1. Introduction

Optical resonances play a vital role in optical physics due to their unique capability to trap light in small volumes [1–4]. As a class of optical resonances, Fabry-Perot resonances have been extensively exploited to design interferometers [5,6], filters [7–10], lasers [11,12], absorbers [13–15], sensors [16–20], antennas [21,22], optical switches [23–26], and Zitterbewegung oscillations [27]. When the round-trip phase inside a cavity equals to multiple times of 2π, Fabry-Perot resonance occurs. It is well-known that metal-dielectric-metal sandwich structures can support Fabry-Perot resonances [28–37]. At near-infrared wavelengths, the reflection phase of noble metal layer is close to –π, which is polarization-insensitive. Also, the propagating phase inside isotropic dielectric layer is polarization-independent. Consequently, the Fabry-Perot resonances in metal-dielectric-metal sandwich structures are polarization-insensitive [28,29,32]. Another common approach to realize Fabry-Perot resonances is to introduce isotropic dielectric defects into one-dimensional (1-D) photonic crystals (PhCs) [38–41]. 1-D PhCs can be treated as optical mirrors when the wavelength of incident light lies inside the photonic bandgaps (PBGs) [42–48]. According to the multiple scattering mechanism, the PBGs in 1-D PhCs shift toward shorter wavelengths as the incident angle increases under both transverse magnetic (TM) and transverse electric (TE) polarizations [42,49,50]. In other words, the PBGs in 1-D PhCs exhibit polarization-insensitive property. The reflection phases of 1-D PhCs inherit polarization-insensitive property. As a result, the Fabry-Perot resonances in 1-D PhCs containing isotropic dielectric defects are also polarization-insensitive [27,51–54].

In recent years, all-dielectric metamaterials have received rich attention in nanophotonics [55–65]. They have been widely utilized to achieve perfect absorption [66–70] and perfect reflection [58,71]. As a class of all-dielectric metamaterials, all-dielectric elliptical metamaterials (EMMs) demonstrate their intriguing ability to achieve light confinement [72], negative refraction [73], and angle-insensitive topological interface states [74]. The iso-frequency curves (IFCs) of all-dielectric EMMs under TM polarization are ellipse. In contrast, the IFCs of all-dielectric EMMs under TE polarization are circles. Consequently, the propagating phases inside all-dielectric EMMs become polarization-sensitive. This polarization-sensitive property of the propagating phases inside all-dielectric EMMs provides us a possibility to achieve polarization-sensitive Fabry-Perot resonances. In this paper, we introduce an all-dielectric EMM defect into a 1-D PhC to achieve an anomalous polarization-sensitive Fabry-Perot resonance. The all-dielectric EMM defect layer is realized by an all-dielectric subwavelength multilayer. When the incident angle is 45 degrees, the wavelength difference of the 2nd Fabry-Perot resonance between TM and TE polarizations reaches 102.26 nm. Enabled by the polarization-sensitive property of the 2nd Fabry-Perot resonance, we achieve high-performance polarization selectivity. Specifically, the optimized polarization extinction ratio (PER) reaches 1.92 × 10⁴. Besides, the optimized PER keeps higher than 10³ in a broad angle range from 30 to 60 degrees. The designed 1-D PhC is composed of silicon (Si) and magnesium fluoride (MgF₂) layers, which can be easily fabricated by electron-beam vacuum deposition [75] or magnetron sputtering technique [76]. Our work offers a viable recipe to achieve polarization-sensitive Fabry-Perot resonances and explore polarization-dependent physical phenomena. It is known that the IFCs of hyperbolic metamaterials (HMMs) are also polarization-dependent [77]. The IFCs of HMMs under TM polarization are hyperbola while those under TE polarization are circles [77]. Therefore, polarization-sensitive Fabry-Perot resonances can also be achieved in 1-D PhCs containing HMM defects [78]. Nevertheless, owing to the inevitable optical absorption in HMMs, the transmittance and PER are intensively limited [78]. Compared with HMMs, all-dielectric EMMs utilized in this work are lossless. Consequently, the transmittance and PER can be greatly improved.

This paper is organized as follows. In Sec. 2, we give the physical mechanism of anomalous polarization-sensitive Fabry-Perot resonances in 1-D PhCs with all-dielectric EMM defects. In Sec. 3, we discuss the realization of polarization-sensitive Fabry-Perot resonances. In Sec. 4, we achieve high-performance polarization selectivity enabled by the polarization-sensitive Fabry-Perot resonances. Finally, the conclusions are given in Sec. 5.

2. Physical mechanism of anomalous polarization-sensitive Fabry-Perot resonance

In this section, we demonstrate the physical mechanism of anomalous polarization-sensitive Fabry-Perot resonances in 1-D PhCs containing all-dielectric EMM defects. First, we recall the polarization-insensitive property of conventional Fabry-Perot resonances in 1-D PhCs containing isotropic dielectric defects. Figure 1(a) shows the schematic of a 1-D PhC containing an isotropic dielectric defect, which can be denoted by (AB)^NC(AB)^N. The well-known Fabry-Perot resonance condition takes the following form

 

Fig. 1. (a) Schematic of a 1-D PhC containing an isotropic dielectric defect (C layer). (b) Schematics of the IFCs of isotropic dielectric C under TM and TE polarizations. (c) Schematic of a 1-D PhC containing an all-dielectric EMM defect (D layer). The EMM defect layer is realized by an all-dielectric subwavelength multilayer (EF)^S. (d) Schematics of the IFCs of EMM D under TM and TE polarizations.

Download Full Size | PDF

The equation of the IFC of isotropic dielectric C under TM (TE) polarization can be expressed as [79]

Figure 1(c) shows the schematic of a 1-D PhC containing an all-dielectric EMM defect, which can be denoted by (AB)^ND(AB)^N. The well-known Fabry-Perot resonance condition takes the following form

Here, ${\varepsilon _\textrm{E}}$ (${\varepsilon _\textrm{F}}$) denotes the relative permittivity of isotropic dielectric E (F), $p = {d_\textrm{E}}/({{d_\textrm{E}} + {d_\textrm{F}}} )$ denotes the duty cycle of isotropic dielectric E, and ${d_\textrm{E}}$ (${d_\textrm{F}}$) denotes the thickness of E (F) layer. Note that Eqs. (5)–(7) are only applicable when the subwavelength condition is satisfied, i.e., ${d_{\textrm{Unit}}} = {d_\textrm{E}} + {d_\textrm{F}} \ll \lambda $ [81].

