Open Access
Add to BibSonomy
Abstract
We propose a six-layer waveguide structure embedded in a single-layer grating based on guided-mode resonance (GMR), which can realize ultra-narrowband filtering with a tunable resonance wavelength. The filtering characteristics were analyzed and calculated by rigorous coupled-wave analysis (RCWA) and COMSOL Multiphysics. The narrowband resonance wavelength and absorption are tuned by changing the geometry and physical parameters of the structure such as the grating period and width, layer thickness, and materials. We designed and calculated the full width at half maximum (FWHM) and resonance absorption spectra in detail under different polarization states of electromagnetic waves. We obtained an absorption FWHM of 8.51e-5 nm for the transverse electric (TE) mode and 0.023 nm for the transverse magnetic (TM) mode, with the absorption coefficients having a value over 99.2%. The GMR filtering structure shows a good sensitivity and figure of merit (FOM) for refractive index sensing. For instance, a very high FOM of 17782.6/RIU for TM incidence is observed. These structures can have possible applications in optical information devices and sensors.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Ultra-narrowband filters play a vital role in many applications such as radar [1], optical satellite communications [2], gas detection [3] and multispectral imaging [4]. Traditional narrowband filters are generally fabricated using multilayer dielectric structures with high/low refractive index alternative dielectric thin films. Interference occurs among the multilayers, and the more layers, the narrower the filtering width [5]. The numerous (generally dozens) of layers require a long production period, rigorous production processes, and high cost. Hessel and Oliner [6] presented a new guided wave theory of Wood’s anomalies for analyzing optical gratings with resonant-propagating spectra. Mori et al. [7] found guided mode resonances (GMRs) in anisotropic grating structures. The grating structures function as good spectral filters in that the energy of forward and backward propagating waves exchange with smooth transmitted and reflected spectra and narrow filter widths. The guided wave mode of the grating waveguide matches the phase of a certain high-order diffraction wave, and resonance occurs. Magnusson and Wang [8,9] proposed the design of guided-mode resonance filters along with simple expressions based on the rigorous coupled-wave theory. Gaylord et al. [10] experimentally demonstrated the GMR grating filters for a wavelength span of 67–100 nm, angles of incidence 0–8°, and peak efficiency ∼80% under the wavelength range 1.5–2.0 µm. As a basic optical element, the GMR filter has significant application potential, such as use in filters [11–13], optical modulators [14–16], optical switches [17–20] and sensors [21,22].
In the past decade, micro/nanostructure preparation has developed rapidly, and much research has focused on narrowband guided-mode resonance filters. In 2012, Buet et al. [23] reported a high angular tolerance and reflectivity with a narrow-bandwidth cavity-resonator-integrated GMR filter, a resonance reflectivity above 74%, and an angular acceptance greater than ± 4.2° for a 1.4 nm narrowband width at a wavelength of 847 nm. In 2014, Zheng et al. [24] demonstrated an efficient angle-insensitive GMR grating filter with a gradient-index layer, showing narrow bandwidth and low sideband reflection for TE-polarized waves. In 2016, Evgeny et al. [25] reported an angularly tolerant and polarization-independent narrow band (approximately 2 nm) spectral filter created with a deep 2D grating made of circular cylinders, with reflectivity remaining above 90% within angles of incidence exceeding 10° for unpolarized light. In addition, Shogo et al. [26] proposed a cavity-resonator-integrated guide-mode resonance band-stop reflector and obtained a stop band with a 3 dB bandwidth of 0.15 nm. In 2017, Zheng et al. [27] investigated a single layer narrow bandwidth GMR grating filter, showing a high reflection of more than 99.9% with sideband reflectance less than 1%, and a bandwidth of 1.1 nm. In 2018, Akhavan et al. [28] proposed a structure composed of a monolayer graphene and a rectangular grating structure, enhancing graphene absorption by 2.3%, and an absorption peak width of 1.3 nm at NIR wavelengths. In 2019, Li et al. [29] designed a large-range wavelength-tunable GMR filter based on a dielectric grating, which can be actively tuned from approximately 491 nm to 690 nm by changing the incident angle. Qing et al. [30] proposed a simple GMR filter composed of a single layer of MoS2, a dielectric grating and a substrate for enhancing the light absorption in the visible range, with a full width at half maximum (FWHM) of 0.51 nm. The narrowband filter also makes it a worthwhile alternative of perfect absorbers. Zhou et al. [31] give a review research progress of different structures and materials based electromagnetic wave absorbers over the past decade; the absorption peak range covers ultraviolet, visible and infrared. Very recently, Z. Liu et al. [32] reported a four-band absorber platform structure, which can produce strong electromagnetic resonance (the maximal absorptance ∼ 100% for each band). X. Liu et al. [33] demonstrated a new kind of resonant absorber via introducing the nano-slit into a photonic film, which provided a high Q factor up to 579.5 nm with very sharp resonant absorption at wavelength 591.5 nm. Mostly, the GMR filtering bandwidth can be easily modulated around 0.1–1.0 nm, but it is useful to investigate the less narrow linewidth (such as under angstrom or megahertz) and the more widely tuned resonance wavelengths. Ultra-narrowband (for example, even less than 0.01 nm) filtering structures show very important values for many optical applications. Moreover, the filtering structures are mostly with three or four layers in the mentioned researches. According to GMR theory, the guided-mode resonance coupled coefficient is closely related to the Fresnel reflection coefficients at interfaces among layers, especially the interface adjacent to the waveguide layer. For higher performance filtering, it’s an alternative to add film layers or increase the interface differences between the waveguide layer and its upper or lower layer.
