W. Wang, S. G. Hanson, Y. Miyamoto, and M. Takeda, "Experimental investigation of local properties and statistics of optical vortices in random wave fields," Phys. Rev. Lett. 94, 103902 (2005).

[CrossRef]
[PubMed]

M. V. Berry, "Index formulae for singular lines of polarization," J. Opt. A, Pure Appl. Opt. 6, 675-678 (2004).

[CrossRef]

M. S. Soskin, V. Denisenko, and R. Egorov, "Topological networks of paraxial ellipse speckle-fields," J. Opt. A, Pure Appl. Opt. 6, S281-S287 (2004).

[CrossRef]

M. S. Soskin, V. Denisenko, and I. Freund, "Optical polarization singularities and elliptic stationary points," Opt. Lett. 28, 1475-1477 (2003).

[CrossRef]
[PubMed]

M. R. Dennis, "Correlations and screening of topological charges in Gaussian random fields," J. Phys. A 36, 6611-6628 (2003).

[CrossRef]

G. Foltin, "The distribution of extremal points of Gaussian scalar fields," J. Phys. A 36, 4561-4580 (2003).

[CrossRef]

O. V. Angelsky, I. I. Mokhun, A. I. Mokhun, and M. S. Soskin, "Interferometric methods in diagnostics of polarization singularities," Phys. Rev. E 65, 036602 (2002).

[CrossRef]

I. Freund, M. S. Soskin, and A. I. Mokhun, "Elliptic critical points in paraxial optical fields," Opt. Commun. 208, 223-253 (2002).

[CrossRef]

M. R. Dennis, "Polarization singularities in paraxial vector fields: morphology and statistics," Opt. Commun. 213, 201-221 (2002).

[CrossRef]

M. V. Berry and M. R. Dennis, "Polarization singularities in isotropic random vector waves," Proc. R. Soc. London, Ser. A 457, 141-155 (2001).

[CrossRef]

M. R. Dennis, "Local properties and statistics of phase singularities in generic wavefields," Proc. SPIE 4403, 13-23 (2001).

[CrossRef]

M. Dennis, "Phase critical point densities in planar isotropic random waves," J. Phys. A 34, L297-L303 (2001).

[CrossRef]

M. V. Berry and M. R. Dennis, "Phase singularities in isotropic random waves," Proc. R. Soc. London, Ser. A 456, 2059-2079 (2000).

[CrossRef]

I. Freund and M. Wilkinson, "Critical-point screening in random wave fields," J. Opt. Soc. Am. 15, 2892-2902 (1998).

[CrossRef]

I. Freund, " '1001' correlations in random wave fields," Waves Random Media 8, 119-158 (1998).

[CrossRef]

I. Freund, "Saddles, singularities, and extrema in random phase fields," Phys. Rev. E 52, 2348-2359 (1995).

[CrossRef]

I. Freund and N. Shvartsman, "Wave-field phase singularities: the sign principle," Phys. Rev. A 50, 5164-5172 (1994).

[CrossRef]

N. Shvartsman and I. Freund, "Vortices in random wave fields: nearest neighbor anticorrelations," Phys. Rev. Lett. 72, 1008-1011 (1994).

[CrossRef]

I. Freund, N. Shvartsman, and V. Freilikher, "Optical dislocation networks in highly random media," Opt. Commun. 101, 247-264 (1993).

[CrossRef]

J. V. Hajnal, "Observation of singularities in electric and magnetic fields of freely propagating microwaves," Proc. R. Soc. London, Ser. A 430, 413-421 (1990).

[CrossRef]

J. F. Nye and J. V. Hajnal, "The wave structure of monochromatic electromagnetic radiation," Proc. R. Soc. London, Ser. A 409, 21-36 (1987).

[CrossRef]

N. B. Baranova, B. Ya. Zel'dovich, A. V. Mamaev, N. Pilipetskii, and V. V. Shkunov, "Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment)," JETP Lett. 33, 195-199 (1981).

M. V. Berry, "Disruption of wavefronts: statistics of dislocations in incoherent Gaussian random waves," J. Phys. A 11, 27-37 (1978).

