Generation of two-dimensional chaotic vector fields from a surface-emitting semiconductor laser: analysis of vector singularities

Characterizing classical periodic orbits from quantum Green's functions in two-dimensional integrable systems: Harmonic oscillators and quantum billiards

A general method is developed to characterize the family of classical periodic orbits from the quantum Green's function for the two-dimensional (2D) integrable systems. A decomposing formula related to the beta function is derived to link the quantum Green's function with the individual classical periodic orbits. The practicality of the developed formula is demonstrated by numerically analyzing the 2D commensurate harmonic oscillators and integrable quantum billiards. Numerical analyses reveal that the emergence of the classical features in quantum Green's functions principally comes from the superposition of the degenerate states for 2D harmonic oscillators. On the other hand, the damping factor in quantum Green's functions plays a critical role to display the classical features in mesoscopic regime for integrable quantum billiards, where the physical function of the damping factor is to lead to the coherent superposition of the nearly degenerate eigenstates.

Exploring the distinction between experimental resonant modes and theoretical eigenmodes: from vibrating plates to laser cavities

Experimentally resonant modes are commonly presumed to correspond to eigenmodes in the same bounded domain. However, the one-to-one correspondence between theoretical eigenmodes and experimental observations is never reached. Theoretically, eigenmodes in numerous classical and quantum systems are the solutions of the homogeneous Helmholtz equation, whereas resonant modes should be solved from the inhomogeneous Helmholtz equation. In the present paper we employ the eigenmode expansion method to derive the wave functions for manifesting the distinction between eigenmodes and resonant modes. The derived wave functions are successfully used to reconstruct a variety of experimental results including Chladni figures generated from the vibrating plate, resonant patterns excited from microwave cavities, and lasing modes emitted from the vertical cavity.

Exploring the origin of the directional emission from a microcavity with a large-aperture surface-emitting laser

The origin of the direction emission from a microcavity is investigated with a large-aperture surface-emitting laser with an equilateral-triangular shape. Experimental results reveal that a wide-spread eigenmode and a localized superscar mode can display quite similar far-field directional emissions. This experimental finding is theoretically confirmed with the quantum-billiard wave function and the approximation of the paraxial propagation.