A volumetric thermal grating (VTG) is a spatially periodic refractive index variation in a volume of gas or liquid, generated by imaging interference fringes into the medium. The fringes can be created and varied by steering laser write beams electronically with acousto- optic (A-O) cells. While the wavelength of the write beams is chosen to be absorbed by a dopant in the VTG medium, a read beam at an off-resonance wavelength can be manipulated by diffraction from the resulting index grating. Potential applications include resonator and amplifier optical isolation prepulse suppression in high-gain amplifiers, noninertial steering of large-diameter laser beams, transfer of phase information between beams to facilitate adaptive optics, Q-switching of chemical lasers, and line selection in broadband lasers. In this paper, we present a preliminary assessment of VTG utility for these optical systems applications by quantitative analysis of the medium density dynamics. In Section 2, we derive a relation between A-O acoustic frequency uncertainty and VTG pointing/steering uncertainty, which also scales desired steering range to required A-O frequency modulation bandwidth. In Section 3, we discuss the temporal response of a doped rare-gas VTG medium. Section 4 is an assessment of VTG beam-steering performance potential using available technology.

The output beam profile of a laser is the consequence of an optical resonator that is usually designed to optimize laser power. For a specific application, however, the intensity profile may lack the desired shape. An optical design that produces the transformation of the nominal 5.2 inch diameter output of a stable, multi-mode, high energy CO2 laser into a narrow line of width 0.005 X 1.0 inches with extremely high brightness (> 90 Kw/cm2) is discussed. The number of modes and power produced by the Electric Discharge Coaxial Laser (EDCL II) at the Phillips Laboratory were controlled by resonator design and intracavity apertures. Gaussian beam propagation, diffractive propagation, and geometric skew aspheric raytrace techniques were used to design an optical train which was fully corrected for all off axis aberrations. The novel use of a cylindrical mirror combined with a slit aperture reimaging technique produced the final line image. Included are measured experimental results that confirmed the design approach.

The output of the Phillips Laboratory's CO2 Electric Discharge Coaxial Laser (EDCL II) is a nominal 13.2 centimeter diameter beam with over one hundred transverse modes and a divergence of over ten milliradians at forty kilowatts. In support of a critical test series, several resonator configurations were examined to reduce the output beam divergence to facilitate production of a beam on-target of 0.005 X 1.0 inches with high irradiance. Resonator reconfiguration of EDCL II with the associated beam shaping optical train and measured experimental results are discussed.

In this paper, an attempt is made to estimate the degree of focussing that results from thermal deformation of solid laser windows without solving the heat equation. Steady state conditions were assumed for spherical, parabolic, and gaussian thermal deformation. Calculations are performed for germanium, potassium-chloride, and zinc-selenide assuming CW power absorption of the window at the infrared wavelength of 10.6 microns. Formulas for the time dependant focal length and temperature rise of the window are developed using the thin lens equation. These formulas are expressed in terms of the density, window dimensions, specific heat, incident power, coefficient of thermal expansion, absorption coefficient, refractive index, refractive index temperature gradient, and laser beam spot size.

Currently there is considerable interest in agile beam-steering technologies for laser radar application that require the ability to point rapidly to a large number of widely spaced objects. Examples of such applications of agile pointing include imaging sensors for tracking and discrimination of military targets, sensors for surveillance and tracking of space objects in peacetime, and optical communication systems. In general, pointing agility allows a laser radar system to operate more efficiently by allowing each system platform to address a large number of separate targets. Pointing agility may be realized in a number of ways; for example, by employing steering mirrors, electro-acoustic and electro-optic devices, electro- optic phased arrays, and micro lens arrays. This paper will review agile beam-steering technologies. In particular, signal-processing techniques and experimental verification of imaging with coherent optical arrays will be addressed.

Beam agility for large aperture optical systems has proven to be a challenging engineering problem. This paper describes optical engineering issues of an agile, 1/2 meter aperture, 30" field of regard telescope. Key system tradeoffs considered in the optical design are discussed.

We investigate the use of a unity-magnification micro-optic beam deflector. The deflector consists of two arrays of positively powered lenslets. The lenslets on each array are arranged in a square grid. Design criteria are based on usefulness in optical data storage devices. The deflector is designed to operate over a +/- 1.6 degree(s) range of deflection angles. We compare modeling results with interferometric analysis of the wavefront from a single lenslet pair. Our results indicate that the device is nearly diffraction limited, but there are substantial wavefront errors at the edges and corners of the lenslets.

We shall describe the design, fabrication, testing, and use of lenses achromatized for 633 nm/ 1064 nm and for 532 nm/1064 nm. These lenses are designed to permit easier and more accurate alignment of beams from YAG lasers. Because the 1064 nm light is not visible and because many YAG lasers are pulsed, aligning the beam trains can be frustrating. The achromats we have built permit the use of HeNe (633 nm) and frequency-doubled YAG (532 nm) lasers for alignment of the high powered 1064 beam.

