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Applied Optics

Applied Optics


  • Vol. 39, Iss. 11 — Apr. 10, 2000
  • pp: 1681–1699

Communicating with Waves Between Volumes: Evaluating Orthogonal Spatial Channels and Limits on Coupling Strengths

David A. B. Miller  »View Author Affiliations

Applied Optics, Vol. 39, Issue 11, pp. 1681-1699 (2000)

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A rigorous method for finding the best-connected orthogonal communication channels, modes, or degrees of freedom for scalar waves between two volumes of arbitrary shape and position is derived explicitly without assuming planar surfaces or paraxial approximations. The communication channels are the solutions of two eigenvalue problems and are identical to the cavity modes of a double phase-conjugate resonator. A sum rule for the connection strengths is also derived, the sum being a simple volume integral. These results are used to analyze rectangular prism volumes, small volumes, thin volumes in different relative orientations, and arbitrary near-field volumes: all situations in which previous planar approaches have failed for one or more reasons. Previous planar results are reproduced explicitly, extending them to finite depth. Depth is shown not to increase the number of communications modes unless the volumes are close when compared with their depths. How to estimate the connection strengths in some cases without a full solution of the eigenvalue problem is discussed so that estimates of the number of usable communications modes can be made from the sum rule. In general, the approach gives a rigorous basis for handling problems related to volume sources and receivers. It may be especially applicable in near-field problems and in situations in which volume is an intrinsic part of the problem.

© 2000 Optical Society of America

OCIS Codes
(110.2990) Imaging systems : Image formation theory
(260.1960) Physical optics : Diffraction theory

David A. B. Miller, "Communicating with Waves Between Volumes: Evaluating Orthogonal Spatial Channels and Limits on Coupling Strengths," Appl. Opt. 39, 1681-1699 (2000)

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  1. I previously have briefly presented the derivation of the communications modes and the sum rule in D. A. B. Miller, “Spatial channels for communicating with waves between volumes,” Opt. Lett. 23, 1645–1647 (1998), and in summary form in D. A. B. Miller, “Communicating with waves between volumes—how many different spatial channels are there?” in Optics in Computing ’98, P. Chavel, D. A. B. Miller, and H. Thienpont, eds., Proc. SPIE 3490, 111–114 (1998).
  2. R. Piestun and D. A. B. Miller, “Degrees of freedom of an electromagnetic wave,” in Eighteenth Congress of the International Commission for Optics, A. J. Glass, J. W. Goodman, M. Chang, A. H. Guenther, and T. Asakura, eds., Proc. SPIE 3749, 110–111 (1999); R. Piestun and D. A. B. Miller, “Electromagnetic degrees of freedom of an optical system,” J. Opt. Soc. Am. A (to be published).
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  7. I omit here for simplicity the two distinct phases and, in the case of light, the two distinct polarizations, the effects of each of which can be viewed as doubling the number of degrees of freedom.
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  20. See, for example, D. Porter and D. S. G. Stirling, Integral Equations (Cambridge U. Press, Cambridge, 1990), for a discussion of these issues.
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  25. The phase-conjugate cavity discussed here has two phase-conjugating mirrors. This configuration differs from the situation with one phase-conjugating mirror and one conventional mirror that is more extensively discussed in the literature. The case with two phase-conjugate mirrors is briefly discussed in, for example, J. F. Lam and W. P. Brown, “Optical resonators with phase-conjugate mirrors,” Opt. Lett. 2, 61–63 (1980).

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