Polarization and coherence for vectorial electromagnetic waves and the ray picture of light propagation

A. Luis

doi:10.2971/jeos.2007.07030

Journal of the European Optical Society - Rapid publications, Vol 2 (2007)

Polarization and coherence for vectorial electromagnetic waves and the ray picture of light propagation

A. Luis

Abstract

We develop a complete geometrical picture of paraxial light propagation including coherence phenomena. This approach applies both for scalar and vectorial waves via the introduction of a suitable Wigner function and can be formulated in terms of an inverted Huygens principle. Coherence is included by allowing the geometrical rays to transport generalized Stokes parameters. The degree of coherence for scalar and vectorial light can be expressed as simple functions of the corresponding Wigner function.

Full Text: PDF

Citation Details

Cite this article

References

A. Luis, "Scalar Wigner function for vectorial fields and spatialangular Stokes parameters" Opt. Commun. 246, 437-443 (2005).

A. Luis, "Properties of spatial-angular Stokes parameters" Opt. Commun. 251, 243-253 (2005).

A. Luis, "Spatial-angular Mueller matrices" Opt. Commun. 263, 141- 146 (2006).

A. Luis, "Overall degree of coherence for vectorial electromagnetic fields and the Wigner function" J. Opt. Soc. Am. A 24, 2070-2074 (2007).

B. Karczewski, "Degree of coherence of the electromagnetic field" Phys. Lett. 5, 191-192 (1963).

E. Wolf, "Unified theory of coherence and polarization of random electromagnetic beams" Phys. Lett. A 312, 263-267 (2003).

S. A. Ponomarenko and E. Wolf, "The spectral degree of coherence of fully spatially coherent electromagnetic beams" Opt. Commun. 227, 73-74 (2003).

E. Wolf, "Comment on 'Complete electromagnetic coherence in the space-frequency domain" Opt. Lett. 29, 1712 (2004).

F. Gori, M. Santarsiero, and R. Borghi, "Maximizing Young's fringe visibility through reversible optical transformations" Opt. Lett. 32, 588-590 (2007).

F. Gori, M. Santarsiero, R. Borghi, and E. Wolf, "Effects of coherence on the degree of polarization in a Young interference pattern" Opt. Lett. 31, 688-670 (2006).

J. Tervo, T. Setälä, and A. T. Friberg, "Degree of coherence for electromagnetic fields" Opt. Express 11, 1137-1143 (2003).

T. Setälä, J. Tervo, and A. T. Friberg, "Complete electromagnetic coherence in the space-frequency domain" Opt. Lett. 29, 328-330 (2004).

T. Setälä, J. Tervo, and A. T. Friberg, "Reply to comment on 'Complete electromagnetic coherence in the space-frequency domain"' Opt. Lett. 29, 1713-1714 (2004).

P. Vahimaa and J. Tervo, "Unified measures for optical fields: degree of polarization and effective degree of coherence" J. Opt. A: Pure Appl. Op. 6, S41-S44 (2004).

T. Setälä, J. Tervo, and A. T. Friberg, "Stokes parameters and polarization contrasts in Young's interference experiment" Opt. Lett. 31, 2208-2210 (2006).

T. Setälä, J. Tervo, and A. T. Friberg, "Contrasts of Stokes parameters in Young's interference experiment and electromagnetic degree of coherence" Opt. Lett. 31, 2669-2671 (2006).

J. Tervo, T. Setälä, and A. T. Friberg, "Theory of partially coherentelectromagnetic fields in the space-frequency domain" J. Opt. Soc. Am. A 21, 2205-2215 (2004).

P. Réfrégier and F. Goudail, "Invariant degrees of coherence of partially polarized light" Opt. Express 13, 6051-6060 (2005).

P. Réfrégier and A. Roueff, "Coherence polarization filtering and relation with intrinsic degrees of coherence" Opt. Lett. 31, 1175- 1177 (2006).

P. Réfrégier, "Symmetries in coherence theory of partially polarized light" J. Math. Phys. 48, 033303 (2007).

H. M. Ozaktas, S. Yüksel, and M. A. Kutay, "Linear algebraic theory of partial coherence: discrete fields and measures of partial coherence" J. Opt. Soc. Am. A 19, 1563-1571 (2002).

