Interaction of counterpropagating discrete solitons in a nonlinear one-dimensional waveguide array

We experimentally investigate the interaction of counterpropagating discrete solitons in a one-dimensional waveguide array in photorefractive lithium niobate. While for low input powers only weak interaction and formation of counterpropagating vector solitons are observed, for higher input powers a growing instability results in discrete lateral shifting of the formed discrete solitons. Numerical modeling shows the existence of three different regimes: stable propagation of vector solitons at low power, instability for intermediate power levels leading to discrete shifting of the two discrete solitons, and an irregular temporal dynamic behavior of the two beams for high input power.     

Lateral field instability and six-wave mixing in a diode laser with broad active area

The electromagnetic field inside a nonlinear active medium of a laser is considered as a system of counterpropagating waves. Such an approach changes radically an earlier studied behavior of the lateral field instability due to self-deformaion (or self-focusing). In our calculations we used an expression for a laser field in the form of two “strong” counterpropagating waves whose complex amplitudes have weak perturbations. Amplitude perturbations of each of the “strong” waves can be presented by two spatial harmonics corresponding to two weak perturbation waves with wave vectors making some tilted angle ±φ with the cavity axis. Thus six waves would participate in the interaction: two counterpropagating strong waves and two pairs of weak waves. Using this approach, we have developed a theory for the propagation of four “weak” perturbation waves in a nonlinear amplifying medium in the presence of two counterpropagating “strong” waves. It is shown that perturbation waves with tilted angle φ⋍0.5–1.2° inside the active region, and respecively, with the side lobes of the far-field pattern at ∼1.7–4°, have the greatest growth increment. These perturbation waves produce lateral intensity modulation with period 10–30 μm for the 0.85 μm lasing wavelength. The appearance of such waves corresponds to the instability threshold of a homogeneous lateral distribution of optical power in a diode laser. The present theory makes it possible to investigate the stability of the homogeneous lateral optical intensity distribution in a diode laser of any design. This allows one to choose a suitable design of a laser with a homogeneous lateral distribution at high radiation power. Translated from Preprint No. 43 (1992) of the Lebedev Physics Institute, Russian Academy of Sciences.     

Interaction of counterpropagating few cycle light pulses in nonlinear dielectric media and radiation generation at combination frequencies in this process

The regularities of the interaction of counterpropagating optical pulses of only a few oscillations of the light field in nonlinear dielectric media are studied theoretically. The temporal structure of the pulse field, due to its interaction with the counterpropagating pulse, is shown to be varied such that the field zeros are the most shifted in time and its extreme values are not shifted. The center of mass of the spectral density is shifted to the short-wavelength region. The efficiency of these phenomena is determined by the energy of the counterpropagating pulse and does not depend on its duration and spectral composition. The possibility of wave generation at tripled and combination frequencies is demonstrated for the media whose size is less than the interaction region. The efficiency of this generation with respect to the phase mutual modulation is shown to be increasing with a decrease in the number of oscillations in colliding pulses.     

Forces exerted on atoms by stochastic laser fields

We present analytical results and numerical simulations for the force exerted on moving atoms in the fields of two counterpropagating waves whose amplitudes or phases are described as stochastic processes. We assume that one field repeats the other with some delay, as would occur when the two fields derive from a common source through a beam splitter and mirrors. We show that, just as with the force exerted by the field of two counterpropagating sequences of π-pulses, or two counterpropagating bichromatic or frequency-modulated waves, the force on an atom in counterpropagating stochastic waves may considerably exceed the force exerted by the field of a single running wave. For comparison we also discuss the interaction of an atom with two counterpropagating waves when one of them is monochromatic and the other one has a stochastic phase. In this case the force substantially exceeds the force exerted by the field of a single running wave but appreciably smaller then the radiative force in the counterpropagating waves in which one field repeats the other with some delay.     

Wave interaction in acoustic resonators with and without hysteresis

Nonlinear interaction of counterpropagating waves in solids is considered by using a general approach taking into account only the cumulative (resonant) nonlinear perturbations giving a nonzero contribution over the period and, consecutively, potentially able to significantly modify the linear solution. Different stress-strain relations are addressed, including those with hysteresis which serve as basic models for the recent acoustic experiments with rock and metals. An important case of the interaction of counterpropagating waves with close amplitudes in a high-Q resonator (bar) with hysteresis is specially addressed and compared with the case of a ring resonator.     

