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Abstract
High-contrast gratings (HCGs) can be designed as a resonator with high-quality factor and surface-normal emission, which are excellent characters for designing optical devices. In this work, we combine HCGs with plasmonic graphene structure to achieve an ultrathin five-band coherent perfect absorber (CPA). The presented CPA can achieve multi- and narrow-band absorption with high intensity under a relatively large incident angle. The good agreement between theoretical analysis and numerical simulated results demonstrates that our proposed HCGs-based structure is feasible to realize CPA. Besides, by dynamically adjusting the Fermi energy of graphene, we realize the active tunability of resonance frequency and absorption intensity simultaneously. Benefitting from the combination of HCGs and the one-atom thickness of graphene, the proposed device possesses an extremely thin feature. Our work proposes a novel method to manipulate coherent perfect absorption and is helpful to design tunable multi-band and ultrathin absorbers.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
As a promising application, absorber has been one of the leading topics in a variety of applications ranging from photodetectors to stealth technologies [1–8]. Up to now, much effort has been devoted to realize perfect or enhanced absorption [9–18]. In general, the traditional absorber is usually made up of metal by eliminating transmission and minimizing reflection in a sandwiched structure [19,20]. Additionally, perfect absorption can be also realized by exploiting critical coupling effect. When leakage rate equals to absorption rate, other energy loss channels are blocked and all the incident light will be absorbed [21,22]. Unfortunately, these methods suffer from some drawbacks. For the traditional absorber, it’s not easy to obtain the actively tunable resonance peak. That is to say, once the structure is designed, the resonance peak is fixed. In this condition, the device has to be remanufactured when one wants to tune the resonance peak. The second method by exploiting coupling effect is confronted with technical challenge, because it is very difficult to maintain the equivalence of coupling rate and dissipative rate. Besides, a common shortcoming of these two methods is that the absorption intensity cannot be dynamically tuned. Considering the above two problems, it is necessary to design an absorber with active tunability for resonance frequency and absorption intensity simultaneously.
In 2010, researchers designed a two-port absorber, which is called CPA and it was firstly and theoretically proposed by Chong et al. [23]. It is demonstrated that time-reversal symmetry of spectral singularities gives rise to the CPA condition [24–29]. From then on, CPA-based devices have attracted increased interest and have been realized with different materials, including graphene and black phosphorus [30–32]. Especially, graphene as a promising platform in optics and optoelectronics has aroused attention due to its linear and nonlinear optical response [33–36]. In nonlinear graphene plasmonics [37], the enhancement of nonlinear performance results from the large propagation wave vectors and light confinement factors. The extinction ratio of the all-optical nonlinear graphene plasmonic switch can also be adjusted by changing the electric field amplitude of the pump light, which leads to a tunability of absorptivity. In this work, we are mainly concerned about the linear optical response of graphene in CPA. Graphene-based CPA has deserved to be explored for achieving modulation depth and spectral shift [38–42], which owes to the tunable Fermi energy of graphene through surface doping and gating voltage configurations [43–46]. However, multi-band CPA based on graphene has not been fully investigated [47–49]. To realize the full potential of optical data channels, multi-channel optical data processing is very important. Therefore, realization of multi-band CPA requires more effective methods. It has been known that optical grating is one of the most fundamental building blocks in optics. In particular, subwavelength gratings have been widely investigated for many years and continue to be an active research area even now. Afterwards, one new type of grating structure, known as the high-contrast grating (HCG), has been proposed, which is composed of periodic high-index materials fully surrounded by low-index materials. HCGs were shown to behave as an optical resonator with high-quality factor, which can be designed as a narrow-band device.
