Fundamental Frequency Wave Research Articles

A way for enhancing second harmonic generation in one-dimensional nonlinear photonic crystals

We investigate one-dimensional nonlinear photonic crystals consisting of ferroelectric domains with the modulated polarization directions. Significant enhancement of second harmonic generation (SHG) is observed from numerical simulations when the frequency of fundamental wave is aimed at the photonic band edge. We devise the model structure with optimal configuration of the polarization directions of the ferroelectric domains in terms of simulated annealing algorithm. The conversion efficiencies of the ‘forward’ and ‘backward’ SHGs can be engineered.

COUNTER-PROPAGATING ENERGY-FLOWS IN NONLINEAR LEFT-HANDED METAMATERIALS

A peculiarity of counter-propagating energy-flows in nonlinear left-handed metamaterials (LHMs) is investigated for the case when the frequency of fundamental wave is in the negative- index range and second-harmonic wave is in the positive-index range. Based on the electromagnetic theory,the comparisons of Manly-Rowe relations for nonlinear materials and process of second- harmonic generation under phase-matching condition in LHMs and RHMs are shown separately. That a surface of nonlinear left-handed metamaterials operates as an effective mirror which reflects the energy in form of second harmonics is demonstrated. Numerical results of fundamental and second-harmonic field intensity distributions are in agreement with theoretical results.

Second-harmonic generation in nonlinear left-handed metamaterials

Based on the electromagnetic theory，the Manly-Rowe relations for nonlinear left-handed metamaterials are studied. Energy conversion process and spatial distribution of forward-propagating wave of fundamental frequency and backward-propagating second harmonic wave under phase-matching condition are investigated. That a surface of nonlinear left-handed metamaterials operates as an effective mirror which reflects the energy in the form of second harmonics is demonstrated. Numerical results of field intensity distribution of a finite thickness metamaterial slab is given. Finally，the importance of phase-matching condition to the investigation of nonlinear left-handed metamaterials is illustrated from the viewpoint of phase-mismatching. This work provides a basis for studying nonlinear left-handed metamaterials.

Giant enhancement of second harmonic generation in multiple photonic quantum well structures made of nonlinear material

We present a general solution of second harmonic generation (SHG) in one-dimensional (1D) inhomogeneous systems. The structure consists of 1D multiple photonic quantum wells (PQWs) made of optical nonlinear material. The optimal arrangement of the polarization directions of the ferroelectric domains in multiple PQWs is determined by a simulated annealing method. We find that the conversion efficiency of SHG can be significantly enhanced when the fundamental wave frequency is aimed at one of the defect states. By tuning the polarization directions of the domains, the conversion efficiencies of “forward” and “backward” SHGs can be flexibly changed.

Multicolor vortex solitons in two-dimensional photonic lattices

We report on the existence and stability of multicolor lattice vortex solitons constituted by coupled fundamental frequency and second-harmonic waves in optical lattices in quadratic nonlinear media. It is shown that the solitons are stable almost in the entire domain of their existence, and that the instability domain decreases with the increase of the lattice depth. We also show the generation of the solitons, and the feasibility of the concept of lattice soliton algebra.

Self-influence of the collapsing internal gravity wave in the inhomogeneous atmosphere

Nonlinear equations for internal gravity waves in the atmosphere in the presence of the inhomogeneous wind velocity leading to the wave collapse are derived. In frameworks of the WKB-solutions justified right up to the collapse point the cubic nonlinearity at the fundamental wave frequency is found. It is shown that the nonlinearity results in displacement of the collapse before the linear collapse point. A comparison between a role of the nonlinearity and viscosity is carried out.

Threshold energy for vector soliton formation in KTP

We present theoretical and experimental results to outline the conditions for the existence of vectorial solitary waves in KTP with imbalanced fundamental frequency waves (FFs). We demonstrate that the minimum energy for soliton formation can be at nonzero fundamental frequency imbalance or at zero imbalance depending on the sign of the phase mismatch.

All-optical programmable switch with XOR gate functions in a doped silica thin film

We demonstrate an all-optical programmable switch that can simulate the function of an XOR logic gate. This gate consists of a doped silica planar waveguide, a laser, and the means to couple two fundamental-frequency waves into different waveguiding modes, along with a second-harmonic wave coupled into one guiding mode. The measured SNR is 5.5 dB.