In this paper, we propose a six-layer waveguide GMR filtering structure with an embedded single-layer grating to realize an ultra-narrow bandwidth and widely tunable wavelength. We compared and studied the effective medium theory (EMT) and rigorous coupled-wave analysis (RCWA) theory for the dispersion characteristics of waveguides. The resonance propagation properties are analyzed and calculated by RCWA theory and COMSOL Multiphysics under different geometry and physics structural parameters with transverse electric (TE) and transverse magnetic (TM) polarization incidence, respectively. The FWHM, resonance absorption wavelength, and spectral sensitivities were calculated in detail, and the results and corresponding physical mechanisms were analyzed.
2. Principle analysis and the structure
2.1 Basic structure of the GMR
The basic guide-mode resonance grating structure is shown in Fig. 1(a). It is composed of three layers: substrate, transition layer, and grating layer, with respective refractive indices, ${n_s}$, ${n_w}$, and ${n_H}$/${n_L}$. The transition layer functions as a guided-mode transmission. The grating layer can be considered a medium layer with an effective refractive index ${n_{eff}}$, as shown in Fig. 1(b). The energy of the electric field is limited and propagates in the waveguide layer, as shown in Fig. 1(c). Here, ${d_w}$ and ${d_g}$ describe the thickness of the waveguide layer and grating layer, respectively, $t$ is the grating width with a high refractive index ${n_H}$, ${n_L}$ is the low refractive index for grating, $\Lambda $ is the grating period with subwavelength dimension, and the filling factor is $f = {t / \Lambda }$. There is also a cover layer on the grating with a refractive index ${n_c}$.
Fig. 1. Basic planar waveguide structure for GMR. (a) The three-layer waveguide grating; (b) The three-layer effective medium waveguide; (c) The field distributions picture of |E| for TE polarization.
The grating layer is similar to a homogeneous medium film, and the basic structure can be equivalent to a uniform planar waveguide and analyzed by EMT [34–36]. For the TE and TM polarization incidence, the effective refractive index of the grating layer is
The excited guided modes can be analyzed and easily calculated using the EMT. However, when the grating period or thickness is much smaller than the incident wavelength, the effective properties of subwavelength gratings cannot be simply described as an effective index, and more rigorous computation must be taken into account. Moharam et al. [37–40] proposed a rigorous coupled-wave analysis to define and solve a subwavelength grating diffraction problem.
As noted in the above references, for incidence of TE polarization, the electric field of the incident region and the transmitted region can be expressed as
Where ${E_0}$ is the electric field of the incident light, ${R_i}$ and ${T_i}$ are the normalized electric field amplitudes of the i-th order backward and forward diffraction, respectively, d is the grating groove depth, ${k_{xi}} = {k_0}[{{n_1}sin\theta - i({{{{\lambda_0}} / \Lambda }} )} ]$, ${k_{l,zi}} = {({k_0^2n_l^2 - k_{xi}^2} )^{{1 / 2}}}\;\;l = 1,2$, and ${k_0}$ is the wave vector of incident light in vacuum.
In the grating region, the spatial harmonic Fourier series of the electric and magnetic fields is expanded as
Where ${\varepsilon _0}$ and ${\mu _0}$ are, respectively, the permittivity and permeability of free space, ${V_{yi}}(z )$ and ${U_{yi}}(z )$ are the normalized amplitudes of the spatial harmonics of electric field and magnetic field of the i-th order, respectively. ${E_{gy}}$ and ${H_{gx}}$ satisfy the Maxwell equations in the grating region, from which the couple wave equations can then be obtained.
For the TM polarization incidence, the magnetic field distribution of the incident and transmitted regions can be expressed as
The spatial harmonic Fourier series of the electric and magnetic fields in the grating region is expanded as
Combining the coupled-wave equations and the boundary condition of the layers, the continuous component of the electromagnetic field at the interface of different media can be obtained, and the energy of each diffraction order can be solved using a set of equations. Different media interfaces affect the coupled coefficient of forward- or backward- propagation of waveguide mode, which is also a key factor to resonance wavelength and width. Thus, more layers and materials could be considered in the structure of GMR. Based on the basic waveguide mode, we established a six-layer waveguide structure to investigate the GMR properties and discuss the relationship between the layers.
2.2 Six-layer GMR waveguide structure and the principle analysis
The six-layer structure is shown in Fig. 2. It consists of three parts: the top is composed of two layers of planar dielectric (d4 and d6, with corresponding refractive indices ${n_4}$ and ${n_6}$) sandwiched with a single grating (d5, with the period Λ). The bottom is a metal film (d1 with refractive index ${n_1}$, e.g., Au). The middle is composed of a dielectric film (d2 with refractive index ${n_2}$) and a microcavity (d3 with refractive index ${n_3}$). In the calculations, many dielectrics were considered as candidates. The grating appears periodically in the x-direction and extends infinitely in the z-direction. It is regarded as a homogeneous dielectric waveguide, and the equivalent refractive index of the grating layer is calculated using Eqs. (1) and (2).
