Assessment of Rational Approximations for Square Root Operator in Bidirectional Beam Propagation Method

Accurate rational approximations to the square root operators are crucial for the bidirectional beam propagation method in simulation of strongly reflective structures. An assessment and comparison of various commonly used rational approximations is performed for both transverse electric (TE) and transverse magnetic (TM) waves. The range of validity and level of accuracy for the different approximations are studied by investigating the structures with varying reflection intensities. Guidelines for accurately modeling of evanescent and propagating modes are provided.