Inspired by this, we propose to use graphene coupled with HCGs to realize tunable ultrathin and multi-band CPA device. Numerical results from finite-difference time-domain (FDTD) simulations demonstrate an excellent consistence with the coupled mode theory (CMT), which further verifies the accuracy of theoretical models and provides further physical insights. By controlling the relative phase of two coherent beams, a flexible tunability of absorption intensity from 98.9% to 0.15% is achieved, which shows the potential application for photoswitch. This modulation depth of 98.75% is quite large, considering that the thickness of our structure is less than 1/1571 of the operation wavelength. In addition to the tunability and multi-band features, the compactness is another significant advantage for our proposed structure. Additionally, we study the spectral response under the illumination of transverse electric (TE) and magnetic (TM) polarized incident waves. Furthermore, the influence of grating periods and structure dimensions on the optical properties of the CPA are investigated in detail. The Brewster’s angle elucidates the dependence of incident angle on spectral response. More importantly, our proposed system is extremely thin with subwavelength thickness on the order of λ0/857−λ0/1571, where λ0 is the operation wavelength. To some extent, these outstanding properties of the proposed CPA demonstrate a great potential for applications in modulators, signal processors and switches.
2. Design and simulations
In this part, we introduce the numerical model in this study and perform simulations using FDTD in the designed structure. The schematic of the proposed system is depicted in Fig. 1. The unit cell composed of a monolayer graphene embedded into the gratings is arranged in a periodic array with a lattice constant P = 70 nm. Initially, HCGs are comprised of high-index material Si (nH = 3.42) and low-index material SiO2 (nL = 1.45), and ambient medium is supposed to be air. The width, height of grating, and the thickness of graphene are set to w = 35 nm, t = 20 nm and Δ = 1 nm, respectively. It is assumed that the system is infinitely large along z-direction. In such a system, we set two electromagnetic waves to propagate from opposite sides. Here, we treat A+ as a forward beam (irradiate towards y+) and A- as a backward beam (irradiate towards y-), respectively, while B+ and B- are output beams. For simplicity, the two input beams are set as plane waves with equal amplitude A ($|{{A_ + }} |= |{{A_ - }} |$) throughout this work. The transfer matrix formalism is used to theoretically analyze the propagation of incident waves and their interactions. Then, the output waves (B±) can be expressed as [42]:
Fig. 1. Schematic diagram of our proposed CPA. A+ and A- represent the amplitudes of input beams, while B+ and B- represent the amplitudes of output waves. This system is composed of graphene and diffraction grating with period P = 70 nm, t = 20 nm and w = 35 nm.
Besides, the graphene film is modeled as a thin layer with the thickness Δ = 1 nm. In mid-infrared region, graphene can be characterized by complex surface conductivity ${\sigma _{GR}} = {\sigma _{{\mathop{\rm int}} er}}\textrm{ + }{\sigma _{{\mathop{\rm int}} ra}}$[50]. In infrared and lower terahertz region, the case where ${E_f} \ge 2{k_B}T$, contribution originating from interband transmission is negligible due to Pauli exclusion principle. Therefore, the conductivity of graphene can be modeled by Drude-like model: ${\sigma _{GR}}(\omega ) = \frac{{i{e^2}}}{{\pi {\hbar ^2}}}\frac{{{E_f}}}{{\omega + i{\tau ^{ - 1}}}}$. Here, $T$ is operation temperature, e is the charge of electron, $\hbar$ is the Planck’s constant, ${k_B}$ is Boltzmann constant, $\omega$ is angular frequency of the incident light, ${E_f}$ is Fermi level and $\tau$ is carrier relaxation time, respectively. In our simulation, Fermi energy of graphene is assumed to ${E_f}\textrm{ = }0.5\textrm{ }e\textrm{V}$.
In our manuscript, graphene is continuous without pattern, which brings great convenience to graphene manufacturing. The manufacturing of grating can use a simple two-step fabrication process including optical lithography and silicon etching [51]. Our proposed system can be fabricated by the preparation method similar to sandwich structure. First, the prepared graphene is transferred onto the bottom grating layer using a wet transfer method [52]. Subsequently, a second optical lithography process was carried out to pattern the same grating layer, then putting onto graphene.
