Showing papers on "Group velocity published in 2020"

Relativistic kinematics of a magnetic soliton.

Abstract: A tenet of special relativity is that no particle can exceed the speed of light. In certain magnetic materials, the maximum magnon group velocity serves as an analogous relativistic limit for the speed of magnetic solitons. Here, we drive domain walls to this limit in a low-dissipation magnetic insulator using pure spin currents from the spin Hall effect. We achieve record current-driven velocities in excess of 4300 meters per second-within ~10% of the relativistic limit-and we observe key signatures of relativistic motion associated with Lorentz contraction, which leads to velocity saturation. The experimental results are well explained through analytical and atomistic modeling. These observations provide critical insight into the fundamental limits of the dynamics of magnetic solitons and establish a readily accessible experimental framework to study relativistic solitonic physics.

Adiabatic frequency shifting in epsilon near zero materials: The role of group velocity

Abstract: The conversion of a photon’s frequency has long been a key application area of nonlinear optics. It has been discussed how a slow temporal variation of a material’s refractive index can lead to the adiabatic frequency shift (AFS) of a pulse spectrum. Such a rigid spectral change has relevant technological implications, for example, in ultrafast signal processing. Here, we investigate the AFS process in epsilon-near-zero (ENZ) materials and show that the frequency shift can be achieved in a shorter length if operating in the vicinity of ${\rm Re}\{{\varepsilon _r}\}\; = \;{0}$Re{er}=0. We also predict that, if the refractive index is induced by an intense optical pulse, the frequency shift is more efficient for a pump at the ENZ wavelength. Remarkably, we show that these effects are a consequence of the slow propagation speed of pulses at the ENZ wavelength. Our theoretical predictions are validated by experiments obtained for the AFS of optical pulses incident upon aluminum zinc oxide thin films at ENZ. Our results indicate that transparent metal oxides operating near the ENZ point are good candidates for future frequency conversion schemes.

Anomalous refraction of optical spacetime wave packets

Abstract: Refraction at the interface between two materials is fundamental to the interaction of light with photonic devices and to the propagation of light through the atmosphere at large1. Underpinning the traditional rules for the refraction of an optical field is the tacit presumption of the separability of its spatial and temporal degrees of freedom. We show here that endowing a pulsed beam with precise spatiotemporal spectral correlations2–4 unveils remarkable refractory phenomena, such as group-velocity invariance with respect to the refractive index, group-delay cancellation, anomalous group-velocity increase in higher-index materials, and tunable group velocity by varying the angle of incidence. A law of refraction for ‘spacetime’ (ST) wave packets5–10 encompassing these effects is verified experimentally in a variety of optical materials. Spacetime refraction defies our expectations derived from Fermat’s principle and offers new opportunities for moulding the flow of light and other wave phenomena. An appropriately designed pulsed beam crossing an interface is shown to enable phenomena including anomalous group-velocity increase in higher-index materials, and tunable group velocity by varying the angle of incidence.

Nonlinear waves behaviors for a coupled generalized nonlinear Schrödinger–Boussinesq system in a homogeneous magnetized plasma

Abstract: Under investigation in this paper is a coupled generalized nonlinear Schrodinger–Boussinesq system, which describes the coupled upper-hybrid and magnetoacoustic modes in a homogeneous magnetized plasma for the bidirectional propagation near the magnetoacoustic speed. Based on the Hirota method, the expressions for the multi-soliton solutions are given. Effects of the group velocity, group dispersion coefficient for the upper-hybrid, and the properties of the magnetic field on the soliton are discussed. Based on the asymptotic analysis, interaction between two solitons is proved to be elastic through the asymptotic analysis. Position at which the maximal distortion occurs is obtained. Multi-soliton interaction is illustrated and investigated. Two prerequisites of the formation and features of the bound state are discussed. For the cases of three solitons, inelastic interaction occurs with phase shifts. Characteristics of the breather and its relation with the bound state and the breather are investigated. Interaction between the bound state (even the breather) and a single soliton is discussed for both cases that they are parallel or not.

