Free electron lasers (FELs) provide a unique physical system for analysis with computer simulations. The only physical constants needed are the electron charge and mass, and the speed of light, in order to accurately represent many complex physical effects. Large simulations requiring CRAY computers have successfully supported many large FEL experiments, but most often, the important physical processes can be simulated on small workstations.

A nonlinear analysis of Free-Electron Laser amplifiers in three-dimensions is described. A set of coupled nonlinear differential equations is derived which governs the self-consistent evolution of either the TE or TM waveguide modes and the trajectories of an ensemble of electrons subject to the radiation and wiggler fields. In particular, we consider magnetostatic field configurations consisting of either (1) a planar polarized wiggler in conjunction with a rectangular waveguide or (2) a helical wiggler and axial guide field combination in conjunction with a cylindrical waveguide. Both self-field and space-charge effects are neglected in the formulation, and the analysis is valid for the high-gain Compton (sometimes called the strong-pump) regime. The analysis is multi-mode in the sense that an arbitrary number of either TE or TM modes may be included. The analysis is in good agreement with Free-Electron Lasers experiments at Lawrence Livermore National Laboratory and the Massachusetts Institute of Technology which employ each of these configurations.

We describe the modeling of an induction-linac based free-electron laser (IFEL) amplifier for producing multi-megawatt levels of microwave power. We have used the Lawrence Livermore National Laboratory (LLNL) free-electron laser simulation code, FRED, and the simulation code for sideband calculations, GINGER for this study. For IFEL amplifiers in the frequency range of interest (200 to 600 GHz), we have devised a wiggler design strategy which incorporates a tapering algorithm that is suitable for free-electron laser (FEL) systems with moderate space-charge effects and that minimizes spontaneous noise growth at frequencies below the fundamental, while enhancing the growth of the signal at the fundamental. In addition, engineering design considerations of the waveguide wall loading and electron beam fill factor in the waveguide set limits on the waveguide dimensions, the wiggler magnet gap spacing, the wiggler period, and the minimum magnetic field strength in the tapered region of the wiggler. As an example, we shall describe an FEL amplifier designed to produce an average power of about 10 MW at a frequency of 280 GHz to be used for electron cyclotron resonance heating of tokamak fusion devices.

This paper reviews the basic characteristics of free-electron laser (FEL) oscillators and describes a group of codes that have been developed to analyze and design rf-linac-driven FELs. The optical performance of an FEL has been treated using 1-D time-dependent (finite pulse) codes that describe the characteristics of the optical temporal pulse shape and spectrum during the evolution of the oscillator from low-intensity small-signal gain conditions to high-intensity large-signal gain conditions. These codes can include frequency-dependent elements, such as narrow-band filters or grating rhombs. Diffraction effects, transverse optical and electron-beam mode properties, misalignments, as well as aberrations on optical elements are modeled with the 3-D code FELEX. This code has now been extended to include the effects of imperfections in the wiggler magnetic field and light emission at higher optical harmonics. A separate accelerator modeling capability allows the use of a numerically-generated electron pulse in FELEX for 3-D integrated numerical FEL simulations.

The free electron laser (FEL) simulation code FELEX is used to examine the operation of stable-unstable FEL resonators. These resonators are stable along one transverse axis and unstable along the orthogonal transverse axis. The simulations utilize a ring resonator with an intracavity focus in the unstable plane near the center of the wiggler (close to the same axial position as the waist in the stable plane) thereby enhancing the coupling between the optical and electron beams. Asymmetric output scraping is performed in the back leg of the ring using a reflective mirror inserted from one side of the unstable axis. Resonators with relatively low equivalent Fresnel number (|Neq|≤10) and magnification (|Mx|≈1.2) are examined. Optical characteristics including the cavity mode profile at various positions inside the resonator are shown.

We numerically examine the preservation of Stokes seed phase in a Raman look-through amplifier. While applying one-dimensional sinusoidal Stokes seed aberrations the fidelity decreases with higher aberration strengths and high spatial frequencies. The amplifier also demonstrates a threshold effect with fidelity degrading rapidly for aberration Fresnel numbers below 1.

A novel theoretical approach to steady state, stimulated Brillouin scattering phase conjugation is presented. A perturbative technique produces highly accurate approximate solutions for both 2-D and 3-D simulations under conditions of interest. This technique permits accurate modeling of backward stimulated Brillouin scattering phase conjugation on a microcomputer. Direct numerical integration is used to verify the validity of the approximate solutions.

Coupling between the signal and idler paraxial differential equations is solved for a diffracted undepleted pump. The solutions are inherently numerical. However, we present one analytic solution, corresponding to negligible diffraction, which agrees with the simulation. Specifically, on input we consider : a sinusodial pump amplitude grating; a plane wave for the signal; and a small amount of energy in the idler.