3. Results and discussions
In general, incident energy is transmitted to a system through a single channel. Based on this context, using the structure in Fig. 1, it is assumed that a plane wave is incident on one side of the system in y-axis direction. In this case, the part of energy will be absorbed, while others will be reflected and transmitted. We can numerically calculate reflection and transmission coefficients, then the absorption can be obtained. As shown in Fig. 2(a), typical resonance responses and absorption enhancement are displayed at around 6.02 µm and 7.73 µm. It is not difficult to prove that the absorption enhancement should be ascribed to graphene surface plasmons (GSPs). The localized electronic excitations strongly couple to and trap the incident light, and enhance the absorption in the surrounding absorption layer. To better understand this optical response and make full use of the absorption, we make detailed calculations and analysis of its electric field distributions under different working frequencies, as shown in Figs. 2(c) and 2(d). Clearly, electric field amplitudes at λ = 6.03 µm and 7.73 µm can reach a larger value than that of incident light, which originates from the excitation of GSPs. It can be found that the phase of resonant wavelength at 7.73 µm has a $2\pi$ conversion, which is called first-order mode (M1). Besides, as shown in Fig. 2(d), it has a phase shift of $4\pi$ in one period, which is called second-order mode (M2). In Fig. 2(a), it is worth noting that absorptivity of 50% is the maximum value in a single channel system. For a thin film, the incoherent absorption ${A^{inc}}$ is related to self-consistent amplitude $\eta$, which can be written as ${A^{inc}} ={-} 2{\eta ^2} - 2\eta$. In our system, graphene is an ultrathin film with symmetric environments, which results in the same refractive index of upper and lower sides of the system. Thus, Fresnel reflection and transmission coefficients are written as $r = \eta$ and $t = 1 + \eta$, respectively. Apparently, ${A^{inc}}$ gets its maximum of 0.5 when $r = {{\textrm{ - }1} / 2}$, $t = {1 / 2}$, $\eta = \textrm{ - }{1 / 2}$. Here, $A_{\max }^{inc} = 0.5$ is called the limit of incoherent absorption.
Fig. 2. (a) The simulated absorption spectra of the graphene-based structure under illumination of single source. (b) Absorption spectra corresponding to the structure with HCGs and LCGs under illumination of two sources. The electric-field (Ey) (in the plane of y = 0) distributions of the unit cell for M1 (c) and M2 (d).
It has been known that the simplest method of overcoming the maximum absorption limit in a single channel system is to employ a back mirror or Bragg mirror. Such a system can block the transmission channel in asymmetric environment. However, if one wants to overcome the limit of 50% in a symmetric system, this method is no longer applicable. Fortunately, this problem can be solved by rationally exploiting two beams because absorption efficiency can be greatly improved by wave interference. Interference is a common wave phenomenon when two or more coherent waves overlap, which will lead to spatial redistribution of energy. For comparing with the condition of single source, we show the simulated spectra when two coherent beams illuminate onto the structure from opposite sides with other parameters fixed. The transmission of beam A will interfere with the reflection of beam B, and the transmission of beam B will also interfere with the reflection of beam A, finally leading to coherent absorption. To verify the enhanced absorption, we plot the spectra in Fig. 2(b). As can be seen that absorption intensity is larger than that of incoherent absorption in Fig. 2(a). Certainly, the absorptivity at M2 is nearly 100%. However, the absorptivity is only 96.18% at M1. This is because the reflection coefficient has a difference with transmission coefficient, which is not conform to the condition of CPA.
HCGs in our proposed structure are crucial to the excitation of GSPs. For comparison, we plot the spectra response corresponding to different structures with HCGs and LCGs, respectively. Here, the refractive index of LCGs is set to nH = 1.45, nL = 1 and ambient medium is supposed to be air. In the presence of HCGs, the blue curve corresponds to the high absorption at resonance wavelength. However, the red curve shows that there is no resonance response when we replace HCGs with LCGs. This optical response clearly indicates that HCGs play a significantly important role in the effective excitation of GSPs. To demonstrate the proposed physical mechanism, we show the electric field distributions in Figs. 2(c) and 2(d). The results clearly show that GSPs are located between the interface of graphene and silicon media in y direction. The detailed analysis of these two modes has been explained above.
The transmission behavior can be illustrated by the typical CMT. We plot the FDTD-simulated (balls) and CMT-calculated (lines) spectra under the condition of single source. Using CMT, the energy amplitude for the system with resonance frequency can be expressed as [53]:
Fig. 3. (a) Calculated transmission, reflection, and absorption spectra are labeled by red, green, and blue balls, respectively. Theoretical results are labeled by solid black line. (b) Absolute values, real and imaginary parts of the effective surface conductivities of graphene.
