Interaction Of Counter-propagating Waves Research Articles

Hierarchy of coupled mode and envelope models for bi-directional microresonators with Kerr nonlinearity

We consider the interaction of counter-propagating waves in a bi-directionally pumped ring microresonator with Kerr nonlinearity. We introduce a hierarchy of the mode expansions and envelope functions evolving on different time scales set by the cavity linewidth and nonlinearity, dispersion, and repetition rate, and provide a detailed derivation of the corresponding hierarchy of the coupled mode and of the Lugiato-Lefever-like equations. An effect of the washout of the repetition rate frequencies from the equations governing the dynamics of the counter-propagating waves is elaborated in details.

Gravity-capillary waves on the free surface of a liquid dielectric in a tangential electric field

Processes of propagation and interaction of nonlinear gravity-capillary waves on the free surface of a deep non-conducting liquid with high dielectric constant under the action of a tangential electric field are numerically simulated. The computational method is based on the time-dependent conformal transformation of the region occupied by the fluid into a half-plane. In the limit of a strong electric field, when the gravitational and capillary forces are negligibly small, there exists an exact analytical solution of the electro-hydrodynamic equations describing propagation without distortions of nonlinear surface waves along (or against) the electric field direction. In the situation where gravity and capillarity are taken into account, the results of numerical simulations indeed show that, for large external field, the waves traveling in a given direction tend to preserve their shape. In the limit of a strong electric field, the interaction of counter-propagating waves leads to the formation of regions, where the electrostatic and dynamic pressures undergo a discontinuity, and the curvature of the surface increases infinitely. The Fourier spectrum of the surface perturbations tends to the power-law distribution (k^-2). In the case of a finite electric field, the wave interaction results in a radiation of massive cascade of small-scale capillary waves that causes the chaotic behavior of the system. The investigated mechanism of interaction between oppositely-traveling waves can enhance development of the capillary turbulence of the fluid surface.

Transient time in nonlinear interaction of counter-propagating waves with the effect of pump absorption and phase mismatching

The parametric interaction of three waves, one of which travel in direction opposite to other, is associated with a number of unusual phenomena that find their applications. One of such phenomena is an extremely long transient process of amplitude changing of the output signal. In this paper, the impact of pump-wave absorption and the phase mismatch magnitude on the course of the process is investigated. It is shown that the absorption lead to significant changes in the process time, and the phase causes changes in dynamics but not in duration of the process.

Formation of Regions with High Energy and Pressure Gradients at the Free Surface of Liquid Dielectric in a Tangential Electric Field

Nonlinear dynamics of the free surface of an ideal incompressible non-conducting fluid with high dielectric constant subjected by strong horizontal electric field is simulated on the base of the method of conformal transformations. It is demonstrated that interaction of counter-propagating waves leads to formation of regions with steep wave front at the fluid surface; angles of the boundary inclination tend to {\pi}/2, and the curvature of surface extremely increases. A significant concentration of the energy of the system occurs at these points. From the physical point of view, the appearance of these singularities corresponds to formation of regions at the fluid surface where pressure exerted by electric field undergoes a discontinuity and dynamical pressure increases almost an order of magnitude.

Jet formation at the interaction of localized waves on the free surface of dielectric liquid in a tangential electric field

Nonlinear dynamics of the free surface of finite depth non-conducting fluid with high dielectric constant subjected to a strong horizontal electric field is considered. Using the conformal transformation of the region occupied by the fluid into a strip, the process of interaction of counter-propagating waves is numerically simulated. The nonlinear solitary waves on the surface can separately propagate along or against the direction of electric field without distortion. At the same time, the shape of the oppositely traveling waves can be distorted as the result of their interaction. In the problem under study, the nonlinearity leads to increasing the wave amplitudes and the duration of their interaction. This effect is inversely proportional to the fluid depth. In the shallow water limit, the tendency to the formation of a vertical liquid jet is observed.

Transient processes in the parametric interaction of counter-propagating waves

We present a comparative analysis of transient processes in media with a negative refractive index for the parametric interaction of co- and counter-propagating waves. The transient time for the interaction of counter-propagating waves is shown to considerably exceed that for the interaction of co-propagating waves. In the case of counter-propagating waves, we present fitting results for the generated wave amplitude as a function of time and for the transient time vs. the amplitude of the pump wave and the length of the medium.

Compression of Nanosecond Pulses upon Reflection from a Thermally Nonlinear Medium

We consider a boundary-value problem for nonlinear total internal reflection of laser pulses from a semi-infinite thermally nonlinear medium. Numerical modeling of the pulse forming upon reflection under the conditions of interaction of counter-propagating waves in a scheme with a retrodirective mirror has been carried out the approximation of noninterfering pulses, the possibility of controlling the shape and compression of the pulse in the nanosecond range of durations has been shown. The results obtained are in qualitative agreement with the known experimental data.