Minimum Group Velocity Research Articles

A new guided mode so-called minimum group velocity in viscoelastic sandwich plates: A parametric numerical study

Zero-Group-Velocity (ZGV) guided mode has recently received particular attention because of its highly sensitive to structural changes, such as defects. Parallel to ZGV, in the present work, we introduce a new guided mode so-called Minimum-Group-Velocity (MGV) that is a remarkable phenomenon in defect detection applications. Strictly speaking, when any two phase-velocity dispersion curves of Lamb modes approach each other without overlapping, we observe this new mode in group-velocity dispersion curves. It is worth noting that this MGV mode has never been addressed in literature. We compute the Lamb-like modes in asymmetric viscoelastic sandwich plates using the Stiffness Matrix Method (SMM). We show that the change in properties of this sandwich can dramatically affect frequency ranges associated with ZGV and MGV modes. However, a linear correlation between phase velocities and this change on viscoelastic properties is discussed, where we observed an interconnection phenomenon in the dispersion curves. This interconnection happens between specific points on the dispersion curves, each corresponding to a ZGV- or MGV-mode. On the other hand, we verify that the detection of changes in level of viscoelastic properties or variations in the thickness of the buffer viscoelastic layer is possible within a limited segment of the damped mode curve.

Flexible all-optical terahertz switch based on electromagnetically induced transparent-like metamaterial

The electromagnetically induced transparent-like metamaterials have received much attention because of their excellent slow-light properties and strong nonlinear effects. They have many promising applications in novel terahertz functional devices, high-sensitivity sensors, and optical storages. In this paper, a flexible terahertz switching device based on the electromagnetically induced transparent-like effect was proposed. The device exhibited a significant slow light phenomenon without pumped laser. Meanwhile, it is demonstrated that the device has a large modulation depth and excellent tunable slow light performance with low-power pumped laser. Its amplitude modulation depth can reach 60.4% and the group delay modulation can reach 32.5 ps. And the minimum group velocity of the device in slow terahertz light can reach 0.69 × 105 m/s. Moreover, the flexible substrate of the proposed device is not easily damaged. It makes the device suited for more complex environments well. Therefore, the device will have great potential for future research on high-performance terahertz switching devices.

Dynamic control over group speed of light in plasma cladded optical fiber: An analytical approach

The ability of plasma frequency to tune the guiding properties of plasma cladded optical fiber is explored and numerically investigated. The identified parameter to manipulate the propagation characteristics of the investigated structure is electron–ion density which can be controlled by varying electric potential. It is shown that the curve of group index vs optical signal frequency can be manipulated significantly by manipulating plasma frequency. Judicious consideration of fiber’s parameters and the values of plasma frequency allow for obtaining minimum or desired group velocity dispersion at a desired optical frequency. Further, ability of manipulation of the slope of group index vs signal frequency curve allows for dispersion management. Possibility of significant variation in group-index is the highlight of the present work and the most impressive feature is that it could be achieved in online condition (by varying plasma frequency with the help of tuning electric field). Since, ratio of plasma to signal frequency is the only important factor in manipulating the propagation properties, the idea presented here can be extended to frequency domains in the range of Terahertz, Microwaves etc. An optical modulator is proposed in the last section on the basis of present investigation.

Geoacoustic parameter estimation using machine learning techniques

The Airy phase region corresponding the minimum group velocity of the dispersive acoustic normal modes in shallow water are extremely sensitive to bottom properties. The group speed minima and the associated frequency data for two lower order modes were used to train a neural network to predict the bottom parameters in a previous study (Potty et al., 2019). The geoacoustic model for the bottom consisted of a sediment layer over acoustic basement. Synthetic data generated by varying the values of the sound speeds in the sediment layer and basement were used to train and evaluate the technique. The output of the neural network was used as the background model for a linear perturbation inversion. Data collected from the Shelf break Primer experiment were used to test the algorithm and the preliminary results were promising. This study will continue the previous work by incorporating higher order modes in the training data, testing with data from other experiments and using other machine learning techniques. The performance of this hybrid approach (neural network combined with linearized inversion) will be compared with fully non-linear inversion, both in terms of accuracy and computation time. [Work supported by the Office of Naval Research.]

New Soliton Solutions of Optical Pulse Envelope E(Z, τ) with Beta Time Derivative

This paper works on optical pulse envelope Ez,τ with beta time derivative that considers in the region of the minimum group-velocity dispersion. Integration algorithms recover soliton solutions. The methods are generalized Kudryashov method and modified exp −Ωξ -expansion function method. A complete spectrum of soliton solutions have thus arisen.

