Showing papers on "Group velocity published in 2004"
TL;DR: An analytical expression for pulse propagation through a semi-infinite CROW in the case of weak coupling is obtained which fully accounts for the nonlinear dispersive characteristics.
Abstract: We use the coupling matrix formalism to investigate continuous-wave and pulse propagation through microring coupled-resonator optical waveguides (CROWs). The dispersion relation agrees with that derived using the tight-binding model in the limit of weak inter-resonator coupling. We obtain an analytical expression for pulse propagation through a semi-infinite CROW in the case of weak coupling which fully accounts for the nonlinear dispersive characteristics. We also show that intensity of a pulse in a CROW is enhanced by a factor inversely proportional to the inter-resonator coupling. In finite CROWs, anomalous dispersions allows for a pulse to propagate with a negative group velocity such that the output pulse appears to emerge before the input as in “superluminal” propagation. The matrix formalism is a powerful approach for microring CROWs since it can be applied to structures and geometries for which analyses with the commonly used tight-binding approach are not applicable.
416 citations
TL;DR: In this article, the authors discussed linear and nonlinear optical wave propagation in a left-handed medium (LHM) or medium of negative refraction (NRM) and used the approach of characterizing the medium response totally by a generalized electric polarization (with a dielectric permittivity {tilde {var_epsilon}}(w, {rvec k})) that can be decomposed into a curl and a non-curl part.
Abstract: We discuss linear and nonlinear optical wave propagation in a left-handed medium (LHM) or medium of negative refraction (NRM). We use the approach of characterizing the medium response totally by a generalized electric polarization (with a dielectric permittivity {tilde {var_epsilon}}(w, {rvec k})) that can be decomposed into a curl and a non-curl part. The description has a one-to-one correspondence with the usual approach characterizing the LHM response with a dielectric permittivity {var_epsilon}<0 and a magnetic permeability {mu}<0. The latter approach is less physically transparent in the optical frequency region because the usual definition of magnetization loses its physical meaning. Linear wave propagation in LHM or NRM is characterized by negative refraction and negative group velocity that could be clearly manifested by ultra-short pulse propagation in such a medium. Nonlinear optical effects in LHM can be predicted from the same calculations adopted for ordinary media using our general approach.
300 citations
TL;DR: The possibility of tuning the wave group velocity in both the linear and nonlinear cases is discussed, and it is shown that group-velocity dispersion, which leads to pulse broadening, can be balanced by the nonlinearity of the media, so resulting in soliton propagation.
Abstract: We study both linear and nonlinear surface waves localized at the interface separating a left-handed (LH) medium (i.e., a medium with both negative dielectric permittivity and negative magnetic permeability) and a conventional [or right-handed (RH)] dielectric medium. We demonstrate that the interface can support both TE- and TM-polarized surface waves-surface polaritons, and we study their properties. We describe the intensity-dependent properties of nonlinear surface waves in three different cases, i.e., when both the LH and RH media are nonlinear and when either of the media is nonlinear. In the case when both media are nonlinear, we find two types of nonlinear surface waves, one with the maximum amplitude at the interface, and the other one with two humps. In the case when one medium is nonlinear, only one type of surface wave exists, which has the maximum electric field at the interface, unlike waves in right-handed materials where the surface-wave maximum is usually shifted into a self-focusing nonlinear medium. We discuss the possibility of tuning the wave group velocity in both the linear and nonlinear cases, and show that group-velocity dispersion, which leads to pulse broadening, can be balanced by the nonlinearity of the media, so resulting in soliton propagation.
295 citations
01 Mar 2004
TL;DR: In this article, the authors demonstrate slow light via population oscillation in semiconductor quantum-well structures for the first time and infer group velocity as low as 9600 m/s from the experimentally measured dispersive characteristics.
Abstract: We demonstrate slow light via population oscillation in semiconductor quantum-well structures for the first time. A group velocity as low as 9600 m/s is inferred from the experimentally measured dispersive characteristics. The transparency window exhibits a bandwidth as large as 2 GHz.
