Abstract

Points within a fully coherent complex scalar optical field, where the amplitude is identically zero but the optical phase has a jump discontinuity, have been widely investigated by the singular-optics community. More recent researches have extended the domain of singular optics to include partially coherent fields. For example, in coherence vortices the phase of the two-point spectral degree of coherence of a partially coherent field exhibits vortex structure around a point where the magnitude of the spectral degree of coherence vanishes. We show that the spectral degree of coherence of Mie scattered partially coherent statistically stationary electromagnetic fields exhibits a rich set of coherence vortices in both the internal and external fields. Specifically, we look at Mie scattering of a stationary beam from a dielectric sphere and study the formation of coherence vortices and their evolution with both the properties of the scattering sphere, and of the incident partially coherent beam.

© 2010 Optical Society of America

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    [CrossRef]

2009 (8)

G. C. G. Berkhout and M. W. Beijersbergen, "Using a multipoint interferometer to measure the orbital angular momentum of light in astrophysics," J. Opt. A: Pure Appl. Opt. 11, 094021 (2009).
[CrossRef]

G. A. Swartzlander, "The optical vortex coronagraph," J. Opt. A: Pure Appl. Opt. 11, 094022 (2009).
[CrossRef]

C. Maurer and S. Bernet and M. Ritsch-Marte, "Refining common path interferometry with a spiral-phase Fourier filter," J. Opt. A: Pure Appl. Opt. 11, 094023 (2009).
[CrossRef]

W. A. Wozniak and M. Banach, "Measurements of linearly birefringent media parameters using the optical vortex interferometer with the Wollaston compensator," J. Opt. A: Pure Appl. Opt. 11, 094024 (2009).
[CrossRef]

Y. Gu and G. Gbur, "Topological reactions of optical correlation vortices," Opt. Commun. 282, 709-716 (2009).
[CrossRef]

R. W. Schoonover, B. J. Davis, and P. S. Carney, "The generalized Wolf shift for cyclostationary fields," Opt. Express 17, 4705-4711 (2009).
[CrossRef]

C. R. Fernandez-Pousa, "Intensity spectra after first-order dispersion of composite models of scalar cyclostationary light," J. Opt. Soc. Am. A 26, 993-1007 (2009).
[CrossRef]

V. Manea, "General interference law for nonstationary, separable optical fields," J. Opt. Soc. Am. A 26, 1907-1914 (2009).
[CrossRef]

2007 (2)

P. Kwee, F. Seifert, B. Willke and K. Danzmann, "Laser beam quality and pointing measurement with an optical resonator," Rev. Sci. Instrum. 78, 073103 (2007).
[CrossRef]

B. J. Davis, "Observable coherence theory for statistically periodic fields," Phys. Rev. A 76, 043843 (2007).
[CrossRef]

2006 (2)

W. Gardner, A. Napolitano, and L. Paura, "Cyclostationarity: Half a Century of Research," Signal Process. 86, 639-697 (2006).
[CrossRef]

G. Gbur and T. D. Visser, "Phase singularities and coherence vortices in linear optical systems," Opt. Commun. 259, 428-435 (2006).
[CrossRef]

2004 (3)

G. Gbur, T. Visser and E. Wolf, "‘Hidden’ singularities in partially coherent wavefields," J. Opt. A: Pure Appl. Opt. 6, S239-S242 (2004).
[CrossRef]

D. M. Palacios, I. D. Maleev, A. S. Marathay and G. A. Swartzlander, "Spatial correlation singularity of a vortex field," Phys. Rev. Lett. 92, 143905 (2004).
[CrossRef]

D. G. Fischer and T. D. Visser, "Spatial correlation properties of focused partially coherent fields," J. Opt. Soc. Am. A 21, 2097-2102 (2004).
[CrossRef]

2003 (3)

2001 (1)

L. J. Allen, H. M. L. Faulkner, M. P. Oxley, and D. Paganin, "Phase retrieval and aberration correction in the presence of vortices in high-resolution transmission electron microscopy," Ultramicroscopy 88, 85-97 (2001).
[CrossRef]

2000 (1)

M. V. Berry, "Making waves in physics: three wave singularities from the miraculous 1830s," Nature 403, 21 (2000).
[CrossRef]

1996 (1)

M. Levesque, A. Mailloux, M. Morin, P. Galarneau, Y. Champagne, O. Plomteux and M. Tiedtke, "Laser pointing stability measurements," Proc. SPIE 2870, 216-224 (1996).