Dispersion tailoring of photonic crystal fibers for flat-top, coherent, and broadband supercontinuum generation

A double-clad AsSe2-based photonic crystal fiber possessing ultra-flat near-zero dispersion has been introduced, here to achieve flat-top and coherent supercontinuum generation at Mid-IR range. Also, the required conditions to obtain flat-top, broadband, and coherent supercontinuum generation have been discussed based on the systematic study carried out here, by GNLSE regarding the input pump pulse characteristics and the dispersion regime. The proposed photonic crystal fiber in this study, presents nearly-zero all-normal dispersion of about D ∼ −3.4 ps(nm.km)−1 corresponding to minimum group velocity dispersion at 6.9 μm. For the pump pulse with λ = 6.9 μm, time duration of T = 50 fs, and low peak power of P = 1 kW, a coherent flat-top supercontinuum generation has been realized with the span of 4.14 μm and 4.97 μm at 8 dB and 20 dB levels, respectively. Moreover, a figure of merit covering the essential characteristics of supercontinuum generation spectra (bandwidth, coherency, and flatness) has been introduced to compare the performance of different structures. It has been shown that β 2 tailoring with near-zero and flat characteristic is essential to achieve higher figure of merit.

Estimation of geoacoustic parameters using machine learning techniques

Modal dispersion of broadband acoustic data has been used extensively to estimate the geoacoustic parameters using perturbation techniques (Rajan et al., 1987), non-linear inversion techniques (Potty et al., 2000) and Bayesian inference (Warner et al., 2015). The Airy phase region corresponding the minimum group velocity of the normal modes are extremely sensitive to bottom properties in comparison with properties of the water column. This talk will explore the sensitivity of the group speed minima and the associated frequencies of the acoustic normal modes to bottom parameters. The group speed minima and the associated frequency data will be used to train a machine-learning algorithm. Synthetic data will be generated for various bottoms and it will be used as the training pool. Data collected from New England Bight, East China Sea, and New England Mud patch will be used to test the algorithm. The value added to the a priori bottom parameter information using the algorithm will be discussed in the context of computational cost associated with the algorithm. [Work supported by the Office of Naval Research.]

Dispersion characteristics of nonreciprocal gyroelectric silicon-on-insulator rectangular waveguide

A C-band rectangular waveguide with gyroelectric semiconductor is designed to study the non-reciprocal propagation characteristics of surface magnetoplasmons (SMPs), which are generated by an external magnetic field. The effective refractive index method is used to obtain the effective refractive index and transverse electric field distribution of the waveguide, and a two-dimensional rectangular waveguide is approximately regarded as a combination of two one-dimensional planar waveguides. The dispersion equation of planar waveguide with <inline-formula><tex-math id="M2">\begin{document}$ {\rm{E}}_{mn}^x$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="15-20190109_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="15-20190109_M2.png"/></alternatives></inline-formula> mode in rectangular waveguide is derived. The influences of the structural parameters of rectangular waveguide and the refractive index of material on the non-reciprocal dispersion relation and time-delay characteristics are analyzed by numerical method. Due to the effect of external magnetic field, the off-diagonal elements of dielectric tensor in magnetic photonic crystal are changed. The generation of electrical anisotropy leads the time reversal symmetry to be broken. As a result, the dispersion curves of the rectangular waveguide are asymmetric with respect to propagation constant, and the complete one-way transmission of SMPs can be realized in the asymmetric frequency region. The dispersion curve tends to be a dispersion curve of planar waveguide as the width of rectangular waveguide increases, but the non-reciprocal frequency range is approximately unchanged. The width of the core region and the refractive index of the side material have a significant influence on the non-reciprocal dispersion characteristics: the group velocity of SMPs decreases with <i>ω</i> and propagation constant decreasing. The group velocity is related to the waveguide width, propagation constant and the operating wavelength. The relationship between the normalized group velocity and the width of the waveguide separately operating at 1530, 1550 and 1565 nm are studied. The group velocity is relatively slow when the width of waveguide’s core region is between 140 nm and 233.5 nm, and the minimum group velocity reaches 5.43 × 10<sup>－2</sup><i>c</i>. As for the slow light effect, the rectangular waveguide is better than planar waveguide. The rectangular waveguide has a large engineering tolerance in the width of core region, which is 93.5 nm. In addition, the dispersion curves of the rectangular waveguide with SiO<sub>2</sub>, Air, Au and Ag as the left and right cladding layers are calculated. As a result, the group velocity is proportional to the refractive index of the side material in the <i>y</i> direction of the rectangular waveguide. The slow light effect is the most obvious when the material is silver, and the minimum transmission speed can reach 2.8 × 10<sup>－3</sup><i>c</i>.

