absolute cross sections and branching ratios,” J. Chem. Phys. 126, 194702 (2007).
[Crossref] [PubMed]

Zouhdi, S.

E.O. Liznev, A.V. Dorofeenko, L. Huizhe, A.P. Vinogradov, and S. Zouhdi, “Epsilon-near-zero material as a unique solution to three different approaches to cloaking,” Appl. Phys. A 100, 321–325 (2010).
[Crossref]

Adv. Mater. (1)

X. Huang, S. Neretina, and M.A. El-Sayed, “Gold nanorods: From synthesis and properties to biological and biomedical applications,” Adv. Mater. 21, 4880–4910 (2009).
[Crossref]

Appl. Phys. A (1)

E.O. Liznev, A.V. Dorofeenko, L. Huizhe, A.P. Vinogradov, and S. Zouhdi, “Epsilon-near-zero material as a unique solution to three different approaches to cloaking,” Appl. Phys. A 100, 321–325 (2010).
[Crossref]

Appl. Phys. B (1)

A. Vial and T. Laroche, “Comparison of gold and silver dispersion laws suitable for FDTD simulations,” Appl. Phys. B 93, 139–143 (2008).
[Crossref]

Appl. Phys. Lett. (3)

J.B. Khurgin and G. Sun, “In search of the elusive lossless metal,” Appl. Phys. Lett. 96, 181102 (2010).
[Crossref]

A.K. Popov and S.A. Myslivets, “Transformable broad-band transparency and amplification in negative-index films,” Appl. Phys. Lett. 93, 191117 (2008).
[Crossref]

A.V. Goncharenko, V.U. Nazarov, and K.R. Chen, “Development of metamaterials with desired broadband optical properties,” Appl. Phys. Lett. 101, 071907 (2012).
[Crossref]

Chem. Soc. Rev. (1)

H. Chen, L. Shao, Q. Li, and J. Wang, “Gold nanorods and their plasmonic properties,” Chem. Soc. Rev. 42, 2679–2724 (2013).
[Crossref]

J. Appl. Phys. (2)

D.C. Pham and S. Torquato, “Strong-contrast expansions and approximations for the effective conductivity of isotropic multiphase composites,” J. Appl. Phys. 94, 6591–6602 (2003).
[Crossref]

C. W. Nan, R. Birringer, D.R. Clarke, and H. Gleiter, “Effective thermal conductivity of particulate composites with interfacial thermal resistance,” J. Appl. Phys. 81, 6692–6699 (1997).
[Crossref]

J. Chem. Phys. (1)

C. Langhammer, B. Kasemo, and I. Zorić, “Absorption and scattering of light by Pt, Pd, Ag, and Au nanodisks: Absolute cross sections and branching ratios,” J. Chem. Phys. 126, 194702 (2007).
[Crossref] [PubMed]

J. Electrostat. (1)

S. Giordano, “Effective medium theory for dispersions of dielectric ellipsoids,” J. Electrostat. 58, 59–76 (2003).
[Crossref]

J. Nanophoton. (2)

A.V. Goncharenko and K.R. Chen, “Strategy for designing epsilon-near-zero nanostructured metamaterials over a frequency range,” J. Nanophoton. 4, 041530 (2010).
[Crossref]

M.J. Roberts, S. Feng, M. Moran, and L. Johnson, “Effective permittivity near zero in nanolaminates of silver and amorphous polycarbonate,” J. Nanophoton. 4, 043511 (2010).
[Crossref]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

J. Phys. Chem. B (1)

P. Hanarp, M. Käll, and D.S. Sutherland, “Optical properties of short range ordered arrays of nanometer gold disks prepared by colloidal lithography,” J. Phys. Chem. B 107, 5768–5772 (2003).
[Crossref]

J. Phys.: Condens. Matter (3)

A.V. Goncharenko, V.Z. Lozovskii, and E.F. Venger, “Effective dielectric response of a shape-distributed particle system,” J. Phys.: Condens. Matter 13, 8217–8234 (2001).

