Showing papers on "Group velocity published in 2019"

Observation of Stimulated Hawking Radiation in an Optical Analogue.

Abstract: The theory of Hawking radiation can be tested in laboratory analogues of black holes We use light pulses in nonlinear fiber optics to establish artificial event horizons Each pulse generates a moving perturbation of the refractive index via the Kerr effect Probe light perceives this as an event horizon when its group velocity, slowed down by the perturbation, matches the speed of the pulse We have observed in our experiment that the probe stimulates Hawking radiation, which occurs in a regime of extreme nonlinear fiber optics where positive and negative frequencies mix

Optical space-time wave packets having arbitrary group velocities in free space.

Abstract: Controlling the group velocity of an optical pulse typically requires traversing a material or structure whose dispersion is judiciously crafted. Alternatively, the group velocity can be modified in free space by spatially structuring the beam profile, but the realizable deviation from the speed of light in vacuum is small. Here we demonstrate precise and versatile control over the group velocity of a propagation-invariant optical wave packet in free space through sculpting its spatio-temporal spectrum. By jointly modulating the spatial and temporal degrees of freedom, arbitrary group velocities are unambiguously observed in free space above or below the speed of light in vacuum, whether in the forward direction propagating away from the source or even traveling backwards towards it.

Time-Periodic Stiffness Modulation in Elastic Metamaterials for Selective Wave Filtering: Theory and Experiment.

Abstract: Elastic waveguides with time-modulated stiffness feature a frequency-periodic dispersion spectrum, where branches merge at multiple integers of half the modulation frequency and over a finite wave number range. In this range, frequency becomes complex, with its real part remaining constant. The vanishing group velocity associated with these flat bands leads to frequency-selective reflection at an interface between a nonmodulated medium and a time-modulated one, which converts a broadband input into a narrow-band output centered at the half modulation frequency. This behavior is illustrated in an elastic waveguide in transverse motion, where modulation is implemented experimentally by an array of piezoelectric patches shunted through a negative electrical capacitance controlled by a switching circuit. The switching schedule defines the modulation frequency and allows the selection of the output frequency. This implementation is suitable for the investigation of numerous properties of time-space modulated elastic metamaterials, such as nonreciprocity and one-way propagation, and can lead to the implementation of novel functionalities for acoustic wave devices operating on piezoelectric substrates.

Classification of propagation-invariant space-time wave packets in free space: Theory and experiments

Abstract: Introducing correlations between the spatial and temporal degrees of freedom of a pulsed optical beam (or wave packet) can profoundly alter its propagation in free space Indeed, appropriate spatiotemporal spectral correlations can render the wave packet propagation-invariant: the spatial and temporal profiles remain unchanged along the propagation axis The spatiotemporal spectral locus of any such wave packet lies at the intersection of the light cone with tilted spectral hyperplanes We investigate $(2+1)\mathrm{D}$ propagation-invariant ``space-time'' light sheets and identify ten classes categorized according to the magnitude and sign of their group velocity and the nature of their spatial spectrum---whether the low spatial frequencies are physically allowed or forbidden according to their compatibility with causal excitation and propagation We experimentally synthesize and characterize all ten classes using an experimental strategy capable of synthesizing space-time wave packets that incorporate arbitrary spatiotemporal spectral correlations

Space–time wave packets that travel in optical materials at the speed of light in vacuum

Abstract: Can an optical pulse traverse a non-dispersive material at the speed of light in vacuum? Because traditional approaches for controlling the group velocity of light manipulate either the material or structural resonances, an absence of dispersion altogether appears to exclude such a prospect. Here we demonstrate theoretically and experimentally that “space–time” wave packets—pulsed beams in which the spatial and temporal degrees of freedom are tightly intertwined—can indeed traverse a non-dispersive transparent optical material at the speed of light in vacuum. We synthesize wave packets whose spatio-temporal spectra lie along the intersection of the material’s light-cone with a spectral hyperplane tilted to coincide with the vacuum light-line. By measuring the group delay interferometrically with respect to a generic reference pulse, we confirm that the wave packet group velocity in a variety of materials (including water, glass, and sapphire) is the speed of light in vacuum.