According to the Helmholtz equation and the boundary conditions of the electromagnetic field, the eigenequation of guided mode transmission under different polarizations is derived as
Where ${d_4}$ is the thickness of waveguide layer, m is the number of modes that the filtering structure allows to propagate, ${\gamma _4}$ is the guided wave vector along the waveguide layer direction (y-axis), $\delta $ is the reflection coefficient between layers characterized by the phase shift, and T is a constant coefficient that connects the phase shift relationships between the layers. ${T_5}\;,\;{\delta _{51}}\;,\;{T_3}\;,\;{\delta _{31}}$ are related to all the other layers and we strictly deduce the relationships as follows
Figure 3 shows the mode dispersion curve of the six-layer GMR waveguide structure under different wavelength ranges: 1400–2000nm and 2200–3000 nm. In Fig. 3(a), the zeroth-order and first-order modes are excited for both TE and TM polarizations, while only the zeroth-order mode is excited in Fig. 3(b). N is the equivalent refractive index of the guided modes and $N = {\beta / {{k_0}}}$. The mode dispersion curves of the guided-mode equivalent index are provided by the EMT method. Figure 4 shows the resonance peak positions of the excited guided modes for TE0, TE1, TM0, and TM1 under the wavelength ranges shown in Fig. 3. The above analysis uses physical parameters ${n_2} = 2.1$ (for example, a ZrO film), ${n_3} = 1$, ${n_4} = 2.33$ (for example, a ZnS film), ${n_6} = 1.45$ (for example, a SiO2 film); the layer of d5 is a composite dielectric grating film of SiO2/MgF2 with an effective refractive index ${n_{eff}}$(1.4037 for TE case and 1.4022 for TM case), which is respectively caclulated according to Eqs. (1) and (2); the layer of d1 is a gold thin film. The grating period Λ = 1500 nm, the width of MgF2 w = 1000 nm, d1 = 120 nm, d2 = 450 nm, d3 = 930 nm, d4 = 460 nm, d5 = 180 nm and d6 = 150 nm. The dielectric layers mainly affect the position of the GMR according to Eqs. (7)–(10), and the thin metal layer mainly acts as an enhanced reflector. The propagation constant is a complex number in Eq. (8). The imaginary part ${\beta ^{^{\prime\prime}}}$, represents the leakage of the guided mode, which determines the resonance linewidths [41]. The spectral linewidth is defined as
Figure 5 presents the absorption spectral properties of the multi-layer waveguide structure. The specific parameters are: Λ = 1500 nm, w = 1000 nm, d1 = 120 nm, d2 = 450 nm, d3 = 930 nm, d4 = 460 nm, d5 = 180 nm, and d6 = 150 nm. The GMR absorption spectrum for both TE0 and TM0 is shown in Fig. 5(a). The resonance peak wavelength is 1550 nm for the TE0 mode and about 2277 nm for the TM0 mode, with a FWHM of 8.51e-5 nm and 0.068 nm, respectively. It shows good filtering properties for both the TE and TM polarizations. Figures 5(b)–(e) give the field distributions of |E| and |H| for TE and TM modes.
Fig. 3. Mode dispersion curve of the six-layer GMR waveguide. (a) Guided modes excited under the wavelength of 1400–2000nm. (b) Guided modes excited under the wavelength of 2200–3000 nm.
Fig. 5. (a) Absorption spectrum of TE and TM polarization. (b)–(c) The field distributions picture of |E| and |H| in TE polarization. (d)–(e) The field distributions picture of |E| and |H| in TM polarization.
Obviously, the very difference of the guided wave propagation vector imaginary part for TE mode and TM mode is the key factor to affect the resonance spectral width. According to the mode dispersion curve in Fig. 3, the equivalent refractive index of different mode can be obtained. Thus, the guided wave vector will be calculated accurately according to Eq. (10), i.e., TE0 mode at a resonance wavelength of 1550 nm with $\beta \textrm{ = }8.3873e6 - j2.7717e - 2\;{(nm)^{ - 1}}\,$, TM0 mode at a resonance of 2277 nm with $\beta \textrm{ = 6}\textrm{.3864}e6 - j2.0228e1\;{(nm)^{ - 1}}\,$. The difference between these two imaginary parts is three orders of magnitude, which is consistent with what is presented in Fig. 5(a), and the imaginary part is ultra-small for TE mode. Such kind of multi-layer structure requires more rigorous mode resonance matched coupling conditions, and high Q resonance occurs.
3. Simulation results and discussions
In this section, the resonance wavelength properties are calculated and analyzed in detail under different geometric and physical parameters i.e., thickness of each layer (d1–d6), grating period (Λ), grating width (w) and the incident angle. COMSOL Multiphysics and MATLAB tools were used for structural modeling and careful calculations.
3.1 Effect of thickness of metal layer (d1) on the performance of the structure
The thicknesses and materials of the thin metal film affect the filtering performance of the GMR structure for both TE and TM polarized incidence. Figure 6(a) shows the different polarization propagation properties under different thicknesses of the Au film. For a TM polarization, the transmission peak value decreases as the metal film thickness increases from 100 nm to 140 nm, as seen in the inner curve. As the thickness changes, the resonance peak wavelength shifts slowly for absorption and reflection, and the peak position is almost unchanged with the thickness d1 > 120 nm. The FWHM changes little and remains almost at approximately 0.023 nm. For a TE polarization, the resonance peak and FWHM both remain unchanged as the thickness changes. The possible reason is that surface plasmon resonance may occurs when TM wave meets a thin metal surface, but it doesn’t happen for TE wave. Figure 6(b) shows the resonance wavelength properties of the absorption for different metal material films. The absorption peaks are present at different positions when using different metal films with the same structure. For TM polarization, the absorption peak is 2150.514 nm, 2150.505 nm, and 2150.478 nm for Au, Ag, and Al films, respectively. For TE polarization, the peak is 1549.9999 nm, 1550.0009 nm and 1549.9998 nm, respectively. The structure parameters are set as: Λ = 1500 nm, w = 1000 nm, d1 = 120 nm, d2 = 460 nm, d3 = 1000 nm, d4 = 460 nm, d5 = 180 nm, d6 = 150 nm and the input lights are with a normal incidence.
Fig. 6. (a) Effect of different thicknesses of Au on the filtering structure. (b) Effect of different metal films for d1.
3.2 Effect of thickness of dielectric layer (d2) and microcavity layer (d3) on the performance of the structure
Figure 7 shows the effect of d2 on the resonance properties for both TE and TM polarization incidence. The resonance absorption peak has a red shift with an increment of 60 nm of d2, and it shifts by approximately 0.0013 nm and 0.114 nm for the TE and TM polarizations, respectively, as shown in Figs. 7(a) and 7(b). Ultra-linewidth resonance spectra were acquired for both TE and TM incidence, as shown in Figs. 7(c) and 7(d). The FWHM shows a much narrower value for TE polarization. For example, FWHM(TE) = 8.51e-5 nm with a peak wavelength of 1550 nm and FWHM(TM) = 0.027 nm with a peak wavelength of 2150.496 nm, a thickness d2 = 450 nm, and absorptions of more than 99.4%. The FWHM increases with d2 for the TE mode, while the opposite is true for the TM mode. The resonance wavelength is different for TE and TM polarizations, so the phase match shift among each layer is very different for the same thickness. A longer TM resonance peak shows enhanced interference between layers, and vice versa for the TE mode. The structure parameters are set as: Λ = 1500 nm, w = 1000 nm, d1 = 120 nm, d3 = 930 nm, d4 = 460 nm, d5 = 180 nm, and d6 = 150 nm.
