Photonic crystal slab between orthogonal polarizers: details on the guided mode resonance wavelength

Abstract

The transmission spectrum of a photonic crystal slab features sharp dips created by guided mode resonances. The same photonic crystal slab placed between orthogonal polarizers shows peaks at the resonances, but the peak wavelength differs from the guided mode resonance wavelength by a few nanometres. We investigate the working principle of the orthogonal polarizer setup and the origin of the wavelength difference for the case of a TE resonance. We show that the peak in the orthogonal polarizer setup is formed by light from the non-resonant TM polarization. The wavelength difference is caused by the phase shift between the resonant TE and the non-resonant TM polarization. We compare our explanation to a temporal coupled-mode approach and the use of a time-domain window function in FDTD. Fig. 6 Polarization ellipses for ⃗ J PCS , i.e. the light directly after the photonic crystal slab, for the different stages of the TE resonance. The ellipses have been calculated from the FDTD results. The numerical values for ⃗ J PCS and ⃗ J out = T Pol 2 ⋅ ⃗ J PCS are shown at the bottom of each figure (the phases are always normalized such that J 1 ∈ ℝ ). The numbers (1)-(6) refer to the wavelengths indicated in Fig. 5 and to the description in Sect. 4. The orientation of the first and second polarizer are indicated with the dashed and solid diagonal lines. Only that part of the elliptically polarized light that is aligned to the second polarizer can pass it. Therefore, the projection of the ellipse onto the second polarizer is shown with dotted lines and the green arrows. These green arrows are the visual representation of ⃗ J out = T Pol 2 ⋅ T PCS ⋅ ⃗ J in . The maximum projected field strength, reached at OP , is indicated with a tick on the second polarizer in all figures. Note that the green arrows only reach this tick for = 608.4 nm , which corresponds to | ⃗ J out | = 0.494 ≈ 1∕2 , and are shorter for every other wavelength, which can be seen in the magnification

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