Abstract

All-dielectric binary gratings, with and without slab waveguides, are designed to generate polarization-independent guided-mode resonance filters (GMRFs) operating in the THz frequency region using the rigorous coupled-wave analysis (RCWA) method. The filling factor and thickness of the grating were adjusted to have equal resonance frequencies of transverse electric (TE)- and transverse magnetic (TM)-polarized THz beams. The single polarization-independent resonance for a binary grating without a slab waveguide was obtained at 0.459 THz with full width at half maximum (FWHM) values of 8.3 and 8.5 GHz for the TE and TM modes, respectively. Moreover, double-layered polarization-independent resonances for binary gratings with slab waveguides were obtained at 0.369 and 0.442 THz with very high Q-factors of up to 284. This is the first study to propose a polarization-independent GMRF with two resonant frequencies.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

The guided-mode resonance (GMR) effect, which occurs in various periodic media, is of great scientific and technical interest. Most GMR filter (GMRF) designs are a combination of a grating on the filter surface and a slab waveguide of the filter substrate [13]. When the diffracted wave generated by the grating propagates along the slab waveguide and satisfies the guiding condition of the slab waveguide, it cannot pass through the GMRF and is reflected. GMRFs are operated under the normal incidence of a linearly polarized plane wave whose electric field vector is parallel (transverse electric, TE) or perpendicular (transverse magnetic, TM) to the grating lines. Typically, the resonance frequencies of one-dimensional (1-D) GMRFs are very sensitive to the polarization direction of the incident wave because of the line structure of the grating. A simple design of a polarization-independent GMRF with the same resonant frequency for TE and TM is a two-dimensional (2-D) structure that is symmetric to the polarization of the incident wave, such as cross-integrated [4], rectangular [57], and circular structures [811]. These 2-D symmetrical GMRFs require complex manufacturing processes. Recently, polarization-independent GMRFs with 1-D structures have been proposed using numerical calculations or computer simulations in the optical domain [1215]. These 1-D structures are based on the grating structures of multilayer dielectric substrates. A polarization-independent GMRF can be obtained by adjusting the separation between multilayer dielectric substrates [12,14]. Lacour et al. introduced a 1-D grating in conical mounting to obtain a polarization-independent GMRF by adjusting the filling factor (FF) and grating thickness [12]. Luo et al. introduced a GMRF with a 1-D grating layer and five-layer substrates. They obtained polarization-independent GMRFs by adjusting the thickness of the interlayer sandwiched between two dielectric layers with high permittivity [14]. In addition, Alasaarela et al. proposed a polarization-independent GMRF that replaced the grating structure with a sinusoidal structure rather than multilayer dielectric substrates [16].

Although several single-layer GMRFs have been proposed in the optical domain [17,18], the single-layer GMRFs are on fused silica, and their implementation is limited because the dimensions of the thickness and period of the GMRFs must be on the nanometer scale to meet the resonance conditions. Because the THz wavelength is longer than the visible wavelength and shorter than the wavelength of microwave radiation, the polarization-independent THz GMRF is simple to manufacture. Recently, two independent 1-D grating structures were introduced for polarization-independent GMRFs in the THz region [19]. However, there are no reports of dielectric single-layer and multilayer polarization-independent GMRFs operating in the THz region.

We propose all-dielectric single- and double-layered polarization-independent GMRFs with a 1-D grating structure operating in the THz region. We studied the polarization-independence of GMRF according to FF and grating thickness. The rigorous coupled-wave analysis (RCWA) method is used to find a polarization-independent GMRF operating in the THz domain. RCWA is an accurate calculation method from Maxwell’s equation for the electromagnetic transmittance and reflection of grating structures, and it has been widely used to design periodic and multi-layered GMRFs [20]. The proposed GMRFs have a low full width at half maximum (FWHM) and a high Q-factor [2123] at THz frequencies. Moreover, a polarization-independent GMRF operating at two resonant frequencies is proposed.

2. Polarization-independent GMRF with grating layer

Figure 1 illustrates a GMRF with a binary grating layer on a slab waveguide (substrate). Although only the grating layer (single layer) exists without the slab waveguide (d2 = 0), GMR can occur in the THz region [2426]. When the THz beam is vertically incident on the GMRF surface, and only the first diffraction mode is considered, the equation satisfying the diffraction and guiding conditions for GMRs can be simplified as [27]

$$\sqrt {{\varepsilon _{inc}}} \le |{c/(f \times \Lambda )} |< \sqrt {{\varepsilon _{avg}}}, $$
where inc and εavg denote the dielectric constant of the incident material, and the average dielectric constant of the GMRF, respectively; and c, f, and Λ denote the speed of light, frequency, and grating period, respectively. Because the dielectric constant of the incident material (εinc) is air, the high-frequency limit where GMR can exist is fixed at 0.588 THz, which is the Rayleigh anomaly frequency ($\textrm{c}/\left( {\sqrt {{\varepsilon_{inc}}} \times \mathrm{\Lambda }} \right)$) [2830]. The value of εavg can be calculated using the dielectric constants of the grating material (ridge) and air (groove), and the grating period and thickness [31]. In this study, we considered the ridge width (FF ${\times} $ Λ) rather than the fixed grating period at 510 µm. Therefore, εavg depends on the cross-sectional area of the ridge, that is, thickness (d1) and ridge width, which can be defined as the product of the FF and Λ. As the FF and d1 increase, εavg increases, and the low-frequency limit at which GMR can exist also shifts to the low-frequency region. In particular, because the field of the TM mode is distributed along the cross-sectional area of the grating layer, the shift in the resonance frequency is more affected than in the TE mode whose electric field vector is parallel to the grating lines [19]. Therefore, changing the cross-sectional area of the ridges by adjusting the FF and d1 yields the same resonant frequency in both the TE and TM modes. Consequently, polarization-independent GMRFs can be realized.

 figure: Fig. 1.

