Bidirectional eigenmode propagation for large refractive index steps

The bidirectional eigenmode propagation (BEP) combines the advantages of the transfer-matrix method for propagation and the mode-matching method (satisfying Maxwell's boundary conditions) at longitudinal large discontinuities for forward and backward travelling eigenvalues including discretized radiation modes. The calculated examples include a grating-assisted codirectional coupler for which 20% radiation losses have been found, and a cleaved waveguide facet with 39% reflected intensity and recapture of radiation modes due to a taperlike structure. The BEP is applicable to various types of optical passive (directional coupler, butt-coupling, taper) and active (DBR-, DFB-, and VCSE-laser, detector) devices with large refractive index differences.