Amplitude-dependent Phase Shift Research Articles

Nonlinear flip-flop quantum walks through potential barriers

The dynamics of nonlinear flip-flop quantum walk with amplitude-dependent phase shifts with pertubing potential barrier is investigated. Through the adjustment between uniform local perturbations and a Kerr-like nonlinearity of the medium we find a rich set of dynamic profiles. We will show the existence of different Hadamard quantum walking regimes, including those with mobile soliton-like structures or self-trapped states. The latter is predominant for perturbations with amplitudes that tend to $\ensuremath{\varphi}\ensuremath{\rightarrow}\ensuremath{\pi}/2$. In this system, the qubit shows an unusual behavior as we increase the amplitudes of the potential barriers and displays a monotonic decrease in the self-trapping ${\ensuremath{\varphi}}_{c}$ with respect to the nonlinear parameter. A chaotic-like regime becomes predominant for intermediate nonlinearity values. Furthermore, we show that, by changing the quantum coins ($\ensuremath{\theta}$) a nontrivial dynamic arises, where coins close to Pauli-$X$ drives the system to a regime with predominant soliton-like structures, while the chaotic behavior are restricted to a narrow region in the $\ensuremath{\chi}\ensuremath{-}\ensuremath{\varphi}$ plane. We believe that is possible to implement and observe the proprieties of this model in an integrated photonic system.

Nonlinear three-state quantum walks

The dynamics of a three-state quantum walk with amplitude-dependent phase shifts is investigated. We consider two representative inputs whose linear evolution is known to display either full dispersion of the wave packet or intrinsic localization on the initial position. The nonlinear counterpart presents much more involved dynamics featuring self-trapping, solitonic pulses, radiation, and chaotic-like behavior. We show that nonlinearity leads to a metastable self-trapped wavepacket component that radiates in the long-time regime with the survival probability $\propto t^{-1/2}$. A sudden dynamical transition from such metastable state to the point when the radiation process is triggered is found for a set of parameters.

The influence of additional phase modulation of an amplitude liquid crystal STLM on the image recognition characteristics in the invariant optical digital correlator

We present the results of measurements of additional phase modulation characteristics of a serial amplitude liquid crystal spatial light modulator HoloEye LC 2002. It is found in which way the phase shift of the liquid crystal spatial light modulator depends on the applied signal. The mathematical simulation of the performance of an invariant diffractive optical-digital correlator based on a liquid crystal spatial light modulator with the amplitude-dependent phase shift is carried out using previously measured data. The correlation filters used in the work are an optimal tradeoff maximum average correlation height filter and a minimum noise and correlation energy optical correlation filter. A method for correlation filters optimization was proposed to compensate for the recognition error caused by the presence of the additional phase modulation. In some cases, the optimization allows one not only to compensate for the recognition error, but also to reduce it.

Higher dimensional bright solitons and their collisions in a multicomponent long wave–short wave system

Bright plane soliton solutions of an integrable (2+1)-dimensional (n + 1)-wave system are obtained by applying Hirota's bilinearization method. First, the soliton solutions of a three-wave system consisting of two short-wave components and one long-wave component are found and then the results are generalized to the corresponding integrable (n + 1)-wave system with n short waves and a single long wave. It is shown that the solitons in the short-wave components (say S(1) and S(2)) can be amplified by merely reducing the pulse width of the long-wave component (say L). Study of the collision dynamics reveals some interesting behaviour: the solitons which split up in the short-wave components undergo shape changing collisions with intensity redistribution and amplitude-dependent phase shifts. Even though a similar type of collision is possible in (1+1)-dimensional multicomponent integrable systems, to our knowledge we report this kind of collision in (2+1) dimensions for the first time. However, solitons which appear in the long-wave component exhibit only elastic collision though they undergo amplitude-dependent phase shifts.

Periodic energy switching of bright solitons in mixed coupled nonlinear Schrödinger equations with linear self-coupling and cross-coupling terms

The bright soliton solutions of the mixed coupled nonlinear Schr\"odinger equations with two components (2-CNLS) with linear self- and cross-coupling terms have been obtained by identifying a transformation that transforms the corresponding equation to the integrable mixed 2-CNLS equations. The study on the collision dynamics of bright solitons shows that there exists periodic energy switching, due to the coupling terms. This periodic energy switching can be controlled by the new type of shape changing collisions of bright solitons arising in a mixed 2-CNLS system, characterized by intensity redistribution, amplitude dependent phase shift, and relative separation distance. We also point out that this system exhibits large periodic intensity switching even with very small linear self-coupling strengths.

Passive system with tunable group velocity for propagating electrical pulses from sub- to superluminal velocities.

We report an observation of tunable group velocity from sub-luminal to superluminal in a completely passive system. Electric pulses are sent along a spatially periodic conducting medium containing a punctual nonlinearity, and the resulting amplitude-dependent phase shift allows us to control dispersion and the propagation velocity at the stop band frequency.

Effect of phase shift in shape changing collision of solitons in coupled nonlinear Schrödinger equations

Soliton interactions in systems modelled by coupled nonlinear Schroedinger (CNLS) equations and encountered in phenomena such as wave propagation in optical fibers and photorefractive media possess unusual features : shape changing intensity redistributions, amplitude dependent phase shifts and relative separation distances. We demonstrate these properties in the case of integrable 2-CNLS equations. As a simple example, we consider the stationary two-soliton solution which is equivalent to the so-called partially coherent soliton (PCS) solution discussed much in the recent literature.

Improving the accuracy of measurement of phase-amplitude response of four-pole networks

The typical block diagram of an instrument used for phase-amplitude response (PAR) measurements includes a high-frequency source (generator) and test signal generator connected in series as well as a two-channel phase difference converter and an indicating device. The investigated four-pole networks are connected between the test signal generator and phase difference converter in one or in both channels simultaneously. All circuits of the PAR meter are synchronized from a common control circuit. The test signal generator produces two high-frequency output signals with an amplitude varying with time. To reduce PAR measurements errors, the amplitude-dependent phase shifts in the investigated four-pole networks acted upon by the test signal are first transferred to a relatively low stable intermediate frequency and only then converted into a code or voltage.

The output signals and noise from a nonlinearity with amplitude-dependent phase shift

On the assumption that each input signal represents only a small part of the total input power, the output signals and output noise spectrum are found by extending the Barrett-Lampard diagonal expansion to the case of the quadrivariate distribution of input amplitude and phase at two different times. This expansion yields a decomposition of the nonlinearity into a summation of generalized Laguerre polynomials with uncorrelated outputs, whose spectra are simply autoconvolutions of the input spectrum. A slight generalization of the notion of memoryless nonlinearity allows this result to he applied very simply to devices, such as limiters and TWT amplifiers, that cause AM-to-PM conversion.