## Spatial channels for communicating with waves between volumes

Optics Letters, Vol. 23, Issue 21, pp. 1645-1647 (1998)

http://dx.doi.org/10.1364/OL.23.001645

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### Abstract

I show that there is an exact, complete method for finding the orthogonal spatial channels, or communications modes, between two arbitrary volumes, and the associated connection strengths, for the case of scalar waves. I also show that the sum of the squared connection strengths is given exactly by a simple volume integral. The method is illustrated by a calculation for a particular extreme pair of volumes, and the communications modes are interpreted physically as the modes of a double phase-conjugate resonator.

© 1998 America

**OCIS Codes**

(110.2990) Imaging systems : Image formation theory

(190.5040) Nonlinear optics : Phase conjugation

(260.1960) Physical optics : Diffraction theory

(350.7420) Other areas of optics : Waves

**Citation**

David A. B. Miller, "Spatial channels for communicating with waves between volumes," Opt. Lett. **23**, 1645-1647 (1998)

http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-23-21-1645

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### References

- D. Gabor, in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1961), Vol. 1, pp. 109–153.
- G. Toraldo di Francia, J. Opt. Soc. Am. 59, 799 (1969).
- General results have also been derived for arbitary shapes of apertures in the eigenfunction picture in the study of propagation through atmospheric turbulence; see, e.g., J. H. Shapiro, in Laser Beam Propagation in the Atmosphere, J. W. Strohbehm, ed. (Springer-Verlag, Berlin, 1978), pp. 171–222.
- It is possible to use one source type rigorously over a closed surface for the case of phase fronts; see D. A. B. Miller, Opt. Lett. 16, 1370 (1991).
- Portions of this research were presented in D. A. B. Miller, Proc. SPIE 3490, 111–114 (1998).
- See, e.g., D. Porter and D. S. G. Stirling, Integral Equations (Cambridge U. Press, Cambridge, 1990), for a discussion of these issues.
- R. Courant and D. Hilbert, Methods of Mathematical Physics, Wiley Classics ed. (Wiley, New York, 1989).
- This process of finding the communications modes is analogous to singular value decomposition of the matrix gji ; to prove the existence and completeness of the sets of eigenfunctions, however, requires results from functional analysis and hence an integral representation of the problem.

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