Accelerating and Decelerating Space-Time Optical Wave Packets in Free Space

Abstract: Although a plethora of techniques are now available for controlling the group velocity of an optical wave packet, there are very few options for creating accelerating or decelerating wave packets whose group velocity varies controllably along the propagation axis. Here we show that "space-time" wave packets in which each wavelength is associated with a prescribed spatial bandwidth enable the realization of optical acceleration and deceleration in free space. Endowing the field with precise spatiotemporal structure leads to group-velocity changes as high as ∼c observed over a distance of ∼20 mm in free space, which represents a boost of at least ∼4 orders of magnitude over X waves and Airy pulses. The acceleration implemented is, in principle, independent of the initial group velocity, and we have verified this effect in both the subluminal and superluminal regimes.

Broadband dispersionless topological slow light.

Abstract: We present a scheme to realize topological slow-light state with low group velocity and vanishing group velocity dispersion. By harnessing the strong interactions between two regular co-propagating topological photonic states in a magneto-optical photonic crystal waveguide, the energy flux transport of light exhibits a peculiar eight-shaped flowing loop within each unit cell of the waveguide. This permits the broadband pulse transporting with low group velocity (ng=13.26), broad bandwidth with a relative bandwidth of 3.08%, large normalized delay-bandwidth product (about 0.409), and vanishing group velocity dispersion. More importantly, they are robust against backscattering from obstacles. Our scheme paves the way to dig into the concept and physics of topology for solving the difficult problems of signal distortion and scattering loss in slow-light systems.

On the directional wave propagation in the tetrachiral and hexachiral lattices with local resonators

Abstract: The wave propagation in the tetrachiral and hexachiral lattices with local resonators are investigated and the wave behaviors with different geometrical parameters are analyzed. In this study, the tetrachiral and hexachiral lattices are assembled with the repeat unit cells and the unit cell contains a ring and a number of massless slender elastic ligaments. The ligaments are rigidly connected to the ring and the ring contains a heavy disk with its surrounding soft elastic annulus, which acts as the local resonators. The governing equations of the lattices are established by energy variation principle and the wave behaviors of the lattices are calculated by solving the eigenvalue problem with the Bloch's theorem. The effects of chiral angles on the distributions of band gaps including the width and position are studied to investigate the effects of the chirality and local resonators on the formation of low-frequency band gaps. The first mode of the phase and group velocities are calculated to analyze the effects of the geometrical parameters on the directional frequency-dependent energy flows in the anisotropic structures. We also use the commercial finite element software COMSOL to simulate and verify the directional wave behaviors in the structure. We find that the first mode of the elastic wave spread only along certain specific directions in the tetrachiral structure. As the chiral angle increases, the speed of wave propagation is reduced, and the direction of wave propagation rotates clockwise. The hexachiral lattice exhibits effective isotropic property in the low frequency range, and the wave propagation velocity gradually decreases with the increase of the frequency of the elastic waves.

Non-Reciprocal, Robust Surface Plasmon Polaritons on Gyrotropic Interfaces

Abstract: Unidirectional surface plasmon polaritons (SPPs) at the interface between a gyrotropic medium and a simple medium are studied in a newly recognized frequency regime wherein the SPPs form narrow, beam-like patterns due to quasi-hyperbolic dispersion. The SPP beams are steerable by controlling parameters such as the cyclotron frequency (external magnetic bias) or the frequency of operation. The bulk band structure along different propagation directions is examined to ascertain a common bulk bandgap, valid for all propagation directions, which the SPPs cross. In addition, group velocity and Poynting vector for the SPPs are presented. The case of a finite-thickness gyrotropic slab is also considered, for which we present the Green function and examine the thickness and loss level required to maintain a unidirectional SPP.

Interaction-Enhanced Group Velocity of Bosons in the Flat Band of an Optical Kagome Lattice.

Abstract: Geometric frustration of particle motion in a kagome lattice causes the single-particle band structure to have a flat $s$-orbital band. We probe this band structure by placing a Bose-Einstein condensate into excited Bloch states of an optical kagome lattice, and then measuring the group velocity through the atomic momentum distribution. We find that interactions renormalize the band structure, greatly increasing the dispersion of the third band, which is nearly non-dispersing the single-particle treatment. Calculations based on the lattice Gross-Pitaevskii equation indicate that band structure renormalization is caused by the distortion of the overall lattice potential away from the kagome geometry by interactions.

Broadband 200-nm second-harmonic generation in silicon in the telecom band.