286 citations
TL;DR: In this article, a waveguide with vanishing second-and third-order dispersion is presented, which can be explained by the strong interaction of the modes with the bulk photonic crystal waveguide.
Abstract: Modes of photonic crystal (PC) line-defect waveguides can have small group velocity away from the Brillouin zone edge. This property can be explained by the strong interaction of the modes with the bulk PC. An anticrossing of “index guided” and “gap guided” modes should be taken into account. To control dispersion, the anticrossing point can be shifted by the change of the PC waveguide parameters. An example of a waveguide is presented with vanishing second- and third-order dispersion.
269 citations
TL;DR: In this article, the authors demonstrate slow light via population oscillation in semiconductor quantum-well structures for the first time and infer group velocity as low as 9600 m/s from the experimentally measured dispersive characteristics.
Abstract: We demonstrate slow light via population oscillation in semiconductor quantum-well structures for the first time. A group velocity as low as 9600 m/s is inferred from the experimentally measured dispersive characteristics. The transparency window exhibits a bandwidth as large as 2 GHz.
264 citations
TL;DR: In this article, a dip-modified log-law was proposed to describe the velocity distribution in smooth uniform open channel flows, and applied to the velocity profile in the region from the near bed to just below the free surface, and transversely, from the center line to the near-wall region of the channel.
Abstract: This paper investigates the mechanism of the dip phenomenon whereby the location of the maximum velocity appears below the free surface vis-a-vis the secondary currents in open-channel flows. It is found that the classical log law gives a good description of the velocity distribution in the inner region if the local shear velocity is introduced into the dimensionless distance, i.e., u*(z)y/ν. In the outer region, where the maximum velocity occurs at some distance below the free surface in a vertical plane, it is found that the velocity deviation from the log law is linearly proportional to the logarithmic distance ln(1-y/h) from the free surface. To this end, the study proposes a dip-modified log law for the velocity distribution in smooth uniform open channel flows. This new law is capable of describing the dip phenomenon, and is applicable to the velocity profile in the region from the near bed to just below the free surface, and transversely, from the center line to the near-wall region of the channel....
258 citations
TL;DR: The self-similar evolution to turbulence of a multi-mode Rayleigh-Taylor mix at small density differences was investigated through particle image velocimetry (PIV) and high-resolution thermocouple measurements as discussed by the authors.
Abstract: The self-similar evolution to turbulence of a multi-mode Rayleigh-Taylor mix at small density differences (A t ∼ 7.5 x 10 -4 ), is investigated through particle image velocimetry (PIV), and high-resolution thermocouple measurements. The density difference has been achieved through a temperature difference in the fluid. Cold fluid enters above the hot in a closed channel to form an unstable interface. This buoyancy-driven mixing experiment allows for long data collection times, short transients, and is statistically steady. First-, second-, and third-order statistics with spectra of velocity and temperature fields are presented. Analysis of the measurements has shed light on the structure of mixing as it develops to a self-similar regime in this flow. The onset of self-similarity is marked by the development of a self-preserving form of the temperature spectra, and the collapse of velocity profiles expressed in self-similar units
184 citations
TL;DR: In this paper, an optical delay line composed of two index-chirped waveguides in a directional coupler structure was proposed and a large delay was realized by a low average group velocity of
Abstract: Previously, we proposed and demonstrated chirped photonic crystal waveguides, in which some structural parameters are gradually changed so that the photonic band characteristic is smoothly shifted. In this letter, we discuss an optical delay line composed of two index-chirped waveguides in a directional coupler structure. A large delay is realized by a low average group velocity of
178 citations
TL;DR: In this article, it was shown that shear waves generally have finite nonzero phase and group velocities in acoustic transversely isotropic (TI) media, where the shear wave velocity in the direction of symmetry axis, VS0, to zero.
