Gaussian Beam Optics Research Articles

Direct measurement of the optical Goos-Hänchen effect in lasers.

The Goos-H\anchen longitudinal shift at total reflection of an optical Gaussian beam is experimentally investigated for only one reflection. The differential experimental method uses the high sensitivity of the eigenstates of a quasi-isotropic laser to small perturbations to measure an intracavity Goos-H\anchen effect for angles of incidence both below and above the critical angle. The measurements are in good agreement with our calculations of the longitudinal shift for Gaussian laser beams.

Small signal gain based on analytic models of thin intense electron beams

We develop the free electron laser theory of the effective energy distribution and the small signal gain for a thin electron beam. The assumption of thinness allows us to treat various transverse locations and electron beam trajectory angles as introducing phase shifts that have the same effect as those introduced by a change in energy of the electron. These ideas extend previous work of Colson et al., Dattoli et al., Scharlemann, and others in five important ways. The first is the ability to treat electron beams with three different classes of matching or symmetry conditions: (i) electron beams with separate betatron matching in each plane. (ii) those with aspect ratio matching, and (iii) crossed matched beams. Manifestations of these symmetries include elliptical cross-sections and electron beams that have modulated spatial profiles. For these we derive analytical expressions for effective energy distributions. Second, two emittance parameters for the electron beam are shown to consolidate into a single parameter that describes most of the energy variation of the effective energy distributions. Thus, the effective energy distribution for a 1:4 ribbon electron beam is nearly equivalent to a distribution for a beam of circular cross-section. Third, these calculations extend to energy distributions, angular distributions, and spatial distributions that all follow Gaussian profiles. Fourth, this model incorporates the description of the incident Gaussian optical beam and the above electron beam dynamics into a single influence function kernel. Emittance, energy spread, diffraction, and gain may be interpreted as limiting the length over which the bunching contributions of the propagating electric fields downstream are important. Fifth, three-dimensional profiles of the optical fields are computed. This work is complementary to the recent work of Yu, Krinsky and Gluckstern in that ours always describes the transition from low gain to high gain for a thin beam and not necessarily the high-gain regime itself. Therefore in this work the parameters of the incident optical beam are included, whereas, their work is not concerned with these parameters. The resulting transverse dependence of the fields may be characterized by an optical beam radius. This optical beam width starts out large compared to the thin electron beam and then, in the example given, contracts to a size that becomes so small that the thin-beam assumption is violated.

Mechanical displacement measurement by single‐mode fiber optic and moving mirror

AbstractIn this paper a theoretical model of a mechanical displacement sensor based on the theory of the optical Gaussian beam emerging from an optical single mode and the recoupling through a multimode optical fiber is presented. The developed model presents a dynamic region of measurements from 0 to 130 μm.

Optical design of a dual-polarization receiver for 220?280 GHz

A 220–280 GHz dual polarization receiver has been built for the James Clerk Maxwell Telescope. Schottky diode mixers cooled to ∼15K by a closed-cycle refrigerator are used to give DSB noise temperatures of 300K and 420K in the two channels. The optical design is based on gaussian-beam optics, and is frequency independent; it allows the significant higher order gaussian modes to propagate unhindered, thus offering the prospect of very high aperture efficiency. The receiver includes a number of novel optical components, including a completely symmetric dual polarization Martin-Puplett interferometer, used as the L.O. injection diplexer; a dielectric waveplate used as an in-line variable polarization splitter; and a dual-polarization in-line tunable Fabry-Perot SSB filter. Measurements of the performance of the optical system are presented.

Use of angular plane-wave spectra in the analysis of three-dimensional weak acousto-optic interaction

We present a method for conveniently calculating three-dimensional weak acousto-optic scattering. In our method the conventional cumbersome volume-scattering triple-integral technique is replaced by an equivalent single-integral formalism, framed in terms of the angular plane-wave spectra of sound, incident light, and scattered light. Our technique is suitable when paraxial conditions apply and is correct to second-order terms in propagation angles. The interaction of spatially separated Gaussian optical and acoustic beams is described as an example.

Three-dimensional theory of the free-electron laser. I. Gain and evolution of optical modes.

A three-dimensional free-electron-laser theory in the small-signal regime is presented. In the first part, we derive an energy theorem which relates the gain and the loss of an optical beam of arbitrary shape, driven by an electron beam of arbitrary profile. We show how this theorem can be applied for gain calculation and optimum resonator design. In the second part, we introduce a generalized description of a Gaussian optical beam. This includes four real parameters: the on-axis intensity and phase, the beam waist, and its radius of curvature. These quantities are made to evolve self-consistently and are governed by a set of ordinary differential equations which are readily integrated numerically. The solution of these equations provides an easy and intuitive means for the understanding of transverse effects induced by the interaction with the electron beam in a way which is considerably simpler than the more accurate large-scale simulation techniques.

