Abstract

We present a new approach for solving diffraction problems by radial gratings. The method, which uses a Cartesian coordinate reference system, allows us to perform the diffraction integral without prior knowledge of the explicit form of the grating-transmission function. As a result of simple physical arguments, it is possible to find analytical expressions for the diffracted field; and therefore the characteristics of the intensity distribution, such as its astigmatism, orientation, and beamwaist position, can be analyzed by means of the properties of the solution. By comparing the curvature radius of the two sections of the diffracted beam with that of the incident beam, we found that the behavior of the ±1 diffraction order can be well explained by means of two effective focal lengths, which depend only on the angular period and the radius of the grating, as well as on the wavelength of the illuminating source. We performed experimental measurements and obtained good agreement between the theoretical predictions and the experimental results.

© 1993 Optical Society of America

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