1994 (1)

1974 (1)

J. F. Nye and M. V. Berry, "Dislocations in wave trains," Proc. Roy. Soc. Lond. A 336, 165-190 (1974).
[CrossRef]

1931 (1)

P. A. M. Dirac, "Quantised singularities in the electromagnetic field," Proc. Roy. Soc. Lond. A 133, 60-72 (1931).
[CrossRef]

1908 (1)

G. Mie, "Beitrage zur Optik Truber Medien speziell kolloidaler Metallosungen," Ann. Phys. 25, 377-442 (1908).
[CrossRef]

Allen, L. J.

L. J. Allen, H. M. L. Faulkner, M. P. Oxley, and D. Paganin, "Phase retrieval and aberration correction in the presence of vortices in high-resolution transmission electron microscopy," Ultramicroscopy 88, 85-97 (2001).
[CrossRef]

Banach, M.

W. A. Wozniak and M. Banach, "Measurements of linearly birefringent media parameters using the optical vortex interferometer with the Wollaston compensator," J. Opt. A: Pure Appl. Opt. 11, 094024 (2009).
[CrossRef]

Beijersbergen, M. W.

G. C. G. Berkhout and M. W. Beijersbergen, "Using a multipoint interferometer to measure the orbital angular momentum of light in astrophysics," J. Opt. A: Pure Appl. Opt. 11, 094021 (2009).
[CrossRef]

Berkhout, G. C. G.

G. C. G. Berkhout and M. W. Beijersbergen, "Using a multipoint interferometer to measure the orbital angular momentum of light in astrophysics," J. Opt. A: Pure Appl. Opt. 11, 094021 (2009).
[CrossRef]

Bernard, P.

Bernet, S.

C. Maurer and S. Bernet and M. Ritsch-Marte, "Refining common path interferometry with a spiral-phase Fourier filter," J. Opt. A: Pure Appl. Opt. 11, 094023 (2009).
[CrossRef]

Berry, M. V.

M. V. Berry, "Making waves in physics: three wave singularities from the miraculous 1830s," Nature 403, 21 (2000).
[CrossRef]

J. F. Nye and M. V. Berry, "Dislocations in wave trains," Proc. Roy. Soc. Lond. A 336, 165-190 (1974).
[CrossRef]

Bogatyryova, G. V.

Carney, P. S.

Champagne, Y.

M. Levesque, A. Mailloux, M. Morin, P. Galarneau, Y. Champagne, O. Plomteux and M. Tiedtke, "Laser pointing stability measurements," Proc. SPIE 2870, 216-224 (1996).

Danzmann, K.

P. Kwee, F. Seifert, B. Willke and K. Danzmann, "Laser beam quality and pointing measurement with an optical resonator," Rev. Sci. Instrum. 78, 073103 (2007).
[CrossRef]

Davis, B. J.

R. W. Schoonover, B. J. Davis, and P. S. Carney, "The generalized Wolf shift for cyclostationary fields," Opt. Express 17, 4705-4711 (2009).
[CrossRef]

B. J. Davis, "Observable coherence theory for statistically periodic fields," Phys. Rev. A 76, 043843 (2007).
[CrossRef]

Dirac, P. A. M.

P. A. M. Dirac, "Quantised singularities in the electromagnetic field," Proc. Roy. Soc. Lond. A 133, 60-72 (1931).
[CrossRef]

Faulkner, H. M. L.

L. J. Allen, H. M. L. Faulkner, M. P. Oxley, and D. Paganin, "Phase retrieval and aberration correction in the presence of vortices in high-resolution transmission electron microscopy," Ultramicroscopy 88, 85-97 (2001).
[CrossRef]

Felde, C. V.

Fern’andez-Pousa, C. R.

Fischer, D. G.

Galarneau, P.

M. Levesque, A. Mailloux, M. Morin, P. Galarneau, Y. Champagne, O. Plomteux and M. Tiedtke, "Laser pointing stability measurements," Proc. SPIE 2870, 216-224 (1996).

M. Morin, P. Bernard and P. Galarneau, "Moment definition of the pointing stability of a laser beam," Opt. Lett. 19, 1379-1381 (1994).
[CrossRef]

Gardner, W.

