Group Velocity Vg Research Articles

Effects of Mass Fluctuation on Thermal Transport Properties in Bulk Bi2Te3

In this paper, we applied large-scale molecular dynamics and lattice dynamics to study the influence of mass fluctuation on thermal transport properties in bulk Bi2Te3, namely thermal conductivity (К), phonon density of state (PDOS), group velocity (v g), and mean free path (l). The results show that total atomic mass change can affect the relevant vibrational frequency on the micro level and heat transfer rate in the macro statistic, hence leading to the strength variation of the anharmonic phonon processes (Umklapp scattering) in the defect-free Bi2Te3 bulk. Moreover, it is interesting to find that the anharmonicity of Bi2Te3 can be also influenced by atomic differences of the structure such as the mass distribution in the primitive cell. Considering the asymmetry of the crystal structure and interatomic forces, it can be concluded by phonon frequency, lifetime, and velocity calculation that acoustic-optical phonon scattering shows the structure-sensitivity to the mass distribution and complicates the heat transfer mechanism, hence resulting in the low lattice thermal conductivity of Bi2Te3. This study is helpful for designing the material with tailored thermal conductivity via atomic substitution.

Subluminal group velocity and dispersion of Laguerre Gauss beams in free space.

That the speed of light in free space c is constant has been a pillar of modern physics since the derivation of Maxwell and in Einstein’s postulate in special relativity. This has been a basic assumption in light’s various applications. However, a physical beam of light has a finite extent such that even in free space it is by nature dispersive. The field confinement changes its wavevector, hence, altering the light’s group velocity vg. Here, we report the subluminal vg and consequently the dispersion in free space of Laguerre-Gauss (LG) beam, a beam known to carry orbital angular momentum. The vg of LG beam, calculated in the paraxial regime, is observed to be inversely proportional to the beam’s divergence θ0, the orbital order ℓ and the radial order p. LG beams of higher orders travel relatively slower than that of lower orders. As a consequence, LG beams of different orders separate in the temporal domain along propagation. This is an added effect to the dispersion due to field confinement. Our results are useful for treating information embedded in LG beams from astronomical sources and/or data transmission in free space.

Effective group index of refraction in non-thermal plasma photonic crystals

Plasma photonic crystals (PPCs) are periodic arrays that consist of alternate layers of micro-plasma and dielectric. These structures are used to control the propagation of electromagnetic waves. This paper presents a survey of research on the effect of non-thermal plasma with bi-Maxwellian distribution function on one dimensional PPC. A plasma with temperature anisotropy is not in thermodynamic equilibrium and can be described by the bi-Maxwellian distribution function. By using Kronig-Penny's model, the dispersion relation of electromagnetic modes in one dimensional non-thermal PPC (NPPC) is derived. The band structure, group velocity vg, and effective group index of refraction neff(g) of such NPPC structure with TeO2 as the material of dielectric layers have been studied. The concept of negative group velocity and negative neff(g), which indicates an anomalous behaviour of the PPCs, are also observed in the NPPC structures. Our numerical results provide confirmatory evidence that unlike PPCs there are finite group velocity and non-zero effective group indexes of refraction in photonic band gaps (PBGs) that lie in certain ranges of normalized frequency. In other words, inside the PBGs of NPPCs, neff(g) becomes non-zero and photons travel with a finite group velocity. In this special case, this velocity varies alternately between 20c and negative values of the order 103c (c is the speed of light in vacuum).

Group velocity enhancement for guided lightwave by band-pulling effect in single-mode silicon comb photonic crystal wires

Photonic crystal waveguides (PCWs), which usually exhibit the slow-light effect near the band edge frequency, may in fact be used to induce higher group velocity (vg). The presence of the band edge, due to periodically carving a strip waveguide (SW) into a PCW of a comb-shape dielectric wire, results in the band-pulling effect. The band-pulling effect, which lifts the fundamental photonic band toward the band gap, not only enhances vg by reducing the effective index but also prevents the band from bending toward the light cone of the core material, leading to additional vg enhancement. The maximum PCW vg (0.43c; c = vacuum light speed) found from numerical modeling was higher than SW vg at all widths and thicknesses, except for extremely low thickness below 80 nm. We found by numerical modeling and experiments that up to 75% enhancement at the 1550 nm wavelength may be achieved in a fabricated single-mode PCW (0.38c) compared with an SW (0.21c) of the same width and thickness. The higher vg was confirmed by measuring the PCW’s group index using ring resonators. The PCW propagation loss of 2.1 dB mm−1 and the bandwidth-distance product of 100 Gb/s-cm were deduced from experimental results. Our findings seemed encouraging for employing PCWs in optical interconnect applications.

