This paper gives brief descriptions of three recent developments not so much in laser resonators themselves as in the tools for analyzing and measuring the quality of laser beams and resonators. These tools include personal computer programs for analyzing laser beams and resonators; a new method for characterizing and measuring the "beam quality" of a laser output beam; and a new "ray-pulse" method of analysis for describing beams and resonators which involve any combination of ultrashort optical pulses, broadband optical signals, and dispersive optical elements.

The review starts with the basic kinetics involved in the power-extraction process in a typical CO(2)-N2 gas dynamic laser (GDL) system, with emphasis on parameters influencing optical resonator design. Devices developed during the later 1960s through the 1980s are described briefly. Power-extraction techniques with stable and unstable resonators, as well as integral master oscillator power amplifier are covered. Attention is focused on parameter analyses including the effects of gain, media index of refraction changes, mirror and coating distortion, and resonator-mirror misalignments. The major steps of an airborne laser laboratory (ALL) GDL program are outlined, and experimental laser device, split stage demonstrator, and ALL GDL diagnostics are discussed.

This paper reviews and discusses the performance of unstable resonators concentrating on the design, analysis, and test of oscillators used on electric discharge and electron-beam pumped laser devices. The work covers over 15 years of device development including pulsed and continuous wave CO2, CO and excimer lasers, both subsonic and supersonic flow. The emphasis is on the review of the energy extraction and beam quality experimental results from a wide range of devices. The effect of flow characteristics on laser performance is discussed. The interaction between the optical mode formation and the laser medium, called the 'Mode-Medium Interaction', is presented in terms of both theoretical and experimental understanding. The device design constraints imposed by optical material limitations is also discussed.

Passive-cavity transverse-mode stability properties such as the transverse-mode discrimination ratio and aberration sensitivity are analyzed. The influence of the diffractive formation of the transverse-mode field distribution on the aberration sensitivity is studied, along with the relationships between this sensitivity measure and the diffractive transverse-mode discrimination in a cavity. It is shown that the passive unstable-cavity mode stability properties are connected with the properties of the central core region of the resonator that is defined by the cavity Fresnel zone structure. Specifically, the transverse-mode discrimination or separation ratio with any perturbation or aberration source is a maximum when there is a constructive interference along with the cavity optic axis between the edge scattered converging wave field from the feedback aperture and the dominant geometric mode of the cavity.

The properties of unstable resonators in which localized amplitude or phase perturbations are induced at the center of the coupling mirror are investigated. Unstable resonators with a non-reflecting central zone have zero geometrical feedback; however, there exists a residual feedback due to diffraction at the mirror edges. Such a residual feedback can be significantly reduced using variable reflectivity mirrors. Negative branch unstable resonators with an opaque focal zone are even more efficient to quench this residual feedback. Enhancement of the feedback coefficient by factors up to 3 is predicted when the phase of the wave reflected at the coupling mirror changes over a restricted zone near its center.

Mode discrimination in a negative branch confocal unstable resonator with a round aperture and spherical mirrors was studied by numerically computing the lowest loss modes and their losses. Selected intensity and phase profiles of the modes are shown. The mode discrimination ratio (DR), the ratio of the fractional feedback powers of the lowest loss mode to the second lowest loss mode, is simply the geometric resonator magnification squared. To study the effects of aberrations on the mode discrimination, an astigmatic and a random phase distortion were introduced in the resonator. In the range of parameters where the far field Strehl ratio exceeded 0.4, the DR remained significantly greater than unity indicating that the resonator maintains good mode discrimination in the presence of these aberrations.

This paper details experimental and numerical studies of the effect of astigmatism on the performance of an unstable ring resonator with eight mirrors, causing a round trip 180 deg beam rotation, or seven mirrors, producing a beam flip. The resonators were studied with integer and integer plus one half equivalent Fresnel numbers and with and without intracavity spatial filtering. The experiment was performed on a CW electric discharge, fast flow CO2 unstable ring resonator with two removable and orthogonal focal line apertures (FLAs). The astigmatism was produced by rotating one cylindrical focusing mirror with respect to the other, producing astigmatism oriented at 45 deg to the focal line axes. Intracavity power, near field intensity distribution, and far field power and beam quality measurements were taken. The far field beam quality behavior with astigmatism was not very sensitive to the Fresnel number, but was dramatically dependent on the number of mirrors.

During a series of experiments to test the concept of using an intracavity spatial filter to improve far field resonator performance, some interesting anomalies with established theory was discovered. A brief description of the gain medium and resonator geometries will be followed by a detailed discussion of the behavior.