Substituting Eq. (5) into the Maxwell’s equations, one can derive the equations of the IFCs of the all-dielectric subwavelength multilayer (EF)^S under TM and TE polarizations [79]

When $\theta \ne 0^\circ $, we have $\varphi _\textrm{D}^{\textrm{TM}} \ne \varphi _\textrm{D}^{\textrm{TE}}$. The propagating phase difference inside the EMM defect layer between TM and TE polarizations can be calculated as

For a fixed incident angle, the Fabry-Perot resonance becomes more polarization-sensitive as the propagating phase difference inside the EMM defect layer between TM and TE polarizations $\Delta {\varphi _\textrm{D}}$ increases. Combing Eqs. (6), (7) and (12), the polarization-sensitive property of the Fabry-Perot resonance can be flexibly tuned by the duty cycle of isotropic dielectric E p.

3. Realization of anomalous polarization-sensitive Fabry-Perot resonance

In this section, we realize an anomalous polarization-sensitive Fabry-Perot resonance in a 1-D PhC containing an all-dielectric EMM defect based on the theoretical model in Sec. 2. The EMM defect layer is realized by a Si/MgF₂ subwavelength multilayer (EF)^S. The relative permittivities of Si and MgF₂ are ${\varepsilon _\textrm{E}} = n_\textrm{E}^2 = {3.48^2}$ and ${\varepsilon _\textrm{F}} = n_\textrm{F}^2 = {1.37^2}$, respectively [82]. We define a scale factor as

Clearly, F is a binary function with respect to p and $\theta $. Then, propagating phase difference inside the EMM defect layer between TM and TE polarizations can be expressed as a binary function with respect to p and $\theta $, i.e.,

As we discussed in Sec. 2, a larger $\Delta {\varphi _\textrm{D}}$ gives rise to a more polarization-sensitive Fabry-Perot resonance. Figure 2 gives the dependence of the scale factor F on the duty cycle p for a fixed incident angle $\theta = 45^\circ $. As the duty cycle increases from 0 to 0.383, the scale factor increases from 0 to 0.122. As the duty cycle continues to increase to 1, the scale factor gradually decreases from to 0. When $p = 0.383$, the scale factor reaches its maximum ${F_{\textrm{max}}} = 0.122$. According to Eqs. (6) and (7), we have ${\varepsilon _{\textrm{D}x}} = 5.7963$ and ${\varepsilon _{\textrm{D}z}} = 2.7750$.

 

Fig. 2. Dependence of the scale factor F on the duty cycle p.

Download Full Size | PDF

For the 1-D PhC (AB)^N, isotropic dielectrics A and B are chosen to be Si and MgF₂, respectively. The thicknesses of A and B layers are selected to be ${d_\textrm{A}} = {d_\textrm{B}} = 134\; \textrm{nm}$. The Bragg wavelength of the 1st order PBG at normal incidence can be calculated as ${\lambda _{\textrm{Brg}}} = 2({{n_\textrm{A}}{d_\textrm{A}} + {n_\textrm{B}}{d_\textrm{B}}} )= 1299.80\; \textrm{nm}$. It is known that as the number of periods $\textrm{N}$ increases, the PBG becomes deeper, giving rise to a larger maximum PER but a narrower operating bandwidth of polarization selectivity. Simultaneously considering the PER and operating bandwidth of polarization selectivity, we set the number of periods to be $\textrm{N} = 4$. For the EMM defect layer (EF)^S, the thickness is selected to be ${d_\textrm{D}} = 640\; \textrm{nm}$. The number of periods is selected to be $\textrm{S} = 20$. Then, the thicknesses of E and F layers can be calculated as ${d_\textrm{E}} = p{d_\textrm{D}}/\textrm{S} = 12.26\; \textrm{nm}$ and ${d_\textrm{F}} = ({1 - p} ){d_\textrm{D}}/\textrm{S} = 19.74\; \textrm{nm}$, respectively. The thickness of the unit cell inside the EMM defect layer is only ${d_{\textrm{Unit}}} = {d_\textrm{E}} + {d_\textrm{F}} = 32\; \textrm{nm}$ (0.025 times of the Bragg wavelength), which ensures the validation of the EMA (details can be seen in Appendix A). In this work, we focus on the 2nd order Fabry-Perot resonance, i.e., $m = 2$. For any incident angle $\theta $, we can obtain the refractive angle inside the EMM defect layer ${\theta _\textrm{D}}$ according to the Snall’s law ${n_0}\textrm{sin}\theta = {n_{\textrm{D}x}}\textrm{sin}{\theta _\textrm{D}}$. Then, we calculate the reflection phases of the left and right 1-D PhCs according to the transfer matrix method (TMM) [83]. Next, we calculate the propagating phase inside the EMM defect layer according to Eqs. (10) and (11). Finally, we obtain the theoretically predicted wavelength of the 2nd Fabry-Perot resonance according to the Fabry-Perot condition with $m = 2$ [i.e., Eq. (4)]. Figure 3(a) gives the dependence of the theoretically predicted wavelength of the 2nd Fabry-Perot resonance on the incident angle under TM and TE polarizations. As demonstrated, the 2nd Fabry-Perot resonance exhibits polarization-sensitive property. As the incident angle increases from $0^\circ $ to $60^\circ $, the 2nd Fabry-Perot resonance under TM polarization shifts from 1682.32 to 1430.01 nm while that under TE polarization shifts from 1682.32 to 1588.99 nm. Figure 3(b) further gives the dependence of the theoretically predicted wavelength difference of the 2nd Fabry-Perot resonance between TM and TE polarizations on the incident angle. As the incident angle increases from $0^\circ $ to $60^\circ $, the theoretically predicted wavelength difference rapidly increases from 0 to 158.98 nm.

 

Fig. 3. (a) Dependence of the theoretically predicted wavelength of the 2nd Fabry-Perot resonance on the incident angle under TM and TE polarizations. (b) Dependence of the theoretically predicted wavelength difference of the 2nd Fabry-Perot resonance between TM and TE polarizations on the incident angle.

