Coherent-mode decomposition of partially polarized, partially coherent sources

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It is shown that any partially polarized, partially coherent source can be expressed in terms of a suitable superposition of transverse coherent modes with orthogonal polarization states. Such modes are determined through the solution of a system of two coupled integral equations. An example, for which the modal decomposition is obtained in closed form in terms of fully linearly polarized Hermite Gaussian modes, is given.
© 2003 Optical Society of America. One of the authors (G. Piquero) acknowledges support from the project BFM2001-1356.
1. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, Cambridge, UK, 1995). 2. R. Gase, T. Gase, and K. Blüthner, “Complex wave-field reconstruction by means of the Page distribution function”, Opt. Lett. 20, 2045–2047 (1995). 3. G. Iaconis and I. A. Walmsley, “Direct measurement of the two-point field correlation function”, Opt. Lett. 21, 1783–1785 (1996). 4. J. Tu and S. Tamura, “Analytic relation for recovering the mutual intensity by means of intensity information”, J. Opt. Soc. Am. A 15, 202–206 (1998). 5. J. Turunen, E. Tervonen, and A. T. Friberg, “Coherence theoretic algorithm to determine the transverse-mode structure of lasers”, Opt. Lett. 14, 627–629 (1989). 6. E. Tervonen, J. Turunen, and A. T. Friberg, “Transverse laser-mode structure determination from spatial coherence measurements: experimental results”, Appl. Phys. B 49, 409–414 (1989). 7. A. E. Siegman and S. W. Townsend, “Output beam propagation and beam quality from a multimode stable-cavity laser”, IEEE J. Quantum Electron. 29, 1212–1217 (1993). 8. B. Lü, B. Zhang, B. Cai, and C. Yang, “A simple method for estimating the number of effectively oscillating modes and weighting factors of mixed mode laser beams behaving like Gaussian Schell-model beams”, Opt. Commun. 101, 49–52 (1993). 9. A. Cutolo, T. Isernia, I. Izzo, R. Pierri, and L. Zeni, “Transverse mode analysis of a laser beam by near- and far-field intensity measurements”, Appl. Opt. 34, 7974–7978 (1995). 10. C. Martínez, F. Encinas-Sanz, J. Serna, P. M. Mejías, and R. Martínez-Herrero, “On the parametric characterization of the transversal spatial structure of laser pulses”, Opt. Commun. 139, 299–305 (1997). 11. F. Encinas-Sanz, J. Serna, C. Martínez, R. Martínez-Herrero, and P. M. Mejías, “Time-varying beam quality factor and mode evolution in TEA CO2 laser pulses”, IEEE J. Quantum Electron. 34, 1835–1838 (1998). 12. C. Martínez, J. Serna, F. Encinas-Sanz, R. Martínez-Herrero, and P. M. Mejías, “Time-resolved spatial structure of TEA CO2 laser pulses”, Opt. Quantum Electron. 32, 18–30 (2000). 13. R. Borghi and M. Santarsiero, “Modal decomposition of partially coherent flat-topped beams produced by multimode lasers”, Opt. Lett. 23, 313–315 (1998). 14. F. Gori, M. Santarsiero, R. Borghi, and G. Guattari, “Intensity-based modal analysis for partially coherent beams with Hermite–Gaussian modes”, Opt. Lett. 23, 989–991 (1998). 15. M. Santarsiero, F. Gori, R. Borghi, and G. Guattari, “Evaluation of the modal structure for light beams with Hermite–Gaussian modes”, Appl. Opt. 38, 5272–5281 (1999). 16. R. Borghi and M. Santarsiero, “Modal structure analysis for a class of axially symmetric flat-topped laser beams”, IEEE J. Quantum Electron. 35, 745–750 (1999). 17. M. Santarsiero, F. Gori, and R. Borghi, “Modal-weight determination for a class of multimode beams”, in Laser Beam and Optics Characterization, H. Weber and H. Laabs, eds. (Optisches Institut, Technische Universität Berlin, Berlin, 2000), pp. 161–170. 18. X. Xue, H. Wei, and A. G. Kirk, “Intensity-based modal decomposition of optical beams in terms of Hermite–Gaussian functions”, J. Opt. Soc. Am. A 17, 1086–1091 (2000). 19. H. Laabs, B. Eppich, and H. Weber, “Modal decomposition of partially coherent beams using the ambiguity function”, J. Opt. Soc. Am. A 19, 497–504 (2002). 20. D. F. V. James, “Change of polarization of light beam on propagation in free space”, J. Opt. Soc. Am. A 11, 1641–1643 (1994). 21. D. F. V. James, “Polarization of light radiated by black-body sources”, Opt. Commun. 109, 209–214 (1994). 22. C. Olson, P. L. Greene, G. W. Wicks, D. G. Hall, and S. Rishton, “High-order azimuthal spatial modes of concentric-circle-grating surface-emitting semiconductor lasers”, Appl. Phys. Lett. 72, 1284–1286 (1998). 23. R. Martínez-Herrero, P. M. Mejías, and J. M. Movilla, “Spatial characterization of partially polarized beams”, Opt. Lett. 22, 206–208 (1997). 24. A. A. Tovar, “Production and propagation of cylindrically polarized Laguerre Gaussian laser beams”, J. Opt. Soc. Am. A 15, 2705–2711 (1998). 25. F. Gori, “Matrix treatment for partially polarized, partially coherent beams”, Opt. Lett. 23, 241 (1998). 26. F. Gori, M. Santarsiero, S. Vicalvi, R. Borghi, and G. Guattari, “Beam coherence-polarization matrix”, J. Eur. Opt. Soc. A Pure Appl. Opt., 7, 941–951 (1998). 27. F. Gori, M. Santarsiero, G. Piquero, R. Borghi, A. Mondello, and R. Simon, “Partially polarized Gaussian Schell-model beams”, J. Opt. Pure Appl. Opt. 3, 1–9 (2001). 28. J. Pu and B. Lu, “Focal shifts in focused nonuniformly polarized beams”, J. Opt. Soc. Am. A 18, 2760–2766 (2001). 29. F. Gori, G. Guattari, C. Palma, and C. Padovani, “Specular cross-spectral density functions”, Opt. Commun. 68, 239–243 (1988). 30. S. K. Berberian, Introduction to Hilbert Space (Oxford U. Press, Oxford, UK, 1961). 31. E. Kreyszig, Introductory Functional Analysis with Applications (Wiley, New York, 1978). 32. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, UK, 1999). 33. E. Wolf, “New theory of partial coherence in the space-frequency domain. Part I: Spectra and cross-spectra of steady-state sources”, J. Opt. Soc. Am. 72, 343–351 (1982). 34. C. Cohen-Tannoudji, B. Diu, and F. Laloe, Quantum Mechanics (Wiley, Paris, 1977). 35. F. Gori, M. Santarsiero, R. Borghi, and G. Guattari, “The irradiance of partially polarized beams in a scalar treatment”, Opt. Commun. 163, 159–163 (1999). 36. C. Brosseau, Fundamentals of Polarized Light (Wiley, New York, 1998). 37. F. Gori, “Collett–Wolf sources and multimode laser”, Opt. Commun. 34, 301–305 (1980). 38. A. Starikov and E. Wolf, “Coherent-mode representation of Gaussian Schell-model sources and of their radiation fields”, J. Opt. Soc. Am. 72, 923–928 (1982). 39. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972). 40. F. Gori, “Mode propagation of the field generated by Collet–Wolf Schell-model sources”, Opt. Commun. 46, 149–154 (1983).