The unfolded single-aperture near-imaging negative branch confocal unstable ring-resonator design is considered. Diffractive properties and mode characteristics of the moderate Fresnel-number baseline-resonator design with Neq = - 10.28 are calculated using three-dimensional FFT, FHT, and virtual source codes. The FFT results are in agreement with those from positive branch unstable resonators having the same Fresnel number. Similar modeling for resonator designs where Neq is varied from - 6.6 to - 12.0 is analyzed, and good mode discrimination is found between the dominant 1 = 0 modes and higher order modes at half integral Fresnel numbers. Both FFT and FHT diffractive codes exhibit increasing loss of accuracy when applied to resonator designs as equivalent Fresnel numbers increase above Neq = 12 - 15. The virtual-code results agree well with the FFT and FHT modeling results for Neq = - 10 to - 25.

An unstable ring resonator design which produces 90 deg beam rotation in a single pass (UR90 or HiQ) has been developed in order to solve the problem of obtaining an unobscured, near diffraction-limited output beam from low-gain laser media requiring saturation of a large transverse gain volume. A computer code was used to model the bare-cavity geometric modes of the UR90 by ray tracing through an equivalent thin lens resonator. Mode footprints of the collimated forward mode and expanding reverse mode showed only partial overlap, indicating that proper aperturing, especially at the gain generator, can aid in reverse mode suppression.

The purpose of the study is to present the basic concepts of coupled-laser devices as well as a historical summary of some of the experimental studies of laser coupling. Focus is concentrated on the experimental efforts with gas and chemical lasers. Divided output single and injection locked lasers, master oscillator and power amplifiers, coupled and multiple output resonators, nonlinear optics coupled devices, and hybrid coupled optical systems are discussed among laser-coupling techniques. Early experiments involving the coupling of carbon dioxide lasers and coupled photolytic iodine lasers are outlined, and works employing nonlinearly coupled devices, intracavity mixing, and gain medium are covered.

Coupling of unstable resonators in circulant arrays is considered, in which the array is invariant with respect to the interchange of any pair of resonators. A proof-of-concept experiment performed with six series coupled CO(2) lasers with confocal unstable resonators is reported. Adjoint coupling was used with two symmetrically placed coupling apertures in each resonator output. The results of measurements of the locking range, supermode content, and beam quality for standing wave and ring resonator arrays are presented and interpreted using simplified models. It is pointed out that adjoint coupled unstable resonators provide a modular scaling configuration with modest phase-locking length control requirements.

Mode competition in confocal unstable resonators loaded with gain-saturable active medium is discussed. Confocal unstable resonators with magnification M = 2 are investigated, with attention focused on resonators with Neq = 3.8924. A numerical approach for searching efficiently stable solutions in cases where the traditional iterative method converges too slow is employed. Two active-medium models, the Rigrod model and CO(2) flow laser model are utilized. Ranges of resonator and medium parameters for stable one-mode lasing are determined. Similar calculations are performed for unstable axisymmetric confocal resonators.

The performance of a system of unstable resonators is addressed. The resonators are coupled to one another through a portion of each output that is mutually shared through reverse (adjoint) waves. The ideal performance of the coupled resonator system is dependent upon operation in a single supermode, insuring that the individual resonator outputs are mutually coherent. A wave optics analysis of two coupled resonators is described. The model considers diffraction effects in Cartesian coordinates and in a single transverse dimension (strip resonator). The sensitivity of coupled resonator performance to the length control of the individual resonators and the strength of coupling between them are evaluated.

An experiment was performed using two cw Ar-ion lasers in Fabry-Perot resonators configured in a Ushaped cavity and coupled through a common end mirror to examine the effect of coupling strength on phase locking. The near field fringe visibilities were measured while varying the reflectivity of the common end mirror from 10% to 90%. Along with the total multiline visibility, the visibilities for single lines at 514.5 nm and 488.0 nm during multiline coupling were also measured. The lasers were also operated on a single line (488.0 nm), and measurements were made on single-line coupling. An RF mode beat at the frequency characteristic of the super cavity was observed for all values of coupling strength. The optimal coupling strength for phase-locked operation for Ar-ion lasers was found to be approximately 25%.

Coupled unstable resonators and phase-matched amplifiers with a master oscillator (MOPA) are studied in the framework of coherent beam combination. Coherent combination is accomplished on multiline CW HF lasers by both approaches. It is shown that the MOPA approach requires a master oscillator with good beam quality in order to diagnose the mutual coherence of the two amplified beams and to demonstrate the narrowing of the far-field central lobe. The coupled-unstable-resonators approach is found to be more difficult due to the coupling-path alignment requirement. Attention is focused on a procedure for equalizing external paths for optimum far-field brightness of multiline phased arrays.