Group velocity in finite graphene superlattices

We have investigated the effects of finite crystal size on the electronic properties of infinite graphene superlattices. After deriving analytical expressions for the dispersion relation and group velocity vg in finite N-period graphene superlattices, we demonstrated that these properties can be dramatically modified by such effects, especially those directly associated with the band structure, such as the Dirac points and the wavevector dependent minigap situated in between them. In particular, it was shown that this minigap disappears and becomes a null-gap curve. It was also shown that the properties of vg differ substantially from those of the infinite superlattice. An interesting difference is that one of the components of vg may attain superluminal values. Our results provide a systematical procedure for describing and understanding the electronic transport and optical characteristics of any finite N-period graphene superlattices, such as the density of states, conductivity and absorption coefficient.

Proposal of Coupled Ring Resonator Based on One-Dimensional Photonic Crystal Nanocavity

We propose the coupled ring resonator based on one-dimensional photonic crystal (1-D PC) nanocavity. The proposed structure is composed by introducing 1-D PC nanocavity into the CROW based on ring resonator, and we expect that it can achieve small group velocity. We investigate the transmission characteristics of the proposed structure by using 2-D scalar finite element method (FEM) for periodic waveguide analysis. We obtained the group velocity vg = 0.033 c with c being light velocity in vacuum because of combining 1-D PC nanocavity and CROW based on ring resonator. Moreover, we consider reduction of footprint of the proposed structure for photonic integration.

Group velocity of the electromagnetic wave packet in a relativistic dispersive medium

This paper presents the fully relativistic, general expression for the group velocity Vg of the electromagnetic wave packet in a relativistic dispersive medium. Motion of the medium is accounted for with the relativistic index of refraction. The general formula for Vg is specialized to a few particular situations that are briefly discussed. The explicit, exact, fully relativistic expression for Vg is relevant to all issues where the electromagnetic wave packet travels through a medium in motion, especially where the velocity of the medium is high or utmost accuracy is essential, e.g. it pertains to the slow light phenomenon, pulsar radiation, GPS, radar, and LIDAR technologies.

Group velocity and nonlocal energy transport velocity in finite photonic structures

We have derived an explicit relation between the group delay velocity vgd(ω), determined by the slope of the dispersion curves, and the nonlocal energy transport velocity vE(ω) in a lossless, finite, one-dimensional photonic crystal. Using this relation, we find a simple link between vgd(ω) and the group velocity vg(ω)(ω) defined in terms of the electromagnetic dwell time. It is shown that vE(ω)≤vgd(ω) for any frequency and vE(ω)=vgd(ω)=vg(ω)(ω) at the resonance frequencies of the transmission coefficient. It was established that the band structure of a finite periodic crystal is of great importance to describe and understand the properties of these velocities. In particular, it was shown that the occurrence of superluminal group delay velocities in these structures is closely related to the existence of null gaps in their dispersion relation. Calculations performed for a half-wave-quarter-wave stack show that the energy velocity remains always subluminal.

STRUCTURE DEPENDENT VARIATIONS OF GROUP VELOCITY, ENERGY LOSS AND CONFINEMENT IN A REGULAR GRATED WAVEGUIDE

The Green's function method in the Dyson's formulation has been employed for the ab initio numerical study of structural effects on the device performances in terms of the minimum group velocity, energy loss and energy confinement in a quasi two-dimensional grated waveguide device model. The structure parameters to be varied in this work consist of the number of the grating teeth (N) and the grating groove depth (g). It is found that those parameters exhibit roughly linear and mostly monotonous variations at the lower resonance. The reduction of the group velocity and enhancement of energy confinement are also shown to be effectively attained by increasing N, while leaving the loss parameter relatively unaffected. On the other hand, the calculated results for the upper resonance wavelength are shown to exhibit consistently non-monotonous responses to increasing g. Similarly distinct behaviors are also found in the relationship between the minimum group velocity (vg, min) and the energy loss (L) as well as that between vg, min and the confined energy (W) for various N and g at the upper resonances. This peculiarly different behaviors are shown to be related to the variations of the associated local density of states with respect to N and g calculated for the upper resonance.

