M. V. Berry, E. Bodenschatz, “Caustics, multiply reconstructed by Talbot interference,” J. Mod. Opt. 46, 349–365 (1999).

[CrossRef]

I. Freund, “Saddle point wave fields,” Opt. Commun. 163, 230–242 (1999).

[CrossRef]

I. Freund, “Critical point explosions in two-dimensional wave fields,” Opt. Commun. 159, 99–117 (1999).

[CrossRef]

A. M. Deykoon, M. S. Soskin, G. A. Swartzlander, “Nonlinear optical catastrophe from a smooth initial beam,” Opt. Lett. 24, 1224–1226 (1999).

[CrossRef]

G. P. Karman, M. W. Beijersbergen, A. van Duiji, D. Bouwmeester, J. P. Woerdman, “Airy pattern reorganization and subwavelength structure in a focus,” J. Opt. Soc. Am. A 15, 884–899 (1998).

[CrossRef]

M. V. Berry, “Wave dislocation reactions in non-paraxial beams,” J. Mod. Opt. 45, 1845–1858 (1998).

[CrossRef]

R. Piestun, J. Shamir, “Generalized propagation-invariant wave fields,” J. Opt. Soc. Am. A 15, 3039–3044 (1998).

[CrossRef]

G. H. Kim, J. H. Jeon, K. H. Ko, H. J. Moon, J. H. Lee, “Optical vortices produced with a nonspiral phase plate,” Appl. Opt. 36, 8614–8621 (1997).

[CrossRef]

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).

[CrossRef]

D. Rozas, Z. S. Sacks, G. A. Swartzlander, “Experimental observation of fluid-like motion of optical vortices,” Phys. Rev. Lett. 79, 3399–3402 (1997).

[CrossRef]

E. Abromochkin, V. Volostnikov, “Spiral-type beams; optical and quantum aspects,” Opt. Commun. 125, 302–323 (1996).

[CrossRef]

M. Brambilla, M. Catteneo, L. A. Lugiato, R. Pirovano, F. Prati, “Dynamical transverse laser patterns. I. Theory,” Phys. Rev. A 49, 1427–1451 (1994).

[CrossRef]
[PubMed]

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, J. P. Woerdman, “Helical wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112, 321–327 (1994).

[CrossRef]

G. Indebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40, 73–87 (1993).

[CrossRef]

I. Freund, N. Shvarstman, V. Freilikher, “Optical dislocation networks in highly random media,” Opt. Commun. 101, 247–264 (1993).

[CrossRef]

G. A. Swartzlander, C. T. Law, “Optical vortex solitons observed in Kerr nonlinear media,” Phys. Rev. Lett. 69, 2503–2506 (1992).

[CrossRef]
[PubMed]

N. R. Heckenberg, R. McDuff, C. P. Smith, A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992).

[CrossRef]
[PubMed]

P. Szwaykowski, J. Ojeda-Casteneda, “Nondiffracting beams and self imaging phenomenon,” Opt. Commun. 83, 1–4 (1991).

[CrossRef]

V. Y. Bazhenov, M. V. Vasnetsov, M. S. Soskin, “Laser beams with screw dislocations in their wavefronts,” JETP Lett. 52, 429–431 (1990).

A. W. Lohman, “An array illuminator based on the Talbot effect,” Optik (Stuttgart) 79, 41–45 (1988).

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

[CrossRef]

M. Abramowitz, I. Stegun, Handbook of Mathematical Functions, Natl. Bur. Stand. Applied Mathematics Series No. 55 (U.S. GPO, Washington, D.C., 1964).

E. Abromochkin, V. Volostnikov, “Spiral-type beams; optical and quantum aspects,” Opt. Commun. 125, 302–323 (1996).

[CrossRef]

V. I. Arnold, Ordinary Differential Equations (MIT Press, Cambridge, Mass., 1973), Chap. 5, pp. 254–268.

V. Y. Bazhenov, M. V. Vasnetsov, M. S. Soskin, “Laser beams with screw dislocations in their wavefronts,” JETP Lett. 52, 429–431 (1990).

G. P. Karman, M. W. Beijersbergen, A. van Duiji, D. Bouwmeester, J. P. Woerdman, “Airy pattern reorganization and subwavelength structure in a focus,” J. Opt. Soc. Am. A 15, 884–899 (1998).

[CrossRef]

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, J. P. Woerdman, “Helical wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112, 321–327 (1994).

[CrossRef]

M. Berry, “Faster than Fourier,” in Quantum Coherence and Reality, J. S. Anandan, J. L. Safko, eds. (World Scientific, London, 1994), pp. 55–65.

