Observation of the Wave Function of a Quantum Billiard from the Transverse Patterns of Vertical Cavity Surface Emitting Lasers

Abstract

We demonstrate experimentally that the near-field and far-field transverse patterns of a large aperture vertical cavity surface emitting laser (VCSEL) can be successfully interpreted as a two-dimensional (2D) billiard system. It is found that the near-field and far-field transverse patterns of a large aperture VCSEL evidently represent the coordinate-space and momentum-space wave functions of a 2D quantum billiard, respectively. The result of this paper suggests that large aperture VCSELs are potentially appropriate physical systems for the wave-function study in quantum problems.

The Influences of Boundary Shapes on Polarization Characteristics and Lasing Modes in Broad-Area Vertical-Cavity Surface-Emitting Lasers With Cryogenic Detuning: Regular Versus Chaotic Cavities

“…The morphology of quasi-periodic linear ridges has been verified to come from the lateral oxide confinement. Based on the quantum billiard model, the structures of quasi-periodic linear ridges can be well reconstructed [6], [7]. At a higher injected current, the overall structures of the lasing modes still presented the feature of the quasi-periodic linear ridges but became vaguer due to the generations of multiple transverse modes.…”

“…On the other hand, in the cryogenic regime, lasing properties of the VCSELs are intimately associated with the lateral boundary confinement [6], [7], [18]. Under these circumstances, it has been confirmed that the VCSELs can be utilized to analogously investigate quantum billiards which are the general models for studying quantum chaos [6]- [9]. To deeply explore the influence of lateral boundary shape on emission characters in VCSELs is not only a meaningful topic for semiconductor laser technology but also for the issue of quantum chaos.…”

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

“…In contrast, the large discontinuities between the current-guiding oxide layer and the semiconductor gain materials ensure that the light wave undergoes total internal reflection at the boundary of transverse confinement. As a consequence, the VCSEL cavity can be considered as a planar waveguide with a dominant wave vector along the longitudinal direction [13,17].…”

“…Eigenmodes of the bounded wave systems are generally associated with the homogeneous Helmholtz equation with boundary conditions [6][7][8]. Two-dimensional (2D) scientific systems such as microwave cavities [9,10], vibrating plates [11], oscillating water tanks [12], and laser resonators [13,14] have been extensively employed to generate wave patterns of resonant modes that are presumed to be the experimental observations for theoretical eigenmodes. However, it is frequently found that there are significant discrepancies between theoretical eigenmodes and experimental observations in the one-to-one correspondence [15][16][17][18].…”

Transverse dynamics in cavity nonlinear optics (2000–2003)

“…Additional papers deal with relative noise intensity [238], transverse standing wave patterns [239], transverse mode locking [240], application to quantum billiards [241], amplitude-squeezed emission from transverse modes [242], and influence of anisotropies [243].…”