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Abstract
Herein, a tunable thermal-optical ultra-narrowband grating absorber is realized. Four ultra-sharp absorption peaks in the infrared region are achieved with the absorption efficiency of 19.89%, 98.41%, 99.14%, and 99.99% at 1144.34 nm, 1190.92 nm, 1268.58 nm, and 1358.70 nm, respectively. Benefiting from an extremely narrow bandwidth (0.27 nm), a maximum Q-factor over 4400 is obtained for the absorber. Moreover, the spectral response can be artificially tuned by controlling the temperature via the strong thermo-optic effect of silicon resonator. The high absorption contrast ratio of 23 dB is demonstrated by only increasing the temperature by 10 °C, showing an order of magnitude better than that of the previously demonstrated performance in the infrared image contrast manipulation. Also, the absorption intensity can be precisely regulated via tuning the polarization state of incident light. Strong tunability extending to temperature and polarization states makes this metasurface promising for applications in a high-performance switch, notch filter, modulator, etc.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Metasurfaces have attracted tremendous interest in the past decade [1] due to the ability to modulate the phase [2,3], amplitude [4,5], polarization [6–10], and other degrees of freedom of light on the subwavelength scales. Since Landy et al. first proposed a perfect absorber based on metasurfaces in 2008 [11], many absorbers have been reported with a near-unity absorption covering the visible and infrared regions [12–15]. Due to the radiation damping and non-radiation losses, however, these absorbers have a relatively wide absorption bandwidth, which inevitably hinders their development in ultra-narrowband functional devices.
Ultra-narrowband perfect absorber, as an important branch of light absorbers, suggested great potential in extensive applications such as biological monitoring [16,17], photodetectors [18–20], multispectral imaging [21–23], and optical modulators [24–26]. For example, Lu et al. proposed an adjustable perfect absorber based on the metal-dielectric-metal nanostructure composed of a period metal nanoring, a dielectric layer, and a metal plate [27,28]. The absorptance and linewidth of the absorber are respectively more than 99% and less than 10 nm, showing the potential application in plasmonic biosensing. Lewi and co-workers demonstrated the way to manipulate the Mie resonances by changing the carrier concentration in spherical silicon and germanium particles [29]. These nanostructures with doping materials show excellent optical response tunability during the change of doping concentration [30,31]. However, it’s not reversible [32]. That is, for the above situations, these absorbers have to be re-optimized in terms of geometric parameters or the doping concentration when the desired operation wavelength is changed. Graphene, a single atomic layer of hexagonally arranged carbon, was also introduced to the metasurfaces [33]. The most attractive property of graphene is that the conductivity can be tuned by applying a bias voltage. For instance, Liu et al. designed a dual-tunable absorber based on hybrid vanadium dioxide-graphene [34]. By tuning the Fermi level from 0.1 eV to 0.7 eV, the absorptance was increased from 45.3% to 94.5%, accompanied by the broadened absorption bandwidth. Nevertheless, the relatively low-Q resonant absorption and the weak measurable light-matter interaction lead to the limited functions in the application of graphene-based optoelectronic devices [35].
Recently, thermally tunable absorbers have been proposed as well [36,37]. Based on the thermal expansion effect of mercury and the mechanism of the regular mercury-based thermometer, Ma et al. reported a mercury-inspired split ring resonator (SRR) with more superior temperature sensing sensitivity than conventional SRRs [38]. The full exploitation of the thermo-optic effect of existing materials also brings new ideas for the design of high-performance thermally tunable modulators. In this paper, high-performance thermal-optical modulation capability is achieved in an ultra-narrowband grating absorber by introducing silicon with a large thermo-optical coefficient. This classic grating-like nanostructure not only shows multiple absorption peaks but also has excellent thermal tunability. The optical responses are analyzed with couple-mode theory (CMT) and calculated by the finite-difference time-domain (FDTD) method. The main mechanism of enhanced absorption can be attributed to the Fabry-Perot resonances. The spectral reflection changed from zero-reflection to total-reflection can be achieved by increasing the temperature value by 10 °C. The absorption contrast ratio also reaches 23 dB. In addition, the absorption efficiency is strongly correlated with polarization angle, suggesting another way to tune the absorption behaviors. This simple but high-efficiency grating nanostructure provides the possibility of optical switching, tunable notch filter, and infrared imaging.