Current-controlled propagation of spin waves in antiparallel, coupled domains

Abstract: Spin waves may constitute key components of low-power spintronic devices. Antiferromagnetic-type spin waves are innately high-speed, stable and dual-polarized. So far, it has remained challenging to excite and manipulate antiferromagnetic-type propagating spin waves. Here, we investigate spin waves in periodic 100-nm-wide stripe domains with alternating upward and downward magnetization in La0.67Sr0.33MnO3 thin films. In addition to ordinary low-frequency modes, a high-frequency mode around 10 GHz is observed and propagates along the stripe domains with a spin-wave dispersion different from the low-frequency mode. Based on a theoretical model that considers two oppositely oriented coupled domains, this high-frequency mode is accounted for as an effective antiferromagnetic spin-wave mode. The spin waves exhibit group velocities of 2.6 km s−1 and propagate even at zero magnetic bias field. An electric current pulse with a density of only 105 A cm−2 can controllably modify the orientation of the stripe domains, which opens up perspectives for reconfigurable magnonic devices. Current pulses of 105 A cm−2 can control the orientation of 100-nm-wide stripe domains in La0.67Sr0.33MnO3 and spin waves of 10 GHz can propagate along these domains with a group velocity of 2.6 km s−1.

The Potential of DAS in Teleseismic Studies: Insights From the Goldstone Experiment

Abstract: Author(s): Yu, C; Zhan, Z; Lindsey, NJ; Ajo-Franklin, JB; Robertson, M | Abstract: Distributed acoustic sensing (DAS) is a recently developed technique that has demonstrated its utility in the oil and gas industry. Here we demonstrate the potential of DAS in teleseismic studies using the Goldstone OpticaL Fiber Seismic experiment in Goldstone, California. By analyzing teleseismic waveforms from the 10 January 2018 M7.5 Honduras earthquake recorded on ~5,000 DAS channels and the nearby broadband station GSC, we first compute receiver functions for DAS channels using the vertical-component GSC velocity as an approximation for the incident source wavelet. The Moho P-to-s conversions are clearly visible on DAS receiver functions. We then derive meter-scale arrival time measurements along the entire 20-km-long array. We are also able to measure path-averaged Rayleigh wave group velocity and local Rayleigh wave phase velocity. The latter, however, has large uncertainties. Our study suggests that DAS will likely play an important role in many fields of passive seismology in the near future.

Wave attenuation and trapping in 3D printed cantilever-in-mass metamaterials with spatially correlated variability.

Abstract: Additive manufacturing has become a fundamental tool to fabricate and experimentally investigate mechanical metamaterials and phononic crystals. However, this manufacturing process produces spatially correlated variability that breaks the translational periodicity, which might compromise the wave propagation performance of metamaterials. We demonstrate that the vibration attenuation profile is strictly related to the spatial profile of the variability, and that there exists an optimal disorder degree below which the attenuation bandwidth widens; for high disorder levels, the band gap mistuning annihilates the overall attenuation. The variability also induces a spatially variant locally resonant band gap that progressively slow down the group velocity until an almost zero value, giving rise to wave trapping effect near the lower band gap boundary. Inspired by this wave trapping phenomenon, a rainbow metamaterial with linear spatial-frequency trapping is also proposed, which have potential applications in energy harvesting, spatial wave filtering and non-destructive evaluation at low frequency. This report provides a deeper understanding of the differences between numerical simulations using nominal designed properties and experimental analysis of metamaterials constructed in 3D printing. These analysis and results may extend to phononic crystals and other periodic systems to investigate their wave and dynamic performance as well as robustness under variability.

Anomalous refraction of optical space-time 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 large. 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 spatio-temporal spectral correlations 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 `space-time' wave packets encompassing these effects is verified experimentally in a variety of optical materials. Space-time refraction defies our expectations derived from Fermat's principle and offers new opportunities for molding the flow of light and other wave phenomena.

What is the maximum differential group delay achievable by a space-time wave packet in free space?

Abstract: The group velocity of ‘space-time’ wave packets – propagation-invariant pulsed beams endowed with tight spatio-temporal spectral correlations – can take on arbitrary values in free space. Here we investigate theoretically and experimentally the maximum achievable group delay that realistic finite-energy space-time wave packets can achieve with respect to a reference pulse traveling at the speed of light. We find that this delay is determined solely by the spectral uncertainty in the association between the spatial frequencies and wavelengths underlying the wave packet spatio-temporal spectrum – and not by the beam size, bandwidth, or pulse width. We show experimentally that the propagation of space-time wave packets is delimited by a spectral-uncertainty-induced ‘pilot envelope’ that travels at a group velocity equal to the speed of light in vacuum. Temporal walk-off between the space-time wave packet and the pilot envelope limits the maximum achievable differential group delay to the width of the pilot envelope. Within this pilot envelope the space-time wave packet can locally travel at an arbitrary group velocity and yet not violate relativistic causality because the leading or trailing edge of superluminal and subluminal space-time wave packets, respectively, are suppressed once they reach the envelope edge. Using pulses of width ∼ 4 ps and a spectral uncertainty of ∼ 20 pm, we measure maximum differential group delays of approximately ±150 ps, which exceed previously reported measurements by at least three orders of magnitude.

