The generalized Fresnel transform and its application to optics Academic Article uri icon


  • We consider the mathematical properties of a class of linear transforms, which we call the generalized Fresnel transforms, and which have wide applications to several areas of optics. Well-known transforms, such as the fractional Fourier transform and the Fresnel transform, can be seen to be special cases of this general transform. By use of an analogy with a quantum harmonic oscillator, we derive mathematical expressions for functions which remain invariant under such transforms, a result which has important applications in the theory of laser resonator modes.

published proceedings

  • Optics Communications

author list (cited authors)

  • James, D., & Agarwal, G. S.

citation count

  • 160

complete list of authors

  • James, Daniel FV||Agarwal, Girish S

publication date

  • May 1996