[CrossRef]

J. F. Nye and M. V. Berry, "Dislocations in wave trains," Proc. R. Soc. London, Ser. A 336, 165-190 (1974).

[CrossRef]

C. E. Shannon, "Communication in the presence of noise," Proc. IRE 37, 10-21 (1949).

[CrossRef]

E. T. Whittaker, "On the functions which are represented by the expansions of the interpolation theory," Proc. R. Soc. Edinburgh, Sect. A: Math. Phys. Sci. 35, 181-194 (1915).

B. A. van Tiggelen, D. Anache, and A. Ghysels, "Role of mean free path in spatial phase correlation and nodal screening," Europhys. Lett. 74, 999-1005 (2006).

[CrossRef]

O. V. Angelsky, I. I. Mokhun, A. I. Mokhun, and M. S. Soskin, "Interferometric methods in diagnostics of polarization singularities," Phys. Rev. E 65, 036602 (2002).

[CrossRef]

N. B. Baranova, B. Ya. Zel'dovich, A. V. Mamaev, N. Pilipetskii, and V. V. Shkunov, "Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment)," JETP Lett. 33, 195-199 (1981).

M. V. Berry, "Index formulae for singular lines of polarization," J. Opt. A, Pure Appl. Opt. 6, 675-678 (2004).

[CrossRef]

M. V. Berry and M. R. Dennis, "Polarization singularities in isotropic random vector waves," Proc. R. Soc. London, Ser. A 457, 141-155 (2001).

[CrossRef]

M. V. Berry and M. R. Dennis, "Phase singularities in isotropic random waves," Proc. R. Soc. London, Ser. A 456, 2059-2079 (2000).

[CrossRef]

M. V. Berry, "Disruption of wavefronts: statistics of dislocations in incoherent Gaussian random waves," J. Phys. A 11, 27-37 (1978).

[CrossRef]

J. F. Nye and M. V. Berry, "Dislocations in wave trains," Proc. R. Soc. London, Ser. A 336, 165-190 (1974).

[CrossRef]

M. V. Berry, "Singularities in waves and rays," in Physics of Defects, R.Balian, M.Kleman, and J.P.Poirier, eds. (North-Holland, 1981), pp. 453-543.

M. S. Soskin, V. Denisenko, and R. Egorov, "Topological networks of paraxial ellipse speckle-fields," J. Opt. A, Pure Appl. Opt. 6, S281-S287 (2004).

[CrossRef]

M. S. Soskin, V. Denisenko, and I. Freund, "Optical polarization singularities and elliptic stationary points," Opt. Lett. 28, 1475-1477 (2003).

[CrossRef]
[PubMed]

M. Dennis, "Phase critical point densities in planar isotropic random waves," J. Phys. A 34, L297-L303 (2001).

[CrossRef]

M. R. Dennis, "Correlations and screening of topological charges in Gaussian random fields," J. Phys. A 36, 6611-6628 (2003).

[CrossRef]

M. R. Dennis, "Polarization singularities in paraxial vector fields: morphology and statistics," Opt. Commun. 213, 201-221 (2002).

[CrossRef]

M. V. Berry and M. R. Dennis, "Polarization singularities in isotropic random vector waves," Proc. R. Soc. London, Ser. A 457, 141-155 (2001).

[CrossRef]

M. R. Dennis, "Local properties and statistics of phase singularities in generic wavefields," Proc. SPIE 4403, 13-23 (2001).

[CrossRef]

M. V. Berry and M. R. Dennis, "Phase singularities in isotropic random waves," Proc. R. Soc. London, Ser. A 456, 2059-2079 (2000).

[CrossRef]

M. S. Soskin, V. Denisenko, and R. Egorov, "Topological networks of paraxial ellipse speckle-fields," J. Opt. A, Pure Appl. Opt. 6, S281-S287 (2004).

[CrossRef]

G. Foltin, "The distribution of extremal points of Gaussian scalar fields," J. Phys. A 36, 4561-4580 (2003).

[CrossRef]

I. Freund, N. Shvartsman, and V. Freilikher, "Optical dislocation networks in highly random media," Opt. Commun. 101, 247-264 (1993).

[CrossRef]

M. S. Soskin, V. Denisenko, and I. Freund, "Optical polarization singularities and elliptic stationary points," Opt. Lett. 28, 1475-1477 (2003).

