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Using Fresnel diffraction integrals, calculations have been made of the irradiance and power distributions in the near field and in the vicinity of the focus for Gaussian beams focused through annular apertures. Universal curves have been plotted which display the calculations in terms of dimensionless parameters. For very large focal length infrared systems it has been found that the irradiance distribution is not symmetrical about the geometrical focal plane as is commonly assumed. Gaussian and sinusoidal phase aberrations in the aperture field have been included.

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Very short optical pulses, traveling in sharp-line resonant absorbers without change of shape, are investigated with a new approximation techmque. Instead of employing the lang-pulse or slowly varying envelope assumption, we have developed a method of approximation based on a series expansion in powers of a small parameter which is related to the electric field strength. The principal advantages of the method are its ability to treat very short pulses, and the simplicity with which it can be extended, both from lower to higher levels of approximation, and from one type of steady-state pulse to another. In this paper we use the approximation method to study very short pulses which require retention of the second-derivative terms in the Maxwell envelope and phase equations. Corrections to the well-known McCall-Hahn results are easily found to first order in the small parameter. As expected, the corrections begin to be important only for picosecond and shorter pulses.