Spin-Wave Phase Inverter upon a Single Nanodefect.

Abstract: Local modification of magnetic properties of nanoelements is a key to design future-generation magnonic devices in which information is carried and processed via spin waves. One of the biggest challenges here is to fabricate simple and miniature phase-controlling elements with broad tunability. Here, we successfully realize such spin-wave phase shifters upon a single nanogroove milled by a focused ion beam in a Co–Fe microsized magnonic waveguide. By varying the groove depth and the in-plane bias magnetic field, we continuously tune the spin-wave phase and experimentally evidence a complete phase inversion. The microscopic mechanism of the phase shift is based on the combined action of the nanogroove as a geometrical defect and the lower spin-wave group velocity in the waveguide under the groove where the magnetization is reduced due to the incorporation of Ga ions during the ion-beam milling. The proposed phase shifter can easily be on-chip integrated with spin-wave logic gates and other magnonic devices...

Broadband topological slow light through higher momentum-space winding

Abstract: Slow-light waveguides can strongly enhance light-matter interaction, but suffer from a narrow bandwidth, increased backscattering, and Anderson localization. Edge states in photonic topological insulators resist backscattering and localization, but typically cross the bulk band gap over a single Brillouin zone, meaning that slow group velocity implies narrow-band operation. Here we show theoretically that this can be circumvented via an edge termination that causes the edge state to wind many times around the Brillouin zone, making it both slow and broadband.

Octave-wide supercontinuum generation of light-carrying orbital angular momentum

Abstract: Nonlinear frequency generation of light-carrying orbital angular momentum (OAM), which facilitates realization of on-demand, frequency-diverse optical vortices, would have utility in fields such as super-resolution microscopy, space-division multiplexing and quantum hyper-entanglement. In bulk media, OAM beams primarily differ in spatial phase, so the nonlinear overlap integral for self-phase matched χ(3) processes remains the same across the 4-fold degenerate subspace of beams (formed by different combinations of spin and orbital angular momentum) carrying the same OAM magnitude. This indistinguishable nature of nonlinear coupling implies that supercontinuum generation, which substantially relies on self/cross-phase modulation, and Raman soliton shifting of ultrashort pulses typically results in multimode outputs that do not conserve OAM. Here, using specially designed optical fibers that support OAM modes whose group velocity can be tailored, we demonstrate Raman solitons in OAM modes as well as the first supercontinuum spanning more than an octave (630 nm to 1430 nm), with the entire spectrum in the same polarization as well as OAM state. This is fundamentally possible because spin-orbit interactions in suitably designed fibers lead to large effective index and group velocity splitting of modes, and this helps tailoring nonlinear mode selectivity such that all nonlinearly generated frequencies reside in modes with high spatial mode purity.

Circumventing the Dephasing and Depletion Limits of Laser-Wakefield Acceleration

Abstract: Author(s): Debus, A; Pausch, R; Huebl, A; Steiniger, K; Widera, R; Cowan, TE; Schramm, U; Bussmann, M | Abstract: Compact electron accelerators are paramount to next-generation synchrotron light sources and free-electron lasers, as well as for advanced accelerators at the TeV energy frontier. Recent progress in laser-plasma driven accelerators (LPA) has extended their electron energies to the multi-GeV range and improved beam stability for insertion devices. However, the subluminal group velocity of plasma waves limits the final electron energy that can be achieved in a single LPA accelerator stage, also known as the dephasing limit. Here, we present the first laser-plasma driven electron accelerator concept providing constant acceleration without electrons outrunning the wakefield. The laser driver is provided by an overlap region of two obliquely incident, ultrashort laser pulses with tilted pulse fronts in the line foci of two cylindrical mirrors, aligned to coincide with the trajectory of the accelerated electrons. Such a geometry of laterally coupling the laser into a plasma allows for the overlap region to move with the vacuum speed of light, while the laser fields in the plasma are continuously being replenished by the successive parts of the laser pulses. Our scheme is robust against parasitic self-injection and self-phase modulation as well as drive-laser depletion and defocusing along the accelerated electron beam. It works for a broad range of plasma densities in gas targets. This method opens the way for scaling up electron energies beyond 10 GeV, possibly towards TeV-scale electron beams, without the need for multiple laser-accelerator stages.

