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Updated: Jun 27, 2026
12:14
The Generation of Higher-order Laguerre-Gauss Optical Beams for High-precision Interferometry
Published on: August 12, 2013
Elliptical beams.
Miguel A Bandres1, Julio C Gutiérrez-Vega
1California Institute of Technology, Pasadena, California 91125, USA. bandres@caltech.edu
Optics Express
|December 10, 2008
Summary
A general solution for elliptic beams (EB) is presented, described by Ince-Gauss or Whittaker-Hill functions. These beams propagate through optical systems and include known special cases like Mathieu-Gauss beams.
Area of Science:
- Optics and Photonics
- Mathematical Physics
Background:
- The paraxial wave equation is fundamental for describing light propagation.
- Specialized beam solutions are crucial for advanced optical applications.
Purpose of the Study:
- To present a general beam solution in elliptic cylindrical coordinates.
- To analyze the properties and special cases of these elliptic beams.
Main Methods:
- Solving the paraxial wave equation in elliptic cylindrical coordinates.
- Utilizing generalized Ince functions and Whittaker-Hill functions.
- Analyzing propagation through ABCD optical systems.
Main Results:
- A general solution for elliptic beams (EB) is derived.
- The complex amplitude is described by generalized Ince or Whittaker-Hill functions.
- Propagation characteristics and square integrability conditions are detailed.
Conclusions:
- The presented elliptic beam solution offers a unified framework for various known beams.
- This work provides a comprehensive understanding of elliptic beam propagation in optical systems.
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