Velocity Matching Research Articles

Crossover from two-frequency pulse compounds to escaping solitons

The nonlinear interaction of copropagating optical solitons enables a large variety of intriguing bound-states of light. We here investigate the interaction dynamics of two initially superimposed fundamental solitons at distinctly different frequencies. Both pulses are located in distinct domains of anomalous dispersion, separated by an interjacent domain of normal dispersion, so that group velocity matching can be achieved despite a vast frequency gap. We demonstrate the existence of two regions with different dynamical behavior. For small velocity mismatch we observe a domain in which a single heteronuclear pulse compound is formed, which is distinct from the usual concept of soliton molecules. The binding mechanism is realized by the mutual cross phase modulation of the interacting pulses. For large velocity mismatch both pulses escape their mutual binding and move away from each other. The crossover phase between these two cases exhibits two localized states with different velocity, consisting of a strong trapping pulse and weak trapped pulse. We detail a simplified theoretical approach which accurately estimates the parameter range in which compound states are formed. This trapping-to-escape transition allows to study the limits of pulse-bonding as a fundamental phenomenon in nonlinear optics, opening up new perspectives for the all-optical manipulation of light by light.

Study of Type II SPDC in Lithium Niobate for High Spectral Purity Photon Pair Generation

Recent advances of high-quality lithium niobate (LN) on insulator technology have revitalized the progress of novel chip-integrated LN-based photonic devices and accelerated application research. One of the promising technologies of interest is the generation of entangled photon pairs based on spontaneous parametric down-conversion (SPDC) in LNs. In this paper, we investigated, theoretically and numerically, Type II SPDC in two kinds of LNs—undoped and 5-mol% MgO doped LNs. In each case, both non-poled and periodically poled crystals were considered. The technique is based on the SPDC under Type II extended phase matching, where the phase matching and the group velocity matching are simultaneously achieved between interacting photons. The proposed approach has not yet been reported for LNs. We discussed all factors required to generate photon pairs in LNs, in terms of the beam propagation direction, the spectral position of photons, and the corresponding effective nonlinearities and walk-offs. We showed that the spectral positions of the generated photon pairs fall into the mid-infrared region with high potential for free-space quantum communication, spectroscopy, and high-sensitivity metrology. The joint spectral analyses showed that photon pairs can be generated with high purities of 0.995–0.999 with proper pump filtering.

Dispersion in dielectric-lined waveguides designed for terahertz-driven deflection of electron beams

We have developed dielectric-lined rectangular waveguide structures for terahertz (THz)-driven ultrafast deflection of 100 keV electron beams. The structures were designed to achieve THz phase velocity matching with co-propagating electron bunches. The phase-matching capability was experimentally confirmed through time-frequency analysis of the broadband coherent THz transmission measured by electro-optic sampling. The analysis determined both the frequency-dependent propagation constants in the electron interaction region and the propagation characteristics of the integrated THz tapered coupler.

Highly efficient THz generation by optical rectification of mid-IR pulses in DAST

We report on efficient THz generation in DAST by optical rectification of intense mid-IR pulses centered at (i) 3.9 μm and (ii) its second harmonic at 1.95 μm. Suppression of multi-photon absorption shifts the onset of saturation of the THz conversion efficiency to pump energy densities, which are almost an order of magnitude higher as compared to conventional pump schemes at 1.5 μm. Despite strong linear absorption at 3.9 μm, DAST exhibits a high optical-to-THz conversion efficiency, which we attribute to resonantly enhanced nonlinearity and advantageous phase matching of the THz phase velocity and group velocity of the driving pulse. At 1.95 μm, we find that low linear and multi-photon absorption in combination with cascaded optical rectification lead to record optical-to-THz conversion efficiencies approaching 6%. The observed high sensitivity of the THz generation to the parameters of the mid-IR driving pulses motivates an in-depth study of the underlying interplay of nonlinear wavelength- and intensity-dependent effects.

