Abstract

In this paper, the absorption characteristics of a hybrid structure composed of a black phosphorus (BP) nanostrip array based on localized surface plasmon resonance (LSPR) and a metal grating slit structure have been analyzed systematically. Firstly, we theoretically investigate light-matter interaction in different dimensions of BP nanostrip arrays along armchair and zigzag direction, revealing the absorption property and anisotropic plasmonic response. Besides, the transmission characteristics of the metal grating slit structure with different geometric dimensions are thoroughly analyzed by the transmission spectra and electric intensity distributions. At last, by combining the two structures, we increased the absorption of BP from 72% to 83.6% at 7.04 µm, and this hybrid BP structure demonstrates high absorption at mid-infrared wavelength regime, predicting a promising future for the directional dependent plasmonic devices based on two-dimensional (2D) materials.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Atomically thin two-dimensional (2D) materials such as transition-metal dichal cogenides (TMDCs), graphene, black phosphorus (BP) and many others have received burgeoning amount of interest recent years due to their exciting physical properties. They exhibit novel optoelectronic, mechanical and thermal properties due to their layered lattice structures, which are the promising materials to emerge as a platform to achieve novel optical and electrical characteristics [15]. Recent years, strong light matter interaction has been observed in 2D layered materials, such as plasmons (the coherent oscillation of electron). For example, due to its inherent atomically thin thickness, graphene provides a unique opportunity by confining plasmons and highly localized electric fields in an extremely thin optical material [68]. It means graphene can offer unprecedented flexibility in the surface plasmonic polaritons (SPPs) research. In addition, the electrical active split ring resonators based on graphene metamaterials on a SiO2/Si substrate were theoretically investigated to shows tunable frequency and amplitude modulation [9]. By depositing graphene patterns on the SiO2/Si layers, the active control of THz wave can be realized, which demonstrates the excellent optical properities and plasmonic characteristics of graphene. In fact, before graphene as an emerging plasmonic material, noble metals such as silver and gold were the preferred choice for plasmonic material [10]. Gold and silver can excite well-confined SPPs at near infrared frequencies due to their large free electron density. Recently, some researches have proved that the SPPs can be demonstrated in graphene with different shapes such as ribbons [1113], disks [14,15] and other shapes or structures [1618]. Compared to conventional surface plasmons in noble metals, the plasmons in 2D materials exhibit tighter confinement (∼λ0/100) [19]. And the absorption efficiency can be increased from less than 2.3% to 30% in the infrared region by nanopatterning a graphene into an array of nanodisks [20]. Although graphene has immense potential for plasmonic applications, there are many drawbacks and limits that cannot be ignored, such as the serious scattering loss, the zero-band gap. These inadequacies actually limit the plasmonic propagation and the spectral application [21]. In fact, MoS2, a member of TMDCs, can also be used as a plasmonic material. The infrared response in TMDCs materials is dominated by plasmons that can be dynamically tuned by electrostatic gating [22]. However, due to its low carrier mobility, the future prospects of field-effect transistors for infrared or far infrared optoelectronics are worrisome. Therefore, the investigation of alternative plasmonic materials with improved performance becomes urgent.

Recent years, BP has attracted extensive attention due to its excellent optical and electrical performance and has been investigated for potential applications including field effect transistors [23,24], hetero-junction p-n diodes [25], photovoltaic devices [26], and photodetectors [27]. Compared with other 2D materials, BP shows some unique characteristics, such as stronger interlayer interaction, higher carrier mobility and tunable band gap. Moreover, BP has a direct band gap for all number of layers, ranging from 0.3 eV for bulk to 2 eV for monolayer [2831]. Owing to the adjustable band gap, BP exhibits a high carrier mobility ranged from 1000 to 10000 cm2/ (V·s) [32]. Therefore, these properties can make BP a more excellent alternative for plasmonic material. Indeed, the most surprising feature of BP is the anisotropy of its band structure, where the in-plane effective electron masses along the two crystal axes differ by an order of magnitude. BP has a larger mobility along the armchair direction, which consequently leads to a larger conductivity than that along the zigzag direction [33]. By utilizing various nanostructures, SPPs mode can be excited in layered BP [34]. And it is worth noticing that interlayer interactions that exist in few-layer of BP will cause the interlayer rearrangement of electrons, which might actually make few-layered BP unstable in the applications. Any variations of the layer numbers and stacking type would cause serious unwanted disturbances to the performance of the device [33]. Therefore, for monolayer BP, such issue could be ignored, which is considered as a natural candidate for broadband optical applications, including the infrared and terahertz branches of the spectrum. What’s more, in contrast to other 2D materials, the anisotropic crystal structure of BP makes it more interesting. The phosphorus atoms form a honeycomb lattice and the conductivity along armchair direction is larger than that along zigzag direction, resulting in in-plane anisotropic properties [3437]. The same as graphene, BP plasmons have a variety of potentially exciting applications. Recent years, it is theoretically demonstrated that surface plasmon resonance can be excited in nanostructured BP ribbon arrays [38,39], square arrays [40] as well as monolayer and multilayer BP film [4144]. And BP's hyperbolic properties were demonstrated at the mid-infrared band, which support ultra-strong field-constrained plasmon, enabling miniaturization of optical devices [45]. And the electro-optic modulator of multilayer BP was demonstrated in the middle infrared regime, which indicates that BP is a very promising material in middle infrared optoelectronic devices for a wide range of applications [46].

Although 2D plasmonic materials provide a distinctive opportunity by confining plasmons in an extremely thin material, they also exhibit a great challenge for light-matter interactions due to their inherent atomically thin thickness. For example, BP has a low absorption of about 17% over a wide spectral band, which is usually insufficient for many practical applications [47]. As a result, several light absorption strategies have been proposed, such as integrated waveguides [48,49], metal reflector [39], direct coupled resonators [50], and plasmonic gratings [47]. However, integrated waveguides are incapable of improving the absorption effectively, which is determined by the length of the waveguide. Therefore, in order to achieve high absorption, a relatively long waveguide is necessary, resulting in a device dimension much longer than the wavelength and limiting the bandwidth of the device due to the large capacitance [1]. However, the metal reflector has a compact structure and can effectively improve the absorption efficiency in resonant manner [39]. Besides, the absorption can also be improved by using the extraordinary optical transmission (EOT) of metal plasmonic grating slit [51]. The EOT phenomenon was originally observed in a 2D array of sub-wavelength holes in a metal film, which is related to the resonant excitation of the electromagnetic incident light on the corrugated metal surface [51]. We know that one way of coupling free-propagating light to surface plasma is utilizing periodic corrugate structures on the surface that satisfy the conservation of energy and momentum [52]. Therefore, a single slit surrounded by periodic grating grooves in the metal surface will also display surface plasmon–enhanced transmission. A hybrid, three-dimensional structure consisting of silicon photonics structure, metallic grating slit structure and BP was demonstrated [53]. In this structure, light is concentrated through metal slit to achieve the enhancement of transmission, and the EOT effect through the nanogap generates a highly concentrated electric field in the BP layer. The electric field amplitude exhibits an enhancement factor relative to output intensity of waveguide grating. The transmission peaks of metal slits are mostly in visible and near infrared bands for its large free electron density [5154]. However, for the coupling of metal’s free electrons is poor, it is difficult to observe significant EOT in far-infrared regime [54]. In addition, BP nanostrip can produce strong anisotropic LSPR in the middle and far infrared band (30-80 µm), and its absorption is basically no more than 50% [3945,55,56]. Few researchers have ever studied to further improve it. Therefore, we design a hybrid structure combining the LSPR and EOT effect to achieve the absorption enhancement of BP at near and middle infrared ranges.

In this paper, we design a hybrid structure consisting of BP nanostrip array and metal grating slit structure to enhance the absorption of BP. At first, we propose the monolayer BP nanostrip array with different geometrical dimensions to demonstrate the anisotropic LSPR behavior. Optical characteristics of the BP nanostrip along two different lattice directions are thoroughly analyzed by absorption spectra. In addition, the transmission of metal grating slit structure has also been analyzed. We compare the transmission spectra of different geometrical dimensions of the grating structures with and without slit, which demonstrates the EOT effect at the slit of metal grating. At last, the hybrid structure consisting of BP nanostrip array and metal grating slit is proposed to illustrate the significant absorption enhancement of BP in mid-infrared wavelength regime. Our hybrid structure can be an ideal candidate for realizing novel and high performance mid-infrared plasmonic applications for high absorption photodetector, electro-optic modulator and the biosensing devices.