Abstract: Acoustic transversely isotropic (TI) media are defined by artificially setting the shear‐wave velocity in the direction of symmetry axis, VS0, to zero. Contrary to conventional wisdom that equating VS0 = 0 eliminates shear waves, we demonstrate their presence and examine their properties. Specifically, we show that SV‐waves generally have finite nonzero phase and group velocities in acoustic TI media. In fact, these waves have been observed in full waveform modeling, but apparently they were not understood and labeled as numerical artifacts.Acoustic TI media are characterized by extreme, in some sense infinite strength of anisotropy. It makes the following unusual wave phenomena possible: (1) there are propagation directions, where the SV‐ray is orthogonal to the corresponding wavefront normal, (2) the SV‐wave whose ray propagates along the symmetry axis is polarized parallel to the P‐wave propagating in the same direction, (3) P‐wave singularities, that is, directions where P‐ and SV‐wave phase velocitie...
160 citations
TL;DR: The experiment shows that the group velocity can indeed exceed c in the fiber; and the first direct observation of the so-called "signal velocity," the speed at which information propagates and that cannot exceed c is reported.
Abstract: We present an easy way of observing superluminal group velocities using a birefringent optical fiber and other standard devices. In the theoretical analysis, we show that the optical properties of the setup can be described using the notion of "weak value". The experiment shows that the group velocity can indeed exceed c in the fiber; and we report the first direct observation of the so-called "signal velocity", the speed at which information propagates and that cannot exceed c.
TL;DR: Time-domain measurements of terahertz surface plasmon polaritons (SPPs) propagating on gratings structured on silicon surfaces show a good agreement with the numerical calculations based on the reduced Rayleigh equation.
Abstract: We present time-domain measurements of terahertz surface plasmon polaritons (SPPs) propagating on gratings structured on silicon surfaces. Using single-cycle pulses of terahertz radiation to excite SPPs in a broad frequency range, we observe that the efficient SPPs scattering on the semiconductor periodic structure introduces significant dispersion and modifies the SPPs propagation. A stop gap, or a frequency range where SPPs are Bragg reflected, is formed by the structure. This gap depends strongly on the Si doping density and type. The resonant scattering at the edge of the gap reduces the group velocity by more than a factor of 2. The measurements show a good agreement with our numerical calculations based on the reduced Rayleigh equation.
TL;DR: Several models for the vertical distribution of the double-averaged (in time and in the plane parallel to the mean bed) longitudinal velocity in the flow region between roughness troughs and roughness tops are suggested in this paper.
Abstract: Several models for the vertical distribution of the double-averaged (in time and in the plane parallel to the mean bed) longitudinal velocity in the flow region between roughness troughs and roughness tops are suggested. We found that the same model for velocity distribution may be applicable to a range of flow conditions and roughness types, which share some common features. The suggested models for velocity distribution in the near-bed region are: (1) Constant velocity; (2) exponential velocity distribution; and (3) linear velocity distribution. The measured velocity distributions may be approximated by a single model or by a combination of models depending on roughness geometry and flow conditions. The validity of these models for velocity distribution is supported by laboratory data.
TL;DR: In this article, a Lagrangian dispersion model driven by velocity fields from large-eddy simulations (LESs) is presented for passive particle dispersion in the planetary boundary layer (PBL).
Abstract: A Lagrangian dispersion model driven by velocity fields from large-eddy simulations (LESs) is presented for passive particle dispersion in the planetary boundary layer (PBL). In this combined LES–Lagrangian stochastic model (LSM), the total velocity is divided into resolved or filtered and unresolved or subfilter-scale (SFS) velocities. The random SFS velocity is modeled using an adaptation of Thomson's LSM in which the ensemble-mean velocity and velocity variances are replaced by the resolved velocity and SFS variances, respectively. The random SFS velocity forcing has an amplitude determined by the SFS fraction of the total turbulent kinetic energy (TKE); the fraction is about 0.15 in the bulk of the simulated convective boundary layer (CBL) used here and reaches values as large as 0.31 and 0.37 in the surface layer and entrainment layer, respectively. For the proposed LES–LSM, the modeled crosswind-integrated concentration (CWIC) fields are in good agreement with the 1) surface-layer similarit...