Continuous variable multimode quantum states via symmetric group velocity matching

Configurable and scalable continuous variable (CV) quantum networks for measurement-based quantum information protocols or multipartite quantum communication schemes can be obtained via parametric down conversion (PDC) in non-linear waveguides. In this work, we exploit symmetric group velocity matching (SGVM) to engineer the properties of the squeezed modes of the PDC. We identify type II PDC in a single waveguide as the best suited process, since multiple modes with non-negligible amount of squeezing can be obtained. We explore, for the first time, the waveguide dimensions, usually only set to ensure single-mode guiding, as an additional design parameter ensuring indistinguishability of the signal and idler fields. We investigate here potassium titanyl phosphate (KTP), which offers SGVM at telecommunications wavelengths, but our approach can be applied to any non-linear material and pump wavelength. This work paves the way toward the engineering of future large-scale quantum networks in the CV regime.

Advanced Electrode Design for Low-Voltage High-Speed Thin-Film Lithium Niobate Modulators

In this paper, we present a novel transmission line architecture in thin-film lithium niobate (TFLN) platforms to improve the velocity match between the microwave and the optical wave. Compared to conventional coplanar waveguide (CPW), the microwave index ( $n_m$ ) of the proposed slotted electrodes can be optimized from 2.1 to 3 while maintaining the high modulation efficiency and 50- $\Omega$ impedance match. Equivalent-circuit model analysis and finite-element simulation are performed. The simulated half-wave voltage (V $_\pi$ ) of 1.2 V and E-O modulation bandwidth greater than 80 GHz is obtained for a 2-cm-long modulator. By utilizing the slotted slow-wave electrode, TFLN Mach-Zehnder modulators with CMOS-compatible operating voltage and 3-dB modulation bandwidth greater than 100 GHz are potentialized.

Integration and evaluation of robotic fused filament fabrication system

Fused filament fabrication (FFF) continues to be among the most widespread additive manufacturing process for making polymeric functional prototypes, and in several cases end-use parts. There is a large installed base of serial-link industrial robots, some of which could be potentially retrofitted with an extruder head as an end-effector to serve as FFF systems with as many as six degrees of freedom compared to 3-axis gantry mechanisms that are typically deployed today. This paper identifies and proposes solutions to key engineering challenges that arise in retrofitting such robotic FFF systems in terms of integrating robot motion controller with extruder controller and evaluating the quality of the fabricated parts. Specifically, we propose an approach for integration and real-time synchronization of controllers to ensure that the extrusion velocity and deposition velocity match closely by building upon an analytical model for predicting road geometry as a function of process parameters. Compared to gantry mechanisms, this is challenging in serial-link industrial robots because of significantly larger and space-variant inertias. Furthermore, to compensate for distortion in the bed surface of the retrofitted robotic FFF system, a bed compensation algorithm based on bilinear interpolation has been developed. We have engineered a fully functional research testbed in which integration and real-time synchronization of controllers is achieved by (1) communicating space-variant process parameters in real-time using TCP/IP sockets, and (2) analog and digital I/O interfacing. Experimental testing shows excellent (R2 = 0.9983) agreement between requested and actual volumetric flow rates and less than 5% errors in extrusion widths and heights in test samples fabricated across the range of physical limits of FFF process parameters. The testbed is also evaluated in terms of the impact of controller synchronization on the part dimensional accuracy for simple and complex geometries. This work can serve as a basis for further engineering innovations towards cost-effectively harnessing the capacity of industrial robots to manufacture geometrically accurate parts using FFF.

Classical nonlinear simulation of low-order modes of Lamb waves in plate

For the classical nonlinear research of low-order modes of Lamb waves, this paper firstly introduces the classical nonlinearity derived from the intrinsic nonlinear induced low-order Lamb waves (S0 and A0 modes). Theoretical and numerical calculations are studied in two aspects. The influence of nonlinear effects on the nonlinear effects of classical nonlinear low-order Lamb waves and the cumulative growth effect are analyzed by finite element simulation. The results show that the nonlinear effect produced by the superelastic material model is greater than the geometric nonlinearity, and the linear elastic material model does not produce nonlinear effects. In addition, as the third-order elasticity increases in the material, the amplitude of the second harmonic gradually increases. The second harmonic generated by the A0 mode with phase velocity mismatch is the S0 mode. It can be seen that the group velocity matching is not a necessary condition for generating the second harmonic. Since the phase velocity matching is not satisfied, there is no cumulative growth effect; The higher the S0 mode phase velocity matching degree, the more obvious the cumulative growth effect, and the second harmonic is the S0 mode.