2. Results and discussion

The LSPR behavior in monolayer BP nanostrip array along two different lattice directions is simulated and analyzed by the anisotropic properties of BP firstly. As illustrated in Fig. 1(a), a schematic diagram of the BP crystal structure is demonstrated. The atoms are arranged in a BP lattice in two directions: the armchair direction which is set as x direction and the zigzag direction which is set as y direction. Figure 1(b) shows the three-dimensional schematic diagram of BP nanostrip array. The inset shows the cross section of the structure. In order to analyze the influence of geometric dimensions on absorption, we compare BP nanostrip structures with various dimensions in simulation. In our design, the hybrid structure consists of periodic monolayer BP nanostrip array, a transparent insulator quartz and a reflective metallic mirror. The metallic mirror is used to reflect light and suppress the transmission, forming a Fabry-Perot cavity together with the insulator quartz and the BP layer, and therefore increases the interaction of light with the monolayer BP [55]. In our simulation, the absorption spectrum of the BP nanostrips array is thoroughly analyzed with a calculation method based on the finite-difference time-domain (FDTD) method [39]. Absorptivity (A) can be calculated with a formula A = 1-R-T, where R is the reflectivity and T is the transmission. Since the metallic mirror suppresses the transmission, thus transmission (T) can be regarded as zero. Then we can calculate the absorptivity using A = 1-R directly.

 

Fig. 1. (a) Schematic diagram of BP crystal structure. (b)The three-dimensional schematic diagram of BP nanostrip array.

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Due to the different atoms structure along the two different lattice directions, there is an unusual in-plane anisotropic electrical and optical property at BP. Here, we employ a simple semi-classical Drude model to describe the optical properties of the monolayer BP. Permittivity ${\varepsilon _j}$ can be expressed by the following formula:

$${\varepsilon _j} = {\varepsilon _r} + \frac{{i{\sigma _j}}}{{s\omega {\varepsilon _0}}}$$
Where ${\varepsilon _r}$ is the relative permittivity, which is taken to 5.76 for the monolayer BP [22], s is thickness of the monolayer BP which is chosen to be 1 nm in our simulation, ${\sigma _j}\; $is BP surface conductivity, j donates the BP lattice direction concerned, $\omega$ is the frequency of the incident light and ${\varepsilon _0}\; $is free space permittivity. It can be seen that the permittivity ${\varepsilon _j}\; $is closely related to the BP surface conductivity ${\sigma _j}$. In Drude model, the conductivity [55] is given as:
$${\sigma _j} = \frac{{i{D_j}}}{{\pi (\omega + \frac{{i\eta }}{\hbar })}}$$
Where $\hbar $ is the Planck constant, and $\eta \; $is chosen to be 10 meV to describe the relaxation rate [39]. Then, ${D_j}\; $is the Drude weight and can be expressed as:
$${D_j} = \frac{{\pi {e^2}n}}{{{m_j}}}$$
Where n is the electron doping, e is the electron charge, and ${m_j}\; $is the electron mass along the x-direction and y-direction that can be described as:
$${m_x} = \frac{{{\hbar ^2}}}{{2\frac{{{\gamma ^2}}}{\Delta } + {\eta _c}}},{m_y} = \frac{{{\hbar ^2}}}{{{v_c}}}$$
For monolayer BP, the dimensions determined by fitting the known anisotropic mass [39] are $\gamma = \frac{{4a}}{\pi }$ eVm, $\Delta $ = 2eV, ${\eta _c} = \frac{{{\hbar ^2}}}{{0.4{m_\textrm{0}}}}$ and ${v_c} = \frac{{{\hbar ^2}}}{{1.4{m_0}}}$, where m0 = 9.10938×10−31 kg is the standard electron rest mass, and a = 0.223 nm is the scale length of BP.

Because of the anisotropic properties of BP, we comprehensively analyze LSPR behavior for monolayer BP nanostrip array along the armchair and zigzag direction. As shown in Fig. 2(a), the absorption spectra of the monolayer BP nanostrip along x direction and y direction at the wavelength of 6-30 µm were plotted. The dimensions for the two different lattice directions are set to be exactly the same. The period (p) is fixed at twice the width (w) of the BP nanostrip, which is p = 2w. It is obviously that there are two absorption peaks, and the corresponding resonance wavelengths are 7.98 and 22.96 µm, respectively. These resonance wavelengths are well consistent with theoretical calculations based on the Fabry-Perot effect [55] with a formula λ = 4nt / (2m + 1), where λ is the resonance wavelength, m is a positive integer, n = 1.94 is the refractive index of quartz, and t = 3 µm is the thickness of quartz. The maximum absorption peak of the periodic BP nanostrip array along x direction is 38.2% at 7.98 µm and 26.9% along y direction at 22.96 µm, respectively. At the first absorption peak, the absorption of BP nanostrip array along x direction is much larger than that along y direction, almost five times larger. This is due to the fact that the effective mass of BP in the armchair direction is less than that in the zigzag direction, and the smaller mass along the armchair direction, the higher resonance frequency. Compared with the zigzag direction, the absorption peak in armchair direction is higher, indicating that BP has more optical loss in the zigzag direction at the corresponding resonance wavelength. In addition, the absorption of BP nanostrip array with and without quartz is compared. As it can be seen from Fig. 2(a), the absorption of BP nanostrip array without quartz is much lower than that with quartz, which indicates that the presence of quartz is necessary. Based on the mechanism of the resonance absorption of the two-layer system, the key problem is that light can penetrate the metal reflector to obtain a large phase change, which will inevitably introduce optical loss into the metal film [57]. Therefore, the introduction of quartz layer can well compensate for the phase mismatch, reduce the total reflection, and increase the absorption of BP layer. Next, we focus on the impact of the dielectric thickness on the absorption spectra of BP nanostrip array. As illustrated in Fig. 2(b), the absorption spectra of the monolayer BP nanostrip array along x direction with the different thicknesses of the quartz was calculated, showing a strong dependence of the absorption resonance on t. It can be seen that there are three absorption peaks at the wavelength range of 6-30 µm when t is 6 µm. It also can be seen that the absorption reaches the maximum at the fixed thickness of 6 µm. Figure 2(c) and Fig. 2(d) present the electric field distribution in Y-Z plane. It can be seen from Fig. 2(c), the electric field intensity reaches the maximum which increases the absorption at the thickness of 6 µm. By contrast, from Fig. 2(d), the electric field intensity at BP is only about three-quarters of its maximum at 3 µm. To demonstrate the localized plasmon resonance behavior, the total electric field intensity for one BP nanostrip unit was calculated in Fig. 2(e). It can be seen that the electric field enhancement is mostly concentrated around the two edges of BP nanostrip array, which resembles the edge modes in graphene ribbon structures [39]. Besides, it can also be noticed that a localized plasmon resonance behavior can be observed with the maximum electric field localized in a deep sub-wavelength regime close to the edges of BP nanostrip unit, which illustrates that the electric dipole behavior expected in the nanostructures exhibits localized plasmon resonances. In addition, the LSPR effect of BP nanostrip array can also be actively controlled by tuning the Fermi level (Ef) or doping with electrostatic gating [8,22]. As demonstrated in Fig. 2(f), the absorption spectra of BP nanostrip arrays for various values of Fermi levels was calculated. It can be seen that the resonance amplitude is enhanced and resonance wavelength shifts slightly as Fermi level increases. This indicates that with the increase of doping concentration, there will be stronger resonance. The relationship between doping concentration and Fermi level can be described as:

$$n = {(\pi {\hbar ^2})^{ - 1}}{({m_x}{m_y})^{0.5}}{k_B}T\ln [{1 + \exp ({E_F}/{k_B}T)} ]$$

 

Fig. 2. (a) Absorption spectra of the monolayer BP nanostrip array with quartz along x direction, y direction and without quartz at the wavelength of 6-30 µm. The thickness of the quartz between BP and metal mirror is 3 µm. The width of the BP strip is 150 nm and the period is 300 nm. (b) Absorption spectra of the monolayer BP nanostrip along x direction at the wavelength of 6-30 µm. The thickness of the quartz between BP and metal mirror is 3 µm and 6 µm, respectively. The width of the BP strip is 150 nm and the period is 300 nm. Electric field intensity distributions with the fixed thickness of 6 µm (c) and 3 µm (d). Inset is the side view of the proposed structure. The width of the BP strip is 150 nm and the period is 300 nm. (e) Calculated total electric field intensity for one BP nanostrip unit cell in Y-Z plane. The thickness of the quartz between BP and metal mirror is 6 µm. The width of the BP strip is 150 nm and the period is 300 nm. (f). Absorption spectra of BP nanostrip arrays for various values of Fermi levels between 0.2 eV and 1 eV. The thickness of the quartz between BP and metal mirror is 3 µm. The width of the BP strip is 150 nm and the period is 300 nm.

