χ(2) cascading phenomena and their applications to all-optical signal processing,mode-locking,pulse compression and solitons

Cascading is the process by which the exchange of energy between optical beams interacting via second order nonlinearities (⁽²⁾) leads to various effects such as nonlinear phase shifts, the generation of new beams, all-optical transistor action, the formation of soliton-like (solitary) waves, etc. Here we review the fundamentals of the processes and discuss experimental verification of the effects and various related applications.     

A cascaded second-order approach to computing third-order scattering of noncollinear acoustic beams

A theoretical development of the third-order nonlinear scattering of sound from two noncollinear ultrasonic beams produced by baffled piston sources is presented. The third-order intermodulation (IM3) frequency components are derived by exploiting cascaded second-order nonlinear effects where the quadratic nonlinear interaction of second-order frequency components with first-order (primary) frequency components is considered. It is shown that cascaded second-order interactions generate intermodulation frequency components that are equivalent to those generated by cubic nonlinear effects. Comparison of measured and modeled amplitude sweeps demonstrate the three-to-one gain in decibels of the amplitudes of the third-order intermodulation frequency components to that of the primary frequency components. Measurements are also presented for the farfield interaction of distantly spaced sources, which results in a highly focused ultrasonic parametric array. Also considered are the nearfield interaction of closely spaced sources, which results in scattering, with good agreement to the theory.     

Letter: The Quantum Theory of the Quadratic Gravity Action for Heterotic Strings

The wave function for the quadratic gravity theory derived from the heterotic string effective action is deduced to first order in by solving a perturbed second-order Wheeler-DeWitt equation, assuming that the potential is slowly varying with respect to . Predictions for inflation based on the solutionto the second-order Wheeler-DeWitt equation continue to hold for this higher-order theory. It is shown how formal expressions for the average paths in minisuperspace {a(t), (t)} for this theory can be used to determine the shifts from the classical solutions a _cl (t) and _cl (t), which occur only at third order in the expansion of the functional integrals representing the expectation values.     

二次谐波产生的非线性相移的解析研究

给出一种分析二阶非线性级联效应的解析方法，对Ⅱ型二次谐波产生的非线性级联效应进行了详细的理论研究和分析。结果表明倍频晶体中正交输入两个振幅不相等的基波分量时，在近相位匹配下二阶非线性级联效应能够产生大的相移。利用本文的解析方法可以对任意二阶非线性相移产生的过程进行优化，从而以最小的需求输入功率来获得特定的相移。还对由非线性相移诱导的且与光强有关的偏振旋转效应和一种基于偏振旋转效应的全光偏振开关进行了分析和讨论。本文的结果对于建立一种基于Ⅱ型倍频晶体中非线性相移诱导偏振旋转效应的新全固化被动锁模飞秒激光装置具有十分重要的意义。     

Quadratic spatial soliton generation by seeded downconversion of a strong harmonic pump beam

Two-dimensional quadratic spatial solitons were generated experimentally near phase-matching conditions for type II frequency doubling in KTP by the seeding of a strong second-harmonic field with a weak input at the fundamental wavelength. The self-trapped beams were shown to be insensitive to the energy, phase, and polarization of the fundamental-frequency seed input beam.     

Phase modulations due to collisions of beam pairs in nonlocal nonlinear media

In this paper, discussed is the evolution of two co-propagating optical beams in parallel in nonlocal Kerr media, governed by the nonlocal nonlinear Schrödinger equation (NNLSE). A simplified model to the NNLSE is presented when the media is strongly nonlocal, which is a bridge between the Snyder–Mitchell model (Snyder and Mitchell Science 276 1538, 1997) and the strongly-nonlocal model (Guo, Luo, Yi, Chi, and Xie Phys. Rev. E. 69 016602, 2004). It is found that when one of the soliton beams is much stronger than the other, the weaker (probe beam) can experience $\pi $ nonlinear phase shift, which can be modulated by the stronger (pump beam), within a rather short propagation distance (about 40-m). The comparisons of analytical solutions of the model with numerical simulations of the NNLSE show that the model is of excellent accuracy in the case of strong nonlocality.     

Monte Carlo study of the generalized reaction-diffusion lattice-gas model system

The reaction-diffusion lattice-gas model is an interacting particle system out of equilibrium whose microscopic dynamics is a combination of Glauber (reaction) and Kawasaki (diffusion) processes; the Glauber ratec(s; x) at sitex when the configuration iss satisfies detailed balance at temperatureT, while the Kawasaki ratec(s; x, y) between nearest-neighbor sitesx andy satisfies detailed balance at a different temperatureT. We report on the phase diagram of that system as obtained from a series of Monte Carlo simulations of steady states in two-dimensional lattices with arbitrary values forT,T, and; this generalizes previous analytical and numerical studies for and/orT. When the rates are implemented by the Metropolis algorithm, the system is observed to undergo various types of first- and second-order (nonequilibrium) phase transitions, e.g., one may identify Onsager (equilibrium) as well as Landau (mean-field) types of continuous phase transitions.Dedicated to Joel L. Lebowitz on the occasion of his 60th birthday.     

