Abstract
We present a systematic overview on laser transverse modes with ray-wave duality. We start from the spectrum of eigenfrequencies in ideal spherical cavities to display the critical role of degeneracy for unifying the Hermite–Gaussian eigenmodes and planar geometric modes. We subsequently review the wave representation for the elliptical modes that generally carry the orbital angular momentum. Next, we manifest the fine structures of eigenfrequencies in a spherical cavity with astigmatism to derive the wave-packet representation for Lissajous geometric modes. Finally, the damping effect on the formation of transverse modes is generally reviewed. The present overview is believed to provide important insights into the ray-wave correspondence in mesoscopic optics and laser physics.
Highlights
In paraxial approximation, the wave equation for spherical resonators was verified to be analogous to the Schrödinger equation for two-dimensional (2D) harmonic oscillators [1]
We presented a thorough overview of the laser transverse modes with ray-wave duality in spherical cavities with and without astigmatism
We first reviewed the eigenfrequency spectrum in an ideal spherical cavity to manifest the critical role of degeneracy in the ray-wave correspondence
Summary
The wave equation for spherical resonators was verified to be analogous to the Schrödinger equation for two-dimensional (2D) harmonic oscillators [1]. Besides the HG and LG eigenmodes, the so-called geometric modes with ray-wave duality can be systematically generated in the degenerate cavities [12,13,14,15,16]. We have exploited the generalized wave-packet state representation to construct the ray-wave connection for the multiple-pass Lissajous dotted patterns [52] Another important aspect of the wave-packet representation is to explore the damping effect that causes the asymmetric structure of the laser mode [53]. We present an overview the fine structure of the characteristic frequency in a spherical cavity subject to astigmatism to obtain the parametric ray equations for Lissajous geometric modes. The astigmatic degenerate cavities can be exploited to generate the geometric modes with transverse patterns to manifest the quantum wave functions.
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