The Control Optics Modelling Package (COMP), is an optical modelling computer program capable of performing ray trace, differential ray trace and diffraction analyses for any optical design. COMP is particularly useful for optical systems that move, whether through interaction with dynamically or thermally varying structures, or optics that are actively controlled to perform particular tasks, such as steering mirrors or segmented mirrors.

We present an example of using a combined ray trace and diffraction modeling code to simulate effects of objective-lens tilt in an optical data storage device.

The design of frustrated total internal reflection (FTIR) shutters for near and middle infrared lasers is reported. The high temporal rate of the shutters made it possible to obtain Q-switched pulses of neodymium lasers with an efficiency close to that of free-running regime. Experiments with pulsed repetition Nd-glass laser show the dynamic apodization of the laser aperture carried out by FTIR shutter improved laser beam divergence. In the middle infrared spectral range, FTIR shutters made of fused quartz and yttrium-aluminum garnet were used. Q-switch of Cr:Tm:Ho:YSGG, Cr:Er:YSGG and Er:YAG lasers was obtained. The experiments have shown the efficiency of these lasers can be further enhanced with some modification of the shutters.

The Krylov matrix method is a powerful numerical algorithm for efficiently and accurately calculating several of the lowest loss transverse bare cavity eigenmodes of unstable optical resonators. In current laser models, loaded cavity modes are calculated by accomplishing a functional expansion in bare cavity eigenmodes. By accomplishing the Krylov analysis, both the bare cavity design parameters and the eigenmode expansion set are calculated simultaneously. This provides a convenient resonator candidate screening process as an intermediate step in the full laser design process and is followed by a loaded cavity analysis when the bare cavity parameters are suitable. This paper reviews the Krylov procedure and discusses a convergence algorithm for it. Examples are presented to demonstrate the method.

This paper describes results of a project to incorporate the transient stimulated rotational Raman scattering (SRRS) physics in a general purpose laser system code capable to end-to-end analysis. The SRRS model includes laser pulse shape, medium excitation and relaxation, and spontaneous scattering as a quantum initiation of the Stokes field. The laser beam may be arbitrarily specified in terms of intensity and phase profile. The diffraction evolution of the beam through the complete optical train to the point of incidence on the target may be treated including near- and far-field diffraction apertures, aberrations, and phase conversion in addition to the special SRRS model. Preliminary analysis of the OMEGA Upgrade laser system is included.

The propagation equations for the mode of a laser with significant variation of the index of refraction in one transverse dimension are simplified by a transformation of the coordinate system. The new z axis is parallel to the resonator optical axis, the curved ray that reproduces itself after a round trip propagation. The apertures of the resonator are offset by the transformation, and the linear variation of the index of refraction is accounted for by the transformation rather than by the addition of an explicit tilt to the phase of the field. The resonator optical axis is well approximated by a quadratic curve. An analytic expression is given for the optimum tilt of the end mirrors. Expressions are also derived for the optical axes of confocal unstable and half-symmetric stable resonators with mirror alignment that is uncorrected for the variation of the index of refraction. Numerical results for a laser with this type of medium-induced aberration are included.

The process of simulating the optical performance of the phased array optical telescope has given us new insight on the role of the array and subaperture chief rays, array aberrations (global) and subaperture (individual telescopes) aberrations. The seven 3rd order Siedel surface aberration paraxial equations are reformulated in terms of phased array and includes a numerical example. In addition, a design method of combining each telescope chief ray to determine the vertex of the reference sphere is described. A theoretical calculation of subaperture piston resulting from array (global) 3rd order aberrations with numerical examples is presented.

This paper describes efforts to develop general optimization capabilities for the design of laser systems. The problem is more complex than lens design and requires a more flexible approach. Some representative lasers systems are discussed, indicating the great variety of applications.

Identification of single reflection and multiple reflection ghosts in high energy laser systems is essential for the safeguard of components, equipment, and personnel. Most ray trace programs require the user to model each path of reflections as an independent optical system. We will describe some of our work on cw and pulsed laser systems with OPTICAD, a program which permits simultaneous display of all ghost paths. We will describe some of its features, such as limiting the search for ghost paths to those which have less than a user specified fraction of the input power.

A detailed analysis of the three-mirror phase-anisotropic cavity was made to determine if it can be used in two-mode gas lasers for high resolution spectroscopy. Both power and spectral characteristics of the two-mode three-mirror CO₂ laser were studied. Laser power and frequency resonances as narrow as 40 kHz with amplitudes of 10 mW and 13 kHz respectively, were obtained in the case of a CO₂/SF₆ laser with the cavity type described above.