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In order to investigate the influence of the structural dimensions of the proposed BP nanostrip array on its LSPR behavior, we further investigate different widths of the BP nanostrip array. As illustrated in Fig. 3(a), the absorption spectra of the monolayer BP nanostrip array along x direction at the six different widths were demonstrated. For a more detailed illustration of the comparison, the enlarged view of the first absorption peak in Fig. 3(a) was plotted in Fig. 3(b). From Fig. 3(b), it is clear that the first absorption peak exhibits a slightly red shift when increasing the width. The absorption peak can reach 72% at 6.9 µm when the width is 150 nm, which is almost eight times larger than the absorption when the width is 50 nm. Obviously, when the period increases, the position of the plasmon resonance shifts to a longer wavelength. This can be explained by the formula of resonant wavelength of BP nanostrip array [22]:

$${\lambda _{spj}} = c\sqrt {\frac{{2\pi {m_j}{\varepsilon _0}({\varepsilon _1} + {\varepsilon _2})p\zeta }}{{n{e^2}}}}$$
Where j denotes the crystal direction, n is the electron doping, ${m_j}\; $is the electron mass along the x-direction and y-direction. For simplicity, we assume that BP nanostrip are suspended in the space so that ${\varepsilon _1} = \; {\varepsilon _2} = 1$. It can be seen that as the period increases, the corresponding resonance wavelength increases as well, thus causing the red shift. Furthermore, the full-width at half-maximum (FWHW) of plasmon resonance peaks become much broader when the widths increase due to more radiative loss of plasmon caused by the reemission of light at longer wavelengths [22]. However, the second absorption peak has barely varied with the change of width. This is because the second absorption peak is originated from the Fabry-Perot effect, not influenced by the structural dimensions of the BP nanostrip array. Therefore, the maximum absorption peak is obtained when the width is 150 nm.

 

Fig. 3. (a) Absorption spectra of the monolayer BP nanostrip array along x direction at the wavelength of 6-30 µm at six different widths (i.e., width = 50, 70, 90, 110, 130 and 150 µm) with a fixed thickness of the quartz of 6 µm. (b) The enlarged view of the first absorption peak in dotted box of Fig. 3(a).

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As can be seen from the above analysis, the BP nanostrip array does not absorb much light at the mid-infrared wavelength regime (i.e. 10-20 µm). The EOT effect of the metal grating slit structure can be adopted to solve this problem. We will firstly analyze the transmission of metal grating slit without BP nanostrip.

As illustrated in Fig. 4(a), a schematic diagram of the metal grating slit structure was demonstrated, in which, f is the period of grating, h is the height of the grating, g is the width of slit and H is the height of slit. And the material of metal grating is selected as gold (Au). Figure 4(b) and Fig. 4(c) present the front view of the input and output grating structures, respectively. We first focus on the impact of the position of patterning gratings on the transmission spectra in Fig. 4(d). It can also be obtained from Fig. 4(d), the total transmission is controlled basically by the input grating, and the output grating structure surface (output end) determines the convergence of transmitted light beams [51]. Therefore, in order to obtain the maximum transmission, a structure with gratings on both surfaces should be adopted. Because the transmission is sensitive to the dimension of the metal grating slit structure, we compare the different dimensions of the metal grating. For the transmission spectral of the metal grating slit shown in Fig. 4(e), the transmission spectral of the metal grating slit with the different periods of the grating was calculated. From Fig. 4(e), obviously, the transmission peak of metal grating slit shows a strong dependence of the resonance wavelength on the period of grating. This dependence may be attributed to the coupled LSPR mode. In addition, as the period increases, the transmission increases significantly at the same time. Due to the smaller period of the grating structure, the excitation of the surface electromagnetic resonance caused by the interaction between the grating gap and the in-phase grating re-emitting mechanism is not significant [58]. Therefore, the maximum transmission peak is obtained when the period is 3 µm. The transmission spectral of the structure with the different heights of the grating was shown in Fig. 4(f). It can be seen from Fig. 4(f), the peak of the first transmission peak is almost the same, but as the height of the grating increases, the peak position shifts, and the offset is about 4 µm. As the height of the grating increases, the second transmission peak decreases sharply. This is because when the grating height is small, polarization charges are generated at the edges of the grating, and the oscillating current generated by the LSPR mode will flow into the groove and oscillates along the surface. It will provide stronger coupling at the upper and lower interfaces of the grating, producing a high transmission [59]. When the height of the grating increases, it is difficult for the oscillating current to flow into the groove to form a strong coupling, so the transmission decreases. Therefore, in order to obtain the maximum transmission, the height of grating should be set as 2 µm. To verify the effect of gap of the slit on the transmission, we calculated the transmission spectral of the structure with the different gap widths of the slit in Fig. 4(g). From Fig. 4(g), as the gap width of the slit increases, there is a red shift in both transmission peaks. This shift may be attributed to the coupling of LSPR mode on the internal interfaces of the slit, which increase the effective index for the cavity mode and then decrease the resonance frequency when the width increases [58]. As it can be seen from the shift of the second absorption peak at low frequency, transmission increases as g increases, which is due to that along the increase of width of the slit, the excitation of a surface resonance originated from the interplay between the groove cavity mode and the in-phase groove reemission mechanism is conspicuous. And the maximum transmission peak is obtained at high frequency when the gap width is 3 µm. In addition, the light might emerge preferentially at certain angles for certain wavelengths [60]. Therefore, we calculated the transmission spectral at different incident angles, and a strong dependence is observed in Fig. 4(h). With the increase of incidence angle, the transmission of metal grating slit decreases obviously. This means that vertical incidence is the best way to get the maximum transmission. In addition, in order to better understand the transmission of grating slit structure, we analyzed the simulation results and obtained the data fitting results based on the coupled mode theory. A general theory of transport processes from multiple input and output ports through a single-mode optical resonator was developed [61]. In this theory, the scattering matrix S is used to demonstrate the general problem of a single optical mode coupled with multiple input and output ports:

$$S\textrm{ = }C\textrm{ + }\frac{{d\cdot {k^ \ast }}}{{j({\omega - {\omega_0}} )+ {\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 \tau }} \right.}\!\lower0.7ex\hbox{$\tau $}}}}$$

 

Fig. 4. (a) Schematic diagram of metal grating slit structure, f is the period of grating, h is the height of the grating, g is the width of slit and H is the height of slit. Inset is the side view of the gap, $\theta $ presents the angle of incident light. (b) The front view of input grating structure and (c) output grating structure. (d) Transmission spectral of the metal grating slit of three different structures. (e)Transmission spectral of the metal grating slit at the wavelength of 6-20 µm with three different periods (i.e., f = 1, 2, and 3 µm) of the grating. (f) Transmission spectral of the metal grating slit at the wavelength of 6-20 µm with four different heights (i.e., h = 2, 2.5, 3, and 3.5 µm) of the grating. (g) Transmission spectral of the metal grating slit at the wavelength of 6-20 µm with three different slit widths (i.e., g = 1, 3, and 5 µm) of the slit. (h) Transmission spectral for various incident angles of the metal grating slit. The yellow dotted line is the fitting result of coupled-mode theory of metal grating structure in the case of vertical incidence.

