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Wave-front conversion between a Gaussian beam with a cylindrical phase function and a plane wave in a monomode on-axis transmission holographic coupler

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1993-12
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Optical Society of America
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We present a coupled-wave-analysis-based treatment for a wave-front conversion problem between a Gaussian beam with a cylindrical phase and a plane wave for a two-dimensional on-axis geometry. A coupled-wave approach to the multiple-scattering process in an inhomogeneous dielectric medium offers a clear physically interpretable description of the diffraction phenomena in volume media as well as the possibility of an intelligible mathematical treatment. An analytical integral solution for the amplitudes of the two modes of diffraction is submitted. High diffraction efficiency (≈1) and the deterioration of reconstruction fidelity are predicted. It is of interest to apply the model to the analysis and design of a monomode holographic fiber-to-fiber coupler, wave-front correctors, and holographic interconnection devices.
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© 1993 Optical Society of America. When this research was initiated, P. Cheben was a fellow from the Czechoslovak government-Complutense University exchange program. The authors appreciate the financial support from these institutions.
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1. B. Borrmann, “Über Extinktionsdiagramme von Quarz”, Phys. Z. 42, 157–162 (1941). 2. P. St. J. Russell, L. Solymar, “The properties of holographic overlap gratings”, Opt. Acta 26, 329–347 (1979). , 3. P. St. J. Russell, “Reconstruction fidelity from volume holograms of finite width and variable index modulation”,J. Opt. Soc. Am. 69, 496–503 (1979). , 4. M. P. Jordan, L. Solymar, “On the properties of a finite reflection type volume hologram”, Opt. Quantum Electron. 10, 503–507 (1978). , 5. P. St. Russell, “Volume holographic finite-beam conversion with perfect fidelity”, Opt. Acta 27, 997–1008 (1980). , 6. P. St. J. Russell, L. Solymar, M. P. Jordan, “Bormann-like effects in volume holography”, presented at ICO-11, Madrid, 1978. 7. L. Solymar, M. P. Jordan, “Two-dimensional transmission type volume holograms for incident plane waves of arbitrary amplitude distribution”, Opt. Quantum Electron. 9, 437–444 (1977). , 8. R. S. Chu, T. Tamir, “Diffraction of Gaussian beams by periodically modulated media for incidence close to a Bragg angle”,J. Opt. Soc. Am. 66, 1438–1440 (1976). , 9. R. S. Chu, T. Tamir, “Bragg diffraction of Gaussian beams by periodically modulated media”,J. Opt. Soc. Am. 66, 220–226 (1976). , 10. V. M. Serdyuk, “The effect of self-diffraction of the writing waves on the diffraction efficiency of volume holograms”, Sov. Phys. Tech. Phys. 34, 1097–1102 (1989). 11. S. Kusch, R. Güther, “Theorie der gekoppelten Wellen für Gauss-strahlen in der volumen Holographie”, Exp. Tech. Phys. 25, 73–78 (1976). 12. W. E. Parry, L. Solymar, “A general solution for two-dimensional volume holograms”, Opt. Quantum Electron. 9, 527–531 (1977). , 13. E. Guibelalde, M. L. Calvo, “A coupled wave analysis for on-axis holographic lenses in generalized coordinates”, Opt. Commun. 59, 331–34 (1986). , 14. L. Solymar, M. P. Jordan, “Analysis of cylindrical-to-plane wave conversion by volume holograms”, Electron. Lett. 12, 143–144 (1976). , 15. M. P. Jordan, L. Solymar, P. St. J. Russell, “Wavefront conversion by volume holograms between cylindrical and plane waves”, Microwaves Opt. Acoust. 2, 156–162 (1978). , 16. M. L. Calvo, P. Cheben, “High-efficiency off-axis holographic coupler”, Opt. Commun. 88, 22–26 (1992). , 17. H. Kogelnik, “Coupled wave theory for thick hologram gratings”, Bell Syst. Tech. J. 48, 2909–2947 (1969). 18. L. Solymar, D. J. Cooke, Volume Holography and Volume Gratings (Academic, Oxford, 1981). 19. In our case, τdepends mainly on the numerical aperture and the core diameter of the optical fiber as well as on the distance between the fiber output face and the input boundary of the hologram (τ≈ 10−2m can be considered in most practical cases). 20. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980). 21. In the on-axis case, when p1≈ p2, there is obviously a negligible influence of the nonzero absorption a on the solution of Eq. (19). In addition, it is self-evident that a small value of parameter Bis determined by this geometry. However, on the other hand, it is necessary to ensure the accomplishment of conditions that characterize the Bragg regime (see Ref. 18, p. 129). 22. R. Courant, D. Hilbert, Methods of Mathematical Physics (Interscience, New York, 1953), Vol. 1, Chap. 5. 23. Rigorous holographic coupler design would require estimation of the case in which the reconstructed wave is a Gaussian beam. This is what really occurs in the first half of the fiber-to-fiber coupler if two-step conversion is accomplished (Gaussian-beam to plane-wave to Gaussian-beam conversion). 24. P. Juncos del Egido, “Diffraction of electromagnetic waves by a volume hologram treated as a periodic grating”, Ph.D. dissertation (Universidad Complutense, Madrid, 1983). 25. Y. Defosse, Y. Renotte, Y. Lion, “Calculation of diffraction efficiencies for spherical and cylindrical holographical lenses”, in Holographical Optics III: Principles and Applications, G. M. Morris, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1507, 277–287 (1991). , 26. D. G. Feitelson, L. Rudolph, E. Schenfeld, “Limitations on optical free-space crossbar-like interconnection networks”, in Optical Interconnections and Networks, H. Bartelt, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1281, 41–52 (1990). , 27. D. Prongué, H. P. Herzig, “HOE for clock distribution in integrated circuits: experimental results”, in Optical Interconnections and Networks, H. Bartelt, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1281, 113–122 (1990). , 28. J. S. Leggatt, G. R. Chamberlin, D. E. Sheat, D. J. McCartney, “Holographically generated optical components for routeing and wavelength division multiplexing applications”, Optical Interconnections and Networks, H. Bartelt, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1281, 227–243 (1990).
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