Fig. 1. Geometry of GMRF. The binary grating comprises the period (Λ), filling factor (FF), ridge width (FF ${\times} $ Λ), ridge thickness (d1), and slab waveguide (substrate) thickness (d2). The THz wave is normal incident from air onto the GMRF (+z-direction with zero incident angle). A linearly polarized THz wave changes the polarization angle (Φ) from 0° to 180°. TE and TM modes are defined when the electric field vector is parallel (TE, Φ = 90°) or perpendicular (TM, Φ = 0° or Φ = 180°) to the grating lines. The reflective indices of both the grating and slab waveguide are considered PET. When d2 = 0, the grating works as a single-layer GMRF.

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Figure 2(a–f) shows 2-D images of the TE and TM modes for different FFs and d1 values of 125, 155, and 220 µm, respectively. In this study, because the resonance frequency of polarization-independent GMRF appears at approximately 0.4 THz, the refractive index of the grating layer, which is semi-crystalline polyethylene terephthalate (PET), was considered as 1.75 at approximately 0.4 THz [32]. In addition, because the absorption of the PET at approximately 0.4 THz is very small, attenuation is not considered in the study. When Eq. (1) is transformed into the frequency domain, where GMR can exist (fGMR),

$$c/\left( {\sqrt {{\varepsilon_{avg}}} \Lambda } \right) \fallingdotseq {f_{LL}}({{\varepsilon_{avg}}} )< {f_{GMR}} < c/\left( {\sqrt {{\varepsilon_{air}}} \Lambda } \right) \fallingdotseq {f_{HL}}({{\varepsilon_{air}}} ), $$
where fLL and fHL denote the low- and high-frequency limits of the resonance region, respectively. As the FF increases, the average dielectric constant increases because the ridge width becomes wider compared with the voids (air) between the ridges. This causes fLL to shift to a lower frequency. In addition, when d1 is thick, fLL shifts to a lower frequency because the cross-sectional area increases. Meanwhile, when the FF approaches 1%, εavg approaches εair. Therefore, fLL approaches fHL, which is fixed at 0.588 THz. The fHL term indicates that the grating period and resonance wavelength are the same. In other words, the resonance wavelength must be greater than the grating period for GMR to occur. We refer to fHLair) as the Rayleigh anomaly. When the THz beam is incident on the GMRF in air, the GMR always occurs at a lower frequency than the corresponding Rayleigh anomaly frequency (fRA). Therefore, the high-frequency limit becomes the Rayleigh anomaly frequency (fHL = fRA). We can observe fRA at 0.588 THz. In particular, the resonance wing part suddenly decreases after 0.588 THz, as shown in Fig. 2(c). All resonant frequencies exist at frequencies lower than fRA, and as the FF and d1 increase, the resonance frequencies move to a lower frequency region.

 figure: Fig. 2.

Fig. 2. RCWA simulation of single-layer (d2 = 0) polarization-independent GMRF. 2-D image of total transmittance for TE mode according to FF and frequency; (a) d1 = 125 µm, (b) d1 = 155 µm, and (c) d1 = 220 µm. 2-D image of total transmittance for TM mode according to FF and frequency; (d) d1 = 125 µm, (e) d1 = 155 µm, and (f) d1 = 220 µm. Distribution of peak resonance frequencies of TE and TM modes; (g) d1 = 125 µm, (h) d1 = 155 µm, and (i) d1 = 220 µm. Total transmittance at the dashed line is shown in Fig. 3.

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Figure 2(g–i) shows a 2-D image of the peak resonance frequencies for the TE and TM modes (see Supplement 1). When the grating thickness is 125 µm, the peak resonance frequencies of the TE and TM modes are separated, as shown in Fig. 2(g). When d1 increases, the peak resonance frequency of the TM mode shifts to lower frequencies faster than that of the TE mode, particularly in the region with a high FF, because the TM mode propagates along the cross-sectional area of the grating layer. Finally, when d1 is 155 µm, the peak resonance frequencies of the TE and TM modes are equal at 0.524 THz with a 60% FF, as shown in Fig. 2(h). As d1 increases, the peak resonance frequencies of the TE and TM modes become equal at two FFs of 38% and 78%, as shown in Fig. 2(i).

Figure 3 shows the total transmittance of the TE and TM modes for the selected FFs, as shown by the dashed lines in Fig. 2(g–i). Figure 3(a) shows the total transmittance of the TM and TE modes at an FF of 60% with d1 = 125 µm. There is no polarization-independent GMRF because the TE and TM mode lines do not contact, as shown in Fig. 2(g). The FWHM of the TE mode is very large, and the peak resonance frequencies of the TE and TM modes are separated as 0.525 and 0.537 THz, respectively. However, when d1 is 155 µm, the polarization-independent GMR is achieved at 0.524 THz with an FF of 60%, as shown in Fig. 3(b). Although the FWHM of the TM mode is very small, that of the TE mode is still very large. For d1 = 220 µm, two polarization-independent GMRFs exist at FFs of 38% and 78%, as shown in Fig. 2(i). However, when the FF is 38%, the polarization-independent GMRF is not favorable because the FWHM of the TE mode is very large, as shown in Fig. 2(c). However, when the FF is 78%, another polarization-independent GMR is achieved at 0.459 THz, as shown in Fig. 3(c). The FWHMs of the TE and TM modes are very similar and have high Q-factors of 55 and 54, respectively. This is a very good characteristic for polarization-independent GMRFs, which can be utilized for applications in devices and systems.

 figure: Fig. 3.

Fig. 3. Total transmittance near peak resonance frequency for TE and TM modes with different FFs, as shown by the dashed lines in Fig. 2(g–i); (a) FF = 60% and d1 = 125 µm, (b) FF = 60% and d1 = 155 µm, and (c) FF = 78% and d1 = 220 µm.

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 figure: Fig. 4.

Fig. 4. Relation between FF and FWHM of TE0,1 and TM0,1 modes when grating thickness (d1) is 220 µm. Blue and red dots represent TE0,1 and TM0,1 modes, respectively.

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For d1 = 220 µm, Fig. 4 shows the FWHM of the TE0,1 and TM0,1 modes for FF values from 70% to 94%. As the FF increases, the FWHM of the TM0,1 mode decreases slowly compared to that of the TE0,1 mode. Both the FWHMs of the TE0,1 and TM0,1 modes are almost identical at an FF of 78%. Although the FWHM decreases as the FF increases, the resonance frequencies of the TE0,1 and TM0,1 modes are separated without an FF of 78%; thus, the polarization-independent GMRF is not obtained.