W. Gardner, A. Napolitano, and L. Paura, "Cyclostationarity: Half a Century of Research," Signal Process. 86, 639-697 (2006).
[CrossRef]

Gbur, G.

Y. Gu and G. Gbur, "Topological reactions of optical correlation vortices," Opt. Commun. 282, 709-716 (2009).
[CrossRef]

G. Gbur and T. D. Visser, "Phase singularities and coherence vortices in linear optical systems," Opt. Commun. 259, 428-435 (2006).
[CrossRef]

G. Gbur, T. Visser and E. Wolf, "‘Hidden’ singularities in partially coherent wavefields," J. Opt. A: Pure Appl. Opt. 6, S239-S242 (2004).
[CrossRef]

H. F. Schouten, G. Gbur, T. D. Visser, and E. Wolf, "Phase singularities of the coherence functions in Young’s interference pattern," Opt. Lett. 28, 968-970 (2003).
[CrossRef]

G. Gbur and T. D. Visser, "Coherence vortices in partially coherent beams," Opt. Commun. 222, 117-125 (2003).
[CrossRef]

Gu, Y.

Y. Gu and G. Gbur, "Topological reactions of optical correlation vortices," Opt. Commun. 282, 709-716 (2009).
[CrossRef]

Kwee, P.

P. Kwee, F. Seifert, B. Willke and K. Danzmann, "Laser beam quality and pointing measurement with an optical resonator," Rev. Sci. Instrum. 78, 073103 (2007).
[CrossRef]

Levesque, M.

M. Levesque, A. Mailloux, M. Morin, P. Galarneau, Y. Champagne, O. Plomteux and M. Tiedtke, "Laser pointing stability measurements," Proc. SPIE 2870, 216-224 (1996).

Mailloux, A.

M. Levesque, A. Mailloux, M. Morin, P. Galarneau, Y. Champagne, O. Plomteux and M. Tiedtke, "Laser pointing stability measurements," Proc. SPIE 2870, 216-224 (1996).

Maleev, I. D.

D. M. Palacios, I. D. Maleev, A. S. Marathay and G. A. Swartzlander, "Spatial correlation singularity of a vortex field," Phys. Rev. Lett. 92, 143905 (2004).
[CrossRef]

Manea, V.

Marathay, A. S.

D. M. Palacios, I. D. Maleev, A. S. Marathay and G. A. Swartzlander, "Spatial correlation singularity of a vortex field," Phys. Rev. Lett. 92, 143905 (2004).
[CrossRef]

Maurer, C.

C. Maurer and S. Bernet and M. Ritsch-Marte, "Refining common path interferometry with a spiral-phase Fourier filter," J. Opt. A: Pure Appl. Opt. 11, 094023 (2009).
[CrossRef]

Mie, G.

G. Mie, "Beitrage zur Optik Truber Medien speziell kolloidaler Metallosungen," Ann. Phys. 25, 377-442 (1908).
[CrossRef]

Morin, M.

M. Levesque, A. Mailloux, M. Morin, P. Galarneau, Y. Champagne, O. Plomteux and M. Tiedtke, "Laser pointing stability measurements," Proc. SPIE 2870, 216-224 (1996).

M. Morin, P. Bernard and P. Galarneau, "Moment definition of the pointing stability of a laser beam," Opt. Lett. 19, 1379-1381 (1994).
[CrossRef]

Napolitano, A.

W. Gardner, A. Napolitano, and L. Paura, "Cyclostationarity: Half a Century of Research," Signal Process. 86, 639-697 (2006).
[CrossRef]

Nye, J. F.

J. F. Nye and M. V. Berry, "Dislocations in wave trains," Proc. Roy. Soc. Lond. A 336, 165-190 (1974).
[CrossRef]

Oxley, M. P.

L. J. Allen, H. M. L. Faulkner, M. P. Oxley, and D. Paganin, "Phase retrieval and aberration correction in the presence of vortices in high-resolution transmission electron microscopy," Ultramicroscopy 88, 85-97 (2001).
[CrossRef]

Paganin, D.

L. J. Allen, H. M. L. Faulkner, M. P. Oxley, and D. Paganin, "Phase retrieval and aberration correction in the presence of vortices in high-resolution transmission electron microscopy," Ultramicroscopy 88, 85-97 (2001).
[CrossRef]

Palacios, D. M.

