Selecting high-order modes in solid state laser resonators

Abstract

The first chapter considered the fundamental processes of laser operation: photon absorp-tion, spontaneous and stimulated emissions. These processes are considered when design-ing a laser gain medium. A four-level laser scheme was also illustrated. Then, the basic components and operating principle of a simple laser system was presented using a diode end-pumped Nd:YAG solid state laser resonator. The second chapter considered laser light as light rays propagating in the resonator and extensively discussed the oscillating field in the laser resonators. It examined the characteristics of the fundamental Gaussian mode and the same theory was applied to higher-order modes. Chapter three started with an introduction to beam shaping and proceeded to present a review of some intra-cavity beam shaping techniques, the use of; graded phase mirrors, diffractive elements – binary phase elements and spiral phase elements. Also, a brief dis-cussion was given on the concept of conventional holography and digital holography. The phase-only spatial light modulator (SLM) was presented, which by default is used to per-form (only) phase modulation of optical fields and how it can be use to perform amplitude modulation also. Finally, a detailed discussion of the digital laser which uses the intra-cavity SLM as a mode selection element was presented, since it was the technique used in the experiment. The elegance of dynamic on-demand mode selection that required only a change of the grey-scale hologram on the SLM was one quality that was exploited in using the digital laser. The next two chapters presented the experiments and results. The concept of the digital laser was first used in the experiment in chapter four, to assemble a stable diode end-pumped Nd:YAG solid state laser resonator. Basically, the cavity was of hemispherical configuration using an intra-cavity SLM (virtual concave mirror) as a back reflector and a flat mirror output coupler. A virtual concave mirror was achieve on the SLM by using phase modulation to generate the hologram of a lens, which when displayed on the SLM made it to mimic a concave mirror. Then the next phase was using symmetric Laguerre-Gaussian mode function, of zero azimuthal order to generate digital holograms that correspond to amplitude absorbing concentric rings. These holograms, combined with the hologram that mimics a concave mirror were used on the SLM to perform high-order Laguerre-Gaussian modes selection in the cavity. The fifth chapter presented the results of the mode selection and considered the purity of the beam at the output coupler by comparing measured modal properties with the theoretical prediction. The outcome confirmed that the modes were of high purity and quality which further implied that the cavity was indeed selecting single pure high-order modes. The results also demonstrated that forcing the cavity to oscillate at higher-order modes (p = 3) extracted ≈ 74% more power from the gain medium compared to the fundamental mode (p = 0), but this extra power is only accessible beyond a critical pump input power of ≈ 38.8 W. Laser brightness describes the potential of a laser beam to achieve high intensities while still maintaining a large Rayleigh range. It is a property that is dependent on beam power and its quality factor. To achieve high brightness one needs to generate a beam that ex-tracts maximum power from the gain with good beam quality. Building on the experiments demonstrated in this study, one can make the correct choices of output coupler’s reflectivity, the laser gain medium’s length and doping concentration and the pump mode overlap for a particular mode to further enhance energy extraction from the cavity, and then using well known extra-cavity techniques to improve the output beams quality factor by transforming the high-order mode back to the fundamental mode. This will effectively achieve higher laser brightness.