M. Berry, “Singularities in waves and rays,” in Physics of Defects, R. Balian, M. Kleman, J.-P. Poirier, eds. (North-Holland, Amsterdam, 1981), pp. 453–549.

M. V. Berry, E. Bodenschatz, “Caustics, multiply reconstructed by Talbot interference,” J. Mod. Opt. 46, 349–365 (1999).

[CrossRef]

M. V. Berry, “Wave dislocation reactions in non-paraxial beams,” J. Mod. Opt. 45, 1845–1858 (1998).

[CrossRef]

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

[CrossRef]

M. V. Berry, C. Upstill, “Catastrophe optics,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1980), pp. 257–346.

M. V. Berry, E. Bodenschatz, “Caustics, multiply reconstructed by Talbot interference,” J. Mod. Opt. 46, 349–365 (1999).

[CrossRef]

M. Brambilla, M. Catteneo, L. A. Lugiato, R. Pirovano, F. Prati, “Dynamical transverse laser patterns. I. Theory,” Phys. Rev. A 49, 1427–1451 (1994).

[CrossRef]
[PubMed]

M. Brambilla, M. Catteneo, L. A. Lugiato, R. Pirovano, F. Prati, “Dynamical transverse laser patterns. I. Theory,” Phys. Rev. A 49, 1427–1451 (1994).

[CrossRef]
[PubMed]

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, J. P. Woerdman, “Helical wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112, 321–327 (1994).

[CrossRef]

B. A. Dubrovin, A. T. Fomenko, S. P. Novikov, Modern Geometry—Methods and Applications (Springer-Verlag, Berlin, 1984,1986,1990), Part II. The geometry and topology of manifolds (1986); Part III. Introduction to homology theory (1990).

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1502 (1987).

[CrossRef]
[PubMed]

B. A. Dubrovin, A. T. Fomenko, S. P. Novikov, Modern Geometry—Methods and Applications (Springer-Verlag, Berlin, 1984,1986,1990), Part II. The geometry and topology of manifolds (1986); Part III. Introduction to homology theory (1990).

I. Freund, N. Shvarstman, V. Freilikher, “Optical dislocation networks in highly random media,” Opt. Commun. 101, 247–264 (1993).

[CrossRef]

I. Freund, “Saddle point wave fields,” Opt. Commun. 163, 230–242 (1999).

[CrossRef]

I. Freund, “Critical point explosions in two-dimensional wave fields,” Opt. Commun. 159, 99–117 (1999).

[CrossRef]

I. Freund, N. Shvarstman, V. Freilikher, “Optical dislocation networks in highly random media,” Opt. Commun. 101, 247–264 (1993).

[CrossRef]

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, San Francisco, 1988), Chap. 4, pp. 73–83.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).

[CrossRef]

I. S. Gradshteyn, I. M. Ryzhik, Tables of Integrals, Series, and Products (Academic, New York, 1965), p. 369, No. 3.616.8.

G. Indebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40, 73–87 (1993).

[CrossRef]

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, J. P. Woerdman, “Helical wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112, 321–327 (1994).

[CrossRef]

G. A. Swartzlander, C. T. Law, “Optical vortex solitons observed in Kerr nonlinear media,” Phys. Rev. Lett. 69, 2503–2506 (1992).

[CrossRef]
[PubMed]

A. W. Lohman, “An array illuminator based on the Talbot effect,” Optik (Stuttgart) 79, 41–45 (1988).

M. Brambilla, M. Catteneo, L. A. Lugiato, R. Pirovano, F. Prati, “Dynamical transverse laser patterns. I. Theory,” Phys. Rev. A 49, 1427–1451 (1994).

[CrossRef]
[PubMed]

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1502 (1987).

[CrossRef]
[PubMed]

J. Milnor, Morse Theory (Princeton U. Press, Princeton, N.J., 1963).

B. A. Dubrovin, A. T. Fomenko, S. P. Novikov, Modern Geometry—Methods and Applications (Springer-Verlag, Berlin, 1984,1986,1990), Part II. The geometry and topology of manifolds (1986); Part III. Introduction to homology theory (1990).

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

[CrossRef]

P. Szwaykowski, J. Ojeda-Casteneda, “Nondiffracting beams and self imaging phenomenon,” Opt. Commun. 83, 1–4 (1991).

[CrossRef]

B. Y. Zel’dovich, N. F. Pilipetsky, V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, Berlin, 1985), Chap. 3.

M. Brambilla, M. Catteneo, L. A. Lugiato, R. Pirovano, F. Prati, “Dynamical transverse laser patterns. I. Theory,” Phys. Rev. A 49, 1427–1451 (1994).