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Where C is the scattering matrix of the direct process, in addition to the resonant auxiliary coupling between the ports, the input and output waves in the port can also be coupled through direct paths, d is the coupling constant of the output waves, k is the coupling constant of the input waves, and ω0 is the center frequency of the resonance. However, the grating slit structure is a two-port symmetry structure, the scattering matrix S1 can be written in another special form:

$${S_1}\textrm{ = exp}({j\vartheta } )\left\{ {\left[ {\begin{array}{{cc}} r&{jv}\\ {jv}&r \end{array}} \right]} \right. + \frac{{{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 \tau }} \right.}\!\lower0.7ex\hbox{$\tau $}}}}{{j({\omega - {\omega_0}} )+ {\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 \tau }} \right.}\!\lower0.7ex\hbox{$\tau $}}}}\left. {\left[ {\begin{array}{{cc}} { - ({r \pm jv} )}&{ \mp ({r \pm jv} )}\\ { \mp ({r \pm jv} )}&{ - ({r \pm jv} )} \end{array}} \right]} \right\}$$

Where ϑ, r and v are constants with r2 + v2 = 1, and ± corresponds to the case where the resonant mode is even (odd) to the mirror. And a symmetric Lorentzian line shape is reproduced only when either r or v is zero [60]. In our structure, the resonant mode is even with respect to the mirror plane, so the transmission can be simplified according to the scattering matrix S1:

$$T\textrm{ = 1 - }\frac{{{\textrm{r}^2}{{({\omega - {\omega_0}} )}^2} + {v^2}{{({{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 \tau }} \right.}\!\lower0.7ex\hbox{$\tau $}}} )}^2} + 2rv({\omega - {\omega_0}} )({{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 \tau }} \right.}\!\lower0.7ex\hbox{$\tau $}}} )}}{{{{({\omega - {\omega_0}} )}^2} + {{({{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 \tau }} \right.}\!\lower0.7ex\hbox{$\tau $}}} )}^2}}}$$

In our transmission simulation results of the grating slit structure in the case of vertical incidence, the center frequencies of the resonance are 23THz and 43THz, respectively. The height of the grating is set as 2 µm and the gap is 1 µm. Since r and v satisfy this relationship r2 + v2 = 1, we set v to 0.25 to facilitate calculation. And 1/τ represents the time-reversed case, that is, the frequency. Therefore, according to these parameters, the fitting result is demonstrated in Fig. 4(h). As it can be seen from the yellow dashed line, the fitting results are well matched with the simulation results. And the slight mismatch of the second peak may be attributed to errors and losses during the simulation.

To verify the effect of width of the slit on the LSPR effect more intuitively, we plotted the electric field distribution in the X-Z plane for two different widths of the slit. Figure 5(a) and Fig. 5(b) shows the electric field distribution of the metal grating slit structure in the X-Z plane at 6.56 µm and 12.3 µm when g = 1 µm, respectively. The wavelengths corresponding to the two peaks of the transmission curve in Fig. 4(g) (g = 1 µm) are 6.56 µm and 12.3 µm, respectively. It is worth noting that the electric field intensity at the slit for the wavelength is 6.56 µm is obviously stronger than that for the wavelength is 12.3 µm. This illustrates that the first transmission peak is higher than the second peak when g = 1 µm, which is consistent with the results in Fig. 4(g). In addition, Fig. 5(a) also indicates that the electric fields are almost concentrated on the edges of the gratings. This may be attributed to the horizontal LSPR mode induced by the horizontal periodic grating structure [62]. And we also plotted the electric field distribution of the structure in the X-Z plane at 10.5 µm and 14.3 µm in Fig. 5(c) and Fig. 5(d), respectively. From Fig. 5(a) and Fig. 5(c), it can be seen that the electric field of the slit in Fig. 5(a) is stronger than that in Fig. 5(c), which is also consistent of the result in Fig. 4(g). From Fig. 5(c), it is obviously clearly that there is no coupling between the left and right localized surface plasmons. In addition, from Fig. 5(b) Fig. 5(d), the electric fields are almost distributed at the upper and lower interface of the slit. This is the result of surface resonance excitation due to the interaction of the groove cavity mode with the in-phase groove re-emission mechanism. It is worth noticing that the electric field intensity concentrated on the upper and lower interface of the slit in Fig. 5(d) is obviously stronger than that in Fig. 5(b), which demonstrates the excitation of surface resonance in Fig. 5(d) is much stronger.

 

Fig. 5. The electric field distribution in the X-Z plane at a wavelength of (a) 6.56µm and (b) 12.3µm when g = 1µm. The electric field distribution in the X-Z plane at a wavelength of (c) 10.5µm and (d) 14.3µm when g = 5µm.

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In order to verify the absorption enhancement of the combination of the BP nanostrip array and the metal grating slit structure, we show the three-dimensional schematic diagram of the hybrid structure in Fig. 6(a). Front view of this structure was plotted in Fig. 6(b). Figure 6(c) shows the absorption spectra of the hybrid structure at the wavelength of 6-20 µm with three different distances. As it can be observed from the absorption curve, the absorption peak red shifts as the distance increases. And the maximum absorption peak is obtained when the distance is 2 µm. Actually, there is a focusing effect associated with the beam phenomenon. The beam with this focal length is the largest [51]. Therefore, this may be attributed to the fact that the largest electric field intensity of the converging beams is just in the BP layer when the distance between the BP nanostrip array and the metal grating slit structure is 2 µm. In order to evaluate the enhanced absorption effect, the absorption of the BP nanostrip array, the transmission of the metal grating slit and the absorption of the hybrid structure were depicted in Fig. 6(d) for comparison. The parameter of BP nanostrip array is selected as w = 150 nm and the thickness of quartz layer is set as 6 µm. The parameter of metal grating slit is set as f = 3 µm, h = 2 µm and g = 3 µm. As it can be seen from Fig. 6(d), the first absorption peak of hybrid structure is slightly higher compared than the major absorption peak of BP nanostrip array. The first absorption peak of the hybrid structure is 83.6% at 7.04 µm. In addition, we also can observe that there are three other absorption peaks at 10-20 µm in the absorption curve of the hybrid structure. In particular, the second absorption peak can even reach 99.92%. This is due to the fact that the high absorption is obtained by combining the LSPR effect produced by BP nanostrip array structure and EOT effect produced by metal grating slit structure. Firstly, when light passes through the metal grating slit structure, a very intense transmitted light is incident on the BP nanostrip array due to the enhancement of the transmission by the input grating and the effect of the output grating on the light convergence. Then through the Fabry-Perot cavity consisting of a metal mirror and a quartz layer, the light passes through the BP layer almost completely with reflection, which greatly increases the absorption of BP. And to better understand the cause of the absorption enhancement, the electric field distribution in the X-Z plane at the absorption peak of 8.9µm in Fig. 6(d) was demonstrated in Fig. 6(e). It can be seen that the enhanced transmitted light is mostly localized at the BP layer and the electric field intensity decreases significantly through BP layer, indicating the strong absorption in this absorptive layer. In addition, we also compared the absorption properties of the hybrid structure with different materials between the BP nanostrip and the Au grating. As demonstrated in Fig. 6(f), the absorption of the hybrid structure with MgF2 between the BP nanostrip and the Au grating is obviously weaker compared that without MgF2. This is due to the fact that the higher refractive index of MgF2 prevents some of the transmitted light from entering the BP layer, resulting in weak absorption. Therefore, placing nothing between the BP nanostrip and the Au grating will be the best choice. Above all, it can be seen that the absorption of BP with hybrid structure at mid-infrared band is obviously higher than that of the BP with nanostrip array structure. That is to say, by combining the LSPR and EOT effect, the well-confined LSPR response of BP at middle infrared band is realized.

