Planar light bullets under conditions of second-harmonic generation

Abstract

We study solutions to second-harmonic-generation equations in two-dimensional media with anomalous dispersion. The analytical solution is obtained in an approximate form of the planar spatiotemporal two-component soliton by means of the averaged Lagrangian method. It is shown that a decrease in the amplitudes of both soliton components and an increase in the value of the transverse coordinate are accompanied by an increase in their temporal duration. Within this variational approach, we have managed to find a stability criterion for the light bullet and a period of oscillations of soliton parameters. Then, we use the obtained form as an initial configuration to carry out the direct numerical simulation of soliton dynamics. We demonstrate stable propagation of spatiotemporal solitons undergoing small oscillations predicted analytically for a long distance. The formation of a two-component light bullet is shown when we launch a pulse only at the fundamental frequency. In addition, we investigate the phase and group-velocity mismatch effects on the propagation of pulses.

Trapping of two-component light bullets in a gradient waveguide with normal group dispersion

“…Since anomalous dispersion supports light bullets in 2D+1 media even without waveguide [6, 8], our principal interest is to investigate waveguide at normal group velocity dispersion. The simulation and observation are conducted up to z = 500 l nl .…”

“…The present study of light bullets in a planar waveguide at quadratic nonlinearity is undertaken as a logical continuation of our previous investigations for homogeneous media [8, 9]. A crucial role of the competition between quadratic nonlinearity, dispersion, diffraction and inhomogeneity was discussed shortly in [10, 11].…”

“…Spatio-temporal solitons, called also light bullets, were carefully studied either theoretically or experimentally by numerous researchers [4, 6, 7]. Recently, in [8, 9] we presented a detailed theory of breathing light bullets in a homogeneous medium with quadratic nonlinearity at anomalous dispersion. Using the averaged Lagrangian method, we derived approximate analytical solutions in the form of two-component planar spatio-temporal solitons.…”

Дифракционный Предел В Теории Световых Пуль

“…При записи (3) и (4) сделано предположение, что выполнены условия фазового и группового синхронизмов. В однородной среде (q = q 1 = q 2 = 0) уравнение (1) и система (3), (4) имеют решения в виде одномерных ( ⊥ ψ = ⊥ ψ 1 = ⊥ ψ 2 = 0) временных керровского и двухчастотного параметрического солитонов [1,7]:…”

“…Следует отметить, что этот метод успешно применялся для решения граничной задачи формирования и распространения временного солитона нелинейного уравнения Шредингера (НУШ) в однородной среде [3]. Кроме того, метод УЛ был использован для учета влияния нелинейных длинноволновых поперечных возмущений на временные солитоны различных уравнений [4,6,7]. Перечисленные здесь исследования касались распространения солитонов в однородных средах в отсутствие рефракции.…”