Supercontinuum generation with femtosecond optical pulse compression in silicon photonic crystal fibers at 2500 nm

In this paper, femtosecond optical pulses compression and supercontinuum generation in a triangular silicon photonic crystal fiber at 2500 nm are investigated. A region of large minimum anomalous group velocity dispersion, negligible higher order dispersions and unique nonlinearity of silicon are used to demonstrate compression of 100 fs initial input optical pulses to 2.5 fs and ultra-broadband supercontinuum generation with very low input pulse energy over short distances of the fiber.

Mach-like capillary-gravity wakes.

We determine experimentally the angle α of maximum wave amplitude in the far-field wake behind a vertical surface-piercing cylinder translated at constant velocity U for Bond numbers Bo(D)=D/λ(c) ranging between 0.1 and 4.2, where D is the cylinder diameter and λ(c) the capillary length. In all cases the wake angle is found to follow a Mach-like law at large velocity, α∼U(-1), but with different prefactors depending on the value of Bo(D). For small Bo(D) (large capillary effects), the wake angle approximately follows the law α≃c(g,min)/U, where c(g,min) is the minimum group velocity of capillary-gravity waves. For larger Bo(D) (weak capillary effects), we recover a law α∼√[gD]/U similar to that found for ship wakes at large velocity [Rabaud and Moisy, Phys. Rev. Lett. 110, 214503 (2013)]. Using the general property of dispersive waves that the characteristic wavelength of the wave packet emitted by a disturbance is of order of the disturbance size, we propose a simple model that describes the transition between these two Mach-like regimes as the Bond number is varied. We show that the new capillary law α≃c(g,min)/U originates from the presence of a capillary cusp angle (distinct from the usual gravity cusp angle), along which the energy radiated by the disturbance accumulates for Bond numbers of order of unity. This model, complemented by numerical simulations of the surface elevation induced by a moving Gaussian pressure disturbance, is in qualitative agreement with experimental measurements.

Modeling Photonic Crystal Fiber for Efficient Soliton-Effect Compression of Femtosecond Optical Pulses at 850 nm

In this paper, we numerically investigate the dynamics of soliton-effect compression of femtosecond optical pulses in silica-core photonic crystal fiber (PCF) at 850 nm using both empirical relations method and symmetrized split-step Fourier method. We propose a novel nano-size silica PCF structure featuring a minimum anomalous group velocity dispersion, small higher-order dispersions and enhanced nonlinearity for efficient soliton-effect compression of femtosecond optical pulses with subnanojoule input pulse energies over small distances.

浅海混响互相关函数与格林函数的关系

Using the bistatic coherent reverberation model based on normal mode theory the effects of the reverberation time and the correlation integral time interval on the cross-correlation of the reverberations which received by two range-departed receivers in shallow water are analyzed in frequency domain. The possibility to retrieval Green’s function is also discussed in this paper. The result shows that the arrival-time structure of Green’s function can be recovered from the cross-correlation if the following conditions are satisfied: (1) the reverberation time is enough to make an approximate diffused field; (2) the correlation integral time interval is double at least of the time scale, the ratio of the maximum of inter-mode interference wavelength to the minimum modal group velocity; (3) the cross-term in the cross-correlation can be cancelled by a vertical source array.

Tunable all-optical delays in a fiber Bragg grating via the strain-tuning technique

A simple and cost-effective technique for generating tunable all-optical delays in a fiber Bragg grating (FBG) by using the strain-tuning method is proposed and experimentally demonstrated. The FBG imprinted in a common single-mode fiber, which is fixed to a strain-tuning setup, is adopted to implement the slow light system, and tunable delays of 0.97 ns and 0.92 ns can be realized by changing the strain and the light wavelength, respectively. The minimum group velocity can be m/s in the FBG, which is 8% of the light speed in vacuum. Experimental results agree well with the theory. The technique provides a very feasible way to control the light group velocity in fiber systems.

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.

