This paper presents a theoretical study relating a general measure of laser beam quality to the amplitude and scale size of phase aberrations at the output aperture. Laser output beam quality has frequently been stated in terms of the Strehl ratio, S, which is the ratio of the far-field centerline intensity with arbitrary phase aberration at the output aperture to the centerline intensity with uniform phase and amplitude at the output aperture. This is based on the belief that the focal spot diameter with aberrations should be roughly l/ig times larger than the spot size for a diffraction limited beam. This need not be the case, especially for a beam which is several times diffraction limited. A more meaningful definition is based on the beam divergence angle within which a certain fraction of the total power flux (e.g., 83%) is contained. Aberrations that arise from ordered disturbances as well as random disturbances (e.g., turbulence) with the laser are examined, using both Fraunhofer and geometric optics whose results are compared to each other. When the far field is calculated for lower order aberrations, tilt and refocus are incorporated, for two strategies: maximizing the Strehl ratio, or maximizing the encircled power. For large aberrations, the former requires a different correction than just minimizing the rms phase aberration. The latter increases the encircled power by 50% as compared to the former for lower ordered aberrations. The results indicate that for a highly aberrated phase distribution at the output aperture, the beam divergence angle may still be small enough to be useful, particularly for small laser wavelengths.

A simple formula has long been in use which relates Strehl intensity of a coherent light source to the root-mean-square (RMS) of the beam phase structure for near-perfect beams: 2 I/Io = e -Φ2 RMS where I/Io is the peak for field intensity ratio and ɸRMS is the root-mean-square of the beam phase. Use of this formula has been generalized to include "power-in-a-bucket" des-criptions of far field behavior, and the tendency is to use the simple description for even larger phase distortions. With the advent of computer models, the far field intensity redistribution due to a specific near field phase structure is readily calculated. A study has been made to relate RMS phase structure to the various standards of far field: peak (Strehl) intensity, power in various "buckets", and radial dimension to capture a fixed percentage of the power. A description of Strehl intensity as a function of RMS phase has been formulated which is slightly more complex and significantly more accurate than the simple exponential currently in use.

The function of a high power laser system is simple in nature: generate coherent radiation, transport and point it through an optical system and finally deliver it to a receiver plane where its function, be it fusion, be it welding, or whatever, is accomplished. While the specific nature of the elements of every system may be different depending greatly on requirements such as power levels, and wavelengths, it is almost always true that if the coherent nature of the laser radiation is to be used to maximum advantage, very careful optical tolerances must be placed on every step of the laser system design and operation.

Solid state lasers for fusion experiments must reliably deliver maximum power to small (approximately .5 mm) targets from stand-off focal distances of 1 m or more. This requirement places stringent limits upon the optical quality of the several major components -- amplifiers, Faraday isolators, spatial filters -- in each amplifier train. Residual static aberrations in optical components are transferred to the beam as it traverses the optical amplifier chain. Although individual components are typically less than λ/20 for components less than 10 cm clear aperture; and less than λ/10 for components less than 20 cm clear aperture; the large number of such components in optical series results in a wavefront error that may exceed one wave for modern solid state lasers. For pulse operation, the focal spot is additionally broadened by intensity dependent nonlinearities. Specific examples of the performance of large aperture components will be presented within the context of the Argus and Shiva laser systems, which are presently operational at Lawrence Livermore National Laboratory. Design requirements upon the larger aperture Nova laser components, up to 74 cm in clear aperture, will also be discussed; these pose a significant challenge to the optical industry.

High energy pulsed and high power CW lasers are considered. The path of the photons is traced from generation in the laser cavity to interaction with a target. At each step along the path, the interaction between aerodynamics and laser radiation must be understood to avoid serious degradation of beam quality. Beam distortion effects are cumulative. Aero-optics as an interdisciplinary technical area has achieved a level of maturity where most pitfalls can be circumvented.

High power laser optical systems often require gas flow in the optical train to control effects such as thermal blooming. The gas flow itself is a source of optical degradation for the laser beam. A series of experimental investigations have been performed for scale simulations of a typical optical train. These included water table simulations for flow field visualization and a gas flow simulation for assessment of optical degradation. Optical and flow turbulence effects for the type of gas used and the method of flow injection have been ascertained. It was determined that substantial optical degradation can be caused by the flow and a number of qualitatively desirable flow implementations were identified.

In laser beam propagation studies, wavefront aberrations introduced by the beam handling optics must be known to truly characterize the atmospheric effects on the laser beam. Hence, careful optical interferometry was performed on a laser beam expander and its associated relay optics, before it was used for propagation experiments. However, recent studies by Bennett, et al.', have shown that interferometric measurements of mirrors with enhanced reflection coatings must be performed at the designed wavelength. Bennett's studies show that measuring these enhanced reflecting coatings off-band produces erroneous wavefront errors. An experiment was performed to see if this interferometric measurement problem existed in our system which contained one enhanced reflecting mirror.

