Anthony Tovar

Eastern Oregon University, Physics, Department Member

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Address: La Grande, Oregon, United States

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David Carson Berry

University of Cincinnati

Alberto Pimpinelli

Université Clermont Auvergne

Adam M Croom

Case Western Reserve University

Tel Aviv University

Carleton University

University of Oslo

Yale University

University of Illinois at Urbana-Champaign

Jonathan D Maltz

Stanford University

Roland Kröger

University of York

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$Research paper thumbnail of Diffraction Analysis$

Diffraction Analysis

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Off-axis multimode light beam propagation in tapered lenslike media including those with spatial gain or loss variation

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Air Drag Mathematics Reference Guide

Concentric-circle-grating, surface-emitting laser beam propagation in complex optical systems

Journal of the Optical Society of America a Optics and Image Science, 1997

Laser beams emitted from concentric-circle-grating, surface-emitting semiconductor lasers are azi... more Laser beams emitted from concentric-circle-grating, surface-emitting semiconductor lasers are azimuthally polarized and have an electric field amplitude profile that can be represented as a J 1 Bessel function multiplied by a Gaussian function, where the arguments of both of the functions are complex. The detailed propagation formulas for these laser beams and similar azimuthally polarized Laguerre-Gaussian beams through optical systems representable by complex ABCD beam matrices are obtained. As a specific example, azimuthally polarized J 1 Bessel-Gaussian laser beam propagation through a laser amplifier with a radial gain profile is considered.

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Beam Modes of Lasers with Misaligned Complex Optical Elements

A recurring theme in my research is that mathematical matrix methods may be used in a wide variet... more A recurring theme in my research is that mathematical matrix methods may be used in a wide variety of physics and engineering applications. Transfer matrix techniques are conceptually and mathematically simple, and they encourage a systems approach. Once one is familiar with one transfer matrix method, it is straightforward to learn another, even if it is from a completely different branch of science. Thus it is useful to overview these methods, and this has been done here. Of special interest are the applications of these methods to laser optics, and matrix theorems concerning multipass optical systems and periodic optical systems have been generalized here to include, for example, the effect of misalignment on the performance of an optical system. In addition, a transfer matrix technique known as generalized beam method has been derived to treat misalignment effects in complex optical systems. Previous theories used numerical or ad hoc analytical solutions to a complicated diffraction integral. The generalized beam matrix formalism was also extended to higher-order beam modes of lasers and used to study mode discrimination in lasers with misaligned complex optical elements.

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<title>Multi-Gaussian beams: a super-Gaussian alternative</title>

Laser Resonators III, 2000

Multi-Gaussian beams: a super-Gaussian alternative

The multi-Gaussian beam shape is proposed as a model for aperture functions and laser beam profil... more The multi-Gaussian beam shape is proposed as a model for aperture functions and laser beam profiles which have a nearly flat top, but whose sides decrease continuously. Beams and apertures of this type represent a simple, elegant, and intuitive alternative to super-Gaussian beams. The design of lasers that have these beams as its eigenmodes is discussed. Such laser resonators would have increased energy extraction from the laser amplifier.

Generalized beam matrices. IV.Optical system design

J Opt Soc Am a Opt Image Sci, 1997

Systematic procedures are presented for determining the optical components needed to produce an a... more 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. © 1997 Optical Society of America [S0740-3232 882

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Spectral behavior and pulse train instabilities of a synchronously pumped mode-locked dye laser

Journal of the Optical Society of America B, 1988

The pulse-train envelope of a synchronously pumped mode-locked dye laser has been experimentally ... more The pulse-train envelope of a synchronously pumped mode-locked dye laser has been experimentally studied as a function of cavity length detuning. When a bandwidth-limiting birefringent tuning filter is included and the cavity is adjusted to the length that yields optimally short (2-psec) pulses, there is a slow (800 kHz), erratic amplitude modulation that provides a 20% variation in pulse energies. As the cavity length is detuned on the order of one part in 104, the modulation vanishes, but the individual pulse lengths increase dramatically. Further detuning results in a clean periodic envelope with a 20% modulation depth and a -5-,usec period. With the birefringent filter removed, the dye-laser wavelength and bandwidth are studied as functions of the cavity length. Temporally, the clean periodic modulation persists at large detunings, but there is no length at which any erratic modulation can be observed without the bandwidth-limiting filter.

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Production and propagation of Hermite–sinusoidal-Gaussian laser beams

Journal of the Optical Society of America A, 1998

Hermite-sinusoidal-Gaussian solutions to the wave equation have recently been obtained. In the li... more 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.

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Sinusoidal-Gaussian beams in complex optical systems

Journal of the Optical Society of America A, 1997

Sinusoidal-Gaussian beam solutions are derived for the propagation of electromagnetic waves in fr... more 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 conventional modes of a rectangular waveguide. In the opposite limit the beams reduce to the familiar fundamental Gaussian form. Alternate hyperbolic-sinusoidal-Gaussian beam solutions are also found.

