Event Detail

Event Type: 
Applied Mathematics and Computation Seminar
Friday, January 14, 2011 - 04:00
GLK 113

Speaker Info

OSU Physics

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.