D. M. Palacios, I. D. Maleev, A. S. Marathay and G. A. Swartzlander, "Spatial correlation singularity of a vortex field," Phys. Rev. Lett. 92, 143905 (2004).
[CrossRef]

Paura, L.

W. Gardner, A. Napolitano, and L. Paura, "Cyclostationarity: Half a Century of Research," Signal Process. 86, 639-697 (2006).
[CrossRef]

Plomteux, O.

M. Levesque, A. Mailloux, M. Morin, P. Galarneau, Y. Champagne, O. Plomteux and M. Tiedtke, "Laser pointing stability measurements," Proc. SPIE 2870, 216-224 (1996).

Polyanskii, P. V.

Ponomarenko, S. A.

Ritsch-Marte, M.

C. Maurer and S. Bernet and M. Ritsch-Marte, "Refining common path interferometry with a spiral-phase Fourier filter," J. Opt. A: Pure Appl. Opt. 11, 094023 (2009).
[CrossRef]

Schoonover, R. W.

Schouten, H. F.

Seifert, F.

P. Kwee, F. Seifert, B. Willke and K. Danzmann, "Laser beam quality and pointing measurement with an optical resonator," Rev. Sci. Instrum. 78, 073103 (2007).
[CrossRef]

Soskin, M. S.

Swartzlander, G. A.

G. A. Swartzlander, "The optical vortex coronagraph," J. Opt. A: Pure Appl. Opt. 11, 094022 (2009).
[CrossRef]

D. M. Palacios, I. D. Maleev, A. S. Marathay and G. A. Swartzlander, "Spatial correlation singularity of a vortex field," Phys. Rev. Lett. 92, 143905 (2004).
[CrossRef]

Tiedtke, M.

M. Levesque, A. Mailloux, M. Morin, P. Galarneau, Y. Champagne, O. Plomteux and M. Tiedtke, "Laser pointing stability measurements," Proc. SPIE 2870, 216-224 (1996).

Visser, T.

G. Gbur, T. Visser and E. Wolf, "‘Hidden’ singularities in partially coherent wavefields," J. Opt. A: Pure Appl. Opt. 6, S239-S242 (2004).
[CrossRef]

Visser, T. D.

G. Gbur and T. D. Visser, "Phase singularities and coherence vortices in linear optical systems," Opt. Commun. 259, 428-435 (2006).
[CrossRef]

D. G. Fischer and T. D. Visser, "Spatial correlation properties of focused partially coherent fields," J. Opt. Soc. Am. A 21, 2097-2102 (2004).
[CrossRef]

G. Gbur and T. D. Visser, "Coherence vortices in partially coherent beams," Opt. Commun. 222, 117-125 (2003).
[CrossRef]

H. F. Schouten, G. Gbur, T. D. Visser, and E. Wolf, "Phase singularities of the coherence functions in Young’s interference pattern," Opt. Lett. 28, 968-970 (2003).
[CrossRef]

Willke, B.

P. Kwee, F. Seifert, B. Willke and K. Danzmann, "Laser beam quality and pointing measurement with an optical resonator," Rev. Sci. Instrum. 78, 073103 (2007).
[CrossRef]

Wolf, E.

Wozniak, W. A.

W. A. Wozniak and M. Banach, "Measurements of linearly birefringent media parameters using the optical vortex interferometer with the Wollaston compensator," J. Opt. A: Pure Appl. Opt. 11, 094024 (2009).
[CrossRef]

Ann. Phys. (1)

G. Mie, "Beitrage zur Optik Truber Medien speziell kolloidaler Metallosungen," Ann. Phys. 25, 377-442 (1908).
[CrossRef]

J. Opt. A: Pure Appl. Opt. (5)

G. C. G. Berkhout and M. W. Beijersbergen, "Using a multipoint interferometer to measure the orbital angular momentum of light in astrophysics," J. Opt. A: Pure Appl. Opt. 11, 094021 (2009).
[CrossRef]

G. A. Swartzlander, "The optical vortex coronagraph," J. Opt. A: Pure Appl. Opt. 11, 094022 (2009).
[CrossRef]

C. Maurer and S. Bernet and M. Ritsch-Marte, "Refining common path interferometry with a spiral-phase Fourier filter," J. Opt. A: Pure Appl. Opt. 11, 094023 (2009).
[CrossRef]