Strong coupling of topological edge states enabling group-dispersionless slow light in magneto-optical photonic crystals

Abstract: We investigate a two-way waveguide constructed by bringing close two identical magneto-optical photonic crystals which each supports a counterpropagating topological one-way edge state. We find a unique slow-light state that exhibits a very small group velocity $({n}_{g}=529.2)$, a zero group-velocity dispersion, distortionless pulse transport, and ease to be magnetically tuned within a broad frequency range, simultaneously. We show that this unique group-dispersionless slow-light state originates from the strong coupling of the two counterpropagating topological states, which causes complete exchange and transfer of energy flow between them, induces a vortexlike close loop of energy transport channel around the source, leads to complete destructive interference in the far field, and finally results in a very slow propagation velocity of electromagnetic waves. These results indicate that deeply digging into the interaction between photonic topological states can help to open up an arena in topological physics and find great potential of applications such as optical buffer memories and enhanced light-matter interaction.

Switchable slow light rainbow trapping and releasing in strongly coupling topological photonic systems

Abstract: We design and present a switchable slow light rainbow trapping (SLRT) state in a strongly coupling topological photonic system made from a magneto-optical photonic crystal waveguide channel. The waveguide channel supports slow light states with extremely small group velocity (vg=2.1×10−6c), low group-velocity dispersion, and a broadband operation bandwidth (3.60–4.48 GHz, near 22% of bandwidth). These slow light states originate from the strong coupling between two counter propagating topological photonic states. Under a gradient magnetic field, different frequency components of a wave packet are separated and stored at different positions for a long temporal duration with high spatial precision (without crosstalk and overlap between the electric fields of different frequencies) to form SLRT. Besides, these SLRT states can be easily switched among the forbidden state, trapped state, and releasing state by tuning the external magnetic field. The results suggest that the topological photonic state can offer a precise route of spatial-temporal-spectral control upon a light signal and find applications for optical buffers, broadband slow light systems, optical filters, wavelength-division multiplexing, and other optical communication devices.

Soliton and quasi-soliton frequency combs due to second harmonic generation in microresonators

Abstract: We report how a doublet of the symmetric oppositely tilted bistable resonance peaks in a microring resonator with quadratic nonlinearity set for generation of the second harmonic can transform into a Kerr-like peak on one side of the linear cavity resonance and into a closed loop structure disconnected from the quasi-linear resonance on the other. Both types of the nonlinear resonances are associated with the formation of the soliton combs for dispersion profiles of a typical LiNbO 3 microring. We report bright quasi-solitons propagating on a weakly modulated low intensity background when the group velocity dispersions have the opposite signs for the fundamental and second harmonic. We also show exponentially localized solitons when the dispersion signsare the same. Finally, we demonstrate that the transition between these two types of soliton states is associated with the closure of the forbidden gap in the spectrum of quasi-linear waves.

Finite-Time Rigidity-Based Formation Maneuvering of Multiagent Systems Using Distributed Finite-Time Velocity Estimators

Abstract: In this paper, finite time rigidity-based formation maneuvering control of single integrator multiagent systems is considered. The target formation graph is assumed to be minimally and infinitesimally rigid, and the desired group velocity is considered to be available only to a subset of the agents. A distributed nonsmooth velocity estimator is used for each agent to estimate the desired group velocity in finite time. Using Lyapunov and input to state stability notions, a finite time distance-based formation maneuvering controller is presented and it is proved that by using the controller, agents converge to the target formation and track the desired group velocity in finite time. Furthermore, it is demonstrated that the designed controller is implementable in local coordinate frames of the agents. Simulation results are provided to show the effectiveness of the proposed control scheme.

Orthogonally polarized frequency comb generation from a Kerr comb via cross-phase modulation.

