Conditions Of Phase Mismatch Research Articles

Quantum Properties in Nonlinear Coupler with Raman Process.

In this work, we have examined the generation of squeezed states of light in a two-waveguide coupler in which Raman processes are active in one waveguide. Both waveguides are mutually linearly interacting through the field’s evanescent waves. We looked at a few interesting cases in which the system generated single mode squeezed states due to spontaneous and stimulated Raman processes. Under specific combinations of design parameters and phase mismatching conditions, squeezed states may take the form of collapses and revivals, or the second quadrature of the optical mode may oscillate completely below the short-noise limit of a coherent state.

Efficient Kerr nonlinearity in RTP induced by electro-optically adjustable cascaded second-order process

This paper reveals an analytical perception of electro-optically tunable cascaded Kerr-lens using RbTiOPO4 (RTP) crystal where the advantageous properties of the crystal have been studied to mitigate the limitations of KTiOPO4 (KTP) and BaB2O4 (BBO) in intracavity high power laser generation. An external electric field application to the z-direction of RTP is introducing a phase mismatch condition leading to a nonlinear phase shift within propagating optical waves. Based on simulated endeavors, a maximum effective nonlinear refractive index of ±1.4053 × 10−13 cm2/W is calculated by developing a phase shift of ∓4.6 rad. In contrast, KTP and RTP both have almost similar optical properties but due to certain special features like higher damage threshold, less walk-off angle etc., RTP is firmly accepted for high power applications. Additionally, this article is augmented to analyze the self-focusing and defocusing phenomenon owing to the non-uniform distribution of radial intensity of the propagating Gaussian beam. To the best of author's knowledge, the present analysis manifests the superior performance of RTP that may pave the way to devise a configurable lens analogous to Kerr-lens having an electro-optically tunable focal length.

Numerical investigation of on-chip wavelength conversion based on InP/In[formula omitted]Ga[formula omitted]As[formula omitted]P[formula omitted] semiconductor waveguide platforms

We design the high confinement InP/In1−xGaxAsyP1−y semiconductor waveguides and investigate the effective wavelength conversion based on this platform. Efficient confinement and mode field area fluctuation at different wavelength is analyzed to achieve the high nonlinear coefficient. The numerical results show that nearly zero phase-mismatch condition can be satisfied through dispersion tailoring of InP/In1−xGaxAsyP1−y waveguides, and the wavelength conversion ranging over 40 nm with the maximum conversion efficiency −26.3 dB is achieved. Meanwhile, the influences of the doping parameter y and pumping wavelength on the bandwidth and conversion efficiency are also discussed and optimized. Our demonstration of the excellent all-optical wavelength conversion properties of the InP/In1−xGaxAsyP1−y waveguides could pave the way towards direct integration telecom band devices on stand semiconductor platforms.

Phase-mismatch dependence of the four-wave mixing effect in semiconductor optical amplifiers.

The phase-mismatch effect due to polarization-dependent mode confinement factor has been shown to be not a crucial problem in semiconductor optical amplifiers (SOAs) and is usually not accounted for. The phase-mismatch four-wave mixing (FWM) process in SOA devices is experimentally reported. The results reveal a sinc-like behavior in the intensity of FWM conjugate as a function of wavelength separation between transverse electric (TE)/transverse magnetic (TM) pumps due to induced confinement factors difference. Efficient FWM occurred for a detuning shift of about 500 GHz, limited by phase-mismatch conditions and determined by coherence length required for low and high frequencies to complete a full phase-match cycle. Phase-match FWM with an infinity coherence length can be fulfilled by proper alignments of co-polarized TE/TM modes of input waves with respect to the birefringent axes of the device structure.

Broadband and robust adiabatic second-harmonic generation by a temperature gradient in birefringently phase-matched lithium triborate crystal.