Download Full Size | PDF

To confirm the accuracy of the theoretical model, we numerically calculate the transmittance spectrum of the 1-D PhC containing an all-dielectric EMM defect (AB)⁴(EF)²⁰(AB)⁴ as a function of the incident angle under TM and TE polarizations according to the TMM [83], as shown in Fig. 4(a). As demonstrated, two Fabry-Perot resonances (1st and 2nd Fabry-Perot resonances) occur inside the PBG. As the incident angle increases from $0^\circ $ to $60^\circ $, the 2nd Fabry-Perot resonance under TM polarization shifts from 1678.02 to 1426.59 nm while that under TE polarization shifts from 1678.02 to 1583.26 nm. The numerical results are in good agreement with the theoretical model. Figure 4(b) further gives the dependence of the numerically calculated wavelength difference of the 2nd Fabry-Perot resonance between TM and TE polarizations on the incident angle. As the incident angle increases from $0^\circ $ to $60^\circ $, the numerically calculated wavelength difference rapidly increases from 0 to 156.67 nm. Compared with conventional Fabry-Perot resonances in 1-D PhCs containing isotropic dielectric defects, the designed Fabry-Perot resonance demonstrates a superior polarization-sensitive property (details can be seen in Appendix B). Also, we numerically calculate the dependence of the Q factor of the 2nd Fabry-Perot resonance on the incident angle under TM and TE polarizations, as shown in Fig. 4(c). As the incident angle increases from $0^\circ $ to $60^\circ $, the numerically calculated Q factor decreases from 2.90 × 10² to 7.58 × 10¹ under TM polarization while that increases from 2.90 × 10² to 8.54 × 10² under TE polarization.

 

Fig. 4. (a) Numerically calculated transmittance spectrum of the 1-D PhC containing an all-dielectric EMM defect (AB)⁴(EF)²⁰(AB)⁴ as a function of the incident angle under TM and TE polarizations. (b) Numerically calculated wavelength difference of the 2nd Fabry-Perot resonance between TM and TE polarizations on the incident angle. (c) Dependence of the numerically calculated Q factor of the 2nd Fabry-Perot resonance on the incident angle under TM and TE polarizations.

Download Full Size | PDF

To more intuitively compare the numerical results with the theoretical model, we give the dependence of the theoretically predicted and numerically calculated wavelengths of the 2nd Fabry-Perot resonance on the incident angle under TM and TE polarizations, as shown in Fig. 5(a). Clearly, the numerical results agree well with the theoretical model. The errors between the theoretically predicted and numerically calculated wavelengths of the 2nd Fabry-Perot resonances are smaller than 5.8 nm (0.37%), indicating that the theoretical model is accurate. The errors originate from the EMA. In addition, we give the dependence of the theoretically predicted and numerically calculated wavelength differences of the 2nd Fabry-Perot resonance between TM and TE polarizations on the incident angle, as shown in Fig. 5(b). The errors between the theoretically predicted and numerically calculated wavelength differences of the 2nd Fabry-Perot resonance between TM and TE polarizations are smaller than 2.3 nm.

 

Fig. 5. (a) Dependence of the theoretically predicted and numerically calculated wavelengths of the 2nd Fabry-Perot resonance on the incident angle under TM and TE polarizations. (b) Dependence of the theoretically predicted and numerically calculated wavelength differences of the 2nd Fabry-Perot resonance between TM and TE polarizations on the incident angle.

Download Full Size | PDF

4. High-performance polarization selectivity enabled by anomalous polarization-sensitive Fabry-Perot resonance

In this section, we achieve high-performance polarization selectivity enabled by the anomalous polarization-sensitive Fabry-Perot resonance. The incident angle is initially set to be $\theta = 45^\circ $. Figure 6(a) gives the transmittance spectrum of the 1-D PhC containing an all-dielectric EMM defect (AB)⁴(EF)²⁰(AB)⁴ under TM and TE polarizations at $\theta = 45^\circ $ according to the TMM [83]. Under TM polarization, a transmittance peak occurs at the wavelength 1518.78 nm owing to the 2nd Fabry-Perot resonance. For TE polarization, a transmittance peak occurs at the wavelength 1621.04 nm owing to the 2nd Fabry-Perot resonance. The wavelength difference between two transmittance peaks reaches 102.26 nm, giving rise to high-performance polarization selectivity. In addition, the Q factors of the 2nd Fabry-Perot resonances under TM and TE polarizations are 1.37 × 10² and 5.25 × 10², respectively. The PER is defined as the transmittance ratio between TM and TE polarizations, i.e., ${T^{\textrm{TM}}}/{T^{\textrm{TE}}}$. Figure 6(b) gives the PER spectrum of the 1-D PhC containing an all-dielectric EMM defect (AB)⁴(EF)²⁰(AB)⁴ at $\theta = 45^\circ $. Enabled by the polarization-sensitive property of the 2nd Fabry-Perot resonance, high-performance polarization selectivity is achieved. At the wavelength 1518.33 nm, the PER reaches its maximum 1.92 × 10⁴. It should be noted that high-performance polarization selectivity can still be achieved if exchanging the positions of Si and MgF₂ layers (E and F layers) within the all-dielectric EMM defect (details can be seen in Appendix C).

 

Fig. 6. (a) Numerically calculated transmittance spectrum of the 1-D PhC containing an all-dielectric EMM defect (AB)⁴(EF)²⁰(AB)⁴ under TM and TE polarizations at $\theta = 45^\circ $. (b) PER spectrum of the 1-D PhC containing an all-dielectric EMM defect (AB)⁴(EF)²⁰(AB)⁴ at $\theta = 45^\circ $.

