Resonant excitation of rossby waves in the equatorial waveguide and their nonlinear evolution

Nonlinear interactions between the baroclinic Rossby waves trapped in the equatorial waveguide and the barotropic Rossby waves freely propagating across the equator are studied within the two-layer model of the atmosphere, or the ocean. It is shown that a barotropic wave can resonantly excite a pair of baroclinic waves with amplitudes much greater than its proper amplitude. The envelopes of the baroclinic waves obey Ginzburg-Landau-type equations and exhibit nonlinear saturation and formation of characteristic "domain-wall" and "dark-soliton" defects.     

Resonant excitation of coastal Kelvin waves by inertia-gravity waves

We reveal a mechanism of resonant excitation of non-dispersive coastal Kelvin waves by pairs of incident/reflected inertia-gravity waves in the rotating stratified fluid. In the simplest rotating shallow water model on the semi-infinite plane we show that the mechanism works for a continuum of incoming waves, and thus should be ubiquitous in the ocean. Subsequent slow evolution of thus excited Kelvin waves is governed by harmonically forced simple-wave equation and leads to nontrivial transport and mixing properties.     

Resonant excitation of intense acoustic waves in crystals

The resonant excitation of an intense elastic wave through nonspecular reflection of a special pump wave in a crystal is described. The choice of the plane and angle of incidence is dictated by the requirement that the excited reflected wave be close to the bulk eigenmode with its energy flow along a free boundary. The resonance parameters have been found for a medium with an arbitrary anisotropy. General relations are concretized for monoclinic, rhombic, and hexagonal systems. A criterion is formulated for an optimal selection of crystals in which the resonant reflection is close to the conversion one, when almost all of the energy from the incident beam of the pump wave falls into the near-surface narrow high-intensity reflected beam. Estimates and illustrations are given for such crystals as an example. The intensity of the reflected beam increases with its narrowing, but its diffraction divergence also increases with this narrowing. Nevertheless, the intensity of the beam can be increased by a factor of 5–10 at sufficiently high frequencies while keeping its divergence at an acceptable level. Amplification by two orders of magnitude can be achieved by compressing the beam in two dimensions through its double reflection.     

Solitary waves in a binary nonlinear waveguide array

Based on the coupled-mode theory, the propagation of light pulses is studied analytically for a system of an infinite number of tunnel-coupled parallel equidistant waveguides of optically nonlinear materials; in the considered system, waveguides with a positive refractive index alternate with waveguides with a negative refractive index. Partial solutions to a system of nonlinear equations describing the evolution of these pulses are found in the case in which fields in adjacent waveguides differ only in the phase factor. For a solitary wave formed by coupled wave packets localized each in its own waveguide, these solutions describe the stationary propagation in a definite direction. It is shown that the coupling strength between waveguides has an effect on the propagation rate of the obtained stationary pulses.     

Resonant nonlinear optics of backward waves in negative-index metamaterials

The extraordinary properties of resonant four-wave mixing of backward and ordinary electromagnetic waves in doped negative-index materials are investigated. The feasibility of independent engineering of the negative refractive index and the nonlinear optical response as well as quantum control of the nonlinear propagation process in such composites is shown due to the coherent energy transfer from a control field to a signal field. Laser-induced transparency, quantum switching, frequency-tunable narrow-band filtering, amplification, and realizing a miniature mirrorless optical parametric generator of the entangled backward and ordinary waves are among the possible applications of the investigated processes.     

Phase transitions of nonlinear waves in quadratic waveguide arrays

We study two-color parametric nonlinear modes in waveguide arrays with a quadratic nonlinear response. We predict theoretically and observe experimentally a new type of phase transition manifested in an abrupt power-controlled change of the mode structure from unstaggered to staggered, due to the interplay of localization and synchronization in parametrically driven discrete systems.     

Controlling the propagation of optical rogue waves in nonlinear graded-index waveguide amplifiers

A unified theory to construct exact optical rogue wave solutions of (1+1)-dimensional nonlinear Schrdinger equation with varying coefficients is proposed. The dynamics of the first-order optical rogue waves in nonlinear graded-index waveguide amplifiers exhibiting self-focusing or self-defocusing Kerr nonlinearity are also investigated. Moreover, under the suitable parameter condition, the propagation characteristics of the rogue waves in the nonlinear optical media are discussed. The properties of the optical rogue waves, such as width, amplitude, and position, can be controlled in the nonlinear optical media.     