Using double-reflective spheres, a UV focusing objective with short focal length and long working distance was designed. This UV focusing objective could work in a wide wavelength range and has the property of antilaser damage. It was applied successfully in a laser focusing system with a spatial filter, with some interesting results.

The full-detailed kinetic model of XeCl laser is developed, which includes self-consistent solution of the electron Boltzmann equation, taking into account the electron collisions both with other and with vibrationally and electronically excited particles as well as the system of equations of plasma chemical kinetics and radiation transfer. 1-D, 2-D and 3-D models are worked out by simplifying the full kinetic model. The approximate kinetics have been verified to agree well with the detailed kinetics for the conditions investigated. These models have been applied to describe the effects of nonuniform pumping and spatial distribution of plasma components on the laser characteristics. The 1-D model of the electric discharge-pumped excimer laser will be presented and the results of 3-D mathematical simulation of the e-beam pumped amplifier with a large aperture will be reported. This model includes 2-D Monte- Carlo simulation of the fast electron transport and 3-D calculation of the amplified spontaneous radiation transfer. The amplified beam intensity distribution is calculated and the optical quality of the output beam is estimated, taking into account the refraction index variation across the amplifier aperture. A fast procedure to find out the laser resonator parameters for the maximal efficiency will be proposed, including the effects of spatial nonuniformity of the active medium.

Composite laser systems including 3-mirror resonator, oscillator-amplifier, and optically coupled lasers, are widely used in laser physics and design. It is necessary to predict the characteristics of these systems with high accuracy. To do this, the diffractive numerical codes were developed which describe the self-consistent propagation of laser beams in a nonlinear active medium. The problem of mathematical simulation of a laser with composite optical resonators will be discussed. The results will be presented for the following systems: injection locked laser, oscillator-amplifier, laser having 3-mirror resonator to achieve line selection, and two optically-coupled lasers. The known optical calculation problem of divergent iterative procedures is solved. As a result, the stability limits of single mode lasing can be found exactly by diffractive numerical calculations. Some examples of calculated dependencies of the critical active medium parameters on the optical system characteristics will be presented. The programs developed are modular in structure, so the type of laser system and active medium can be varied independently. The results will be presented for the CO2 laser and for the medium with saturated gain. An optical system may have any symmetry, including plane and circular symmetry.

This paper describes a modelling technique used to explore three dimensional (3D) image irradiance distributions formed by high numerical aperture (NA > 0.5) lenses in homogeneous, linear films. This work uses a 3D modelling approach that is based on a plane- wave decomposition in the exit pupil. Each plane wave component is weighted by factors due to polarization, aberration, and input amplitude and phase terms. This is combined with a modified thin-film matrix technique to derive the total field amplitude at each point in a film by a coherent vector sum over all plane waves. Then the total irradiance is calculated. The model is used to show how asymmetries present in the polarized image change with the influence of a thin film through varying degrees of focus.

The application of feedback to produce bistable states in a molecular system was first considered by Szoke and then extended and demonstrated by Gibbs. The final configuration is similar to a laser, having two resonator mirrors enclosing a molecular system, but with the intensity decreased. Such behavior is similar to a laser at threshold but the control variable is the electrical input and the output is the radiated beam. Video systems can also provide a simple optical feedback system. Such systems are inherently slow, and limited to video rates, however, they possess many control variables and are simple to adjust interactively. Such systems have been used and reported in the literature for image processing and for generation of optical bistable states. Here such a system lends itself readily to modeling certain aspects of laser dynamics.

Lenses with variable focus may find extensive applications in industrial production of optical devices. The variable-focus lenses considered in this work may be used most efficiently in laser systems wherein the radiation initially has linear polarization. Consideration is being given to the principles of operation of switchable lenses. The aberration of such lenses is analyzed, the data on control elements having a large angular aperture are presented, and a practical example of a variable-focus lens is given.

The ray-optic model is used for analysis of aberrations of a planar gradient lens. The aberrations are calculated using optical Lagrange equations and numerical solution of ray- equation. Requirements for index distribution of core and substrate are established.

Intracavity phase distortions of radiation in the active medium of copper-vapor lasers are experimentally studied. By means of expansion of radiation wavefront deformations in Zernike polynomials, an analysis of aberrations spectrum contributing to the deformations is carried out. Device of phase-conjugated intracavity adaptive system designed to correct the deformations and technique of controlling the system are presented. The proposed technique avoids using computer-aided calculation of adaptive mirror control signals, which increases operation speed of the system and therefore correction precision.

This work shows a proposed mathematical methodology for self-localization of imaging systems and their numerical solution, with evaluation through numerical simulations. This methodology has many applications for localization of cameras with reference to a pre-defined coordinate system.

