Far-field Intensity Distribution Research Articles

Performance criteria and limitations of electrooptic waveguide array deflectors

Fraunhofer diffraction theory was used to obtain the far-field output intensity distributions of various electrooptic waveguide deflectors. The behavior of single prism elements, arrays of identical or phase-staggered prism elements, and arrays of channel waveguide elements is described by the same analytic technique. The optical beam deflection can be continuous or discontinuous. Electrode capacitances are determined. The capabilities of different deflectors are assessed by comparing number of resolvable spots, power, bandwidth, and cross talk. Comparisons are made with experimental data. Simple phase distributions are demonstrated to be useful for determining most deflection parameters, including the power per unit bandwidth.

Electromagnetic field scattering by a triangular aperture

The multiple Laplace transform has been applied to analysis and computation of scattering by a double triangular aperture. Results are obtained which match far-field intensity distributions observed in experiments. Arbitrary polarization components, as well as in-phase and quadrature-phase components, may be determined, in the transform domain, as a continuous function of distance from near to far-field for any orientation, aperture, and transformable waveform. Numerical results are obtained by application of numerical multiple inversions of the fully transformed solution.

Partially coherent sources which produce the same far-field intensity distribution as a laser

It is shown that certain partially coherent model sources whose intensity distribution and degree of coherence are both gaussian will generate the same far-field intensity distributions as a completely coherent laser source.

Intensity mapping optical aberrations

Intensity mapping aberrations for high average power laser beams are examined from the point of view of diffraction theory. For the Fresnel ripple aberrations, it was determined that indeed they behave like a circular diffraction grating where energy is diffracted into the far wings of the far-field intensity distribution without significantly affecting the width of the central diffraction lobe, only its energy. It was further established that the effect of such aberrations on the far field may well be characterized by techniques where the aberration is randomized, and on-axis intensities are obtained through approximate methods.

Adaptive laser resonator

The feasibility of compensating for intracavity phasefront distortions using a multidither zonal COAT system has been demonstrated insided an unstable resonator cavity using a CO2 electric discharge laser. Experimental data are presented that verify that intracavity-induced degradation of the near-field and far-field intensity distributions can be corrected and the extracted output power improved by using adaptive resonator techniques.

Performance of an unstable repetitive pulsed CO2 laser oscillator

Mode control experiments were performed with an unstable TEA repetitive pulsed CO2 laser oscillator. Near- and far-field intensity distributions were obtained that are consistent with theoretical values for a diffraction-limited beam. Performance of the same laser with a stable optical cavity is also given as a reference.

Intensity interferometry in the spatial domain*

Intensity interferometry, as developed by Hanbury Brown and Twiss for stellar observation, has shown relative insensitivity to atmospheric scintillation. However, with classical sources, the limitations placed on this technique by quantum noise and detector efficiency are severe. This situation is vastly improved when laser illumination is employed. Generalizing a form of the mutual coherence function, we derive the far-zone behavior of the mutual intensity function for an intermediate time average. This result is used to reconstruct the irradiance distribution of a spatially rough source. The far-field intensity distribution is recorded spatially for one time-resolution unit of the detector. The resulting spatial signal is autocorrelated and related to the intensity distribution over the source. Thus, without averaging in the time domain, a spatial Fourier-transform relation is derived between the far-field intensity correlation and the source irradiance, similar to the results of Hanbury Brown and Twiss.

An experimental study of unstable confocal CO2resonators

The results of an experimental study to determine the spatial properties of unstable confocal resonator modes and their influence upon both the fractional output coupling and the far-field angular divergence are presented. The radial intensity distributions of the lowest order circulating mode within CO 2 unstable resonators and the corresponding near- and far-field patterns have been measured. The radial profiles exhibit a significantly nonuniform intensity distribution consistent with the results of recent theoretical analysis. The far-field intensity distribution as well as the fractional output coupling have been investigated for a number of unstable confocal resonator geometries. For modes contained within the uniform-gain region of the laser tube, the experimental results are in excellent agreement with Siegman's unstable resonator analysis.

Effect of a turbulent medium on the near- and far-field diffraction of a circular aperture

The near- and far-field diffraction due to a circular aperture illuminated with partially coherent light produced by a turbulent medium has been theoretically studied. Formulations are developed for investigating the near- and far-field diffraction patterns. The phase structure function, which is generated by the turbulent medium and determines the partially coherent condition of a light beam passing through it, is assumed to take both the Gaussian form and the 5/3-power law. Numerical results concerning the far-field intensity distribution and the axial intensity distribution in the near-field region are presented in diagrams and discussed.