Resonant nonlinear interactions between atmospheric waves in the polar summer mesopause region

Data obtained from the mobile SOUSY VHF radar at And(ya/Norway in summer 1987 have been used to study the nonlinear interactions between planetary waves, tides and gravity waves in the polar mesosphere, and the instability of background atmosphere above the mesopause. It is observed that 35-h planetary wave, diurnal, semidiurnal and terdiurnal tides are the prominent perturbations in the Lomb-Scargle spectra of the zonal wind component. By inspecting the frequency combinations, several triads are identified. By bispectral analysis it is shown that most bispectral peaks stand for quadratic coupling between tidal harmonics or between tide and planetary or gravity wave, and the height dependence of bispectral peaks reflects the variation of wave-wave interactions. Above the mesopause, the occurrence heights of the maximum L-S power spectral peaks corresponding to the prominent wave components tend to increase with their frequencies. This may result from the process in which two low frequency waves interact to generate a high frequency wave. Intensities of the planetary wave and tides increase gradually, arrive at their maxima, and then decay quickly in turn with increasing height. This kind of scene correlates with a "chain" of wave-wave resonant interactions that shifts with height from lower frequency segment to higher frequency segment. By instability analysis, it is observed that above the mesopause, the Richardson number becomes smaller and smaller with height, implying that the turbulent motion grows stronger and stronger and accordingly the background atmosphere more and more instable. It is suggested that the wave-wave sum resonant interaction and the wave dissipation due to instability are two dominant dynamical processes that occur in the mesopause region. The former invokes the energy transfer from lower frequency waves to higher frequency waves. The latter results in the heating of the atmosphere and accelerating of the background flow.     

Parametric excitation of spin waves in a nonlinear magnetostatic resonator

A theory of spin wave parametric instability is developed that simultaneously allows for cubic anisotropy and first- and second-order uniaxial anisotropies. The contributions of various anisotropies to a dispersion relation and first-and second-order nonlinearity coefficients are considered. A technique for studying the parametric instability of oscillations in magnetostatic resonators that relies on measuring their Q factors is proposed. Measuring data are used to determine the relaxation frequencies of parametrically excited spin waves in yttrium iron garnet films at frequencies close to 1 GHz. It is shown that a nonlinearity in the bias dependence of the spin wave frequencies should be allowed for in studying the relaxation parameters of ferrites.     

Sound scattering by spatially localized inhomogeneities in a shallow-water waveguide in the presence of internal waves

A method is developed for solving the problem of sound scattering by concentrated inhomogeneities in a waveguide of small depth in the presence of internal waves (IW) typical of an oceanic shelf. The sound field fluctuations related to the motion of a model scatterer (a soft spheroid) and to the propagation of the IW are calculated and analyzed. It is shown that the field of internal waves considerably affects the scattered sound field even when the source-receiver and source-scatterer distances are relatively small (about several kilometers). This effect depends not only on the amplitude of the IW, but on their propagation direction as well.     

TE waves in a symmetric dielectric slab waveguide with a Kerr-like nonlinear permittivity

The propagation characteristics of TE waves guided by a film with a Kerr-like nonlinear permittivity are investigated theoretically. The dispersion equations for positive and negative nonlinear coefficients are derived by introducing the maximum field amplitude as a parameter for the nonlinearity. Typical numerical results for dispersion characteristics are shown. For a hollow waveguide with positive nonlinear coefficient, the threshold power flow is determined numericlly from the viewpoint of applications to optical power clipping. It is found that the threshold power flow is proportional to the square root of the unperturbed permittivity difference between the film, and cladding.     

Nonlinear TE-polarized quasi-surface waves in a symmetric optical waveguide with a nonlinear core

A theory of nonlinear polarized symmetric quasi-surface waves in a symmetric planar structure with a nonlinear core and linear coatings has been proposed. The nonlinearity of the core is caused by exciton-photon interaction and optical exciton-biexciton conversion. The dispersion laws for propagating waves have been obtained and studied.     

Resonant double excitation observed in the near-threshold evolution of the photoexcited F K alpha satellite intensity in NaF

We present a precise measurement of the photoexcited F K alpha satellite intensity's evolution for NaF from [1s2p] double excitation threshold to saturation. A direct comparison between the observed evolution and the x-ray absorption spectrum was successfully made, and the contribution of multielectron transitions to the absorption spectrum was clearly resolved for the first time. A resonance-like feature observed in the near-threshold evolution is attributed to the [1s2p]3p(2) resonant double excitation as confirmed by calculations.     