Threshold of orientational self-focusing of a Gaussian optical beam in nematic liquid crystals

A numerical calculation method was developed for determination of the threshold of orientational self-focusing of a Gaussian optical beam incident normally on a homeotropically oriented nematic liquid crystal.

Resonance asymmetry and frequency shifts of stabilized CO2/OsO4laser under conditions of self-focusing of radiation in nonlinearly absorbing medium

An experimental investigation was made of the asymmetry of a resonance of saturated absorption and of frequency shifts exhibited by a stabilized CO2/OsO4 laser as a function of the following: the conditions during photorecording of the output beam in an external nonlinearly absorbing cell, the 192OsO4 vapor pressure, and the radiation intensity. A quantitative characteristic was introduced to describe the resonance asymmetry. A study was made of the radial distribution of the resonance asymmetry of a Gaussian laser beam at the exit from the absorption cell. A linear relationship was found between the resonance asymmetry and the shift of the laser frequency. A dispersive profile acquired by the resonance and the resultant resonance asymmetry together with the shift of the stabilized frequency were described by a theoretical model based on self-focusing of a Gaussian optical beam in a nonlinearly absorbing medium.

Theory and experiment on optical transverse intensity bistability in the transmission through a nonlinear thin (nematic liquid crystal) film

A theory is presented for the transverse intensity distribution bistability of a Gaussian optical beam after its passage through a nonlinear thin film. The equations governing the intensity distribution are cast in the form analogous to optical bistability in a longitudinal cavity (a Fabry-Perot interferometer), i.e., into two coupled transcendental equations from which multiple solutions are obtained. This formalism allows one to examine various physical approximations in obtaining the equations, and to improve on these approximations. It also lucidly illustrates the mechanisms of transverse intensity distribution bistability. The theoretical predictions are verified with quantitative experimental results on thin films of nematic liquid crystals.

Correlation function of the intensity fluctuations of a Gaussian optical beam in a random medium containing largescale discrete scatterers

Correlation function of the intensity fluctuations of a Gaussian optical beam in a random medium containing largescale discrete scatterers

Geometrical Interpretation of Gaussian Beam Optics

The relationship between conventional optics and Gaussian beam optics is discussed. Geometrical concepts such as image and object planes, pupil plane, F-number, resolution, and depth of field are discussed for Gaussian beams and are given a precise meaning in terms of the Gaussian beam parameters. The approach is useful in the design of laser scanning systems and holographic optical memory systems.

Log-Amplitude Mean for Laser-Beam Propagation in the Atmosphere*

An integral expression is evaluated for the log-amplitude mean value of a gaussian or laser-like optical beam propagating along a horizontal path in a turbulent atmosphere. The mean-value integral expression has been taken from an analysis by Schmeltzer for a gaussian beam in the atmosphere. The expressions presented here for the log-amplitude mean value depend on the product of a strength factor, which is the log-amplitude variance for a point source, and a multiplying factor that depends on the source beam size. Numerical results for the beam-size-dependent factor are given for a wide range of beam sizes, wavelengths, and path lengths. Numerical results are also presented for the mean on-axis irradiance and mean beam size, for focused and collimated gaussian beams. These will find application in the design of systems for laser communication in the atmosphere. The data are obtained by combining our results for the log-amplitude mean with published data for the variance. The integral expression used here for the log-amplitude mean value is based on an assumption which restricts the range of validity of our results. The conditions necessary for its validity are discussed.

Acoustic Light Modulators Using Optical Heterodyne Mixing

Acoustic light modulators are discussed in which the optical carrier is reinserted in the diffracted, frequency-shifted light beam. Reinsertion is accomplished in a novel fashion using a Kösters prism. In contrast to the usual acoustic modulator, the diffracted light is power modulated at the acoustic frequency. Modulation bandwidth and depth are each calculated as a function of the optical and acoustic beam parameters, assuming a Gaussian optical beam and rectangular acoustic beam. It is shown that the modulation bandwidth increases proportional to the optical beam diffraction angle and equals the inverse of the transit time of the sound across the waist of the optical beam. The optimum modulation depth, for a given acoustic power, corresponds to approximate equality of the optical and acoustic diffraction angles. Confirming experiments in the frequency range 250/350 MHz are described.