New Families of Complex Hyperbolic-Secant Refractive-Index Profiles through the Factorization Method

Abstract

New families of complex-valued refractive-index profiles of the hyperbolic-secant type are constructed by means of the factorization method. These are included in the class of widely-studied PT-symmetric ones and are a generalization of the well-known (real-valued) hyperbolic-secant refractive-index profiles. Also, the analytic expressions for the corresponding modal fields are obtained and the interlacing of the zeroes of the real and imaginary parts is elucidated. In addition, a bi-orthogonal description of these modal fields is given, as the related differential operators are non-Hermitian. In turn, this allows to establish the orthogonality of eigenmodes in a similar way as it is done in the Hermitian case.