Showing papers on "Group velocity published in 2005"

Active control of slow light on a chip with photonic crystal waveguides

Abstract: It is known that light can be slowed down in dispersive materials near resonances. Dramatic reduction of the light group velocity-and even bringing light pulses to a complete halt-has been demonstrated recently in various atomic and solid state systems, where the material absorption is cancelled via quantum optical coherent effects. Exploitation of slow light phenomena has potential for applications ranging from all-optical storage to all-optical switching. Existing schemes, however, are restricted to the narrow frequency range of the material resonance, which limits the operation frequency, maximum data rate and storage capacity. Moreover, the implementation of external lasers, low pressures and/or low temperatures prevents miniaturization and hinders practical applications. Here we experimentally demonstrate an over 300-fold reduction of the group velocity on a silicon chip via an ultra-compact photonic integrated circuit using low-loss silicon photonic crystal waveguides that can support an optical mode with a submicrometre cross-section. In addition, we show fast (approximately 100 ns) and efficient (2 mW electric power) active control of the group velocity by localized heating of the photonic crystal waveguide with an integrated micro-heater.

Observation of pulse delaying and advancement in optical fibers using stimulated Brillouin scattering

Abstract: We demonstrate experimentally that it is possible to control optically the group velocity of an optical pulse as it travels along an optical fiber. To achieve this control we use the effect of Stimulated Brillouin Scattering. In our experiments we have achieved changes in the group index of 10-3 in several kilometer-length fibers, thus leading to pulse delaying and advancement in the range of tens of nanoseconds. We believe that this is the first evidence of such optically-controlled strong delay changes in optical fibers. In this paper we derive the basic theory behind these group-delay changes and we demonstrate the effect in two kinds of fibers which are conventionally used.

Real-Space Observation of Ultraslow Light in Photonic Crystal Waveguides

Abstract: We show the real-space observation of fast and slow pulses propagating inside a photonic crystal waveguide by time-resolved near-field scanning optical microscopy. Local phase and group velocities of modes are measured. For a specific optical frequency we observe a localized pattern associated with a flat band in the dispersion diagram. During at least 3 ps, movement of this field is hardly discernible: its group velocity would be at most c/1000. The huge trapping times without the use of a cavity reveal new perspectives for dispersion and time control within photonic crystals.

Slow-light optical buffers: capabilities and fundamental limitations

Abstract: This paper presents an analysis of optical buffers based on slow-light optical delay lines. The focus of this paper is on slow-light delay lines in which the group velocity is reduced using linear processes, including electromagnetically induced transparency (EIT), population oscillations (POs), and microresonator-based photonic-crystal (PC) filters. We also consider slow-light delay lines in which the group velocity is reduced by an adiabatic process of bandwidth compression. A framework is developed for comparing these techniques and identifying fundamental physical limitations of linear slow-light technologies. It is shown that slow-light delay lines have limited capacity and delay-bandwidth product. In principle, the group velocity in slow-light delay lines can be made to approach zero. But very slow group velocity always comes at the cost of very low bandwidth or throughput. In many applications, miniaturization of the delay line is an important consideration. For all delay-line buffers, the minimum physical size of the buffer for a given number of buffered data bits is ultimately limited by the physical size of each stored bit. We show that in slow-light optical buffers, the minimum achievable size of 1 b is approximately equal to the wavelength of light in the buffer. We also compare the capabilities and limitations of a range of delay-line buffers, investigate the impact of waveguide losses on the buffer capacity, and look at the applicability of slow-light delay lines in a number of applications.