Fig. 7. Effect of different thicknesses of the dielectric film d2 on the resonance absorption properties: absorption spectrum for TE (a) and TM (b) polarization; the FWHM contour map for TE (c) and TM (d) polarization.
Figure 8 shows the effect of the thickness of d3 on the resonance properties. As d3 increases in size from 910 nm to 970 nm, the resonance peak shows a red shift of about 0.00058 nm for TE polarization, and the FWHM increases from 5.15e-5 nm to 2.48e-4 nm, as shown in Figs. 8(a) and 8(c). For TM polarization, the resonance peak has a blue shift of 0.061 nm as d3 changes from 970 nm to 1030 nm, and the FWHM decreases from 0.034 nm to 0.015 nm, as shown in Figs. 8(b) and 8(d). There should be a half wave loss for the TM mode on the boundary of the waveguide layer, and according to the guided-mode Eigen Eq. (7), the resonance wavelength is decided by the two adjacent layers (d3 and d5) of the waveguide. The peak wavelength increases with the thickness of d3 for the TE mode, and vice versa for TM mode.
Fig. 8. Effect of different thicknesses of microcavity d3 on the resonance absorption properties: absorption spectrum for TE (a) and TM (b) polarization; the FWHM contour map for TE (c) and TM (d) polarization.
3.3 Effect of thickness of waveguide layer (d4) on the performance of the structure
Figure 9 shows the effect of the thickness of d4 on the resonance absorption properties of the GWR filtering structure under different incidences of TE and TM polarization. The resonance peaks both present red shifts, as shown in Figs. 9(a) and 9(b). The shift is 3.78 nm and 10.9 nm as d4 changes from 456 nm to 464 nm separately for TE and TM polarization. The filtering linewidth also changes with different polarization incidence, as shown in Figs. 9(c) and 9(d). For a TE mode, the FWHM shows an ultra-narrow linewidth which changes from 5.76e-5 nm to 1.30e-4 nm. The TM mode shows a greater linewidth centered at 2.3e-2 nm with very small changes. The FWHM is mainly related to the imaginary part of the guided mode propagation constant, which is dependent on the internal relations of the multi-layer structure as shown in Eq. (10), resulting in a greater loss for TM guided mode propagation than that for TE mode.
Fig. 9. Effect of different thicknesses of the waveguide layer d4 on the resonance absorption properties: absorption spectrum for TE (a) and TM (b) polarization; the FWHM contour map for TE (c) and TM (d) polarization.
3.4 Effect of the embedded grating on the performance of the structure
We will now discuss the influences of the embedded grating layer, including the grating layer thickness (d5), grating period (Λ), and grating width (w).
Figure 10 shows the resonance absorption properties for different grating thicknesses. The resonance peak is blueshifted for TE polarization and redshifted for TM polarization, as shown in Figs. 10(a) and 10(b). The differing shifts in the resonance wavelength are due to the half-wave loss on the boundary for the TM mode, which shows an influence similar to that caused by the thickness of d3. The corresponding spectral widths are shown in Figs. 10(c) and 10(d). The resonance peak only shifts by approximately 2.4e-3 nm (from 1550.00105 nm to 1549.99866 nm) as d5 increases from 160 nm to 210 nm. A FWHM of 8.51e-5 nm with very high absorption is obtained when d5 = 180 nm for a normal TE incidence. The absorption coefficients change significantly with the thickness, possibly because the very narrow linewidth is more sensitive to the structure and the higher performance filter requires more rigid geometry structures. For a normal TM incidence, the resonance peak changes about 9.17 nm (from 2145.761 nm to 2154.935 nm) as d5 increases from 160 nm to 200 nm, with the FWHM showing a relatively narrow width from 0.022 nm to 0.024 nm.
Fig. 10. Effect of different thicknesses of grating layer d5 on the resonance absorption properties: absorption spectrum for TE (a) and TM (b) polarization; the FWHM contour map for TE (c) and TM (d) polarization.
Figure 11 shows the resonance absorption properties under different grating periods for different polarization incidences. As the grating period increases, the resonance peaks both have red shifts, as seen in Figs. 11(a) and 11(b). As the grating period changes from 1498 nm to 1502 nm, the resonance peak shifts from 1548.22 nm to 1551.78 nm for TE polarization and from 2148.61 nm to 2152.42 nm for TM polarization. According to the GMR effect, a longer resonance wavelength requires a longer period for the phase match. Figures 11(c) and 11(d) show that the spectra linewidth varies differently under these circumstances. As the grating period is increased, the FWHM decreases from 1.01e-4 nm to 7.38e-5 nm for TE polarization, but the FWHM changes from 0.023 nm to 0.024 nm for TM polarization. The absorption coefficients both show a very high value of more than 99%. The grating period thus primarily affects the resonance wavelength position, but it hardly affects the absorption coefficient.
Fig. 11. Effect of different grating period Λ on the resonance absorption properties: absorption spectrum for TE (a) and TM (b) polarization; the FWHM contour map for TE (c) and TM (d) polarization.
