Nonlinear Mode Conversion Research Articles

Nonlinear Mode Conversion of Special Beams Based on Local Quasi-Phase-Matching

Nonlinear Mode Conversion of Special Beams Based on Local Quasi-Phase-Matching

Asymmetric nonlinear-mode-conversion in an optical waveguide with PT symmetry

Asymmetric mode transformation in waveguide is of great significance for on-chip integrated devices with one-way effect, while it is challenging to achieve asymmetric nonlinear-mode-conversion (NMC) due to the limitations imposed by phase-matching. In this work, we theoretically proposed a new scheme for realizing asymmetric NMC by combining frequency-doubling process and periodic PT symmetric modulation in an optical waveguide. By engineering the one-way momentum from PT symmetric modulation, we have demonstrated the unidirectional conversion from pump to second harmonic with desired guided modes. Our findings offer new opportunities for manipulating nonlinear optical fields with PT symmetry, which could further boost more exploration on on-chip nonlinear devices assisted by non-Hermitian optics.

Simultaneous nonlinear wavelength and mode conversion for high-brightness blue sources

We investigate frequency doubling of focused Bessel-like higher order fiber modes in a one-dimensionally quasi-phase matched structured KTP crystal. A single higher-order fiber mode, L P 0 , 7 , was generated at 971 nm using a fiber optical parametric amplifier pumped by sub-nanosecond pulses at 1064 nm. Frequency doubling to 485.5 nm was achieved with a maximum conversion efficiency of 48%, which produced a highly structured blue beam without any brightness improvement with respect to the fundamental beam. By optimizing the phase mismatch, we also experimentally demonstrate clean on-axis conversion—resulting from cascaded χ ( 2 ) : χ ( 2 ) processes, which is in good agreement with our numerical simulations, that give rise to brightness enhancement.

Parametric autoresonant excitation of the nonlinear Schrödinger equation.

Parametric excitation of autoresonant solutions of the nonlinear Schrodinger (NLS) equation by a chirped frequency traveling wave is discussed. Fully nonlinear theory of the process is developed based on Whitham's averaged variational principle and its predictions verified in numerical simulations. The weakly nonlinear limit of the theory is used to find the threshold on the amplitude of the driving wave for entering the autoresonant regime. It is shown that above the threshold, a flat (spatially independent) NLS solution can be fully converted into a traveling wave. A simplified, few spatial harmonics expansion approach is also developed for studying this nonlinear mode conversion process, allowing interpretation as autoresonant interaction within triads of spatial harmonics.

Modeling of nonlinear interactions between guided waves and fatigue cracks using local interaction simulation approach

This article presents a parallel algorithm to model the nonlinear dynamic interactions between ultrasonic guided waves and fatigue cracks. The Local Interaction Simulation Approach (LISA) is further developed to capture the contact-impact clapping phenomena during the wave crack interactions based on the penalty method. Initial opening and closure distributions are considered to approximate the 3-D rough crack microscopic features. A Coulomb friction model is integrated to capture the stick-slip contact motions between the crack surfaces. The LISA procedure is parallelized via the Compute Unified Device Architecture (CUDA), which enables parallel computing on powerful graphic cards. The explicit contact formulation, the parallel algorithm, as well as the GPU-based implementation facilitate LISA’s high computational efficiency over the conventional finite element method (FEM). This article starts with the theoretical formulation and numerical implementation of the proposed algorithm, followed by the solution behavior study and numerical verification against a commercial finite element code. Numerical case studies are conducted on Lamb wave interactions with fatigue cracks. Several nonlinear ultrasonic phenomena are addressed. The classical nonlinear higher harmonic and DC response are successfully captured. The nonlinear mode conversion at a through-thickness and a half-thickness fatigue crack is investigated. Threshold behaviors, induced by initial openings and closures of rough crack surfaces, are depicted by the proposed contact LISA model.