Electromagnetically induced transparency in V -, Λ -, and cascade-type schemes beyond steady-state analysis

Abstract: We analyze the electromagnetically induced transparency (EIT) in $V$-, $\ensuremath{\Lambda}$-, and cascade-type schemes in a time-dependent way via the Schr\"odinger-Maxwell formalism. We derive explicitly the analytical expressions of the space-time dependent probe field, the corresponding phase shift, absorption or amplification, group velocity, and group velocity dispersion for all the three schemes. These simple analytical expressions not only demonstrate explicitly the similarities and essential differences of the three schemes but also provide a convenient basis for investigating how the many-body effects in solids modify the magnitude, spectral shape, and space and time dependence of EIT and EIT-related quantum coherence phenomena.

Extrinsic optical scattering loss in photonic crystal waveguides: role of fabrication disorder and photon group velocity.

Abstract: Formulas are presented that provide clear physical insight into the phenomenon of extrinsic optical scattering loss in photonic crystal waveguides due to random fabrication imperfections such as surface roughness and disorder. Using a photon Green-function-tensor formalism, we derive explicit expressions for the backscattered and total transmission losses. Detailed calculations for planar photonic crystals yield extrinsic loss values in overall agreement with experimental measurements, including the full dispersion characteristics. We also report that loss in photonic crystal waveguides scales inversely with group velocity, at least, thereby raising serious questions about future low-loss applications based on operating frequencies that approach the photonic band edge.

Guided subwavelength plasmonic mode supported by a slot in a thin metal film

Abstract: We demonstrate the existence of a bound optical mode supported by a slot in a thin metallic film deposited on a substrate, with slot dimensions much smaller than the wavelength. The modal size is almost completely dominated by the near field of the slot. Consequently, the size is very small compared with the wavelength, even when the dispersion relation of the mode approaches the light line of the surrounding media. In addition, the group velocity of this mode is close to the speed of light in the substrate, and its propagation length is tens of micrometers at the optical communication wavelength.

Surface-Plasmon-Assisted Guiding of Broadband Slow and Subwavelength Light in Air

Abstract: A class of axially uniform waveguides is introduced, employing a new mechanism to guide light inside a low-index dielectric material without the use of photonic band gap, and simultaneously exhibiting subwavelength modal size and very slow group velocity over an unusually large frequency bandwidth. Their basis is the presence of plasmonic modes on the interfaces between dielectric regions and the flat unpatterned surface of a bulk metallic substrate. These novel waveguides allow for easy broadband coupling and exhibit absorption losses limited only by the intrinsic loss of the metal.

Three-dimensional array of dielectric spheres with an isotropic negative permeability at infrared frequencies

Abstract: A negative effective permeability is shown to exist at infrared frequencies in a three-dimensional collection of polaritonic spheres This is demonstrated by an effective medium theory which relates the Mie resonances of the constituent spheres to the bulk response of the composite The derived permittivity and permeability are shown to be isotropic The results are verified by a comparison with multiple-scattering photonic band calculations The existence of an anomalous dispersion region with a negative group velocity and the appropriate signs associated with the imaginary parts of the permittivity and permeability are also discussed

Wideband and low dispersion slow light by chirped photonic crystal coupled waveguide

Abstract: Previously, we discussed an optical delay device consisting of a directional coupler of two different photonic crystal (PC) waveguides. It generates wideband and low dispersion slow light. However, it is easily degraded by a large reflection loss for a small imperfection of the coupling condition. In this paper, we propose and theoretically discuss a PC coupled waveguide, which allows more robust slow light with lower loss. For this device, unique photonic bands with a zero or negative group velocity at the inflection point can be designed by the structural tuning. Finite difference time domain simulation demonstrates the stopping and/or back and forth motion of an ultrashort optical pulse in the device combined with the chirped structure. For a signal bandwidth of 40 GHz, the average group index of the slow light will be 450, which gives a 1 ns delay for a device length of 670 μm. The theoretical total insertion loss at the device and input/output structures is as low as 0.11 dB.

