Laser Transverse Modes with Ray-Wave Duality: A Review

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.

Excitation of Laguerre-Gaussian and geometric modes in a dye laser

“…4 can be compared in qualitative form to the data [11], where the formation of several types of non-planar elliptical geometric modes was observed during asymmetric selective end-pumping of an Nd:YVO 4 laser in a planospherical resonator. In works [2,3,[11][12][13] and in a number of other publications, non-planar modes with 3, 4, 5 and 7 spots were observed. In our experiments, we observed these modes as well, and we also obtained non-planar modes with 8, 11 and 13 spots of azimuthal structures (Fig.…”

“…4b) and 4 (photo not shown) low-intensity spots was difficult, probably due to the weak overlap of these beam structures with the pump profile. A comparison of all these dye laser beam profiles with the known beam profiles of geometric modes of solid-state lasers [2,3] indicates the nature of the modes in Fig. 4 as a family of non-planar geometric modes.…”

“…Taking into account the cylindrical symmetry of the resonator, structureless annular beams should be classified as Laguerre-Gaussian LG 0,l vortex modes. The structured beams were similar to LG 0,l petal modes, which are known to be a result of coherent addition of 2 vortex modes with opposite helicities [1][2][3][4][5][6]. The diameters of the laser beams were 5-9 times larger than the diameter of the fundamental mode and, therefore, corresponded to higher-order modes, such as the LG 0,10 and LG 0,16 modes shown in Fig.…”

“…Structured beams at the laser output arise due to variety of resonator transverse modes. Several comprehensive reviews and original studies on methods of transverse modes selection in lasers, both "classical" like Hermite-Gaussian, Laguerre-Gaussian, Ince-Gaussian and so-called geometric modes were published recently, see for example [1][2][3][4][5]. The "toolkit" for controlling the mode composition inside a resonator includes various techniques that affect the amplitude, phase, polarization of laser radiation, its gain and losses [1][2][3][4][5][6].…”

“…Several comprehensive reviews and original studies on methods of transverse modes selection in lasers, both "classical" like Hermite-Gaussian, Laguerre-Gaussian, Ince-Gaussian and so-called geometric modes were published recently, see for example [1][2][3][4][5]. The "toolkit" for controlling the mode composition inside a resonator includes various techniques that affect the amplitude, phase, polarization of laser radiation, its gain and losses [1][2][3][4][5][6]. The recent impressive achievement here was the "digital laser" based on an intra-cavity spatial light modulator (SLM), with which one can set almost any required beam profile on the SLM matrix and obtain it at the laser output [7].…”