The 2-D spectral image and 3-D total transmittance image of the TE and TM modes at an FF of 78% is shown in Fig. 5(a) and (b), respectively. As the polarization angle increases, the resonance widths of the TE0,1 and TM0,1 modes are almost identical. Moreover, the resonance frequency is fixed at 0.459 THz, which is a favorable polarization-independent GMRF. Meanwhile, the Rayleigh anomaly frequency (fRA) is clearly observed at 0.588 THz. Finally, a polarization-independent GMRF at 0.459 THz is achieved with the same FWHM resonances for the TE0,1 and TM0,1 modes of 8.3 and 8.5 GHz, respectively, for the grating with Λ = 510 µm, FF = 78%, and d1 = 220 µm.

 figure: Fig. 5.

Fig. 5. (a) 2-D image of total transmittance at FF of 78% according to the polarization of incident THz beam and frequency. (b) 3-D image of total transmittance at FF of 78% according to the polarization of incident THz beam and frequency.

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3. Polarization-independent GMRF with grating and slab waveguide layers

If the thickness of the slab waveguide (d2) is sufficiently thick to distribute a high-order electromagnetic field, multimode GMR can occur [33,34]. The high-order TE and TM modes occur sequentially as d2 increases. When d2 is sufficiently thick to create a multimode GMR, the resonance frequencies of the TE and TM modes can be matched in the high- and low-order modes. A polarization-independent GMRF with a small FF can be obtained if d2 is large. However, as d2 increases, absorption by the material increases, resulting in a smaller Q-factor. Therefore, a grating structure with a large FF is required to obtain a GMRF with a high Q-factor. As d1 and d2 increase, the peak resonance frequencies of the TM modes move faster to the lower frequency region than that of the TE modes (see Supplement 1). Therefore, polarization-independent GMRFs can be obtained at multiple frequencies, which implies that multiple polarization-independent GMRs can be obtained. From the RCWA simulation, a polarization-independent GMRF was obtained at two frequencies with a small FWHM. Figure 6(a) and (b) shows the relation between the FF and resonance frequency for the TE and TM modes, respectively, for d1 = 250 µm and d2 = 300 µm. GMRs with very high Q-factors occur at both ends of the TE and TM modes when the FF changes. The resonance width near the middle of the FF for both the TE and TM modes is relatively wide compared to the resonance width near both ends of the FF. The overlapped peak resonance frequencies of the TE and TM modes are shown in Fig. 6(c). Six polarization-independent GMRs were obtained. When the FF is nearly 50%, the resonance width is very wide, as shown by the TE1,1, TE2,1, and TM2,1 modes in Fig. 6(a) and (b). However, when the FF is 81%, as shown by the horizontal dashed line in Fig. 6(c), two polarization-independent GMRs are obtained simultaneously.

 figure: Fig. 6.

Fig. 6. RCWA simulation of double-layered (d1 = 250 µm, d2 = 300 µm) polarization-independent GMRF. 2-D image of total transmittance according to FF and frequency; (a) TE mode, (b) TM mode, and (c) Distribution of peak resonance frequencies of TE and TM modes. Total transmittance at the dotted line is shown in Fig. 7.

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Figure 7 shows total transmittance with an FF of 81%. Owing to the multiple reflections by the GMRF, the baselines of the total transmittances do not approach 1, and have a large oscillation in the spectrum. Although the resonance frequencies of the TE and TM modes are not perfectly matched, they are very similar. The first GMR frequencies of the TE0,1 and TM0,1 modes are both 0.3690 THz. The second GMR frequencies of the TE1,1 and TM1,1 modes are 0.4415 and 0.4419 THz, respectively. There is only a 0.4-GHz difference between the two resonance frequencies. If d1 and d2 are varied, multiple GMRs depending on the FF can be generated. However, we first propose a polarization-independent GMRF with two different resonant frequencies in a single FF.

 figure: Fig. 7.

Fig. 7. Total transmittance for TE and TM modes with an FF of 81%, as shown by the dashed lines in Fig. 6(c).

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Figure 8 shows the FWHM of the TE0,1, TE1,1, TM0,1, and TM1,1 modes for the FF. When the FF is 81%, as shown by the vertical dotted line, the FWHMs of the TE0,1, TM0,1, and TM1,1 modes are less than 2.7 GHz. The FWHM of the TE1,1 mode decreases with increasing FF, and the FWHM is 6.2 GHz for an FF of 81%. As the FF approaches approximately 90%, the FWHMs of the TE and TM modes are very small and nearly equal. However, because the ridge width and grating period are very similar at a very high FF, the resonance depth is excessively small. The 2-D and 3-D images in Fig. 9(a) and (b), respectively, show the relation between the polarization angle and resonance frequency at an FF of 81%. Polarization-independent GMRFs can be obtained at frequencies of 0.369 and 0.442 THz. Unlike the resonance of the TM2,1 mode, the resonances of the TM0,1 and TM1,1 modes always maintain the resonance frequencies, even if the polarization of the incident THz beam is changed. Moreover, the polarization-independent GMRF for both the TE0,1 and TM0,1 modes has a very high Q-factor of 284, which is higher than the Q-factors of 71 and 164 for the TE1,1 and TM1,1 modes, respectively.

 figure: Fig. 8.

Fig. 8. Relation between FF and FWHM of TE and TM modes. Blue and red dots represent TE0,1 and TM0,1 modes, respectively, whereas blue and red circles represent TE1,1 and TM1,1 modes, respectively.

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 figure: Fig. 9.

Fig. 9. (a) 2-D image of total transmittance at the FF of 81% according to the polarization of incident THz beam and frequency. (b) 3-D image of total transmittance at the FF of 81% according to the polarization of incident THz beam and frequency.

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Table 1 summarizes a comparison of polarization-independent GMRFs for the grating layer, and the grating and slab waveguide layers for the resonance frequency, FWHM, and Q-factor. It was possible to obtain GMRFs with excellent characteristics for a relatively high FF. In addition, in the grating and slab waveguide layer structure, a high-order mode was formed, and a GMRF with a high Q-factor of up to 284 was obtained. The proposed GMRFs have the potential for THz applications in communication and sensing in the future.

