Chaotic Billiard Lasers

TL;DR

This chapter explores chaotic billiard lasers as a physical platform for quantum chaos, detailing theoretical and experimental insights into how chaos influences light emission and lasing properties in optical microcavities.

Contribution

It provides a comprehensive derivation of Maxwell-Bloch equations for chaotic microcavity lasers and bridges nonlinear lasing with chaotic wavefunctions.

Findings

Chaos-assisted light emission demonstrated in experiments

Theoretical framework linking chaos with lasing properties

Derived Maxwell-Bloch equations for chaotic microcavities

Abstract

This chapter provides an overview of chaotic billiard lasers as a prominent branch of quantum chaos. These lasers offer an ideal experimental platform for demonstrating the principles of quantum chaos within a physical system. We begin by introducing the fundamental principles of chaotic ray dynamics in optical microcavities, where the transition from regular to fully chaotic dynamics fundamentally alters the underlying wavefunctions and lasing properties. A central focus is placed on "chaos-assisted light emission," which serves as a practical manifestation of "chaos-assisted tunneling" -- a hallmark phenomenon in the study of quantum chaos. We discuss both theoretical frameworks and experimental validations, demonstrating how chaotic orbits facilitate the coupling between evanescently localized modes and far-field emission. Furthermore, exploring how the presence of a gain medium influences established results from quantum chaos research remains a fundamental and intriguing problem in physics. To address this, we establish a rigorous and comprehensive derivation of the Maxwell-Bloch equations for two-dimensional microcavity lasers, specifically examining their application to fully chaotic, stadium-shaped billiard lasers. By bridging the gap between nonlinear lasing processes and chaotic wavefunctions, this chapter highlights the unique potential of chaotic billiards for controlling light-matter interactions and shaping the next generation of unconventional coherent light sources.