This paper reviews the current level of theoretical understanding and experimental confirmation of the properties of unstable optical resonators for laser oscillators. A primary conclusion is that for any laser system characterized by a moderate gain per pass and a Fresnel number greater than a few times unity the unstable resonator provides the best practical resonator design for obtaining a high-quality near-diffraction-limited output laser beam combined with efficient energy extraction from the laser medium.

Unstable optical resonators.

An analysis of optical second-harmonic generation internal to the laser cavity is presented. It is shown that the maximum second-harmonic power generated in this way is equal to the maximum fundamental power available from the laser. Further, it is found that there exists a value of nonlinearity that optimally couples the harmonic out for all power levels of the laser. The magnitude of the nonlinearity required for optimum coupling is shown to be proportional to the linear losses at the fundamental and inversely proportional to the saturation parameter for the laser transition. For the YAlG:Nd laser at 1.06 μ using Ba 2 NaNb 5 O 15 as the nonlinear material, the required crystal length for optimum coupling is given by l\min{c}\max{2}(cm)\simeq 2.7 \times 10^{2}L/f where L is the linear round-trip loss and f is the ratio of the fundamental power density in the nonlinear crystal to that in the laser medium. For low-loss cavities, optimum coupling can thus be achieved for crystal lengths of 1 cm or less. The use of a mirror or mirrors within the cavity, reflecting at the harmonic, is considered as a means to couple out the total harmonic in one direction. Considerations of temperature stability and the finite oscillating linewidth of the laser are shown to favor a configuration with a single harmonic mirror located on the same surface as the fundamental mirror.

Theory of intracavity optical second-harmonic generation

The passive and hybrid Q-switching and mode-locking of solid-state lasers, dye lasers, semiconductor lasers and gas lasers is reviewed. The dynamics of saturable absorbers and reverse saturable absorbers is illustrated. The nanosecond pulse generation by passive and hybrid Q-switching of low-gain active media is described. The picosecond and femtosecond pulse generation by passive and hybrid mode-locking in low-gain and high-gain active media is analysed. The performance data of passively and hybridly mode-locked cw femtosecond dye lasers are collected. The pulse shortening of ultra-fast pulses with saturable absorbers in intra-cavity and extra-cavity configurations is discussed.

/pdf/passive-q-switching-and-mode-locking-for-the-generation-of-59azkkaa4g.pdf

Passive Q-switching and mode-locking for the generation of nanosecond to femtosecond pulses

An acoustooptic loss modulator made by bonding an X-cut quartz transducer to a fused silica scattering medium offers a practical means for repetitively Q-switching continuously pumped Nd : YAlG lasers at repetition rates up to 50 kHz. The peak power output of a multitransverse mode laser is typically enhanced by a factor of about 500 relative to CW operation at low (≪5 kHz) repetition rates and by larger factors when the transverse mode structure is suitably restricted. At high repetition rates, the peak power becomes smaller and the average power output approaches the CW level. The theoretical Q-switching behavior derived from the rate equations governing an ideal four-level laser is presented in graphical form, and is found to describe the observed behavior well when the laser is restricted to oscillation in the TEM 00 transverse mode. Similar calculations for Q-switched intracavity second harmonic generation indicate that the peak output power available at the second harmonic slightly exceeds that available at the fundamental, and that the harmonic coupling necessary to optimally couple the Q-switched laser is several orders of magnitude smaller than that required for CW intracavity conversion. Experiments using Ba 2 NaNb 5 O 15 For intracavity Q-switched harmonic generation roughly verified these predictions. A peak power output of 220 watts at 0.532 µ in the TEM 00 mode was achieved. Surface pitting of the nonlinear crystal after a few hours of operation prevented a thorough comparison with the calculated results. Preliminary experiments using the doubled Q-switched Nd : YAlG laser and an ammonia dihydrogen phosphate crystal to generate ultraviolet (the 0.266-µ harmonic) yielded a peak output power of 40 watts.

An experimental and theoretical study of high repetition rate Q-switched Nd: YA1G lasers

A simple but general formulation for the unified analysis of many different varieties of unstable optical resonators is obtained by expressing the round-trip Huygens' integral for the resonator in terms of the round-trip paraxial ray matrix. Complicated multielement resonators, ring resonators, and unstable resonators with variable-reflectivity output mirrors are thereby all reduced to a single equivalent collimated-beam diffraction problem. Essential assumptions in the analysis are that all elements in the resonator obey paraxial ray theory and that there is only one significant output coupler or limiting aperture per round trip inside the resonator. The only parameters needed to describe an arbitrary unstable resonator in this formulation are the round-trip magnification M and either the equivalent Fresnel number N eq or else an equivalent collimated Fresnel number N_{c} = [2M^{2}/(M^{2} - 1)] N_{eq} , plus for variable-reflectivity mirrors a specification of the mirror reflectivity profile.

A canonical formulation for analyzing multielement unstable resonators

The optimum coupling for intracavity second harmonic generation has been theoretically studied. It has been shown that, both for a four- and three-level laser, one can get as much power at the second harmonic wavelength as that which can be obtained at the laser wavelength. It is also shown that, for both cases, an optimum value for lw/w_{0} exists, where l is the nonlinear crystal length, and w and w 0 are the spot sizes of the laser beam, respectively, in the laser material and in the nonlinear crystal.

Optimum coupling for intracavity second harmonic generation

The static and dynamic behavior of a single-mode 4-level solid-state laser has been studied both theoretically and experimentally. In the theoretical section, the usual rate equations are modified in order to take into account the spatial variation of the inverted population due to the cavity field. These theoretical results have been verified with the help of a CW Nd-YAG laser. The experimental results on the output power and on the transient behavior are in good agreement with the theory within the accuracy of the experimental results (∼ 15 percent).

Static and dynamic behavior of a single-mode Nd-YAG laser

A mode-locked ruby laser has been built, utilizing a new kind of prism ring cavity that gives reliable single-transverse-mode operation. The cavity also operates in single-transverse mode when Q switched and when operated in normal lasing action.

Single-transverse-mode mode-locked ruby laser

An unstable ring resonator has been studied, both theoretically and experimentally; quasi-traveling-wave operation is obtained with a high ratio of the powers of the two opposite rotating waves and with diffraction-limited output beams.

R. Polloni

Papers

Optimum coupling for intracavity second harmonic generation

Static and dynamic behavior of a single-mode Nd-YAG laser

Single-transverse-mode mode-locked ruby laser

An unstable ring resonator