G. Grynberg, A. Maître, and A. Petrossian, "Flowerlike patterns generated by a laser beam transmitted through a rubidium cell with single feedback mirror," Phys. Rev. Lett. 72, 2379–2382 (1994).

[CrossRef]
[PubMed]

M. A. Vorontsov and W. J. Firth, "Pattern formation and competition in nonlinear optical systems with twodimensional feedback," Phys. Rev. A 49, 2891–2903 (1994).

[CrossRef]
[PubMed]

M. A. Vorontsov, "Akhseals' as a new class of spatialtemporal instabilities of optical fields," Sov. J. Quantum Electron. 23, 269–271 (1993).

[CrossRef]

W. J. Firth and M. A. Vorontsov, "Adaptive phase distortion suppression in nonlinear system with feedback mirror," J. Mod. Opt. 40, 1841–1846 (1993).

[CrossRef]

M. Tamburrini, M. Bonavita, S. Wabnitz, and E. Santamato, "Hexagonally patterned beam filamentation in a thin liquidcrystal film with a single feedback mirror," Opt. Lett. 18, 855–857 (1993).

[CrossRef]
[PubMed]

W. F. Ames, Numerical Methods for Partial Differential Equations (Academic, San Diego, Calif., 1992).

A. A. Vasiliev, D. Casasent, I. N. Kompanets, and A. V. Parfionov, Spatial Light Modulators (Radio i Sviaz, Moscow, 1987).

G. D'Alessandro and W. J. Firth, "Hexagonal spatial patterns for a Kerr slice with a feedback mirror," Phys. Rev. A 46, 537–548 (1992).

[CrossRef]

E. V. Degtiarev and M. A. Vorontsov, "Optical design kit of nonlinear spatial dynamics," in Self-Organization in Optical Systems and Applications in Information Technology, M. A. Vorontsov and W. B. Miller, eds. (Springer-Verlag, Berlin, 1995).

[CrossRef]

G. O. Reynolds, J. B. DeVelis, G. B. Parrent, Jr., and B. J. Thompson, The New Physical Optics Notebook: Tutorials in Fourier Optics (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1989).

[CrossRef]

M. A. Vorontsov and W. J. Firth, "Pattern formation and competition in nonlinear optical systems with twodimensional feedback," Phys. Rev. A 49, 2891–2903 (1994).

[CrossRef]
[PubMed]

W. J. Firth and M. A. Vorontsov, "Adaptive phase distortion suppression in nonlinear system with feedback mirror," J. Mod. Opt. 40, 1841–1846 (1993).

[CrossRef]

G. D'Alessandro and W. J. Firth, "Hexagonal spatial patterns for a Kerr slice with a feedback mirror," Phys. Rev. A 46, 537–548 (1992).

[CrossRef]

N. B. Abraham and W. J. Firth, "Overview of transverse effects in nonlinear optical systems," J. Opt. Soc. Am. B 7, 951–962 (1990).

[CrossRef]

W. J. Firth, "Spatial instabilities in a Kerr medium with single feedback mirror," J. Mod. Opt. 37, 151–153 (1990).

[CrossRef]

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

G. Grynberg, A. Maître, and A. Petrossian, "Flowerlike patterns generated by a laser beam transmitted through a rubidium cell with single feedback mirror," Phys. Rev. Lett. 72, 2379–2382 (1994).

[CrossRef]
[PubMed]

M. A. Vorontsov, V. Yu. Ivanov, and V. I. Shmalhausen, "Rotatory instability of the spatial structure of light fields in nonlinear media with two-dimensional feedback," in Laser Optics of Condensed Matter: Proceedings of the 3rd Binational USA–USSR Symposium (Plenum, New York, 1988), pp. 507–517.

[CrossRef]

A. A. Vasiliev, D. Casasent, I. N. Kompanets, and A. V. Parfionov, Spatial Light Modulators (Radio i Sviaz, Moscow, 1987).

L. A. Lugiato, "Spatio-temporal structures. Part 1," Phys. Rep. 219, 293–310 (1992).

[CrossRef]

G. Grynberg, A. Maître, and A. Petrossian, "Flowerlike patterns generated by a laser beam transmitted through a rubidium cell with single feedback mirror," Phys. Rev. Lett. 72, 2379–2382 (1994).

