Polarization Rotation and Mode Splitting in Photonic Crystal Line-Defect Waveguides

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 Schro¨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 q 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.