Slow light in a semiconductor waveguide at gigahertz frequencies

Abstract: We experimentally demonstrate slow-down of light by a factor of three in a 100 μm long semiconductor waveguide at room temperature and at a record-high frequency of 16.7 GHz. It is shown that the group velocity can be controlled all-optically as well as through an applied bias voltage. A semi-analytical model based on the effect of coherent population oscillations and taking into account propagation effects is derived and is shown to well account for the experimental results. It is shown that the carrier lifetime limits the maximum achievable delay. Based on the general model we analyze fundamental limitations in the application of light slowdown due to coherent population oscillations.

Experimental demonstration of the slow group velocity of light in two-dimensional coupled photonic crystal microcavity arrays

Abstract: We recently proposed two-dimensional coupled photonic crystal microcavity arrays as a route to achieve a slow-group velocity of light (flat band) in all crystal directions. In this letter we present the experimental demonstration of such structures with a measured group velocity below 0.008c and discuss the feasibility of applications such as low-threshold photonic crystal lasers with increased output powers, optical delay components, and sensors.

Laser-based ultrasonic generation and detection of zero-group velocity Lamb waves in thin plates

Abstract: A novel laser-based ultrasonic technique for the inspection of thin plates and membranes is presented, in which a modulated continuous-wave laser source is used to excite narrow bandwidth Lamb waves. The dominant feature in the acoustic spectrum is a sharp resonance peak that occurs at the minimum frequency of the first-order symmetric Lamb mode, where the group velocity of the Lamb wave goes to zero while the phase velocity remains finite. Experimental results with the laser source and receiver on epicenter demonstrate that the zero-group velocity resonance generated with a low-power modulated excitation source can be detected using a Michelson interferometer coupled to a lock-in amplifier. This resonance peak is sensitive to the thickness and mechanical properties of plates and may be suitable, for example, for the measurement and mapping of nanoscale thickness variations.

Reynolds Stresses and Velocity Distributions in a Wave-Current Coexisting Environment

Abstract: To investigate changes in the mean velocity profile owing to the interaction between waves and a current, the horizontal and vertical velocity components in the oscillating fluid were measured by a two-dimensional laser anemometer in a recirculating wave tank. The observed instantaneous velocity data concerning waves following and opposing a current were analyzed to obtain the Eulerian-mean velocity, the wave-current Reynolds stress, and the wave-current turbulent intensities. The wave-current Reynolds stress behaves differently when current direction changes. The general characteristic of the Eulerian-mean velocity is greatly affected by the wave-current Reynolds stress. The mean velocity for waves following (opposing) a current is reduced (increased) towards the free surface, when compared with the logarithmic profile. These velocity data were used to verify the results by velocity equations based on the phase-averaged Prandtl momentum-transfer theory. In addition, measurement of water-surface elevations revealed that the phase-averaged waveform for a pure wave is peaked near the crest but flatter near the trough and the variation of the water surface is well predicted by the third-order Stokes wave equation. The original pattern of the waveform varies due to the wave-current interaction, but the current direction only minimally affects the attenuation of the surface waves.

Dispersion and attenuation in a Smith-Purcell free electron laser

Abstract: It has previously been shown that the electron beam in a Smith-Purcell free-electron laser interacts with a synchronous evanescent wave. At high electron energy, the group velocity of this wave is positive and the device operates on a convective instability, in the manner of a traveling-wave tube. For operation as an oscillator, the gain must exceed the losses in the external feedback system. At low electron energy, the group velocity of the synchronous evanescent wave is negative and the device operates on an absolute instability, like a backward-wave oscillator, and no external feedback is required. For oscillation to occur, the current must exceed the so-called start current. At an intermediate energy, called the Bragg condition, the group velocity ${v}_{g}$ of the evanescent wave vanishes and both the gain and the attenuation due to resistive losses in the grating diverge. It is shown that near the Bragg condition the gain depends on ${v}_{g}^{\ensuremath{-}1/3}$, while the attenuation depends on ${v}_{g}^{\ensuremath{-}1}$. Since the attenuation increases faster than the gain near the Bragg condition, the Smith-Purcell free-electron laser cannot operate at the point of maximum gain. The effects of resistive losses become increasingly important as Smith-Purcell free-electron lasers move to shorter wavelengths.

