Existing algorithms for bidirectional optical beam propagation proposed to
simulate reflective integrated photonic devices do not propagate evanescent
fields correctly. Thus inaccuracy and instability problems can arise when
fields have significant evanescent character. We propose complex representa
tions of the propagation operator by choosing either a complex reference wa
ve number or a complex representation of Fade approximation to address this
issue, Therefore correct evolution of both propagating waves and evanescen
t waves can be simultaneously realized, significantly reducing the inaccura
cy and instability problems. Both test problems and practical problems are
presented for demonstration.