[CrossRef]
[PubMed]

J. V. Moloney and A. C. Newell, Nonlinear Optics (Addison-Wesley, Redwood City, Calif., 1991).

A. S. Monin and A. M. Yaglom, Statistical Fluid Mechanics (MIT Press, Cambridge, Mass., 1975), Vol. 2.

J. V. Moloney and A. C. Newell, Nonlinear Optics (Addison-Wesley, Redwood City, Calif., 1991).

M. A. Vorontsov and I. P. Nikolaev, "Nonlinear 2-D feedback optical systems: new approaches for adaptive wavefront correction," in Atmospheric Propagation and Remote Sensing III, W. A. Flood and W. B. Miller, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 2222, 413–422 (1994).

[CrossRef]

A. A. Vasiliev, D. Casasent, I. N. Kompanets, and A. V. Parfionov, Spatial Light Modulators (Radio i Sviaz, Moscow, 1987).

G. O. Reynolds, J. B. DeVelis, G. B. Parrent, Jr., and B. J. Thompson, The New Physical Optics Notebook: Tutorials in Fourier Optics (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1989).

[CrossRef]

G. Grynberg, A. Maître, and A. Petrossian, "Flowerlike patterns generated by a laser beam transmitted through a rubidium cell with single feedback mirror," Phys. Rev. Lett. 72, 2379–2382 (1994).

[CrossRef]
[PubMed]

G. O. Reynolds, J. B. DeVelis, G. B. Parrent, Jr., and B. J. Thompson, The New Physical Optics Notebook: Tutorials in Fourier Optics (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1989).

[CrossRef]

M. A. Vorontsov, V. Yu. Ivanov, and V. I. Shmalhausen, "Rotatory instability of the spatial structure of light fields in nonlinear media with two-dimensional feedback," in Laser Optics of Condensed Matter: Proceedings of the 3rd Binational USA–USSR Symposium (Plenum, New York, 1988), pp. 507–517.

[CrossRef]

G. O. Reynolds, J. B. DeVelis, G. B. Parrent, Jr., and B. J. Thompson, The New Physical Optics Notebook: Tutorials in Fourier Optics (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1989).

[CrossRef]

R. K. Tyson, Principles of Adaptive Optics (Academic, San Diego, Calif., 1991).

A. A. Vasiliev, D. Casasent, I. N. Kompanets, and A. V. Parfionov, Spatial Light Modulators (Radio i Sviaz, Moscow, 1987).

M. A. Vorontsov and W. J. Firth, "Pattern formation and competition in nonlinear optical systems with twodimensional feedback," Phys. Rev. A 49, 2891–2903 (1994).

[CrossRef]
[PubMed]

W. J. Firth and M. A. Vorontsov, "Adaptive phase distortion suppression in nonlinear system with feedback mirror," J. Mod. Opt. 40, 1841–1846 (1993).

[CrossRef]

M. A. Vorontsov, "Akhseals' as a new class of spatialtemporal instabilities of optical fields," Sov. J. Quantum Electron. 23, 269–271 (1993).

[CrossRef]

M. A. Vorontsov and K. V. Shishakov, "Phase-distortion suppression in nonlinear cavities with gain," J. Opt. Soc. Am. B 9, 71–77 (1992).

[CrossRef]

M. A. Vorontsov, V. Yu. Ivanov, and V. I. Shmalhausen, "Rotatory instability of the spatial structure of light fields in nonlinear media with two-dimensional feedback," in Laser Optics of Condensed Matter: Proceedings of the 3rd Binational USA–USSR Symposium (Plenum, New York, 1988), pp. 507–517.

[CrossRef]

E. V. Degtiarev and M. A. Vorontsov, "Optical design kit of nonlinear spatial dynamics," in Self-Organization in Optical Systems and Applications in Information Technology, M. A. Vorontsov and W. B. Miller, eds. (Springer-Verlag, Berlin, 1995).

[CrossRef]

M. A. Vorontsov and I. P. Nikolaev, "Nonlinear 2-D feedback optical systems: new approaches for adaptive wavefront correction," in Atmospheric Propagation and Remote Sensing III, W. A. Flood and W. B. Miller, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 2222, 413–422 (1994).