Internally resonant guided waves arising from quadratic classical nonlinearities with damping

Taking into account damping effects, the propagation-distance dependence of the amplitude of nonlinear guided waves arising from an internal resonance was investigated. In the analysis of Lamb-wave propagation, we introduced nonlinear quadratic effects derived from both geometric and material nonlinearities, referred to as classical nonlinearities, and damping effects by expressing the Lamé constants as complex numbers. Assuming a small detuning from the phase matching condition with respect to wavenumber and frequency, and using the method of multiple scales and self-adjointness of the governing equations with boundary conditions, the amplitude equations describing the nonlinear coupling of the two wave modes are derived as solvability conditions. This derivation also provides both physical and mathematical insights into both the phase and group velocity matching conditions. Numerical results obtained from these amplitude equations show that because of the nonlinear coupling an internal resonance between the two modes can occur under the above matching conditions. Without detuning, one mode increases monotonically in amplitude while the other decreases monotonically. Nevertheless, their changes gradually decrease with propagation distance, and each amplitude converges to a finite value. However, with wavenumber and frequency detuning, both amplitudes increase and decrease cyclically with propagation distance, resulting in a weakening of this resonance. Furthermore, results with damping effects show an attenuation of both amplitudes with propagation distance, which limits the distance resonance waves can propagate.

Fully Distributed Region-Reaching Control with Collision Avoidance for Multi-robot Systems

SUMMARYThis paper proposes a fully distributed continuous region-reaching controller for multi-robot systems which can effectively eliminate the chattering issues and the negative effects caused by discontinuities. The adaptive control gain technique is employed to solve the distributed region-reaching control problem. By performing Lyapunov function-based stability analysis, it is shown that all the robots can move cohesively within the desired region under the proposed distributed control algorithm. In addition, collision avoidance and velocity matching within the moving region can be guaranteed under properly designed control gains. Simulation examples are given to verify the capabilities of the proposed control method.

Numerical Investigation of High-Purity Polarization-Entangled Photon-Pair Generation in Non-Poled KTP Isomorphs

We investigated the high-purity entangled photon-pair generation in five kinds of “non-poled” potassium titanyl phosphate (KTP) isomorphs (i.e., KTiOPO4, RbTiOPO4, KTiOAsO4, RbTiOAsO4, and CsTiOAsO4). The technique is based on the spontaneous parametric down-conversion (SPDC) under Type II extended phase matching (EPM), where the phase matching and the group velocity matching are simultaneously achieved between the interacting photons in non-poled crystals rather than periodically poled (PP) KTPs that are widely used for quantum experiments. We discussed both theoretically and numerically all aspects required to generate photon pairs in non-poled KTP isomorphs, in terms of the range of the beam propagation direction (or the spectral range of photons) and the corresponding effective nonlinearities and beam walk-offs. We showed that the SPDC efficiency can be increased in non-poled KTP isomorphs by 29% to 77% compared to PPKTP cases. The joint spectral analyses showed that photon pairs can be generated with high purities of 0.995–0.997 with proper pump filtering. In contrast to the PPKTP case, where the EPM is achieved only at one specific wavelength, the spectral position of photon pairs in the non-poled KTP isomorphs can be chosen over the wide range of 1883.8–2068.1 nm.

A Novel Proportional Navigation Based Method for Robotic Interception Planning With Final Velocity Control

This paper presents a new method for robot interception planning based on the proportional navigation. Guidance laws are basically developed for aerospace applications where a pursuer impacts a target using these methods, however in the robotic application it is required to have a smooth grasp between the robot and the goal. In this method, a new term is considered for longitude axis to have the control on the final approaching velocity. The proposed method not only ensures the position and velocity match (also referred to as rendezvous) but also can be used to set the final closing velocity to any desired value. Approaching velocity can be zero for grasping the goal or a specific known velocity for hitting it in a controlled manner. It is shown that the capture region of the proposed approach is wider that other proportional navigation based methods. The proposed method is implemented on Qbot-2 and its performance is experimentally validated.

