Applied Maths Seminar: Poladian -- Wave equations with eigenvalue-dependent boundary conditions (and why they come up in modern optical fibre design)

Leon Poladian, University of Sydney 

Wave equations with eigenvalue-dependent boundary conditions (and why they come up in
modern optical fibre design) 

Wednesday 7th Oct 14:05-14:55pm, Eastern Avenue Lecture Theatre.  

The propagating modes of conventional optical fibres correspond to eigenfunctions of
wave equations that decay "exponentially" in the transverse direction.  In the last
decade a new type of fibre has become popular: one that does not completely confine the
light and thus the transverse fields no longer decay.  These modes (called leaky modes)
can be obtained by applying, instead, an outward radiation condition.  The theoretical
and numerical investigation of these modes on a finite domain requires the manipulation
of eigenvalue-dependent boundary conditions.  I will discuss various approaches (of more
or less utility) from the literature and some that I have explored over the last few
years.