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Production and propagation of cylindrically polarized Laguerre–Gaussian laser beams

Journal of the Optical Society of America A, 1998

The x-polarized and y-polarized beam modes of simple confining circularly symmetric spherical-mir... more The x-polarized and y-polarized beam modes of simple confining circularly symmetric spherical-mirror laser resonators may be represented with Laguerre-Gaussian functions. The corresponding r-and -polarized beam-mode profiles are found to be represented by a different Laguerre-Gaussian mode set. Though similar in name, these cylindrically polarized modes are fundamentally different from their rectangularly polarized counterparts. For example, the fundamental x-polarized mode is Gaussian, which has a maximum at the center of the beam, while the fundamental -polarized mode has a null at the beam center. The complete propagation characteristics of several types of azimuthally polarized Laguerre-Gaussian beams through optical systems representable by complex ABCD matrices are obtained. Cylindrically polarized Laguerre-Gaussian beams may be produced by inserting the appropriate Brewster window into a simple confining circularly symmetric laser resonator.

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Propagation of flat-topped multi-Gaussian laser beams

Journal of the Optical Society of America A, 2001

The multi-Gaussian beam shape is proposed as a model for aperture functions and laser beam profil... more The multi-Gaussian beam shape is proposed as a model for aperture functions and laser beam profiles that have a nearly flat top but whose sides decrease continuously. Beams and apertures of this type represent a simple, elegant, and intuitive alternative to super-Gaussian beams, which are important in a number of applications such as laser resonator design. Analytical formulas are developed for the propagation of these beams through free space and optical systems representable by ABCD matrices.

Generalized beam matrices. II. Mode selection in lasers and periodic misaligned complex optical systems

Journal of the Optical Society of America A, 1996

A generalized beam matrix method is used to investigate the mode structure of astigmatic misalign... more 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.

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Concentric-circle-grating, surface-emitting laser beam propagation in complex optical systems

Journal of the Optical Society of America A, 1997

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Hermite–sinusoidal-Gaussian beams in complex optical systems

Journal of the Optical Society of America A, 1998

sinusoidal-Gaussian beams in complex optical systems," J. Opt. Soc. Am. A 15, 954-961 (1998).

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

Journal of the Optical Society of America A, 1991

Propagation of Laguerre-Bessel-Gaussian beams

Journal of the Optical Society of America A, 2000

New exact solutions to the paraxial wave equation are obtained in the form of a product of Laguer... more New exact solutions to the paraxial wave equation are obtained in the form of a product of Laguerre polynomials, Bessel functions, and Gaussian functions. In the limit of large Laguerre-Gaussian beam size, the Bessel factor dominates and the solution sets reduce to the modes of closed resonators, hollow metal waveguides, and dielectric waveguides. In the opposite limit the solutions reduce to Laguerre-Gaussian modes of open resonators and graded-index waveguides. These solutions are valid for electromagnetic waves traveling through free space, and they are valid for propagation through circularly symmetric optical systems representable by ABCD matrices as well. An interesting feature of the new solution set is the existence of three mode indices, where only two are required for an orthogonal expansion. As an example, Laguerre-Gaussian beam propagation through an optical system that contains a Bessel-like amplitude filter is discussed.

Generalized Sylvester theorems for periodic applications in matrix optics

Journal of the Optical Society of America A, 1995

Citation Details

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$Research paper thumbnail of Diffraction Analysis$

Diffraction Analysis

Let us know how access to this document benefits you.

Off-axis multimode light beam propagation in tapered lenslike media including those with spatial gain or loss variation

Download

Air Drag Mathematics Reference Guide

Concentric-circle-grating, surface-emitting laser beam propagation in complex optical systems

Journal of the Optical Society of America a Optics and Image Science, 1997

Download

Beam Modes of Lasers with Misaligned Complex Optical Elements

Download

<title>Multi-Gaussian beams: a super-Gaussian alternative</title>

Laser Resonators III, 2000

Multi-Gaussian beams: a super-Gaussian alternative

Generalized beam matrices. IV.Optical system design

J Opt Soc Am a Opt Image Sci, 1997

Download

Spectral behavior and pulse train instabilities of a synchronously pumped mode-locked dye laser

Journal of the Optical Society of America B, 1988

Download

Production and propagation of Hermite–sinusoidal-Gaussian laser beams

Journal of the Optical Society of America A, 1998

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Sinusoidal-Gaussian beams in complex optical systems

Journal of the Optical Society of America A, 1997

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Production and propagation of cylindrically polarized Laguerre–Gaussian laser beams

Journal of the Optical Society of America A, 1998

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Propagation of flat-topped multi-Gaussian laser beams

Journal of the Optical Society of America A, 2001

The multi-Gaussian beam shape is proposed as a model for aperture functions and laser beam profil... more The multi-Gaussian beam shape is proposed as a model for aperture functions and laser beam profiles that have a nearly flat top but whose sides decrease continuously. Beams and apertures of this type represent a simple, elegant, and intuitive alternative to super-Gaussian beams, which are important in a number of applications such as laser resonator design. Analytical formulas are developed for the propagation of these beams through free space and optical systems representable by ABCD matrices.

Generalized beam matrices. II. Mode selection in lasers and periodic misaligned complex optical systems

Journal of the Optical Society of America A, 1996

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Concentric-circle-grating, surface-emitting laser beam propagation in complex optical systems

Journal of the Optical Society of America A, 1997

Download

Hermite–sinusoidal-Gaussian beams in complex optical systems

Journal of the Optical Society of America A, 1998

sinusoidal-Gaussian beams in complex optical systems," J. Opt. Soc. Am. A 15, 954-961 (1998).

Download

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

Journal of the Optical Society of America A, 1991