Open laser resonators based on the self-imaging property of periodic fields (the Talbot effect) are studied theoretically and experimentally. Numerical simulations in one-dimensional cartesian geometry have revealed that the fundamental mode losses in such resonators decrease as the number of periods is increased. Convergence to a fundamental mode takes place in a few round-trips (< 10) with a moderate number of periods (< 20). Experimental tests with a TEA-CO₂ laser have verified the periodic and self-imaging properties of the emitted field. An equivalent self-imaging configuration for cylindrical symmetry is proposed.

An output beam with a nearly ideal focal spot can be obtained by combining an unstable ring resonator with 90 deg beam rotation with a lasing medium which has gain that would be too low for the effective use of a more conventional unstable resonator. As an example, results are presented of a simulation of an oxygen-iodine transfer laser with moderate gain. The simulation included a fairly detailed representation of the laser kinetics, including the effect of transverse gas flow. Results of the simulation include laser mode profiles and far-field patterns.

The mode control and mode distribution properties of ring resonators employing self-imaging and a 90 deg mode rotation are discussed. Such resonator designs are shown to have a very uniform distribution for the dominant mode and superior mode eigenvalue magnitude separation. These properties are very useful for designing resonators with a high quality factor, i.e., those with low magnifications.

A resonator based on a positive branch confocal unstable resonator with toroidal curvature mirrors is presented. The mirrors have different radii of curvature in perpendicular directions. In one direction, the curvature (main curvature) is strong, and it governs the main properties of the resonator. In the perpendicular direction, there is a weaker (secondary) curvature acting to decrease resonator's sensitivity to mirror tilts. Resonators of different size, gain, and output coupling are examined, and attention is given to phase distributions, near-field intensity, beam quality, and intensity distribution. Focus is placed on basic eigenmodes for uniform and nonuniform gains, mirror tilt, and phase perturbations. High far-field intensity and increased power-extraction efficiency in nonuniform active media in such a resonator are emphasized.

A variety of resonator designs that may be scalable to large high-power HF overtone lasers are discussed. Multipass resonators with multiple turning mirrors and with common turning mirrors are included in the discussion. Geometric optics are utilized in analyzing these concepts. Emphasis is placed on gain saturation, amplified-spontaneous-emission and parasitic control by gain segmentation, alignment tolerances, and diffractive beam spillage. It is concluded that for moderate powers, the multipass concept with separate turning mirrors is preferable, while for higher powers, a concept with common turning mirrors may be chosen.

Recent developments in RF excitation of gas discharge lasers have shown that the output power can be area sealed through the use of annular or planar formats, rather than the more conventional length scaling which has characterised diffusion-cooled lasers until now. For CO2 lasers, this holds the promise of new types of compact lasers with a range of applications in industry and elsewhere, which use novel resonators to extract good quality beams from the unconventional, large area gain geometry. Here we present an analysis of one such resonator, which consists of a spherical mirror Herriott cell enclosed by a Fabry Perot resonator. Optical system parameters are configured for coupling to an annular discharge and results given for both a passive cavity and for its operation when coupled to a large area CO2 discharge.

An advanced annular resonator has been developed for extracting power from an annular gain region. The new resonator possesses improved mode control and polarization control compared with previous concepts. The principles of operation of the new resonator are described, including a discussion of several different implementation options. A specific embodiment was selected for detailed evaluation. For the specific design, performance predictions based on computer simulation are presented.

This paper describes the geometric analysis of the reverse mode in a Decentered Annular Ring Resonator (DARR). The reverse mode is an astigmatic diverging wave whose phase front is a elliptic paraboloid with higher order aberrations. At the decentered hole in the scraper, the reverse mode is a bat-wing footprint whose size is dependent on the compact leg length.

An advanced designn of an annular resonator with improved mode and polarization control has been fabricated and tested. This resonator for extracting power from an annular gain region was tested using a multi-wavelength, hydrogen fluoride (HF) gain cell. Experimental results of the beam quality, spectral distribution, misalignment sensitivity, and forward to reverse mode power ratios are described.

A pulsed CO2 electric discharge fast flowing gain medium is used to test three unstable resonators which are forced to oscillate in an L = 3 azimuthal mode. This Higher Order Azimuthal Mode Unstable Resonator could be used to form a 'natural mode' resonator which would be unaffected by support struts necessary in an annular gain medium. Six equally spaced intracavity radial struts, and a suitable diameter on-axis obscuration, produce 180 degree phase changes between adjacent sectors of the six-sector near field pattern, and six radial lobes in the far field with no on-axis intensity. A phase plate, constructed by applying a half step coating to every other adjacent sector, corrects the far field.

A corner cube constructed using three long radius spherical mirrors has been found to correct for astigmatism and can produce diffraction limited focused retroreflected light. Laser resonators using focusing corner cubes exhibit alignment insensitivity and an ability to track a wandering gain medium. These are both very desirable properties for long FEL lasers. A computer analysis of various types of misalignments is presented.