Figure 12 shows the resonance absorption properties under different grating widths for different polarization incidences. The low/high interval refractive index dielectric materials of MgF2 and SiO2 are used in the calculations, and w is the width of the low refractive index region of grating. The higher grating width denotes a lower grating effective index. The resonance peaks both have blue shifts corresponding to the increase in grating width, as shown in Figs. 12(a) and 12(b). The shift value is 0.072 nm and 1.39 nm, respectively, for a grating width with an increment of 80 nm for TE and TM polarization. The spectra linewidth has negligible change, and the FWHM changes from 5.71e-5 nm to 9.33e-5 nm for TE polarization and from 0.022 nm to 0.025 nm for TM polarization, as seen in Figs. 12(c) and 12(d).
Fig. 12. Effect of different grating width w on the resonance absorption properties: absorption spectrum for TE (a) and TM (b) polarization; the FWHM contour map for TE (c) and TM (d) polarization.
The results and analysis of these calculations show that the linewidth and absorption coefficient of the TM mode change slightly with respect to the grating parameters, whereas the resonance peak wavelength is highly affected by the period for both TE and TM polarization incidences.
3.5 Effect of the thickness of d6 on the performance of the filtering structure
Figure 13 shows resonance absorption properties under different covering layer thicknesses. The resonance peaks are both redshifted as the thickness increases, with the peak position being much more sensitive for TM incidence, as seen in Figs. 13(a) and 13(b). As d6 increases from 130 nm to 170 nm, the peak position experiences a red shift of 0.088 nm for TE polarization, and 11.31 nm for TM polarization. The thickness of d6 affects TM mode resonance much more than that for TE mode due to the polarization selection of the subwavelength grating below the layer. The spectra linewidth also changes differently as seen in Figs. 13(c) and 13(d). The linewidth changes from 8.43e-5 nm to 8.51e-5 nm for TE polarization, while only changing from 0.022 nm to 0.025 nm for TM polarization. It has a more stable FWHM for the TE mode than in the case of changing d5 thickness. The covering thin film is used to protect the grating layer and maintain a more stable bandwidth.
Fig. 13. Effect of different thicknesses of covering layer d6 on the resonance absorption properties: absorption spectrum for TE (a) and TM (b) polarization; the FWHM contour map for TE (c) and TM (d) polarization.
3.6 Angular effect on the performance of the filtering propagations
We analyze the absorption characteristics of the GMR filtering structure for normal incidence light in Sections 3.1–3.5. The incident angle also affects the resonance wavelength and FWHM for both the TE and TM polarizations, as shown in Fig. 14. For the TE polarization, the resonance peak is blueshifted by 33.6 nm as the incidence angle changes from normal to an oblique incidence of 3°. The maximum value of the absorption peak decreases rapidly, as shown in Fig. 14(a). For a TM polarization, the peak is redshifted by 53.79 nm under the same change in incident angle, as seen in Fig. 14(b), and the maximum value of absorption peak remains more than 93.4%. Table 1 shows the results of the resonance wavelength, maximum absorption, and FWHM under different incident angles for different polarization incidences. The absorption of TE polarization changes more sensitively and is much lower as increasing the oblique incidence angle, for such an ultra-narrow width needs more rigorous matched coupling condition. The missing absorption can be improved by adjusting the thickness of microcavity d3 with a minor change, i.e., as the absorption reduced from 0.994 to 0.273 (TE polarization in Table 1), it could go back to 0.988 according to decrease the air cavity thickness from 930 nm to 850 nm with almost the same resonance wavelength and width.
Fig. 14. Effect of incident angle on the absorption resonance properties of the filtering structure: (a) TE polarization; (b) TM polarization.
Table 1. The variance of resonance wavelength, absorption, and FWHM with the incident angle
Above all, we discussed the absorption spectral properties which are regulated and controlled by the structure parameters and light incidence. The resonant absorption peak can be tuned flexibly via the parameters under a linear relationship. To describe the relationship more clearly, Fig. 15 summarized the resonance wavelength results from Fig. 7 to Fig. 14, which gives out the moving value and direction of the peak. The results show that the resonance peaks shift in different positions for TE and TM under the parameters of d3, d5 and incident angle θ, that is a redshift for TE polarization and a blueshift for TM polarization, as seen Fig. 15(b), (d) and (h). These three parameters are directly related to guided-mode layer d4, as the Fresnel reflection occurs between the interface of d3 and d4 or d5 and d4 under normal or oblique incidence, there is a phase difference of π between TE mode and TM mode. In our structure, the guided-mode propagation only occurs in the waveguide layer d4, and evanescent wave propagation occurs in other layers. The phenomenon of TM mode in our study is similar to that of the plasmonic structure system, because only TM mode can be stimulated and transmitted for a surface plasmonic system.
Fig. 15. The relationship between the filtering structure parameters and resonance wavelengths under different polarization incidences: (a) ∼(e) the resonant peak is tuned via the thickness from d2 to d6; (f) the resonant peak is tuned via the period of grating layer; (g) the resonant peak is tuned via the width of the low refractive index dielectric for grating layer; (h) the resonant peak is tuned via the incidence angle.
The linear relationship slope for the parameters in Fig. 15 can also point out the trade-off factors to the design and possible preparation study. For TE polarization, the most critical factors to the resonance peak are grating period Λ and thickness of d4, the thickness of d6 makes a little bit of difference, then the grating silt width w, and the thicknesses of d2, d3 and d5 affect the peak slightly. For TM polarization, the ranking of them is respectively Λ, d4, d6, d5, w, d2 and d3. The incident angle is a very critical factor for both polarizations, especially reducing the absorption of TE as seen in Table 1.
4. Applications of the GMR filtering devices
4.1 Application of filtering
In Section 3, the filtering characteristics of the proposed structure are analyzed in detail under TE and TM polarizations. The structure shows good filtering properties with an ultra-narrow FWHM and a tunable resonance peak. A linewidth of less than 8.51e-5 nm can be achieved for a TE polarization incidence and 0.023 nm for a TM polarization incidence. The filtering resonance wavelength can be tuned flexibly under the layer thickness, grating period/width, and incident angle of the structure. It shows great potential application in the field of high-precision optical signal processing (e.g., direct extraction of ultra-narrow band characteristic signals in the optical domain, hyperfine segmentation of the wideband spectrum, optical real-time high-precision Fourier transform), and single-longitudinal-mode narrow-linewidth light source generation, among others.