An exact analysis of the hole grating beam sampler with finite width and hole size is presented, based only on the approximations used in the diffraction integral. It is shown that no beam can be exactly reconstructed in the sampling process. The error introduced by the sampling is dependent on the frequency distribution in the sampled beam.

The degradation due to random segment jitter and phase mismatch on the average far field, on axis irradiance of a laser beam transmitted from a telescope with a segmented primary mirror is computed. The derived expression is exact within the stated assumptions and offers a more accurate alternative, for this application, to the commonly used Strehl approximation.

It is well known that diffraction in an optical train will produce near-field Fresnel intensity ripples. A previous paper by Avizonis, O'Neil , and Hedin hypothesized that these Fresnel ripples would be mapped by typical water cooled laser mirrors producing surface distortions, which in turn would cause a drop in peak far-field intensity. This Fresnel ripple mapping phenomenon was studied by developing a detailed finite element model of a one inch by one inch segment of a water cooled laser mirror. The model was loaded with a uniform surface heat flux with various orientations of Fresnel intensity ripples superimposed upon it. A nonlinear steady-state heat transfer analysis was per-formed to determine the temperature distribution within the model. A thermal deformation analysis was then performed and the mirror surface distortion was computed. All analyses were performed using the NASTRAN finite element computer code. The results showed that the mirror indeed mapped the Fresnel intensity ripples. The mapping effect was shown to be insignificant for the particular cases analyzed, but projected results indicated that the Fresnel ripple mapping phenomenon could be significant for higher power and/or shorter wavelength laser systems.

Laser-induced optical distortion in laser window materials may seriously impair the performance of a high power optical system. The distortions result from refractive index changes produced by laser-induced thermal gradients. The thermo-optic effect (dn/dT), thermal expansion, and stress-optic effect all contribute to the loss of far field intensity. Experimental measurements of thermal lensing in ZnSe and experiments to monitor the distortion of laser-irradiated fluoride materials are presented. For a well behaved Gaussian beam profile the window distortion produces a thermal lensing effect in ZnSe which changes the focus but produces only slight distortion; refocusing of the optical system can restore the on-target intensity in this situation. In general, the laser-induced distortions will follow the beam profile variations. Irregular beam intensity profiles introduce greater distortion than uniform beam profiles.

Exciplex lasers operate at visible and near ultraviolet wavelengths and the medium homogeneity requirement to produce a near diffraction-limited beam from such a laser is suite stringent: (δρ/ρ) rms-5x10-5. This study addresses flow and acoustic issues involved in achieving good beam quality from a rep-pulsed system. A specially designed blowdown facility was used to demonstrate experimentally that the required level of baseline flow homogeneity could be achieved. Theoretical models were developed to understand the performance of an acoustic attenuation system involving sidewall mufflers placed immediately upstream and downstream of the laser cavity. The flow clearing process after single and multiple pulses with such mufflers has been studied in the blowdown facility using movie interferometry.

Measurements of the thermally induced optical distortion of an active-mirror laser amplifier are presented along with a comparison of measured and calculated distortion. A discussion of a means for compensation for these distortions is also presented.

Continuous wave hydrogen-fluoride lasers designed to yield high mass to power utilization efficiency contain active medium inhomogeneities which have the potential of introducing large correlated medium aberrations. Reduction of the magnitude of the correlated medium aberrations by proper orientation of adjacent laser nozzle modules are investigated using geometric and diffractive wave optics analysis. Two significantly different high mass efficiency designs were examined, the axisymmetric and hypersonic wedge. Detailed gas dynamic calculations were made to estimate the index of refraction variations in these three-dimensional mixing, reacting and lasing flowfields. The geometric and diffractive wave analyses were performed to establish the optical path differences (OPD's) introduced by multiple rows of the basic nozzle array unit. Comparisons between the geometric and diffractive analyses showed that the geometric treatment would place an upper limit on the OPD's to be expected from multiple nozzle arrays. Alignment of rows of the axisymmetric nozzle array with the lasing axis was found to have a catastrophic effect on the beam quality of the device. However, by properly skewing the rows of nozzles, it was possible to reduce the degradation in beam quality. Similarly, worst case orientations for the hypersonic wedge array were identified and skewing of the trailing edge of the hypersonic wedge with respect to the optical axis was shown to significantly minimize beam quality degradation.