Wideband thin-film lithium niobate modulator with low half-wave-voltage length product

A novel thin-film lithium niobate (TFLN) electro-optic modulator is proposed and demonstrated. LiNbO3-silica hybrid waveguide is adopted to maintain low optical loss for an electrode spacing as narrow as 3 µm, resulting in a low half-wave-voltage length product of only 1.7 V·cm. Capacitively loaded traveling-wave electrodes are employed to reduce the microwave loss, while a quartz substrate is used in place of a silicon substrate to achieve velocity matching. The fabricated TFLN modulator with a 5-mm-long modulation region exhibits a half-wave voltage of 3.4 V and a merely less than 2 dB roll-off in an electro-optic response up to 67 GHz.

Numerical Investigation of High-Purity Entangled Photon-Pair Generation in Ba3Mg3(BO3)3F3 Crystals

We investigate the high-purity entangled photon pair generation in a recently developed borate crystal, Ba3Mg3(BO3)3F3. The technique is based on the spontaneous parametric down-conversion under the extended phase matching (EPM), where the phase matching and the group velocity matching between the interacting photons are satisfied simultaneously in bulk crystals with point symmetry of orthorhombic mm2 (thus showing biaxial birefringence). We will discuss all the theoretical aspects required for the generation of photon pairs in mm2 biaxial crystals, which are much more complex than the cases of uniaxial crystals (e.g., β-BaB2O4 and LiNbO3) and periodically poled crystals that are widely used in the field. Our study includes theoretical and numerical investigations of two types of EPM and their corresponding effective nonlinearities and spatial walk-offs. The results show that two types of EPM are satisfied over the specific range in the direction of pump wave vector, corresponding to its spectral ranges of 876.15–1052.77 nm for Type I and 883.92–914.33 nm for Type II. The joint spectral analyses show that photon-pairs can be generated with high purities of 0.997 with a proper pump filtering (for Type II), and 0.833 even without pump filtering (for Type I).

Efficient computations for linear feedback control problems for target velocity matching of Navier-Stokes flows via POD and LSTM-ROM

<p style='text-indent:20px;'>An efficient computing method for a target velocity tracking problem of fluid flows is considered. We first adopts the Lagrange multipliers method to obtain the optimality system, and then designs a simple and effective feedback control law based on the relationship between the control <inline-formula><tex-math id="M1">\begin{document}$ {{\boldsymbol f}} $\end{document}</tex-math></inline-formula> and the adjoint variable <inline-formula><tex-math id="M2">\begin{document}$ {{\boldsymbol w}} $\end{document}</tex-math></inline-formula> in the optimality system. We consider a reduced order modeling (ROM) of this problem for real-time computing. In order to improve the existing ROM method, the deep learning technique, which is currently being actively researched, is applied. We review previous research results and some computational results are presented.

Study on matching effect of operating variables and particle motion behavior in Teeter Bed Separator

ABSTRACT Water velocity and bed density are most important operating variables affecting the separation of coal particles in Teeter Bed Separator (TBS). In this paper, experimental investigation is carried out to evaluate the matching effect of operating variables on the performance of TBS for separating a coal sample with size of 1–0.25 mm. Furthermore, the particle motion based on the Euler-Euler simulation approach and slip velocity model is analyzed to explain the experiment phenomenon. Experiment results show that at a constant cut density (δ50), two operating variables present a negative relationship. When a considerable clean coal yield is produced, the matching of a lower water velocity with higher bed density displays more desirable performance. The performance difference at different matching operation is also reflected in the separation of narrow size particles. The simulation results and theoretical analysis on particle motion illustrate that coal particles are separated more significantly according to their density at the operating condition of lower water velocity matching higher bed density. The study is of great importance to offer the reference of operating variables controlling and develop numerical simulation study for TBS.

Second-harmonic generation of temporally low-coherence light

In this Letter, we study the second-harmonic (SH) generation of temporally low-coherence light using the statistical optics method. By introducing the statistical characteristics of low-coherence light into the nonlinear coupled wave equation, we predict the self-convolution relationship between the power spectral density of the second-harmonic and that of the fundamental wave and demonstrate it in experiments. The effects of phase matching and group velocity matching on the second-harmonic bandwidth and conversion efficiency are analyzed, which is beneficial to improve the efficiency of low-coherent SH light. Combining the statistics optics and nonlinear optics, our research provides a suitable mathematical model for the study of nonlinear frequency conversion processes of temporally low-coherence light. Due to its statistical characteristics and temporal incoherence, low-coherence SH light would have further applications in uniform illumination, quantum optics, metrology, and so on.