Variational symplectic particle-in-cell simulation of nonlinear mode conversion from extraordinary waves to Bernstein waves

In this paper, the nonlinear mode conversion of extraordinary waves in nonuniform magnetized plasmas is studied using the variational symplectic particle-in-cell simulation. The accuracy of the nonlinear simulation is guaranteed by the long-term accuracy and conservativeness of the symplectic algorithm. The spectra of the electromagnetic wave, the evolution of the wave reflectivity, the energy deposition profile, and the parameter-dependent properties of radio-frequency waves during the nonlinear mode conversion are investigated. It is illustrated that nonlinear effects significantly modify the physics of the radio-frequency injection in magnetized plasmas. The evolutions of the radio-frequency wave reflectivity and the energy deposition are observed, as well as the self-interaction of the Bernstein waves and mode excitations. Even for waves with small magnitude, nonlinear effects can also become important after continuous wave injections, which are common in the realistic radio-frequency wave heating and current drive experiments.

Nonlinear Alfvén wave dynamics at a 2D magnetic null point: ponderomotive force

Context : In the linear, {\beta}=0 MHD regime, the transient properties of MHD waves in the vicinity of 2D null points are well known. The waves are decoupled and accumulate at predictable parts of the magnetic topology: fast waves accumulate at the null point; whereas Alfv\'en waves cannot cross the separatricies. However, in nonlinear MHD mode conversion can occur at regions of inhomogeneous Alfv\'en speed, suggesting that the decoupled nature of waves may not extend to the nonlinear regime. Aims: We investigate the behaviour of low-amplitude Alfv\'en waves about a 2D magnetic null point in nonlinear, {\beta}= 0 MHD. Methods: We numerically simulate the introduction of low-amplitude Alfv\'en waves into the vicinity of a magnetic null point using the nonlinear LARE2D code. Results: Unlike in the linear regime, we find that the Alfv\'en wave sustains cospatial daughter disturbances, manifest in the transverse and longitudinal fluid velocity, owing to the action of nonlinear magnetic pressure gradients (viz. the ponderomotive force). These disturbances are dependent on the Alfv\'en wave and do not interact with the medium to excite magnetoacoustic waves, although the transverse daughter becomes focused at the null point. Additionally, an independently propagating fast magnetoacoustic wave is generated during the early stages, which transports some of the initial Alfv\'en wave energy towards the null point. Subsequently, despite undergoing dispersion and phase-mixing due to gradients in the Alfv\'en-speed profile (Grad c_A \neq 0) there is no further nonlinear generation of fast waves. Conclusions: We find that Alfv\'en waves at 2D cold null points behave largely as in the linear regime, however they sustain transverse and longitudinal disturbances - effects absent in the linear regime - due to nonlinear magnetic pressure gradients.

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.

CONNECTING THE SUN AND THE SOLAR WIND: THE FIRST 2.5-DIMENSIONAL SELF-CONSISTENT MHD SIMULATION UNDER THE ALFVÉN WAVE SCENARIO

The solar wind emanates from the hot and tenuous solar corona. Earlier studies using 1.5 dimensional simulations show that Alfv\'{e}n waves generated in the photosphere play an important role in coronal heating through the process of non-linear mode conversion. In order to understand the physics of coronal heating and solar wind acceleration together, it is important to consider the regions from photosphere to interplanetary space as a single system. We performed 2.5 dimensional, self-consistent magnetohydrodynamic simulations, covering from the photosphere to the interplanetary space for the first time. We carefully set up the grid points with spherical coordinate to treat the Alfv\'{e}n waves in the atmosphere with huge density contrast, and successfully simulate the solar wind streaming out from the hot solar corona as a result of the surface convective motion. The footpoint motion excites Alfv\'{e}n waves along an open magnetic flux tube, and these waves traveling upwards in the non-uniform medium undergo wave reflection, nonlinear mode conversion from Alfv\'{e}n mode to slow mode, and turbulent cascade. These processes leads to the dissipation of Alfv\'{e}n waves and acceleration of the solar wind. It is found that the shock heating by the dissipation of the slow mode wave plays a fundamental role in the coronal heating process whereas the turbulent cascade and shock heating drive the solar wind.

Nonlinear computer-generated holograms

We propose a novel technique for arbitrary wavefront shaping in quadratic nonlinear crystals by introducing the concept of computer-generated holograms (CGHs) into the nonlinear optical regime. We demonstrate the method experimentally showing a conversion of a fundamental Gaussian beam pump light into the first three Hermite-Gaussian beams at the second harmonic in a stoichiometric lithium tantalate nonlinear crystal, and we characterize its efficiency dependence on the fundamental power and the crystal temperature. Nonlinear CGHs open new possibilities in the fields of nonlinear beam shaping, mode conversion, and beam steering.

