Devices

  • Kenneth Smith
  • R. M. Thomson

Abstract

Consider an optical wave propagating along the +z -direction, so that it may be written as
$$u(x,y,t) = \operatorname{Re} [\tilde u(x,y){e^{i(\omega t - \beta z)}}]$$
(9.1)
The basic problem of optical-beam propagation is: Given the complex wave amplitude ũ o(xo, yo) across an input plane z o, find the complex amplitude and phase ũ(x, y) of the wave across any later output plane, z. The most common wave used in analysis is one having a Gaussian variation in amplitude across the wavefront:
$$\begin{gathered} \tilde u(x,y) = {\left( {\frac{{2e}}{\pi }} \right)^{1/2}}\frac{1}{\omega }\exp \left( { - \frac{{i\pi {x^2}}}{\lambda }\frac{{{x^2} + {y^2}}}{{\tilde q}}} \right) \hfill \\ \frac{1}{{\tilde q}} = \frac{1}{R} - i\frac{\lambda }{{\pi {\omega ^2}}} \hfill \\ \end{gathered} $$
(9.2)
where R is the radius of the spherical wave and w is the spot size.

Keywords

Vibrational Energy Population Inversion Electron Number Density Vibrational Temperature Translational Energy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1978

Authors and Affiliations

  • Kenneth Smith
    • 1
  • R. M. Thomson
    • 1
  1. 1.University of LeedsLeedsEngland

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