Collapse IAP RAS1 Influence of peripheral field on structure of nonlinear focus arising at propagation of a wave beam in cubic nonlinear media Vlasov S.N. IAP RAS Russia, N-Novgorod, Uljanov street,46,

Collapse IAP RAS2 Contents 1.Jntroduction. Motivation. 2.Construction of solution. The first order approximation. 3.The second order approximation. Influence of periphery of beam. 4.Numerical modelling of influence of "wings" on field in nonlinear focus.

Collapse IAP RAS3 1. Intoduction The initial equation - transverse Laplacian, Self-focusing part of beam “Wings" of beam or nonself-focusing to a part of a beam Amplitude structure of a beam at self-focusing - Point of a collapse

Collapse IAP RAS4 Ray structure of self-focusing an axially symmetric beam

Collapse IAP RAS5 Self-simular solution of V.I. Talanov (1966) 1. Ray structure of self-focusing an axially symmetric beam self-simular solution of first type

Collapse IAP RAS6 Ray structure of self-focusing an axially symmetric beam self-simular solution of second type 2.

Collapse IAP RAS7 Cross-section structures of a beam, showing the dependences of growth rate of a field at nonlinear focus from cross-section structures

Collapse IAP RAS8 2. Construction of solution. The first order approximation[L,P,S,S;K,Sh,Z] (4) or

Collapse IAP RAS9

10 Comparison of amplitudes of homogeneous beams Comparison of phases of homogeneous beams

Collapse IAP RAS11 Dependences of power of homogeneous beams from cross-section coordinate The real part of potential

Collapse IAP RAS12 и Dependence on value

Collapse IAP RAS13 The explanatory to a way of a choice of a principle of growth rate of a field on an axis Self-focusing part of beam “Wings" of beam or nonself- focusing to a part of a beam The first way The second way

Collapse IAP RAS14 First way

Collapse IAP RAS15 Second way

Collapse IAP RAS16 3. The second order approximation.

Collapse IAP RAS17 Dependence of amplitude on cross-section coordinate at и and phase

Collapse IAP RAS18 Dependence of amplitude on cross-section coordinate at various parameters and

Collapse IAP RAS19

Collspse IAP RAS20 4. Results of numerical calculations. Dependence of the amplitude of a field on axes, the equation

Collapse IAP RAS21. Dependence of the amplitude of a field on axes, the equation

Collapse IAP RAS22 Dependence of the maximal field on size of an initial field for a various degree of focusing

Collapse IAP RAS23 Dependence of a field in the center of a cavity from time

Collapse IAP RAS24 Dependence of a field on an axis in system with the combined nonlinearity

Литература 1.Таланов В.И. "О самофокусировке волновых пучков в нелинейных средах", Письма ЖЭТФ, 1965, т.2, n.5, с Власов С.Н., Петрищев В.А, Таланов В.И. "Усредненное описание волновых пучков в линейных и нелинейных средах", Изв.ВУЗ'ов, Радиофизика, 1971, т.14, n.9, с Захаров В.Е., Сынах В.С., О характере особенности при самофокусировке, ЖЭТФ, 1975, т.68, в.3, с Collapse IAP RAS

4. Луговой В.Н., Прохоров А.М., Теория распространения мощного лазерного излучения в нелинейной среде, УФН, 1973, т.111, в.2, с Власов С.Н., Таланов В.И., Самофокусировка волн, ИПФ РАН, Нижний Новгород, 1997, с Власов С.Н., Пискунова Л.В., Таланов В.И., Структура поля вблизи особенности, возникающей при самофокусировке в кубичной среде, ЖЭТФ, 1978, т.75, в.5, с Wood D., The self-focusing singularity in nonlinear Schrodinger equation. Studies in applied mathematics, 1984, v.84, n.2, p.102 Collapse IAP RAS

8. McLaughlin D.W., Papanicolaou G.C., Sulem C., Sulem P.L., Focusing singularity of the cubic Schrodinger equation, Phys. Rev. A, 1986, V.34, n.2, p LeMesurier B.L., Papanicolaou G.C., Sulem C., Sulem P.L., Local structure of the self-focusing singularity of the cubic Schrodinger equation, Physica D, 1988, v.32, p Kosmatov N.E., Shvets V.F., Zakharov V.E., Computer simulation of wave collapses in the nonlinear Schrodinger equation, Physica D, 1991, v.52, p Fraiman G.M., Smirnov A.I., The interaction representation in the self-focusing theory, Physica D, 1991, v.52, p Berge L., Physics reports, Wave collapse in physics: principles and applications to light and plasma physics, 1998, v.303, n.5-6, p Collapse IAP RAS

13. Ю.Н.Овчинников, И.М.Сигал, Многопараметрическое семейство коллапсирующих решений критического нелинейного уравнения Шредингера в размерности D=2, ЖЭТФ, 2003г., т.124, в.1(7), с Fraiman G.M., Litvak A.G., Talanov V.I., Vlasov S.N., Optical self-focusing: stationary beams and femtosecond pulses, in book Self-focusing in the past and present, Schwinger 15. Таланов В.И., Автомодельные волновые пучки в нелинейном диэлектрике, Изв. ВУЗ Радиофизика, 1966, т.9, в.2, с Ю.Н.Овчинников, И.М.Сигал, Коллапс в нелинейном уравнении Шредингера критической размерности {}, Письма в ЖЭТФ, 2002г., т.75, в.7 с В.Н.Гольдберг, В.И.Таланов, Р.Э. Эрм, Самофокусировка аксиально симметричных волновых пучков, ВУЗ'ов, Радиофизика, 1967, т.10, n.5, с. 574 Collapse IAP RAS

18. В.И.Таланов, "О фокусировке света в кубичных средах", Письма ЖЭТФ, 1970, т.11, n.6, с С.Н.Гурбатов, С.Н.Власов, К теории самодействия интенсивных световых пучков в плавно неоднородных средах, Изв.ВУЗ'ов, Радиофизика, 1976, т.19, n.8, с Бондаренко Н.Г., Еремина И.В., Таланов В.И., Уширение спектра при самофокусировке света в стеклах, Письма в ЖЭТФ, 12, в.3, 125(1970), поправка, Письма в ЖЭТФ, 12, 386 (1970) 21. Бондаренко Н.Г., Еремина И.В., Макаров А.И., Использование явления СФ для исследования пробоя при сверхкоротком взаимодействии света с веществом, в сб. Квантовая электроника, Наукова Думка, Киев, 33, с.89(1987) 22. Tzortzakis S., Sudrie L., Franko M., Prade B et al., Self-guided propagation of ultrashort IR laser pulses in fused silica, Phys. Rev. Letts., 87, n.21, (2001) Collapse IAP RAS

23. С.Н.Власов, Л.В.Пискунова, В.И.Таланов, Трехмерный волновой коллапс в модели нелинейного уравнения Шредингера, ЖЭТФ, 1989, т.95, n.6, с.1945 Collapse IAP RAS