Slow packets of electromagnetic waves in magnetized plasma with ferrite grains

The propagation of narrow Gaussian electromagnetic wave packets in the collisionless magnetized plasma with ferrite grains (MPFG) is studied. In this system, in the frequency range close to the frequency of the electron cyclotron resonance, which coincides with the frequency of the ferromagnetic resonance, the dispersion of the electric permittivity (electron subsystem) and magnetic permeability (ferrite grain subsystem) must be taken into account simultaneously. The refractive index η of MPFG can be negative and with increase in frequency becomes positive passing through zero. The strong dispersion of η and the group velocity vg results in the spreading of the wave packets, which propagate with velocity much smaller than the speed of light. Their phase velocity is negative if η<0 and positive if η>0. For η<0, the group velocity can have a maximum at some frequency. The wave packets centered at this frequency are weakly spreading. The existence of slow waves in the frequency range, where η≤0, may be a general property of left handed media.

Exact dielectric constant of inhomogeneous crystal and its influence on propagation of electromagnetic (EM) wave: A quantum mechanical approach

We present an exact treatment of electromagnetic wave propagation in a crystal medium with varying dielectric constant via quantum mechanical approach. Quantum mechanical equation involving dielectric constant was defined for incoming linearly polarized monochromatic electromagnetic wave derived from a re-normalized relativistic Langrangian equation, . Considering that the spatial waveform of the field inside the field medium is not sinusoidal, we applied the Fourier transform to obtain the dispersion relation and as such, the group velocity vg of the waveform using the mean energy flux and energy density. The frequency of the forward propagating field and the reflected field that depicts the interaction of the field with the crystal, which on other hand explains the frequency range at which the crystal exhibit anti-reflection behavior, was also determined. Key words: Dielectric constant, quantum mechanical approach, inhomogeneous crystal, group velocity, Langrangian equation, Fourier transforms.

Evaluation of the Green’s function of disordered graphene

An accurate simulation of Green's function and self-energy function of non-interacting electrons in disordered graphenes are performed. Fundamental physical quantities such as the elastic relaxation time {\tau}e, the phase velocity vp, and the group velocity vg are evaluated. New features around the Dirac point are revealed, showing hints that multi-scattering induced hybridization of Bloch states plays an important role in the vicinity of the Dirac point.

Limitation of the electromagnetic cloak with dispersive material

Based on causality, the limitation of the electromagnetic cloak with dispersive material is investigated in this letter. The results show that perfect invisibility cannot be achieved because of the dilemma that either the group velocity Vg diverges or a strong absorption is imposed on the cloaking material. It is an intrinsic conflict which originates from the demand of causality. However, the total cross section can really be reduced through the approach of coordinate transformation. A simulation of finite-difference time-domain method is performed to validate our analysis.

Modeling of Loss-Induced Superluminal and Negative Group Velocity in Two-Port Ring-Resonator Circuits

The group velocity vg of light in two-port ring- resonator (TPRR) circuits with loss is theoretically studied. We point out four possible operation regimes, i.e., slow light with positive vg, slow light with negative vg, fast light with negative vg, and fast light with positive vg, where slow means |vg| c, with c denoting the velocity of light in vacuum. The temporal behavior of pulses passing through the TPRR for the four operation regimes and the potential of slow light TPRR either with positive or negative vg for sensing applications are also discussed.

Zero dispersion slow light with low leakage loss in defect Bragg fiber

By introducing a defect layer into the periodic cladding of Bragg fiber, the core mode and the defect mode may anticross near their cutoff inside band gap. The defect location suppresses and flattens dramatically the group velocity (vg) of coupled core mode and the defect thickness changes gradually its dispersion. Theoretical investigation reveals zero dispersion and zero dispersion slope at various low vg’s can be achieved simultaneously at arbitrary wavelengths. Specially, the proper defect in the sixth bilayer leads to the lowest vg of 0.074 of light speed in vacuum at 1550nm. The optical energy is confined well in the core and the leakage loss is sufficiently low.