Download Full Size | PDF

Then, the incident angle is changed to be $\theta = 60^\circ $. Figure 7(a) gives the transmittance spectrum of the 1-D PhC containing an all-dielectric EMM defect (AB)⁴(EF)²⁰(AB)⁴ under TM and TE polarizations at $\theta = 60^\circ $ according to the TMM [83]. Under TM polarization, a transmittance peak occurs at the wavelength 1430.01 nm owing to the 2nd Fabry-Perot resonance. For TE polarization, a transmittance peak occurs at the wavelength 1588.99 nm owing to the 2nd Fabry-Perot resonance. The wavelength difference between two transmittance peaks reaches 158.98 nm, giving rise to high-performance polarization selectivity. In addition, the Q factors of the 2nd Fabry-Perot resonances under TM and TE polarizations are 7.58 × 10¹ and 8.54 × 10², respectively. Figure 7(b) gives the PER spectrum of the 1-D PhC containing an all-dielectric EMM defect (AB)⁴(EF)²⁰(AB)⁴ at $\theta = 60^\circ $. Enabled by the polarization-sensitive property of the 2nd Fabry-Perot resonance, high-performance polarization selectivity is achieved. At the wavelength 1429.28 nm, the PER reaches its maximum 2.06 × 10⁵.

 

Fig. 7. (a) Numerically calculated transmittance spectrum of the 1-D PhC containing an all-dielectric EMM defect (AB)⁴(EF)²⁰(AB)⁴ under TM and TE polarizations at $\theta = 60^\circ $. (b) PER spectrum of the 1-D PhC containing an all-dielectric EMM defect (AB)⁴(EF)²⁰(AB)⁴ at $\theta = 60^\circ $.

Download Full Size | PDF

From Fig. 4(b), one can see that the wavelength difference of the 2nd Fabry-Perot resonance between TM and TE polarizations remains at a high level in a broad angle range. Consequently, high-performance polarization selectivity can be achieved in a broad angle range. Figure 8 gives the optimized PER of the 1-D PhC containing an all-dielectric EMM defect (AB)⁴(EF)²⁰(AB)⁴ at different incident angles. As the incident angle increases from $20^\circ $ to $60^\circ $, the optimized PER dramatically increases from 1.21 × 10² to 2.06 × 10⁵. The optimized PER keeps higher than 10³ in a broad angle range from $30^\circ $ to $60^\circ $.

 

Fig. 8. Optimized PER of the 1-D PhC containing an all-dielectric EMM defect (AB)⁴(EF)²⁰(AB)⁴ at different incident angles. The black dashed line represents PER = 10³.

Download Full Size | PDF

5. Conclusion

In summary, we realize an anomalous polarization-sensitive Fabry-Perot resonance in a 1-D PhC containing all-dielectric EMM defect. Owing to the polarization-sensitive property of the propagating phase inside the all-dielectric EMM layer, the wavelength difference of the Fabry-Perot resonance between TM and TE polarizations is larger than 100 nm when the incident angle is 45 degrees. Enabled by the polarization-sensitive property of the Fabry-Perot resonance, high-performance polarization selectivity with an optimized PER on the order of 10⁴ can be achieved. Our work offers a viable recipe, well within the reach of current fabrication technique, to explore polarization-dependent physical phenomena and devices.

Appendix A: validation of EMA

In this appendix, we give a comparison of the transmittance spectrum of the Si/MgF₂ subwavelength multilayer (EF)²⁰ and the homogeneous layer with the effective relative permittivity tensor calculated by the EMA under TM and TE polarizations at $\theta = 45^\circ $, as shown in Figs. 9(a) and 9(b). The thicknesses of Si and MgF₂ layers can ${d_\textrm{E}} = 12.26\; \textrm{nm}$ and ${d_\textrm{F}} = 19.74\; \textrm{nm}$, respectively. As demonstrated, the transmittance spectrum of the Si/MgF₂ subwavelength multilayer (EF)²⁰ is almost identical with that of the homogeneous layer. Therefore, the EMA is approximately accurate.

 

Fig. 9. Transmittance spectra of the Si/MgF₂ subwavelength multilayer (EF)²⁰ and the homogeneous layer with the effective relative permittivity tensor calculated by the EMA under (a) TM and (b) TE polarizations at $\theta = 45^\circ $.

Download Full Size | PDF

Appendix B: polarization-dependent property of Fabry-Perot resonance in conventional 1-D PhC containing isotropic dielectric defect

In this appendix, we discuss the polarization-dependent property of the 2nd Fabry-Perot resonances in a conventional 1-D PhC containing an isotropic dielectric (AB)⁴C(AB)⁴ for comparison. For the 1-D PhC (AB)^N, isotropic dielectrics A and B are chosen to be Si and MgF₂, respectively. The thicknesses of A and B layers are selected to be ${d_\textrm{A}} = {d_\textrm{B}} = 134\; \textrm{nm}$. The Bragg wavelength of the 1st order PBG at normal incidence can be calculated as ${\lambda _{\textrm{Brg}}} = 2({{n_\textrm{A}}{d_\textrm{A}} + {n_\textrm{B}}{d_\textrm{B}}} )= 1299.80\; \textrm{nm}$. For the isotropic dielectric defect layer C, the thickness is selected to be ${d_\textrm{C}} = 550\; \textrm{nm}$. We numerically calculate the transmittance spectrum of the 1-D PhC containing an isotropic dielectric defect (AB)⁴C(AB)⁴ as a function of the incident angle under TM and TE polarizations according to the TMM [73], as shown in Fig. 10(a). As demonstrated, two Fabry-Perot resonances (1st and 2nd Fabry-Perot resonances) occur inside the PBG. As the incident angle increases from $0^\circ $ to $60^\circ $, the 2nd Fabry-Perot resonance under TM polarization shifts from 1474.71 to 1366.65 nm while that under TE polarization shifts from 1474.71 to 1417.75 nm. Figure 10(b) further gives the dependence of the numerically calculated wavelength difference of the 2nd Fabry-Perot resonance between TM and TE polarizations on the incident angle. As the incident angle increases from $0^\circ $ to $60^\circ $, the numerically calculated wavelength difference increases from 0 to 51.10 nm. Comparing Figs. 4(b) and 10(b), the maximum wavelength difference of the 2nd Fabry-Perot resonance in the designed 1-D PhC containing an all-dielectric defect reaches 3.11 times of that in the conventional 1-D PhC containing an isotropic dielectric.

 

Fig. 10. (a) Numerically calculated transmittance spectrum of the 1-D PhC containing an isotropic dielectric defect layer (AB)⁴C(AB)⁴ as a function of the incident angle under TM and TE polarizations. (b) Numerically calculated wavelength difference of the 2nd Fabry-Perot resonance between TM and TE polarizations on the incident angle.

