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Transmission of dipole radiation through interfaces and the phenomenon of anti-critical angles

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Abstract

The field of an oscillating electric dipole d, embedded in a medium with index of refraction n1, can be considered as a superposition of traveling and evanescent waves, when represented as an angular spectrum. For this representation we adopt the z-axis as the prefered direction in space, and we let the dipole be located on the z-axis at z = H (see figure). Each wave in the spectrum has a wave vector k, and we indicate by k|| the component of the wave vector parallel to the xy-plane. Then the angular spectrum is a superposition of plane waves running over all possible values of k||. Since the wave number of the radiation in medium n1 is k = n1 ω/ c , where ω is the angular frequency, the value of k|| can exceed the value of the wave number. Then the z-component of the wave vector is imaginary, and therefore these waves decay exponentially in amplitude in the directions away from the plane z = H. These are the evanescent waves, which will normally only contribute to the near field of the dipole.

© 2003 Optical Society of America

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