Application of the local mode theory to nonlinear waveguides

Local mode theory for two counterpropagating waves in nonlinear waveguides is formulated. This model allows us to describe the transverse effects as well as the counterpropagating waves interaction in optical waveguides. The results are applied to the analysis of the nonlinear Fabry-Perot waveguide resonator and are compared with the conventional coupled mode theory solution.     

Stimulated radiation pressure acting on an atom nonadiabatically interacting with the field of counterpropagating frequency-modulated waves

The stimulated radiation pressure acting on an atom nonadiabatically interacting with the field of counterpropagating frequency-modulated waves is shown to reach high values typical for the rapid adiabatic passage of the instantaneous frequency of the field of the counterpropagating waves through resonance with an atomic transition. Under the appropriate choice of interaction parameters, the radiation pressure changes insignificantly in a wide range of atomic velocities.     

Transverse and soliton instabilities due to counterpropagation through a reflection grating in Kerr media

Transverse instabilities are shown to accompany counterpropagation of optical beams through reflection gratings in Kerr media. The instability threshold of continuous waves is analytically derived, and it is shown that the presence of the grating broadens and narrows the stability region of plane waves in focusing and defocusing media, respectively. Furthermore, counterpropagating soliton stability is numerically investigated and compared with the transverse modulation instability analysis, revealing an underlying physical link.     

Coherent momentum transfer due to interaction between three-level atoms and counterpropagating laser pulses

A theoretical analysis is presented of the change in the momentum of a three-level atom due to its interaction with counterpropagating laser pulses that overlap in time. The two lower energy states of the atom are metastable; i.e., a lambda-type configuration of atomic levels is considered. The cases of two and four counterpropagating pulses having different carrier frequencies are considered. In the case of adiabatic atom-field interaction, it is shown that the atom’s momentum can change by an integer multiple of the photon momentum and the corresponding standard deviation is small as compared to the photon momentum squared.     

Counterpropagating waves on the sea surface (Results of Natural Microwave Experiment)

This paper is devoted to the analysis of the results of the natural experiment on the study of nonlinear dynamics of surface waves by microwave methods. During the experiment, waves traveling in opposition to the wind and the dominant wave system were detected by high-resolution microwave radar methods. An analysis of the results of microwave sounding made it possible to obtain a space-frequency spectrum of counterpropagating waves, to estimate their intensity, and to relate the fact of counterpropagating wave generation to experimental conditions. It was shown that the generation of counterpropagating waves under conditions of this experiment can be interpreted on the basis of the mechanism of the cubic interaction of surface gravity waves.     

Modulational instability and pattern formation in the field of noncollinear pump beams

We study pattern formation that is due to modulational instability of noncollinear counterpropagating beams. Angular misalignment of the pumps over a broad range leads to the generation of lines oriented perpendicular to the plane of the pump beams. A theoretical expression for the angular separation of the lines is in close agreement with observations. Outside this range, for both small and large misalignments, we observe squeezed hexagonal patterns.     

Magnetic-grating free-induction decay and magnetic-grating echo using ultrafast excitation pulses

The interaction of atoms with ultrafast, counterpropagating optical fields is considered. The magnetic degeneracy and hyperfine splitting of the atomic levels are included in the calculations, which are carried out for arbitrary polarizations of the incident fields. The counterpropagating fields produce spatial harmonics in the ground state density matrix (gratings) which can be monitored by backscattering of a traveling wave probe pulse. Two types of excitation schemes are analyzed. The Magnetic-Grating Free-Induction Decay (MGFID) consists of excitation with a single counterpropagating wave field, while the Magnetic-Grating Echo (MGE) involves excitation by two counterpropagating wave fields, separated in time by T. The atomic response to the probe pulse is calculated in lowest-order perturbation theory for atoms cooled below the Doppler limit of laser cooling. Both the MGFID and MGE signals consist of pulses having a duration of order of the excited state lifetime, modulated at frequencies corresponding to the various hyperfine transitions. As a function of the delay between pulses, the signals oscillate at frequencies determined by the ground state hyperfine splittings. General expressions for the MGFID and MGE signals are derived and specific results are presented for the D₂ line in Na.     