TL;DR: In this article, a finite element method (FEM) is used to calculate wave propagation characteristics for built-up thin-walled structures, such as the modal density, the group velocity and the waveform.
TL;DR: In this paper, a formula for the small-signal gain of a Smith-Purcell free-electron laser was derived, where the electron beam was modeled as a moving plasma dielectric, and the evanescent wave was assumed to be a periodic waveguide with a rectangular profile.
Abstract: A formula is derived for the small-signal gain of a Smith-Purcell free-electron laser. The theory describes the electron beam as a moving plasma dielectric, and assumes that the electron beam interacts with an evanescent mode traveling along the surface of a periodic waveguide with a rectangular profile. The phase velocity of the evanescent wave is synchronous with the electron velocity, but the group velocity is actually negative. The electron beam amplifies the evanescent wave, which does not itself radiate. According to this picture, the radiation observed emanating from the grating is Smith-Purcell radiation enhanced by the bunching of the electrons due to the interaction with the evanescent mode. There will also be radiation from the part of the evanescent mode that is outcoupled from the ends of the grating. This radiation appears at a lower frequency than the Smith-Purcell radiation. The new results explain both the gain and the radiation observed in the experiments of Urata and Walsh, and the cube-root current dependence of the gain inferred by Bakhtyari, Walsh, and Brownell.
TL;DR: In this article, the authors investigated the features of Love waves in a layered functionally graded piezoelectric structure, and the mathematical model was established on the basis of the elastic wave theory, and WKB method was applied to solve the coupled electromechanical field differential equation.
TL;DR: In this paper, the authors demonstrate tunable control of the group velocity of a weak probe pulse from subluminal to superluminous, using an extended ε-Lambda-type system with two extra control fields and an extra energy level.
Abstract: We demonstrate tunable control of the group velocity of a weak probe pulse from subluminal to superluminal. The model is an extended $\ensuremath{\Lambda}$-type system with two extra control fields and an extra energy level. Phase variation of one of the control fields imparts the tunability in the group velocity along with other interesting spectral behavior in the absorption spectrum.
TL;DR: In this article, a theoretical method for predicting the longitudinal dispersion coefficient is developed based on the transverse velocity distribution in natural streams, which is the most appropriate model for explaining the complex behavior of the transversal velocity structure of irregular natural streams.
Abstract: In this study, a theoretical method for predicting the longitudinal dispersion coefficient is developed based on the transverse velocity distribution in natural streams. Equations of the transverse velocity profile for irregular cross sections of the natural streams are analyzed. Among the velocity profile equations tested in this study, the beta distribution equation, which is a probability density function, is considered to be the most appropriate model for explaining the complex behavior of the transverse velocity structure of irregular natural streams. The new equation for the longitudinal dispersion coefficient that is based on the beta function for the transverse velocity profile is developed. A comparison of the proposed equation with existing equations and the observed longitudinal dispersion coefficient reveals that the proposed equation shows better agreement with the observed data compared to other existing equations.
TL;DR: These approaches are validated by a conventional shear wave time-of-flight approach, and they are accurate within 4% on various homogeneous tissue-mimicking phantoms.
Abstract: The shear wave velocity is one of a few important parameters that characterize the mechanical properties of bio-materials. In this paper, two noninvasive methods are proposed to measure the shear velocity by inspecting the shear wave interference patterns. In one method, two shear wave sources are placed on the opposite two sides of a sample, driven by the identical sinusoidal signals. The shear waves from the two sources interact to create interference patterns, which are visualized by the vibration sonoelastography technique. The spacing between the pattern bands equals half of the shear wavelength. The shear velocity can be obtained by taking the product of the wavelength and the frequency. An alternative method is to drive the two vibration sources at slightly different frequencies. In this case, the interference patterns no longer remain stationary. It is proved that the apparent velocity of the moving patterns is proportional to the shear velocity in the medium. Since the apparent velocity of the patterns can be measured by analysing the video sequence, the shear velocity can be obtained thereafter. These approaches are validated by a conventional shear wave time-of-flight approach, and they are accurate within 4% on various homogeneous tissue-mimicking phantoms.