A simple set of equations is identified which accurately predict the performance of large multimode stable resonators. Extremely good agreement between theoretical predictions and experimental measurements of beam diameters has been verified for several different size and wavelength lasers. The equations are easily incorporated into computer spread-sheet programs to simplify the process of designing optical systems for experiments with high energy lasers (HEL's) within the laboratory.

When the paraxial wave equation is used to include diffraction in nonlinear opics problems, expansion of the fields in a series of Gauss-Laguerre or Gauss-Hermite functions results in nonlinear coupling coefficients which are integrals of products of Laguerre or Hermite polynomials. A recursive technique is described for the evaluation of these coupling integrals. The method is then applied to power-dependent Raman scattering in focused geometry, power-dependent Raman scattering in a ring resonator, and diffractive propagation in optical parametric amplifiers.

An interplanetary mission to the outermost planets would require laser-beam communications. This can be carried out using a Nd:YAG diode-pumped laser on the spacecraft and high data rates can be achieved. The gaussian beam propagation characteristics of the laser are used to derive the receiver specifications using avalanche photodiode detection. M-ary Pulse Position Modulation is assumed for deriving the power efficiency since this gives the highest power efficiency.

The mixing efficiency of a heterodyne laser radar system is a critical performance factor. This paper deals with a special system configuration whereby a laser radar beam is directed by a remote agile mirror. In order to track the target, the mirror surface normal must point halfway between the vector direction to the target and the laser radar's telescope aperture plane normal. Ideally, the mirror's surface must be perfectly flat to avoid any distortion of the return target signal. The effect of mirror surface aberrations upon the heterodyne laser radar's mixing efficiency, and therefore upon the system signal-to-noise ratio, is the the subject of this paper. A computer model is used is used to introduce the spatial wavefront distortions upon the return plane wave signal (representing a point target) and to represent the field pattern on the detector plane using a 2-D discrete Fourier transform. The relative mixing efficiency is calculated for several classical types of mirror surface aberrations using Zernike polynomial representations. Effects such as thermal gradients across the face of the mirror, thermal gradients between the front and the back of the mirror and gravity loading of the mirror are modeled. The mirror surface height aberrations are expressed in wavelengths in order to increase the general applicability of the results. The imperfect mirror surface acts like a phase grating which changes the spatial phase of the reflected plane wave return signal. Mixing efficiency is computed relative to the mixing efficiency that would be obtained with a perfect undistorted plane wave return signal. It is assumed that the local oscillator produces a uniform intensity and constant spatial phase plane wave signal at the telescope aperture plane. The mirror diameter is assumed to be 2.4 times larger than the telescope aperture diameter. This keeps the telescope aperture fully illuminated for a target angles of up to 65 degrees with respect to the mirror surface normal. Results are presented for both a finite extent and infinite extent detector aperture. Example diffraction patterns are plotted in a 3-D surface plot form to provide a visual appreciation of the effects of the mirror surface aberrations.

A method for numerically propagating a beam in the vicinity of an index discontinuity has been developed. Current methods of numerical beam propagation handle propagation up to the interface and beyond it, but not in the region where part of the beam is in one medium and the rest in the other. The new method allows an accurate modelling of the aberrations introduced by optics, e.g. steeply curved lens surfaces, where aberrations are introduced over a finite distance. The basic idea behind the method is to separately propagate the light which is in each of the refracting media.

A new semiclassical theory of single mode, homogeneously broadened lasers is presented and applied to injected lasers. The injected fields are incorporated through the mirror boundary conditions. The properties of injected lasers with stable resonators (Fabry-Perot) and positive branch, confocal unstable resonators (PBCUR) are examined. Results from,the new model are compared to other published works.

Phase locking of ring lasers can be accomplished by coupling via reverse waves. In one embodiment, a portion of the forward wave output from one laser is coupled into the reverse wave of another, with reverse wave suppressor mirrors used to couple each reverse wave output into the forward wave of the same laser. In an alternate approach, the reverse wave output of one laser is coupled into the forward wave of another, with a portion of each forward output being retro-reflected into the reverse wave of the same laser. A one dimensional model of the coupling schemes is presented, which predicts the result of mirror detuning. The coupling concept is demonstrated by a CO2 laser experiment with UR90 resonators. Predictions of the theory are verified, including the variation of piston phase difference with resonator length for the forward-to-reverse and reverse-forward schemes.