Abstract: Silicon is well known for its strong third-order optical nonlinearity, exhibiting efficient supercontinuum and four-wave mixing processes. A strong second-order effect that is naturally inhibited in silicon can also be observed, for example, by electrically breaking the inversion symmetry and quasi-phase matching the pump and the signal. To generate an efficient broadband second-harmonic signal, however, the most promising technique requires matching the group velocities of the pump and the signal. In this work, we utilize dispersion engineering of a silicon waveguide to achieve group velocity matching between the pump and the signal, along with an additional degree of freedom to broaden the second harmonic through the strong third-order nonlinearity. We demonstrate that the strong self-phase modulation and cross-phase modulation in silicon help broaden the second harmonic by 200 nm in the O-band. Furthermore, we show a waveguide design that can be used to generate a second-harmonic signal in the entire near-infrared region. Our work paves the way for various applications, such as efficient and broadband complementary-metal oxide semiconductor based on—chip frequency synthesizers, entangled photon pair generators, and optical parametric oscillators. Advances in silicon engineering now allow waveguides to deliver frequency doubled light across the entire near-infrared spectrum, an important range for biological imaging and optical communication. Second-harmonic generation, which is normally restricted in silicon because of its underlying crystal symmetry, can be observed by applying strong electric field in silicon, however, the spectral response remains quite narrow to a few nanometers. Neetesh Singh from the Massachusetts Institute of Technology, in Cambridge, United States, and colleagues report a very broadband response of 100s of nanometers using silicon waveguides containing rows of diode junctions. When an electric field is applied to the waveguide, the diodes disrupt the typical silicon symmetry and enable second-harmonic generation from a pump laser. Modifying the cross section of the waveguide to ensure that pump and signal pulses travel though the waveguide at similar velocities enabled generation of frequency doubled light with a broader bandwidth than seen with current silicon or any other material based microstructures.

Evaluation of disbonds at various interfaces of adhesively bonded aluminum plates using all-optical excitation and detection of zero-group velocity Lamb waves

Abstract: Inspection of adhesively bonded metallic plates, commonly used in aircraft structures, remains challenging for modern non-destructive testing (NDT) techniques. When a probing ultrasound (US) wave interacts with the plate boundaries, it produces multiple propagating guided waves (or Lamb modes). Analysis of these waves can be complicated due to a strong geometrical dispersion. However, recent studies showed that for specific frequencies zero-group velocity (ZGV) modes exist. Any changes in a bounded structure, like delaminations, drastically alter the conditions for zero-group velocity waves, thus making this method highly sensitive for NDT applications. Laser ultrasound (LU) provides a very broad bandwidth of the generated waves, thus it is a feasible tool for a spectroscopy-based investigation of the ZGV modes. In this paper, we demonstrate an application of high-repetition rate LU with a non-contact fiber-optic Sagnac interferometer on receive for high resolution imaging of delaminations in a structure consisting of 3 epoxy-bonded aluminum plates. The investigation is supported by numerical analysis of Lamb waves existing in the structure to determine ZGV modes sensitive to delaminations at particular bonding interfaces. Tracking the selected modes permits imaging and identification of defects. We also show that mean frequency estimation of the ZGV modes can improve the contrast-to-noise ratio compared to an amplitude of the single ZGV frequency.

Impact of point source and mass loading sensitivity on the propagation of an SH wave in an imperfectly bonded FGPPM layered structure

Abstract: The aim of the present study is to analyze the propagation behavior of an SH wave in a layered structure constituted of a functionally graded piezo-poroelastic material (FGPPM) layer imperfectly bonded to an FGPPM half-space influenced by a stress point source of disturbance situated at the interface. Mass loading sensitivity of the considered structure is also analyzed by assuming a deposition of an infinitesimally thin layer at the free surface. A mathematical model for mechanical and electrical dynamics of the said material is developed for both considered structures in distinct cases. Appropriate Green’s functions for both layer and half-space are derived by using admissible boundary conditions. The dispersion relation of an SH wave is obtained for both cases, and the obtained results are also validated with classical results of Love wave. The impact of various influencing parameters like functional gradient parameters, imperfectness parameter, piezoelectric coupling parameter, and piezo-porous coupling parameter on the phase velocity of an SH wave is analyzed graphically for a BaTiO$$_3$$-crystal layer and PZT-5H half-space. Moreover, for the case of the mass loading sensitivity, the influencing parameters are also studied for the deposition of a sensitive ZnO layer. Variation of group velocity with wave number is also sketched out graphically.