TL;DR: In this paper, surface plasmons at the interface between metal and a dielectric with strong optical amplification are analyzed theoretically, and it is shown that proper choice of optical indices of the dielectrics medium results in an infinitely large effective refractive index of surface waves.
Abstract: Surface plasmons at the interface between metal and a dielectric with strong optical amplification are analyzed theoretically. It is shown that proper choice of optical indices of the dielectric medium results in an infinitely large effective refractive index of surface waves. Such resonant plasmons have extremely low group velocity and are localized within a vanishingly small distance near the interface. The plasmon-related anomalies in the UV reflection spectra are predicted for nanoscale gratings on a surface of a silver film covered by a concentrated dye solution with high optical amplification.
TL;DR: In this article, the design and fabrication of photonic crystal structures exhibiting electromagnetic bands that are flattened in all crystal directions is presented, i.e., whose frequency variation with a wave vector is minimized.
Abstract: We present the design and fabrication of photonic crystal structures exhibiting electromagnetic bands that are flattened in all crystal directions, i.e., whose frequency variation with a wave vector is minimized. Such bands can be used to reduce group velocity of light propagating in an arbitrary crystal direction, which is of importance for the construction of miniaturized tunable optical delay components and low-threshold photonic crystal lasers, and the study of nonlinear optics phenomena.
TL;DR: In this article, the authors discuss unique light localizations in photonic crystal line defect waveguides based on two different concepts: an additional defect doping that breaks the symmetry of the line defect and chirping of the waveguide structure.
Abstract: In this paper, we discuss unique light localizations in photonic crystal line defect waveguides based on two different concepts. The first concept is an additional defect doping that breaks the symmetry of the line defect. Even though such a defect is open to the line defect, the optical field is well confined around the defect at cutoff frequencies of the line defect. This expands the design flexibility of microcavities and allows effective mode controls such as the single-mode operation. The lasing action of such cavities in a GaInAsP photonic crystal slab was experimentally observed by photopumping at room temperature. The second concept is a chirping of the waveguide structure. The photonic band of a waveguide mode has a band edge, at which the group velocity becomes zero. The band-edge condition shifts in a chirped line defect waveguide, so guided light reaches a zero group velocity point and is localized. A macroscopic behavior of this phenomenon was experimentally observed in a waveguide fabricated into a silicon-on-insulator substrate. In addition, a microscopic behavior was theoretically investigated, which suggested its applicability to a group delay device.
TL;DR: In this paper, the authors present extensive three-wave mixing measurements of the wave-vector mismatch and obtain improved Sellmeier equations for KTiOPO 4, and demonstrate a type-II extended phase-matching bandwidth of 100 nm for second-harmonic generation in periodically poled KTIOPO4, centered at the fundamental wavelength of 1584 nm.
Abstract: Under extended phase-matching conditions, the first frequency derivative of the wave-vector mismatch is zero and the phase-matching bandwidth is greatly increased. We present extensive three-wave mixing measurements of the wave-vector mismatch and obtain improved Sellmeier equations for KTiOPO 4 . We observed a type-II extended phase-matching bandwidth of 100 nm for second-harmonic generation in periodically poled KTiOPO 4 , centered at the fundamental wavelength of 1584 nm. Applications in quantum entanglement and frequency metrology are discussed.
TL;DR: In this paper, the authors investigated theoretically and experimentally the velocity distributions of turbulent open channel flow with bed suction, and derived a modified logarithmic law based on this assumption.
Abstract: This study investigates theoretically and experimentally the velocity distributions of turbulent open channel flow with bed suction. A velocity profile with a slip velocity at the bed surface and an origin displacement under the bed surface is proposed and discussed. Based on this assumption, a modified logarithmic law is derived. The measured experimental velocity distribution verifies the accuracy of the theoretically derived profile. The data show a significant increase in the near bed velocity and a velocity reduction near the water surface, resulting in the formation of a more uniform velocity distribution. The values of the origin displacement, slip velocity and shear velocity are found to increase with increasing relative suction. The measured data show the occurrence of two flow regions in the suction zone: a transitional region in which the velocity readjusts rapidly; and an "equilibrium" region.