Download Full Size | PDF

Appendix C: high-performance polarization selectivity when exchanging the positions of Si and MgF₂ layers within the all-dielectric EMM defect

In this appendix, we demonstrate that high-performance polarization selectivity can still be achieved if exchanging the positions of Si and MgF₂ layers (E and F layers) within the all-dielectric EMM defect. After exchanging the positions of Si and MgF₂ layers, the 1-D PhC containing an all-dielectric EMM defect can be denoted by (AB)⁴(FE)²⁰(AB)⁴. Figure 11(a) gives the transmittance spectrum of the 1-D PhC containing an all-dielectric EMM defect (AB)⁴(FE)²⁰(AB)⁴ under TM and TE polarizations at $\theta = 45^\circ $ according to the TMM [83]. Under TM polarization, a transmittance peak occurs at the wavelength 1513.87 nm owing to the 2nd Fabry-Perot resonance. For TE polarization, a transmittance peak occurs at the wavelength 1612.18 nm owing to the 2nd Fabry-Perot resonance. The wavelength difference between two transmittance peaks reaches 98.31 nm, giving rise to high-performance polarization selectivity. In addition, the Q factors of the 2nd Fabry-Perot resonances under TM and TE polarizations are 1.45 × 10² and 5.82 × 10², respectively. Figure 11(b) gives the PER spectrum of the 1-D PhC containing an all-dielectric EMM defect (AB)⁴(FE)²⁰(AB)⁴ at $\theta = 45^\circ $. Enabled by the polarization-sensitive property of the 2nd Fabry-Perot resonance, high-performance polarization selectivity is achieved. At the wavelength 1513.47 nm, the PER reaches its maximum 2.05 × 10⁴. Hence, high-performance polarization selectivity can still be achieved after exchanging the positions of Si and MgF₂ layers within the all-dielectric EMM defect. The underlying reason is that the EMA do not dependent on the positions of the components in metamaterials [79,80].

 

Fig. 11. (a) Numerically calculated transmittance spectrum of the 1-D PhC containing an all-dielectric EMM defect (AB)⁴(FE)²⁰(AB)⁴ under TM and TE polarizations at $\theta = 45^\circ $. (b) PER spectrum of the 1-D PhC containing an all-dielectric EMM defect (AB)⁴(FE)²⁰(AB)⁴ at $\theta = 45^\circ $.

Download Full Size | PDF

Funding

Basic and Applied Basic Research Foundation of Guangdong Province (2021A1514010050, 2022A1515010726, 2023A1515011024); National Natural Science Foundation of China (12104105, 12264028, 12304420, 12364045); Science and Technology Program of Guangzhou (202201011176); Natural Science Foundation of Jiangxi Province (20232BAB201040, 20232BAB211025); Start-up Funding of Guangdong Polytechnic Normal University (2021SDKYA033); Interdisciplinary Innovation Fund of Nanchang University (2019-9166-27060003).

Disclosures

The authors declare that there are no conflicts of interest related to this article.

Data availability

Data underlying the results presented in this paper are available from the corresponding authors upon reasonable request.

References

1. A. E. Miroshnichenko, S. Flach, and Y. S. Kivshar, “Fano resonances in nanoscale structures,” Rev. Mod. Phys. 82(3), 2257–2298 (2010). [CrossRef]  

2. P. Lalanne, C. Sauvan, and J. P. Hugonin, “Photon confinement in photonic crystal nanocavities,” Laser Photonics Rev. 2(6), 514–526 (2008). [CrossRef]  

3. Y. Akahane, T. Asano, B.-S. Song, and S. Noda, “High-Q photonic nanocavity in a two-dimensional photonic crystal,” Nature 425(6961), 944–947 (2003). [CrossRef]  

4. F. Wang, G. Dukovic, L. E. Brus, and T. F. Heinz, “The optical resonances in carbon nanotubes arise from excitons,” Science 308(5723), 838–841 (2005). [CrossRef]  

5. T. Wei, Y. Han, H.-L. Tsai, and H. Xiao, “Miniaturized fiber inline Fabry-Perot interferometer fabricated with a femtosecond laser,” Opt. Lett. 33(6), 536–538 (2008). [CrossRef]  

6. T. Paixão, F. Araújo, and P. Antunes, “Highly sensitive fiber optic temperature and strain sensor based on an intrinsic Fabry-Perot interferometer fabricated by a femtosecond laser,” Opt. Lett. 44(19), 4833–4836 (2019). [CrossRef]  

7. H. Němec, L. Duvillaret, F. Garet, P. Kužel, P. Xavier, J. Richard, and D. Rauly, “Thermally tunable filter for terahertz range based on a one-dimensional photonic crystal with a defect,” J. Appl. Phys. 96(8), 4072–4075 (2004). [CrossRef]  

8. Y. Li, L. Qi, J. Yu, Z. Chen, Y. Yao, and X. Liu, “One-dimensional multiband terahertz graphene photonic crystal fibers,” Opt. Mater. Express 7(4), 1228–1239 (2017). [CrossRef]  

9. L. Zhang, W. Yu, J.-Y. Ou, Q. Wang, X. Cai, B. Wang, X. Li, R. Zhao, and Y. Liu, “Midinfrared one-dimensional photonic crystal constructed from two-dimensional electride material,” Phys. Rev. B 98(7), 075434 (2018). [CrossRef]  

10. X. Qin and Y. Li, “Superposition of ε-near-zero and Fabry-Perot transmission modes,” Phys. Rev. Appl. 16(2), 024033 (2021). [CrossRef]  

11. S. O’Brien and E. P. O’Reilly, “Theory of improved spectral purity in index patterned Fabry-Pérot laser,” Appl. Phys. Lett. 86(20), 201101 (2005). [CrossRef]  

12. A. Bogris, C. Mesaritakis, S. Deligiannidis, and P. Li, “Fabry-Perot lasers as enablers for parallel reservoir computing,” IEEE J. Sel. Top. Quantum Electron. 27(2), 1–7 (2021). [CrossRef]  

13. H. Zhang, F. Ling, and B. Zhang, “Broadband tunable terahertz metamaterial absorber based on vanadium dioxide and Fabry-Perot cavity,” Opt. Mater. 112, 110803 (2021). [CrossRef]  