Tables Icon

Table 1. Comparison of polarization-independent GMRFs for grating layer, and grating and slab waveguide layers

4. Conclusion

We have shown that polarization-independence occurs in the binary grating structure GMRF, which consists of a grating layer, or grating and slab waveguide layers. The grating period and layer thickness are important parameters for designing polarization-independent GMRFs because these parameters can shift the resonance frequency. If the grating period is excessively large, then the diameter of the THz beam must be sufficiently large to cover a sufficient number of ridges in the grating. Therefore, we considered the FF rather than the grating period. As the FF and layer thickness are increased, the GMR frequencies of the TE and TM modes shift to the low-frequency region. Because the resonant frequency shift of the TM mode is faster than that of the TE mode, the resonance frequencies of the two modes are matched at a specific FF and layer thickness, that is, polarization-independent GMRF can be obtained. We obtained a polarization-independent GMR with a high Q-factor from the GMRF consisting only of a grating layer structure. In addition, when the GMRF has a grating and slab waveguide layer structure, two GMRs with very high Q-factors were obtained at an FF of 81%. Therefore, by adjusting the FF and thickness of the layers, it is possible to obtain a GMRF having at least one favorable resonance with a high Q-factor. The proposed thick grating layer, with and without a slab waveguide, is difficult to manufacture using femtosecond laser machining. Therefore, in this study, polarization-independent GMRFs could not be implemented experimentally, but if a new manufacturing method is developed, this experiment will be carried out. We believe that these binary grating structures could be used as narrowband polarization-independent filters in the THz domain, for applications such as THz communications and sensing.

Funding

National Research Foundation of Korea (2019R1A2B5B01070261).

Disclosures

The authors declare no conflicts of interest.

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.

Supplemental document

See Supplement 1 for supporting content.

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4. K. Kintaka, T. Majima, K. Hatanaka, J. Inoue, and S. Ura, “Polarization-independent guided-mode resonance filter with cross-integrated waveguide resonators,” Opt. Lett. 37(15), 3264–3266 (2012). [CrossRef]  

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6. C.-H. Park, Y.-T. Yoon, and S.-S. Lee, “Polarization-independent visible wavelength filter incorporating a symmetric metal-dielectric resonant structure,” Opt. Express 20(21), 23769–23777 (2012). [CrossRef]  

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References

  • View by:

  1. J. H. Barton, R. C. Rumpf, R. W. Smith, C. Kozikowsk, and P. Zellner, “All-dielectric frequency selective surfaces with few number of periods,” PIER B 41, 269–283 (2012).
    [Crossref]
  2. S. S. Wang and R. Magnusson, “Theory and applications of guided-mode resonance filters,” Appl. Opt. 32(14), 2606–2613 (1993).
    [Crossref]
  3. S. Tibuleac and R. Magnusson, “Reflection and transmission guided-mode resonance filters,” J. Opt. Soc. Am. A 14(7), 1617–1626 (1997).
    [Crossref]
  4. K. Kintaka, T. Majima, K. Hatanaka, J. Inoue, and S. Ura, “Polarization-independent guided-mode resonance filter with cross-integrated waveguide resonators,” Opt. Lett. 37(15), 3264–3266 (2012).
    [Crossref]
  5. S. Peng and G. M. Morris, “Resonant scattering from two-dimensional gratings,” J. Opt. Soc. Am. A 13(5), 993–1005 (1996).
    [Crossref]
  6. C.-H. Park, Y.-T. Yoon, and S.-S. Lee, “Polarization-independent visible wavelength filter incorporating a symmetric metal-dielectric resonant structure,” Opt. Express 20(21), 23769–23777 (2012).
    [Crossref]
  7. T. Clausnitzer, A. V. Tishchenko, E.-B. Kley, H.-J. Fuchs, D. Schelle, O. Parriaux, and U. Kroll, “Narrowband, polarization-independent free-space wave notch filter,” J. Opt. Soc. Am. A 22(12), 2799–2803 (2005).
    [Crossref]
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  15. D. Wu, X. Sui, J. Yang, and Z. Zhou, “Binary blazed grating-based polarization-independent filter on silicon on insulator,” Front. Optoelectron. 5(1), 78–81 (2012).
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  16. T. Alasaarela, D. Zheng, L. Huang, A. Priimagi, B. Bai, A. Tervonen, S. Honkanen, M. Kuittinen, and J. Turunen, “Single-layer one-dimensional nonpolarizing guided-mode resonance filters under normal incidence,” Opt. Lett. 36(13), 2411–2413 (2011).
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  18. Y. Ding and R. Magnusson, “Doubly resonant single-layer bandpass optical filters,” Opt. Lett. 29(10), 1135–1137 (2004).
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  22. Y. Han, J. Yang, X. He, J. Huang, J. Zhang, D. Chen, and Z. Zhang, “High quality factor electromagnetically induced transparency-like effect in coupled guided-mode resonant systems,” Opt. Express 27(5), 7712–7718 (2019).
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2021 (1)

H. S. Bark, K.-H. Jang, K. Lee, Y. U. Jung, and T.-I. Jeon, “THz guided-mode resonance notch filter with variable filtering strength,” Sci. Rep. 11(1), 1307 (2021).
[Crossref]

2020 (1)

M. Lawrence, D. R. Barton, J. Dixon, J.-H. Song, J. V. D. Groep, M. L. Brongersma, and J. A. Dionne, “High quality factor phase gradient metasurfaces,” Nat. Nanotechnol. 15(11), 956–961 (2020).
[Crossref]

2019 (3)

2018 (3)

2017 (1)

S.-G. Lee, S.-H. Kim, K.-J. Kim, and C.-S. Kee, “Polarization-independent electromagnetically induced transparency-like transmission in coupled guided-mode resonance structures,” Appl. Phys. Lett. 110(11), 111106 (2017).
[Crossref]

2016 (1)

2015 (1)

