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Wide-angle polarization selectivity based on anomalous defect mode in photonic crystal containing hyperbolic metamaterials

Feng Wu, Mingyuan Chen, and Shuyuan Xiao

Open Access Open Access

Abstract

Conventional defect modes in all-dielectric 1D photonic crystals (PCs) are polarization-insensitive. This poses a great challenge in achieving high-performance polarization selectivity. In this Letter, we introduce a defect layer into a 1D PC containing hyperbolic metamaterials to achieve an anomalous defect mode with polarization-sensitive characteristics. As the incident angle increases, such a defect mode remains almost unshifted under transverse magnetic polarization, while strongly shifting toward shorter wavelengths under transverse electric polarization. The polarization-sensitive characteristics of the defect mode can be well explained by the Fabry–Perot resonance condition. Assisted by the polarization-sensitive defect mode, wide-angle polarization selectivity with an operating angle width up to 54.8° can be realized. Our work provides a route to designing wide-angle linear polarizers using simple 1D structures, which would be useful in liquid crystal display and Q-switched lasers.

© 2022 Optica Publishing Group

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Supplementary Material (1)

NameDescription
Supplement 1       In this supplementary material, we give a numerical example on the polarization-insensitive characteristic of conventional defect modes and analyze the effect of the absorption within hyperbolic metamaterial layers on the polarization selectivity.

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 (4)
Fig. 1.
Fig. 1. (a) 1D PCCH. The HMM layer is mimicked by a subwavelength Si–ITO multilayer (CD)4. The whole structure can be denoted [(CD)4B]12. (b) Two components of the effective relative permittivity tensor of the subwavelength Si–ITO multilayer (CD)4 as a function of the wavelength. (c) Reflectance spectrum of the structure [(CD)4B]12 as a function of the incident angle under TM and TE polarizations.

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Fig. 2.
Fig. 2. (a) Designed 1D PCCH with dielectric defect layer. The whole structure can be denoted (AB)6E(AB)6, where (AB)12 is the previously designed 1D PCCH and E is a dielectric (HfO2) defect layer. (b) Transmittance spectrum of the structure (AB)6E(AB)6 as a function of the incident angle under TM and TE polarizations.

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Fig. 3.
Fig. 3. Phase as a function of the incident angle at the wavelength of the defect mode (λ = 1318.6 nm) under (a) TM and (b) TE polarizations.

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Fig. 4.
Fig. 4. (a) Transmittance at wavelength of defect mode (λ = 1318.6 nm) as a function of incident angle under TM and TE polarizations. (b) Corresponding polarization selection ratio.

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Equations (9)

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ε D = ε inf − ω P 2 ω 2 + i γ ω ,
ε A x = f ε C + ( 1 − f ) ε D ,
1 ε A z = f ε C + 1 − f ε D ,
Φ = ( k A z d A + k B z d B ) | λ Brg = π ,
∂ Φ ∂ k x = ( ∂ k A z ∂ k x d A + ∂ k B z ∂ k x d B ) | λ Brg > 0 ,
d A > d Amin = λ Brg 2 1 R e ( ε A x ) [ 1 − ε B / R e ( ε A z ) ] ,
d B = ( λ Brg / 2 ) − R e ( ε A x ) d A ε B .
φ PCCH,Left + 2 φ E + φ PCCH,Right = 2 m π ( m = 0 , 1 , … ) .
2 φ E = 2 k E z d E = 2 k 0 n E 2 − sin 2 θ ,
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