Parametric wave interaction in one-dimensional nonlinear photonic crystal with randomized distribution of second-order nonlinearity

We theoretically study the parametric wave interaction in nonlinear optical media with randomized distribution of the quadratic nonlinearity $\chi ^{(2)}$ . In particular, we discuss the properties of second and cascaded third harmonic generation. We derive analytical formulas describing emission properties of such harmonics in the presence of $\chi ^{(2)}$ disorder and show that the latter process is governed by the characteristics of the constituent processes, i.e. second harmonic generation and sum frequency mixing. We demonstrate the role of randomness on various second and third harmonic generation regimes such as Raman?CNath and ?erenkov nonlinear diffraction. We show that the randomness-induced incoherence in the wave interaction leads to deterioration of conversion efficiency and angular spreading of harmonic generated in the processes relying on transverse phase matching such as Raman?CNath interaction. On the other hand, the ?erenkov frequency generation is basically insensitive to the domain randomness.     

Structural phase transition in elpasolite-like (NH4)2KWO3F3

A new chemical compound, (NH₄)₂KWO₃F₃, was synthesized. The Rietveld-refined crystal structure was found to be cubic at room temperature and to belong to the elpasolite family (space group ). The heat capacity and unit cell parameters were studied within a broad temperature range. A second-order phase transition was found to occur at 235.4 K and to be well described in terms of phenomenological theory. Hydrostatic pressure broadens the temperature interval of stability of the cubic phase (dT₀/dp = −10.8 K GPa⁻¹). A possible model of structural ordering based on a comparison of the entropy parameters and electron density distribution in oxygen and fluorine atoms is discussed.     

Novel glass-forming ferroelectric liquid-crystal material of high second-order nonlinearity

We report on a novel ferroelectric liquid-crystal material with an exceptionally large and stable nonlinear optical response. The material shows a phase transition from theSmC* mesophase to the glassy state near room temperature. This allowed us to state-freeze a stable nonlinear optically active configuration close to room temperature at 10° C for one day. The stored orientations can easily be forced to relax back by heating slightly above the glass-transition temperature. The material and the freezing process have been characterized in detail by analyzing the frequency-doubling process of the fundamental radiation of a Nd: YAG laser in the liquid crystal. Under favourable conditions, we obtained second-order susceptibilities as large as _zzz = 0.5 pm/V.     

The beam propagation factors and the kurtosis parameters of a Lorentz beam

Based on the second-order moments, the beam propagation factors and the kurtosis parameters of a Lorentz beam have been investigated. The M² value of a Lorentz beam is verified to be . The analytical expressions of the kurtosis parameters have been derived. The kurtosis parameter varies upon the propagation, and it is decided by two ratios z/z_rx and z/z_ry. The kurtosis parameter versus the two ratios z/z_rx and z/z_ry is plotted and discussed in detail. This work is of benefit to the practical application of laser sources that produce highly divergent beams.     

Application of types-N and -O spaces to examples of exact solutions of the gravitational equations

Analysis of the exact solutions of the gravitational equations corresponding to the collision of two gravitational plane waves (typeN) and light-like beams (typeO) and also a Kerr-Schild wave metric with conformally flat background is used to formulate theorems that indicate the resulting type of spacetime if the initial gravitational fields belong to typesN andO. A type-D Weyl matrix always appears, which is due to the nonlinear super-position of gravitational fields, in contrast to the superposition of weak gravitational fields, when the sum of the Weyl matrices for the initial fields corresponds to dropping nonlinear terms in both the curvature tensor and the field equations.Work performed under the auspices of the Russian State Scientific-Technical Program Astronomiya.Krasnoyarsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 77–82, May, 1995.     

Accurate switching intensities and length scales in quasi-phase-matched materials

We consider unseeded type I second-harmonic generation in quasi-phase-matched quadratic nonlinear materials and derive an accurate analytical expression for the evolution of the average intensity. The intensity-dependent nonlinear phase mismatch that is due to the cubic nonlinearity induced by quasi phase matching is found. The equivalent formula for the intensity of maximum conversion, the crossing of which changes the one-period nonlinear phase shift of the fundamental abruptly by pi , corrects earlier estimates [Opt. Lett. 23, 506 (1998)] by a factor of 5.3. We find the crystal lengths that are necessary to obtain an optimal flat phase versus intensity response on either side of this separatrix intensity.     