4.2 Application of optics sensing
Sensors play an important role in modern production and life, including gas sensors [42], biosensors [43], and temperature sensors [44], with filtering properties that are highly sensitive to such structures. The microcavity layer d3 can be filled with different materials for different sensing applications. Two main parameters are used to evaluate the performance of sensors: sensitivity(S) and figure of merit (FOM). The sensitivity is defined as
where $\Delta \lambda $ is the offset of the resonance wavelength, and $\Delta n$ is the refractive index variation of the sensing layer.The figure of merit is a quality factor, which is defined as
Different gases or liquids can be used to fill the microcavity layer, changing the absorption spectrum for d3 as shown in Fig. 16. As the microcavity refractive index changes from 1 to 1.0005, the absorption peak has a red shift from 2150.514 nm to 2150.718 nm, as shown in Fig. 16(a). As the refractive index changes from 1.3 to 1.35, the peak has a red shift from 2411.628 nm to 2434.611 nm, as shown in Fig. 16(b). The sensing sensitivity is the relationship between the peak wavelength shift and the refractive index, which presents a very good linearity in our study. The sensitivity was, respectively for TE and TM polarization, 409 nm/RIU with an FOM of 17782.6/RIU, and 462 nm/RIU with an FOM of 5250/RIU. The structure can be considered a good candidate as an optical sensor for gas or liquid detection. The sensitivities, FWHM, and FOM of the refractive index sensors are listed in Refs. [45–50], as shown in Table 2, which were compared with our work under similar changes in refractive index. The plasmonic structure with high absorption shows good refractive index sensing properties, which is also good candidate of refractive index sensor. The sensing sensitivities and spectral characteristics of the refractive index sensors based on surface plasmon are also listed in Refs. [51–55], as shown in Table 3. The FWHM shows very good performance in our simulation, approximately two to three orders of magnitude lower than that in the references, and thus, a very high FOM.
Fig. 16. The refractive index sensing properties for the six-layer waveguide structure under TM incidence: (a) the absorption spectra changing under refractive indices from 1.0 to 1.0005; (b) the absorption spectra changing under refractive indices from 1.3 to 1.35.
Table 2. Comparison of the sensing performances of refractive index sensors in references
Table 3. The sensing properties of refractive index sensors based on surface plasmon in references
5. Conclusion
In conclusion, we proposed a six-layer waveguide structure embedded in a single-layer grating based on the GMR and analyzed the spectral filtering characteristics under TE and TM polarization incidence. For the TE mode, the FWHM is ultra-narrow, even less than 8.51e-5 nm, with a very high absorption of more than 99.9% near the resonance wavelength range of approximately 1550 nm. For the TM mode, the FWHM is relatively narrow, approximately 0.023 nm, with a high absorption of more than 99% near the resonance wavelength range of approximately 2150 nm. The resonance wavelength can be tuned by changing the layer thickness, grating period, and incident angle. According to the results, the resonance peak wavelength is mainly affected by the grating period, waveguide layer thickness, and incident angle for both TE and TM polarizations, with the same influences on the FWHM for the TE mode. For the TM mode, the FWHM and absorption coefficient change slightly with respect to the geometric parameters. The design and results show important values for potential applications in optical communication, noise suppression, optical amplifiers, and optical sensing.
Funding
National Natural Science Foundation of China (61705151); Teaching Team Foundation of Soochow University (2018).
Acknowledgements
This work was supported in part by the National Natural Science Foundation of China (61705151) and the 2018 Teaching Team Program of Optical-course Construction, Soochow University.
Disclosures
The authors declare no conflicts of interest.
References
1. B. Schwarz, “Mapping the world in 3D,” Nat. Photonics 4(7), 429–430 (2010). [CrossRef]
2. Z. Sodnik, H. Lutz, B. Furch, and R. Meyer, “Optical satellite communications in Europe,” presented at the Free-Space Laser Communication Technologies XXII2010.