W. Wang, Q. Liu, G. Zhu, X. Li, S. He, T. Sa, X. Gao, and Y. Wang, “Polarization-insensitive concentric circular grating filters featuring a couple of resonant peaks,” IEEE Photonics J. 7(5), 1–10 (2015).
[Crossref]

2014 (1)

2013 (3)

M. S. Amin, J. W. Yoon, and R. Magnusson, “Optical transmission filters with coexisting guided-mode resonance and Rayleigh anomaly,” Appl. Phys. Lett. 103(13), 131106 (2013).
[Crossref]

R. Magnusson, “Flat-top resonant reflectors with sharply delimited angular spectra: an application of the Rayleigh anomaly,” Opt. Lett. 38(6), 989–991 (2013).
[Crossref]

S. Luo, L. Chen, Y. Bao, N. Yang, and Y. Zhu, “Non-polarizing guided-mode resonance grating filter for telecommuniations,” Optik 124(21), 5158–5160 (2013).
[Crossref]

2012 (4)

D. Wu, X. Sui, J. Yang, and Z. Zhou, “Binary blazed grating-based polarization-independent filter on silicon on insulator,” Front. Optoelectron. 5(1), 78–81 (2012).
[Crossref]

C.-H. Park, Y.-T. Yoon, and S.-S. Lee, “Polarization-independent visible wavelength filter incorporating a symmetric metal-dielectric resonant structure,” Opt. Express 20(21), 23769–23777 (2012).
[Crossref]

J. H. Barton, R. C. Rumpf, R. W. Smith, C. Kozikowsk, and P. Zellner, “All-dielectric frequency selective surfaces with few number of periods,” PIER B 41, 269–283 (2012).
[Crossref]

K. Kintaka, T. Majima, K. Hatanaka, J. Inoue, and S. Ura, “Polarization-independent guided-mode resonance filter with cross-integrated waveguide resonators,” Opt. Lett. 37(15), 3264–3266 (2012).
[Crossref]

2011 (1)

2009 (1)

2008 (1)

Y. Nazirizadeh, U. Lemmer, and M. Gerken, “Experimental quality factor determination of guided-mode resonances in photonic crystal slabs,” Appl. Phys. Lett. 93(26), 261110 (2008).
[Crossref]

2005 (2)

2004 (2)

2003 (1)

2002 (1)

Z. S. Liu and R. Magnusson, “Concept of multiorder multimode resonant optical filters,” IEEE Photon. Technol. Lett. 14(8), 1091–1093 (2002).
[Crossref]

1997 (1)

1996 (2)

1993 (1)

1907 (1)

L. Rayleigh, “On the dynamical theory of gratings,” Proc. R. Soc. Lond. A 79(532), 399–416 (1907).
[Crossref]

Alasaarela, T.

Amin, M. S.

M. S. Amin, J. W. Yoon, and R. Magnusson, “Optical transmission filters with coexisting guided-mode resonance and Rayleigh anomaly,” Appl. Phys. Lett. 103(13), 131106 (2013).
[Crossref]

Bai, B.

Bao, Y.

S. Luo, L. Chen, Y. Bao, N. Yang, and Y. Zhu, “Non-polarizing guided-mode resonance grating filter for telecommuniations,” Optik 124(21), 5158–5160 (2013).
[Crossref]

Bark, H. S.

Barton, D. R.

M. Lawrence, D. R. Barton, J. Dixon, J.-H. Song, J. V. D. Groep, M. L. Brongersma, and J. A. Dionne, “High quality factor phase gradient metasurfaces,” Nat. Nanotechnol. 15(11), 956–961 (2020).
[Crossref]

Barton, J. H.

J. H. Barton, R. C. Rumpf, R. W. Smith, C. Kozikowsk, and P. Zellner, “All-dielectric frequency selective surfaces with few number of periods,” PIER B 41, 269–283 (2012).
[Crossref]

Böhmler, J.

S. Engelbrecht, K.-H. Tybussek, J. Sampaio, J. Böhmler, B. M. Fischer, and S. Sommer, “Monitoring the isothermal crystallization kinetics of PET-A using THz-TDS,” J. Infrared Milli Terahz Waves 40(3), 306–313 (2019).
[Crossref]

Borges, B.-H. V.

Brongersma, M. L.

M. Lawrence, D. R. Barton, J. Dixon, J.-H. Song, J. V. D. Groep, M. L. Brongersma, and J. A. Dionne, “High quality factor phase gradient metasurfaces,” Nat. Nanotechnol. 15(11), 956–961 (2020).
[Crossref]

Chen, D.

Chen, L.

S. Luo, L. Chen, Y. Bao, N. Yang, and Y. Zhu, “Non-polarizing guided-mode resonance grating filter for telecommuniations,” Optik 124(21), 5158–5160 (2013).
[Crossref]

Clausnitzer, T.

Ding, Y.

Dionne, J. A.

M. Lawrence, D. R. Barton, J. Dixon, J.-H. Song, J. V. D. Groep, M. L. Brongersma, and J. A. Dionne, “High quality factor phase gradient metasurfaces,” Nat. Nanotechnol. 15(11), 956–961 (2020).
[Crossref]

Dixon, J.

M. Lawrence, D. R. Barton, J. Dixon, J.-H. Song, J. V. D. Groep, M. L. Brongersma, and J. A. Dionne, “High quality factor phase gradient metasurfaces,” Nat. Nanotechnol. 15(11), 956–961 (2020).
[Crossref]

Engelbrecht, S.

S. Engelbrecht, K.-H. Tybussek, J. Sampaio, J. Böhmler, B. M. Fischer, and S. Sommer, “Monitoring the isothermal crystallization kinetics of PET-A using THz-TDS,” J. Infrared Milli Terahz Waves 40(3), 306–313 (2019).
[Crossref]

Fan, Z.

Fang, X.

Fischer, B. M.

S. Engelbrecht, K.-H. Tybussek, J. Sampaio, J. Böhmler, B. M. Fischer, and S. Sommer, “Monitoring the isothermal crystallization kinetics of PET-A using THz-TDS,” J. Infrared Milli Terahz Waves 40(3), 306–313 (2019).
[Crossref]

Fu, X.

Fuchs, H.-J.

Gao, X.