Mode conversion in quadratic nonlinear crystals

We propose a novel all-optical, nonlinear mode-conversion scheme based on cascaded three-wave-mixing phase-matched interactions in quadratic nonlinear crystals. We demonstrate the method experimentally by performing all-optical mode conversion of an input 1636 nm Hermite-Gaussian mode from the zeroth order to the first order using two periodically poled LiNbO(3) crystals. Nonlinear mode conversion of an input beam into a higher order, orthogonally polarized output beam can be realized using only one quasiperiodic nonlinear structure. Moreover, it can be enhanced for conversion of complex modes, e.g., Laguerre-Gaussian or Bessel modes.

Observation of and model for nonlinear mode conversion in a non-neutral plasma

The nonlinear interaction of the two lowest Trivelpiece–Gould modes in a non-neutral plasma has been observed. Because of coupling in the nonlinear terms of the continuity and momentum equations, the two modes can exchange energy and convert one to the other. This can be modeled using the cold fluid equations and the averaging method. Experimentally, this process always stops with the lower frequency mode dominating the final state. Numerical integration of the model suggests that this occurs because the higher frequency mode is more strongly damped than the lower frequency mode.

Laboratory study of some lightning-induced effects in the ionospheric plasma

Laboratory experiments have been conducted at MIT, using the student-built Versatile Toroidal Facility (VTF), to investigate some ionospheric plasma effects produced by lightning-induced whistler waves. Lower hybrid waves, generated by the lightning-induced whistler waves, can cause a chain of extensive plasma effects, such as the acceleration of electrons and ions and the spectral broadening of plasma waves. Two mechanisms by which whistler waves generate lower hybrid waves can be important in the ionosphere. One is the simultaneous excitation of lower hybrid waves and low-frequency mode waves by intense whistler waves. The other is the nonlinear mode conversion of whistler waves into lower hybrid waves in the presence of short-scale field-aligned density striations. The effect of lower hybrid waves on the spectra of Langmuir waves has been investigated. The results of VTF laboratory experiments show that lower hybrid waves can beat with Langmuir waves to produce frequency-upshifted and frequency-downshifted Langmuir waves, broadening the spectra of Langmuir waves. The intensity of these beat waves, however, depends upon the angle of wave propagation with respect to the background magnetic field.

Quantum nondemolition measurements of the phase and polarization Stokes parameters of optical fields

We propose a new method for performing continuous quantum nondemolition measurements (QNDM) of the polarization characteristics of light, the signal photon number, and the Stokes parameters of light. For devices that implement such measurements we take cubically nonlinear double-filament optical fibers with tunnel coupling of the filaments. Such a system employs a four-mode mixing of the waves (two probe modes and two signal modes). Linear optical elements needed for preliminary and subsequent conversion of the Stokes parameters are also used. We show that measurements of one Stokes parameter can be used for QNDM of the phase difference between the two initial modes. Here the accuracy of such measurements is determined by the initial fluctuations of the Stokes parameters of the probe modes and by the size of the nonlinear mode conversion coefficient in the optical fibers.

On the generation of auroral radio emissions at harmonics of the lower ionospheric electron cyclotron frequency: X, O and Z mode maser calculations

Electron cyclotron maser emission has been suggested as a possible explanation of ground‐based observations of auroral radio waves at twice and three times the lower ionospheric electron cyclotron frequency (2ƒce and 3ƒce). Preliminary theoretical work concluded that direct maser excitation at the first and second harmonics of the free space extraordinary mode (X2 and X3) could exceed collisional ionospheric damping rates, although growth rates were low. Recently, however, ground‐based observations indicate that these emissions are predominantly O mode polarized. Therefore a reassessment of the lower ionospheric cyclotron maser as an emission mechanism is necessary. In this paper, kinetic cyclotron maser instability calculations are extended to include the trapped Z mode for varying thermal energies and auroral potential drops within the context of a realistic ionospheric electron distribution model. It is found that when the local upper hybrid frequency is in the close vicinity of 2ƒce or 3ƒce, harmonic Z mode (Z2 and Z3) growth rate is shown to be exceedingly high. This finding suggests that an indirect mechanism that involves linear or nonlinear mode conversion of the excited harmonic Z mode into the ordinary (O) mode is a possible emission mechanism.

