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A polarizing beam splitter using negative refraction of photonic crystals

Vito Mocella, Principia Dardano, Luigi Moretti, and I. Rendina

Open Access Open Access

Abstract

Light passing through a photonic crystal can undergo a negative or a positive refraction. The two refraction states can be functions of the contrast index, the incident angle and the slab thickness. By suitably using these properties it is possible to realize very simple and very efficient optical components to route the light. As an example we present a passive device acting as a polarizing beam splitter where TM polarization is refracted in positive direction whereas TE component is negatively refracted.

©2005 Optical Society of America

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Supplementary Material (1)

Media 1: MOV (2484 KB)     

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Figures (6)
Fig. 1.
Fig. 1. When the incoming wavelength is larger than the lattice period of the PhC the medium can be considered homogeneous and the dispersion surfaces are spheres (a). When the wavelength decreases the spheres approach one another and a Bragg gap appears (b). The conservation of the tangential component of the wavevector in the external medium, k → i , determines the wavevectors in the PhC: P 1 O → , P 2 O → , P 1 H → , P 2 H → (c).

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Fig. 2.
Fig. 2. Dispersion (equi-frequency) surface for an air hole square lattice PhC in silicon (ε=11.9), r/a=0.195, in two adjacent Brillouin zones along the ΓX direction for TM polarization (E along the holes’ axis). By increasing the normalized frequency from 0.06 to 0.1848, the dispersion surfaces intersect over the lower 0-band (a). In such a case the upper 1-band has to be considered as well to get the complete dispersion surface, where the Bragg gap 2π/λ0 occurs (b).

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Fig. 3.
Fig. 3. Band diagram of the PhC of Fig. 2 for TM polarization (a). The regions along the XM direction, where many wavevectors are allowed for a given frequency, are highlighted in gray and labeled as α-β-γ. The dispersion surfaces corresponding to a frequency in region β (b) and region γ (c) show the overlap of different bands.

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Fig. 4.
Fig. 4. Band diagram for TM and TE polarization referring to the same PhC as in Fig. 2, along the XM direction (a). Λ0 /a as a function of ωn (b). The difference between the two polarization states is apparent.

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Fig. 5
Fig. 5 (2.42 Mb) Movie versus time of FDTD simulation for TM (a) and TE polarization (b). The incident wave (λ=1.55 μm) has a Gaussian profile with 4 μm FWHM and impinges at an angle 20.57° over a PhC square lattice of air holes in silicon with r/a=0.195, a=0.64 μm. The grid size in calculation is 15 nm, in x and z direction.

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Fig. 6.
Fig. 6. The power flows of the refracted beams and of the reflected beam as a function of the wavelength for TE (a) and TM (b) polarization.

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Equations (4)

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k → 2 = k → 2 ∙ k → = ( ω c ) 2 ε ˜ ( k → , ω )
I + max → t = 2 m Λ 0 2
I − max → t = ( 2 m − i ) Λ 0 2 m = 1,2 …
t = 2 m Λ 0 TE 2 = ( 2 m − 1 ) Λ 0 TM 2
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