TL;DR: In this paper, a variable semiconductor optical buffer based on the electromagnetically induced transparency in a quantum dot waveguide is theoretically investigated with feasible parameters for applications to a 40 Gbps optical network.
Abstract: A variable semiconductor optical buffer based on the electromagnetically induced transparency in a quantum dot waveguide is theoretically investigated with feasible parameters for applications to a 40 Gbps optical network. We show the refractive index and absorption spectra of the quantum dot waveguide at various pump levels, which exhibit an optimal pump power for maximum slow-down factor, in agreement with the previous experimental observation using a Pr-doped solid. The group velocity slow-down factor is theoretically analysed as a function of the pump intensity at different broadened linewidths. Inhomogeneous broadening in self-assembled quantum dots degrades the slow-down factor. In order to reduce the inhomogeneous broadening effects, we propose to use a resonant microcavity structure with quantum dots embedded in the active layer to enhance the slow-down factor.
TL;DR: In this paper, a model describing the generation of THz pulses by optical rectification and the detection of THZ pulses by electro-optic sampling is presented, where physical phenomena such as dispersion, group velocity mismatch, multiple reflections and diffraction are represented by one dimensional transfer functions.
Abstract: A model describing the generation of THz pulses by optical rectification and the detection of THz pulses by electro-optic sampling is presented. The model is comprehensive and mostly analytical: physical phenomena such as dispersion, group velocity mismatch, multiple reflections and diffraction are represented by one dimensional transfer functions. The model is compared with experimental results and shows good agreement with experiments. It is shown that including diffraction is crucial for retrieving the details of the THz spectrum.
TL;DR: It is shown that the group index strongly depends on the number of cavities in the system, especially for operation at the center frequency, and the nonlinear phase sensitivity shows an enhancement proportional to the square of the groupIndex.
Abstract: In this paper, we derive the exact dispersion relation of one dimensional periodic coupled-resonator optical waveguides of finite length, from which the reduced group velocity of light is obtained. We show that the group index strongly depends on the number of cavities in the system, especially for operation at the center frequency. The nonlinear phase sensitivity shows an enhancement proportional to the square of the group index (or light slowing ratio). Aperiodic coupled ring-resonator optical waveguides with optimized linear properties are then synthesized to give an almost ideal nonlinear phase shift response. For a given application and bandwidth requirement, the nonlinear sensitivity can be increased by either decreasing resonator length or by using higher-order structures. The impact of optical loss, including linear and two-photon absorption is discussed in post-analysis.
TL;DR: In this article, the negative group velocity was demonstrated theoretically and experimentally in the time domain using modulated Gaussian pulses, where the output pulse peak emerged from the loaded transmission line prior to the input peak entering the line.
Abstract: We have simulated and constructed a one-dimensional metamaterial composed of a periodically loaded transmission line that exhibits both negative and positive group velocities in a band of effective negative index of refraction. The negative group velocity or, equivalently, the negative group delay, is demonstrated theoretically and experimentally in the time domain using modulated Gaussian pulses. Due to this negative delay, we can show an output pulse peak emerging from the loaded transmission line prior to the input peak entering the line, i.e., the output pulse precedes the input pulse. The fact that this surprising behavior does not violate the requirements of relativistic causality is illustrated with time-domain simulations, which show that discontinuities in the pulse waveforms are traveling at exactly the speed of light in vacuum. The pulse-reshaping mechanism underlying this behavior is also illustrated using time-domain simulations.
TL;DR: Over the timescale of the velocity measurements, which is principally determined by the residence time in the coil, the local velocity fluctuations are seen to be small compared to the local velocities, confirming that the data acquisition times achieved are rapid enough to capture 'instantaneous' images of the flow field.