Broadband quasi-phase-matched optical parametric generation in phase reversal optical superlattice devices

We have theoretically investigated the generation of ultra-flat broadband optical parametric generation (OPG) in the communication band using a lithium niobate based domain engineered phase reversal optical superlattice (PROS) structure by group velocity matching (GVM) technique. The simulation results show an ultra-flat broadband OPG of acceptance FWHM bandwidth Δλ = 210 nm centered at 1.55 μm in 10 mm long device with 19 μm period operating at 20 °C for 775 nm fixed pump wavelength. The selection of the period and pump wavelength relies on the group velocities of the signal and idler wavelengths close to zero-group velocity dispersion (GVD) point to achieve broadband OPG. The PROS quasi-phase matching (QPM) device generates broader and ultra-flat OPG compared to the conventional periodic QPM counterparts. Further, the variation in the flatness of the broadband QPG due to the change in the location and width of the phase reversal (PR) domain in the device is discussed.

Simulation and analysis of the PMN-PT based phased array transducer with the high sound velocity matching layer

The finite element modeling (FEM) simulation and comparison of electroacoustic properties of the PMN-PT based phased arrays with high sound velocity (HSV) and low sound velocity (LSV) matching layers were investigated. The simulated keff of HSV layer based phased arrays (2.7 MHz) is higher than that of LSV matching layer based phased arrays, which reveals that the higher energy conversion efficiency is obtained. The vibration modal analysis shows that the average value of displacement ratio Rdisp of HSV matching layer based arrays (2.7 MHz) is 0.850, which is larger than that of LSV layer based arrays, indicating that the transmission efficiency of longitudinal energy can be enhanced with HSV matching layer. The interaction of transverse vibration between the adjacent elements for HSV layer based arrays become much weaker, which reduce the acoustic energy loss and the interference of transverse wave. The simulation results of echo performance illustrate that the relative error of all data is controlled at 2%, which proves that the FEM simulation has excellent accuracy compare to the practical results. The measured -6 dB bandwidth of the HSV layer based arrays (2.7 MHz) is 7.28 % higher than that of the LSV layer based arrays while the relative sensitivity is almost the same. Besides, the simulated results of electroacoustic properties of phased arrays with different center frequencies demonstrate that the -6 dB bandwidth increased by an average of 7.03 % and the crosstalk level decreased by an average of 1.91 dB when using the HSV matching layer. The crosstalk and clutter wave caused by the transverse vibration can be reduced by applying the HSV matching layer and thus a shorter pulse-echo response and enhancement of the bandwidth of the arrays can be obtained.

Experimental investigation of dispersive wave generation and evolution in a tellurite microstructured optical fiber

A four-hole tellurite microstructured optical fiber (MOF) was designed and fabricated based on TeO2–Bi2O3–ZnO–Na2O (TBZN), and the fiber loss was 0.1 dB/m@1550 nm. Based on a 3 m tellurite MOF, dispersive wave (DW) generation and evolution was experimentally investigated at the pump wavelengths of 1778 nm, 1812 nm, and 1878 nm. With the increase of the average pump power, DWs trapped by optical solitons were observed at the blue edge wavelength, but their formation became more and more difficult with the pump wavelength shifting far away from the zero-dispersion wavelength. The variation pattern of center wavelengths and peak powers of the fundamental optical solitons and DWs were investigated: the center wavelength distribution satisfied the group velocity matching; the peak power of the fundamental DW gradually exceeded that of the fundamental optical soliton with the increase of the average pump power. Furthermore, using the generalized nonlinear Schrödinger equation, simulation on the generation of DWs and optical solitons was carried out at 1778 nm, 40 mW, the result of which agreed well with the experimental observation. This investigation is instructive for DW applications in tunable laser sources, wavelength conversion, and time frequency metrology.