Engineering Commons^™

Effects Of Gaussian Fields On The Stability Of Inhomogeneously Broadened Lasers, Pitak Chenkosol, Lee W. Casperson

Electrical and Computer Engineering Faculty Publications and Presentations

Under some conditions, spontaneous coherent pulsations are known to occur in the output beams of inhomogeneously broadened laser oscillators. These lasers typically operate with a Gaussian transverse field distribution, while the corresponding theoretical models assume a uniform-plane-wave field. The effects of a Gaussian field on the stability criteria of single-mode inhomogeneously broadened ring laser oscillators are considered in this study. It is found that in comparison to a plane wave a Gaussian field variation still permits low-threshold spontaneous pulsations but reduces the parameter space over which these pulsations can be observed.

Recurring Beams In Hollow Metal Waveguides: Paraxial Approximation, Lee W. Casperson

Electrical and Computer Engineering Faculty Publications and Presentations

For optical and near-optical applications in electromagnetics, the directed propagation of waves in free space and in lenslike media is often in the Cartesian form of Gaussian or more general Hermite-sinusoidal-Gaussian beams. It has been shown that recurring (rather than continuing) forms of such beams are possible in the paraxial approximation for certain hollow metal waveguides, in which multiple reflections from the waveguide walls may occur. Limitations on this recurrence behavior implicit in use of the paraxial approximation are considered here, and estimates are obtained for the maximum propagation distance before the onset of significant distortion of the recurring beams.

Gaussian Beams In Hollow Metal Waveguides: Experiment, Marius Ghita, Lee W. Casperson

Electrical and Computer Engineering Faculty Publications and Presentations

Gaussian beams have been widely used for propagating electromagnetic waves in free space and in certain other optical systems. It has been suggested that recurring forms of such beams might also be useful for propagation in planar or rectangular metal waveguides. Experimental verification of the recurrence of the Gaussian field distribution in metal waveguides is reported here.

Gaussian Beams In Hollow Metal Waveguides, Lee W. Casperson

Electrical and Computer Engineering Faculty Publications and Presentations

Various families of Gaussian beams have been explored previously to represent the propagation of nearly plane electromagnetic waves in media having at most quadratic transverse variations of the index of refraction and the gain or loss in the vicinity of the beam. However, such beams cannot directly represent the wave solutions for propagation in planar or rectangular waveguides, and sinusoidal mode functions are more commonly used for such waveguides. On the other hand, it is also useful to consider the possibility of recurring Gaussian beams that have an approximately Gaussian transverse profile at certain distinct planes along the propagation path. …

Grazing Reflection Of Gaussian Beams, Lee W. Casperson

Electrical and Computer Engineering Faculty Publications and Presentations

The reflectivities of most surfaces are higher for grazing or near-90-deg angles of incidence than for more perpendicular or near-zero-deg angles. Grazing-incidence configurations are especially important in the development of lasers and optical systems that operate in the far-ultraviolet and soft-x-ray regions of the spectrum, where transparent or highly reflecting media are almost unknown. Analytical solutions of the paraxial wave equation are obtained for the grazing reflection and complex interference effects that take place when a Gaussian beam interacts at shallow angles with a reflecting surface.

Production And Propagation Of Hermite–Sinusoidal-Gaussian Laser Beams, Lee W. Casperson, Anthony A. Tovar

Electrical and Computer Engineering Faculty Publications and Presentations

Hermite–sinusoidal-Gaussian solutions to the wave equation have recently been obtained. In the limit of large Hermite–Gaussian beam size, the sinusoidal factors are dominant and reduce to the conventional modes of a rectangular waveguide. In the opposite limit the beams reduce to the familiar Hermite–Gaussian form. The propagation of these beams is examined in detail, and resonators are designed that will produce them. As an example, a special resonator is designed to produce hyperbolic-sine-Gaussian beams. This ring resonator contains a hyperbolic-cosine-Gaussian apodized aperture. The beam mode has finite energy and is perturbation stable.

Sinusoidal-Gaussian Beams In Complex Optical Systems, Lee W. Casperson, Dennis G. Hall, Anthony A. Tovar

Electrical and Computer Engineering Faculty Publications and Presentations

Sinusoidal-Gaussian beam solutions are derived for the propagation of electromagnetic waves in free space and in media having at most quadratic transverse variations of the index of refraction and the gain or loss. The resulting expressions are also valid for propagation through other real and complex lens elements and systems that can be represented in terms of complex beam matrices. The solutions are in the form of sinusoidal functions of complex argument times a conventional Gaussian beam factor. In the limit of large Gaussian beam size, the sine and cosine factors of the beams are dominant and reduce to the …

Generalized Beam Matrices. Iv. Optical System Design, Anthony A. Tovar, Lee W. Casperson

Electrical and Computer Engineering Faculty Publications and Presentations

Systematic procedures are presented for determining the optical components needed to produce an arbitrary transformation of a Gaussian light beams's spot size, radius of curvature, displacement, and direction of propagation. As an example, an optical system is considered that spatially separates the two coincident Gaussian beams produced by a high-diffraction-loss resonator that uses a Gaussian variable-reflectivity output coupler. In addition, an ABCDGH reverse matrix theorem and an ABCDGH Sylvester theorem are also derived. These matrix theorems may be used to satisfy special constraints inherent in the design of multipass and periodic optical systems.

