### Applied Math Seminar with University Scholar Jianke Yang

#### Monday, November 13

- 11-02-2017
- By CEMS

Speaker: Professor Jianke Yang

Department of Mathematics & Statistics

UVM and University Scholar

Day and time: Monday, November 13, 4:30 - 5:30 pm.

Location: 223 Votey

Title: All-real spectra in optical systems with arbitrary gain-and-loss distributions

Abstract

A method for constructing optical potentials with an arbitrary distribution of gain and loss and completely real spectrum is presented.

For each arbitrary distribution of gain and loss, several classes of refractive-index profiles with freely tunable parameters are obtained

such that the resulting complex potentials, although being non-parity-time-symmetric in general, still feature all-real spectra for a wide range of parameters.

Under parameter tuning in these potentials, a phase transition can also occur, where pairs of complex eigenvalues appear in the spectrum. In some classes of these potentials, a distinctive feature of the phase transition is that the complex eigenvalues may bifurcate out from an interior continuous eigenvalue inside the continuous spectrum. These non-parity-time-symmetric complex potentials generalize the concept of parity-time-symmetric potentials to allow for more flexible gain-and-loss distributions while still maintaining all-real spectra and the phenomenon of phase transition.