14. S. Tavana, A. Zarifkar, and M. Miri, “Tunable terahertz perfect absorber and polarizer based on one-dimensional anisotropic graphene photonic crystal,” IEEE Photonics J. 14(3), 1–9 (2022). [CrossRef]  

15. E. Gao, H. Li, C. Liu, B. Ruan, M. Li, B. Zhang, and Z. Zhang, “Dynamically tunable bound states in the continuum supported by asymmetric Fabry-Pérot resonance,” Phys. Chem. Chem. Phys. 24(34), 20125–20129 (2022). [CrossRef]  

16. M. Sovizi and M. Aliannezhadi, “Design and simulation of high-sensitivity refractometric sensors based on defect modes in one-dimensional ternary dispersive photonic crystal,” J. Opt. Soc. Am. B 36(12), 3450–3456 (2019). [CrossRef]  

17. S. Surdo and G. Barillaro, “Impact of fabrication and bioassay surface roughness on the performance of label-free resonant biosensors based on one-dimensional photonic crystal microcavities,” ACS Sens. 5(9), 2894–2902 (2020). [CrossRef]  

18. J. Chen, C. Xue, Y. Zheng, L. Wu, C. Chen, and Y. Han, “Micro-fiber-optic acoustic sensor based on high-Q resonance effect using Fabry-Pérot etalon,” Opt. Express 29(11), 16447–16454 (2021). [CrossRef]  

19. B.-F. Wan, Y. Xu, Z.-W. Zhou, D. Zhang, and H.-F. Zhang, “Theoretical investigation of a sensor based on one-dimensional photonic crystals to measure four physical quantities,” IEEE Sens. J. 21(3), 2846–2853 (2021). [CrossRef]  

20. A. Panda, P. D. Pukhrambam, F. Wu, and W. Belhadj, “Graphene-based 1D defective photonic crystal biosensor for real-time detection of cancer cells,” Eur. Phys. J. Plus 136(8), 809 (2021). [CrossRef]  

21. W. Fuscaldo, P. Burghignoli, P. Baccarelli, and A. Galli, “Graphene Fabry-Perot cavity leaky-wave antennas: Plasmonic versus nonplasmonic solutions,” IEEE Trans. Antennas Propagat. 65(4), 1651–1660 (2017). [CrossRef]  

22. D. Comite, S. K. Podilchak, M. Kuznetcov, V. G.-Z. Buendía, P. Burghignoli, P. Baccarelli, and A. Galli, “Wideband array-fed Fabry-Perot cavity antenna for 2-D beam steering,” IEEE Trans. Antennas Propagat. 69(2), 784–794 (2021). [CrossRef]  

23. D. Vujic and S. John, “Pulse reshaping in photonic crystal waveguides and microcavities with Kerr nonlinearity: Critical issues for all-optical switching,” Phys. Rev. A 72(1), 013807 (2005). [CrossRef]  

24. G. Ma, J. Shen, Z. Zhang, Z. Hua, and S. H. Tang, “Ultrafast all-optical switching in one-dimensional photonic crystal with two defects,” Opt. Express 14(2), 858–865 (2006). [CrossRef]  

25. V. Eckhouse, I. Cestier, G. Eisenstein, S. Combrié, G. Lehoucq, and A. De Rossi, “Kerr-induced all-optical switching in a GaInP photonic crystal Fabry-Perot resonator,” Opt. Express 20(8), 8524–8534 (2012). [CrossRef]  

26. A. Bassi, F. Prati, and L. A. Lugiato, “Optical instabilities in Fabry-Perot resonators,” Phys. Rev. A 103(5), 053519 (2021). [CrossRef]  

27. S. Lovett, P. M. Walker, A. Osipov, A. Yulin, P. U. Naik, C. E. Whittaker, I. A. Shelykh, M. S. Skolnick, and D. N. Krizhanovskii, “Observation of Zitterbewegung in photonic microcavities,” Light: Sci. Appl. 12, 126 (2023). [CrossRef]  

28. F. Villa, T. Lopez-Rios, and L. E. Regalado, “Electromagnetic modes in metal-insulator-metal structures,” Phys. Rev. B 63(16), 165103 (2001). [CrossRef]  

29. S. Shu, Z. Li, and Y. Y. Li, “Triple-layer Fabry-Perot absorber with near-perfect absorption in visible and near-infrared regime,” Opt. Express 21(21), 25307–25315 (2013). [CrossRef]  

30. D. Zhao, L. Meng, H. Gong, X. Chen, Y. Chen, M. Yan, Q. Li, and M. Qiu, “Ultra-narrow-band light dissipation by a stack of lamellar silver and alumina,” Appl. Phys. Lett. 104(22), 221107 (2014). [CrossRef]  

31. Z. Li, S. Butun, and K. Aydin, “Large-area, lithography-free super absorbers and color filters at visi1ble frequencies using ultrathin metallic films,” ACS Photonics 2(2), 183–188 (2015). [CrossRef]  

32. H. Kocer, S. Butun, Z. Li, and K. Aydin, “Reduced near-infrared absorption using ultra-thin lossy metals in Fabry-Perot cavities,” Sci. Rep. 5, 8157 (2015). [CrossRef]  

33. Z. Li, E. Palacios, S. Butun, H. Kocer, and K. Aydin, “Omnidirectional, broadband light absorption using large-area, ultrathin lossy metallic film coatings,” Sci. Rep. 5, 15137 (2015). [CrossRef]  

34. S. S. Mirshafieyan, T. S. Luk, and J. Guo, “Zeroth order Fabry-Perot resonance enabled ultra-thin perfect light absorber using percolation aluminum and silicon nanofilms,” Opt. Mater. Express 6(4), 1032–1042 (2016). [CrossRef]  

35. K. V. Sreekanth, Q. Ouyang, S. Han, K.-T. Yong, and R. Singh, “Giant enhancement in Goos-Hänchen shift at the singular phase of a nanophotonic cavity,” Appl. Phys. Lett. 112(16), 161109 (2018). [CrossRef]  

36. J. Lv, D. Chen, Y. Du, T. Wang, X. Zhang, Y. Li, L. Zhang, Y. Wang, R. Jordan, and Y. Fu, “Visual detection of thiocyanate based on Fabry-Perot etalons with a responsive polymer brush as the transducer,” ACS Sens. 5(2), 303–307 (2020). [CrossRef]  