Having studied the mechanism of CPA, the effect of geometrical features on the absorption can be easily understood. In order to optimize absorption efficiency, we give the detailed calculation and analysis in Fig. 4, which contains the period P, width w, height t and refractive index (RI) of the background. As can be seen from Fig. 4(a), resonance positions show a redshift when the period changes from 60 nm to 90 nm. The excited resonance frequency of the mode is calculated as ${\omega _0} = \sqrt {{{2{e^2} \times {E_f}} / {{h^2}{\varepsilon _0}({\varepsilon _{r1}} + {\varepsilon _{r2}})P}}}$, where ${\varepsilon _{r1}}$, ${\varepsilon _{r2}}$ and P are the material permittivity above and below the graphene, grating period, respectively. From this formula, we can infer that resonance frequency is inversely proportional to $\sqrt P$ approximately. In other words, increasing P leads to a decrease of resonance frequency, which is in agreement with the simulation results.
Fig. 4. (a) Numerically simulated absorption of the CPA with various P. (b) The wavelength at the absorption window as a function of the width of Si, which varies from 35 to 55 nm with interval of 5 nm. (c) Absorption spectra for different t. (d) Dependence of the absorption spectra on different refractive indices of the surrounding medium when other parameters are fixed.
Figure 4(b) describes the evolution of absorption spectra with varying w. Apparently, resonance wavelengths show a redshift variation as w changes from 35 nm to 55 nm, which originates from the change of effective permittivity. Increasing the width of Si is equivalent to increase the effective permittivity when the period is fixed, resulting in a pronounced redshift. Our simulated result is consistent with the former research [55]. For an absorber, it is very meaningful to increase absorptivity. For example, in terms of energy harvesting, a higher absorption means a less energy dissipation. From Figs. 4(a)-(b), we can find that absorptivity at certain resonance wavelengths still keep high in spite of the change of P and w. This characteristic enables the absorber to change the resonance wavelength without reducing the absorption performance, which plays a modulating role in fabrication. In addition, different modes possess different absorption intensities, so the mode with high absorption intensity could be precisely chosen in the application.
Next, the dependence of absorption spectra on thickness of Si is shown in Fig. 4(c). It is demonstrated that CPA can be achieved under a wide range with thickness values changing from 3 to 22.5 nm. In fact, CPA still can be obtained when t reaches to 200 nm (not shown here). This is really crucial to the practical implementation of the proposed device, since the thickness of ultrathin grating layer might be slightly changed during the fabrication process. Interestingly, the absorption characteristic of M1 is different from that of M2 with increasing t. For M1, the resonance wavelength shows a dramatical redshift as we gradually increase t. For M2, resonance wavelength also shows a dramatical redshift only in the region of 3 to 10 nm, while it tends to be a stable value with increasing t from 10 to 22.5 nm. This interesting result can be well explained by the distribution of electric field. As can be seen from Fig. 2(c) that the electric field energy is concentrated in the graphene layer and grating layer, indicating that the graphene and grating both dominate in M1. Consequently, the absorption performance will be changed with tuning the dimension of grating when the parameter of graphene is fixed. Similarly, for M2, the electric field energy is concentrated in the graphene layer and Si grating layer from 3 to 10 nm, which presents the same tendency as M1. However, when t is larger than 10 nm, there is almost no electric field energy concentrated in the system, so resonance wavelength tends to be a stable value. Additionally, above results indicate that the thickness of the proposed structure can in principle be as low as 7 nm, which is much thin compared to previously proposed structures [56–58]. Hence, the currently presented structure achieves a CPA response with a much more compact and subwavelength thin configuration. These results provide a reference for the optimization of optical performance in CPA.
