Effects on squeezing and sub-poissonian of light in fourth harmonic generation up to first-order Hamiltonian interaction

The effects on squeezing and sub-poissonian of light in fourth harmonic generation (FHG) are investigated based on the fully quantum mechanically up to the first order Hamiltonian interaction in gt, where g is the coupling constant between the modes per second and t is the interaction time between the waves during the process in a nonlinear medium. FHG is a process in which an incident laser beam of the fundamental frequency ω interacts with a nonlinear medium to produce the harmonic frequency at 4ω. The coupled Heisenberg equations of motion involving real and imaginary parts of the quadrature operators are established. The occurrence of amplitude squeezing effects in both the quadratures of the radiation field in the fundamental mode is investigated and found to be dependent on the selective phase values of the field amplitude. The photon statistics of the pump mode in this process have also been investigated and found to be sub-poissonian in nature. It is found that there is no possibility to produce squeezed light in the harmonic mode up to first-order interaction in gt. Further, we have found the case up to second-order Hamiltonian interaction in gt that the normal squeezing in the harmonic mode is directly depends upon the fourth-order squeezing of the initial pump field. This gives a method of converting higher-order (fourth-order) squeezing into normal squeezing in the harmonic mode and vice versa.     

Resonant interaction of a magneto-hydrodynamic wave with its second harmonic in a planar plasma filled waveguide

To describe the nonlinear interactions of a magneto-hydrodynamic wave with its second harmonic propagating in a planar waveguide filled with cold magnetized plasma, coupled mode equations have been derived. Solution of these equations shows the possibility of energy transfer between the fundamental and the second harmonic.     

PARAMETRIC SIMULTONS IN ONE-DIMENSIONAL NONLINEAR LATTICES

Parametric simultaneous solitary wave (simulton) excitations are shown to be possible in nonlinear lattices. Taking a one-dimensional diatomic lattice with a cubic potential as an example, we consider the nonlinear coupling between the upper cut-off mode of acoustic branch (as a fundamental wave) and the upper cut-off mode of optical branch (as a second harmonic wave). Based on a quasi-discreteness approach the Karamzin－Sukhorukov equations for two slowly varying amplitudes of the fundamental and the second harmonic waves in the lattice are derived when the condition of second harmonic generation is satisfied. The lattice simulton solutions are given explicitly and the results show that these lattice simultons can be nonpropagating when the wave vectors of the fundamental wave and the second harmonic waves are exactly at π/a (where a is the lattice constant) and zero, respectively.     

Propagation of high-frequency gravitational waves in vacuum: Nonlinear effects

Linear and nonlinear perturbations of vacuum space-times are examined in the approximation of high frequencies. In order to do this, it is necessary to extend the concept of coordinate gauge transformations to the case of nonlinear terms. The generation of the second harmonic is studied by investigating perturbations of the tetrad components of the Weyl tensor. Propagation equations determining the amplitudes of these perturbations are derived. Finally, the relative motion in a system of test particles under the influence of both main wave and second harmonic as seen by a free falling observer is investigated. If inertial forces are absent, the second harmonic gives rise to oscillations in two transverse-traceless modes and in a transverse-scalar mode. The amplitude of the latter mode is proportional to the shear of the ray congruence along which the perturbations propagate.     

Non-one-dimensional optical solitons and ideal fluid dynamics

Influence of transverse effects on the propagation of light beams in gradient glass fiber and on the pulsed mode of the second harmonic generation is investigated. Within the approaches under consideration the equations for the pulse or beam field envelopes are reduced to a system of hydrodynamictype equations for amplitudes and eikonals. These equations are used to describe the vortex and non-vortex beam channeling modes and the propagation of light bullets.     

Elastic nonlinearity parameters of tetragonal crystals

The equations of motion for the propagation of finite amplitude elastic waves in crystals of tetragonal symmetry have been derived starting from the expression for the elastic strain energy. The equations have been solved for a finite amplitude sinusoidal wave propagating along the pure mode directions which are [100], [110] and [001] for the tetragonal group TI. The solutions corresponding to longitudinal wave propagation yield expressions for the amplitudes of the fundamental and generated second harmonic for these directions in terms of certain combinations of second and third order elastic constants of the medium. The results will aid the experimenter to determine these constants using ultrasonic harmonic generation technique.     

