Journal ArticleDOI
Fractal modes of unstable lasers with polygonal and circular mirrors
TLDR
In this paper, an explicit asymptotic theory for the lowest-loss mode, in terms of a superposition of successively magnified edge waves, was constructed for unstable lasers.About:
This article is published in Optics Communications.The article was published on 2001-12-15. It has received 37 citations till now. The article focuses on the topics: Fractal & Superposition principle.read more
Citations
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Journal ArticleDOI
Physics of Nonhermitian Degeneracies
TL;DR: A summary of a talk delivered at the Second International Workshop on Pseudo-hermitian Hamiltonians in Quantum Physics (Prague, 14-16 June 2004) can be found in this paper.
Journal ArticleDOI
Mode degeneracies and the petermann excess-noise factor for unstable lasers
TL;DR: In this article, the Horwitz-Southwell asymptotic theory of the spectrum is used to show that the peaks occur near N = s − 1/8 (s integer).
Journal ArticleDOI
The computation of the spectra of highly oscillatory Fredholm integral operators
TL;DR: In this article, the authors consider two competing bases: a basis of Legendre polynomials and a basis consisting of modified Fourier functions (cosines and shifted sines), and derive detailed asymptotic estimates of the rate of decay of the coefficients.
Journal ArticleDOI
The spectral problem for a class of highly oscillatory Fredholm integral operators
TL;DR: In this article, the spectral properties of a complex-symmetric Fredholm integral operator with highly oscillatory kernel were studied, showing that the spectrum consists of infinitely many discrete eigenvalues and giving a precise description of the way in which they converge to the origin.
Journal ArticleDOI
Fresnel diffraction and fractal patterns from polygonal apertures
TL;DR: In this article, two compact analytical descriptions of Fresnel diffraction patterns from polygonal apertures under uniform illumination are detailed. And the usefulness of the formulations is illuminated in the context of a virtual source theory that accounts for two transverse dimensions, which permits calculation of fractal unstable-resonator modes of arbitrary order and unprecedented accuracy.
References
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Book
Table of Integrals, Series, and Products
TL;DR: Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integral Integral Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequality 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
Book
Fractal Geometry: Mathematical Foundations and Applications
TL;DR: In this article, a mathematical background of Hausdorff measure and dimension alternative definitions of dimension techniques for calculating dimensions local structure of fractals projections of fractality products of fractal intersections of fractalities.
Journal ArticleDOI
On the Weierstrass-Mandelbrot fractal function
Michael V Berry,Z. V. Lewis +1 more
TL;DR: In this article, the scaling properties of the Weierstrass spectrum y n can be studied analytically in terms of a representation obtained by using the Poisson summation formula.
Book ChapterDOI
IV Catastrophe Optics: Morphologies of Caustics and Their Diffraction Patterns
Michael V Berry,C. Upstill +1 more
TL;DR: In this paper, the authors discuss the morphologies of caustics and their diffraction patterns in catastrophe optics, and discuss the diffraction catastrophes that both clothe and underlie caustic structures.