The electric field distribution is a result of electromagnetic waves coupling with each other in the whole surrounding medium. It is affected by the shape of the irradiated structure, the wavelength of incident light, and the RI of whole surrounding medium. According to this background, we show the dependence of absorption spectra on different RI of the surrounding medium when other parameters are fixed, and t is set to 20 nm. Here, the value of the background index in the FDTD simulation increases from 1 to 1.5. As can be seen from Fig. 4(d), M2 almost remains unchanged with changing RI of the surrounding medium. Overall, M1 shows a different tendency comparing with M2, which origins from the distribution of electric field of M1. As shown in Fig. 2(c), the electric field energy for M1 not only concentrates in graphene and Si, but also in the air. Therefore, the change of RI induces the shift of spectra response. However, for M2, there is barely electric field when t is larger than 10 nm. So, resonance wavelength for M2 remains unchanged with changing RI of the surrounding medium. The exhibited sensitivity of the resonance wavelength to RI also suggests further possible application as a sensor device.
4. Five-band absorber
In many practical applications, multi-band absorbers are all-important for spectroscopic imaging, sensing and detectors, because the multi-band absorber can selectively detect the frequency and has strong interference-free ability to the surrounding environment. For this purpose, we optimize parameters to obtain multi-band CPA and the corresponding spectral curve is shown in Fig. 5(a). In this section, the structural dimensions are as follows: P = 100 nm, w = 75 nm, and Fermi energy is set to 0.5 eV. It is clear that five absorption bands can be gained. Figures 5(b)-(f) show distributions of electric field for the five resonance wavelengths. Compared with previously reported CPA devices, our proposed system offers clear advantages over other designs, especially in thickness and multi-band absorption. Firstly, our proposed structure is simple, perfectly symmetric and compact, which is beneficial for spectroscopic applications. Compared with other cross-shape and multi-layer structures [48,59], our design is easier and more convenient to prepare. Secondly, considering the requirement of multi-channel in data processing, our proposed design can realize five bands absorption, which is more than that of other works [60]. Additionally, relative to the previous CPA systems with thickness of few hundred nanometers, our proposed system is extremely thin with thickness as low as 7 nm, which provides the opportunity to realize integrated electronic devices. Consequently, in some extent, our proposed system is more superior in structural property and CPA performance.
Fig. 5. (a) The simulated absorption of CPA under P = 100 nm, w = 75 nm. (b-f) The electric-field (Ez) (in the plane of y = 0) distributions at the five resonance wavelengths.
Most of absorbers have the limitation of fixed absorption intensity. For some applications, it is expected to keep absorption frequency constant and regulate absorption intensity. Therefore, the tunability of absorption intensity is also crucial. The three-dimensional map in Fig. 6(a) describes normalized absorption intensity as a function of phase difference from 0 to $4\pi$. For more intuitive, the corresponding two-dimensional map is plotted in the inset of Fig. 6(b). A proper phase modulation of the input coherent beams leads to destructive interference. The destructive interference prevents the scatting output from escaping the absorption channel, indicating a complete absorption of the coherent input beams. More importantly, the corresponding absorption intensity can be tuned from 98.9% to 0.15%. Note that this modulation depth of 98.75% is quite large, considering that the thickness of our structure is less than 1/1571 of the operation wavelength. These results demonstrate that the propagating coherent signal can be modulated between almost completely absorbed and transparent state. With this characteristic, the structure we introduced can be flexibly switched between ON and OFF by adjusting the phase difference. In addition, in terms of data processing, this property of CPA allows one optical signal to be strongly regulated by another coherent optical signal without the need for material nonlinearity, which provides a route towards the realization of optical switches [61] and logical gates [62].
Fig. 6. Dependence of the normalized total output intensities on the phase difference for three-dimensional map (a) and two-dimensional map (b). (c) Normalized total output intensities as a function of phase modulation at one of the resonance wavelengths. (d) Absorption as a function of wavelength and Fermi energy with other parameters fixed.