37. A. J. Taal, C. Lee, J. Choi, B. Hellenkamp, and K. L. Shepard, “Toward implantable devices for angle-sensitive, lens-less, multifluorescent, single-photon lifetime imaging in the brain using Fabry-Perot and absorptive color filters,” Light: Sci. Appl. 11, 24 (2022). [CrossRef]  

38. T. Hattori, N. Tsurumachi, and H. Nakatsuka, “Analysis of optical nonlinearity by defect states in one-dimensional photonic crystals,” J. Opt. Soc. Am. B 14(2), 348–355 (1997). [CrossRef]  

39. H. Jiang, H. Chen, H. Li, Y. Zhang, J. Zi, and S. Zhu, “Properties of one-dimensional photonic crystals containing single-negative materials,” Phys. Rev. E 69(6), 066607 (2004). [CrossRef]  

40. L.-G. Wang and S.-Y. Zhu, “Giant lateral shift of a light beam at the defect mode in one-dimensional photonic crystals,” Opt. Lett. 31(1), 101–103 (2006). [CrossRef]  

41. G. Zheng, M. Qiu, F. Xian, Y. Chen, L. Xu, and J. Wang, “Multiple visible optical Tamm states supported by graphene-coated distributed Bragg reflectors,” Appl. Phys. Express 10(9), 092202 (2017). [CrossRef]  

42. Y. Fink, J. N. Winn, S. Fan, C. Chen, J. Michel, J. D. Joannopoulos, and E. L. Thomas, “A dielectric omnidirectional reflector,” Science 282(5394), 1679–1682 (1998). [CrossRef]  

43. Y. Chen, D. Zhang, L. Zhu, Q. Fu, R. Wang, P. Wang, H. Ming, R. Badugu, and J. R. Lakowicz, “Effect of metal film thickness on Tamm plasmon-coupled emission,” Phys. Chem. Chem. Phys. 16(46), 25523–25530 (2014). [CrossRef]  

44. I. V. Timofeev, D. N. Maksimov, and A. F. Sadreev, “Optical defect mode with tunable Q factor in a one-dimensional anisotropic photonic crystal,” Phys. Rev. B 97(2), 024306 (2018). [CrossRef]  

45. Y. Peng, J. Xu, H. Dong, X. Dai, J. Jiang, S. Qian, and L. Jiang, “Graphene-based low-threshold and tunable optical bistability in one-dimensional photonic crystal Fano resonance heterostructure at optical communication band,” Opt. Express 28(23), 34948–34959 (2020). [CrossRef]  

46. N. A. Vanyushkin, A. H. Gevorgyan, and S. S. Golik, “Approximation of one-dimensional rugate photonic crystals using symmetric ternary photonic crystals,” Optik 242, 167343 (2021). [CrossRef]  

47. F. Wu, X. Wu, S. Xiao, G. Liu, and H. Li, “Broadband wide-angle multilayer absorber based on a broadband omnidirectional optical Tamm state,” Opt. Express 29(15), 23976–23987 (2021). [CrossRef]  

48. F. Wu, M. Chen, and S. Xiao, “Wide-angle polarization selectivity based on anomalous defect mode in photonic crystal containing hyperbolic metamaterials,” Opt. Lett. 47(9), 2153–2156 (2022). [CrossRef]  

49. R. G. Bikbaev, S. Y. Vetrov, and I. V. Timofeev, “Hyperbolic metamaterial for the Tamm plasmon polariton application,” J. Opt. Soc. Am. B 37(8), 2215–2220 (2020). [CrossRef]  

50. M. Gryga, D. Ciprian, L. Gembalova, and P. Hlubina, “Sensing based on Bloch surface wave and self-referenced guided mode resonances employing a one-dimensional photonic crystal,” Opt. Express 29(9), 12996–13010 (2021). [CrossRef]  

51. C.-J. Wu and Z.-H. Wang, “Properties of defect modes in one-dimensional photonic crystals,” Prog. Electromagn. Res. 103, 169–184 (2010). [CrossRef]  

52. A. H. Aly and E. A. Elsayed, “Defect mode properties in a one-dimensional photonic crystal,” Phys. B 407(1), 120–125 (2012). [CrossRef]  

53. G. Du, X. Zhou, C. Pang, K. Zhang, Y. Zhao, G. Lu, F. Liu, A. Wu, S. Akhmadaliev, S. Zhou, and F. Chen, “Efficient modulation of photonic bandgap and defect modes in all-dielectric photonic crystals by energetic ion beams,” Adv. Opt. Mater. 8(19), 2000426 (2020). [CrossRef]  

54. J. Yang, H. Zhang, T. Wang, I. De Leon, R. P. Zaccaria, H. Qian, H. Chen, and G. Wang, “Strong coupling of Tamm plasmons and Fabry-Perot modes in a one-dimensional photonic crystal heterostructure,” Phys. Rev. Appl. 18(1), 014056 (2022). [CrossRef]  

55. S. Jahani and Z. Jacob, “All-dielectric metamaterials,” Nat. Nanotechnol. 11, 23–36 (2016). [CrossRef]  

56. K. Vynck, D. Felbacq, E. Centeno, A. I. Căbuz, D. Cassagne, and B. Guizal, “All-dielectric rod-type metamaterials at optical frequencies,” Phys. Rev. Lett. 102(13), 133901 (2009). [CrossRef]  

57. J. C. Ginn, I. Brener, D. W. Peters, J. R. Wendt, J. O. Stevens, P. F. Hines, L. I. Basilio, L. K. Warne, J. F. Ihlefeld, P. G. Clem, and M. B. Sinclari, “Realizing optical magnetism from dielectric metamaterials,” Phys. Rev. Lett. 108(9), 097402 (2012). [CrossRef]  

58. P. Moitra, B. A. Slovick, Z. G. Yu, S. Krishnamurthy, and J. Valentine, “Experimental demonstration of a broadband all-dielectric metamaterial perfect reflector,” Appl. Phys. Lett. 104(17), 171102 (2014). [CrossRef]  

59. A. Andryieuski, S. M. Kuznetsova, and A. V. Lavrinenko, “Applicability of point-dipoles approximation to all-dielectric metamaterials,” Phys. Rev. B 92(3), 035114 (2015). [CrossRef]  