 

Fig. 6. (a) Schematic diagram of the hybrid structure. (b) Front view of this hybrid structure, d is the distance between the BP nanostrip array and the metal grating slit structure. (c) Absorption spectra of the hybrid structure along x direction at the wavelength of 6-20 µm with three different distances (i.e., d = 1, 2 and 3 µm). (d) The absorption spectra of the BP nanostrip array, the transmission spectra of the metal grating slit structure and the absorption spectra of the hybrid structure. (e) The electric field distribution in the X-Z plane at the absorption peak of 8.9µm in Fig. 6(d). (f) Absorption spectra of the hybrid structure with different materials (i.e., air and MgF2) between the BP nanostrip and the Au grating.

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3. Conclusion

In conclusion, the hybrid structure consisting of BP nanostrip array and metal grating slit structure is proposed. By properly analyzing the absorption characteristics of the BP nanostrip array, the anisotropic behavior in the absorption spectra is predicted when exciting BP LSPR mode along two different directions (armchair and zigzag). And by changing the geometry dimensions, efficient tuning of the plasmon resonance can be facilitated. Besides, we also present a systematic investigation on the effect of transmission of the metal grating slit structure by transmission spectra and electric intensity distribution. By means of altering the dimension of the metal grating slit structure, the greatly enhanced transmission is obtained and the maximum transmission efficiency can almost reach 75% in optimal dimensions. At last, by combining the LSPR and EOT effect, the absorption characteristics of the hybrid structure are analyzed. The enhanced absorption can be achieved up to 99.92% at the resonance wavelength of 8.9 µm. To conclude, the high performance makes this hybrid structure an excellent candidate for all-optical and optoelectronic devices. Moreover, the results open up possibilities of devising BP-based plasmons in the application of optical electric detection and sensing at mid-infrared region.

Funding

National Key Research and Development Project (2018YFB2200500, 2018YFB2202800); National Natural Science Foundation of China (61534004, 61604112, 61622405, 61851406, 61874081).

Disclosures

The authors declare no conflicts of interest.

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References

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  1. F. Xia, H. Wang, D. Xiao, M. Dubey, and A. Ramasubramaniam, “Two-dimensional material nanophotonics,” Nat. Photonics 8(12), 899–907 (2014).
    [Crossref]
  2. F. H. Koppens, T. Mueller, P. Avouris, A. Ferrari, M. Vitiello, and M. Polini, “Photodetectors based on graphene, other two-dimensional materials and hybrid systems,” Nat. Nanotechnol. 9(10), 780–793 (2014).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  17. S. Ke, B. Wang, H. Huang, H. Long, K. Wang, and P. Lu, “Plasmonic absorption enhancement in periodic cross-shaped graphene arrays,” Opt. Express 23(7), 8888–8900 (2015).
    [Crossref]
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    [Crossref]
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    [Crossref]
  20. Z. Fang, Y. Wang, A. E. Schlather, Z. Liu, P. M. Ajayan, F. J. García de Abajo, P. Nordlander, X. Zhu, and N. J. Halas, “Active Tunable Absorption Enhancement with Graphene Nanodisk Arrays,” Nano Lett. 14(1), 299–304 (2014).
    [Crossref]
  21. X. Ni, L. Wang, J. Zhu, X. Chen, and W. Lu, “Surface plasmons in a nanostructured black phosphorus flake,” Opt. Lett. 42(13), 2659–2662 (2017).
    [Crossref]
  22. L. Han, L. Wang, H. Xing, and X. Chen, “Active Tuning of Midinfrared Surface Plasmon Resonance and Its Hybridization in Black Phosphorus Sheet Array,” ACS Photonics 5(9), 3828–3837 (2018).
    [Crossref]
  23. H. Wang, X. Wang, F. Xia, L. Wang, H. Jiang, Q. Xia, M. L. Chin, M. Dubey, and S. J. Han, “Black phosphorus radio-frequency transistors,” Nano Lett. 14(11), 6424–6429 (2014).
    [Crossref]
  24. M. Buscema, D. J. Groenendijk, S. I. Blanter, G. A. Steele, H. S. J. van der Zant, and A. Castellanos-Gomez, “Fast and broadband photoresponse of few-layer black phosphorus field-effect transistors,” Nano Lett. 14(6), 3347–3352 (2014).
    [Crossref]
  25. Y. Deng, Z. Luo, N. J. Conrad, H. Liu, Y. Gong, S. Najmaei, P. M. Ajayan, J. Lou, X. Xu, and P. D. Ye, “Black phosphorus-monolayer MoS2 van der Waals heterojunction p-n diode,” ACS Nano 8(8), 8292–8299 (2014).
    [Crossref]
  26. M. Buscema, D. J. Groenendijk, G. A. Steele, H. S. van der Zant, and A. Castellanos Gomez, “Photovoltaic effect in few-layer black phosphorus PN junctions defined by local electrostatic gating,” Nat. Commun. 5(1), 4651 (2014).
    [Crossref]
  27. M. Engel, M. Steiner, and P. Avouris, “Black phosphorus photodetector for multispectral, high-resolution imaging,” Nano Lett. 14(11), 6414–6417 (2014).
    [Crossref]
  28. Y. Du, C. Ouyang, S. Shi, and M. Lei, “Ab initio studies on atomic and electronic structures of black phosphorus,” J. Appl. Phys. 107(9), 093718 (2010).
    [Crossref]
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  44. D. A. Prishchenko, V. G. Mazurenko, M. I. Katsnelson, and A. N. Rudenko, “Coulomb interactions and screening effects in few-layer black phosphorus: a tight-binding consideration beyond the long-wavelength limit,” 2D Mater. 4(2), 025064 (2017).
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  49. N. Youngblood, C. Chen, S. J. Koester, and M. Li, “Waveguide-integrated black phosphorus photodetector with high responsitivity and low dark current,” Nat. Photonics 9(4), 247–252 (2015).
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  52. H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martinmoreno, F. J. Garciavidal, and T. W. Ebbesen, “Beaming Light from a Subwavelength Aperture,” Science 297(5582), 820–822 (2002).
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  56. J. Nong, W. Wei, W. Wang, G. Lan, Z. Shang, J. Yi, and L. Tang, “Strong coherent coupling between graphene surface plasmons and anisotropic black phosphorus localized surface plasmons,” Opt. Express 26(2), 1633–1644 (2018).
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  57. C. Fang, Y. Liu, G. Han, Y. Shao, Y. Huang, and Y. Hao, “Porous Structures for Absorption Enhancement in Black Phosphorus Active Layer Based on Plasmonic Nanocavity,” IEEE Photonics J. 9(6), 4800210 (2017).
  58. T. H. Isaac, J. Gómez Rivas, J. R. Sambles, W. L. Barnes, and E. Hendry, “Surface plasmon mediated transmission of subwavelength slits at THz frequencies,” Phys. Rev. B 77(11), 113411 (2008).
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2019 (1)

2018 (4)

Q. Fo, L. Pan, X. Chen, Q. Xu, C. Ouyang, and W. Zhang, “Anisotropic plasmonic response of black phosphorus nanostrip in terahertz metamaterials,” IEEE Photonics J. 10(3), 1–9 (2018).
[Crossref]

J. Nong, W. Wei, W. Wang, G. Lan, Z. Shang, J. Yi, and L. Tang, “Strong coherent coupling between graphene surface plasmons and anisotropic black phosphorus localized surface plasmons,” Opt. Express 26(2), 1633–1644 (2018).
[Crossref]

M. Gao, N. Zhang, D. Ji, H. Song, Y. Liu, and Q. Gan, “Super absorbing metasurfaces with hybrid Ag-Au nanostructures for surface-enhanced Raman spectroscopy sensing of drugs and chemicals,” Small Methods 2(7), 1800045 (2018).
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L. Han, L. Wang, H. Xing, and X. Chen, “Active Tuning of Midinfrared Surface Plasmon Resonance and Its Hybridization in Black Phosphorus Sheet Array,” ACS Photonics 5(9), 3828–3837 (2018).
[Crossref]

2017 (8)

X. Ni, L. Wang, J. Zhu, X. Chen, and W. Lu, “Surface plasmons in a nanostructured black phosphorus flake,” Opt. Lett. 42(13), 2659–2662 (2017).
[Crossref]

H. Lu, Y. Gong, D. Mao, X. Gan, and J. Zhao, “Strong plasmonic confinement and optical force in phosphorene pairs,” Opt. Express 25(5), 5255–5263 (2017).
[Crossref]

C. Fang, Y. Liu, G. Han, Y. Shao, Y. Huang, and Y. Hao, “Porous Structures for Absorption Enhancement in Black Phosphorus Active Layer Based on Plasmonic Nanocavity,” IEEE Photonics J. 9(6), 4800210 (2017).