Compared with metal-based micro/nanostructures, one of the main advantages of graphene-based hybrid metamaterials is the active tunability of resonance frequency. At present, most of CPA is only used for adjusting the absorption intensity, but the resonance frequency cannot be effectively tuned. In this work, the system we proposed can realize the tunability of resonance frequency and absorption intensity simultaneously. In the following calculations, we only change the Fermi energy of graphene with other parameters fixed to investigate the active tunability. As mentioned above, the charge-carrier density in graphene can be altered through tuning electronic doping, which makes graphene a potential material for the wide-tunable modulator. As shown in Fig. 6(d), the CPA shows a blueshift with the increase of Fermi energy [55], while the absorption intensity still maintains the high level. This tunability characteristic of graphene-based CPA makes it more attractive than metal-based devices that cannot efficiently tune optical responses. In fact, the effect on CPA originates from the real and imaginary parts of graphene conductivity. Especially, benefitting from the excitation of GSPs, graphene enhances the adjustment of absorption, which reduces the gain coefficient in the system. Consequently, we simultaneously realized absorption modulation by utilizing phase difference of coherent beams and the active tunability of wavelength by changing Fermi energy of graphene.
Figure 7(a) shows the CPA performance under illumination of TE and TM waves. For TM incident wave, the absorption peaks exhibit five high absorption efficiencies. However, absorption under illumination of TE incident wave, the absorption efficiency is very weak. It can be understood that the direction of the electric field is parallel to that of grating, which cannot excite GSPs. Conversely, for TM incident wave, the electric field is perpendicular to grating, which can efficiently induce GSPs. Subsequently, Fig. 7(b) shows the angular dispersions of the absorption efficiency at various polarization angles for TM configuration. As can be seen, the absorption efficiency is nearly independent when polarization angle changes from 0° to 45°. Electric field perpendicular to grating makes contributions to excitation of GSPs when polarization angle varies from 0° to 45°. While, the electric field paralleled to the direction of the grating mainly makes contribution to resonance as polarization angle varies from 45° to 90°. In this case, the excitation of GSPs is getting weaker and weaker, then leading to the decrease of confined light.
Fig. 7. (a) The simulated absorption of CPA under illumination of TE and TM polarized incident waves, respectively. (b) Absorption spectra of the CPA with various polarization angles for TM configuration, remaining structural parameters are the same as those in Fig. 1. (c) Absorption spectra of the CPA with various incident angles.
An absorber should ensure high absorption efficiency when the incident angle changes. Considering the performance of this sort of device may be angle dependent, we calculate the effects of oblique incidence on absorption properties. Clearly, Fig. 7(c) demonstrates that the CPA can be realized when the incident angle varies from 0° to 55°. Note that absorption intensity gradually decreases as the incident angle over 55°. In fact, the gain coefficient shows different behaviors for TE and TM waves [63]. For TM wave, CPA condition is related to Brewster’s angle. When the incident angle is smaller than the Brewster’s angle, gain coefficient increases gradually as incident angle increases. However, the situation is completely different when incident angle is larger than the Brewster’s angle. This phenomenon can be explained through analyzing energy density and Poynting vector. Ref. [54] has proved that energy density is smaller in the CPA system than the surrounding vacuum when incident angle is larger than the Brewster’s angle. More specifically, the waves are absorbed mainly by its boundary, while CPA has a lower-energy density inside, resulting in a low absorption value. These results show that absorption is not limited to the normal incident angle, and the energy can be highly absorbed even the angle extended to at least 55°. This feature is particularly important when the incident angle is not vertical. Thus, the designed CPA device operates well over a wide range of incident angle, which is favorable to practical applications.
4. Conclusion
In summary, we demonstrate a new tunable and ultrathin five-band CPA in a simple structure based on graphene and HCGs. The simulation results show that CPA can be achieved with HCGs and cannot be obtained with LCGs. By altering the relative phase of the two counter-propagating coherent beams, coherent absorption intensity can be tuned continuously. Benefitting from the tunable conductivity of graphene, the proposed CPA realizes the simultaneous tunability of absorption intensity and resonance frequency. Meanwhile, the proposed CPA can act as a wide-angle absorber with angular tolerance as high as 55° for TM polarized illumination. The proposed device can also work as CPA even the thickness of the grating approaches extremely small values, as it is proved in Fig. 4(c). Based on these simulations and analysis results, we present an in-depth result concerning the graphene-based CPA. Our proposed system may show potential applications for incident energy harvesting at mid-infrared region.
Funding
Natural Science Foundation of Hunan Province (2020JJ5565); National Natural Science Foundation of China (11947062, 51671086, 61505052, 61775055).
Disclosures
The authors declare no conflicts of interest.
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