W. Wang, Q. Liu, G. Zhu, X. Li, S. He, T. Sa, X. Gao, and Y. Wang, “Polarization-insensitive concentric circular grating filters featuring a couple of resonant peaks,” IEEE Photonics J. 7(5), 1–10 (2015).
[Crossref]

Gerken, M.

Y. Nazirizadeh, U. Lemmer, and M. Gerken, “Experimental quality factor determination of guided-mode resonances in photonic crystal slabs,” Appl. Phys. Lett. 93(26), 261110 (2008).
[Crossref]

Granet, G.

Groep, J. V. D.

M. Lawrence, D. R. Barton, J. Dixon, J.-H. Song, J. V. D. Groep, M. L. Brongersma, and J. A. Dionne, “High quality factor phase gradient metasurfaces,” Nat. Nanotechnol. 15(11), 956–961 (2020).
[Crossref]

Han, Y.

Hatanaka, K.

He, S.

W. Wang, Q. Liu, G. Zhu, X. Li, S. He, T. Sa, X. Gao, and Y. Wang, “Polarization-insensitive concentric circular grating filters featuring a couple of resonant peaks,” IEEE Photonics J. 7(5), 1–10 (2015).
[Crossref]

He, X.

Herzig, H. P.

Honkanen, S.

Huang, J.

Huang, L.

Inoue, J.

Jang, K.-H.

H. S. Bark, K.-H. Jang, K. Lee, Y. U. Jung, and T.-I. Jeon, “THz guided-mode resonance notch filter with variable filtering strength,” Sci. Rep. 11(1), 1307 (2021).
[Crossref]

Jeon, T.-I.

Jung, Y. U.

H. S. Bark, K.-H. Jang, K. Lee, Y. U. Jung, and T.-I. Jeon, “THz guided-mode resonance notch filter with variable filtering strength,” Sci. Rep. 11(1), 1307 (2021).
[Crossref]

Kee, C.-S.

S.-G. Lee, S.-H. Kim, K.-J. Kim, and C.-S. Kee, “Polarization-independent electromagnetically induced transparency-like transmission in coupled guided-mode resonance structures,” Appl. Phys. Lett. 110(11), 111106 (2017).
[Crossref]

Kim, G. J.

H. S. Bark, G. J. Kim, and T.-I. Jeon, “Transmission characteristics of all-dielectric guided-mode resonance filter in the THz region,” Sci. Rep. 8(1), 13570 (2018).
[Crossref]

Kim, K.-J.

S.-G. Lee, S.-H. Kim, K.-J. Kim, and C.-S. Kee, “Polarization-independent electromagnetically induced transparency-like transmission in coupled guided-mode resonance structures,” Appl. Phys. Lett. 110(11), 111106 (2017).
[Crossref]

Kim, S.-H.

S.-G. Lee, S.-H. Kim, K.-J. Kim, and C.-S. Kee, “Polarization-independent electromagnetically induced transparency-like transmission in coupled guided-mode resonance structures,” Appl. Phys. Lett. 110(11), 111106 (2017).
[Crossref]

Kintaka, K.

Kley, E.-B.

Kozikowsk, C.

J. H. Barton, R. C. Rumpf, R. W. Smith, C. Kozikowsk, and P. Zellner, “All-dielectric frequency selective surfaces with few number of periods,” PIER B 41, 269–283 (2012).
[Crossref]

Kroll, U.

Kuittinen, M.

Lacour, D.

Lawrence, M.

M. Lawrence, D. R. Barton, J. Dixon, J.-H. Song, J. V. D. Groep, M. L. Brongersma, and J. A. Dionne, “High quality factor phase gradient metasurfaces,” Nat. Nanotechnol. 15(11), 956–961 (2020).
[Crossref]

Lee, K.

H. S. Bark, K.-H. Jang, K. Lee, Y. U. Jung, and T.-I. Jeon, “THz guided-mode resonance notch filter with variable filtering strength,” Sci. Rep. 11(1), 1307 (2021).
[Crossref]

Lee, K. J.

Lee, S. B.

Lee, S.-G.

S.-G. Lee, S.-H. Kim, K.-J. Kim, and C.-S. Kee, “Polarization-independent electromagnetically induced transparency-like transmission in coupled guided-mode resonance structures,” Appl. Phys. Lett. 110(11), 111106 (2017).
[Crossref]

Lee, S.-S.

Lemmer, U.

Y. Nazirizadeh, U. Lemmer, and M. Gerken, “Experimental quality factor determination of guided-mode resonances in photonic crystal slabs,” Appl. Phys. Lett. 93(26), 261110 (2008).
[Crossref]

Li, X.

W. Wang, G. Zhu, Q. Liu, X. Li, T. Sa, X. Fang, H. Zhu, and Y. Wang, “Angle- and polarization-dependent spectral characteristics of circular grating filters,” Opt. Express 24(10), 11033–11042 (2016).
[Crossref]

W. Wang, Q. Liu, G. Zhu, X. Li, S. He, T. Sa, X. Gao, and Y. Wang, “Polarization-insensitive concentric circular grating filters featuring a couple of resonant peaks,” IEEE Photonics J. 7(5), 1–10 (2015).
[Crossref]

Liu, Q.

W. Wang, G. Zhu, Q. Liu, X. Li, T. Sa, X. Fang, H. Zhu, and Y. Wang, “Angle- and polarization-dependent spectral characteristics of circular grating filters,” Opt. Express 24(10), 11033–11042 (2016).
[Crossref]

W. Wang, Q. Liu, G. Zhu, X. Li, S. He, T. Sa, X. Gao, and Y. Wang, “Polarization-insensitive concentric circular grating filters featuring a couple of resonant peaks,” IEEE Photonics J. 7(5), 1–10 (2015).
[Crossref]

Liu, Z. S.

Z. S. Liu and R. Magnusson, “Concept of multiorder multimode resonant optical filters,” IEEE Photon. Technol. Lett. 14(8), 1091–1093 (2002).
[Crossref]

Luo, S.

S. Luo, L. Chen, Y. Bao, N. Yang, and Y. Zhu, “Non-polarizing guided-mode resonance grating filter for telecommuniations,” Optik 124(21), 5158–5160 (2013).
[Crossref]

Magnusson, R.