[CrossRef]
[PubMed]

M. Brambilla, M. Catteneo, L. A. Lugiato, R. Pirovano, F. Prati, “Dynamical transverse laser patterns. I. Theory,” Phys. Rev. A 49, 1427–1451 (1994).

[CrossRef]
[PubMed]

D. Rozas, Z. S. Sacks, G. A. Swartzlander, “Experimental observation of fluid-like motion of optical vortices,” Phys. Rev. Lett. 79, 3399–3402 (1997).

[CrossRef]

I. S. Gradshteyn, I. M. Ryzhik, Tables of Integrals, Series, and Products (Academic, New York, 1965), p. 369, No. 3.616.8.

D. Rozas, Z. S. Sacks, G. A. Swartzlander, “Experimental observation of fluid-like motion of optical vortices,” Phys. Rev. Lett. 79, 3399–3402 (1997).

[CrossRef]

B. Y. Zel’dovich, N. F. Pilipetsky, V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, Berlin, 1985), Chap. 3.

I. Freund, N. Shvarstman, V. Freilikher, “Optical dislocation networks in highly random media,” Opt. Commun. 101, 247–264 (1993).

[CrossRef]

A. E. Siegman, Lasers (University Science Books, Mill Valley, Calif., 1986).

A. M. Deykoon, M. S. Soskin, G. A. Swartzlander, “Nonlinear optical catastrophe from a smooth initial beam,” Opt. Lett. 24, 1224–1226 (1999).

[CrossRef]

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).

[CrossRef]

V. Y. Bazhenov, M. V. Vasnetsov, M. S. Soskin, “Laser beams with screw dislocations in their wavefronts,” JETP Lett. 52, 429–431 (1990).

M. Abramowitz, I. Stegun, Handbook of Mathematical Functions, Natl. Bur. Stand. Applied Mathematics Series No. 55 (U.S. GPO, Washington, D.C., 1964).

S. H. Strogatz, Nonlinear Dynamics and Chaos (Addison-Wesley, Reading, Mass., 1994), Chap. 6, pp. 174–180.

A. M. Deykoon, M. S. Soskin, G. A. Swartzlander, “Nonlinear optical catastrophe from a smooth initial beam,” Opt. Lett. 24, 1224–1226 (1999).

[CrossRef]

D. Rozas, Z. S. Sacks, G. A. Swartzlander, “Experimental observation of fluid-like motion of optical vortices,” Phys. Rev. Lett. 79, 3399–3402 (1997).

[CrossRef]

G. A. Swartzlander, C. T. Law, “Optical vortex solitons observed in Kerr nonlinear media,” Phys. Rev. Lett. 69, 2503–2506 (1992).

[CrossRef]
[PubMed]

P. Szwaykowski, J. Ojeda-Casteneda, “Nondiffracting beams and self imaging phenomenon,” Opt. Commun. 83, 1–4 (1991).

[CrossRef]

M. V. Berry, C. Upstill, “Catastrophe optics,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1980), pp. 257–346.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).

[CrossRef]

V. Y. Bazhenov, M. V. Vasnetsov, M. S. Soskin, “Laser beams with screw dislocations in their wavefronts,” JETP Lett. 52, 429–431 (1990).

E. Abromochkin, V. Volostnikov, “Spiral-type beams; optical and quantum aspects,” Opt. Commun. 125, 302–323 (1996).

[CrossRef]

G. P. Karman, M. W. Beijersbergen, A. van Duiji, D. Bouwmeester, J. P. Woerdman, “Airy pattern reorganization and subwavelength structure in a focus,” J. Opt. Soc. Am. A 15, 884–899 (1998).

[CrossRef]

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, J. P. Woerdman, “Helical wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112, 321–327 (1994).

[CrossRef]

B. Y. Zel’dovich, N. F. Pilipetsky, V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, Berlin, 1985), Chap. 3.

M. V. Berry, “Wave dislocation reactions in non-paraxial beams,” J. Mod. Opt. 45, 1845–1858 (1998).

[CrossRef]

M. V. Berry, E. Bodenschatz, “Caustics, multiply reconstructed by Talbot interference,” J. Mod. Opt. 46, 349–365 (1999).

[CrossRef]

G. Indebetouw, “Optical vortices and their propagation,” J. Mod. Opt. 40, 73–87 (1993).

[CrossRef]

R. Piestun, J. Shamir, “Generalized propagation-invariant wave fields,” J. Opt. Soc. Am. A 15, 3039–3044 (1998).

[CrossRef]

G. P. Karman, M. W. Beijersbergen, A. van Duiji, D. Bouwmeester, J. P. Woerdman, “Airy pattern reorganization and subwavelength structure in a focus,” J. Opt. Soc. Am. A 15, 884–899 (1998).