An instability in the output of a high-power unstable resonator cw CO2 thiser is analyzed in terms of a perturbative effect of an acoustic wave which is induced by laser heating. This may be either a three-wave process, in which the dominant mode of the laser couples to another laser mode separated from it by an acoustic frequency, or a two-wave process in which the acoustic wave modulates the cavity loss. Both processes depend on the refractive index perturbation by the acoustic wave. In the three-wave process, the two electromagnetic waves de-excite the lasing gas and the resultant heat deposition leads to the excitation of the acoustic wave. The phasing of the three waves is such that the interaction is unstable. It leads to an enhancement of the output coupling coefficient and in the nonlinear stage a complete shutdown of the laser. In the two-wave process, the acoustic wave is driven by nonuniform heating caused by nonuniformity of the optical eigenmode and changes of the cavity flux. Our analysis was extended to a simple one dimensional model of a supersonic laser, which was determined to be stable. A related problem of the alignment sensitivity of the cw CO2 laser was explained in terms of a temperature gradient along the gas-flow direction, which is transverse to the laser axis. The difference in path length, between the mirrors, through the density wedge can lead to unstable alignment.

Recent experiments have demonstrated a significant power loss (as great as 50%) from the central far-field spot of a pulsed CO2 electric-discharge laser. Our theory shows that saturation effects that follow the unstable resonator mode variations can create index variations. These index variations lead to a phase grating, and power losses result from diffraction off the grating.

Cavity-induced beam distortion might be reduced by a phase conjugating mirror inside the laser. The promise and problems of doing this in a high-power laser are discussed. After reviewing the oscillation mode theory of resonators with phase conjugators, we discuss the practical limitations at high power. The main issues are (1) availability of pump energy for conjugation, (2) degraded conjugation at high power, and (3) outcoupling the energy from the laser.

Optical phase conjugation by degenerate and spin-resonant four-wave mixing in Hg1-xCdxTe has been studied. Three mechanisms have been identified: conduction band nonparabolicity, electron spin rewcance, and photoexcited plasma. Values of the third order nonlinear susceptibility χ(3) for x-values of 0.216 - 0.232 range from 10-8 - 10-7 esu (conduction band nonnarabolicity) through 10-4 esu (electron suin resonance) to rb3 x 10-2 esu (photo-excited plasma). These measurements are of use in evaluating the potential of Hgl_xCdxTe for correction of wavefront distortions by optical phase conjugation.

We will discuss how novel arrangements of conventional static/linear optical elements can compensate for many classes of time varying distortion in a high power optical train. Precision corner arrays, lens arrays and K mirror arrays are all applicable as pseudo conjugation elements in certain classes of problems. In some cases multipassing (four or more passes) of a distorting medium can offer improved performance. Although the compensation is more limited than available from nonlinear phase compensation, problems with thresholds, pumps and frequency translations are eliminated.

This paper describes the various carbon dioxide laser fusion systems at Los Alamos from the point of view of an optical designer. The types of phase aberrations present in these systems, as well as the beam cleanup techniques that can be used to improve the beam optical quality, are discussed. As this is a review article, some previously published results are also used where relevant.

This paper briefly reviews the application and limitations of adaptive optics using discrete components to the problems encountered in high-power laser beam conditioning. These problems include static surface figure errors, randomly varying wavefront aberrations due to thermal distortion of the optics, and inhomogeneties within the laser cavity, as well as precise pointing of the beam in the presence of vibration. The capabilities of current devices such as deformable mirrors and wavefront sensors are reviewed. The prospects for removing some of these limitations are considered.

The Local Optical Correction System (LOCS), currently in fabrication, is a next generation beam control concept. The LOCS is designed to demonstrate full aperture sampling of the outgoing wavefront, alignment and stabilization using an inertially stabilized reference, and correction of local optical train errors. Sampling is by a low efficiency holographic grating on the 60 cm primary mirror. The grating diffracts a visible (0.6328 micron) probe beam into a wavefront sensor behind the secondary mirror. Wavefront information is processed in real time, and a deformable mirror is actuated to modify the out going beam. The primary emphasis is on the removal of internally generated distortions. System delivery to the Air Force Weapons Laboratory is currently scheduled for November 1981. Preliminary testing should be completed by May 1982.

In this paper we review the major elements of a HEL wavefront sensing and control system with particular emphasis on experimental demonstrations and hardware components developed at Lockheed Missiles & Space Company, Inc. The review concentrates on three important elements of wavefront control: wavefront sampling, wavefront sensing and active mirrors. Methods of wavefront sampling by diffraction gratings are described. Some new developments in wavefront sensing are explored. Hardware development efforts of fast steering mirrors and eage controlled deformable mirrors are described.

The use of adaptive optics has been increasingly proposed as a solution to a variety of optical phase distortion problems. Deformable (rubber) mirror concepts have utilized numerous design techniques for phase distortion correction. Deformable mirror requirements are reviewed for several applications along with projected requirements to meet the demands of future optical systems. Actuator and mirror design requirements are addressed along with their interrelationship with electronic driver design.