C. Chen, N. Youngblood, R. Peng, D. Yoo, D. A. Mohr, and M. Li, “Three-Dimensional Integration of Black Phosphorus Photodetector with Silicon Photonics and Nanoplasmonics,” Nano Lett. 17(2), 985–991 (2017).
[Crossref]

R. Peng, K. Khaliji, N. Youngblood, R. Grassi, T. Low, and M. Li, “Mid-infrared Electro-Optic Modulation in Few-layer Black Phosphorus,” Nano Lett. 17(10), 6315–6320 (2017).
[Crossref]

F. Xiong, J. Zhang, Z. Zhu, X. Yuan, and S. Qin, “Strong anisotropic perfect absorption in monolayer black phosphorous and its application as tunable polarizer,” J. Opt. 19(7), 075002 (2017).
[Crossref]

J. Wang and Y. Jiang, “Infrared absorber based on sandwiched two-dimensional black phosphorus,” Opt. Express 25(5), 5206–5216 (2017).
[Crossref]

D. A. Prishchenko, V. G. Mazurenko, M. I. Katsnelson, and A. N. Rudenko, “Coulomb interactions and screening effects in few-layer black phosphorus: a tight-binding consideration beyond the long-wavelength limit,” 2D Mater. 4(2), 025064 (2017).
[Crossref]

2016 (8)

A. Nemilentsau, T. Low, and G. W. Hanson, “Anisotropic 2D Materials for Tunable Hyperbolic Plasmonics,” Phys. Rev. Lett. 116(6), 066804 (2016).
[Crossref]

Z. Liu and K. Aydin, “Localized surface plasmons in nanostructured monolayer black phosphorus,” Nano Lett. 16(6), 3457–3462 (2016).
[Crossref]

D. C. Serrano, J. S. Gomez-Diaz, A. A. Melcon, and A. Alù, “Black phosphorus plasmonics: anisotropic elliptical propagation and nonlocality-induced canalization,” J. Opt. 18(10), 104006 (2016).
[Crossref]

N. Mao, J. Tang, L. Xie, J. Wu, B. Han, and J. Zhang, “Optical Anisotropy of Black Phosphorus in the Visible Regime,” J. Am. Chem. Soc. 138(1), 300–305 (2016).
[Crossref]

X. Ling, S. Huang, E. H. Hasdeo, L. Liang, and M. S. Dresselhaus, “Anisotropic Electron-Photon and Electron-Phonon Interactions in Black Phosphorus,” Nano Lett. 16(4), 2260–2267 (2016).
[Crossref]

X. Wang and S. Lan, “Optical properties of black phosphorus,” Adv. Opt. Photonics 8(4), 618–655 (2016).
[Crossref]

Z. Bao, H. Wu, and Y. Zhou, “Edge plasmons in monolayer black phosphorus,” Appl. Phys. Lett. 109(24), 241902 (2016).
[Crossref]

W. Tang, L. Wang, X. Chen, C. Liu, A. Yu, and W. Lu, “Dynamic metamaterial based on the graphene split ring high-Q Fano-resonnator for sensing applications,” Nanoscale 8(33), 15196–15204 (2016).
[Crossref]

2015 (3)

S. Ke, B. Wang, H. Huang, H. Long, K. Wang, and P. Lu, “Plasmonic absorption enhancement in periodic cross-shaped graphene arrays,” Opt. Express 23(7), 8888–8900 (2015).
[Crossref]

K. Lam and J. Guo, “Plasmonics in strained monolayer black phosphorus,” J. Appl. Phys. 117(11), 113105 (2015).
[Crossref]

N. Youngblood, C. Chen, S. J. Koester, and M. Li, “Waveguide-integrated black phosphorus photodetector with high responsitivity and low dark current,” Nat. Photonics 9(4), 247–252 (2015).
[Crossref]

2014 (12)

J. Qiao, X. Kong, Z. Hu, F. Yang, and W. Ji, “High-mobility transport anisotropy and linear dichroism in few-layer black phosphorus,” Nat. Commun. 5(1), 4475 (2014).
[Crossref]

T. Low, R. Roldán, H. Wang, F. Xia, P. Avouris, L. M. Moreno, and F. Guinea, “Plasmons and screening in monolayer and multilayer black phosphorus,” Phys. Rev. Lett. 113(10), 106802 (2014).
[Crossref]

J. R. Piper and S. Fan, “Total Absorption in a Graphene Monolayer in the Optical Regime by Critical Coupling with a Photonic Crystal Guided Resonance,” ACS Photonics 1(4), 347–353 (2014).
[Crossref]

Y. C. Du, H. Liu, Y. X. Deng, and P. D. Ye, “Device Perspective for Black Phosphorus Field-Effect Transistors Contact Resistance, Ambipolar and Scaling,” ACS Nano 8(10), 10035–10042 (2014).
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F. Xia, H. Wang, D. Xiao, M. Dubey, and A. Ramasubramaniam, “Two-dimensional material nanophotonics,” Nat. Photonics 8(12), 899–907 (2014).
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F. H. Koppens, T. Mueller, P. Avouris, A. Ferrari, M. Vitiello, and M. Polini, “Photodetectors based on graphene, other two-dimensional materials and hybrid systems,” Nat. Nanotechnol. 9(10), 780–793 (2014).
[Crossref]

Z. Fang, Y. Wang, A. E. Schlather, Z. Liu, P. M. Ajayan, F. J. García de Abajo, P. Nordlander, X. Zhu, and N. J. Halas, “Active Tunable Absorption Enhancement with Graphene Nanodisk Arrays,” Nano Lett. 14(1), 299–304 (2014).
[Crossref]

H. Wang, X. Wang, F. Xia, L. Wang, H. Jiang, Q. Xia, M. L. Chin, M. Dubey, and S. J. Han, “Black phosphorus radio-frequency transistors,” Nano Lett. 14(11), 6424–6429 (2014).
[Crossref]

M. Buscema, D. J. Groenendijk, S. I. Blanter, G. A. Steele, H. S. J. van der Zant, and A. Castellanos-Gomez, “Fast and broadband photoresponse of few-layer black phosphorus field-effect transistors,” Nano Lett. 14(6), 3347–3352 (2014).
[Crossref]

Y. Deng, Z. Luo, N. J. Conrad, H. Liu, Y. Gong, S. Najmaei, P. M. Ajayan, J. Lou, X. Xu, and P. D. Ye, “Black phosphorus-monolayer MoS2 van der Waals heterojunction p-n diode,” ACS Nano 8(8), 8292–8299 (2014).
[Crossref]

M. Buscema, D. J. Groenendijk, G. A. Steele, H. S. van der Zant, and A. Castellanos Gomez, “Photovoltaic effect in few-layer black phosphorus PN junctions defined by local electrostatic gating,” Nat. Commun. 5(1), 4651 (2014).
[Crossref]

M. Engel, M. Steiner, and P. Avouris, “Black phosphorus photodetector for multispectral, high-resolution imaging,” Nano Lett. 14(11), 6414–6417 (2014).
[Crossref]

2013 (3)