Effects of the cross-phase modulation on the propagation of femtosecond optical pulses in photonic crystal fibers

The propagation of two femtosecond pulses in the region with minimum group-velocity dispersion, influenced by the cross-phase modulation (XPM) in photonic crystal fiber (PCF), is investigated in this paper. The adaptive split-step Fourier method is used to simulate the generalized nonlinear Schrodinger equations (GNSE). The numerical results show that the combination of the Raman scattering and XPM can make the spectrum and the pulse shape changed, inducing the pulse compression and supercontinuum generation. The Raman effect from molecular vibrations, which can make the pulse spectrum in anomalous-dispersion region to be more symmetrical, is also discussed.

Interfacial capillary–gravity waves due to a fundamental singularity in a system of two semi-infinite fluids

The interfacial capillary-gravity waves due to a transient fundamental singularity immersed in a system of two semi-infinite immiscible fluids of different densities are investigated analytically for two- and three- dimensional cases. The two-fluid system, which consists of an inviscid fluid overlying a viscous fluid, is assumed to be incompressible and initially quiescent. The two fluids are each homogeneous, and separated by a sharp and stable interface. The Laplace equation is taken as the governing equation for the inviscid flow, while the linearized unsteady Navier-Stokes equations are used for the viscous flow. With surface tension taken into consideration, the kinematic and dynamic conditions on the interface are linearized for small-amplitude waves. The singularity is modeled as a simple mass source when immersed in the inviscid fluid above the interface, or as a vertical point force when immersed in the viscous fluid beneath the interface. Based on the integral solutions for the interfacial waves, the asymptotic wave profiles are derived for large times with a fixed distance-to-time ratio by means of the generalized method of stationary phase. It is found that there exists a minimum group velocity, and the wave system observed will depend on the moving speed of the observer. Two schemes of expansion of the phase function are proposed for the two cases when the moving speed of an observer is larger than, or close to the minimum group velocity. Explicit analytical solutions are presented for the long gravity-dominant and the short capillary-dominant wave systems, incorporating the effects of density ratio, surface tension, viscosity and immersion depth of the singularity.

Far-field scattering microscopy applied to analysis of slow light, power enhancement, and delay times in uniform Bragg waveguide gratings

A novel method is presented for determining the group index, intensity enhancement and delay times for waveguide gratings, based on (Rayleigh) scattering observations. This far-field scattering microscopy (FScM) method is compared with the phase shift method and a method that uses the transmission spectrum to quantify the slow wave properties. We find a minimum group velocity of 0.04c and a maximum intensity enhancement of ~14.5 for a 1000-period grating and a maximum group delay of ~80 ps for a 2000-period grating. Furthermore, we show that the FScM method can be used for both displaying the intensity distribution of the Bloch resonances and for investigating out of plane losses. Finally, an application is discussed for the slow-wave grating as index sensor able to detect a minimum cladding index change of 10(-8), assuming a transmission detection limit of 10(-4).

Slow light waves at sonic propagation speed in active photonic lattices

Stimulated cross-cavity photon emission and carrier depletion in closely packed microlaser arrays supports the propagation of long-range intercavity oscillations in the coupled populations of coherent photons and carriers. The related periodic variations in the cavity radiation envelopes propagate as slow optical waves over the array at sonic group velocity. Externally driven excitation of such waves is investigated by numerical simulations and compared with theoretically obtained dispersion relation. While the theoretical minimum group velocity tends to zero at the lattice dispersion band edges, the requirement that the spatial decay constant be much smaller than the inverse lattice period limits the useful parameter regime. The lowest observed propagation velocities are of the order of the sound speed (km/s), a five order of magnitude reduction.

Localized propagation modes guided by shear discontinuities in photonic crystals

We propose and analyze shear discontinuities as a new type of defect in photonic crystals. This defect can support guided modes with minimum group velocity dispersion (GVD) and maximum bandwidth, provided that the shear shift equals half the lattice constant. A mode gap emerges when the shear shift is different than half the lattice constant. The shear shift can be used to tune the bandwidth, group velocity, and group velocity dispersion (GVD) of the guided mode. The necessary condition for the existence of guided modes along the shear plane is discussed.

Undular bore solution of the Camassa-Holm equation

Modulation theory is developed for a periodic peakon solution of the Camassa-Holm equation. An explicit simple wave solution of these modulation equations is then derived; this simple wave describing the evolution into an undular bore of an initial step. The characteristic on which the expansion fan occurs (propagating at a nonlinear group velocity) has a turning point, illustrating the fact that there is a minimum nonlinear group velocity at which the waves can propagate. A linear analytical solution, based on an integral of the Airy function, is then derived to describe the evanescent portion of the undular bore behind the turning point. Good agreement is found between the modulation theory plus Airy integral solution and numerical solutions.