Breaking of balanced and unbalanced equatorial waves

A clear-cut signature of a wave-breaking event is irreversible modification of the mean flow. In this paper, we provide examples of different breaking mechanisms and show that breaking scenario of equatorial waves in the beta-plane shallow water model is determined by the degree of balance between the zonal component of the Coriolis force and the pressure gradient. Our analysis is based on a specially designed numerical method which guarantees two essential conditions to simulate nonlinear equatorial waves: (i) the scheme converges toward weak solutions including shocks and (ii) preserves the steadiness of balanced stationary solutions. This allows for accurate diagnostics of Lagrangian invariants of motion such as passive tracer density or potential vorticity. For unbalanced waves, the lack of balance leads to shock formation in finite time. In shock fronts, the variation of the dissipation rate induces a nonadvective potential vorticity flux and violates the local potential vorticity conservation valid for smooth solutions. This dissipative breaking mechanism is generic for unbalanced waves and is associated with enhanced mixing. For long, balanced (Rossby) waves, breaking consists in appearance of recirculation regions. It results in the formation of propagating patterns, the equatorial modons, which trap fluid particles. Such breaking occurs during the propagation of Rossby wave packets with positive geopotential anomaly and is strengthened by decreasing fluid depth. The modons are robust and collide quasielastically with Kelvin waves.     

Relativistic excitation of beat waves in a plasma in the presence of an external magnetic field

Summary A theoretical investigation of the nonlinear relativistic excitation of the longitudinal electron plasma wave at the beat frequency of two colinear laser beams has been made in a hot, collisionless and homogeneous plasma in the presence of an external magnetic field. The relativistic Vlasov equation has been solved to obtain the nonlinear response of magnetized electrons. It is observed that the power conversion efficiency of the excited-electron plasma wave at the difference frequency is much higher for the relativistic calculation than that for the nonrelativistic calculations. It is further noticed that the power conversion efficiency of the beat wave excitation increases slowly with the external magnetic field when the colinear laser beams propagate transverse to the direction of the external magnetic field, whereas it is almost unaffected when the incident waves propagate parallel to the direction of the magnetic field.

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Riassunto Si è effettuata una ricerca teorica dell'eccitazione relativistica nonlineare dell'onda longitudinale del plasma dell'elettrone ad una frequenza di battimento di due raggi laser colineari in un plasma omogeneo, caldo e senza collisioni, in presenza di un campo magnetico esterno. è stata risolta l'equazione di Vlasov relativistica per ottenere la risposta nonlineare di elettroni magnetizzati. Si osserva che l'efficacia di conversione di potenza dell'onda di plasma degli elettroni eccitati alla frequenza di differenza è molto superiore per il calcolo relativistico che quella per i calcoli non relativistici. Si nota inoltre che l'efficacia di conversione di potenza dell'eccitazione d'onda di battimento aumenta lentamente con il campo magnetico esterno quando i raggi laser colineari si propagano trasversalmente rispetto alla direzione del campo magnetico esterno, mentre rimane quasi immutata quando le onde incidenti si propagano parallelamente alla direzione del campo magnetico.

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Резюме Проводится теоретическое исследование нелинейного релятивистского возбуждения продольных электронных плазменных волн на частоте биений двух соосных лазерных пучков в торячей, бесстолкновительной и однородной плазме в присутствии внешнего магнитного поля. Чтобы получить нелинейный отклик электронов в магнитном поле, решается релятивистское уравнение Власова. Получается, что эффективность конверсии мощности для возбужденной электронной плазменной волны на разностной частоте оказывается много большей для релятивистских вычислений, чем для нерелятивистских вычислений. Затем отмечается, что эффективность возбуждения биений увеличивается медленно с ростом внешнего магнитного поля, когда соосные лазерные пучки распространяются поперек направления внешнего магнитного поля, тогда как эффективность возбуждения почти не изменяется, когда падающие волны распространяются параллельно направлению магнитного поля.

     

非线性光波导中基波和二次谐波的模场分布研究

非线性波导是一种重要的光量子器件。采用马卡梯里近似,可以近似描述波导的模场分布特征。针对ee-e准相位匹配的周期极化铌酸锂波导,分析波长为1 064 nm的基波和532 nm的二次谐波的基模模场分布。结果表明:如果波导为嵌入型正方形波导,基波和二次谐波的光斑基本为圆形,基波场分布范围较大;在截面正方形边长为5 μm并且芯区比包层折射率略高0.02时,波导就能将两种光波场基本约束在芯区中,但是这种波导边长为0.5 μm时约束能力就变得很差;如果采用芯区与包层折射率差别较大的波导,芯区边长为0.5 μm就可以将两种场分布基本约束在芯区中。结果对分析其他类型的非线性波导的模场分布具有指导意义。