3. G. M. Gibson, B. Sun, M. P. Edgar, D. B. Phillips, N. Hempler, G. T. Maker, G. P. Malcolm, and M. J. Padgett, “Real-time imaging of methane gas leaks using a single-pixel camera,” Opt. Express 25(4), 2998–3005 (2017). [CrossRef]
4. P. J. Lapray, X. Wang, J. B. Thomas, and P. Gouton, “Multispectral filter arrays: recent advances and practical implementation,” Sensors 14(11), 21626–21659 (2014). [CrossRef]
5. H. D. Polster, “Reflection from a Multilayer Filter,” J. Opt. Soc. Am. 39(12), 1038–1043 (1949). [CrossRef]
6. A. Hessel and A. A. Oliner, “A New Theory of Wood's Anomalies on Optical Gratings,” Appl. Opt. 4(10), 1275–1297 (1965). [CrossRef]
7. S. Mori, K. Mukai, J. Yamakita, and K. Rokushima, “Analysis of dielectric lamellar gratings coated with anisotropic layers,” J. Opt. Soc. Am. A 7(9), 1661–1665 (1990). [CrossRef]
8. R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61(9), 1022–1024 (1992). [CrossRef]
9. S. S. Wang and R. Magnusson, “Theory and applications of guided-mode resonance filters,” Appl. Opt. 32(14), 2606–2613 (1993). [CrossRef]
10. D. L. Brundrett, E. N. Glytsis, and T. K. Gaylord, “Normal-incidence guided-mode resonant grating filters: Design and experimental demonstration,” Opt. Lett. 23(9), 700–702 (1998). [CrossRef]
11. C. Lenaerts, V. Moreau, Y. F. Lion, and Y. L. Renotte, “Narrow bandwidth wavelength filter by guided mode resonance,” Opt. Eng. 43(11), 2631–2639 (2004). [CrossRef]
12. C. L. Hsu, Y. C. Liu, C. M. Wang, M. L. Wu, Y. L. Tsai, Y. H. Chou, C. C. Lee, and J. Y. Chang, “Bulk-micromachined optical filter based on guided-mode resonance in silicon-nitride membrane,” J. Lightwave Technol. 24(4), 1922–1928 (2006). [CrossRef]
13. E. Sakat, G. Vincent, P. Ghenuche, N. Bardou, C. Dupuis, S. Collin, F. Pardo, R. Haïdar, and J. L. Pelouard, “Free-standing guided-mode resonance band-pass filters: from 1D to 2D structures,” Opt. Express 20(12), 13082–13090 (2012). [CrossRef]
14. T. Katchalski, G. Levy-Yurista, A. A. Friesem, G. Martin, R. Hierle, and J. Zyss, “Light modulation with electro-optic polymer-based resonant grating waveguide structures,” Opt. Express 13(12), 4645–4650 (2005). [CrossRef]
15. X. Liu, T. Starr, A. F. Starr, and W. J. Padilla, “Infrared spatial and frequency selective metamaterial with near-unity absorbance,” Phys. Rev. Lett. 104(20), 207403 (2010). [CrossRef]
16. H. Zhou, F. Ding, Y. Jin, and S. He, “Terahertz Metamaterial modulators based on absorption,” Prog. Electromagn. Res. 119, 449–460 (2011). [CrossRef]
17. A. E. Bieber and T. G. Brown, “Coupling anomalies in SimGen/Si/SiO2 waveguide systems,” Opt. Express 10(20), 1139–1144 (2002). [CrossRef]
18. A. Mizutani, H. Kikuta, and K. Iwata, “Numerical study on an asymmetric guided-mode resonant grating with a Kerr medium for optical switching,” J. Opt. Soc. Am. A 22(2), 355–360 (2005). [CrossRef]
19. Z. Ren, Y. Sun, S. Zhang, K. Zhang, J. Hu, and Z. Lin, “Active optical switches based on polarization-tuned guided-mode resonance filters for optical communication,” Opt. Commun. 426, 383–387 (2018). [CrossRef]
20. Q. M. Ngo, S. Kim, S. H. Song, and R. Magnusson, “Optical bistable devices based on guided-mode resonance in slab waveguide gratings,” Opt. Express 17(26), 23459–23467 (2009). [CrossRef]
21. L. Liang, X. Hu, L. Wen, Y. Zhu, X. Yang, J. Zhou, Y. Zhang, I. E. Carranza, J. Grant, C. Jiang, D. R. S. Cumming, B. Li, and Q. Chen, “Unity Integration of Grating Slot Waveguide and Microfluid for Terahertz Sensing,” Laser Photonics Rev. 12(11), 1800078 (2018). [CrossRef]
22. P. Quoc-Hung, N. Nguyen-Huu, and Y. L. Lo, “Optimized Double-Layered Grating Structures for Chem/Biosensing in Midinfrared Range,” IEEE Sens. J. 14(9), 2938–2946 (2014). [CrossRef]
23. X. Buet, E. Daran, D. Belharet, F. Lozes-Dupuy, A. Monmayrant, and O. Gauthier-Lafaye, “High angular tolerance and reflectivity with narrow bandwidth cavity-resonator-integrated guided-mode resonance filter,” Opt. Express 20(8), 9322–9327 (2012). [CrossRef]
24. G. Zheng, J. Cong, L. Xu, and W. Su, “Angle-insensitive and narrow band grating filter with a gradient-index layer,” Opt. Lett. 39(20), 5929–5932 (2014). [CrossRef]
25. E. Popov, A. L. Fehrembach, Y. Brûlé, G. Demésy, and P. Boyer, “Two-dimensional grating for narrow-band filtering with large angular tolerances,” Opt. Express 24(13), 14974–14985 (2016). [CrossRef]
26. S. Ura, M. Nakata, K. Yanagida, J. Inoue, and K. Kintaka, “Cavity-resonator-integrated guided-mode resonance band-stop reflector,” Opt. Express 24(13), 15120–15127 (2016). [CrossRef]
27. G. Zheng, X. Zou, L. Xu, and J. Wang, “Single layer narrow bandwidth angle-insensitive guided-mode resonance bandstop filters,” Optik 130, 19–23 (2017). [CrossRef]
28. A. Akhavan, S. Abdolhosseini, H. Ghafoorifard, and H. Habibiyan, “Narrow Band Total Absorber at Near-Infrared Wavelengths Using Monolayer Graphene and Sub-Wavelength Grating Based on Critical Coupling,” J. Lightwave Technol. 36(23), 5593–5599 (2018). [CrossRef]
29. C. Li, K. Zhang, Y. Zhang, Y. Cheng, and W. Kong, “Large-range wavelength tunable guided-mode resonance filter based on dielectric grating,” Opt. Commun. 437, 271–275 (2019). [CrossRef]