[CrossRef]
[PubMed]

I. Freund, M. S. Soskin, and A. I. Mokhun, "Elliptic critical points in paraxial optical fields," Opt. Commun. 208, 223-253 (2002).

[CrossRef]

I. Freund and M. Wilkinson, "Critical-point screening in random wave fields," J. Opt. Soc. Am. 15, 2892-2902 (1998).

[CrossRef]

I. Freund, " '1001' correlations in random wave fields," Waves Random Media 8, 119-158 (1998).

[CrossRef]

I. Freund, "Saddles, singularities, and extrema in random phase fields," Phys. Rev. E 52, 2348-2359 (1995).

[CrossRef]

N. Shvartsman and I. Freund, "Vortices in random wave fields: nearest neighbor anticorrelations," Phys. Rev. Lett. 72, 1008-1011 (1994).

[CrossRef]

I. Freund and N. Shvartsman, "Wave-field phase singularities: the sign principle," Phys. Rev. A 50, 5164-5172 (1994).

[CrossRef]

I. Freund, N. Shvartsman, and V. Freilikher, "Optical dislocation networks in highly random media," Opt. Commun. 101, 247-264 (1993).

[CrossRef]

B. A. van Tiggelen, D. Anache, and A. Ghysels, "Role of mean free path in spatial phase correlation and nodal screening," Europhys. Lett. 74, 999-1005 (2006).

[CrossRef]

J. W. Goodman, Statistical Optics (Wiley, 1985).

J. W. Goodman, Laser Speckle and Related Phenomena, J.C.Dainty, ed. (Springer, 1984).

J. V. Hajnal, "Observation of singularities in electric and magnetic fields of freely propagating microwaves," Proc. R. Soc. London, Ser. A 430, 413-421 (1990).

[CrossRef]

J. F. Nye and J. V. Hajnal, "The wave structure of monochromatic electromagnetic radiation," Proc. R. Soc. London, Ser. A 409, 21-36 (1987).

[CrossRef]

B. I. Halperin, "Statistical mechanics of topological defects," in Physics of Defects, R.Balian, M.Kleman, and J.P.Poirier, eds. (North-Holland, 1981), pp. 813-857.

W. Wang, S. G. Hanson, Y. Miyamoto, and M. Takeda, "Experimental investigation of local properties and statistics of optical vortices in random wave fields," Phys. Rev. Lett. 94, 103902 (2005).

[CrossRef]
[PubMed]

N. B. Baranova, B. Ya. Zel'dovich, A. V. Mamaev, N. Pilipetskii, and V. V. Shkunov, "Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment)," JETP Lett. 33, 195-199 (1981).

W. Wang, S. G. Hanson, Y. Miyamoto, and M. Takeda, "Experimental investigation of local properties and statistics of optical vortices in random wave fields," Phys. Rev. Lett. 94, 103902 (2005).

[CrossRef]
[PubMed]

O. V. Angelsky, I. I. Mokhun, A. I. Mokhun, and M. S. Soskin, "Interferometric methods in diagnostics of polarization singularities," Phys. Rev. E 65, 036602 (2002).

[CrossRef]

I. Freund, M. S. Soskin, and A. I. Mokhun, "Elliptic critical points in paraxial optical fields," Opt. Commun. 208, 223-253 (2002).

[CrossRef]

O. V. Angelsky, I. I. Mokhun, A. I. Mokhun, and M. S. Soskin, "Interferometric methods in diagnostics of polarization singularities," Phys. Rev. E 65, 036602 (2002).

[CrossRef]

J. F. Nye and J. V. Hajnal, "The wave structure of monochromatic electromagnetic radiation," Proc. R. Soc. London, Ser. A 409, 21-36 (1987).

[CrossRef]

J. F. Nye and M. V. Berry, "Dislocations in wave trains," Proc. R. Soc. London, Ser. A 336, 165-190 (1974).

[CrossRef]

J. F. Nye, Nature Focusing and Fine Structure of Light (IOP, 1999).

N. B. Baranova, B. Ya. Zel'dovich, A. V. Mamaev, N. Pilipetskii, and V. V. Shkunov, "Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment)," JETP Lett. 33, 195-199 (1981).