Thin film devices for all-optical switching and processing via quadratic non-linearities

Quadratic non-linear optical effects, specifically the phase-shift that a fundamental frequency wave experiences through cascading during second-harmonic-generation and the successive down-conversion, are a viable route to all-optical signal processing in integrated optics geometries. We review the most relevant device concepts and their potential applications, with examples of experimental results and prospects for implementation in non-linear thin films.

Second-harmonic generation by a Gaussian beam on a fourth-order optical nonlinearity in the interior of an isotropic and gyrotropic medium

A theoretical investigation is made of second- harmonic generation in the interior of an isotropic and gyrotropic medium on a fourth-order optical nonlinearity. It is shown that a correct description of this experimentally detected effect requires taking into account the spatially finite nature of the fundamental-frequency wave, giving rise to a small longitudinal (directed along the beam axis) component of the electric field. Quadrature formulas are derived for the transverse distribution of the second harmonic field and for the total power of the harmonic. A detailed study is made of the special cases of tight focusing of the pump (fundamental-frequency) wave at the centre of a long medium and of exact phase matching. In these cases the quadrature expressions can be reduced to an analytic form. A study is reported of the characteristic features of the transverse profile of the second-harmonic intensity and of the dependence of the harmonic power on the state of polarisation of the pump wave.

Double hump solitary waves in quadratic media with walk-off-domain of existence, stability and decay scenarios

We analytically determine the domain of existence of double hump solitary wave solutions in quadratic media with walk-off. Although a linear stability analysis reveals that these solutions are always unstable the instability gain can be very small for certain parameters. This has important implications for all-optical switching applications. The ultimate decay is prompted by the destruction of an exact phase difference π between the two humps of the fundamental frequency wave and follows different scenarios.

Quasi-phase matched cascaded second order processes in poled organic polymer waveguides

For cascading second order optical nonlinearities realized by quasi-phase matching conditions we have calculated the change of intensity and the nonlinear phase shift of the fundamental frequency wave passing through a waveguide based on poled organic polymers. The pump depletion and attenuation of the radiation are taken into account. By a grating-like method leading to simplified equations it becomes easy to investigate quasi-phase matching with any periodic dependence of the electric poling field and for any depletion of the fundamental wave. For the special case of low pump depletion Kramers-Kronig-like relations are discussed.

Competition between subharmonic and sideband secondary instabilities on a falling film

The secondary instabilities on a falling film which cause a monochromatic wave to evolve into solitary waves are examined with a weakly nonlinear theory. The unique phase speed dispersion relation dictated by inertia and capillarity is found to favor a nonlinear, two-wave subharmonic resonance that causes neighboring crests to coalesce. This occurs when the fundamental wave frequency is below a critical value ωc which can be approximated by a nonlinear resonant frequency. An entire band of secondary waves are excited by this static subharmonic mechanism such that the coalescence occurs nonuniformly. The lower half of this band of secondary waves travels faster than the fundamental and induces the coalesced waves to move faster than the slower fundamental. For monochromatic waves with frequencies above ωc, a three-wave oscillatory sideband instability is triggered which generates two secondary waves that are slower than the fundamental. This sideband instability involves a long-wave modulation that causes several crests to coalesce simultaneously. Both secondary transitions are important intermediate stages of the route to spatiotemporal chaos involving solitary waves.

Losses of high-intensity optical radiation in transparent nonlinear media

One of the possible mechanisms of loss of energy by high intensity optical radiation in media with a quadratic nonlinearity is considered. The source of losses is nonphase-matched second-harmonic generation when the doubled frequency lies within an absorption region of a crystal. A detailed study is reported of the influence of absorption at the second-harmonic frequency on the propagation of the fundamental-frequency wave for different ratios of the characteristic lengths (absorption, nonlinear, coherence, and quasistatic). It is shown that in some cases nonlinear losses of the fundamental-frequency radiation may be considerable and can limit the efficiency of phase-matched nonlinear optical processes.