W. A. Wozniak and M. Banach, "Measurements of linearly birefringent media parameters using the optical vortex interferometer with the Wollaston compensator," J. Opt. A: Pure Appl. Opt. 11, 094024 (2009).
[CrossRef]

G. Gbur, T. Visser and E. Wolf, "‘Hidden’ singularities in partially coherent wavefields," J. Opt. A: Pure Appl. Opt. 6, S239-S242 (2004).
[CrossRef]

J. Opt. Soc. Am. A (3)

Nature (1)

M. V. Berry, "Making waves in physics: three wave singularities from the miraculous 1830s," Nature 403, 21 (2000).
[CrossRef]

Opt. Commun. (3)

G. Gbur and T. D. Visser, "Phase singularities and coherence vortices in linear optical systems," Opt. Commun. 259, 428-435 (2006).
[CrossRef]

Y. Gu and G. Gbur, "Topological reactions of optical correlation vortices," Opt. Commun. 282, 709-716 (2009).
[CrossRef]

G. Gbur and T. D. Visser, "Coherence vortices in partially coherent beams," Opt. Commun. 222, 117-125 (2003).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. A (1)

B. J. Davis, "Observable coherence theory for statistically periodic fields," Phys. Rev. A 76, 043843 (2007).
[CrossRef]

Phys. Rev. Lett. (1)

D. M. Palacios, I. D. Maleev, A. S. Marathay and G. A. Swartzlander, "Spatial correlation singularity of a vortex field," Phys. Rev. Lett. 92, 143905 (2004).
[CrossRef]

Proc. Roy. Soc. Lond. A (2)

J. F. Nye and M. V. Berry, "Dislocations in wave trains," Proc. Roy. Soc. Lond. A 336, 165-190 (1974).
[CrossRef]

P. A. M. Dirac, "Quantised singularities in the electromagnetic field," Proc. Roy. Soc. Lond. A 133, 60-72 (1931).
[CrossRef]

Proc. SPIE (1)

M. Levesque, A. Mailloux, M. Morin, P. Galarneau, Y. Champagne, O. Plomteux and M. Tiedtke, "Laser pointing stability measurements," Proc. SPIE 2870, 216-224 (1996).

Rev. Sci. Instrum. (1)

P. Kwee, F. Seifert, B. Willke and K. Danzmann, "Laser beam quality and pointing measurement with an optical resonator," Rev. Sci. Instrum. 78, 073103 (2007).
[CrossRef]

Signal Process. (1)

W. Gardner, A. Napolitano, and L. Paura, "Cyclostationarity: Half a Century of Research," Signal Process. 86, 639-697 (2006).
[CrossRef]

Ultramicroscopy (1)

L. J. Allen, H. M. L. Faulkner, M. P. Oxley, and D. Paganin, "Phase retrieval and aberration correction in the presence of vortices in high-resolution transmission electron microscopy," Ultramicroscopy 88, 85-97 (2001).
[CrossRef]

Other (11)

D. M. Paganin, Coherent X-ray Optics (Oxford University Press, New York, 2006).

M. Mishchenko, L. Travis and A. Lacis, Scattering, Absorption, and Emission of Light by Small Particles, 3rd electronic release (Cambridge University Press, United Kingdom, 2002).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1983).

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University Press, Cambridge, 2007).

M. Soskin and M. Vasnetsov, "Singular optics," in Progress in Optics, E.Wolf, ed., (North-Holland, Amsterdam, 2001) Vol. 42, pp. 219-276.

G. Gbur, "Optical and coherence vortices and their relationships," in Eighth International Conference on Correlation Optics, M. Kujawinska and O. V. Angelsky, eds. Proc. SPIE 7008, 70080N-1-70080N-7 (2008).

C. Matlzer, "MATLAB functions for Mie scattering and absorption," IAP Res. Rep. No. 02-08, June (2002).

M. R. Dennis, K. O’Holleran and M. J. Padgett, "Singular optics: optical vortices and polarization singularities" in Progress in Optics, E. Wolf, ed., (North-Holland, Amsterdam, 2009) 53, 293-363.

J. F. Nye, Natural Focusing and Fine Structure of Light (Institute of Physics Publishing, 1999).

M. Born and E. Wolf, Principles of Optics, 7th (expanded) edition (Cambridge University Press, Cambridge, 1999).

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge University Press, Cambridge, 1995).

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