Three-wave Parametric Interaction Research Articles

Hardness and Young's modulus of BaGa4S7 and BaGa4Se7 nonlinear optical crystals

We report hardness and Young's modulus measurements of two recently developed non-chalcopyrite, non-centrosymmetric crystals, BaGa4S7 and BaGa4Se7, which seem very promising for three-wave parametric interactions in the mid-IR part of the spectrum between 5 and 18 μm. The obtained averaged values for the hardness from nanoindentation tests, converted into Vickers hardness number, are 556 kg/mm2 for the sulphide and 336 kg/mm2 for the selenide compound, respectively. Knowledge of these values will be essential for proper polishing and fabrication of optical elements, the wide use and commercialization of these novel non-oxide nonlinear crystals, which possess a number of other advantages over classical chalcopyrites operating in the same spectral window.

Influence of two-stream relativistic electron beam parameters on the space-charge wave with broad frequency spectrum formation

We developed a cubic non-linear theory describing the dynamics of the multiharmonic space-charge wave (SCW), with harmonics frequencies smaller than the two-stream instability critical frequency, with different relativistic electron beam (REB) parameters. The self-consistent differential equation system for multiharmonic SCW harmonic amplitudes was elaborated in a cubic non-linear approximation. This system considers plural three-wave parametric resonant interactions between wave harmonics and the two-stream instability effect. Different REB parameters such as the input angle with respect to focusing magnetic field, the average relativistic factor value, difference of partial relativistic factors, and plasma frequency of partial beams were investigated regarding their influence on the frequency spectrum width and multiharmonic SCW saturation levels. We suggested ways in which the multiharmonic SCW frequency spectrum widths could be increased in order to use them in multiharmonic two-stream superheterodyne free-electron lasers, with the main purpose of forming a powerful multiharmonic electromagnetic wave.

Parametric interaction of optical waves in metamaterials under low-frequency pumping

The influence of phase effects under three-wave parametric interaction and low-frequency pumping in metamaterials is studied in the case of a negative refractive index at a signal-wave frequency. It is found that the efficiency of the backward signal-wave amplification is the higher, the greater the ratio of the intensities of the idler and signal waves at the input to the metamaterial. An increase in the idler wave intensity at the input by five times, as compared to the signal-wave intensity, leads to a nonlinear increase in the signal-wave amplification by almost 20 times. According to the analytic expressions obtained in the constant-intensity approximation, the choice of the optimal parameters for the pump intensity, total length of the metamaterial and phase detuning will facilitate the implementation of regimes of effective amplification and generation of the signal wave. A comparison is made with the results obtained in the constant-field approximation, and a numerical estimate of the expected efficiency of the frequency conversion is presented. Control of frequency and pump power is shown to make possible the smooth tuning of the parametric converter frequency. The developed method can be used to design frequency converters based on nonlinear metamaterials.

Phase Effects of the Parametric Interaction in Metamaterials

We study the phase effects of the three-wave parametric interaction in metamaterials considering the negative refraction at the frequency of a signal wave. We analyze the efficiency of energy conversions between two direct waves with respect to the energy of the backward signal wave along with the dynamics of the signal-wave amplification in metamaterials. We show that there exist optimum values of the fundamental-wave intensity and the phase mismatch at which the efficiency of conversion is maximum. We obtain an analytic expression for the optimum value of the relative length of the metamaterial and present a numerical evaluation of the expected value for efficiency of the frequency parametric conversion in dielectric waveguides. A sufficient enhancement in the signal-wave amplification, which is possible at optimum values of the pump intensity and the metamaterial total length, leads to the parametric generation of the signal wave. Changing the frequency and power of the pump wave, one can realize a regular tuning of the frequencies of parametric converters.

Strongly Enhanced Stimulated Brillouin Backscattering in an Electron-Positron Plasma.

Stimulated Brillouin backscattering of light is shown to be drastically enhanced in electron-positron plasmas, in contrast to the suppression of stimulated Raman scattering. A generalized theory of three-wave coupling between electromagnetic and plasma waves in two-species plasmas with arbitrary mass ratios, confirmed with a comprehensive set of particle-in-cell simulations, reveals violations of commonly held assumptions about the behavior of electron-positron plasmas. Specifically, in the electron-positron limit three-wave parametric interaction between light and the plasma acoustic wave can occur, and the acoustic wave phase velocity differs from its usually assumed value.