2. Design of high-Q ultra-narrowband absorbers
In this section, the schematic view of the grating absorber (GA) is shown in Fig. 1(a), which can be realized by the standard techniques of magnetron sputtering and electron beam lithography [39]. First, two materials are deposited sequentially on a clean metal film. Then, periodic slits are etched on it using electron beam lithography. The absorber composed of three parts: grating layer (Si), transition layer (Al2O3), and thick substrate (Ag). h1, h2, and h3 denote the thicknesses of the three parts from top to bottom, respectively. w is the width of gaps in the grating layer. p is the grating period. The permittivity of Si, Al2O3, and Ag are taken from Palik’s book [40]. The FDTD method based on solving Maxwell’s equations is employed to simulate the optical response. In all numerical simulations, periodic boundary conditions are set along x-direction and y-direction, and perfectly matched layers are applied along the z-direction. The accurate reflectivity (R) and transmissivity (T) of the system can be obtained. It’s worth noting that the transmissivity is close to zero due to the opaque thick substrate. Thus, the absorptance of the presented structure can be expressed as A = 1 - R.
Fig. 1. (a) Schematic diagram of the grating absorber. (b) Absorption spectra of the proposed nanostructure by FDTD (black lined) and CMT (red dashed), respectively.
The absorption spectra of the ultra-narrowband absorber under normal incidence are shown in Fig. 1(b) with the geometric parameters p=1100 nm, h1=520 nm, h2=530 nm, h3=100 nm, and w=40 nm. Unless otherwise specified, geometry parameters are with their default values. It is observed that a series of ultra-sharp absorption peaks are obtained at λ1=1144.34 nm, λ2=1190.92 nm, λ3=1268.58 nm, and λ4=1358.70 nm. The absorption intensity of these absorption peaks (λ2-λ4) all exceeds 98%. Particularly, the absorption peak λ4 reaches 99.99%, which means near-perfect absorption. Meanwhile, the bandwidths, i.e., full-width at half-maximum (FWHM), of λ1, λ2, λ3, and λ4 are down to 0.72 nm, 0.27 nm, 0.33 nm, 3.96 nm, respectively. The ultra-small FWHM makes the absorber possess remarkable selective absorption of single wavelength, which is desired in photoelectric detection and dynamic control of light flow. In addition, based on the definition of Q = λi/FWHM, the calculated Q-factors of λ1, λ2, λ3, and λ4 are 1589, 4411, 3844, and 343, respectively. We further utilize temporal CMT to quantitatively analyze the physical mechanism of absorption peaks. For a nanostructure with lossy material, the absorption of the system can be expressed as [41,42]:
where δ represents the energy dissipated in lossy material as resistive heat (internal loss rate), and γ describes the radiation loss of resonant cavity energy to the free space (leakage loss rate). It’s obvious that the absorption will reach 100% when the internal loss rate equals the leakage loss rate at the resonance frequency (ω0). There is a three-step method to obtain the δ and γ. Firstly, assume that there is no loss in the materials and set the imaginary part of permittivity to zero. Thus, based on the Qγ = ω0/2γ, the γ can be calculated. Then, introduce metal loss and calculate the total quality factor Qtotal. Finally, the δ can be obtained by Qtotal = (QδQγ)/(Qδ + Qγ) and Qδ = ω0/2δ [43]. For this high-Q resonant cavity, the fields decay very slowly and the quality factor is determined from the slope of the envelope of the decaying signal. Based on Q=-ωrlog10(e)/(2 m), the Q factor of each peak can be obtained, where ωr and m represent resonant frequency and slope of the decaying. As shown in Fig. 1(b), the CMT curve (dashed line) shows excellent agreement with the FDTD curve, especially at the resonance positions. The absorption intensity at the non-resonance regions calculated by CMT is slightly lower than that calculated by the FDTD method since CMT assumes zero loss during the whole calculation process.
3. Analysis of the physical mechanism
The performance of the perfect absorber can be well understood by considering the effective medium theory. Since the slit width is much smaller than the operating wavelength, the effective medium theory is applicable for this structure [44]. If the impedance matching condition is satisfied, it is possible to obtain a perfect absorber with near-zero reflectance at a given wavelength [45], whose effective impedance is influenced by the geometry of the metasurface, such as period, slit width, and thickness. According to Ref. [46], the impedance Z can be expressed as
The S11 and S21 respectively represent the scattering matrix coefficients of reflection and transmission under normal incidence. The real and imaginary parts of impedance at the wavelengths (λ1-λ4) are plotted in Fig. 2(a). As shown in Fig. 2(a), it is observed that the real (Re (Z)) and imaginary (Im (Z)) parts of impedance of the GA are close to 1 and 0 at λ2-λ4, respectively, which means the impedance (Z) of GA near-perfectly matching to the free space. Therefore, the reflection at these resonant wavelengths is extremely inhibited. However, at λ1, the impedance does not exactly match to the free space and the imaginary part is negative. Thus, a relatively high reflection is obtained. According to CMT, the fitted δ and γ are calculated as 8.32×1010 Hz and 4.66×109 Hz, and there is almost an order of magnitude difference between them. This explains why the absorption of GA only reaches 19.89% at λ1. Figures 2(b)-(e) show the electric field intensity distributions from λ1 to λ4. At λ1, the electric field is mainly confined in the slit, and the partial field distributes on the surface of grating layer (Si). However, at λ2-λ4, the enhanced electric field is almost entirely present in the slit. Besides, the horizontal Fabry-Perot resonances are generated due to the silicon strips reflecting the waves at the back and forth sides [47–49], and make a major contribution to the absorption peaks. According to Fig. 3(c), the reflection dips are redshifted and their intensity fluctuates as the thickness of grating layer increases, which demonstrates the excitation of Fabry-Perot modes [50,51]. Moreover, the strong localized field in the slits with different phase configurations will result in destructive interfering in the far-field, leading to the significantly suppressed reflection [51–53]. The bottom metal substrate and the top Si grating layer work as the cavity mirrors with the middle Al2O3 buffer layer, will lead to the low dissipation rates, which then produce the ultra-narrow bandwidth [52]. Meanwhile, the δ and γ at λ2, λ3 and λ4 are 1.31×1010 Hz and 1.42×1010 Hz, 1.33×1010 Hz and 1.77×1010 Hz, 1.50×1010 Hz and 1.73×1010 Hz, respectively. The approximately equal internal loss rate and leakage loss rate indicate the presence of ultra-high intensity absorption peak at λ2-λ4.
