R E S E A R C H   I N T E R E S T S

The work that is currently keeping me busy is explained at a basic level in the picture pages. Here is a more general overview :

• Liquid microdroplets and jets as self-assembled resonators for organic-dye lasers
• Lasing from nanoporous zeolite microcrystals containing organic dye as guest molecules
• Rare-earth-doped fibers with oval cross section
• Design of passive optical resonator devices (WDM, filters, switches, directional couplers)
• Quantum-cascade microcylinder lasers with oval cross-section
• Quantum well lasers using metallic-mirror microresonators
• Corner diffraction effects in GaN microresonators with poygonal (e.g. hexagonal) shape
• Cylinder resonators with metallic inclusions, fibers with non-concentric core and cladding

• Frequency-dependent linear response theory in low-dimensional conductors at finite damping, and semiclassical evaluation of the resulting expressions.
• Evidence of the KAM transition and classical phase space transport in wave calculations
• Classical dynamics in ``centrifugal billiards''
  Two-dimensional euclidean billiards with an additional $1/r^2$ potential arise naturally in the study of deformed droplets (and nuclei) with axial symmetry.
• Billiards with three degrees of freedom
  A promising approach to the little-studied case of truly three-dimensional billiards would be to consider them as deformations of some body of revolution like the centrifugal billiard or a truncated cylinder. Complications like Arnold diffusion and non-KAM behavior can thus be controlled. We are studying cylinders with tilted caps.
• Interplay between mode-specific Q-spoiling, spatial hole burning, and gain saturation in ARC
  The experimental agreement with our predictions for lasing directionality in deformed droplets has not yet been tested at a fully quantitative level. This is due in large part to the intricate multimode lasing scenario which arises because of spatial hole burning, and which must be taken into account in determining the weighting of different lasing modes.
• Novel experimental realizations of ARC devices
  Microdroplets in aerosols have proved to be well suited for initial tests of our predictions. Similar physics applies to glass spheres and microdisc lasers where it is currently of great interest to manipulate the cavity shape so as to couple light out in a highly directional manner, as opposed to the inefficient isotropic emission pattern from perfectly symmetric devices. Design of such cavities can be guided by an understanding of the nonlinear ray dynamics.

• Semiclassical, tunneling and localization corrections to the ray-optics model for ARCs
  These corrections are especially important for system sizes far from the classical regime, which are in fact of great practical interest. I am including tunneling at a WKB level.
• Application of the theory of ARCs to electronic devices
  Microstructures can be envisaged which support quasibound states associated with classically trapped regions of a mixed phase space. This constitutes a generalization of the ARC principle.
• Semiclassical determination of the spectrum of hamiltonian systems in the mixed regime
  No complete solution exists to date for the semiclassical quantization of systems whose classical phase space contains both chaotic and regular components, as is the case in convex ARCs.