Abstract

The fundamental laws of wave propagation at an interface, the laws of reflection, refraction, and diffraction are arrived at from a consideration of wave scattering from an array of scattering centers. It is shown that the number, spacing, and dimension of the scattering centers decide whether the laws of reflection and refraction or the more comprehensive law of normal scattering is obeyed. An exact equation for the summation of the phases and amplitudes of scattered waves arriving at a point is developed. Scattered ray directions are arrived at from the analytical behavior of this equation, and the region of validity of the solutions is discussed. It is shown that the length of the array plays as important a role as the spacing of the scattering centers. The modulation of diffracted ray intensity with an increase in scattering center size is identified and investigated. An expression for far-field distance is arrived at based on numerical simulation and is valid for all scattered angles.

© 2006 Optical Society of America

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