C. E. Shannon, "Communication in the presence of noise," Proc. IRE 37, 10-21 (1949).

[CrossRef]

N. B. Baranova, B. Ya. Zel'dovich, A. V. Mamaev, N. Pilipetskii, and V. V. Shkunov, "Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment)," JETP Lett. 33, 195-199 (1981).

I. Freund and N. Shvartsman, "Wave-field phase singularities: the sign principle," Phys. Rev. A 50, 5164-5172 (1994).

[CrossRef]

N. Shvartsman and I. Freund, "Vortices in random wave fields: nearest neighbor anticorrelations," Phys. Rev. Lett. 72, 1008-1011 (1994).

[CrossRef]

I. Freund, N. Shvartsman, and V. Freilikher, "Optical dislocation networks in highly random media," Opt. Commun. 101, 247-264 (1993).

[CrossRef]

M. S. Soskin, V. Denisenko, and R. Egorov, "Topological networks of paraxial ellipse speckle-fields," J. Opt. A, Pure Appl. Opt. 6, S281-S287 (2004).

[CrossRef]

M. S. Soskin, V. Denisenko, and I. Freund, "Optical polarization singularities and elliptic stationary points," Opt. Lett. 28, 1475-1477 (2003).

[CrossRef]
[PubMed]

O. V. Angelsky, I. I. Mokhun, A. I. Mokhun, and M. S. Soskin, "Interferometric methods in diagnostics of polarization singularities," Phys. Rev. E 65, 036602 (2002).

[CrossRef]

I. Freund, M. S. Soskin, and A. I. Mokhun, "Elliptic critical points in paraxial optical fields," Opt. Commun. 208, 223-253 (2002).

[CrossRef]

W. Wang, S. G. Hanson, Y. Miyamoto, and M. Takeda, "Experimental investigation of local properties and statistics of optical vortices in random wave fields," Phys. Rev. Lett. 94, 103902 (2005).

[CrossRef]
[PubMed]

B. A. van Tiggelen, D. Anache, and A. Ghysels, "Role of mean free path in spatial phase correlation and nodal screening," Europhys. Lett. 74, 999-1005 (2006).

[CrossRef]

W. Wang, S. G. Hanson, Y. Miyamoto, and M. Takeda, "Experimental investigation of local properties and statistics of optical vortices in random wave fields," Phys. Rev. Lett. 94, 103902 (2005).

[CrossRef]
[PubMed]

E. T. Whittaker, "On the functions which are represented by the expansions of the interpolation theory," Proc. R. Soc. Edinburgh, Sect. A: Math. Phys. Sci. 35, 181-194 (1915).

I. Freund and M. Wilkinson, "Critical-point screening in random wave fields," J. Opt. Soc. Am. 15, 2892-2902 (1998).

[CrossRef]

N. B. Baranova, B. Ya. Zel'dovich, A. V. Mamaev, N. Pilipetskii, and V. V. Shkunov, "Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment)," JETP Lett. 33, 195-199 (1981).

B. A. van Tiggelen, D. Anache, and A. Ghysels, "Role of mean free path in spatial phase correlation and nodal screening," Europhys. Lett. 74, 999-1005 (2006).

[CrossRef]

M. S. Soskin, V. Denisenko, and R. Egorov, "Topological networks of paraxial ellipse speckle-fields," J. Opt. A, Pure Appl. Opt. 6, S281-S287 (2004).

[CrossRef]

M. V. Berry, "Index formulae for singular lines of polarization," J. Opt. A, Pure Appl. Opt. 6, 675-678 (2004).

[CrossRef]

I. Freund and M. Wilkinson, "Critical-point screening in random wave fields," J. Opt. Soc. Am. 15, 2892-2902 (1998).

[CrossRef]

M. Dennis, "Phase critical point densities in planar isotropic random waves," J. Phys. A 34, L297-L303 (2001).

[CrossRef]

M. V. Berry, "Disruption of wavefronts: statistics of dislocations in incoherent Gaussian random waves," J. Phys. A 11, 27-37 (1978).

[CrossRef]

M. R. Dennis, "Correlations and screening of topological charges in Gaussian random fields," J. Phys. A 36, 6611-6628 (2003).