Coherent wave-packet evolution in coupled bands

Abstract: We develop a formalism for treating coherent wave-packet dynamics of charge and spin carriers in degenerate and nearly degenerate bands. We consider the two-band case carefully in view of spintronics applications, where transitions between spin-split bands often occur even for relatively weak electromagnetic fields. We demonstrate that much of the semiclassical formalism developed for the single-band case can be generalized to multiple bands, and examine the nontrivial non-Abelian corrections arising from the additional degree of freedom. Along with the center of mass motion in crystal momentum and real space, one must also take into account the probability amplitudes to characterize the dynamics between the bands. We derive the wave packet energy up to the first order gradient correction and obtain the equations of motion for the real- and $k$-space center of the wave packet, as well as for the probability amplitudes. These equations include the non-Abelian Berry curvature terms and a non-Abelian correction to the group velocity. As an example, we apply our formalism to describe coherent wave packet evolution under the action of an electric field, demonstrating that it leads to electrical separation of spins. A sizable separation will be observed, with a large degree of tunability, making this mechanism a practical method of generating a spin polarization. We then turn our attention to a magnetic field, where we recover Larmor precession, which cannot be obtained from a single-band point of view. In this case, the gradient energy correction can be regarded as due to a magnetic moment from the self-rotation of the wave packet, and we calculate its value for the light holes in the spherical four-band Luttinger model.

Direct Observation of Bloch Harmonics and Negative Phase Velocity in Photonic Crystal Waveguides

Abstract: The eigenfield distribution and the band structure of a photonic crystal waveguide have been measured with a phase-sensitive near-field scanning optical microscope. Bloch modes, which consist of more than one spatial frequency, are visualized in the waveguide. In the band structure, multiple Brillouin zones due to zone folding are observed, in which positive and negative dispersion is seen. The negative slopes are shown to correspond to a negative phase velocity but a positive group velocity. The lateral mode profile for modes separated by one reciprocal lattice vector is found to be different.

Resonator mode in chains of silver spheres and its possible application

Abstract: A transversal mode with zero group velocity and nonzero phase velocity that can exist in chains of silver nanospheres in the optical frequency range is theoretically studied. It is shown that the external source radiating a narrow-band nonmonochromatic signal can excite in the chain a mixture of standing and slowly traveling waves. The standing-wave component (named the resonator mode) is strongly dominating. The physical reason for such a regime is a sign-varying distribution of power flux over the cross section of the chain. A possible application of the resonator mode for evanescent-wave enhancement and for subwavelength imaging in the visible is discussed.

Response dynamics of the frequency comb output from a femtosecond fiber laser.

Abstract: The frequency comb from a mode-locked fiber laser can be stabilized through feedback to the pump power. An understanding of the mechanisms and bandwidth governing this feedback is of practical importance for frequency comb design and of basic interest since it provides insight into the rich nonlinear laser dynamics. We compare experimental measurements of the response of a fiber-laser frequency comb to theory. The laser response to a pump-power change follows that of a simple low-pass filter with a time constant set by the gain relaxation time and the system-dependent nonlinear loss. Five different effects contribute to the magnitude of the response of the frequency comb spacing and offset frequency but the dominant effects are from the resonant contribution to the group velocity and intensity-dependent spectral shifts. The origins of the intensity-dependent spectral shifts are explained in terms of the laser parameters.

