Journal ArticleDOI
Electromagnetic Beam Fields
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TLDR
In this article, it was shown that the usual paraxial theory for the Hermite Gaussian or Laguerre Gaussian beams, produced by some lasers, can be replaced by a more general theory which is precise according to Maxwell's equations.Abstract:
An electromagnetic beam is defined using mathematical properties of the associated angular spectrum of plane waves. It is found that the usual paraxial theory for the Hermite Gaussian or Laguerre Gaussian beams, produced by some lasers, can be replaced by a more general theory which is precise according to Maxwell's equations. In this theory the beams exhibit an amplitude distribution over any plane normal to the direction of propagation which can be described using prolate spheroidal wave functions. As the degree of collimation is increased, these beams asymptotically take on the familiar Gaussian amplitude cross section. However, as the divergence from focus is increased, these beams asymptotically approach modified dipole fields. It is found that two, mutually exclusive, classes of beam fields exist. For each beam in one class there is always a complementary beam in the other class. As the degree of collimation is increased, complementary beams become almost identical. Complementary beams contain elect...read more
Citations
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An angular spectrum representation approach to the Goos-Hänchen shift
TL;DR: In this article, the angular spectrum representation of the reflection of a beam of light at a plane interface is treated using angular spectrum representations, and the Goos-Hanchen shift is found to be proportional to the first derivative of the phase of the reflectance, which gives rise to a shift of the reflected beam along its direction of propagation.
Journal ArticleDOI
Unified operator approach for deriving Hermite-Gaussian and Laguerre-Gaussian laser modes.
TL;DR: It is shown that by using the plane-wave representation of the fundamental Gaussian mode as a seed function, all higher-order beam modes can be derived by acting with differential operators on this fundamental solution.
Journal ArticleDOI
High-aperture beams.
TL;DR: Different ways of defining high-aperture generalizations to paraxial beams are reviewed for both scalar beams and electromagnetic beams and the different approaches are divided into three types.
Posted Content
Gaussian, Hermite-Gaussian, and Laguerre-Gaussian beams: A primer
TL;DR: In this article, the authors present a didactic and self-contained overview of Gauss-Hermite and Gauss Laguerre laser beam modes using the plane wave representation of the fundamental Gaussian mode as seed function and derive higher-order beam modes by acting with differential operators on this fundamental solution.
References
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Book
Principles of Optics
TL;DR: In this paper, the authors discuss various topics about optics, such as geometrical theories, image forming instruments, and optics of metals and crystals, including interference, interferometers, and diffraction.
Principles of Optics
TL;DR: In this article, the authors discuss various topics about optics, such as geometrical theories, image forming instruments, and optics of metals and crystals, including interference, interferometers, and diffraction.
Journal ArticleDOI
Introduction to Fourier Optics
Joseph W. Goodman,Mary E. Cox +1 more
TL;DR: The second edition of this respected text considerably expands the original and reflects the tremendous advances made in the discipline since 1968 as discussed by the authors, with a special emphasis on applications to diffraction, imaging, optical data processing, and holography.
Book
Introduction to Fourier optics
TL;DR: The second edition of this respected text considerably expands the original and reflects the tremendous advances made in the discipline since 1968 as discussed by the authors, with a special emphasis on applications to diffraction, imaging, optical data processing, and holography.