Order–order transition structural state in titanium monoxide TiO<Subscript>1.0</Subscript>

A new class of defect structures in which point defects of a crystal lattice simultaneously occupy sites of two different superstructures is proposed. The formation of these structural modifications is due to a second-order order–order phase transition that does not occur to the end. The allowable relation between the long-range order parameters in the structural modification formed by a combination of the monoclinic (M ₅ X ₅)_mon (space group C2/m (A2/m)) and the cubic (M ₅ X ₅)_cub (space group Pm3m) of the superstructures is studied using an atom–vacancy ordering in titanium monoxide TiO_1.0. The thermodynamic calculations show that the proposed structural modification is equilibrium and must form instead of assumed high-temperature cubic phase (Ti₅O₅)_cub.     

Two-dimensional nonlinear beam shaping

We develop a technique for two-dimensional arbitrary wavefront shaping in quadratic nonlinear crystals by using binary nonlinear computer generated holograms. The method is based on transverse illumination of a binary modulated nonlinear photonic crystal, where the phase matching is partially satisfied through the nonlinear Raman-Nath process. We demonstrate the method experimentally showing a conversion of a fundamental Gaussian beam pump light into three Hermite-Gaussian and three Laguerre-Gaussian beams in the second harmonic. Two-dimensional binary nonlinear computer generated holograms open wide possibilities in the field of nonlinear beam shaping and mode conversion.     

Generation of large fifth-order nonlinear phase shifts by use of lossless χ(2) cascaded nonlinear processes

It is shown that the cascaded fifth-order nonlinear phase shifts will increase with energy loss in the cascaded processes. Essentially different from the multi-photon absorption accompanied with inherent material nonlinearities, the loss of fundamental wave in a cascaded process is controllable and suppressible. By introducing difference frequencies generated from the reaction between the fundamental and its second harmonic after the cascaded processes, the fundamental wave can be free of energy loss, while the large cascaded fifth-order nonlinear phase shift is maintained.     

Generation and weak beam control of two-dimensional multicolored arrays in a quadratic nonlinear medium

We report on the first experimental observation of 2D multicolored transverse arrays in a quadratic nonlinear medium under the pump of two crossly overlapped femtosecond beams. The 2D reproducible patterns are caused by cascaded noncollinear quadratic nonlinear couplings between the input pulses and quadratic spatial solitons originated from spatial breakup of one of the input beams with spatial ellipticity. A seed supercontinuum pulse is then diffracted and amplified with phase preservation, resulting in the formation of up-converted multicolor 2D transverse arrays. By seeding with weak second harmonic pulses, the 2D multicolored transverse patterns are suppressed due to weak beam control of the induced quadratic spatial solitons.     

Generation of large fifth-order nonlinear phase shifts by use of lossless<Emphasis Type="Italic">χ</Emphasis><Superscript>(2)</Superscript> cascaded nonlinear processescascaded nonlinear processes

It is shown that the cascaded fifth-order nonlinear phase shifts will increase with energy loss in the cascaded processes. Essentially different from the multi-photon absorption accompanied with inherent material nonlinearities, the loss of fundamental wave in a cascaded process is controllable and suppressible. By introducing difference frequencies generated from the reaction between the fundamental and its second harmonic after the cascaded processes, the fundamental wave can be free of energy loss, while the large cascaded fifth-order nonlinear phase shift is maintained.     

Self-repeating properties of four-petal Gaussian vortex beams in quadratic index medium

In this paper, we investigate the propagation properties of four-petal Gaussian vortex (FPGV) beams propagating through the quadratic index medium, obtaining the analytical expression of FPGV beams. The effects of beam order n, topological charge m and beam waist ${\omega }_0$ are investigated. Results show that quadratic index medium support periodic distributions of FPGV beams. A hollow optical wall or an optical central principal maximum surrounded by symmetrical sidelobes will occur at the center of a period. At length, they will evolve into four petals structure, exactly same as the intensity distributions at source plane.     

Study of the crystallography of slip in the alloy Ni3Al

It has been established that cubic slip is an effective mechanism for the strain of the Ni₃A1 alloy even at room temperature. Traces of cubic slip were observed in an electron microscope for all degrees of strain. The critical spalling stress in the plane of the cube is small and approximately 2.5 kg/mm². In a two-phase alloy consisting of segregations, '-phase (Ni₃Al) and a disordered matrix (-phase), the traces of cubic slip generated in the ordered phase which have reached the phase boundary, are even continued into the segregations of the disordered phase.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 7, pp. 42–47, July, 1971.