Fig. 2. (a) The real and imaginary parts of impedance of GA. (b)-(e) The distributions of electric field at λ1-λ4, respectively.
Fig. 3. Effects of different geometrical parameters of GA on the optical response: period (a), width of slit in the grating layer (b), thickness of grating layer (c), and thickness of transition layer (d).
The optical responses of GA are also simulated and analyzed in detail by tuning geometrical parameters. As shown in Fig. 3(a), as grating period p increases, all reflection dips are shifted toward longer wavelengths with different degrees, and the reflection dip λ2 shows the largest redshift of about 9 nm. Apart from some fluctuations in reflectance (λ1-λ3), the bandwidths of those dips remain nanometer-scale. It is worth noting that the reflection peak λ4 is linearly redshifted with the increased period but the intensity changes inconspicuously. This characteristic of the guided mode resonance has been demonstrated [54], suggesting the ultra-narrowband absorption peak at λ4 caused by the guide mode resonance.
As shown in Fig. 3(b), the increase of the slit width w leads to the blueshifts of the dips. The shift for the reflection dip at λ1 is only 1 nm. This can be explained that since the electric field is partially limited in the slit. Therefore, the position of the λ1 is less affected by the variation of gap size compared to the other dips. In addition, the varied intensity of reflection dips can be attributed to the disruption of the Fabry-Perot resonance caused by the change of the slit width. For the same reason, the effects of thickness of grating layer h1 and transition layer h2 on the optical response intensity exhibit similar trends in Fig. 3(c-d). The above analysis of the effects of geometric parameters on the spectral responses help us find the best performance in the manufacturing process. In a word, narrow FWHM and high spectral absorption intensity can still be maintained over a relatively large range of geometric parameter variations.
4. High-performance thermal-optical modulators
Recently, there has been extensive research interest in thermal-optical modulators, which can effectively modulate the degrees of freedom of light by introducing temperature variations to change the optical properties of materials. Although the modulation rate of thermal-optical modulation is lower than that of electro-optical modulation, it has less energy loss in the long-wavelength range [55]. Benefiting from the Si with a large thermo-optic coefficient (1.86×10−4/°C, much higher than other materials), the designed GA has the capability to carry out thermal manipulation [56]. It is important to point out that this part of the simulation only considers the thermo-optic effect of silicon. Figure 4(a) plotted the variation of reflectance spectra with increasing temperature. It is clear that all reflection dips are redshifted significantly when the temperature increases from 22 °C to 52 °C. Meanwhile, the intensity remains almost constant. In addition, Fig. 4(b) demonstrates that the redshifts of those dips all are linear. We define the sensitivity of temperature as S=Δλ/ΔT and the figure of merit as FOM = S/FWHM. The temperature sensitivity S for λ1-λ4 are 3.43×10−2 nm/°C, 6.11×10−2 nm/°C, 6.87×10−2 nm/°C, and 3.80×10−2 nm/°C, respectively. The FOMs can reach 4.76×10−2 °C-1, 2.26×10−1 °C-1, 2.82×10−1 °C-1, and 0.96×10−2 °C-1, respectively. In the case of λ2, the reflection dip can be shifted by one FWHM at the wavelength range while only a mere 4.42 °C increase in temperature is needed. Combined with its extremely narrow bandwidth (0.27 nm), the GA undoubtedly has excellent temperature tunable characteristics and shows great potential in thermal-optical modulation.