Numerical simulations of the pulse build-up in a Q-switched laser reveal a considerable change in the beam spatial profile during the pulse evolution, on a nanosecond time scale. Such changes were measured experimentally, and the measured temporal evolution of the beam profile is shown to be in good agreement with the theoretical results. The time evolution of the spatial profile translates into an evolution of the beam quality parameter M²; for typical experimental conditions, in a Nd:YAG laser utilizing a variable reflectivity mirror resonator¹, M² is very close to a value of 1 at the beginning of the pulse, and increases smoothly throughout the pulse to reach a value of approximately 2 in correspondence of the pulse trailing edge.

As the laser industry becomes more mature and sophisticated, more attention is being given to the quality of the beam profile. Burn patterns and visual analysis of reflected beam spots have been the primary technology of the past. Currently, the sophistication and performance of electronic beam analysis has been greatly advanced with a variety of methods available. No one technology provides all of the answers for every circumstance of beam profile analysis. Each provides different advantages, depending on the needs of the user. The latest technological advances are stand-alone instruments that perform very lucid beam profile displays, as well as sophisticated quantitative analysis. These new instruments enable researchers and laser users to obtain much higher laser performance.

This paper describes a method used to align a complex resonator using a wavefront sensor. A brief description of the optical resonator and the phase aberration caused by the resonator misalignment that most greatly degrades the beam quality of the device is followed by a discussion of a low power HF alignment laser injection technique that was used successfully to align the laser by imaging the output aperture to a wavefront sensor. The wavefront phase was displayed in isometric form on a quasi-realtime display in order to determine the alignment position of the resonator's key optical element. High power lasing test wavefront phase data confirms this method results in a well-aligned resonator.

The optical cavity of the Boeing visible free electron laser was reconfigured from a concentric cavity to a glancing incidence ring resonator in late 1989 and was operated until December 1990. the crucial requirement for the optical cavity of an FEL is to provide an optical mode which is spatially and temporally matched to the electron beam as it moves through the wiggler. Several new optical diagnostics were developed to determine when the above requirement was satisfied. This paper will discuss those diagnostics which achieved and maintained the alignment of the ring resonator within tolerance to lase and measured the quality of lasing. The new diagnostics included measurements of the focus position and Rayleigh range of the ring resonator optics to determine the spatial match of the optical mode through the wiggler, and a measurement of the position of the optical axis for multiple passes around the ring resonator to determine the stability of the resonator alignment. Accelerator performance was determined by measuring the electron beam pulse width and charge, which indicated electron beam brightness, and by measuring the width of the spontaneous emission spectrum, which gave an indication of the alignment between the electron beam and the optical axis. Temporal overlap of electron and optical pulses was assured by measuring the optical cavity length. In addition, several other diagnostics which indicated FEL performance will be described: optical energy per micropulse, small signal gain, ringdown loss, laser pulse width, laser wavelength, and time resolved spectroscopy.

A visible light (670 nm) laser diode was used as a variable coherence length source to measure dispersion characteristics in single-mode fibers. The diode's spectral width, measured against increasing drive current, was found to change from about 16 nanometers to less than 0.2 nanometer. The corresponding change in coherence length is from about 25 micrometers to 2.5 mm.

An alignment system is being developed to align the feedback leg of a high energy laser resonator. The system uses a low energy visible laser, and a two axis position detector to compare the relative tilt of two alignment reference surfaces at either end of the feedback leg. Preliminary tests of the system in the lab have demonstrated subarcsecond alignment capability.

An infrared Hartmann-type wavefront sensor was assembled from a 32 X 32 lenslet array, fabricated by a binary-optic process on a germanium substrate, and a 128 X 128 pixel InSb detector, manufactured by Amber Engineering, Inc. The sensor was used to measure the wavefront of a hydrogen-fluoride laser beam from the TRW Alpha Verification Module.

One of the key issues in the development of space-based lasers is the optimization (minimization) of output beam quality and jitter. This paper describes an experiment that identifies and quantifies the sources of jitter and vibration in the output beam of a highly complex annular resonator using a technique involving correlation of accelerometer measurements of mirror motion to spatial and temporal aberrations in the output beam.

In this paper, the two systems developed at the Institute of Atmospheric Optics, USSR, are considered. The systems are intended for monitoring wave front parameters and phase control. The two systems supplement one another: one of them operates in the IR-range while the second one functions in the visible wavelength range.

The location of focal planes and waists can be calculated using the equivalent Gaussian beam method. Predictions can be made for both Gaussian and top-hat (flat phase, flat irradiance profile) beams. A Fresnel number relationship is given where the waist of top-hat beams can be either within or outside the far field region. Experimental implications of this focal plane shift for top-hat and gaussian beams are discussed. The most important implication is that calculated reference power-in-the-bucket curves, used to calculate beam quality, may be off as much as 5% for top-hat beams, when not taking into account focal shifts for some optical systems.