S. Z. Butler, S. M. Hollen, L. Cao, Y. Cui, J. A. Gupta, H. R. Gutiérrez, T. F. Heinz, S. S. Hong, J. Huang, A. F. Ismach, E. Johnston-Halperin, M. Kuno, V. V. Plashnitsa, R. D. Robinson, R. S. Ruoff, S. Salahuddin, J. Shan, L. Shi, M. G. Spencer, M. Terrones, W. Windl, and J. E. Goldberger, “Progress, Challenges, and Opportunities in Two-Dimensional Materials Beyond Graphene,” ACS Nano 7(4), 2898–2926 (2013).
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S. Sekwao and J. P. Leburton, “Electrical tunability of soft parametric resonance by hot electrons in graphene,” Appl. Phys. 103(14), 143108 (2013).
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X. M. Wang, Z. Z. Cheng, K. Xu, H. K. Tsang, and J. B. Xu, “High Responsitivity Graphene/Silicon Heterostructure Waveguide Photodetectors,” Nat. Photonics 7(11), 888–891 (2013).
[Crossref]

2012 (5)

Q. H. Wang, K. Kalantar-Zadeh, A. Kis, J. N. Coleman, and M. S. Strano, “Electronics and optoelectronics of two-dimensional transition metal dichalcogenides,” Nat. Nanotechnol. 7(11), 699–712 (2012).
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J. Christensen, A. Manjavacas, S. Thongrattanasiri, Frank H. L. Koppens, and F. J. García de Abajo, “Graphene Plasmon Waveguiding and Hybridization in Individual and Paired Nanoribbons,” ACS Nano 6(1), 431–440 (2012).
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A. Yu Nikitin, F. Guinea, F. J. Garcia-Vidal, and L. Martin-Moreno, “Surface plasmon enhanced absorption and suppressed transmission in periodic arrays of graphene ribbons,” Phys. Rev. B 85(8), 081405 (2012).
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H. Yan, X. Li, B. Chandra, G. Tulevski, and F. Xia, “Tunable infrared plasmonic devices using graphene insulator stacks,” Nat. Nanotechnol. 7(5), 330–334 (2012).
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C. J. Badioli, M. Alonso-González, P. Thongrattanasiri, S. Huth, F. Osmond, and F. H. L. Koppens, “Optical Nano-Imaging of GateTunable Graphene Plasmons,” Nature 487(7405), 77–81 (2012).
[Crossref]

2011 (2)

S. C. H. Lui, Z. Q. Li, K. F. Mak, E. Cappelluti, and T. F. Heinz, “Observation of an electrically tunable band gap in trilayer graphene,” Nat. Phys. 7(12), 944–947 (2011).
[Crossref]

Y. Liu, R. Cheng, L. Liao, H. L. Zhou, J. W. Bai, G. Liu, L. X. Liu, Y. Huang, and X. F. Duan, “Plasmon resonance enhanced multicolour photodetection by graphene,” Nat. Commun. 2(1), 579 (2011).
[Crossref]

2010 (3)

F. Xia, D. B. Farmer, Y. Lin, and P. Avouris, “Graphene field-effect transistors with high on/off current ratio and large transport band gap at room temperature,” Nano Lett. 10(2), 715–718 (2010).
[Crossref]

Y. Du, C. Ouyang, S. Shi, and M. Lei, “Ab initio studies on atomic and electronic structures of black phosphorus,” J. Appl. Phys. 107(9), 093718 (2010).
[Crossref]

Ø Prytz and E. Flage-Larsen, “The influence of exact exchange corrections in vander Waals layered narrow bandgap black phosphorus,” J. Phys.: Condens. Matter 22(1), 015502 (2010).
[Crossref]

2009 (1)

F. OuYang, J. Xiao, R. Guo, H. Zhang, and H. Xu, “Transport properties of T-shaped and crossed junctions based on graphene nanoribbons,” Nanotechnology 20(5), 055202 (2009).
[Crossref]

2008 (1)

T. H. Isaac, J. Gómez Rivas, J. R. Sambles, W. L. Barnes, and E. Hendry, “Surface plasmon mediated transmission of subwavelength slits at THz frequencies,” Phys. Rev. B 77(11), 113411 (2008).
[Crossref]

2007 (1)

T. V. Teperik, V. V. Popov, and F. J. García de Abajo, “Total light absorption in plasmonic nanostructures,” J. Opt. A: Pure Appl. Opt. 9(9), S458–S462 (2007).
[Crossref]

2005 (1)

2003 (4)

F. J. García-Vidal, H. J. Lezec, T. W. Ebbesen, and L. Martín-Moreno, “Multiple Paths to Enhance Optical Transmission through a Single Subwavelength Slit,” Phys. Rev. Lett. 90(21), 213901 (2003).
[Crossref]

S. Fan and W. Suh, “Temporal coupled-mode theory for the Fano resonance in optical resonators,” J. Opt. Soc. Am. A 20(3), 569–572 (2003).
[Crossref]

A. Melloni, F. Morichetti, and M. Martinelli, “Optical slow wave structures,” Opt. Photonics News 14(11), 44–48 (2003).
[Crossref]

F. J. Garciavidal, L. Martinmoreno, H. J. Lezec, and T. W. Ebbesen, “Focusing light with a single subwavelength aperture flanked by surface corrugations,” Appl. Phys. Lett. 83(22), 4500–4502 (2003).
[Crossref]

2002 (2)

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martinmoreno, F. J. Garciavidal, and T. W. Ebbesen, “Beaming Light from a Subwavelength Aperture,” Science 297(5582), 820–822 (2002).
[Crossref]

S. Collin, F. Pardo, R. Teissier, and J. L. Pelouard, “Horizontal and vertical surface resonances in transmission metallic gratings,” J. Opt. A: Pure Appl. Opt. 4(5), S154–S160 (2002).
[Crossref]

2001 (1)

1983 (1)

S. Narita, Y. Akaham, Y. Tsukiyama, K. Muro, S. Mori, S. Endo, M. Taniguchi, M. Seki, S. Suga, A. Mikuni, and H. Kanzaki, “Electrical and optical properties of black phosphorus single crystals,” Physica 117-118, 422–424 (1983).
[Crossref]

1981 (1)

Y. Maruyama, S. Suzuki, K. Kobayashi, and S. Tanuma, “Synthesis and some properties of black phosphorus single crystals,” Physica 105(1-3), 99–102 (1981).
[Crossref]

Ajayan, P. M.

Z. Fang, Y. Wang, A. E. Schlather, Z. Liu, P. M. Ajayan, F. J. García de Abajo, P. Nordlander, X. Zhu, and N. J. Halas, “Active Tunable Absorption Enhancement with Graphene Nanodisk Arrays,” Nano Lett. 14(1), 299–304 (2014).
[Crossref]

Y. Deng, Z. Luo, N. J. Conrad, H. Liu, Y. Gong, S. Najmaei, P. M. Ajayan, J. Lou, X. Xu, and P. D. Ye, “Black phosphorus-monolayer MoS2 van der Waals heterojunction p-n diode,” ACS Nano 8(8), 8292–8299 (2014).
[Crossref]

Akaham, Y.

S. Narita, Y. Akaham, Y. Tsukiyama, K. Muro, S. Mori, S. Endo, M. Taniguchi, M. Seki, S. Suga, A. Mikuni, and H. Kanzaki, “Electrical and optical properties of black phosphorus single crystals,” Physica 117-118, 422–424 (1983).
[Crossref]

Alonso-González, M.

C. J. Badioli, M. Alonso-González, P. Thongrattanasiri, S. Huth, F. Osmond, and F. H. L. Koppens, “Optical Nano-Imaging of GateTunable Graphene Plasmons,” Nature 487(7405), 77–81 (2012).
[Crossref]

Alù, A.

D. C. Serrano, J. S. Gomez-Diaz, A. A. Melcon, and A. Alù, “Black phosphorus plasmonics: anisotropic elliptical propagation and nonlocality-induced canalization,” J. Opt. 18(10), 104006 (2016).
[Crossref]

Avouris, P.

