The frequency degeneracy range of transverse mode in an off-axis end-pumped solid-state lasers

Abstract

The degenerate phenomena of transverse modal frequency in an off-axis end-pumped solidstate lasers was researched based on a semi-confocal cavity. Experimental results showed that at the large off-axis distance the transverse mode pattern changed from the Hermite-Gaussian mode to the geometric mode and finally back to the Hermite-Gaussian mode as cavity length varied. At the large off-axis distance, the degeneracy range of transverse mode patterns was a cavity length to mirrors radius ratio from 0.4958 to 0.5092 and the frequency degeneracy range was a cavity length to mirrors radius ratio from 0.4974 to 0.5025. The degeneracy range by observing beating frequency changes was more accurate and more useful than the method by comparing the transverse pattern changes. Furthermore, it was found that the off-axis pumping did not significantly alter the degeneracy position and range. 1.IntroductionUnder the principle of paraxial approximation, laser transverse modes in spherical cavities exhibit various eigenmodes, such as Hermite-Gaussian (HG) modes in cartesian coordinate and Laguerre-Gaussian (LG) modes in cylindrical coordinate [1,2]. Theoretical frameworks and experimental evidence suggested that structured light, according to specific requirements, can be synthesized within the spherical resonator [3][4][5]. Innumerable effort has been devoted to researching the degenerate phenomena of transverse modes in recently two decades [6][7][8][9][10][11][12][13]. By utilizing the degenerate method of transverse modes, people might obtain different structured lights. These structured lights could be applied in many fields, such as trapping nanoparticles[14], optical communication and optical device [15]. The method of transverse modes so far was mainly focused on frequency degenerating of transverse modes [10][11][12]16], it might also result from phase locking of modes [17]. As for the frequency degenerating of transverse modes, theory and results of it had been researched substantially [11,12,16,18,19]. But there were few researches on how wide the stable degenerate region was, to our knowledge. If there were some methods to analyze the detailed degeneracy process in the resonator, it will greatly promote the practical applications of the transverse modal degeneracy. It could help to judge whether the degenerate phenomena occurred or not. And the stable degenerate region was