Characterization of dispersive surface waves using continuous wavelet transforms

Abstract: In this paper, we propose a method of surface waves characterization based on the deformation of the wavelet transform of the analysed signal. An estimate of the phase velocity (the group velocity) and the attenuation coefficient is carried out using a model-based approach to determine the propagation operator in the wavelet domain, which depends nonlinearly on a set of unknown parameters. These parameters explicitly define the phase velocity, the group velocity and the attenuation. Under the assumption that the difference between waveforms observed at a couple of stations is solely due to the dispersion characteristics and the intrinsic attenuation of the medium, we then seek to find the set of unknown parameters of this model. Finding the model parameters turns out to be that of an optimization problem, which is solved through the minimization of an appropriately defined cost function. We show that, unlike time-frequency methods that exploit only the square modulus of the transform, we can achieve a complete characterization of surface waves in a dispersive and attenuating medium. Using both synthetic examples and experimental data, we also show that it is in principle possible to separate different modes in both the time domain and the frequency domain

A modified law-of-the-wall applied to oceanic bottom boundary layers

Abstract: [1] Near the bottom, the velocity profile in the bottom boundary layer over the continental shelf exhibits a characteristic law-of-the-wall that is consistent with local estimates of friction velocity from near-bottom turbulence measurements. Farther from the bottom, the velocity profile exhibits a deviation from the law-of-the-wall. Here the velocity gradient continues to decrease with height but at a rate greater than that predicted by the law-of-thewall with the local friction velocity. We argue that the shape of the velocity profile is made consistent with the local friction velocity by the introduction of a new length scale that, near the boundary, asymptotes to a value that varies linearly from the bottom. Farther from the boundary, this length scale is consistent with the suppression of velocity fluctuations either by stratification in the upper part of the boundary layer or by proximity to the free surface. The resultant modified law-of-the-wall provides a good representation of velocity profiles observed over the continental shelf when a local estimate of the friction velocity from coincident turbulence observations is used. The modified law-ofthe-wall is then tested on two very different sets of observations, from a shallow tidal channel and from the bottom of the Mediterranean outflow plume. In both cases it is argued that the observed velocity profile is consistent with the modified law-of-the-wall. Implicit in the modified law-of-the-wall is a new scaling for turbulent kinetic energy dissipation rate. This new scaling diverges from the law-of-the-wall prediction above 0.2D (where D is the thickness of the bottom boundary layer) and agrees with observed profiles to 0.6D.

Ultraslow light propagation in an inhomogeneously broadened rare-earth ion-doped crystal.

Abstract: We show that coherent population oscillations effect allows us to burn a narrow spectral hole (26 Hz) within the homogeneous absorption line of the optical transition of an erbium ion-doped crystal. The large dispersion of the index of refraction associated with this hole permits us to achieve a group velocity as low as 2.7 m/s with a transmission of 40%. We especially benefit from the inhomogeneous absorption broadening of the ions to tune both the transmission coefficient, from 40% to 90%, and the light group velocity from 2.7 m/s to 100 m/s.

Gain-assisted pulse advancement using single and double Brillouin gain peaks in optical fibers.

Abstract: We report the first experimental demonstration of pulse advancement with gain in optical fibers based on stimulated Brillouin scattering. Two experimental configurations are investigated and compared. One is to make the pulse propagate in a region slightly detuned from a gain peak where the group velocity change is negative and the other is to make use of the large anomalous dispersion appearing between two gain peaks. We experimentally show that the second method produces pulse advancement with lower distortion than the first one.

Monte Carlo simulation of Joule heating in bulk and strained silicon

Abstract: This work examines the details of Joule heating in silicon with a Monte Carlo method including efficient, analytic models for the electron bands, acoustic and optical phonon dispersion. We find that a significant portion of the initially generated phonons have low group velocity, and therefore low contribution to heat transport, e.g., optical phonons or acoustic modes near the Brillouin zone edge. The generated phonon spectrum in strained silicon is different from bulk silicon at low electric fields due to band splitting and scattering selection rules which favor g-type and reduce f-type phonon emission. However, heat generation is essentially the same in strained and bulk silicon at high fields, when electrons have enough energy to emit across the entire phonon spectrum despite the strain-induced band splitting. The results of this study are important for electro-thermal analysis of future silicon nanoscale devices.

