Off-axis Propagation Research Articles

Off-axis Gaussian beam propagation through planar waveguides with a hyperbolic secant refractive index profile

A study of the off-axis Gaussian beam propagation through an inhomogeneous planar optical waveguide with hyperbolic secant refractive index profile is carried out using the model of Kogelnik and Li. Beam half-width evolution with refractive index parameters, wavelength and displacement of the Gaussian beam from the axis is analysed. Similarly, a comparison with beam propagation in square-law media is presented.

Simple and exact analytic solution for oblique propagation in a cholesteric liquid crystal

A cholesteric liquid crystal (CLC) is periodically inhomogeneous along its spirality axis. An exact analytic solution for oblique (i.e., off-axis) propagation in a CLC is presented for the first time. The solution involves only the addition and multiplication of 4 × 4 matrices, and it can be evaluated to an arbitrary degree of precision because it is expressed as a uniformly convergent series. ©1996 John Wiley & Sons, Inc.

Experimental study of the geometric group-delay dispersion in graded-index media

We use the highly sensitive method of spatially coherent white-light interferometry to measure the geometric group-delay dispersion in graded-index media. Our measurements confirm previous analyses that the geometric dispersion produced by off-axis beam propagation is anomalous (negative), hence may be used to eliminate the ubiquitous positive dispersion in optical systems. Fabrication of large index-gradient waveguides optimal for dispersion compensation is discussed.

Directional coupler using a leaky wave of an anisotropic waveguide

A novel waveguide directional coupler configuration consisting of a slab of anisotropic material with identical waveguides on both surfaces is proposed. By off-axis propagation the radiative part of a leaky wave provides a coupling between waveguides. The length of total power transfer depends on the slab's thickness and propagation angle relative to the optic axis.

Wide-angle full vectorial beam propagation method

A wide-angle full vectorial beam propagation method is developed and presented. The hybrid nature of the electromagnetic vector field and wide-angle off-axis propagation are considered simultaneously for the first time.

Elastic-plastic analysis of crack propagation with branching

A numerical procedure is described for the elastic-plastic finite element analysis of crack propagation with branching. The constraint equations are used to model the closing and opening of the crack. The constraint conditions are imposed by using the penalty method for self-similar crack propagation and the elimination method for off-axis propagation. Multiple constraints are used to determine the contact mode at the crack branching point. Frictional sliding on the contacting crack surfaces under cyclic loads is also considered in the numerical procedure. The method is then applied to (i) self-similar crack growth in a single edge notch specimen, (ii) self-similar propagation followed by interfacial splitting in a center-cracked 0° composite plate and (iii) bifurcation of a crack in a compact tension specimen.

Off-axis complex-argument polynomial-Gaussian beams in optical systems

Off-axis light-beam propagation in optical systems representable by complex ABCD matrices is considered in detail. The results are presented in terms of modal parameter transformations similar to Kogelnik’s ABCD law. The modes emphasized here can be expressed in terms of polynomial-Gaussian functions of complex argument. These modes may be both astigmatic and asymmetric and can describe the propagation of off-axis beams of light in lenslike media with spatial gain or loss variation.

On-axis and off-axis propagation of Gaussian beams in gradient index media

The object-image formula and an expression for the lateral magnification are obtained for a gradient radial index medium used with Gaussian beams. Angular acceptance conditions for on-axis and off-axis incidence are discussed. Meridional and sagittal sections of a Gaussian beam are analyzed, and numerical methods are used to find the evolution of the beam. The eccentricity parameter of the elliptical spot and the astigmatism of the beam are obtained as a function of propagation distance.