[CrossRef]

G. Foltin, "The distribution of extremal points of Gaussian scalar fields," J. Phys. A 36, 4561-4580 (2003).

[CrossRef]

N. B. Baranova, B. Ya. Zel'dovich, A. V. Mamaev, N. Pilipetskii, and V. V. Shkunov, "Dislocations of the wavefront of a speckle-inhomogeneous field (theory and experiment)," JETP Lett. 33, 195-199 (1981).

I. Freund, N. Shvartsman, and V. Freilikher, "Optical dislocation networks in highly random media," Opt. Commun. 101, 247-264 (1993).

[CrossRef]

M. R. Dennis, "Polarization singularities in paraxial vector fields: morphology and statistics," Opt. Commun. 213, 201-221 (2002).

[CrossRef]

I. Freund, M. S. Soskin, and A. I. Mokhun, "Elliptic critical points in paraxial optical fields," Opt. Commun. 208, 223-253 (2002).

[CrossRef]

I. Freund and N. Shvartsman, "Wave-field phase singularities: the sign principle," Phys. Rev. A 50, 5164-5172 (1994).

[CrossRef]

I. Freund, "Saddles, singularities, and extrema in random phase fields," Phys. Rev. E 52, 2348-2359 (1995).

[CrossRef]

O. V. Angelsky, I. I. Mokhun, A. I. Mokhun, and M. S. Soskin, "Interferometric methods in diagnostics of polarization singularities," Phys. Rev. E 65, 036602 (2002).

[CrossRef]

W. Wang, S. G. Hanson, Y. Miyamoto, and M. Takeda, "Experimental investigation of local properties and statistics of optical vortices in random wave fields," Phys. Rev. Lett. 94, 103902 (2005).

[CrossRef]
[PubMed]

N. Shvartsman and I. Freund, "Vortices in random wave fields: nearest neighbor anticorrelations," Phys. Rev. Lett. 72, 1008-1011 (1994).

[CrossRef]

C. E. Shannon, "Communication in the presence of noise," Proc. IRE 37, 10-21 (1949).

[CrossRef]

E. T. Whittaker, "On the functions which are represented by the expansions of the interpolation theory," Proc. R. Soc. Edinburgh, Sect. A: Math. Phys. Sci. 35, 181-194 (1915).

J. V. Hajnal, "Observation of singularities in electric and magnetic fields of freely propagating microwaves," Proc. R. Soc. London, Ser. A 430, 413-421 (1990).

[CrossRef]

J. F. Nye and J. V. Hajnal, "The wave structure of monochromatic electromagnetic radiation," Proc. R. Soc. London, Ser. A 409, 21-36 (1987).

[CrossRef]

M. V. Berry and M. R. Dennis, "Polarization singularities in isotropic random vector waves," Proc. R. Soc. London, Ser. A 457, 141-155 (2001).

[CrossRef]

J. F. Nye and M. V. Berry, "Dislocations in wave trains," Proc. R. Soc. London, Ser. A 336, 165-190 (1974).

[CrossRef]

M. V. Berry and M. R. Dennis, "Phase singularities in isotropic random waves," Proc. R. Soc. London, Ser. A 456, 2059-2079 (2000).

[CrossRef]

M. R. Dennis, "Local properties and statistics of phase singularities in generic wavefields," Proc. SPIE 4403, 13-23 (2001).

[CrossRef]

I. Freund, " '1001' correlations in random wave fields," Waves Random Media 8, 119-158 (1998).

[CrossRef]

B. I. Halperin, "Statistical mechanics of topological defects," in Physics of Defects, R.Balian, M.Kleman, and J.P.Poirier, eds. (North-Holland, 1981), pp. 813-857.

M. V. Berry, "Singularities in waves and rays," in Physics of Defects, R.Balian, M.Kleman, and J.P.Poirier, eds. (North-Holland, 1981), pp. 453-543.

J. W. Goodman, Statistical Optics (Wiley, 1985).

J. W. Goodman, Laser Speckle and Related Phenomena, J.C.Dainty, ed. (Springer, 1984).

J. F. Nye, Nature Focusing and Fine Structure of Light (IOP, 1999).