Ph.D. Research: Physical Optics and Semiclassical Systems
My Ph.D. work was done with
Jens Nöckel at the University of Oregon on certain optical systems and the mathematics (semiclassics, nonlinear dynamics, quantum chaos, electromagnetic perturbation theory) that could be applied to them. My
dissertation (2006) covers some of my work in this area. See my CV for more info and publications.
Distorted sphere optical resonators
Whispering gallery waves/modes in distorted spheres (ex: a Silica, primarily oblate ellipsoid grown from melting the tip of an optical fiber) can exhibit directional emission (or input coupling) even when the radial distortion in the equatorial plane is only a percent or so.
Microspheres can thus realize the function of optical oval resonators, which can be more difficult to make.
Goos-Hänchen optical modes
Modeling a simple cavity (length
L) with a circular/spherical perfectly electrically conducting (PEC) mirror of radius
R, 0 < (
R-
L) ~ λ <<
L, and a planar dielectric layered (thin-film) mirror, we discovered the first known optical modes that owe their existance to the Goos-Hänchen (GH) effect (which laterally shifts light striking the dielectric mirror). The GH shift creates a large stable island or torus in the phase space of classical (ray) dynamics through a saddle-point bifurcation. The stable region allows cone shaped (non-paraxial) wave modes to exist, with the apex of the cone slightly below the surface of the dielectric mirror, and the base of the cone being a ring (generally with azimuthal oscillation) on the spherical mirror with a lattitude of typically between 30 and 70 degrees.
The GH modes are a very interesting example of how adding a minimal wave effect to ray optical model (minimal in the sense that the GH shift is zero order in the far field spread angle of a beam) can alter the ray dynamics which then alters the physical waves.
The next phenomena and theory I discuss is similar, in that a zero order perturbation theory in a small parameter which is similar to the spread angle, has a large effect on modes.
An important difference is that the GH modes can exist if the waves are scalar (e.g. acoustic waves), whereas the subject of the next section requires vectorial (transverse) waves, because polarization is coupled to spatial structure.
Mixing of orbital-angular-momentum modes (Laguerre-Gauss modes) in small cavities via an effective spin-orbit coupling