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Edge diffraction of a convergent wave. Diffraction of Lagguerre Gaussian beams by a circular aperture


Livanos, Alexander Constantine R. (1975) Edge diffraction of a convergent wave. Diffraction of Lagguerre Gaussian beams by a circular aperture. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/KDAN-7033.



Closed form solutions have been derived for the focal plane diffraction patterns of (a) a convergent spherical wave illuminating a segment of a circular aperture and (b) a convergent Gaussian beam diffracted by an infinite edge. The theoretical results agree with the experiments showing that the edge produces a spike of light with intensity variation inversely proportional to the squared distance from the center, that the pattern is symmetric in the focal plane, and that in the case of the uniform illumination the intensity has high spatial frequency components while for the Gaussian case the pattern does not ring when the edge is positioned symmetrically in the beam.

In addition, the near focus intensity distribution for a convergent uniform amplitude wave illuminating a semicircular aperture is presented, and it is shown that the fact that the radiation pattern is symmetric only at the focal plane can be used very effectively to determine the exact location of that plane.


The diffraction of a Laguerre Gaussian beam (TEM[subscript p,l] mode of a laser resonator) by a circular aperture is presented here. We calculate the electric field for the Fresnel region, and study the loss of power as a function of relative aperture size and mode index, showing that the conventional rule of thumb in selecting apertures by "going out a few times w[subscript o]" is not accurate for large mode indices.

Item Type:Thesis (Dissertation (Ph.D.))
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Engineering and Applied Science
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • George, Nicholas A.
Thesis Committee:
  • Unknown, Unknown
Defense Date:25 September 1974
Record Number:CaltechETD:etd-11112003-093137
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4502
Deposited By: Imported from ETD-db
Deposited On:11 Nov 2003
Last Modified:21 Dec 2019 02:22

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