Wavepacket Distortion Research Articles

Theoretical analysis of the dispersion of Lamb waves forming a wave packet of finite-bandwidth using the method of multiple scales

In ultrasonic guided wave inspections, incident waves propagate as a finite-bandwidth wave packet. During propagation, the shape of the wave packet is distorted because of dispersion even if there are no viscous or scattering effects. Although the presence of distortion is well known, how the wave packet is distorted has not been sufficiently investigated. We use the method of multiple scales (MMS), a perturbative scheme, to investigate the dispersion of the Lamb waves comprising the finite-bandwidth wave packet. Solutions obtained by the MMS to order O(ε2) show that the shape of an input wave-packet remains invariant during propagation along the waveguide. The wave packet propagates with a group velocity obtained from a classical analysis. The O(ε3)-order MMS solutions exhibit a symmetric distortion of the shape, whereas the O(ε4)-order MMS solutions feature symmetric and anti-symmetric distortion. For the derivation of the O(ε3)- and O(ε4)-order MMS solutions, the Fourier transform of the wave-packet shape is introduced. The proposed MMS solutions were verified by comparing them with the numerical time-domain solutions constructed from the classical frequency-domain solutions.The strength of the distortion depends on propagation mode, input frequency, and shape of the input wave packet. Because the wave-packet distortion induces a shift and reduction of the peak, the propagation velocity is different from the group velocity. For long-distance inspections, the proposed method provides the precise propagation velocity and details of the propagation-mode selection.

Non-reciprocal behavior of one-dimensional piezoelectric structures with space-time modulated electrical boundary conditions

Propagation of longitudinal acoustic waves in a one-dimensional piezoelectric structure with space-time modulated electrical boundary conditions is investigated. An analytical model allowing the calculation of eigenmodes for spatially continuous shifts of electrical boundary conditions is compared with finite difference time domain simulation results for a discrete set of time-varying spatially fixed conditions. Both models predict that such a structure behaves as a nonreciprocal device exhibiting unidirectional propagation properties in some frequency ranges. The modulus and direction of the modulation speed vector strongly affect this nonreciprocal behavior. Moreover, other nonlinear phenomena such as frequency up and down conversions, wave packet distortion, and parasitic echoes occurring in such systems are investigated in detail. The importance of these phenomena is discussed in the context of nonlinear acoustic wave-based components for radio-communication systems.

Effective Zitterbewegung of bosonic Bogoliubov quasi-particle with effective spin-orbital coupling

The conventional Zitterbewegung (ZB) refers to the jittering motion of a particle or wavepacket in space induced by the spin-orbital coupling. Here we show that the analogue of Zitterbewegung of bosonic Bogoliubov quasi-particle manifests itself in a form of periodic distortion of wave packet because of its dynamics is governed by a non-hermitian operator. The effective spin-orbital coupling (SOC) is due to the fact that the two modes (pseudo-spin) in the Bogoliubov de Gennes (BdG) equation are coupled to the spatial momentum. These results are illustrated with spin wave excitations in antiferromagnet and phonon excitations in BEC system.

Two-photon interference in the telecom C-band after frequency conversion of photons from remote quantum emitters.

Efficient fibre-based long-distance quantum communication via quantum repeaters relies on deterministic single-photon sources at telecom wavelengths, potentially exploiting the existing world-wide infrastructures. For upscaling the experimental complexity in quantum networking, two-photon interference (TPI) of remote non-classical emitters in the low-loss telecom bands is of utmost importance. Several experiments have been conducted regarding TPI of distinct emitters, for example, using trapped atoms1, ions2, nitrogen vacancy centres3,4, silicon vacancy centres5, organic molecules6 and semiconductor quantum dots7,8. However, the spectral range was far from the highly desirable telecom C-band. Here, we exploit quantum frequency conversion to realize TPI at 1,550 nm with single photons stemming from two remote quantum dots. We thereby prove quantum frequency conversion9-11 as a bridging technology and a precise and stable mechanism to erase the frequency difference between independent emitters. On resonance, a TPI visibility of 29 ± 3% has been observed, limited only by the spectral diffusion processes of the individual quantum dots12,13. The local fibre network used covers several rooms between two floors of the building. Even the addition of up to 2 km of fibre channel shows no influence on the TPI visibility, proving the photon wavepacket distortion to be negligible. Our studies pave the way to establish long-distance entanglement distribution between remote solid-state emitters including interfaces with various quantum hybrid systems14-16.

Quantum evolution in disordered transport

We analyze the propagation of quantum states in the presence of weak disorder. In particular, we investigate the reliable transmittance of quantum states, as potential carriers of quantum information, through disorder-perturbed waveguides. We quantify wave-packet distortion, backscattering, and disorder-induced dephasing, which all act detrimentally on transport, and identify conditions for reliable transmission. Our analysis relies on the treatment of the nonequilibrium dynamics of ensemble-averaged quantum states in terms of quantum master equations.

Observation of wave packet distortion during a negative-group-velocity transmission.

In Physics, causality is a fundamental postulation arising from the second law of thermodynamics. It states that, the cause of an event precedes its effect. In the context of Electromagnetics, the relativistic causality limits the upper bound of the velocity of information, which is carried by electromagnetic wave packets, to the speed of light in free space (c). In anomalously dispersive media (ADM), it has been shown that, wave packets appear to propagate with a superluminal or even negative group velocity. However, Sommerfeld and Brillouin pointed out that the “front” of such wave packets, known as the initial point of the Sommerfeld precursor, always travels at c. In this work, we investigate the negative-group-velocity transmission of half-sine wave packets. We experimentally observe the wave front and the distortion of modulated wave packets propagating with a negative group velocity in a passive artificial ADM in microwave regime. Different from previous literature on the propagation of superluminal Gaussian packets, strongly distorted sinusoidal packets with non-superluminal wave fronts were observed. This result agrees with Brillouin's assertion, i.e., the severe distortion of seemingly superluminal wave packets makes the definition of group velocity physically meaningless in the anomalously dispersive region.