T. Low, R. Roldán, H. Wang, F. Xia, P. Avouris, L. M. Moreno, and F. Guinea, “Plasmons and screening in monolayer and multilayer black phosphorus,” Phys. Rev. Lett. 113(10), 106802 (2014).
[Crossref]

M. Engel, M. Steiner, and P. Avouris, “Black phosphorus photodetector for multispectral, high-resolution imaging,” Nano Lett. 14(11), 6414–6417 (2014).
[Crossref]

F. H. Koppens, T. Mueller, P. Avouris, A. Ferrari, M. Vitiello, and M. Polini, “Photodetectors based on graphene, other two-dimensional materials and hybrid systems,” Nat. Nanotechnol. 9(10), 780–793 (2014).
[Crossref]

F. Xia, D. B. Farmer, Y. Lin, and P. Avouris, “Graphene field-effect transistors with high on/off current ratio and large transport band gap at room temperature,” Nano Lett. 10(2), 715–718 (2010).
[Crossref]

Aydin, K.

Z. Liu and K. Aydin, “Localized surface plasmons in nanostructured monolayer black phosphorus,” Nano Lett. 16(6), 3457–3462 (2016).
[Crossref]

Badioli, C. J.

C. J. Badioli, M. Alonso-González, P. Thongrattanasiri, S. Huth, F. Osmond, and F. H. L. Koppens, “Optical Nano-Imaging of GateTunable Graphene Plasmons,” Nature 487(7405), 77–81 (2012).
[Crossref]

Bai, J. W.

Y. Liu, R. Cheng, L. Liao, H. L. Zhou, J. W. Bai, G. Liu, L. X. Liu, Y. Huang, and X. F. Duan, “Plasmon resonance enhanced multicolour photodetection by graphene,” Nat. Commun. 2(1), 579 (2011).
[Crossref]

Bao, Z.

Z. Bao, H. Wu, and Y. Zhou, “Edge plasmons in monolayer black phosphorus,” Appl. Phys. Lett. 109(24), 241902 (2016).
[Crossref]

Barnes, W. L.

T. H. Isaac, J. Gómez Rivas, J. R. Sambles, W. L. Barnes, and E. Hendry, “Surface plasmon mediated transmission of subwavelength slits at THz frequencies,” Phys. Rev. B 77(11), 113411 (2008).
[Crossref]

Blanter, S. I.

M. Buscema, D. J. Groenendijk, S. I. Blanter, G. A. Steele, H. S. J. van der Zant, and A. Castellanos-Gomez, “Fast and broadband photoresponse of few-layer black phosphorus field-effect transistors,” Nano Lett. 14(6), 3347–3352 (2014).
[Crossref]

Bolivar, P. H.

Buscema, M.

M. Buscema, D. J. Groenendijk, S. I. Blanter, G. A. Steele, H. S. J. van der Zant, and A. Castellanos-Gomez, “Fast and broadband photoresponse of few-layer black phosphorus field-effect transistors,” Nano Lett. 14(6), 3347–3352 (2014).
[Crossref]

M. Buscema, D. J. Groenendijk, G. A. Steele, H. S. van der Zant, and A. Castellanos Gomez, “Photovoltaic effect in few-layer black phosphorus PN junctions defined by local electrostatic gating,” Nat. Commun. 5(1), 4651 (2014).
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F. Xiong, J. Zhang, Z. Zhu, X. Yuan, and S. Qin, “Strong anisotropic perfect absorption in monolayer black phosphorous and its application as tunable polarizer,” J. Opt. 19(7), 075002 (2017).
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Nanoscale (1)

W. Tang, L. Wang, X. Chen, C. Liu, A. Yu, and W. Lu, “Dynamic metamaterial based on the graphene split ring high-Q Fano-resonnator for sensing applications,” Nanoscale 8(33), 15196–15204 (2016).
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Figures (6)

Fig. 1.
Fig. 1. (a) Schematic diagram of BP crystal structure. (b)The three-dimensional schematic diagram of BP nanostrip array.
Fig. 2.
Fig. 2. (a) Absorption spectra of the monolayer BP nanostrip array with quartz along x direction, y direction and without quartz at the wavelength of 6-30 µm. The thickness of the quartz between BP and metal mirror is 3 µm. The width of the BP strip is 150 nm and the period is 300 nm. (b) Absorption spectra of the monolayer BP nanostrip along x direction at the wavelength of 6-30 µm. The thickness of the quartz between BP and metal mirror is 3 µm and 6 µm, respectively. The width of the BP strip is 150 nm and the period is 300 nm. Electric field intensity distributions with the fixed thickness of 6 µm (c) and 3 µm (d). Inset is the side view of the proposed structure. The width of the BP strip is 150 nm and the period is 300 nm. (e) Calculated total electric field intensity for one BP nanostrip unit cell in Y-Z plane. The thickness of the quartz between BP and metal mirror is 6 µm. The width of the BP strip is 150 nm and the period is 300 nm. (f). Absorption spectra of BP nanostrip arrays for various values of Fermi levels between 0.2 eV and 1 eV. The thickness of the quartz between BP and metal mirror is 3 µm. The width of the BP strip is 150 nm and the period is 300 nm.
Fig. 3.
Fig. 3. (a) Absorption spectra of the monolayer BP nanostrip array along x direction at the wavelength of 6-30 µm at six different widths (i.e., width = 50, 70, 90, 110, 130 and 150 µm) with a fixed thickness of the quartz of 6 µm. (b) The enlarged view of the first absorption peak in dotted box of Fig. 3(a).
Fig. 4.
Fig. 4. (a) Schematic diagram of metal grating slit structure, f is the period of grating, h is the height of the grating, g is the width of slit and H is the height of slit. Inset is the side view of the gap, $\theta $ presents the angle of incident light. (b) The front view of input grating structure and (c) output grating structure. (d) Transmission spectral of the metal grating slit of three different structures. (e)Transmission spectral of the metal grating slit at the wavelength of 6-20 µm with three different periods (i.e., f = 1, 2, and 3 µm) of the grating. (f) Transmission spectral of the metal grating slit at the wavelength of 6-20 µm with four different heights (i.e., h = 2, 2.5, 3, and 3.5 µm) of the grating. (g) Transmission spectral of the metal grating slit at the wavelength of 6-20 µm with three different slit widths (i.e., g = 1, 3, and 5 µm) of the slit. (h) Transmission spectral for various incident angles of the metal grating slit. The yellow dotted line is the fitting result of coupled-mode theory of metal grating structure in the case of vertical incidence.
Fig. 5.
Fig. 5. The electric field distribution in the X-Z plane at a wavelength of (a) 6.56µm and (b) 12.3µm when g = 1µm. The electric field distribution in the X-Z plane at a wavelength of (c) 10.5µm and (d) 14.3µm when g = 5µm.
Fig. 6.
Fig. 6. (a) Schematic diagram of the hybrid structure. (b) Front view of this hybrid structure, d is the distance between the BP nanostrip array and the metal grating slit structure. (c) Absorption spectra of the hybrid structure along x direction at the wavelength of 6-20 µm with three different distances (i.e., d = 1, 2 and 3 µm). (d) The absorption spectra of the BP nanostrip array, the transmission spectra of the metal grating slit structure and the absorption spectra of the hybrid structure. (e) The electric field distribution in the X-Z plane at the absorption peak of 8.9µm in Fig. 6(d). (f) Absorption spectra of the hybrid structure with different materials (i.e., air and MgF2) between the BP nanostrip and the Au grating.

Equations (9)

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ε j = ε r + i σ j s ω ε 0
σ j = i D j π ( ω + i η )
D j = π e 2 n m j
m x = 2 2 γ 2 Δ + η c , m y = 2 v c
n = ( π 2 ) 1 ( m x m y ) 0.5 k B T ln [ 1 + exp ( E F / k B T ) ]
λ s p j = c 2 π m j ε 0 ( ε 1 + ε 2 ) p ζ n e 2
S  =  C  +  d k j ( ω ω 0 ) + 1 / 1 τ τ
S 1  = exp ( j ϑ ) { [ r j v j v r ] + 1 / 1 τ τ j ( ω ω 0 ) + 1 / 1 τ τ [ ( r ± j v ) ( r ± j v ) ( r ± j v ) ( r ± j v ) ] }
T  = 1 -  r 2 ( ω ω 0 ) 2 + v 2 ( 1 / 1 τ τ ) 2 + 2 r v ( ω ω 0 ) ( 1 / 1 τ τ ) ( ω ω 0 ) 2 + ( 1 / 1 τ τ ) 2

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