Majima, T.

Mazulquim, D. B.

Morris, G. M.

Muniz, L. V.

Nakagawa, W.

Nazirizadeh, Y.

Y. Nazirizadeh, U. Lemmer, and M. Gerken, “Experimental quality factor determination of guided-mode resonances in photonic crystal slabs,” Appl. Phys. Lett. 93(26), 261110 (2008).
[Crossref]

Neto, L. G.

Niederer, G.

Park, C.-H.

Parriaux, O.

Peng, S.

Plumey, J.-P.

Priimagi, A.

Rayleigh, L.

L. Rayleigh, “On the dynamical theory of gratings,” Proc. R. Soc. Lond. A 79(532), 399–416 (1907).
[Crossref]

Rumpf, R. C.

J. H. Barton, R. C. Rumpf, R. W. Smith, C. Kozikowsk, and P. Zellner, “All-dielectric frequency selective surfaces with few number of periods,” PIER B 41, 269–283 (2012).
[Crossref]

R. C. Rumpf, “Design and optimaization of nano-optical element by coupling fabrication to optical behavior,” Ph.D. Dissertation, University of Central Florida (2006).

Sa, T.

W. Wang, G. Zhu, Q. Liu, X. Li, T. Sa, X. Fang, H. Zhu, and Y. Wang, “Angle- and polarization-dependent spectral characteristics of circular grating filters,” Opt. Express 24(10), 11033–11042 (2016).
[Crossref]

W. Wang, Q. Liu, G. Zhu, X. Li, S. He, T. Sa, X. Gao, and Y. Wang, “Polarization-insensitive concentric circular grating filters featuring a couple of resonant peaks,” IEEE Photonics J. 7(5), 1–10 (2015).
[Crossref]

Sampaio, J.

S. Engelbrecht, K.-H. Tybussek, J. Sampaio, J. Böhmler, B. M. Fischer, and S. Sommer, “Monitoring the isothermal crystallization kinetics of PET-A using THz-TDS,” J. Infrared Milli Terahz Waves 40(3), 306–313 (2019).
[Crossref]

Schelle, D.

Shao, J.

Smith, R. W.

J. H. Barton, R. C. Rumpf, R. W. Smith, C. Kozikowsk, and P. Zellner, “All-dielectric frequency selective surfaces with few number of periods,” PIER B 41, 269–283 (2012).
[Crossref]

Sommer, S.

S. Engelbrecht, K.-H. Tybussek, J. Sampaio, J. Böhmler, B. M. Fischer, and S. Sommer, “Monitoring the isothermal crystallization kinetics of PET-A using THz-TDS,” J. Infrared Milli Terahz Waves 40(3), 306–313 (2019).
[Crossref]

Song, J.-H.

M. Lawrence, D. R. Barton, J. Dixon, J.-H. Song, J. V. D. Groep, M. L. Brongersma, and J. A. Dionne, “High quality factor phase gradient metasurfaces,” Nat. Nanotechnol. 15(11), 956–961 (2020).
[Crossref]

Sui, X.

D. Wu, X. Sui, J. Yang, and Z. Zhou, “Binary blazed grating-based polarization-independent filter on silicon on insulator,” Front. Optoelectron. 5(1), 78–81 (2012).
[Crossref]

Tervonen, A.

Tibuleac, S.

Tishchenko, A. V.

Turunen, J.

Tybussek, K.-H.

S. Engelbrecht, K.-H. Tybussek, J. Sampaio, J. Böhmler, B. M. Fischer, and S. Sommer, “Monitoring the isothermal crystallization kinetics of PET-A using THz-TDS,” J. Infrared Milli Terahz Waves 40(3), 306–313 (2019).
[Crossref]

Ura, S.

Wang, S. S.

Wang, W.

W. Wang, G. Zhu, Q. Liu, X. Li, T. Sa, X. Fang, H. Zhu, and Y. Wang, “Angle- and polarization-dependent spectral characteristics of circular grating filters,” Opt. Express 24(10), 11033–11042 (2016).
[Crossref]

W. Wang, Q. Liu, G. Zhu, X. Li, S. He, T. Sa, X. Gao, and Y. Wang, “Polarization-insensitive concentric circular grating filters featuring a couple of resonant peaks,” IEEE Photonics J. 7(5), 1–10 (2015).
[Crossref]

Wang, Y.

W. Wang, G. Zhu, Q. Liu, X. Li, T. Sa, X. Fang, H. Zhu, and Y. Wang, “Angle- and polarization-dependent spectral characteristics of circular grating filters,” Opt. Express 24(10), 11033–11042 (2016).
[Crossref]

W. Wang, Q. Liu, G. Zhu, X. Li, S. He, T. Sa, X. Gao, and Y. Wang, “Polarization-insensitive concentric circular grating filters featuring a couple of resonant peaks,” IEEE Photonics J. 7(5), 1–10 (2015).
[Crossref]

Wu, D.

D. Wu, X. Sui, J. Yang, and Z. Zhou, “Binary blazed grating-based polarization-independent filter on silicon on insulator,” Front. Optoelectron. 5(1), 78–81 (2012).
[Crossref]

Yang, J.

Y. Han, J. Yang, X. He, J. Huang, J. Zhang, D. Chen, and Z. Zhang, “High quality factor electromagnetically induced transparency-like effect in coupled guided-mode resonant systems,” Opt. Express 27(5), 7712–7718 (2019).
[Crossref]

D. Wu, X. Sui, J. Yang, and Z. Zhou, “Binary blazed grating-based polarization-independent filter on silicon on insulator,” Front. Optoelectron. 5(1), 78–81 (2012).
[Crossref]

Yang, N.

S. Luo, L. Chen, Y. Bao, N. Yang, and Y. Zhu, “Non-polarizing guided-mode resonance grating filter for telecommuniations,” Optik 124(21), 5158–5160 (2013).
[Crossref]

Yi, K.

Yoon, J. W.