First and second sound in a two-dimensional harmonically trapped Bose gas across the Berezinskii–Kosterlitz–Thouless transition

We theoretically investigate first and second sound of a two-dimensional (2D) atomic Bose gas in harmonic traps by solving Landau’s two-fluid hydrodynamic equations. For an isotropic trap, we find that first and second sound modes become degenerate at certain temperatures and exhibit typical avoided crossings in mode frequencies. At these temperatures, second sound has significant density fluctuation due to its hybridization with first sound and has a divergent mode frequency towards the Berezinskii–Kosterlitz–Thouless (BKT) transition. For a highly anisotropic trap, we derive the simplified one-dimensional hydrodynamic equations and discuss the sound-wave propagation along the weakly confined direction. Due to the universal jump of the superfluid density inherent to the BKT transition, we show that the first sound velocity exhibits a kink across the transition. These predictions might be readily examined in current experimental setups for 2D dilute Bose gases with a sufficiently large number of atoms, where the finite-size effect due to harmonic traps is relatively weak.     

双共焦波导结构二次谐波太赫兹回旋管谐振腔设计

准光共焦波导具有功率容量大、模式密度低的特点,能够有效地减少模式竞争对回旋管互作用的影响,有利于高次谐波太赫兹回旋管的设计.为提高太赫兹准光回旋管的互作用效率,在共焦柱面波导的基础上,研究了一种新型高频互作用结构——双共焦波导结构,设计了一种330 GHz二次谐波双共焦结构回旋管谐振腔并对其进行了理论分析和粒子模拟.研究结果表明,双共焦谐振腔中的高阶模式能够与高次电子回旋谐波发生稳定的相互作用,并且没有模式竞争现象,具备工作在太赫兹波段的潜力.相比普通共焦波导谐振腔,双共焦谐振腔能够增强准光回旋管的注波互作用强度,提高回旋管的输出功率和工作效率.此外,结果还表明双共焦波导中的电磁波模式是一种由两个独立的共焦波导模式叠加而成的混合模式.利用这种混合模式有望实现太赫兹回旋管的单注双频工作,为新型太赫兹辐射源的研究提供了新的途径.     

Impedance matching in photonic crystal microcavities for second-harmonic generation

By numerically integrating the three-dimensional Maxwell equations in the time domain with reference to a dispersive quadratically nonlinear material, we study second-harmonic generation in planar photonic crystal microresonators. The proposed scheme allows efficient coupling of the pump radiation to the defect resonant mode. The outcoupled generated second harmonic is maximized by impedance matching the photonic crystal cavity to the output waveguide.     

Nonlinear equations for quasi-monochromatic waves near a caustic in a dispersive dissipative medium with cubic or quadratic nonlinearity

The behavior of a quasi-monochromatic nonlinear wave near a caustic is considered. Nonlinear ordinary differential equations for a dispersive dissipative medium with a cubic or quadratic nonlinearity are derived. For the latter medium, nonstationary equations describing it near the caustic are presented with allowance for the dissipative dispersive terms. These equations yield ordinary ones for quasi-monochromatic waves. The amplitude of the second harmonic is expressed in terms of the squared amplitude of the first harmonic. The amplitude of the second harmonic, as well as the solution as a whole, increases near the caustic.     

Study of nonlinear light scattering in water in the region of the second optical harmonic of laser radiation

The frequency-angular spectrum of nonlinear light scattering in water in the region of the second optical harmonic of picosecond Nd³⁺YAG laser radiation is studied. It is shown that this scattering occurs by the four-photon interaction mechanism. Statistical treatment of the spectra of four-photon scattering in the collinear interaction mode revealed a structure related to the frequency of infrared radiation caused by vibrations of cluster complexes of water molecules.     

On the possibility of soliton-like double-frequency propagation of femtosecond pulses in an optical fiber under conditions of second harmonic generation

A soliton-like mode of double-frequency propagation of femtosecond pulses during second harmonic generation (SHG) in optical fibers is predicted on the basis of computer simulation. The essence of this mode is that, under certain conditions, the central part of the pulses of both the fundamental and the second harmonic waves propagate without a change in the intensity of either wave. This mode can be realized by either of two schemes of the SHG process. In the first scheme, the second harmonic enters a nonlinear medium with some definite input amplitude and definite phase shift with respect to the fundamental wave. In the other scheme, the second harmonic has a zero input amplitude and a phase shift is introduced into the interacting waves in particular cross sections of the medium.     