Phase-matched nonlinear processes exhibit a tradeoff between the conversion efficiency and the acceptance bandwidth. Adiabatic nonlinear processes, in which the phase mismatch varies slowly along the interaction length, enable us to overcome this tradeoff, allowing an efficient frequency conversion with broad spectral and thermal bandwidths. Until now, the variation in the phase mismatch condition was mainly based on quasi-phase matching in ferroelectric crystals. However, this solution is limited to low power sources. Here, instead, we study the adiabatic second harmonic in birefringently phase-matched lithium triborate crystal, enabling us to handle much higher power levels. The variation in the phase mismatch is achieved by inducing a temperature gradient along the crystal. By using a 50mm long crystal, the adiabatic process provided a temperature bandwidth of 18°C, 5.4 times wider than what is achieved when the same crystal is held at the fixed phase-matching temperature. The conversion efficiency exceeded 60% for a 0.9millijoule pump pulse.

Effects of nonlinear phase in cascaded mode-locked Nd:YVO4 laser.

A diode-pumped mode-locked Nd:YVO4 laser via positive cascaded second-order Kerr lens using periodically poled MgO:LN at 1064 nm was reported. Mode-locking performances including output power, bandwidth, pulse duration, and time-bandwidth product were studied under different phase-mismatched conditions. The induced nonlinear phase combined with soft aperture effect yield a stable mode-locked operation in a wide phase-mismatched range (-8π < ∆kL < -π). Additionally, the mode-locking bandwidth was broadened by self-phase modulation and the time-bandwidth product was increased to be more than twice the ideal product for a sech2 pulse shape. Under 11 W diode pump power, the measured average power, pulse repetition rate and pulse duration are 1.3 W, 186 MHz and 2.8 ps, respectively.

Broadband, efficient, and robust quasi-parametric chirped-pulse amplification.

Quasi-parametric chirped pulse amplification (QPCPA) is a new scheme that enables the amplification of chirped signal pulses without back conversion by depleting the idler pulses. In this paper, we present a numerical study on the bandwidth, efficiency, and robustness of QPCPA. Self-locked phase among the interacting waves is found to be the underlying mechanism for the suppression of back conversion, which allows signal efficiency approaching to the quantum limit even under the phase-mismatch condition, and thus greatly increases the phase-mismatch tolerance of QPCPA. We demonstrate that QPCPA can break through the trade-off between the efficiency and bandwidth encountered in conventional optical parametric amplification, hence supporting highly efficient amplification of few-cycle pulses.

Proposal for electro-optically tunable Kerr-Lens in BBO crystal by cascaded second-order process

In this report, a linear electro-optically tunable non-phase matched second-order nonlinear process is transformed into a cascaded second-order nonlinear process in a bulk BBO crystal to generate the effect of electro-optically tunable Kerr-type nonlinearity. A phase mismatch condition is created by applying an electric field to the x–z plane of the crystal which introduces a nonlinear phase shift between the launched and reconverted fundamental waves from the generated second harmonic wave. The sign of this nonlinear phase shift is easily changed by changing the polarity of applied electric field. The nonuniform radial intensity distribution of incident Gaussian beam introduces a curvature to the fundamental wavefront which focuses or defocuses the incident beam while propagating through the medium. Hence, a positive or negative lens is established within the crystal. The focal length of that lens is also tuned by tuning the applied electric field. The maximum calculated effective nonlinear refractive index due to nonlinear phase shift is ±6.6508×10−14cm2/W.

The effect of gas pressure and slit width on the high order harmonic generation in helium-filled slab waveguide

We measured the dependence of the intensity of high harmonics on the gas pressure in slab waveguide. The phase matching of 61st high harmonic was obtained according to the quadratic dependence of the increase in efficiency with pressure. For higher order harmonics such as H91, periodic oscillations of the harmonic intensity with gas pressure was observed. We also studied the effect of the slit width of the slab waveguide on the high harmonics generation. The influence of the slit width on laser transverse mode and phase mismatching conditions can be used to explain this effect.