On the Structure of the Velocity Field over Progressive Mechanically-Generated Water Waves

The structure of the velocity field over a propagating wave of fixed frequency is examined. The vertical and horizontal velocities were measured in a transformed Eulerian wave-following frame of reference in a wind-wave research facility at Stanford University. Experimental results are given for seven different wind speeds in the range 140–402 cm s−1, with 1 Hz, 2.54 cm nominal amplitude, mechanically-generated sinusoidal water waves. The mean velocity profiles have a log-linear form with a wake free-stream characteristic. The constant C which characterizes these profiles decreases with increasing wind speed, as a result of the variation of surface roughness condition between the transition region and the fully rough regime. The wave-associated stresses with their main component at twice the fundamental wave frequency were found to be significant. Therefore, the nonlinear terms encountered in the wave-induced Navier-Stokes equations associated with these stresses cannot be neglected, and linearization of the above equations is not permissible. The wave-induced velocity field and the wave-perturbed turbulence were found to depend significantly on the ratio of the wave speed to the mean free-stream wind velocity, c/Uδ0.

Nonlinear forces on a horizontal cylinder beneath waves

Measurements of forces experienced by a submerged horizontal cylinder with its axis parallel to the crests in deep-water waves reveal nonlinear components with frequencies up to three times the fundamental wave frequency. The dominant nonlinear contribution to the loading is at the third order in the wave amplitude, and, for Keulegan-Carpenter numbers approaching 2, its magnitude was found to be as much as one-half that of the inertia force. It is suggested that the third-order force is associated with circulation generated by steady streaming in the oscillatory boundary layer on the cylinder. At higher Keulegan-Carpenter numbers, form drag becomes increasingly important, and velocity measurements close to the cylinder show the rapid development of the wake. Observations of nonlinear features of the transmitted waves are also discussed.

Influence of phase mismatching in a nonlinear crystal and in air on intracavity frequency conversion of ultrashort pulses

A theoretical analysis is made of intracavity second harmonic generation of ultrashort laser pulses under conditions of active modulation for the cavity (resonator) losses. An allowance is made of the changes in the phases of the light waves at the fundamental and second-harmonic frequencies in a nonlinear crystal and in air. It is shown that both linear and nonlinear changes in the phases of the light waves during the interaction process have a strong influence on the time characteristics and on the efficiency of second harmonic generation: the shape of the pulses of the fundamental-frequency wave becomes strongly distorted and a complex time structure is formed in the case of the second harmonic pulses. The solution of the problem makes it possible to find the conditions under which minimal distortions occur in the shape of the pulses of the converted radiation but the conversion efficiency remains maximal.

Investigation of the efficiency of second harmonic generation by two types of interaction and optimization of laser radiation parameters

The efficiency of second harmonic generation by oo–e and oe–e interactions of laser radiation characterized by different angular and spectral distributions was investigated under conditions of a strong energy exchange between the fundamental-frequency wave and its second harmonic. The parameters of the laser radiation and of the nonlinear crystal were optimized. It was found that efficient doubling was obtained when the fundamental-frequency laser radiation was polarized linearly and this was true of both the oo–e and oe–e interactions. In the oe–e case the conversion efficiency was very sensitive to the width of the laser spectrum.

Second harmonic generation in a medium with a variable permittivity

An analysis is made of second harmonic generation in a medium with a quadratic radial variation in the permittivity. It is found that the efficiency of conversion of the fundamental-frequency wave to the second-harmonic signal is highest on the resonator axis and decreases rapidly with the radius.

Nonlinear mode coupling of surface acoustic waves on an isotropic solid

The nonlinear mode coupling between two co-directional quasi-harmonic Rayleigh surface waves on an isotropic solid is analysed using the method of multiple scales. This procedure yields a system of six semi-linear hyperbolic partial differential equations with the same principal part governing the slow variations in the (complex) amplitudes of the two fundamental, the two second harmonic and the two combination frequency waves at the second stage of the perturbation expansion. A numerical solution of these equations for excitation by monochromatic signals at two arbitrary frequencies, indicates that there is a continuous transfer of energy back and forth among the fundamental, second harmonic and combination frequency waves due to mode coupling. The mode coupling tends to be more pronounced as the frequencies of the interacting waves approach each other.