Rules of selection for spontaneous coherent states in mesoscopic systems: using the microcavity laser as an analog study

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.

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

We demonstrate experimental generation of two-dimensional (2D) chaotic vector fields from a surface-emitting microcavity laser with precisely control of the operating temperature and the operating current. The 2D optical vector field is found to be formed by frequency locking of two linearly polarized laser modes with different chaotic spatial structures. The eigenfunction expansion method is used to reconstruct the experimental wave function for analyzing the properties of the vector singularities. It is shown that the distribution of vector singularities obeys the sign rule of nearest-neighbor singularities in the phase space of the vector field.

Formation of long-lived, scarlike modes near avoided resonance crossings in optical microcavities

We study the formation of long-lived states near avoided resonance crossings in open systems. For three different optical microcavities (rectangle, ellipse, and semistadium) we provide numerical evidence that these states are localized along periodic rays, resembling scarred states in closed systems. Our results shed light on the morphology of long-lived states in open mesoscopic systems.

Wave functions with localizations on classical periodic orbits in weakly perturbed quantum billiards

We analytically investigate quantum wave functions with localizations on classical periodic orbits (POs) in the circular billiards. We construct the coherent states which are the coherent superpositions of nearly degenerate eigenstates and found to be localized around single classical POs. With the constructed coherent states, we can analytically express the mesoscopic eigenstates in the weakly perturbed systems, which are found to be localized on the ensemble of classical POs. Furthermore, these coherent states can be utilized to study the quantum vortex structures in quantum billiards.

Devil's staircase in three-dimensional coherent waves localized on Lissajous parametric surfaces

We experimentally demonstrate the significance of the longitudinal-transverse coupling in the mesoscopic regime by using a high-Q laser resonator as an analog experiment. The longitudinal-transverse coupling is found to lead to the three-dimensional (3D) coherent waves that are localized on the parametric surfaces with Lissajous transverse patterns. More strikingly, experimental results reveal that the mode locking of the 3D coherent states forms a nearly complete Devil's staircase with the hierarchical ordering.

Quantum signatures of nonlinear resonances in mesoscopic systems: efficient extension of localized wave functions

We investigate the quantum signatures of classical nonlinear resonances by making the analytic connection between the quantum wave functions and the classical periodic orbits for the uncoupled systems. It is found that the highly efficient extension of the localized coherent states within the classical caustics is an intriguing phenomenon in mesoscopic systems with nonlinear resonances. With the theoretical analysis, we experimentally demonstrate that the laser resonator with an intracavity saturable absorber can be employed to visualize the wave patterns analogous to the quantum wave functions associated with Fermi resonance.