An image-relayed corner-cube ring free electron laser (FEL) resonator has been investigated theoretically and experimentally. The laser beam is outcoupled from the resonator by using an annular 'scraper' mirror which is image-relayed to the FEL wiggler by two intracavity telescopes of unequal magnifications. The resulting FEL resonator has significant advantages over both conventional and grazing incidence resonators owing to drastically reduced mirror alignment tolerances together with the achievement of good mode control.

The key optical components for a grazing-incidence ring resonator are considered. Grazing-incidence mirrors are described, and attention is focused on a surface-fabrication process, mirror size, shape, and curvature, and single-crystal silicon substrate used for coating. Surface roughness, mechanical contact profilometry, optical interferometry, and wavefront errors are discussed, as well as normal-incidence mirrors. Consideration is given to grazing-incidence, normal-incidence high-reflectance, and sideband-suppression thin-film coatings. Alignment procedures and tools including dynamic alignment, a fast steering mirror, and coarse path-length adjustment with an outcoupler mount are covered.

The RF Linear Accelerator Free Electron Laser is usually operated in the oscillator mode. For high power operation, a ring resonator configuration with grazing angle incidence optics is the preferred choice. In this paper, we describe the modeling of such an oscillator configuration using full wave optics. The steady state mode structure of the resonator is obtained using Fox-Li type of calculation. We start with a gaussian field and propagate this field through the wiggler and the optical components of the resonator. The field at the end of one iteration through the resonator is compared with the field at the start of the iteration. This process is repeated until the field shape and the cavity power levels reach steady state reproducibility to within a couple of percent. The FEL interaction is modeled by tracking the motion of thousands of electrons through the wiggler and averaging their energy loss. Betatron motion of the electrons is taken into account as are any field and misalignment errors in the fabrication of the wiggler. We have used this numerical model to investigate the effects of (i) misalignment of mirrors, (ii) aberration of the mirrors, (iii) the efficacy of compensatory misalignment techniques, and (iv) the dependence of the performance of the FEL on the outcoupling fraction.

A gain model for optical extraction from the CW chemical oxygen-iodine laser medium is described. It uses a simplified, temperatuire-dependent, chemical kinetics package which consists of several reactions between molecular oxygen, atomic and molecular iodine, water, and helium. The Heidner I2 dissociation mechanism is included to allow for incomplete dissociation. Gas flow is treated using a premixed, one-dimensional stream-tube model which accounts for gas expansion and heat release in the cavity. Collisional cross-relaxation effects upon the Doppler-broadened line are treated using a Fokker-Planck diffusion model of the velocity distribution of the upper and lower laser levels. This model, in conjunction with geometric optics, multimode model of an unstable standing-wave confocal resonator, is used to examine the influence of incomplete velocity cross-relaxation and longitudinal mode separation upon the output power and mode spectrum of the laser. It is shown that lasing will occur on all available modes even when the mode separation is less than the collision linewidth.

A three-dimensional model of an excimer laser cavity has been used to assess the performance of a flowing XeF laser system. The laser operates with a two-sided electron beam pump, a converging flow channel, and a confocal unstable resonator with a decentered optical axis. The effects on the performance of the laser from changes in the laser gas temperature, electron beam pumping conditions, and resonator parameters are evaluated.

A loaded-gain model of a CW flowing oxygen-iodine medium is described, and its principal assumptions and approximations are discussed. The model includes pumping of the upper laser level by O(2)(1 Delta), deactivation losses by water, and stimulated emission. The solution of the model in the absence of flux is obtained, from which a small-signal gain is determined. The model is solved for the output power from a Fabry-Perot resonator as a function of the medium and resonator parameters. It is shown that the maximum available power from the medium is determined by the O(2)(1 Delta) concentration at the nozzle exit plane.

Analytical and numerical results for guardband criteria for unstable-resonator mode calculations are discussed. The energy-loss guardband derivation is outlined, guardband criteria based on the point-by-point accuracy of the computed amplitude of the complex field are determined, and point-accuracy guardband calculations are presented. Using the criteria established, the new guardband calculated for the propagation step, N(c) = 9.5 and N(eq) = 3.56, is found to be much larger than previous calculations. It is pointed out that the power calculations are nearly the same for these guardband requirements and those based on a percent energy loss.

This paper describes the general methodology for computationally tracking an arbitrarily polarized complex monochromatic field through an arbitrary optical system, composed of reflectors, in 3 space. The polarization properties of the field can be spatially varying allowing for spatially dependent angles of incidence and surface, eg., coating, properties. The Jones calculus is employed which is amenable to the complex field description that is employed with diffractive propagations.