Abstract
In a line-defect waveguide of a planer photonic crystal (PhC), we found a new rotational state of polarised light, which exhibits `polarisation rotation' on the PhC plane, when a phase mismatch $m$ was added to the air-hole alignment of the waveguide, where mode splitting was simultaneously observed in the dispersion curve. To account for the polarisation rotation together with the mode splitting, we propose a two-state model that is constructed from Schr{\o}dinger equation obtained from the equation for electromagnetic waves. The proposed two-state model gives an explanation on the relation between the polarisation-rotational angle $\theta$ and the mismatch $m$ and on its rotational direction (i.e., clockwise or anticlockwise direction) that depends on the mode. Using the two-state model, we also discuss the angular momenta of the polarised light in the PhC waveguide, which are directly related to the Stokes parameters that characterise the polarisation rotations.
Highlights
In a line-defect waveguide of a planer photonic crystal (PhC), the polarization of light can rotate on the two dimensional PhC plane by addition of a phase mismatch to the air-hole alignment of the waveguide, which occurs without non-linear optical interactions
We infer from our numerical simulations that the polarization rotation is intimately connected with the mode splitting, because they occur simultaneously, triggered by the addition of m. (Because of the above reasons, the mechanism of the rotational light obtained in our research is completely different from that of a gap vortex with non-linear interactions; the rotation that we found is spatial rotation, not temporal rotation seen for the localized vortex.)
NUMERICAL RESULTS FOR MODE SPLITTING AND POLARIZATION ROTATION
Summary
In a line-defect waveguide of a planer photonic crystal (PhC), the polarization of light can rotate on the two dimensional PhC plane by addition of a phase mismatch to the air-hole alignment of the waveguide, which occurs without non-linear optical interactions (e.g., optical Kerr effects and photorefractive effects). The presence of light rotation, given as an optical vortex that carries angular momentum, in photonic bandgap media [1,2,3,4] via such non-linear interactions has been found in theoretical and experimental investigations [5,6,7,8,9,10]; This mechanism is attributed to the localized vortex state induced by those non-linear effects in the bandgap media, which is sometimes called a gap vortex This is an analogous concept to a gap soliton in the bandgap media [11, 12]. We will gain a qualitative understanding of the simultaneous polarization rotation and mode splitting from our
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