60. J. Yi, M. Guo, R. Feng, B. Ratni, L. Zhu, D. H. Werner, and S. N. Burokur, “Design and validation of all-dielectric metamaterial medium for collimating orbital-angular-momentum vortex waves at microwave frequencies,” Phys. Rev. Appl. 12(3), 034060 (2019). [CrossRef]  

61. J. Zi, Y. Li, X. Feng, Q. Xu, H. Liu, X.-X. Zhang, J. Han, and W. Zhang, “Dual-functional terahertz waveplate based on all-dielectric metamaterial,” Phys. Rev. Appl. 13(3), 034042 (2020). [CrossRef]  

62. A. V. Hlushchenko, D. V. Novitsky, and V. R. Tuz, “Trapped-mode excitation in all-dielectric metamaterials with loss and gain,” Phys. Rev. B 106(15), 155429 (2022). [CrossRef]  

63. S. Zhang, M. Qin, B. Wu, and E. Wu, “All-dielectric Si metamaterials with electromagnetically induced transparency and strong gap-mode electric field enhancement,” Opt. Commun. 530, 129143 (2023). [CrossRef]  

64. L. Huang, L. Xu, D. A. Powell, W. J. Padilla, and A. E. Miroshnichenko, “Resonant leaky modes in all-dielectric metasystems: Fundamentals and applications,” Phys. Rep. 1008, 1–66 (2023). [CrossRef]  

65. F. Wu, T. Liu, and S. Xiao, “Polarization-sensitive photonic bandgaps in hybrid one-dimensional photonic crystals composed of all-dielectric elliptical metamaterials and isotropic dielectrics,” Appl. Opt. 62(3), 706–713 (2023). [CrossRef]  

66. M. A. Cole, D. A. Powell, and I. V. Shadrivov, “Strong terahertz absorption in all-dielectric Huygens’ metasurfaces,” Nanotechnology 27(42), 424003 (2016). [CrossRef]  

67. J. Tian, Q. Li, P. A. Belov, R. K. Sinha, W. Qian, and M. Qiu, “High-Q all-dielectric metasurface: Super and suppressed optical absorption,” ACS Photonics 7(6), 1436–1443 (2020). [CrossRef]  

68. M. Peng, F. Qin, L. Zhou, H. Wei, Z. Zhu, and X. Shen, “Material-structure integrated design for ultra-broadband all-dielectric metamaterial absorber,” J. Phys.: Condens. Matter 34(11), 115701 (2022). [CrossRef]  

69. J. Yu, B. Ma, A. Ouyang, P. Ghosh, H. Luo, A. Pattanayak, S. Kaur, M. Qiu, P. Belov, and Q. Li, “Dielectric super-absorbing metasurfaces via PT symmetry breaking,” Optica 8(10), 1290–1295 (2021). [CrossRef]  

70. M. Guo, X. Wang, H. Zhuang, D. Tang, B. Zhang, and Y. Yang, “Broadband carbon-based all-dielectric metamaterial absorber enhanced by high-contrast gratings based spoof surface plasmon polaritons,” Phys. Scr. 98(3), 035518 (2023). [CrossRef]  

71. P. Moitra, B. A. Slovick, W. Ii, I. I. Kravchencko, D. P. Briggs, S. Krishnamurthy, and J. Valentine, “Large-scale all-dielectric metamaterial perfect reflectors,” ACS Photonics 2(6), 692–698 (2015). [CrossRef]  

72. S. Jahani and Z. Jacob, “Transparent subdiffraction optics: nanoscale light confinement without metal,” Optica 1(2), 96–100 (2014). [CrossRef]  

73. A. Al Sayem, M. R. C. Mahdy, and M. S. Rahman, “Broad angle negative refraction in lossless all dielectric or semiconductor based asymmetric anisotropic metamaterial,” J. Opt. 18(1), 015101 (2016). [CrossRef]  

74. F. Wu, H. Li, S. Hu, Y. Chen, and Y. Long, “Angle-insensitive topological interface states in hybrid one-dimensional photonic crystal heterostructures containing all-dielectric metamaterials,” Opt. Lett. 48(11), 3035–3038 (2023). [CrossRef]  

75. F. Wang, Y. Z. Cheng, X. Wang, D. Qi, H. Luo, and R. Z. Gong, “Effective modulation of the photonic band gap based on Ge/ZnS one-dimensional photonic crystal at the infrared band,” Opt. Mater. 75, 373–378 (2018). [CrossRef]  

76. S. Jena, R. B. Tokas, P. Sarkar, J. S. Misal, S. M. Haque, K. D. Rao, S. Thakur, and N. K. Sahoo, “Omnidirectional photonic band gap in magnetron sputtered TiO₂/SiO₂ one-dimensional photonic crystal,” Thin Solid Films 599, 138–144 (2016). [CrossRef]  

77. A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamatreials,” Nat. Photonics 7(12), 948–957 (2013). [CrossRef]  

78. Q. Wei, J. Wu, Z. Guo, Y. Sun, Y. Li, H. Jiang, Y. Yang, and H. Chen, “Omnidirectional defect mode in one-dimensional photonic crystal with a (chiral) hyperbolic metamaterial defect,” Opt. Express 31(2), 1432–1441 (2023). [CrossRef]  

79. L. Ferrari, C. Wu, D. Lepage, X. Zhang, and Z. Liu, “Hyperbolic metamaterials and their applications,” Prog. Quantum Electron. 40, 1–40 (2015). [CrossRef]  

80. B. Wood, J. B. Pendry, and D. P. Tsai, “Directed subwavelength imaging using a layered metal-dielectric system,” Phys. Rev. B 74(11), 115116 (2006). [CrossRef]  

81. V. E. Babicheva, M. Y. Shalaginov, S. Ishii, A. Boltasseva, and A. V. Kildishev, “Finite-width plasmonic waveguides with hyperbolic multilayer cladding,” Opt. Express 23(8), 9681–9689 (2015). [CrossRef]  

82. E. Palik, Handbook of Optical Constants of Solids I (Academic Press, San Diego, CA, 1985).

83. P. Yeh, Optical Waves in Layered Media (Wiley, New York, 1988).