This paper describes the continuing advances in laser resonators and optical beam propagation that emerged in the decades following the 1960s, growing out of the fundamental concepts from that era reviewed in an earlier paper. It also presents a brief look forward at some of the continued innovations now emerging in these areas.

Laser beams and resonators: Beyond the 1960s

Stable-unstable resonators have proved suitable for the extraction of a high-quality beam from a gain area that consists of a rectangular slab. Such gain areas have two substantially different transverse dimensions, and the resonators are stable in the small dimension while unstable in the larger one. Using off-axis unstable resonators avoids a central beam obscuration and improves beam quality. The adaptation of stable-unstable resonators to annular gain areas is described in this paper. The resulting resonators are stable in the radial direction and unstable in the azimuthal direction. Different unstable resonators, wound to match the annular geometry, are presented. The resonator modes are calculated numerically using a 3D-diffraction code that considers gain and misalignment. Resonator design parameters are obtained from a geometrical description of the resonator. Experimental results from a diffusion-cooled CO/sub 2/ laser confirm theoretical predictions and show that the resonators are capable of extracting beams that are nearly diffraction-limited with high efficiency from an annular gain medium. Output powers of 2 kW have been obtained from a gain length of 1.8 m. >

Azimuthally unstable resonators for high-power CO/sub 2/ lasers with annular gain media

Optical cavities with imperfect geometries have resonant transverse field modes whose spatial descriptions usually deviate from known mathematical functions. Numerical methods are therefore used to approximate the fields inside the cavities, and one method is reviewed that is in current use by groups designing large interferometric systems for gravitational wave detection. The method suffers from a large increase in computational time as the finesse of the cavity is increased. A modified method is presented that cuts down the computational time significantly (by factors of 10–100 in the cases considered) without affecting the accuracy of the results.

Fast estimation of transverse fields in high-finesse optical cavities

Propagation offset characteristics of annular laser beams from confocal unstable resonators through the natural atmosphere

The effects of pressure and temperature variations on the determination of water-vapor densities from ruby-laser radar returns are considered At the center of the 69438-A water-vapor line, the thermal dependence of the absorption cross section is almost negligible while the pressure dependence is not Water-vapor densities should be deduced from the line strength, which is independent of pressure, rather than the absorption coefficient as has been done previously The 69438-A line strength and line width were measured over a fixed-length atmospheric path using a ruby laser as 017 cm−1 g−1 cm2 and 0098 cm−1 bar−1 (295 K), respectively, with standard error estimates of 16 and 9%

Determination of atmospheric water-vapor densities from measurements of the 6943.8-Å absorption line strength

It is shown how fast Fourier transform techniques can be used to efficiently, numerically evaluate (convolution) integrals of the form often encountered in open resonator eigenmode calculations.

Direct application of the fast fourier transform to open resonator calculations.

The general theoretical requirements for making multisurfaced (resonant) reflectors frequency-tunable are described. Specifically, reflectors that can be used to stabilize and control the lasing spectrum of ruby lasers are considered. Fabry-Perot ring analysis showed that a four-surface reflector (two parallel sapphire flats) with a spacer (stellite) having close to the ideal thermal expansion coefficient, for thermal frequency tunability, could be used to continuously tune a ruby laser near 6944 A more than 0.3 A with a spectral width less than ±0.01 A.

M. M. Johnson

Papers

Direct application of the fast fourier transform to open resonator calculations.

Continuously Tunable Resonant Ruby Laser Reflector