Coupling between photonic crystal waveguides

A calculation procedure for evaluation of the coupling length of two parallel coupled channel waveguides in a planar photonic crystal is proposed. The first step of the calculation is evaluation of the band structure of a photonic crystal containing two coupled linear defects. The eigenvalue corresponding to eigenstates localized in the linear defect (the waveguide) is split due to the coupling. This splitting is treated within the coupled-mode theory that yields a simple relation between the splitting and the coupling length. The MIT photonic bands code is used to evaluate the coupling between channel waveguides in silicon.¹ These calculations show that in contrast to the finite-difference time-domain approach, the method is effective for three-dimensional light propagation.