Performance of an unstable oscillator on a 30-kW CW gas dynamic laser

Mode-control experiments at a 30-kW CW power level with an unstable resonator at a high Fresnel number were performed on a gas dynamic laser. Near- and far-field intensity distributions were obtained that are consistent with theoretical values for an approximately twice diffraction-limited beam. Under these conditions, the output power was more than half of the maximum multi-mode power.

Effect of spherical aberration on the Fraunhofer diffraction of an optical system illuminated by partially coherent light

Far-field intensity distribution has been plotted for a circular aperture suffering from spherical aberration and illuminated by quasi-monochromatic partially space-coherent light. Gaussian and besinc forms of correlation have been assumed. It is shown that higher values of coefficient of aberration can be tolerated as the value of number of correlation intervals contained in the aperture increases.

The Far-field Diffraction Properties of AperturesII. Generalized Annular Apertures with Besinc Correlated Illumination.

The properties of the far-field intensity distribution due to generalized annular apertures, illuminated with partially coherent Besinc-correlated light, have been studied with particular emphasis on the encircled energy distribution and the variation of the degree of coherence in the diffracted field. A different approach than the usual has been used to derive analytical expressions suitable for computation. Numerical results are presented for a few representative apertures. Among other things, the two-point resolution is discussed according to three criteria and it is shown that the degree of coherence in the diffracted field is not generally stationary.

Properties of an unstable confocal resonator CO<inf>2</inf>laser system

The results of an experimental and theoretical study of the properties of a confocal unstable resonator used with a conventional CO <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> -N <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> -He laser operating at 10.6 μ are presented. Measurements were made of the near- and far-field intensity distribution of the aligned resonator for Fresnel numbers of 3.7, 6.1, and 7.1. Fundamental mode operation was achieved in all cases. Beam steering and mode degradation associated with mirror misalignment were also studied experimentally. Suitable geometric models have been developed to account for 1) the sensitivity of the resonator output coupling and center far-field intensity to variations in the resonator length and mirror curvatures, and 2) the sensitivity of the beam direction and power to angular misalignment of the mirrors.

Surface and volume scattering, surface-damage, and optical homogeneity studies of ruby crystals and their connection with laser-emission characteristics

Results of our investigation of the optical homogeneity of ruby crystals and its relation to the main laser-emission characteristics (i.e., beam divergence, far-field intensity distribution, energy output, and spectra of modes) are described. Good correlation has been found between the laser characteristics and the optical properties of the investigated ruby samples. On the basis of the experimental data, the different sources of the optical inhomogeneity of the ruby crystals grown by the Verneuil method and their influence on the laser characteristics are analyzed. It is shown, in particular, that internal mechanical strains have the most injurious effect on the beam divergence, the intensity distribution, and the mode-selection conditions. It is found that a volume light scattering contribution in laser energy losses is, to a large extent, due to the Rayleigh component of scattering. Laser-produced surface-damage experiments with ruby and sapphire crystals are also described. A variable pulse duration between <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1-400 \mu</tex> s under normal laser operation and 30-ns Q-switched pulsed laser operation have been employed in these experiments. Optical and structural surface properties and their effect on a surface-damage threshold have been studied and the mechanism of laser-produced surface damage is discussed.

On the determination of stationary spatial coherence

A solution is presented for the spatial coherence, μ, over an arbitrary plane aperture in terms of observable quantities. It is assumed that the aperture illumination is quasi-monochromatic and spatially-stationary. Fourier transform methods are used to obtain a closed-form solution of the integral equation relating the spatial coherence (μ), the far-field intensity (I), and the aperture intensity(I a). The solution is expressed as a product of the Fourier transform ofI and a function depending onI a. The special case of uniform aperture intensity yields particularly simple results. In this case, μ is given by knowledge of only the Fourier transform ofI and a factor capable of a very simple geometric interpretation in terms of the aperture area. Some general properties of μ are observed and then related to characteristics of the aperture and far-field intensity distributions. Applications of the results to the problem of measuring the spatial coherence are discussed. Finally, in order to illustrate the usefulness of the results, μ is obtained for a specific far-field intensity distribution.