Generation of dissipative structures in self-oscillating ring systems upon parametric interaction of spin waves

A quasi-periodic sequence of pulses in a self-oscillating ring system with a resonant amplifier and a ferromagnetic film has been generated upon three-wave parametric interaction of spin waves. It is established that the generated pulses are analogs of dissipative bright solitons, which are formed as a result of competition between amplification and loss, as well as between time dispersion and nonlinearity. To describe the mechanism of formation of these structures, we have proposed a model in the form of three parametrically coupled differential equations with amplification and a differential equation of linear oscillator. Under certain assumptions, this model has analytical solutions in time in the form of structures with a profile similar to that of bright solitons.

To the theory of formation a wide multiharmonic spectrum in two-stream relativistic electron beam

The quadratic nonlinear theory of multiharmonic interactions of space charge wave harmonics which increasing owing to the effect of two-stream instability in a two-stream relativistic electron beam is constructed. The multiple three-wave parametric resonance interactions take into consideration. The analysis of the influence of two-stream relativistic beam parameters on the frequency spectrum form of growing multiharmonic space charge wave excited in the investigated system is carried out

Multimode phonon cooling via three-wave parametric interactions with optical fields

We discuss the possible cooling of different phonon modes via three-wave mixing interactions of vibrational and optical modes. Since phonon modes exhibit a variety of dispersion relations or frequency spectra with diverse spatial structures, depending on the shape and size of the sample, we formulate our theory in terms of relevant spatial mode functions for the interacting fields in any given geometry. Our general formulation is applicable to cooling of any low-frequency excitation mode in matter which can give appreciable inelastic light scattering via the modulation of the optical dielectric function. We discuss the possibility of Dicke-like collective effects in phonon cooling and present explicit results for simultaneous cooling of two-phonon modes via the anti-Stokes up-conversions. We show that the bimodal cooling should be observable experimentally.

Generation of Chaotic Microwave Pulses in Ferromagnetic Film Ring Oscillators Under External Influence

This study reports on the experimental results of chaotic microwave (MW) pulse generation in a ferromagnetic film ring oscillator under pulse-modulated (PM) and narrowband noise forces. Chaotic dynamics of the investigated self-oscillatory system is produced through three-wave parametric interactions of spin waves. It is shown, that periodical sequences of chaotic MW pulses are generated under a PM force and solitary chaotic MW pulses are generated under a noise force. Such pulses are formed through forced chaos synchronization. For description of forced chaos synchronization phenomenon, a ferromagnetic film ring oscillator model with nonlinear amplification and delay time is constructed. This model is based on the use of the Landau-Lifshitz equation, magnetostatic approximation and the Holstein-Primakoff transformation. Calculation results of chaos suppression under an external harmonic force are demonstrated.

Optically pumped coherent mechanical oscillators: the laser rate equation theory and experimental verification

We develop a theory describing the operation of an opto-mechanical oscillator as a phonon laser using a set of coupled equations that is analogous to the standard set of laser rate equations. We show that laser-like parameters that characterize gain, stored energy, threshold, efficiency, oscillation frequency linewidth, and saturation power can be introduced for an opto-mechanical oscillator driven by photo-thermal or radiation pressure forces. We then apply the theoretical model to the experimental results for photo-thermally driven oscillations in a Si waveguide opto-mechanical resonator and show good agreement between the theory and experiments. We also consider the microscopic mechanism that transforms the energy of incoherent thermal phonons into coherent oscillations of a single phonon mode and show remarkable parallels with the three-wave parametric interactions in optics and also with opto-electronic oscillators used in microwave photonics.

PbIn_6Te_10: new nonlinear crystal for three-wave interactions with transmission extending from 17 to 25 µm

We have grown single crystals of PbIn6Te10, with clear transparency from 3 to 20 µm, and showed that this new nonlinear material possesses sufficient birefringence for phase-matching of three-wave parametric interactions and a nonlinear coefficient of 51 pm/V.

Pulse dynamics upon three-wave parametric interaction in the presence of cubic and quadratic nonlinearities

The features of the three-wave parametric interaction in a medium with quadratic and cubic nonlinearities upon low-frequency pumping and nonzero detuning from the phase matching were studied. It has been shown that the common wave packet formed by the signal and idle waves is decayed into partial pulses, whose dynamics is determined by effective dispersion parameters. The presence of two types of nonlinearities extends the possibilities of controlling the dynamics of the forming partial pulses due to the variation of the pump wave power. The velocity of recession of partial pulses can reach large values and even exceed the speed of light in the vacuum.