Numerical Simulation for ICRF Minority-Ion Heating in a Tokamak

Ion cyclotron range of frequencies (ICRF) heating in the two-ion hybrid resonance regime is numerically studied and the results are compared with those of the heating experiments on the JET tokamak. The kinetic one-dimensional analysis of the ICRF wave is coupled with the anisotropic Fokker-Planck equation and the one-dimensional transport code, Spatial transport coefficients are inferred from those of the drift wave model and a phenomenological internal disruption is introduced. Calculated power deposition profiles agree well with experimental results. Degradation of confinement with increasing heating power, profile modification due to the off-axis heatinq and heat pulse propagation after the internal disruption are well reproduced by our simulation model.

Experimental study of anisotropy dependent geodesic lenses

The effect of anisotropy on focal lengths of geodesic lenses has been investigated with a novel experimental method. The measured relative difference for TE and TM (transverse electric and transverse magnetic)-mode focal lengths, for 10 degrees off-axis propagation, was 6.33%; this compares well with the theoretical prediction of 6.6%.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Betatron motion and optical deflection in free-electron lasers.

Transverse displacement of the electron beam at input to the wiggler induces betatron oscillation, imparting a sinusoidal transverse displacement to the gain medium seen by the optical beam. As the light propagates down this ``rippled'' medium it is guided by the dispersion, thereby acquiring some transverse sinusoidal displacement. At output from the wiggler the optical beam in general has acquired some transverse component of velocity, that is, it propagates off axis. As the e-beam displacement fluctuates statistically with every pulse, the optical output direction jitters around the nominal axis. The jitter is estimated with a model that includes off-axis optical propagation through a rippled gain medium but neglects feedback of the off-axis light on the e beam. The model is solved in perturbation theory. The jitter is calculated at the final aperture of the optical system beyond the wiggler. The result is (normalized to the final aperture diffraction) (rms focused jitter)/(diffraction width)${\mathit{\ensuremath{\simeq}}\mathit{\ensuremath{\Vert}}\mathit{n}}_{\mathrm{i}}$\ensuremath{\Vert}(w${\ensuremath{\lambda}}_{\mathrm{\ensuremath{\beta}}}$a${\ensuremath{\lambda}}_{\mathrm{bb}}$\ensuremath{\Delta} where ${r}_{b}$ is the e-beam radius, w is the optical beam radius (1/${e}^{2}$ intensity), \ensuremath{\lambda} is the optical wavelength, ${n}_{i}$ is the imaginary optical index on axis in e beam, ${\ensuremath{\lambda}}_{\ensuremath{\beta}}$ is the betatron wavelength, a is the rms e-beam transverse displacement, L is the wiggler length, and \ensuremath{\Delta}(L) is a damped oscillating function of L. For the proposed Paladin free-electron laser at \ensuremath{\lambda}=10 \ensuremath{\mu}m on the Advanced Test Accelerator (ATA), this implies (jitter)/(diffraction)0.25a/${r}_{b}$.

Definition of anisotropic aberrations in planar lenses

Using recently developed techniques for calculating the effective index of refraction for off-axis propagation in Ti : LiNbO <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</inf> waveguides and extraordinary ray tracing in uniaxial crystals we demonstrate numerically and define anisotropic aberrations and focal lengths in planar geodesic lenses for on-axis and off-axis wave propagation.

Angular-gain spectrum of free-electron lasers.

The theory of free-electron lasers is extended to include the new coupling between an electron beam and optical wave propagating at an angle theta in an arbitrary harmonic. The coupling allows the laser to be tuned to a wider range of wavelengths and to include the effects of emittance in the electron beam. The formulation of the results in terms of coupling constants means that the existing knowledge of high gain, low gain, weak optical fields, strong optical fields, and short pulses in free-electron lasers can be immediately generalized to off-axis propagation in an arbitrary harmonic.

Unstable resonator alignment using off-axis Gaussian beam propagation

Efficient and safe operation of a laser requires precise alignment of the resonator. This paper describes a method for aligning an unstable resonator very accurately with off-axis injection of the alignment beam utilizing multiple reflections of the Gaussian beam inside the resonator.