Passive resonator modes of aligned and unaberrated adjoint-coupled resonators have been calculated using full 3D wave optics. They are observed to have unexpected properties which degrade the associated beam quality. The principle of adjoint coupling is based upon injecting a coupling wave "backward", i.e., in the adjoint direction, into a given resonator element. This adjoint coupling wave is expected to undergo a number of round trip passes internal to the resonator element, compressing via demagnification to the Fresnel core of the resonator element, and emerging via diffraction fully aligned with the optical axis of the resonator element. This study has found that the modes of such an adjoint-coupled system do not show the expected behavior for the coupling wave components of the mode. Components do not fully compress to the Fresnel core, but emerge prematurely and misaligned relative to the optical axis. This results in a Strehl ratio and beam quality degradation for the associated element factor of the coupled system far field pattern. A simple gaussian beam analog calculation of the coupling wave behavior supports this conclusion and allows detailed analyses of the features of the far field of the coupled resonator element.

We investigate the effects of amplified spontaneous emission on laser amplifier performance. In particular, we are interested in the dependence of gain, signal to noise ratio and efficiency on excitation, facet reflectivity and input laser intensity.

Doppler-broadened gas lasers can be influenced by the process of the relaxation of the velocity distribution of the lasing species due to elastic collisions. The homogeneous line width is increased to account for the broadening of the atomic resonance due to the collisional phase shift of the radiation, in the simplest treatment of this process. When a treatment of velocity redistribution due to elastic collisions must also be included, the collision-time-approximation to the transport integral equation is commonly used. The iodine laser that will be discussed here uses helium as a buffer gas, so the iodine atoms collide with helium atoms far more frequently than with any other molecule. The ratio of masses for these two atoms is so large that the collision-time-approximation may not be valid. Here we describe a rate-equation model for the oxygen-iodine laser that incorporates the Fokker-Planck equation for the redistribution of the iodine velocities. This numerical model is used to calculate the spectrum of longitudinal modes and the variation of laser efficiency with length.

Recently Jeffers showed experimentally that a high performance HF laser operating on the first overtone transition (HF( v=2 ) + hv → HF( v=0 )+2hv ) was feasible. Since his initial experimental demonstration of efficient operation of a cold reaction HF overtone laser, there has been a renewed interest in the HF laser system. The approximately 1.3 micron radiation available from the overtone lasing transition coupled with the high chemical efficiency available from the HF gain medium make the overtone laser an attractive candidate for those applications requiring a high power beam to propagate either over long distances or through the atmosphere.

Coherent amplifications of short pulse XeCl lasers are theoretically studied using multi-level Maxwell-Bloch equations including real vibrational-rotational structures of a gain spectrum of XeCl. The model can successfully predict coherent effects such as the quantum beat caused by spectrum overlaptions of several vibrational-rotational transitions involved in the short pulse laser spectrum. Saturation of amplified energy caused by formation of a 2 π-pulse-like pulse. Since a pulse area necessary for the production of a 2π-pulse-like pulse which depletes all the upper state populations accessible to the laser spectrum depends on the laser pulse width, an effective saturation energy is a function of the laser pulse width. When absorption in the amplifier media is not negligible to the small-signal gain, an effective u-pulse-like pulse is generated instead of a 2π-pulse-like pulse. The laser pulse width is shortened by the π or 2π-pulse-like pulse formation, and even shorter pulses than the linear limitation defined by the gain spectrum width can be generated if the amplified pulse intensity becomes very strong.

The electron kinetics of electron-ten-irradiated Ar/HCI gas mixtures subjected to an externally applied electric field were simulated by a time dependent kinetic code. This code calculated simultaneously both the electron energy distribution function and the densities c-f the various relevant neutral and ionic species. The effect of the large cross sections for vibrational and rotational excitation of HCI by electron impact on the electron energy distribution was taken into account. The code predictions were compared with results of experimental measurements of electron density and drift velocity. The simulation retrieved qualitatively the negative differential conductivity(NDC), which was observed experimentally. However, the quantitative agreement between the code predictions and the experimental results was unsatisfactory.

A well-known characteristic of gain-guided heterostructure lasers without any deliberate longitudinal asymmetry is a difference in the output power from the two facets. A possible explanation of this behavior is explored using a computer code based on the beam propagation method. Lasers with longitudinally varying degrees of lateral spreading of the current from under the conducting stripe were simulated. Output power curves are similar to experimental values.

The NASTRAN finite element code was used to simulate the temperature transients in the active area of laser diode arrays caused by driving the array with a pulsed waveform. A ten-stripe multi-quantum-well (MQW) structure was used. The thermal impedance of the array was also determined and compared to experimental values obtained by monitoring the threshold dependance of the device during pulsed and cw operation. The single-stripe diode was also modeled for comparison purposes.