Generation of tunable infrared femtosecond pulses via parametric visible-to-infrared frequency conversion

We propose two methods for ultrashort pulse parametric visible-to-infrared frequency conversion, that are directly applied to extend the tuning range of a commercial Ti:sapphire laser-noncollinear optical parametric amplifier system. The first method is based on broadband noncollinear four-wave optical parametric amplification in fused silica, and the second is based on cascaded three-wave parametric interaction in a single BBO crystal. The proof-of-principle experiments demonstrate generation of sub30-fs, 20 µJ pulses, broadly tunable across the infrared (1‐3 µm) spectral range.

Parametric interaction and compression of optical pulses in field of high-power pump wave

It is shown that, in the undepleted pump approximation, the nonlinear problem of the three-wave parametric interaction under the conditions of phase mismatch can be reduced to a problem of linear interaction of the signal and idle waves with a strong low-frequency pump wave. The whole wave packet formed by the two waves breaks down to partial pulses whose dynamics is controlled by effective dispersion parameters. This can be accompanied by the compression of either one of the pulses that comprises the wave packet or the whole wave packet.

Classification of angular quasi-phase matching loci in periodically poled uniaxial crystals

We performed an exhaustive determination and classification of all the possible angular quasi-phase matching (AQPM) directions of three-wave nonlinear optical parametric interactions in periodically poled uniaxial crystals. We report 74 classes of AQPM loci depending on the wavelength dispersion of the principal refractive indices, the period of inversion of the sign of the second-order electric susceptibility, and on the eight possible combinations of polarization of the three interacting waves. Their complete classification is summarized in a schematic table providing the topological understanding of AQPM. The cases of second harmonic and difference-frequency generations in 5%MgO:PPLN are detailed.

Complete classification of the direction loci for three-wave collinear quadratic parametric interactions in biaxial acentric crystals

One new topological classification of the phase-matching direction loci for sum/difference frequency generation in biaxial acentric crystals is presented. Based on nine fundamental axial wave constant mismatches, 12 locus indices are used to distinguish permissible direction loci. Totally 66 kinds of combined loci belonging to 30 main classes are found and categorized by a set of ternary-digit class symbols or equivalently by sequence numbers. They are well illustrated in a classification diagram, indicative of 170 possible transitions among the loci. By an analysis of the dispersion of refractive indices, the historic “optically well-behaved crystals” are redefined and improved with simplified classification diagrams and corresponding schematic stereographic projections.

Specific architectures for optical parametric oscillators

Optical parametric oscillators are coherent light sources showing properties that are not encountered with usual laser sources. This article deals with optical architectures that take advantage of the specific properties of the three-wave mixing parametric interaction. We show that optical cavities can be specifically designed to increase either the optical conversion of the parametric process or to reduce dramatically the emitted line width. To cite this article: A. Berrou et al., C. R. Physique 8 (2007).

Asymptotic treatment of the three-wave nonlinear parametric interaction

A novel integral representation suitable for the study of asymptotic ($L/L_{0}\,{\gg}\,1$, $L$ being the plasma length and $L_{0}$ the basic gain length) stability of the inhomogeneous three-wave interaction is formulated and applied to the special case of uniform gain and ramp wavenumber mismatch. The absolute instability condition is $\kappa L_{0} \,{<}\, \pi /8$ ($\kappa$ being the mismatch gradient), with the wave conversion performed in a zone of width $4/\kappa L_{0}$ located at the boundary of wave incidence.

Spatial solitons in type II quasiphase-matched slab waveguides.

The existence and dynamics of one-dimensional spatial solitons formed upon propagation in quasiphase-matched gratings, through three-wave parametric interaction, is analyzed. We study the general case in which the grating exhibits a periodic modulation of both the refractive index and the second-order susceptibility. It is demonstrated that for negative effective wave vector mismatch the induced third-order nonlinearities increase the domain of soliton instability. Finally, the dependence of the efficiency of the second harmonic generation process in the soliton regime, on the parameters of the grating, is discussed.

Overlap optimization in semiconductor waveguides by wafer bonding

In this work, we show that the use of a wafer-bonding technique, wherein an inverted half-waveguide structure is bonded on the upright half to form a complete waveguide, optimizes the overlap factor present in three-wave parametric interactions realized in 43m semiconductor waveguides. These optimized waveguides can be used for efficient frequency-mixing devices which detect or emit infrared light.