D. B. Mazulquim, K. J. Lee, J. W. Yoon, L. V. Muniz, B.-H. V. Borges, L. G. Neto, and R. Magnusson, “Efficient band-pass color filters enabled by resonant modes and plasmons near the Rayleigh anomaly,” Opt. Express 22(25), 30843–30851 (2014).
[Crossref]

M. S. Amin, J. W. Yoon, and R. Magnusson, “Optical transmission filters with coexisting guided-mode resonance and Rayleigh anomaly,” Appl. Phys. Lett. 103(13), 131106 (2013).
[Crossref]

Yoon, Y.-T.

Zellner, P.

J. H. Barton, R. C. Rumpf, R. W. Smith, C. Kozikowsk, and P. Zellner, “All-dielectric frequency selective surfaces with few number of periods,” PIER B 41, 269–283 (2012).
[Crossref]

Zhang, J.

Zhang, Z.

Zheng, D.

Zhou, Z.

D. Wu, X. Sui, J. Yang, and Z. Zhou, “Binary blazed grating-based polarization-independent filter on silicon on insulator,” Front. Optoelectron. 5(1), 78–81 (2012).
[Crossref]

Zhu, G.

W. Wang, G. Zhu, Q. Liu, X. Li, T. Sa, X. Fang, H. Zhu, and Y. Wang, “Angle- and polarization-dependent spectral characteristics of circular grating filters,” Opt. Express 24(10), 11033–11042 (2016).
[Crossref]

W. Wang, Q. Liu, G. Zhu, X. Li, S. He, T. Sa, X. Gao, and Y. Wang, “Polarization-insensitive concentric circular grating filters featuring a couple of resonant peaks,” IEEE Photonics J. 7(5), 1–10 (2015).
[Crossref]

Zhu, H.

Zhu, Y.

S. Luo, L. Chen, Y. Bao, N. Yang, and Y. Zhu, “Non-polarizing guided-mode resonance grating filter for telecommuniations,” Optik 124(21), 5158–5160 (2013).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (3)

S.-G. Lee, S.-H. Kim, K.-J. Kim, and C.-S. Kee, “Polarization-independent electromagnetically induced transparency-like transmission in coupled guided-mode resonance structures,” Appl. Phys. Lett. 110(11), 111106 (2017).
[Crossref]

Y. Nazirizadeh, U. Lemmer, and M. Gerken, “Experimental quality factor determination of guided-mode resonances in photonic crystal slabs,” Appl. Phys. Lett. 93(26), 261110 (2008).
[Crossref]

M. S. Amin, J. W. Yoon, and R. Magnusson, “Optical transmission filters with coexisting guided-mode resonance and Rayleigh anomaly,” Appl. Phys. Lett. 103(13), 131106 (2013).
[Crossref]

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Supplementary Material (1)

NameDescription
Supplement 1       Supplementary for Fig.2 and Fig. 6

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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Figures (9)

Fig. 1.
Fig. 1. Geometry of GMRF. The binary grating comprises the period (Λ), filling factor (FF), ridge width (FF ${\times} $ Λ), ridge thickness (d1), and slab waveguide (substrate) thickness (d2). The THz wave is normal incident from air onto the GMRF (+z-direction with zero incident angle). A linearly polarized THz wave changes the polarization angle (Φ) from 0° to 180°. TE and TM modes are defined when the electric field vector is parallel (TE, Φ = 90°) or perpendicular (TM, Φ = 0° or Φ = 180°) to the grating lines. The reflective indices of both the grating and slab waveguide are considered PET. When d2 = 0, the grating works as a single-layer GMRF.
Fig. 2.
Fig. 2. RCWA simulation of single-layer (d2 = 0) polarization-independent GMRF. 2-D image of total transmittance for TE mode according to FF and frequency; (a) d1 = 125 µm, (b) d1 = 155 µm, and (c) d1 = 220 µm. 2-D image of total transmittance for TM mode according to FF and frequency; (d) d1 = 125 µm, (e) d1 = 155 µm, and (f) d1 = 220 µm. Distribution of peak resonance frequencies of TE and TM modes; (g) d1 = 125 µm, (h) d1 = 155 µm, and (i) d1 = 220 µm. Total transmittance at the dashed line is shown in Fig. 3.
Fig. 3.
Fig. 3. Total transmittance near peak resonance frequency for TE and TM modes with different FFs, as shown by the dashed lines in Fig. 2(g–i); (a) FF = 60% and d1 = 125 µm, (b) FF = 60% and d1 = 155 µm, and (c) FF = 78% and d1 = 220 µm.
Fig. 4.
Fig. 4. Relation between FF and FWHM of TE0,1 and TM0,1 modes when grating thickness (d1) is 220 µm. Blue and red dots represent TE0,1 and TM0,1 modes, respectively.
Fig. 5.
Fig. 5. (a) 2-D image of total transmittance at FF of 78% according to the polarization of incident THz beam and frequency. (b) 3-D image of total transmittance at FF of 78% according to the polarization of incident THz beam and frequency.
Fig. 6.
Fig. 6. RCWA simulation of double-layered (d1 = 250 µm, d2 = 300 µm) polarization-independent GMRF. 2-D image of total transmittance according to FF and frequency; (a) TE mode, (b) TM mode, and (c) Distribution of peak resonance frequencies of TE and TM modes. Total transmittance at the dotted line is shown in Fig. 7.
Fig. 7.
Fig. 7. Total transmittance for TE and TM modes with an FF of 81%, as shown by the dashed lines in Fig. 6(c).
Fig. 8.
Fig. 8. Relation between FF and FWHM of TE and TM modes. Blue and red dots represent TE0,1 and TM0,1 modes, respectively, whereas blue and red circles represent TE1,1 and TM1,1 modes, respectively.
Fig. 9.
Fig. 9. (a) 2-D image of total transmittance at the FF of 81% according to the polarization of incident THz beam and frequency. (b) 3-D image of total transmittance at the FF of 81% according to the polarization of incident THz beam and frequency.

Tables (1)

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Table 1. Comparison of polarization-independent GMRFs for grating layer, and grating and slab waveguide layers

Equations (2)

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ε i n c | c / ( f × Λ ) | < ε a v g ,
c / ( ε a v g Λ ) f L L ( ε a v g ) < f G M R < c / ( ε a i r Λ ) f H L ( ε a i r ) ,

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