Coherence vortices in Mie scattering of
statistically stationary partially coherent
fields

doi:10.1364/OE.18.006628

Coherence vortices in Mie scattering of statistically stationary partially coherent fields

Madara L. Marasinghe, Malin Premaratne, and David M. Paganin »View Author Affiliations

Optics Express, Vol. 18, Issue 7, pp. 6628-6641 (2010)
http://dx.doi.org/10.1364/OE.18.006628

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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.

OCIS Codes
(030.1640) Coherence and statistical optics : Coherence
(290.4020) Scattering : Mie theory
(290.5850) Scattering : Scattering, particles
(050.4865) Diffraction and gratings : Optical vortices
(260.6042) Physical optics : Singular optics

ToC Category:
Coherence and Statistical Optics

History
Original Manuscript: December 15, 2009
Revised Manuscript: February 19, 2010
Manuscript Accepted: March 8, 2010
Published: March 16, 2010

Citation
Madara L. Marasinghe, Malin Premaratne, and David M. Paganin, "Coherence vortices in Mie scattering of statistically stationary partially coherent fields," Opt. Express 18, 6628-6641 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-7-6628

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References

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).
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] [PubMed]
G. Gbur and T. D. Visser, "Coherence vortices in partially coherent beams," Opt. Commun. 222, 117-125 (2003). [CrossRef]
M. V. Berry, "Making waves in physics: three wave singularities from the miraculous 1830s," Nature 403, 21 (2000). [CrossRef] [PubMed]
J. F. Nye and M. V. Berry, "Dislocations in wave trains," Proc. Roy. Soc. Lond. A 336, 165-190 (1974). [CrossRef]
M. Soskin and M. Vasnetsov, "Singular optics," in Progress in Optics, E.Wolf, ed., (North-Holland, Amsterdam, 2001) Vol. 42, pp. 219-276. [CrossRef]
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]
P. A. M. Dirac, "Quantised singularities in the electromagnetic field," Proc. Roy. Soc. Lond. A 133, 60-72 (1931). [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]
G. Gbur and T. D. Visser, "Phase singularities and coherence vortices in linear optical systems," Opt. Commun. 259, 428-435 (2006). [CrossRef]
G. V. Bogatyryova, C. V. Felde, P. V. Polyanskii, S. A. Ponomarenko, M. S. Soskin, and E. Wolf, "Partially coherent vortex beams with a separable phase," Opt. Lett. 28, 878-880 (2003). [CrossRef] [PubMed]
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).
Y. Gu and G. Gbur, "Topological reactions of optical correlation vortices," Opt. Commun. 282, 709-716 (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] [PubMed]
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]
D. M. Paganin, Coherent X-ray Optics (Oxford University Press, New York, 2006).
G. Mie, "Beitrage zur Optik Truber Medien speziell kolloidaler Metallosungen," Ann. Phys. 25, 377-442 (1908). [CrossRef]
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).
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] [PubMed]
M. Morin, P. Bernard and P. Galarneau, "Moment definition of the pointing stability of a laser beam," Opt. Lett. 19, 1379-1381 (1994). [CrossRef] [PubMed]
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). [CrossRef]
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] [PubMed]
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).
W. Gardner, A. Napolitano, and L. Paura, "Cyclostationarity: Half a Century of Research," Signal Process. 86, 639-697 (2006). [CrossRef]
B. J. Davis, "Observable coherence theory for statistically periodic fields," Phys. Rev. A 76, 043843 (2007). [CrossRef]
V. Manea, "General interference law for nonstationary, separable optical fields," J. Opt. Soc. Am. A 26, 1907-1914 (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] [PubMed]
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]

Ann. Phys.

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

J. Opt. A: Pure Appl. Opt.

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

Nature

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

Opt. Commun.

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

Opt. Express

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

Opt. Lett.

Phys. Rev. A

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

Phys. Rev. Lett.

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] [PubMed]

Proc. Roy. Soc. Lond. A

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

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). [CrossRef]

Rev. Sci. Instrum.

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] [PubMed]

Signal Process.

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

Ultramicroscopy

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] [PubMed]

Other

D. M. Paganin, Coherent X-ray Optics (Oxford University Press, New York, 2006).
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. 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. 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).
M. Soskin and M. Vasnetsov, "Singular optics," in Progress in Optics, E.Wolf, ed., (North-Holland, Amsterdam, 2001) Vol. 42, pp. 219-276. [CrossRef]
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).

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

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

[3] 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] [PubMed]

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

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

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

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

[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]

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

[10] 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]

[11] 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]

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

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

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

[15] G. V. Bogatyryova, C. V. Felde, P. V. Polyanskii, S. A. Ponomarenko, M. S. Soskin, and E. Wolf, "Partially coherent vortex beams with a separable phase," Opt. Lett. 28, 878-880 (2003). [CrossRef] [PubMed]

[16] 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).

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

[18] 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] [PubMed]

[19] 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]

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

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

[22] 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).

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

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

[25] 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] [PubMed]

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

[27] 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). [CrossRef]

[28] 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] [PubMed]

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

[30] 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.

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

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

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

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

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

[36] 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]

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