Group dynamics and wave resonances in a narrow gap: modes and reduced group velocity

Abstract: The spatial and temporal structure of the resonant fluid response in a narrow gap (the so-called gap resonance) between two identical fixed boxes is investigated experimentally. Transient wave groups are used to excite the gap resonance from different wave approach directions. This shows a strong beating pattern and a very long duration, reflecting that gap resonance is a multi-mode resonant and weakly damped phenomenon. For head sea excitation the linear transfer function of the mode. Gap resonance can be driven through different mechanisms, e.g. linear excitation and a nonlinear frequency-doubling process. Significant wave group structure is shown in the gap, and the group structure is more distinct in the case with frequency doubling, i.e. long wave, excitation. Then it is clearer visually that the groups originate at the end of the gap, propagate along the gap and are then partially reflected from the other end. The groups within the gap are very clear because the group velocity is close to constant for the first few gap resonance modes, and much smaller than that for free waves on the open sea. In contrast, the phase speed of waves in the gap is larger than that for free waves outside. Only in the limit of short waves do the group velocity and phase speed of the gap modes tend to those of deep-water free waves. The group and phase speeds from these experiments match well the theoretical forms given by Molin et al. (Appl. Ocean Res., vol. 24 (5), 2002, pp. 247–260), albeit for a slightly different box cross-sectional shape.

Optical wave-packet with nearly-programmable group velocities

Abstract: During the process of Bessel beam generation in free space, spatiotemporal optical wave-packets with tunable group velocities and accelerations can be created by deforming pulse-fronts of injected pulsed beams. So far, only one determined motion form (superluminal or luminal or subluminal for the case of group velocity; and accelerating or uniform-motion or decelerating for the case of acceleration) could be achieved in a single propagation path. Here we show that deformed pulse-fronts with well-designed axisymmetric distributions (unlike conical and spherical pulse-fronts used in previous studies) allow us to obtain nearly-programmable group velocities with several different motion forms in a single propagation path. Our simulation shows that this unusual optical wave-packet can propagate at alternating superluminal and subluminal group velocities along a straight-line trajectory with corresponding instantaneous accelerations that vary periodically between positive (acceleration) and negative (deceleration) values, almost encompassing all motion forms of the group velocity in a single propagation path. Such unusual optical wave-packets with nearly-programmable group velocities may offer new opportunities for optical and physical applications. Unprecedented control of optical beams has allowed demonstration of superluminal or subluminal beams by controlling the phase of the wave-packet. Here, nearly-programmable control of a beam’s group velocity results in alternating acceleration and deceleration regimes in a single propagation path.

Local Rossby Wave Packet Amplitude, Phase Speed, and Group Velocity: Seasonal Variability and Their Role in Temperature Extremes

Abstract: Transient Rossby wave packets (RWPs) are a prominent feature of the synoptic to planetary uppertropospheric flow at the midlatitudes. Their demonstrated role in various aspects of weather and climate prompts the investigation of characteristic properties like their amplitude, phase speed, and group velocity. Traditional frameworks for the diagnosis of the two latter have so far remained nonlocal in space or time, thus preventing a detailed view on the spatiotemporal evolution of RWPs. The present work proposes a method for the diagnosis of horizontal Rossby wave phase speed and group velocity locally in space and time. The approach is based on the analytic signal of upper-tropospheric meridional wind velocity and RWP amplitude, respectively. The new diagnostics are first applied to illustrative examples from a barotropicmodel simulation and the real atmosphere. The main seasonal and interregional variability features of RWP amplitude, phase speed, and group velocity are then explored using ERA5 reanalysis data for the time period 1979–2018. Apparent differences and similarities in these respects between the Northern and Southern Hemispheres are also discussed. Finally, the role of RWP amplitude and phase speed during central European short-lived and persistent temperature extremes is investigated based on changes of their distribution compared to the climatology of the region. The proposed diagnostics offer insight into the spatiotemporal variability of RWP properties and allow the evaluation of their implications at low computational demands.

Comprehensive Viscoelastic Characterization of Tissues and the Inter-relationship of Shear Wave (Group and Phase) Velocity, Attenuation and Dispersion.