L. Gao, J.T.K. Wan, K.W. Yu, and Z.Y. Li, “Effective non-linear optical properties of metal-dielectric composites of spheroidal particles,” J. Phys.: Condens. Matter 12, 6825–6836 (2000).

L. Gao, Z.Y. Li, and K.W. Yu, “Enhancement of optical nonlinearity through shape distribution,” J. Phys.: Condens. Matter 13, 7271–7282 (2001).

Nano Lett. (1)

S. Yokogava, S.P. Burgos, and H.A. Atwater, “Plasmonic color filters for CMOS image sensor applications,” Nano Lett. 12, 4349–4354 (2012).
[Crossref]

Nature (1)

S. Xiao, V. P. Drachev, A. V. Kildishev, X. Ni, U. K. Chettiar, H. K. Yuan, and V. M. Shalaev, “Loss-free and active optical negative-index metamaterials, Nature 466, 735–738 (2010).
[Crossref] [PubMed]

Nature Photon. (2)

P. Moitra, Y. Yang, Z. Anderson, I.I. Kravchenko, D.P. Briggs, and J. Valentine, “Realization of an all-dielectric zero-index optical metamaterial,” Nature Photon. 7, 791–795 (2013).
[Crossref]

R. Maas, J. Parsons, N. Engheta, and A. Polman, “Experimental realization of an epsilon-near-zero metamaterial at visible wavelengths,” Nature Photon. 7, 907–912 (2013).
[Crossref]

Opt. Express (2)

Opt. Lett. (1)

Opt. Mater. Express (1)

Phil. Trans. Roy. Soc. A (1)

J.C. Maxwell Garnett, “Colours in metal glasses and in metallic films,” Phil. Trans. Roy. Soc. A 203, 385–420 (1904).
[Crossref]

Phys. Rev. B (5)

S. Datta, C.T. Chan, K.M. Ho, and C.M. Soukoulis, “Effective dielectric constant of periodic composite structures,” Phys. Rev. B 48, 14936–14943 (1993).
[Crossref]

G. Castaldi, S. Savoia, V. Galdi, A. Alu, and N. Engheta, “Analytical study of subwavelength imaging by uniaxial epsilon-near-zero metamaterial slabs,” Phys. Rev. B 86, 115123 (2012).
[Crossref]

S. Feng and K. Halterman, “Coherent perfect absorption in epsilon-near-zero metamaterials,” Phys. Rev. B 86, 165103 (2012).
[Crossref]

A. Alu, M.G. Silveirinha, A. Salandrino, and N. Engheta, “Epsiolon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern,” Phys. Rev. B 75, 155410 (2007).
[Crossref]

C. Kurter, J. Abrahams, G. Shvets, and S.M. Anlage, “Plasmonic scaling of superconducting metamaterials,” Phys. Rev. B 88, 180510(R) (2013).
[Crossref]

Phys. Rev. E (1)

L. Gao, L.P. Gu, and Z.Y. Li, “Optical bistabity and tristability in nonlinear metal/dielectric composite media of nonspherical particles,” Phys. Rev. E 68, 066601 (2003).
[Crossref]

Phys. Rev. Lett. (1)

M.A. Noginov, G. Zhu, M. Mayy, B.A. Ritzo, N. Noginova, and V.A. Podolskiy, “Stimulated emission of surface plasmon polaritons,” Phys. Rev. Lett. 101, 226806 (2008).
[Crossref] [PubMed]

Physics-Uspekhi (1)

A.N. Lagarkov, A.K. Sarychev, V.N. Kissel, and G. Tartakovsky, “Superresolution and enhancement in metamaterials,” Physics-Uspekhi 52, 959–967 (2009).
[Crossref]

Roc. R. Soc. Lond. A (1)

R.T. Bonnecaze and J.F. Brady, “The effective conductivity of random suspensions of spherical particles,” Roc. R. Soc. Lond. A 432, 445–465 (1991).
[Crossref]

Other (1)

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Figures (5)