Generalized Beam Matrices. Iii. Application To Diffraction Analysis, Lee W. Casperson, Anthony A. Tovar

Electrical and Computer Engineering Faculty Publications and Presentations

In analogy with Huygen’s wavelets a new method based on Gaussian beamlets is used to develop a conventional diffraction integral formalism for paraxial optical systems representable by complex 2×2 ABCD Gaussian beam matrices. This method, along with a new phase parameter transformation, is then used to produce a new diffraction integral for studying the propagation of light beams with arbitrary spatial profiles through much more general misaligned complex optical systems representable by 3×3 ABCDGH beam matrices.

Generalized Beam Matrices. Ii. Mode Selection In Lasers And Periodic Misaligned Complex Optical Systems, Lee W. Casperson, Anthony A. Tovar

Electrical and Computer Engineering Faculty Publications and Presentations

A generalized beam matrix method is used to investigate the mode structure of astigmatic misaligned optical systems with loss or gain. In these optical systems the usual real-argument polynomial-Gaussian beams are not eigenfunctions, and off-axis complex-argument polynomial beams must be used. New beam transformations for these complex-argument modes are reported. Stability criteria are developed, and mode selection in laser resonators that contain tilted, displaced, or curved complex optical elements is discussed.

Beam Propagation In Parabolically Tapered Graded-Index Waveguides, Anthony A. Tovar, Lee W. Casperson

Electrical and Computer Engineering Faculty Publications and Presentations

To a good approximation, the electromagnetic-propagation characteristics of graded-index waveguides can be written in terms of polynomial-Gaussian modes. For uniform quadratic-index waveguides the behavior of these modes is well known. However, there are sometimes practical reasons for using tapered waveguides, but detailed propagation solutions are known for only a few specific taper functions. The parabolic taper is perhaps the most important special case, and the solution-generating techniques that we generalize are used to obtain analytic solutions for this case.

Oscillation Frequency In High-Gain Lasers, Lee W. Casperson

Electrical and Computer Engineering Faculty Publications and Presentations

The calculation of the oscillation frequency of a single-mode laser oscillator is examined systematically. Mode-pulling formulas are developed for a variety of laser systems, and the limitations of a standard approximation are explored.

Numerical Solutions Of Continuous Wave Beam In Nonlinear Media, Jeffrey Huang

Dissertations and Theses

Deformation of a Gaussian beam is observed when it propagates through a plasma. Self-focusing of the beam may be observed when the intensity of the laser increases the index of refraction of plasma gas.

Due to the difficulties in solving the nonlinear partial differential equation in Maxwell's wave equation, a numerical technique has been developed in favor of the traditional analytical method. Result of numerical solution shows consistency with the analytical method. This further suggests the validity of the numerical technique employed.

A three dimensional graphics package was used to depict the numerical data obtained from the calculation. Plots from …

Beam Propagation In Periodic Quadratic-Index Waveguides, Lee W. Casperson

Electrical and Computer Engineering Faculty Publications and Presentations

Several techniques are described for studying the propagation of off-axis polynomial Gaussian beams in media having straight axes and periodic z variations of the quadratic refraction and loss coefficients. For some periodic variations, exact analytical solutions of the paraxial equations are possible, and for sufficiently slow variations, WKB solutions can always be obtained. All results are expressed in conventional beam matrix form.

Propagation Of Airy-Hermite-Gaussian Waveguide Modes In Free Space, Lee W. Casperson, O. M. Stafsudd, Leroy V. Sutter, Jonathan Gary Grossman

Electrical and Computer Engineering Faculty Publications and Presentations

The cavity modes of metal strip waveguide lasers are most simply expressed in terms of Airy-Hermite-Gaussian functions. The free space propagation of the resulting beam modes has been examined, and both near- and far-field patterns have been calculated and measured. Phase plates may be useful for enhancing the far-field intensity.

