Double EIM and scalar BPM analyses of birefringence and wavelength shift for TE and TM polarized fields in bent planar lightwave circuits

Planar lightwave circuits (PLCs) are the technology of optical devices. In order to raise the integration density. PLCs including several kinds of the waveguide are needed bent waveguides to connect two straight waveguides. It is well known that optical power is lost at the entrance and exit of the bent waveguides and by bending effect [1]. The hending loss contains both losses. A number of theoretical trealments have been done to determne and reduce the radiation losses in curved waveguides [Z] [8]. In this paper, in the process of the FD-BPM cdculation to obtain the propagating field from the initial field, we can obtain the propagation constants through calculating the phase difference between the fields of the two consecutive steps in the propagation direction for each of TE and TM modes. Dividing calculated propagation constants by the free-space propagation constant, the effective guide indices can be obtained. The index difference between the two orthogonal modes is used to calculate the wavelength shift.