Abstract: We experimentally demonstrate that a single microresonator can emit two orthogonally polarized individually coherent combs: (i) a strong polarized soliton comb and (ii) an orthogonally polarized continuous wave seeded weaker comb, generated from the first one via cross-phase modulation, sharing the repetition rate of the soliton comb. Experimental results show that the power of the transverse electric-polarized seed can be well below the threshold of comb generation (e.g., 0.1 mW). In addition, simulations show that a dark pulse could be generated in the anomalous dispersion regime by a bright soliton when the two orthogonally polarized modes have the same group velocity in the microresonator.

Local Phase Velocity Based Imaging: A New Technique Used for Ultrasound Shear Wave Elastography

Abstract: Ultrasound shear wave elastography is an imaging modality for noninvasive evaluation of tissue mechanical properties. However, many current techniques overestimate lesions dimension or shape especially when small inclusions are taken into account. In this paper, we propose a new method called local phase velocity-based imaging (LPVI) as an alternative technique to measure tissue elasticity. Two separate acquisitions with ultrasound push beams focused once on the left side and once on the right side of the inclusion were generated. A local shear wave velocity is then recovered in the frequency domain (for a single frequency or frequency band) for both acquired data sets. Finally, a two-dimensional shear wave velocity map is reconstructed by combining maps from two separate acquisitions. Robust and accurate shear wave velocity maps are reconstructed using the proposed LPVI method in calibrated liver fibrosis tissue mimicking homogeneous phantoms, a calibrated elastography phantom with stepped cylinder inclusions and a homemade gelatin phantom with ex vivo porcine liver inclusion. Results are compared with an existing phase velocity-based imaging approach and a group velocity-based method considered as the state of the art. Results from the phantom study showed that increased frequency improved the shape of the reconstructed inclusions and contrast-to-noise ratio between the target and background.

Imaging gigahertz zero-group-velocity Lamb waves

Abstract: Zero-group-velocity (ZGV) waves have the peculiarity of being stationary, and thus locally confining energy. Although they are particularly useful in evaluation applications, they have not yet been tracked in two dimensions. Here we image gigahertz zero-group-velocity Lamb waves in the time domain by means of an ultrafast optical technique, revealing their stationary nature and their acoustic energy localization. The acoustic field is imaged to micron resolution on a nanoscale bilayer consisting of a silicon-nitride plate coated with a titanium film. Temporal and spatiotemporal Fourier transforms combined with a technique involving the intensity modulation of the optical pump and probe beams gives access to arbitrary acoustic frequencies, allowing ZGV modes to be isolated. The dispersion curves of the bilayer system are extracted together with the quality factor Q and lifetime of the first ZGV mode. Applications include the testing of bonded nanostructures. Zero-group-velocity Lamb waves, which are surface waves with reduced losses and high Q factor, have many potential applications. The authors image such waves in 2 dimensions, and in the GHz range, with a bilayer using a time-resolved imaging technique with an ultra-short-pulse laser.

Mixed structures of optical breather and rogue wave for a variable coefficient inhomogeneous fiber system

Abstract: Breathers and rogue waves are two special types of soliton and play significant role in optical fibers. In this work, the mixed breather and rogue wave solution is constructed for a variable coefficient inhomogeneous fiber system via the Darboux transformation method. The impacts on the mixed wave of the first- and second-order group velocity dispersions (GVD), are discussed, respectively. The spectral eigenvalue parameter control is also studied. The pulse wave width, amplitude and wave density can be controlled by the variable GVD functions and spectral eigenvalue parameter. Especially, two types of rogue wave solutions can be derived from the mixed solution.

Changing the speed of optical coherence in free space.

Abstract: It is typically assumed that the fluctuations associated with a stationary broadband incoherent field propagate in free space at the speed of light in vacuum c. Here we introduce the concept of “coherence group velocity” which, in analogy to the group velocity of coherent pulses, is the speed of the peak of the coherence function. We confirm experimentally that incorporating a judicious spatio-temporal spectral structure into a field allows tuning its coherence group velocity in free space. Utilizing light from a superluminescent diode, we interferometrically measure the group delay encountered by the cross-correlation of a structured field synthesized from this source with the unstructured diode field. By tracking the propagation of this cross-correlation function, we measure coherence group velocities in the range of 12c to −6c.

Ultrabroadband 3D invisibility with fast-light cloaks.