Modes Of A Laser Resonator With A Retroreflecting Corner Cube Mirror, Guosheng Zhou, Anthony J. Alfrey, Lee W. Casperson

Electrical and Computer Engineering Faculty Publications and Presentations

The self-consistent integral equation for the field distribution of the resonant modes in a resonator with a tilted retroreflecting corner cube mirror is solved. The corner cube acts like a convex lens with radius of curvature -L cot²Ө in the rotation direction (L is the cavity length and Ө the rotation angle) and like a flat plane in the direction of the rotation axis. The field distribution can be described in terms of Hermite-Gaussian functions, and these results have been confirmed experimentally using an Ar-ion laser. The equivalent beam matrix for a reflecting corner cube is also found.

Modes Of A Laser Resonator With A Retroreflecting Roof Mirror, Guosheng Zhou, Lee W. Casperson

Electrical and Computer Engineering Faculty Publications and Presentations

The self-consistent integral equation for the field distribution of the resonant modes in a resonator with a tilted retroreflecting roof mirror is solved. The field distribution in the direction of the roof can be described in terms of Hermite-Gaussian functions. The beam matrix for a retroreflecting roof is found, and a new type of resonator which does not need precise alignment is proposed.

Modes Of A Laser Resonator With A Retroreflective Mirror, Guosheng Zhou, Lee W. Casperson

Electrical and Computer Engineering Faculty Publications and Presentations

The self-consistent integral equation for the field distribution of the resonant modes in an inclined retroreflective grating resonator is solved in the limit of large Fresnel numbers. The transverse field distribution in the direction perpendicular to the grating grooves can be described in terms of Hermite-Gaussian functions provided that λ « d « w, where λ is the wavelength, d is the grating spacing, and w is the beam spot size.

Beam Deflection In A Pulsed Chemical Laser Amplifier, J. Munch, Lee W. Casperson, E. C. Rea

Electrical and Computer Engineering Faculty Publications and Presentations

Analyses and experiments have been performed to investigate deflection of a Gaussian beam propagating through an amplifying medium possessing a strong transverse gain gradient. The analysis includes effects due to dispersion and gain steering. The experiments were performed in a high power pulsed chemical laser amplifier using a cw frequency stabilized laser as a source. Time dependent beam deflection due to the interaction of the gain gradient with the finite radius of curvature of the propagating beam was observed.

Beam Modes In Complex Lenslike Media And Resonators, Lee W. Casperson

Electrical and Computer Engineering Faculty Publications and Presentations

General sets of higher-order beam modes are derived for light propagation in media having spatial variations of the gain or loss. The resulting expressions are also valid for propagation through conventional optical elements and graded transmission filters. The four basic mode sets obtained include off-axis Hermite-Gaussian and Laguerre-Gaussian modes of both real and complex argument. A procedure is developed for finding the resonant modes of laser oscillators containing arbitrary complex lens elements, and the mode stability properties of lasers can be interpreted physically by means of these formulas.

Gaussian Modes In High Loss Laser Resonators, Lee W. Casperson, Susan D. Lunnam

Electrical and Computer Engineering Faculty Publications and Presentations

Matrix techniques are applied to the mode analysis of laser resonators having spherical mirrors and Gaussian profiles of the mirror reflectivity. These same analytical methods provide a useful approximation to the mode and loss characteristics of conventional resonators having an abrupt discontinuity of the reflectivity. Mode selection in apertured waveguides and resonators is also discussed.

Air Breakdown In A Radial-Mode Focusing Element, Lee W. Casperson, Mohammad Shabbir Shekhani

Electrical and Computer Engineering Faculty Publications and Presentations

A new radial focusing device is described that condenses an incident laser beam to an extremely intense and uniformly illuminated focal spot. The focal region is useful for many applications. When used with a 10.6-µm CO₂ TEA laser source, a disk-shaped air-breakdown spark results, and the properties of this spark have been investigated.

Gaussian Light Beams In Inhomogeneous Media, Lee W. Casperson

Electrical and Computer Engineering Faculty Publications and Presentations

Vector wave solutions are obtained for the propagation of beams of light in media having slow spatial variations of the gain, loss, or index of refraction. The formalism developed here is applicable to a wide range of problems, and an exa mple considered in detail is the propagation of off-axis beams in lenslike laser materials and optical waveguides. A procedure is also described for the diagnosis of localized dielectric inhomogeneities such as plasmas by means of Gaussian laser beams.

The Gaussian Mode In Optical Resonators With A Radial Gain Profile, Lee W. Casperson, Amon Yariv

Electrical and Computer Engineering Faculty Publications and Presentations

The dependence of the parameters of the Gaussian mode in laser resonators on the properties of the medium in the cavity is studied. Experimental verification of the theoretical results is presented. It is found that the modes in a high‐gain laser may differ widely from the usual free space resonator results. Also, resonator configurations which in free space are unstable may, with a suitable medium, support low‐loss Gaussian modes.