A. Luis, "Degree of coherence for vectorial electromagnetic fields as the distance between correlation matrices" J. Opt. Soc. Am. A 24, 1063-1068 (2007).

A. Luis, "Ray picture of polarization and coherence in a Young interferometer" J. Opt. Soc. Am. A 23, 2855-2860 (2006).

D. Dragoman, "The Wigner distribution function in optics and optoelectronics" Prog. Optics 37, 1-56 (1997).

A. Torre, Linear Ray and Wave Optics in Phase Space (Elsevier, Amsterdam, The Netherlands, 2005).

M. J. Bastiaans, "The Wigner distribution function applied to optical signals and systems" Opt. Commun. 25, 26-30 (1978).

M. J. Bastiaans, "Wigner distribution function and its application to first-order optics" J. Opt. Soc. Am. 69, 1710-1716 (1979).

R. Simon and N. Mukunda, "Optical phase space, Wigner representation, and invariant quality parameters" J. Opt. Soc. Am. A 17, 2440-2463 (2000).

A. T. Friberg, "On the existence of a radiance function for finite planar sources of arbitrary states of coherence" J. Opt. Soc. Am. A 69, 192-198 (1979).

E. C. G. Sudarshan, "Quantum theory of radiative transfer" Phys. Rev. A 23, 2802-2809 (1981).

E. C. G. Sudarshan, "Quantum electrodynamics and light rays" Physica A 96, 315-320 (1979).

E. C. G. Sudarshan, "Pencils of rays in wave optics" Phys. Lett. A 73, 269-272 (1979).

A. Luis, "Complementary Huygens principle for geometrical and nongeometrical optics" Eur. J. Phys. 28, 231-240 (2007).

M. J. Bastiaans, "New class of uncertainty relations for partially coherent light" J. Opt. Soc. Am. A 1, 711-715 (1984).

M. J. Bastiaans, "Application of the Wigner distribution function to partially coherent light" J. Opt. Soc. Am. A 3, 1227-1238 (1986).

H. Lajunen, P. Vahimaa, and J. Tervo, "Theory of spatially and spectrally partially coherent pulses" J. Opt. Soc. Am. A 22, 1536- 1545 (2005).

M. A. Alonso, "Radiometry and wide-angle wave fields III: partial coherence" J. Opt. Soc. Am. A 18, 2502-2511 (2001).

A. Luis, "Negativity, diffraction and interference for nongeometrical waves" Opt. Commun. 266, 426-432 (2006).

J. C. Várilly and J. M. Gracia-Bondía, "The Moyal representation for spin" Ann. Phys. (N. Y.) 190, 107-148 (1989).

J. M. Gracia-Bondía, T. W. Marshall, and E. Santos, "A phase-space description of the Stern-Gerlach phenomenon" Phys. Lett. A 183, 19-23 (1993).

J. M. Gracia-Bondía and J. C. Várilly, "Phase-space representation for Galilean quantum particles of arbitrary spin" J. Phys. A 21, L879- L884 (1988).

A. Luis, "Polarization ray picture of coherence for vectorial electromagnetic waves" Phys. Rev. A 76, 043827 (2007).

R. Martínez-Herrero and P. M. Mejías, "Maximum visibility under unitary transformations in two-pinhole interference for electromagnetic fields" Opt. Lett. 32, 1471-1473 (2007).

F. Gori, M. Santarsiero, and R. Borghi, "Vector mode analysis of a Young interferometer" Opt. Lett. 31, 858-860 (2006).

M. Santarsiero, F. Gori, R. Borghi, and G. Guattari, "Vector-mode analysis of symmetric two-point sources" J. Opt. A: Pure Appl. Op. 9, 593-602 (2007).

R. Barakat, "Degree of polarization and the principal idempotents of the coherency matrix" Opt. Commun. 23, 147-150 (1977).

J. C. Samson and J. V. Olson, "Generalized Stokes vectors and generalized power spectra for second-order stationary vectorprocesses" SIAM J. Appl. Math. 40, 137-149 (1981).

A. Luis, "Maximum visibility in interferometers illuminated by vectorial waves" Opt. Lett. 32, 2191-2193 (2007).