Abstract: We report shear wave phase and group velocity, dispersion and attenuation in oil-in-gelatin viscoelastic phantoms and in vivo liver data. Moreover, we measured the power law coefficient from each dispersion curve and used it, together with the shear wave velocity, to calculate an approximate value for attenuation that agrees with independent attenuation measurements. Results in phantoms exhibit good agreement for all parameters with respect to independent mechanical measurements. For in vivo data, the livers of 20 patients were scanned. Results were compared with pathology scores obtained from liver biopsies. Across these cases, increases in shear wave dispersion and attenuation were related to increased steatosis score. It was found that shear wave dispersion and attenuation are experimentally linked, consistent with simple predictions based on the rheology of tissues, and can be used individually or jointly to assess tissue viscosity. Thus, this study indicates the possible utility of using shear wave dispersion and attenuation to non-invasively and quantitatively assess steatosis.

Slow Light in Subwavelength Grating Waveguides

Abstract: Structural slow light is the dispersion engineering process by which the group velocity of light can be drastically reduced in a periodic waveguide structure. Enabling large group delay and enhancing the light-matter interaction on a subwavelength scale, on-chip slow light is of great interest in a vast array of fields such as non-linear optic, sensing, laser physics, telecommunication and computing. In this work, we experimentally demonstrate, for the first time, slow light in subwavelength grating waveguides on the silicon-on-insulator platform. We present a comprehensive numerical study in analytical modelling and 3-D FDTD. Multiple waveguides variations were fabricated using an electron-beam lithography process. Figures of merit such as group index, bandwidth and loss-per-delay are examined in both theory and experiment. A maximum measured group index of 47.74 with a loss-per-delay of 103.37 dB/ns has been achieved near the wavelength of 1550 nm. A broad bandwidth of 8.82 nm was measured, in which the group index remains larger than 10. We also show that the region of slow light operation can be shifted over a large wavelength span by controlling a single design parameter.

Backward volume vs Damon–Eshbach: A traveling spin wave spectroscopy comparison

Abstract: We compare the characteristics of electrically transduced Damon–Eshbach spin-wave (DESW) and backward volume spin-wave (BVSW) configurations within the same, 30 nm thick, ferromagnetic, CoFeB waveguide. Sub-micrometer U-shaped antennas are used to deliver the necessary in-plane and out-of-plane RF fields. We measure the spin-wave transmission with respect to in-plane field orientation, frequency, and propagation distance. Unlike DESW, BVSWs are reciprocally transduced and collected for either direction of propagation, but their ability to transport energy is lower than DESWs for two reasons. This arises first because BVSWs are inductively transduced less efficiently than DESWs. Also, in the range of wavevectors (∼5 rad μm−1) typically excited by our antennas, the group velocity of BVSWs stays lower than that of DESW, which leads to reduced propagation ability that impact transmission signals in an exponential manner. In contrast, the group velocity of DESWs is maximum at low fields and decreases continuously with the applied field. The essential features of the measured SW characteristics are well reciprocated by a simple, 1D analytical model, which can be used to assess the potential of each configuration.We compare the characteristics of electrically transduced Damon–Eshbach spin-wave (DESW) and backward volume spin-wave (BVSW) configurations within the same, 30 nm thick, ferromagnetic, CoFeB waveguide. Sub-micrometer U-shaped antennas are used to deliver the necessary in-plane and out-of-plane RF fields. We measure the spin-wave transmission with respect to in-plane field orientation, frequency, and propagation distance. Unlike DESW, BVSWs are reciprocally transduced and collected for either direction of propagation, but their ability to transport energy is lower than DESWs for two reasons. This arises first because BVSWs are inductively transduced less efficiently than DESWs. Also, in the range of wavevectors (∼5 rad μm−1) typically excited by our antennas, the group velocity of BVSWs stays lower than that of DESW, which leads to reduced propagation ability that impact transmission signals in an exponential manner. In contrast, the group velocity of DESWs is maximum at low fields and decreases continuou...

Control of elastic shear waves by periodic geometric transformation: cloaking, high reflectivity and anomalous resonances

Abstract: A doubly periodic geometric transformation is applied to the problem of out of plane shear wave propagation in a doubly periodic perforated elastic medium. The technique leads to the design of a system of radially anisotropic and inhomogeneous shells surrounding the void inclusions, that can be tuned to give the desired filtering properties. For a regular transformation, the transformed elastic system displays the same dispersion properties than the original homogeneous one, but for overlapping and unfolding transformations new filtering properties can be obtained, which include anomalous resonances at zero and finite frequencies. Low-frequency homogenisation reveals how it is possible to tune the phase and group velocity in the long-wave limit at any value, or to obtain a zero frequency band gap for Neumann boundary conditions. The dispersion properties of the medium are studied both semi-analytically by the multipole expansion and numerically by the finite element methods. Several applications are shown, including the transmission problem throughout a grating of void inclusions and an interface in a waveguide, where the capability of the proposed model is quantitatively demonstrated by computing the transmitted power flow. Finally, we gave a demonstration of defect modes in a waveguide and of tuning the transformation for the research of Dirac points.