Solution of Hartree-Fock equations in coordinate space for axially symmetric nuclei

As an alternative to the conventional deformed harmonic oscillator basis expansion, a method is developed in which the coupled integro-differential Hartree-Fock equations are solved directly in coordinate space for a simple effective interaction. The single particle wave functions are obtained on a finite mesh by minimizing a discretized energy functional and solving the resulting finite difference equations using the Lanczos algorithm. Expressions to correct the total energy to second order in the mesh spacing are derived, and the accuracy of the method is demonstrated by numerical comparison with spherical results. Applications and advantages of this new technique are briefly discussed.     

Nonlinear dynamics of a pipe conveying pulsating fluid with combination,principal parametric and internal resonances

Nonlinear dynamics of a hinged–hinged pipe conveying pulsatile fluid subjected to combination and principal parametric resonance in the presence of internal resonance is investigated. The system has geometric cubic nonlinearity due to stretching effect out of immovable support conditions at both ends. The pipe conveys fluid at a velocity with a harmonically varying component over a constant mean velocity. For appropriate choice of system parameters, the natural frequency of the second mode is approximately three times that of the first mode for a range of mean flow velocity, activating a three-to-one internal resonance. The analysis is carried out using the method of multiple scales by directly attacking the governing nonlinear integro-partial-differential equations and the associated boundary conditions. The set of first-order ordinary differential equations governing the modulation of amplitude and phase is analyzed numerically for combination parametric resonance and principal parametric resonance. Stability, bifurcation and response behavior of the pipe are investigated. The amplitude and frequency detuning of the harmonic velocity perturbation are taken as the control parameters. The system exhibits response in the directly excited and indirectly excited modes due to modal interaction. Dynamic response of the system is presented in the form of phase plane trajectories, Poincare maps and time histories. A wide array of dynamical behavior is observed illustrating the influence of internal resonance.     

Second harmonic generation by modal phase matching involving optical and plasmonic modes

The feasibility of a modal phase matching scheme between optical modes and surface plasmonic modes is demonstrated: in fact, the high effective index of a plasmonic mode allows us to obtain phase matching even in semiconductors showing a large dispersion between fundamental and second harmonic wavelengths. We design a realistic device to obtain Type-II second harmonic generation in AlGaAs-based waveguides; whereas one of the two pumps is carried by a plasmonic mode, the generated second harmonic signal is guided inside the AlGaAs multilayer, and hence it is not hampered by high propagation losses.     

Comparative study of vibrations in submonolayer structures of potassium on Pt(111)

We present results of a comparative study of the vibrational spectrum and local density of phonon states in ordered p(2 x 2) and (√3 x √3)R30° structures formed by potassium atoms on the Pt(111) surface. The calculations were performed with tight-binding interatomic interaction potentials. It was found that the mode associated with vertical displacements of K adatoms has an energy of about 20 meV in both K structures. The strength and energy of this mode slightly decreases with increasing coverage. This result is in good agreement with available experimental data. As in time-resolved second harmonic generation measurements, we observed low frequency modes for both structures considered, which are caused by the interaction of potassium with the second layer of the substrate.     

Mode Selection for a Terahertz Gyrotron Based on a Pulse Magnet System

The TE_6,11 mode has been selected as a candidate for the second harmonic operation of a terahertz gyrotron at 1007.68 GHz. The predicted efficiency is 8.6 percent for the output power 0.38 kW. Time-dependent, multi-mode calculations have been carried out to investigate stability of a single-mode operation at second harmonic. It has been found that with the beam current 0.111 A and the magnetic field 19.282 T the second harmonic operation in the TE_6,11 mode is possible.     

Microscopic description of static quadrupole moments of 2 1 + states by time-dependent HF equations

Large quadrupole moments of 1-phonon states of sperical nuclei are shown to follow in a simple and direct way from time-dependent HF equations using the self-consistent perturbation expansion. Whereas the first order describes harmonic quadrupole oscillations, anharmonic terms arise in second order. The scattering of quasiparticles by quasi-particle pairs, which is neglected in RPA calculations, but included in this paper, leads to a second order response of the system and is shown to produce a strong enhancement of the quadrupole moments. Explicit results are obtained with a pairing-plus-quadrupole interaction and discussed within a schematic two level model.     

Mode Cooperation in a Submillimeter Wave FU Series Gyrotron

At certain gyrotron operating conditions, mode cooperation instead of mode competition takes place between a fundamental and a second harmonic mode. This means the phase bunching of a gyrating electron beam under the second harmonic operation reduces the starting current for the fundamental operation and increases total output power as well as beam efficiency. Such mode cooperation is observed in experiments and confirmed by computer simulations for submillimeter wave Gyrotron FU II.