Plasma emission by a nonlinear beam instability in a weakly magnetized plasma

In a recent series of publications, a new theory of electromagnetic radiation with emission frequency close to the plasma frequency and/or its harmonic (i.e., the plasma emission) was presented. In this theory, the emission of radiation takes place as a result of excitation of long wavelength modes by a nonlinear beam-plasma instability, which are converted to radiative electromagnetic waves by a nonlinear mode conversion process. Unlike standard theories, the new theory predicts high radiation growth rate. In all the previous efforts on this theory, however, effects due to the presence of constant background magnetic field were ignored. The purpose of this article is to generalize the new theory to the case of weakly magnetized plasmas.

Efficient soliton compression by fast adiabatic amplification

It is shown that a properly tailored, rapidly increasing gain along the distance of propagation in a monomode fiber can provide fast but still adiabatic soliton amplification and therefore high-quality one-soliton compression for fiber lengths even shorter than the characteristic dispersive length. With the variational approach an explicit expression is given for the required variation of the inhomogeneous gain, and its validity is demonstrated by comparison with direct numerical simulations that include the calculation of the pure soliton component. It is also shown by analytical and numerical perturbation analysis that the compression scheme is stable with respect to small deviations from the ideal soliton form and gain variation. Finally, it is demonstrated that efficient soliton compression can also be obtained by cascading of instantaneous optical amplifiers in an intermediate fiber with higher dispersion, where nonlinear mode conversion preserves the soliton character of the amplified pulse. The practical implementation of these compressor schemes is discussed.

Nonlinear mode conversion with chaotic soliton generation at plasma resonance

The resonant absorption of electromagnetic waves near the critical density in inhomogeneous plasmas is studied. A driven nonlinear Schr\odinger equation for the mode-converted oscillations is derived by multiple-scaling techniques. The model is simulated numerically. The generic transition from a stationary to a time-dependent solution is investigated. Depending on the parameters, a time-chaotic behavior is found. By a nonlinear analysis, based on the inverse scattering transform, solitons of a corresponding integrable equation are identified as the dominant coherent structures of the chaotic dynamics. Finally, a map is presented which predicts chaotic soliton generation and emission at the critical density. Its qualitative behavior, concerning the bifurcation points, is in excellent agreement with the numerical simulations.

Electron-Cyclotron Maser Emission and Propagation in Solar Microwave Spike Bursts

AbstractAn improved model of the generation and propagation of cyclotron-maser radiation in flaring loops is discussed, which incorporates competition between driving of the maser instability and maser-induced relaxation of the unstable plasma. This model enables previous large discrepancies between the build-up, relaxation, and observed timescales to be resolved for solar microwave spike bursts. Also, it implies that emission via fundamental o-mode and second-harmonic x-mode instabilities can compete more effectively against fundamental x-mode emission than has previously been thought. Propagation of the radiation to the observer is discussed both theoretically and with reference to ray tracing calculations and it is shown that the observed levels of MHD waves in the corona make it significantly easier for the radiation to escape than in the unperturbed case. In the absence of nonlinear processes or mode conversion we argue that the escaping radiation is generated by either fundamental o-mode or second-harmonic x-mode instabilities.

The nonlinear optics of plasmas

It is well known that plasmas exhibit many of the characteristics of a non-linear optical medium when intense electromagnetic waves are incident upon it. These include harmonic generation, simulated Brillouin and Raman scattering, degenerate and resonant four wave mixing, self-focusing and parametric amplification. In addition, plasmas demonstrate certain unique nonlinear phenomena such as nonlinear mode conversion, two plasmon decay and relativistic self-focusing. The nonlinear optics of plasmas is therefore at once both challenging and rich for an experimentalist. It is challenging because many of the nonlinear optical phenomena occur simultaneously in a plasma. Also, when the plasma modes, characteristic of many of these instabilities, become large, kinetic effects and wave-wave interactions become extremely important. On the other hand, the plasma medium can be directly probed using coherent Thomson scattering technique revealing the richness of the physics. Experiments carried out by the author and his collaborators over the past decade are summarized and future directions for this field outlined in this paper.