Semilinear coherent oscillator with reflection-type photorefractive gratings

The saturation intensity, oscillation spectrum, and temporal dynamics of oscillation are studied for a semilinear coherent oscillator with two counterpropagating pump waves and a photorefractive crystal with dominating reflection gratings. The instability of the single-frequency oscillation spectrum is revealed, similar to that known for an oscillator with dominating transmission gratings. The experimental manifestation of this transition in the output characteristics of the oscillator is favourably compared with numerical calculations. PACS 42.65.Hw; 05.45.-a; 42.65.Pc; 42.65.Sf     

Interaction of solitons in a medium with relaxation of gain and saturable absorption

Results of numerical simulation of soliton interaction in a laser with relaxation of gain and saturable saturation are presented. Interactions of co-and counterpropagating fast and slow solitons are analyzed. Typical scenarios of collisions and new resulting soliton-like structures are found.     

Synchronization of Distributed Electron–Wave Self-Oscillatory Systems with a Backward Wave

We present the results of studying the phenomenon of synchronization in distributed electron–wave self-oscillatory systems with a counterpropagating wave. General laws governing the appearance of the classical synchronization in distributed systems are revealed. We propose methods for increasing the synchronization bandwidth by using the distributed input of a signal to the interaction space by means of coupled waveguide structures. Transient processes in nonautonomous self-oscillation regimes are studied. In particular, the effect of ultrafast synchronization is found. The possibility of chaotic synchronization in a gyro-oscillator with a counterpropagating wave under the action of a deterministic chaotic signal is shown. Mutual oscillation regimes in a system of two distributed oscillators with coupled waveguide systems are studied.     

Interaction of counterpropagating electromagnetic waves in an absorbing plate inside a waveguide

The interaction of two counterpropagating coherent transverse electric and transverse magnetic electromagnetic waves in an absorbing plate that is placed in a waveguide with an arbitrary transverse cross section is analyzed. It is assumed that the waves with different initial phases are incident on the plate boundaries from two sides. An analytical expression for the interference transmission coefficient with respect to power is derived. Several physical features of the tunneling interference in the plate are revealed. It is demonstrated that a scenario in which an electromagnetic energy flux exists on the left-hand side of the plate and vanishes on the right-hand side or vice versa is possible at certain relations of the initial phases and amplitudes of the counterpropagating waves.     

Experimental observation of modulation instability and optical spatial soliton arrays in soft condensed matter

In this Letter we report observations of optically induced self-organization of colloidal arrays in the presence of unpatterned counterpropagating evanescent waves. The colloidal arrays formed along the laser propagation axis are shown to be linked to the breakup of the incident field into optical spatial solitons, the lateral spacing of the arrays being related to modulation instability of the soft condensed matter system.     

Collinear interaction of optical waveguide modes with an increasing space-charge wave

Collinear interaction of optical modes in a thin-film semiconductor waveguide with a space-charge wave increasing along its propagation direction has been investigated. Analytical solutions to the equations of coupled unidirectional and counterpropagating waveguide modes at their phase matching are obtained for the first time, and the dependence of the mode conversion efficiency on the space-charge wave amplification level, the coupling coefficient, and the length of the interaction region of optical modes is analyzed.     

Stimulated radiation pressure acting on an atom nonadiabatically interacting with the field of counterpropagating frequency-modulated waves

The stimulated radiation pressure acting on an atom nonadiabatically interacting with the field of counterpropagating frequency-modulated waves is shown to reach high values typical for the rapid adiabatic passage of the instantaneous frequency of the field of the counterpropagating waves through resonance with an atomic transition. Under the appropriate choice of interaction parameters, the radiation pressure changes insignificantly in a wide range of atomic velocities. Original Russian Text ? V.I. Romanenko, L.P. Yatsenko, 2007, published in Pis’ma v Zhurnal éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2007, Vol. 86, No. 12, pp. 868–872.     

Ensemble of ultra-high intensity attosecond pulses from laser-plasma interaction

The efficient generation of intense X-rays and γ-radiation is studied. The scheme is based on the relativistic mirror concept, i.e., a flying thin plasma slab interacts with a counterpropagating laser pulse, reflecting part of it in the form of an intense ultra-short electromagnetic pulse having an up-shifted frequency. In the proposed scheme a series of relativistic mirrors is generated in the interaction of the intense laser with a thin foil target as the pulse tears off and accelerates thin electron layers. A counterpropagating pulse is reflected by these flying layers in the form of an ensemble of ultra-short pulses resulting in a significant energy gain of the reflected radiation due to the momentum transfer from flying layers.