Free-space optical delay line using space-time wave packets.

Abstract: An optical buffer featuring a large delay-bandwidth-product—a critical component for future all-optical communications networks—remains elusive. Central to its realization is a controllable inline optical delay line, previously accomplished via engineered dispersion in optical materials or photonic structures constrained by a low delay-bandwidth product. Here we show that space-time wave packets whose group velocity is continuously tunable in free space provide a versatile platform for constructing inline optical delay lines. By spatio-temporal spectral-phase-modulation, wave packets in the same or in different spectral windows that initially overlap in space and time subsequently separate by multiple pulse widths upon free propagation by virtue of their different group velocities. Delay-bandwidth products of ~100 for pulses of width ~1 ps are observed, with no fundamental limit on the system bandwidth. Delay lines are a critical part of future optical communications. Here, the authors create a delay line in free space by tuning the group velocities of multiple inline space-time wavepackets to introduce different delays.

Off-axis optical vortices using double-Raman singlet and doublet light-matter schemes

Abstract: We study the formation of off-axis optical vortices propagating inside a double-Raman gain atomic medium. The atoms interact with two weak probe fields as well as two strong pump beams which can carry orbital angular momentum (OAM). We consider a situation when only one of the strong pump lasers carries an OAM. A particular superposition of probe fields coupled to the matter is shown to form specific optical vortices with shifted axes. Such off-axis vortices can propagate inside the medium with sub- or superluminal group velocity depending on the value of the two-photon detuning. The superluminal optical vortices are associated with the amplification as the energy of pump fields is transferred to the probe fields. The position of the peripheral vortices can be manipulated by the OAM and intensity of the pump fields. We show that the exchange of optical vortices is possible between individual probe beams and the pump fields when the amplitude of the second probe field is zero at the beginning of the atomic cloud. The model is extended to a more complex double Raman doublet interacting with four pump fields. In contrast to the double-Raman-singlet, now the generation of the off-axis sub- or superluminal optical vortices is possible even for zero two-photon detuning.

Shear wave structure of a transect of the Los Angeles basin from multimode surface waves and H/V spectral ratio analysis

Abstract: We use broad-band stations of the ‘Los Angeles Syncline Seismic Interferometry Experiment’ (LASSIE) to perform a joint inversion of the Horizontal to Vertical spectral ratios (H/V) and multimode dispersion curves (phase and group velocity) for both Rayleigh and Love waves at each station of a dense line of sensors. The H/V of the autocorrelated signal at a seismic station is proportional to the ratio of the imaginary parts of the Green’s function. The presence of low-frequency peaks (∼0.2 Hz) in H/V allows us to constrain the structure of the basin with high confidence to a depth of 6 km. The velocity models we obtain are broadly consistent with the SCEC CVM-H community model and agree well with known geological features. Because our approach differs substantially from previous modelling of crustal velocities in southern California, this research validates both the utility of the diffuse field H/V measurements for deep structural characterization and the predictive value of the CVM-H community velocity model in the Los Angeles region. We also analyse a lower frequency peak (∼0.03 Hz) in H/V and suggest it could be the signature of the Moho. Finally, we show that the independent comparison of the H and V components with their corresponding theoretical counterparts gives information about the degree of diffusivity of the ambient seismic field.

Walk-off controlled self-starting frequency combs in χ(2) optical microresonators

Abstract: Investigations of frequency combs in χ(3) optical microresonators are burgeoning nowadays. Changeover to χ(2) resonators promises further advances and brings new challenges. Here, the comb generation entails not only coupled first and second harmonics (FHs and SHs) and two dispersion coefficients but also a substantial difference in the group velocities – the temporal walk-off. We predict walk-off controlled highly stable comb generation, which is drastically different from that known in the χ(3) case. This includes the general notion of antiperiodic states; formation of localized coherent antiperiodic steady states (solitons), where the FH and SH envelopes move with a common velocity without shape changes; characterization of a new vast family of antiperiodic solitons; and the dependence of comb spectra on the pump power and the group velocity difference.