Fig. 1
Fig. 1 Geometry of the composite under consideration: suspension of randomly oriented and variously shaped metal spheroids with the permittivity ε1 embedded in a dielectric host with the permittivity ε0.
Fig. 2
Fig. 2 The effective permittivity of a suspension of gold spheroids in a Teflon host with Reεeff fitted to zero with 10% bandwidth at λ0 = 875 nm. The parameters of the spheroids are L1 = 0.0325, L2 = 0.883, L3 = 0.8945, f1 = 0.077, f2 = 0.0014, f3 = 0.0016 (solid curves) and L1 = 0.053, L2 = 0.882, L3 = 0.9907, f1 = 0.0013, f2 = 0.00068, f3 = 0.078 (dashed curves) (here and below L i L ( i )).
Fig. 3
Fig. 3 The rms vs λ0 for a suspension of gold spheroids in a Teflon host with Reεeff fitted to zero with 10% and 15% bandwidths.
Fig. 4
Fig. 4 The imaginary part of the effective permittivity of a suspension of gold spheroids in a Teflon host with Reεeff fitted to zero with 10% bandwidth. Solid curves and dashed curves correspond to two different branches. The respective values of λ0 are shown in the inset.
Fig. 5
Fig. 5 The intensity absorption for composite films of different thickness t made of gold spheroids in a Teflon host with Reεeff fitted to zero with λ0 = 900 nm and 10% bandwidth.

Equations (15)

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η ( χ i ) = ω 1 ω 2 | Re ε eff ( χ i , ω ) | 2 d ω ,
ε eff = D ¯ E = i = 1 N f i ε 1 E ¯ i + ( 1 f ) ε 0 E L i = 1 N f i E ¯ i + ( 1 f ) E L ,
E ¯ i = 1 3 [ ε 1 L ( i ) ε 0 + ( 1 L ( i ) ) ε 1 + 2 ε 1 L ( i ) ε 0 + ( 1 L ( i ) ) ε 1 ] E L = 1 3 E L ε 1 ε 0 [ β ( i ) + 2 β ( i ) ] ,
β ( i ) = ε 1 ε 0 ε 0 + L ( i ) ( ε 1 ε 0 ) , β ( i ) = ε 1 ε 0 ε 0 + L ( i ) ( ε 1 ε 0 ) ,
L ( i ) + 2 L ( i ) = 1 .
ε eff = ε 0 1 + i = 1 N f i [ β ( i ) ( 1 L ( i ) ) + 2 β ( 1 L ( i ) ) ] / 3 1 i = 1 N f i [ β ( i ) L ( i ) + 2 β L ( i ) ] / 3 .
ε eff = ε 0 ( 1 + i = 1 N f i α i 1 f + s i = 1 N f i α i ) ,
γ ( i ) = 0 1 ( s + L ) 1 P i ( L ) d L , γ ( i ) = 0 1 [ s + ( 1 L ) / 2 ] 1 P i ( L ) d L ,
ε eff ( ooo ) ε 0 1 + 2 f β ¯ 1 f β .
ε eff ( poo ) ε 0 1 + [ f 1 β ( 1 ) + 2 f 2 β ( 2 ) + 2 f 3 β ( 3 ) ] / 3 1 [ f 1 β ( 1 ) + f 2 β ( 2 ) + f 3 β ( 3 ) ] / 3 ,
ε eff ( ppo ) ε 0 1 + [ f 1 β ( 1 ) + f 2 β ( 2 ) + 2 f 3 β ( 3 ) ] / 3 1 [ f 1 β ( 1 ) + f 2 β ( 2 ) + f 3 β ( 3 ) ] / 3 .
ε eff ( ppp ) ε 0 1 + 2 f β ¯ 1 f β ,
P i ( L ) = Δ i 1 χ ( L L i + Δ i L i ) χ [ L + L i + Δ i ( 1 L i ) ] ,
γ ( i ) = 1 Δ i ln s + L i ( 1 Δ i ) + Δ i s + L i ( 1 Δ i ) , γ ( i ) = 2 Δ i ln 2 s + 1 L i ( 1 Δ i ) Δ i 2 s + 1 L i ( 1 Δ i ) .
δ ( rms ) Δ i ( r ) = δ ( rms ) Δ i d L d r ,

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