Abstract: An invisibility cloak should completely hide an object from an observer, ideally across the visible spectrum and for all angles of incidence and polarizations of light, in three dimensions. However, until now, all such devices have been limited to either small bandwidths or have disregarded the phase of the impinging wave or worked only along specific directions. Here, we show that these seemingly fundamental restrictions can be lifted by using cloaks made of fast-light media, termed tachyonic cloaks, where the wave group velocity is larger than the speed of light in vacuum. On the basis of exact analytic calculations and full-wave causal simulations, we demonstrate three-dimensional cloaking that cannot be detected even interferometrically across the entire visible regime. Our results open the road for ultrabroadband invisibility of large objects, with direct implications for stealth and information technology, non-disturbing sensors, near-field scanning optical microscopy imaging, and superluminal propagation. Three-dimensional invisibility cloaks are either limited in bandwidth or disregard the phase of the impinging wave or work only in specific directions. Here, the authors report that these restrictions can be lifted by using cloaks made of fast-light media where the wave group velocity is larger than the speed of light in vacuum.

What is the maximum differential group delay achievable by a space-time wave packet in free space?

Abstract: The group velocity of 'space-time' wave packets $-$ propagation-invariant pulsed beams endowed with tight spatio-temporal spectral correlations $-$ can take on arbitrary values in free space. Here we investigate theoretically and experimentally the maximum achievable group delay that realistic finite-energy space-time wave packets can achieve with respect to a reference pulse traveling at the speed of light. We find that this delay is determined solely by the spectral uncertainty in the association between the spatial frequencies and wavelengths underlying the wave packet spatio-temporal spectrum $-$ and not by the beam size, bandwidth, or pulse width. We show experimentally that the propagation of space-time wave packets is delimited by a spectral-uncertainty-induced `pilot envelope' that travels at a group velocity equal to the speed of light in vacuum. Temporal walk-off between the space-time wave packet and the pilot envelope limits the maximum achievable differential group delay to the width of the pilot envelope. Within this pilot envelope, the space-time wave packet can locally travel at an arbitrary group velocity and yet not violate relativistic causality because the leading or trailing edge of superluminal and subluminal space-time wave packets, respectively, are suppressed once they reach the envelope edge. Using pulses of width $\sim$4ps and a spectral uncertainty of $\sim$ 20 pm, we measure maximum differential group delays of approximately $\pm$ 150 ps, which exceed previously reported measurements by at least three orders of magnitude.

Does group velocity always reflect elastic modulus in shear wave elastography

Abstract: Dynamic elastography is an attractive method to evaluate tissue biomechanical properties. Recently, it was extended from US- and MR-based modalities to optical ones, such as optical coherence tomography for three-dimensional (3-D) imaging of propagating mechanical waves in subsurface regions of soft tissues, such as the eye. The measured group velocity is often used to convert wave speed maps into 3-D images of the elastic modulus distribution based on the assumption of bulk shear waves. However, the specific geometry of OCE measurements in bounded materials such as the cornea and skin calls into question elasticity reconstruction assuming a simple relationship between group velocity and shear modulus. We show that in layered media the bulk shear wave assumption results in highly underestimated shear modulus reconstructions and significant structural artifacts in modulus images. We urge the OCE community to be careful in using the group velocity to evaluate tissue elasticity and to focus on developing robust reconstruction methods to accurately reconstruct images of the shear elastic modulus in bounded media.

Investigation of guided wave properties of anisotropic composite laminates using a semi-analytical finite element method

Abstract: Composite materials have been widely used in various applications, and guided waves are often used as a non-destructive testing tool to inspect defects or damage in composite laminates which are assemblies of multiple composite layers. These can have anisotropic material properties and arbitrary fibre orientation such that the guided wave properties of Lamb and shear-horizontal modes are direction-dependent. The group velocity of each wave mode is therefore to be considered with a component parallel to the wave propagation direction and a component perpendicular to the wave propagation direction. In this article, a semi-analytical finite element method is developed to model composite laminates with arbitrary fibre orientation and anisotropic material properties in each layer. Galerkin's principle is used to derive the weak forms of the governing equations, and an energy velocity formulation is used to calculate the parallel and perpendicular energy velocities. The finite element solutions are compared with available analytical and numerical solutions in the literature for forward waves, and excellent agreement is demonstrated. On this basis, the guided wave properties of backward waves have also been investigated. It is well understood that in an isotropic plate, the energy velocity of a backward wave is directed opposite to the phase velocity. However, in a composite laminate, the energy velocity of a backward wave is normally not exactly opposed to (180° out of phase with) the phase velocity but exhibits a skew angle. The angular dependences of wave properties of the forward and backward waves are investigated in this article.