Transverse-Magnetic BPM Analysis of a Step-Index Slab Waveguide Expressed by a Sigmoid Function

Power conserving property of the propagating transverse-magnetic wave in a strongly guiding waveguide is demonstrated using the beam-propagation method with a transformed field. A step-index profile is expressed by a sigmoid function. A tilted, asymmetrical waveguide and a Y-branching waveguide with high index contrast are analyzed and discussed.