A Memory-efficient Strategy for the FDTD Implementation Applied to the Photonic Crystals Problems

The Finite Difierence Time Domain (FDTD) method is well suited for the com- putation of the photonic crystals problems. However, this technique has the drawback of high computer memory requirements, when involving complex structures. In this paper, a modifled array implementation for the FDTD algorithm, with increased memory e-ciency, is presented and applied to studies on the abnormal refraction phenomena of the electromagnetic propagat- ing in the photonic crystals. The novel approach is based on memory-mapped flles, which is a mechanism of manipulating memory in Windows or Linux operating system. By using this mechanism, we make use of memory space more availably in allocating and implementing mul- tidimensional arrays for FDTD algorithm. The computed examples are given in the paper to prove the feasibility and accuracy of this strategy. A detailed discussion is presented for the case of the electromagnetic propagating in two-dimensional photonic crystals, formed by parallel air cylinders in a dielectric medium. The results show that some interesting relations can be obtained between the incident and the refraction angles with the group velocity (Vg) and the energy velocity (Ve).

Effect of third-order dispersion on subpicosecond pulse propagation in photonic-crystal waveguides

We have experimentally investigated the effects of dispersion on subpicosecond pulse propagation over two-dimensional (2D) photonic-crystal-slab line-defect waveguides by time domain measurements. Using a heterodyne detection technique, pulse shapes after propagating along the waveguide were recorded as cross-correlated traces. When the pulse central frequency approached the band edge of the guided mode, the pulses were temporally delayed and their shapes were found to be broadened asymmetrically; this effect originated from the group velocity dispersion (GVD), encompassing higher-order dispersion effects. Theoretical pulse shapes, including third-order dispersion (TOD), agreed well with the experimental results. When the group velocity (vg) reached 0.08c, c being the speed of light, we found a GVD of ∼5.0ps2∕mm and a TOD of ∼0.3ps3∕mm. Experimentally obtained vg, GVD, and TOD characteristics agreed well with those obtained from 2D plane-wave-expansion band calculations.

Experimental investigation of slow light propagation in degenerate two-level system

Slowing a light pulse in a degenerate two-level system is observed with a double-frequency sweeping technique. The effects of coupling beam intensity, cell temperature and frequency detunings of the coupling and probe beams in resonance, on the slowing of light propagation in such a system are investigated. It is found that group velocities depend strongly on polarization combinations. A group velocity vg=6760m/s of light pulses in caesium vapour is obtained under the optimal parameters.

Enhanced group velocity in composite media of particles with non-spherical shape or shape distribution

Effective medium approximation is derived to estimate the effective refractive index ne and the group velocity vg in two-phase composites in which one of the components is non-spherical, and even distributed in shape. Enhanced group velocity may be achieved through the suitable adjustment of the particles' shape and shape distribution. The range of the volume fractions, in which the group velocity is enhanced, will expand, once we take into account the non-spherical shape or the shape distribution. Therefore, the non-spherical shape and shape distribution play crucial roles in determining the group velocity in two-phase composites.

Calculation of propagation loss in photonic crystal waveguides by FDTD technique and Padé approximation

The propagation losses in single-line defect waveguides in a two-dimensional (2D) square-lattice photonic crystal (PC) consisted of infinite dielectric rods and a triangular-lattice photonic crystal slab with air holes are studied by finite-difference time-domain (FDTD) technique and a Padé approximation. The decaying constant β of the fundamental guided mode is calculated from the mode frequency, the quality factor (Q-factor) and the group velocity vg as β=ω/(2Qvg). In the 2D square-lattice photonic crystal waveguide (PCW), the decaying rate ranged from 103 to 10−4cm−1 can be reliably obtained from 8×103-item FDTD output with the FDTD computing time of 0.386ps. And at most 1ps is required for the mode with the Q-factor of 4×1011 and the decaying rate of 10−7cm−1. In the triangular-lattice photonic crystal slab, a 104-item FDTD output is required to obtain a reliable spectrum with the Q-factor of 2.5×108 and the decaying rate of 0.05cm−1.