Quantum noise in parametric amplification under phase-mismatched conditions

This paper studies quantum noise in parametric amplification under phase-mismatched conditions. The equations of motion of the quantum-mechanical field operators, which include phase mismatch under unsaturated conditions are first derived from the Heisenberg equation. Next, the noise figure is evaluated using the solutions of the derived equations. The results indicate that phase mismatch scarcely affects noise property in phase-insensitive amplification while it has a notable effect in case of phase-sensitive amplification.

Simple method of optimizing second-harmonic generation under imperfect phase-mismatching conditions caused by group-velocity mismatch and group-velocity dispersion

A simple method of thickness optimization of a nonlinear optical crystal used for second-harmonic generation involving group-velocity mismatching and group-velocity dispersion is discussed on the basis of the feature parameter ΔS. An approximate analysis formula for thickness with respect to the maximum second-harmonic intensity is obtained, which is applicable to the optimization of second-harmonic generation.

Deep-subwavelength waveguiding via inhomogeneous second-harmonic generation

We theoretically investigate second-harmonic generation in extremely narrow, subwavelength semiconductor and dielectric waveguides. We discuss a guiding mechanism characterized by the inhibition of diffraction and the suppression of cutoff limits in the context of a light trapping phenomenon that sets in under conditions of general phase and group velocity mismatch between the fundamental and the generated harmonic.

Propagation dynamics and X-pulse formation in phase-mismatched second-harmonic generation

This paper concerns the theoretical, numerical, and experimental study of the second-harmonic-generation (SHG) process under conditions of phase and group-velocity mismatch and aims to demonstrate the dimensionality transition of the SHG process caused by the change of the fundamental wave diameter. We show that SHG from a narrow fundamental beam leads to the spontaneous self-phase-matching process with, in addition, the appearance of angular dispersion for the off-axis frequency components generated. The angular dispersion sustains the formation of the short X pulse in the second harmonic (SH) and is recognized as three-dimensional (3D) dynamics. On the contrary, the large-diameter fundamental beam reduces the number of the degrees of freedom, does not allow the generation of the angular dispersion, and maintains the so-called one-dimensional (1D) SHG dynamics, where the self-phase-matching appears just for axial components and is accompanied by the shrinking of the SH temporal bandwidth, and sustains a long SH pulse formation. The transition from long SH pulse generation typical of the 1D dynamics to the short 3D X pulse is illustrated numerically and experimentally by changing the conditions from the self-defocusing to the self-focusing regime by simply tuning the phase mismatch. The numerical and experimental verification of the analytical results are also presented.

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.

Two-color interface vortex solitons

We study the existence and properties of vortex solitons supported by an interface between two distinct optical lattices imprinted in nonlinear quadratic media. We analyze the impact of guiding parameters of lattices and phase mismatching conditions on the existence and stability of two-color interface vortex solitons. The salient point is that interface vortex solitons feature highly asymmetric profiles, and are stable throughout almost the entire existence domain.

Multipole-mode interface solitons in quadratic nonlinear photonic lattices

We address the properties of nonlinear multipole modes supported by an interface between two distinct optical lattices imprinted in two-dimensional nonlinear quadratic media. Such multipole-mode solitons feature out of phase between neighboring lobes, which may be located in two different sides of the lattices. We analyze the impact of guiding parameters of lattices on the existence and stability of multipole-mode interface solitons in different phase mismatching conditions. Remarkably, our results show that multipole-mode interface solitons have the highly asymmetric shape and they are stable in the broad range of system parameters.

Complete spatial and temporal locking in phase-mismatched second-harmonic generation

We experimentally demonstrate simultaneous phase and group velocity locking of fundamental and generated second harmonic pulses in Lithium Niobate, under conditions of material phase mismatch. In phase-mismatched, pulsed second harmonic generation in addition to a reflected signal two forward-propagating pulses are also generated at the interface between a linear and a second order nonlinear material: the first pulse results from the solution of the homogeneous wave equation, and propagates at the group velocity expected from material dispersion; the second pulse is the solution of the inhomogeneous wave equation, is phase-locked and trapped by the pump pulse, and follows the pump trajectory. At normal incidence, the normal and phase locked pulses simply trail each other. At oblique incidence, the consequences can be quite dramatic. The homogeneous pulse refracts as predicted by material dispersion and Snell's law, yielding at least two spatially separate second harmonic spots at the medium's exit. We thus report the first experimental results showing that, at oblique incidence, fundamental and phase-locked second harmonic pulses travel with the same group velocity and follow the same trajectory. This is direct evidence that, at least up to first order, the effective dispersion of the phase-locked pulse is similar to the dispersion of the pump pulse.