Fig. 4. (a) The simulation reflectance spectra of GA when the temperature rises from 22 °C to 52 °C. (b) The wavelength position of absorption peak (λ1-λ4) as the function of temperature rises from 22 °C to 52 °C. (c) Reflectance spectra of GA with slit widths of 40 nm (top) and 42 nm (bottom) at 22 °C, 27 °C, and 32 °C, respectively. (d) Schematic diagram of infrared image contrast switching for types A and B GA in different temperatures. (e) Normalized electric field distribution from top to bottom corresponds to point (I), (II), and (III) in (c), respectively. (f) Difference intensity spectra and contrast ratio of type A and type B at temperature from 22 °C to 32 °C, respectively.
We further design a metasurface composed of two kinds of GAs to achieve temperature-adjusting infrared image contrast switching, include types A and B. The geometric parameters of types A and B are the same except that the slit widths are 40 nm and 42 nm, respectively. As shown in Fig. 4(c), for type A (w = 40 nm) at 1190.92 nm, the optical responses are zero-reflection (I), partial-reflection (II), and total-reflection (III), reflectively, when the temperature increasing from 22 °C to 32 °C. Furthermore, an almost opposite phenomenon occurs for type B (w = 42 nm) at 1190.92 nm, which allows the presented metasurface to achieve different degrees of absorption of incident light in different regions at the same temperature. Figure 4(d) plots a schematic diagram of infrared image contrast switching based on this idea. The black, gray, white squares represent total-absorption, partial-absorption, and zero-absorption, respectively. The increasing temperature results in a significant change in image contrast. Naturally, more meaningful images can be obtained when more types of GAs are arranged in a reasonable way. Examples: adjusting the temperature required for image contrast switching by changing the slit width difference, adjusting the bandwidth in which the contrast image can exist by selecting different FWHM reflection dips. It is worthwhile pointing out that the process of image contrast switching is reversible, and the temperature difference required to achieve high contrast is one order of magnitude improvement of the previously reported [57]. Meanwhile, with the appropriate devices, such as local heaters [58], GAs have the potential to achieve quick and sensitive image switching. Figure 4(e) shows the normalized electric field distribution of points (I), (II), and (III) in Fig. 4(c). The electric field intensity weakens with the temperature rising, which fully embodies the variation of absorption intensity. To quantitatively describe the performance of the thermal-optical modulator in more detail, the difference intensity spectra and the contrast ratio curves of types A and B are plotted in Fig. 4(f). It can be observed that the maximum difference intensity can exceed 90% when the temperature rises from 22 °C to 32 °C. We define formula 10log10(A22°C/A32°C) as the absorption contrast ratio, where A22°C and A32°C denote the absorption of the metasurface at the temperature of 22 °C to 32 °C, respectively. The absorption contrast ratio also reaches 23 dB, indicating an ultra-high image contrast ratio. Therefore, it is reasonable to assume that higher contrast ratio will be obtained when GAs are more reasonably and accurately combined.
We further investigate the relationship between absorption peak and polarization angle of incident light. As shown in Fig. 5(a), some absorption peaks are weakened while some new absorption peaks emerge. Figure 5(b) plots the comparison of spectra under TM and TE polarization illumination. Under TM polarization illumination, the absorption peak at λ2 exists, but the absorption peak λ5 is not found. However, the situation is opposite when the incident light with TE polarization illumination. To study the quantitative relationship of them, we plot the variation of absorption intensity of λ2 and λ5 with polarization angle in Fig. 5(c). It can be seen that the absorption intensity curve is highly coincident with Malus's law curve. It means that the absorption intensity can be flexibly tailored by tuning the polarization state of incident light.
Fig. 5. (a) Absorption spectra of GA under incident light with different polarization angles. (b) Absorption spectra of GA under incident light with TM (0°) and TE (90°) polarization. (c) The absorption intensity of peak (λ2 and λ5) as a function of the polarization angle.
5. Conclusion
In summary, we theoretically present a grating nanostructure that can achieve the multi-band ultra-narrow perfect absorption in the infrared band. Four high-Q absorption peaks are obtained and the maximum Q-factor value reaches 4411. Based on this ultra-sharp resonant absorption platform, the GA realizes the high difference intensity of 90% and the absorption contrast ratio of 23 dB in the thermal-optical modulation by increasing the surrounding temperature by 10 °C. Therefore, it implies a high-performance optical switch. The strong correlation between the intensity of the absorption peak and the polarization angle of the incident light also suggests a way to quantitatively control the absorption behaviors for the high-performance thermal-optical modulator. These features clearly provide GA with potential application for all-optical switching, tunable notch filter, multispectral modulator, etc.
Funding
National Natural Science Foundation of China (62065007, 51761015, 11764020, 11804134); Natural Science Foundation of Jiangxi Province (20202BBEL53036, 20202BAB201009, 20182BCB22002).
Disclosures
The authors declare that they have no competing interests.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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