Event Type:

Applied Mathematics and Computation Seminar

Date/Time:

Friday, January 14, 2011 - 04:00

Location:

GLK 113

Guest Speaker:

David Foster

Institution:

OSU Physics

Abstract:

The vectorial differential equation describing the

propagation of light has solutions which are "paraxial": the amplitude

is confined to a region along an axis of propagation. An

approximation leads to a parabolic differential equation, the exact

solutions of which are the Gaussian wave modes described in the common

texts of optical physics. These solutions, which are simply scalar

fields multiplied by a constant vector, describe well the behavior of

both laser beams and the standing wave eigenmodes of two-mirror

resonators. For resonators, the higher order Gaussian modes come in

sets of modes that are "degenerate", having identical

eigenfrequencies. Accurate, non-adiabatic numerical simulation in

small, high quality resonators reveals the degeneracy is in fact

broken. The partitioning of the degenerate mode sets into eigenmodes

depends in a nontrivial way on both the vectorial nature of

electromagnetic fields and on boundary phase shifts at the mirrors of

the resonator. The mode subspace can be reduced by symmetry and a

careful perturbative treatment reduces the eigenfunction problem to

the simple diagonalization of 2x2 perturbation operator matrices.