On the identification of plasma sheet flapping waves observed by Cluster

Abstract: [1] Runov et al. [2003] and Sergeev et al. [2003, 2004] have reported on low-frequency oscillations of the plasma sheet generated by some impulsive source in the center of the magnetospheric tail and propagating toward the flanks, with velocities that range from a few tens to a few hundreds of km/s. To interpret the finding, a number of wave modes have been invoked and then discarded, for either the group velocities or propagation directions were inconsistent with the observations. In the present paper we examine the MHD ballooning-type waves first described by Safargaleev and Maltsev [1986] who termed them internal “gravitational” waves, as a possible candidate to match the observed flapping motions. The role of gravity is played by the centrifugal force, acting on hot plasma in a curved magnetic field. The corresponding dispersion relation indicates propagation in the positive/negative azimuthal direction with a group velocity dependent on the wave number across the magnetic field, half-thickness of the current sheet, and thermal velocity of ions in the neutral sheet. The calculated group velocity ranges from 40 to 400 km/s, being consistent with the observations.

Uniform coil optical resonator and waveguide: transmission spectrum, eigenmodes, and dispersion relation

Abstract: The coil optical resonator (COR) is an optical microfiber coil tightly wound on an optical rod. The resonant behavior of this all-pass device is determined by evanescent coupling between the turns of the microfiber. This paper investigates the uniform COR with N turns. Its transmission characteristics are surprisingly different from those of the known types of resonators and of photonic crystal structures. It is found that for certain discrete sequences of propagation constant and interturn coupling, the light is completely trapped by the resonator. For N →∞, the COR spectrum experiences a fractal collapse to the points corresponding to the second order zero of the group velocity. For a relatively small coupling between turns, the COR waveguide behavior resembles that of a SCISSOR (side-coupled integrated spaced sequence of resonators), while for larger coupling it resembles that of a CROW (coupled resonator optical waveguide).

Smith-Purcell free electron laser and method of operating same

Abstract: A free electron laser for generating a Smith-Purcell radiation. In one embodiment, the free electron laser includes a grating having a grating surface, an electron emitter for generating a beam of electrons, and a guiding member positioned therebetween the electron emitter and the grating for directing the beam of electrons along a path extending over the grating surface of the grating with a focal point so that in operation a Smith-Purcell radiation and an evanescent wave are generated by interaction of the beam of electrons with the grating. In operation, the beam current of the beam of electrons is equal to or greater than a threshold current and the group velocity of the evanescent wave is substantially close to zero or negative so that the evanescent wave travels backward to allow electrons in the beam of electrons are bunched by interaction with the evanescent wave to substantially enhance the Smith-Purcell radiation over the range of wavelengths.

Near field acoustic holography with particle velocity transducers

Abstract: Near field acoustic holography is usually based on measurement of the pressure. This paper describes an investigation of an alternative technique that involves measuring the normal component of the acoustic particle velocity. A simulation study shows that there is no appreciable difference between the quality of predictions of the pressure based on knowledge of the pressure in the measurement plane and predictions of the particle velocity based on knowledge of the particle velocity in the measurement plane. However, when the particle velocity is predicted close to the source on the basis of the pressure measured in a plane further away, high spatial frequency components corresponding to evanescent modes are not only amplified by the distance but also by the wave number ratio (kz∕k). By contrast, when the pressure is predicted close to the source on the basis of the particle velocity measured in a plane further away, high spatial frequency components are reduced by the reciprocal wave number ratio (k∕kz). ...

Delay–bandwidth product and storage density in slow-light optical buffers

Abstract: The properties of slow-light optical delay lines, with low group velocity induced by electromagnetically induced transparency, population oscillations and photonic crystal filter structures, are analysed. It is shown that there are fundamental limitations on the delay–bandwidth product and the maximum storage density of data in slow-light devices.