Phonon optics in semiconductors: Phonon generation and electron-phonon scattering inn-GaAs epilayers: I. Theory

In this paper we give a theoretical account of the generation of acoustic phonons during hot carrier relaxation and recombination at donors in $n$-GaAs at liquid helium temperatures. We give explicit expressions for the effects of carrier screening on both the piezoelectric and deformation-potential scattering. The relative scattering rates are shown to depend on the propagation direction of the phonons, the electron temperature, the carrier concentration and the phonon polarization. The effects of off-axis phonon propagation and the finite aperture of the detectors used in the recent experiments of Narayanamurti, Logan, Chin, and Lax is explicitly taken into account in the calculations. The relationship of these calculations to more traditional transport measurements, such as the mobility is discussed.

Off-axis propagation of a laser beam in low visibility weather conditions

The role of non-small-angle scattering is examined for off-axis laser beam propagation under low visibility weather conditions. The near-axis radiance distribution function is obtained from a radiative transfer equation with the aid of the small-angle approximation. The contribution of the non-small-angle scattering is described via another transfer equation with the on-axis radiance as an external source, and this equation is solved in the diffusion approximation. Numerical results for radiational and advective fogs are presented to show the importance of non-small-angle scattering in the case of off-axis detection.

Guided-radiation mode interaction in off-axis propagation in anisotropic optical waveguides with application to direct-intensity modulators

A closed-form solution of the coupled-mode equations is derived for the guided–radiation mode interaction in optical waveguides by using a Lorentzian approximation to the coupling-factor distribution. This solution does not neglect reconversion from radiation to guided modes as did the previous perturbation solution. It is thus more accurate for the case of higher-order guided modes for which the power attenuation due to radiation conversion exhibits an oscillatory form and the ’’effective’’ perturbation assumption that the coupling factor is independent of the phase constant is not valid. Peaks in the mode conversion characteristics at certain eigenvalues of the relevant guided mode can be physically interpreted as the coupling to leaky waves. Illustrative examples and related discussions are given for the polarization-rotated (TE→TM) guided-to-radiation mode conversion in off-axis propagation in an anisotropic LiNbO3 waveguide. Also, an electro-optic direct-intensity modulator is described where the angle of propagation is used instead of a dc field to set a bias point for linear modulation.

Experimental study of propagation of electrostatic ion waves in a magnetic field

The results of an experimental investigation of electrostatic ion waves in an rf-generated argon plasma supported by a longitudinal magnetic field is presented. For off-axis wave propagation, observations agree quite well with the theoretical predictions of Joyce and Dory. Observations for parallel propagation, however, yield a dispersion curve exhibiting structure not predicted by linear theory.

Geometric acoustic attenuation at gigacycle frequencies in single crystals of quartz

Successive acoustic echo amplitudes have been calculated from a model for microwave frequency acoustic propagation based on ray optics that ignores any intrinsic attenuation. The computed echoes resemble experimental acoustic decay patterns generated by microwave pulses in single crystals of piezoelectric materials. The attenuation has been found to be due to off-axis propagation of the acoustic energy in the crystal and to acoustic phase averaging by the microwave transducers used to couple energy in and out of the crystal. Calculated acoustic echo patterns show the changes caused by various crystal orientations and different crystal endface parallelisms at several frequencies. It is found that the number of echoes and the amplitude of the last few echoes are frequency independent and are determined by the crystal geometry alone. On the other hand, the character of all but the last few echoes is dominated by phase averaging effects over the crystal end wall and is strongly frequency-dependent. Experimental data is presented showing the changes in the nulls and maximums of the echo patterns with frequency and the changes in acoustic patterns produced by altering the endface parallelism by flexing the crystal. Measured acoustic echo patterns of flexed and unflexed crystals are discussed. It is shown that flexing has increased the number of observable echoes by factors from 4 to 10 for various samples, has improved the average intensity of comparable echoes by amounts varying from 4 to 14 db, and has reduced the apparent acoustic attenuation from an unflexed value of 1.86×10-1db/cm to 1.63×10-2db/cm for a particular sample.