[CrossRef]

J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).

[CrossRef]

V. Y. Bazhenov, M. V. Vasnetsov, M. S. Soskin, “Laser beams with screw dislocations in their wavefronts,” JETP Lett. 52, 429–431 (1990).

I. Freund, N. Shvarstman, V. Freilikher, “Optical dislocation networks in highly random media,” Opt. Commun. 101, 247–264 (1993).

[CrossRef]

P. Szwaykowski, J. Ojeda-Casteneda, “Nondiffracting beams and self imaging phenomenon,” Opt. Commun. 83, 1–4 (1991).

[CrossRef]

E. Abromochkin, V. Volostnikov, “Spiral-type beams; optical and quantum aspects,” Opt. Commun. 125, 302–323 (1996).

[CrossRef]

I. Freund, “Saddle point wave fields,” Opt. Commun. 163, 230–242 (1999).

[CrossRef]

I. Freund, “Critical point explosions in two-dimensional wave fields,” Opt. Commun. 159, 99–117 (1999).

[CrossRef]

M. W. Beijersbergen, R. P. C. Coerwinkel, M. Kristensen, J. P. Woerdman, “Helical wavefront laser beams produced with a spiral phase plate,” Opt. Commun. 112, 321–327 (1994).

[CrossRef]

N. R. Heckenberg, R. McDuff, C. P. Smith, A. G. White, “Generation of optical phase singularities by computer-generated holograms,” Opt. Lett. 17, 221–223 (1992).

[CrossRef]
[PubMed]

A. M. Deykoon, M. S. Soskin, G. A. Swartzlander, “Nonlinear optical catastrophe from a smooth initial beam,” Opt. Lett. 24, 1224–1226 (1999).

[CrossRef]

A. W. Lohman, “An array illuminator based on the Talbot effect,” Optik (Stuttgart) 79, 41–45 (1988).

M. Brambilla, M. Catteneo, L. A. Lugiato, R. Pirovano, F. Prati, “Dynamical transverse laser patterns. I. Theory,” Phys. Rev. A 49, 1427–1451 (1994).

[CrossRef]
[PubMed]

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064–4075 (1997).

[CrossRef]

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1502 (1987).

[CrossRef]
[PubMed]

G. A. Swartzlander, C. T. Law, “Optical vortex solitons observed in Kerr nonlinear media,” Phys. Rev. Lett. 69, 2503–2506 (1992).

[CrossRef]
[PubMed]

D. Rozas, Z. S. Sacks, G. A. Swartzlander, “Experimental observation of fluid-like motion of optical vortices,” Phys. Rev. Lett. 79, 3399–3402 (1997).

[CrossRef]

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

[CrossRef]

M. Berry, “Singularities in waves and rays,” in Physics of Defects, R. Balian, M. Kleman, J.-P. Poirier, eds. (North-Holland, Amsterdam, 1981), pp. 453–549.

M. V. Berry, C. Upstill, “Catastrophe optics,” in Progress in Optics, E. Wolf, ed. (North-Holland, Amsterdam, 1980), pp. 257–346.

M. Berry, “Faster than Fourier,” in Quantum Coherence and Reality, J. S. Anandan, J. L. Safko, eds. (World Scientific, London, 1994), pp. 55–65.

S. H. Strogatz, Nonlinear Dynamics and Chaos (Addison-Wesley, Reading, Mass., 1994), Chap. 6, pp. 174–180.

V. I. Arnold, Ordinary Differential Equations (MIT Press, Cambridge, Mass., 1973), Chap. 5, pp. 254–268.

B. A. Dubrovin, A. T. Fomenko, S. P. Novikov, Modern Geometry—Methods and Applications (Springer-Verlag, Berlin, 1984,1986,1990), Part II. The geometry and topology of manifolds (1986); Part III. Introduction to homology theory (1990).

J. Milnor, Morse Theory (Princeton U. Press, Princeton, N.J., 1963).

A. E. Siegman, Lasers (University Science Books, Mill Valley, Calif., 1986).

B. Y. Zel’dovich, N. F. Pilipetsky, V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, Berlin, 1985), Chap. 3.

I. S. Gradshteyn, I. M. Ryzhik, Tables of Integrals, Series, and Products (Academic, New York, 1965), p. 369, No. 3.616.8.

M. Abramowitz, I. Stegun, Handbook of Mathematical Functions, Natl. Bur. Stand. Applied Mathematics Series No. 55 (U.S. GPO, Washington, D.C., 1964).

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, San Francisco, 1988), Chap. 4, pp. 73–83.