[CrossRef]

A. S. Monin and A. M. Yaglom, Statistical Fluid Mechanics (MIT Press, Cambridge, Mass., 1975), Vol. 2.

W. J. Firth, "Spatial instabilities in a Kerr medium with single feedback mirror," J. Mod. Opt. 37, 151–153 (1990).

[CrossRef]

W. J. Firth and M. A. Vorontsov, "Adaptive phase distortion suppression in nonlinear system with feedback mirror," J. Mod. Opt. 40, 1841–1846 (1993).

[CrossRef]

G. Giusfredi, J. F. Valley, R. Pon, G. Khitrova, and H. M. Gibbs, "Optical instabilities in sodium vapor," J. Opt. Soc. Am. B 5, 1181–1191 (1988).

[CrossRef]

N. B. Abraham and W. J. Firth, "Overview of transverse effects in nonlinear optical systems," J. Opt. Soc. Am. B 7, 951–962 (1990).

[CrossRef]

M. A. Vorontsov and K. V. Shishakov, "Phase-distortion suppression in nonlinear cavities with gain," J. Opt. Soc. Am. B 9, 71–77 (1992).

[CrossRef]

L. A. Lugiato, "Spatio-temporal structures. Part 1," Phys. Rep. 219, 293–310 (1992).

[CrossRef]

G. D'Alessandro and W. J. Firth, "Hexagonal spatial patterns for a Kerr slice with a feedback mirror," Phys. Rev. A 46, 537–548 (1992).

[CrossRef]

M. A. Vorontsov and W. J. Firth, "Pattern formation and competition in nonlinear optical systems with twodimensional feedback," Phys. Rev. A 49, 2891–2903 (1994).

[CrossRef]
[PubMed]

G. Grynberg, A. Maître, and A. Petrossian, "Flowerlike patterns generated by a laser beam transmitted through a rubidium cell with single feedback mirror," Phys. Rev. Lett. 72, 2379–2382 (1994).

[CrossRef]
[PubMed]

M. A. Vorontsov, "Akhseals' as a new class of spatialtemporal instabilities of optical fields," Sov. J. Quantum Electron. 23, 269–271 (1993).

[CrossRef]

J. V. Moloney and A. C. Newell, Nonlinear Optics (Addison-Wesley, Redwood City, Calif., 1991).

M. A. Vorontsov and I. P. Nikolaev, "Nonlinear 2-D feedback optical systems: new approaches for adaptive wavefront correction," in Atmospheric Propagation and Remote Sensing III, W. A. Flood and W. B. Miller, eds., Proc. Soc. Photo-Opt. Instrum. Eng. 2222, 413–422 (1994).

[CrossRef]

For an input field with homogeneous intensity distribution the term R|A(r,0,t)|^{2} gives rise to an insignificant spatially uniform phase shift ū = R|A_{0}|^{2}, which can be removed by redefinition of u.

M. A. Vorontsov, V. Yu. Ivanov, and V. I. Shmalhausen, "Rotatory instability of the spatial structure of light fields in nonlinear media with two-dimensional feedback," in Laser Optics of Condensed Matter: Proceedings of the 3rd Binational USA–USSR Symposium (Plenum, New York, 1988), pp. 507–517.

[CrossRef]

A. A. Vasiliev, D. Casasent, I. N. Kompanets, and A. V. Parfionov, Spatial Light Modulators (Radio i Sviaz, Moscow, 1987).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

E. V. Degtiarev and M. A. Vorontsov, "Optical design kit of nonlinear spatial dynamics," in Self-Organization in Optical Systems and Applications in Information Technology, M. A. Vorontsov and W. B. Miller, eds. (Springer-Verlag, Berlin, 1995).

[CrossRef]

G. O. Reynolds, J. B. DeVelis, G. B. Parrent, Jr., and B. J. Thompson, The New Physical Optics Notebook: Tutorials in Fourier Optics (Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash., 1989).

[CrossRef]

R. K. Tyson, Principles of Adaptive Optics (Academic, San Diego, Calif., 1991).

A. S. Monin and A. M. Yaglom, Statistical Fluid Mechanics (MIT Press, Cambridge, Mass., 1975), Vol. 2.

W. F. Ames, Numerical Methods for Partial Differential Equations (Academic, San Diego, Calif., 1992).