Soliton pulse compression through cascaded quadratic nonlinearity in difference-frequency generation

Cascaded nonlinearity based soliton pulse compression in the process of femtosecond difference frequency generation is studied theoretically. A set of simplified coupled wave equations under the conditions of large phase mismatch and matched group velocities is obtained, which reveals the physical mechanism of soliton compression in this process. Numerical simulations demonstrate that in the presence of group velocity dispersion and equivalent cross phase modulation, both the pump and the signal pulses can be compressed with a high compression ratio.

Role of phase matching in pulsed second-harmonic generation: Walk-off and phase-locked twin pulses in negative-index media

The present investigation is concerned with the study of pulsed second-harmonic generation under conditions of phase and group velocity mismatch, and generally low conversion efficiencies and pump intensities. In positive-index, nonmetallic materials, we generally find qualitative agreement with previous reports regarding the presence of a double-peaked second harmonic signal, which comprises a pulse that walks off and propagates at the nominal group velocity one expects at the second-harmonic frequency, and a second pulse that is ``captured'' and propagates under the pump pulse. We find that the origin of the double-peaked structure resides in a phase-locking mechanism that characterizes not only second-harmonic generation, but also ${\ensuremath{\chi}}^{(3)}$ processes and third-harmonic generation. The phase-locking mechanism that we describe occurs for arbitrarily small pump intensities, and so it is not a soliton effect, which usually relies on a threshold mechanism, although multicolor solitons display similar phase locking characteristics. Thus, in second harmonic generation a phase-matched component is always generated, even under conditions of material phase mismatch: This component is anomalous, because the material does not allow energy exchange between the pump and the second-harmonic beam. On the other hand, if the material is phase matched, phase locking and phase matching are indistinguishable, and the conversion process becomes efficient. We also report a similar phase-locking phenomenon in negative index materials. A spectral analysis of the pump and the generated signals reveals that the phase-locking phenomenon causes the forward moving, phase-locked second-harmonic pulse to experience the same negative index as the pump pulse, even though the index of refraction at the second-harmonic frequency is positive. Our analysis further shows that the reflected second-harmonic pulse generated at the interface and the forward-moving, phase-locked pulse appear to be part of the same pulse initially generated at the surface, part of which is immediately back-reflected, while the rest becomes trapped and dragged along by the pump pulse. These pulses thus constitute twin pulses generated at the interface, having the same negative wave vector, but propagating in opposite directions. Almost any break of the longitudinal symmetry, even an exceedingly small ${\ensuremath{\chi}}^{(2)}$ discontinuity, releases the trapped pulse which then propagates in the backward direction. These dynamics are indicative of very rich and intricate interactions that characterize ultrashort pulse propagation phenomena.

Analysis of phase mismatch in magneto-optic Bragg diffraction

The magneto-optic (MO) coupled-mode equations for magnetostatic waves (MSWs) and guided optical waves (GOWs) under phase-mismatch conditions were deduced and applied to the noncollinear interaction with magnetostatic backward volume waves (MSBVWs) in obliquely magnetized yttrium-iron-garnet (YIG) film using single-element microstrip line transducer. The diffraction efficiency (DE) of the incident TE0-mode light was calculated. For the case of magnetization along the MSBVW propagation direction, the calculated results are in good agreement with the experimental data. In contrast, by using an appropriately tilted bias magnetic field the DE can be increased by 6dB and is insensitive to the phase mismatch induced by the change of magnetization direction. Thus, the optimization of the direction of the bais magnetic field is an effective method for improving the diffraction performance and increasing the MO bandwidth of the Bragg cells.