I. Edge Diffraction of a Convergent Wave. II. Diffraction of Laguerre Gaussian Beams by a Circular Aperture

Citation

Livanos, Alexander Constantine R. (1975) I. Edge Diffraction of a Convergent Wave. II. Diffraction of Laguerre Gaussian Beams by a Circular Aperture. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/KDAN-7033. https://resolver.caltech.edu/CaltechETD:etd-11112003-093137

Abstract

PART I. 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. PART II. 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.

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