30. Y. M. Qing, H. F. Ma, S. Yu, and T. J. Cui, “Ultra-narrowband absorption enhancement in monolayer transition-metal dichalcogenides with simple guided-mode resonance filters,” J. Appl. Phys. 125(21), 213108 (2019). [CrossRef]
31. J. Zhou, Z. Liu, X. Liu, G. Fu, G. Liu, J. Chen, C. Wang, H. Zhang, and M. Hong, “Metamaterial and nanomaterial electromagnetic wave absorbers: structures, properties and applications,” J. Mater. Chem. C 8(37), 12768–12794 (2020). [CrossRef]
32. Z. Liu, X. Liu, Y. Wang, G. Liu, and C. Tang, “Silicon Antennas Metasurface Based Light Absorber With Quantitatively Adjustable Operating Frequency and Intensity,” IEEE J. Sel. Top. Quantum Electron. 27(1), 1–6 (2021). [CrossRef]
33. X. Liu, G. Fu, G. Liu, J. Wang, Q. Yi, H. Yang, W. Tan, and Z. Liu, “Nano-slit assisted high-Q photonic resonant perfect absorbers,” Opt. Express 29(4), 5270–5278 (2021). [CrossRef]
34. H. Kikuta, H. Yoshida, and K. Iwata, “Ability and limitation of effective medium theory for subwavelength gratings,” Opt. Rev. 2(2), 92–99 (1995). [CrossRef]
35. C. W. Haggans, L. Li, and R. K. Kostuk, “Effective-medium theory of zeroth-order lamellar gratings in conical mountings,” J. Opt. Soc. Am. A 10(10), 2217–2225 (1993). [CrossRef]
36. P. Lalanne and D. Lemercier-Lalanne, “On the effective medium theory of subwavelength periodic structures,” J. Mod. Opt. 43(10), 2063–2085 (1996). [CrossRef]
37. M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of metallic surface-relief gratings,” J. Opt. Soc. Am. A 3(11), 1780–1787 (1986). [CrossRef]
38. M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 71(7), 811–818 (1981). [CrossRef]
39. M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12(5), 1068–1076 (1995). [CrossRef]
40. M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. A 12(5), 1077–1086 (1995). [CrossRef]
41. S. M. Norton, T. Erdogan, and G. M. Morris, “Coupled-mode theory of resonant-grating filters,” J. Opt. Soc. Am. A 14(3), 629–639 (1997). [CrossRef]
42. G. Lu, S. Park, K. Yu, R. S. Ruoff, L. E. Ocola, D. Rosenmann, and J. Chen, “Toward Practical Gas Sensing with Highly Reduced Graphene Oxide: A New Signal Processing Method To Circumvent Run-to-Run and Device-to-Device Variations,” ACS Nano 5(2), 1154–1164 (2011). [CrossRef]
43. F. Xing, G. X. Meng, Q. Zhang, L. T. Pan, P. Wang, Z. B. Liu, W. S. Jiang, Y. Chen, and J. G. Tian, “Ultrasensitive flow sensing of a single cell using graphene-based optical sensors,” Nano Lett. 14(6), 3563–3569 (2014). [CrossRef]
44. J. Zhu and Z. Xu, “Tunable temperature sensor based on an integrated plasmonic grating,” Opt. Mater. Express 9(2), 435–440 (2019). [CrossRef]
45. Y. Li, Y. Liu, Z. Liu, Q. Tang, L. Shi, Q. Chen, G. Du, B. Wu, G. Liu, and L. Li, “Grating-assisted ultra-narrow multispectral plasmonic resonances for sensing application,” Appl. Phys. Express 12(7), 072002 (2019). [CrossRef]
46. J. Chen, W. Fan, T. Zhang, C. Tang, X. Chen, J. Wu, D. Li, and Y. Yu, “Engineering the magnetic plasmon resonances of metamaterials for high-quality sensing,” Opt. Express 25(4), 3675–3681 (2017). [CrossRef]
47. L. Qin, S. Wu, C. Zhang, and X. Li, “Narrowband and Full-Angle Refractive Index Sensor Based on a Planar Multilayer Structure,” IEEE Sens. J. 19(8), 2924–2930 (2019). [CrossRef]
48. B. Liu, C. Tang, J. Chen, N. Xie, J. Yuan, H. Tang, and X. Zhu, “Metal-substrate-enhanced magnetic dipole resonance in metamaterials for high-performance refractive index sensing,” Opt. Mater. Express 8(7), 2008–2016 (2018). [CrossRef]
49. J. Chen, J. Yuan, Q. Zhang, H. Ge, C. Tang, Y. Liu, and B. Guo, “Dielectric waveguide-enhanced localized surface plasmon resonance refractive index sensing,” Opt. Mater. Express 8(2), 342–347 (2018). [CrossRef]
50. G. Li, Y. Shen, G. Xiao, and C. Jin, “Double-layered metal grating for high-performance refractive index sensing,” Opt. Express 23(7), 8995–9003 (2015). [CrossRef]
51. J. Chen, C. Yang, P. Gu, Y. Kuang, C. Tang, S. Chen, and Z. Liu, “High Sensing Properties of Magnetic Plasmon Resonance by Strong Coupling in Three-Dimensional Metamaterials,” J. Lightwave Technol. 39(2), 562–565 (2021). [CrossRef]
52. J. Chen, C. Peng, S. Qi, Q. Zhang, C. Tang, X. Shen, H. Da, L. Wang, and G.-S. Park, “Photonic Microcavity-Enhanced Magnetic Plasmon Resonance of Metamaterials for Sensing Applications,” IEEE Photonics Technol. Lett. 31(2), 113–116 (2019). [CrossRef]
53. J. Chen, H. Nie, C. Peng, S. Qi, C. Tang, Y. Zhang, L. Wang, and G.-S. Park, “Enhancing the Magnetic Plasmon Resonance of Three-Dimensional Optical Metamaterials via Strong Coupling for High-Sensitivity Sensing,” J. Lightwave Technol. 36(16), 3481–3485 (2018). [CrossRef]
54. J. Chen, S. Qi, X. Hong, P. Gu, R. Wei, C. Tang, Y. Huang, and C. Zhao, “Highly sensitive 3D metamaterial sensor based on diffraction coupling of magnetic plasmon resonances,” Results Phys. 15, 102791 (2019). [CrossRef]
55. J. Chen, H. Nie, C. Tang, Y. Cui, B. Yan, Z. Zhang, Y. Kong, Z. Xu, and P. Cai, “Highly sensitive refractive-index sensor based on strong magnetic resonance in metamaterials,” Appl. Phys. Express 12(5), 052015 (2019). [CrossRef]
