Design and implementation of an experimental system for the generation of vortex beams using a solid-state laser
[Objective]Optical vortex beams have wide application prospects in quantum information,light detection and ranging,and optical communication.Vortex beam generation is the first and key part of the problem yet to be solved for these applications.However,generating vortex beams with high beam quality remains a challenge.Because the most common vortex beams,Laguerre-Gaussian beams,are the eigenmodes of the laser cavity,generating vortex beams directly using lasers has the advantages of high purity and high power compared with the extra-cavity method.To generate vortex beams directly using diode end-pumped solid-state lasers,this study aims to analyze the generation principle of vortex beams in solid-state lasers.This principle is based on the rate equations of population inversion and cavity photon density.Then,an experimental vortex laser system is designed,and the experimental platform is built.[Methods]This study establishes space-dependent rate equations for population inversion in the laser medium and photon density in the laser cavity.By solving the rate equations,we obtain the threshold pump power of the laser modes in a steady state.The pump power is dependent on the overlapping integral of the normalized pump intensity and the normalized photon density in the laser cavity.Then,we calculate the overlapping integral of the flattop ring pump beam and the Laguerre-Gaussian modes.The overlapping integral and the mode threshold change with the change in the radius of the pump beam.By adjusting the radius of the pump beam,the cavity modes can be selectively exited,and a specific vortex beam can be generated.According to this principle,an experimental scheme for the diode end-pumped solid-state vortex laser is designed.The collimated fiber-coupled output beam of the diode is tailored to a ring distribution using a circular opaque disk of 2 mm diameter.The ring pump beam is focused into the Nd:YAG laser crystal,which has a 2 mm thickness and 10 mm diameter.The radius of the ring pump beam in the laser crystal can be controlled by adjusting the longitudinal position of the focusing lens.The laser cavity comprises the coated planar end face of the laser crystal and the concave output coupler.The cavity has an optimized length of 20 cm,and the output coupler has an optimized radius of curvature of 50 cm.The phase structure of the output beam is measured using a Mach-Zehnder interferometer.A spherical beam is formed in the reference arm to interfere with the measured beam in another arm of the interferometer.The interferogram shows the phase structure of the output beam.[Results]When the focusing lens is at its initial position,the laser operates in the fundamental Gaussian mode.The output intensity has the Gaussian distribution,and the interferogram manifests a series of concentric rings.When the focusing lens has a longitudinal displacement of 0.9 mm toward the laser crystal,the laser has the output of the first-order vortex beam.The beam has a donut intensity distribution and a spiral interferogram.The helical direction can be controlled by tilting the output coupler.Furthermore,when the focusing lens has a longitudinal displacement of 1.2 mm toward the laser crystal,the laser has the output of the second-order vortex beam.[Conclusions]Vortex beam generation is demonstrated using the azimuthal order controlled by adjusting the pump beam and their helicities controlled by tilting the output coupler.This platform enables students to directly generate vortex beams using solid-state lasers and observe the phase characteristics of these beams.The platform helps students understand the cavity mode theory and its phase characteristics and provides strong support for teaching-related courses.
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