Abstract

This paper discusses a modification of a maximum power-transfer theorem whose essential features were developed by Alan F. Kay and by Giorgio V. Borgiotti. It is shown that a C₂ rotation symmetry with respect to the optic axis is a sufficient symmetry restriction for the shape of each aperture, and that the phase as well as the amplitude of the illuminating field can be included in a statement of the theorem if it is applied to confocal instead of flat surfaces. The modified statement of the theorem is that a maximum power-transfer coefficient between apertures in two confocal surfaces, whose shapes have C₂ symmetry, is obtained when the illumination of one surface is identical to that of a confocal resonator having the same geometry and operating in the lowest diffraction-loss eigenmode, and that the power-transfer coefficient, T, is then related to the full-pass diffraction loss, D, by $T={(1-D)}^{\frac{1}{2}}$. It is further shown that the eigenfunctions of the confocal-resonator equation are identical to those of the extremum power-transfer condition, and that these functions form a complete orthogonal set. The actual solution for surfaces of rectangular shape is compared with results obtained for illumination with a gaussian-amplitude distribution. It turns out that attempts to minimize power radiated into sidelobes by using gaussian-amplitude distributions have been very close to the optimum solution of this problem.

© 1969 Optical Society of America

Near Fields of Truncated-Gaussian Apertures*

J. P. Campbell and L. G. DeShazer
J. Opt. Soc. Am. 59(11) 1427-1429 (1969)

Diffraction of Gaussian Laser Beams by a Semi-Infinite Plane

J. E. Pearson, T. C. McGill, S. Kurtin, and A. Yariv
J. Opt. Soc. Am. 59(11) 1440-1445 (1969)

Application of Optical Scintillation Measurements to Turbulence Diagnostics*

Frederick P. Carlson
J. Opt. Soc. Am. 59(10) 1343-1347 (1969)

Two Families of Apodization Problems

C. W. McCutchen
J. Opt. Soc. Am. 59(9) 1163-1171 (1969)

Effect of Truncation of Line-Spread and Edge-Response Functions on the Computed Optical Transfer Function

M. E. Rabedeau
J. Opt. Soc. Am. 59(10) 1309-1311 (1969)