Coupling effect of piezoelectric wafer transducers in distortions of primary Lamb wave modes

Piezoelectric wafer transducers (PWT) are widely used for Lamb wave based damage detection schemes. The size of the damage that can be detected is dependent on the wavelength of the Lamb wave employed. Thus it is essential to explore the higher frequency range within the (fundamental) bandwidth of S0 and A0 modes, however below the cut-off frequencies of A1 and S1. It is observed that the Lamb wave modes S0 and A0 generated using PWT undergo distortion within this fundamental bandwidth. This behavior is experimentally observed for different PWT sizes and types. The nature of this observed distortion is very different from the distortion of wave modes due to dispersion. In addition, the distortion, in many cases, tends towards the appearance of new wave modes close to the S0 and A0 modes. To understand this experimental observation, a theoretical study is performed. First, finite element (FE) simulations of Lamb waves considering pin-force, thermal analogy, and couple field models of surface mounted PWT are carried out. These simulation studies reveal that the wavepacket distortion can be attributed mostly to electro-mechanical coupling effect of the PWT. Next, the dispersion plot of piezoelectric layer considering electro-mechanical coupling is obtained using spectral finite element (SFE) method. These dispersion characteristics of the PWT are found to be significantly different from the conventional Lamb wave dispersion characteristics and may explain the experimental observation.

Single-photon propagation through dielectric bandgaps

Theoretical models of photon traversal through quarter-wave dielectric stack barriers that arise due to Bragg reflection predict the saturation of the propagation time with the barrier length, known as the Hartman effect. This saturation is sensitive to the addition of single dielectric layers, varying significantly from sub-luminal to apparently super-luminal and vice versa. Our research tests the suitability of photonic bandgaps as an optical model for the tunneling process. Of particular importance is our observation of subtle structural changes in dielectric stacks drastically affecting photon traversal times, allowing for apparent sub- and super-luminal effects. We also introduce a simple model to link HOM visibility to wavepacket distortion that allows us to exclude this as a possible cause of the loss of contrast in the barrier penetration process.

Plasmon assisted transmission of single photon wavepacket

Hong–Ou–Mandel interferometer was explored to investigate shape distortion and phase dispersion of single photon wavepacket in surface plasmon assisted transmission. We found that the distortion and dispersion in this process can be neglected under some experimental conditions. Our experiment may also be useful in temporal measurement of the surface plasmon assisted transmission process.

Space‐time evolution of wave packets through superlattices

We briefly discuss the transfer matrix approach applied to study the space-time evolution of electron and electromagnetic wave packets through a semiconductor superlattice. We present some exact calculations for Gaussian wave packets, with centroid lying in distinct but qualitatively different energy regions. Our approach provides a clear explanations of wave packet distortion as well as of a distortionless transmission process. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Evolution and tunneling time of electron wave packets through a superlattice

We present a formalism to study the evolution of a wave packet inside and outside a scattering superlattice. Time series of specific Gaussian packets, centered at an arbitrary energy ${E}_{o},$ exhibit interesting back-scattering, trapping, and transmission effects. These effects depend on whether the energy ${E}_{o}$ is in a gap, coincides with a resonance, or is an arbitrary point in a band of the superlattice. The time evolution depends strongly on the transmission coefficient and on the superlattice tunneling time. We show that because of the reduced wave-packet distortion and the high intensity difference between the back-scattered and the transmitted wave, for ${E}_{o}$ in a gap, it is convenient to look at the back-scattered wave packet to study the superlattice tunneling time.

Femtosecond Light Wave Packets

We analyze propagation of ultra short light pulses in a transparent, dispersive, nonlinear medium. A general formula for femtosecond wave packet evolution is developed and applied to specific problems. Theoretical and experimental results for wave packet distortion by lenses, wave packet rotation in birefringent media and group velocity matching in sum frequency generation are presented. Numerical results for splitting of femtosecond wave packets in dispersive Kerr media are also presented. PACS numbers: 42.65.Jx, 42.65.Re

Barrier penetration by wave packets and the tunneling times

An interesting analytical expression is obtained for the coordinate probability distribution of a wave packet transmitted through a potential barrier. In the large-time asymptotics the distribution is given in terms of the transmission amplitude and the phase-space quasidistribution of the initial (not necessarily pure) state. The distortion of a (broad) wave packet due to the barrier penetration is determined by two timelike parameters, given by the energy derivative of the complex transmission amplitude. The resulting change of the packet shape reveals a dependence on the detector position and incorporates a possible speed-up effect and a negative dispersion.

Wave packet distortion and time delay

The distortion of wave packets in potential scattering is studied, and two characterizations of distortion are proposed. When the energy derivative of the scattering amplitude does not change appreciably over the spectral width of the incident wave packet, the characterizations of distortion produce simple formulas and lead to an interesting connection between distortion and time delay.

Interferometric measurement of femtosecond pulse distortion by lenses

An interferometric method for measurement of femtosecond pulse distortion caused by lenses is described. The linear method allows measurements at low intensity with precision approaching 1 fs. Data for several high numerical aperture microscope objective lenses are presented showing single pass wavepacket distortion between 9 and 18 fs.