Narrow Results

We theoretically study a ring-in-ring resonator which is coupled with a straight waveguide to yield coupled-resonator-induced transparency. Its absorption spectrum has a narrow transparency peak with respect to low group velocity, analogizing to that in electromagnetically induced transparency. The transparency peak, the phase difference between the split modes, dispersion, and group velocity can be controlled by changing reflection coefficients. Explicit expression of the group velocity at resonance are derived and discussed, the group velocity can be reached to 10⁴m/s-10⁶m/s orders of magnitude with proper choice of the parameters.

Electron group velocity for graphene under uniform strain is obtained analytically by using the tight-binding (TB) approximation. Such closed analytical expressions are useful in order to calculate the electronic, thermal and optical properties of strained graphene. These results allow to understand the behavior of electrons when graphene is subjected to strong strain and nonlinear corrections, for which the usual Dirac approach is no longer valid. Some particular cases of uniaxial and shear strain were analyzed. The evolution of the electron group velocity indicates a break-up of the trigonal warping symmetry, which is replaced by a warping consistent with the symmetry of the strained reciprocal lattice. To do this, analytical expressions for the shape of the first Brillouin zone (BZ) of the honeycomb strained reciprocal lattice are provided. Finally, the Fermi velocity becomes strongly anisotropic, i.e., for a strong pure shear strain (20% of the lattice parameter), the two inequivalent Dirac cones merge and the Fermi velocity is zero in one of the principal axis of deformation. We found that nonlinear terms are essential to describe the effects of deformation for electrons near or at the Fermi energy.

Based on the hexagonal honeycomb structure and the tri-ligament chiral honeycomb structure, this paper proposes a hybrid material structure with low-frequency elastic wave suppression below 100Hz. Based on the finite element method and Bloch’s theorem, the energy band structure was calculated, and the formation of the band gap and the wave-propagation properties of the structure were carefully studied, the wave attenuation performance of the composite structure was simulated, and the influence of material properties and geometric parameters on the width and position of the band-gap distribution was discussed. The results show that the structure can generate a good band gap in the low-frequency range of 100Hz, and the wave propagation is suppressed obviously. Demonstrating its potential in practical applications, the research in this paper provides a theoretical basis for the manufacture of low-frequency vibration damping equipment and instruments, and provides a scheme for the design of metamaterials with low-frequency band gaps.

Group velocity and dispersion property of slow light in one-dimensional photonic crystal with different defect layer thicknesses are studied. It is found that the increase of defect layer thickness will induce the decrease of group velocity, which is an advantage to the design of optical buffer. However, the dispersion slope is increased, inducing a limited factor to keep the shape of ultra-short pulses. Then the effect of slight violation of defect layer thicknesses, refractive index and incident angle on the slow light is studied. The result shows that these influences are smaller at the first gap which is useful for the practical uses.

In this paper, we proposed a model for controlling the group velocity of the transmitted and reflected pulses in a slab medium doped by four-level quantum dot nanostructure. Here, an infrared signal field interacted by quantum dot nanostructure can affect the behavior of reflected and transmitted pulses. We show that in the presence and absence of infrared pulses, the other controllable parameters have essential roles for controlling the slow and fast light propagation through the medium. Moreover, we found that the simultaneous slow and fast light can be obtained for the transmitted and reflected pulses by infrared signal field. Our proposed model may be useful for ultrahigh density optical memories in quantum communication systems or in various fields of all-optical systems.

Tunable phase control of the slow and fast light propagation through a defect slab medium doped by four-level InGaN/GaN quantum dot structure is demonstrated. By solving the Schrödinger and Poisson’s equations self-consistently, a spherical InGaN quantum dot with GaN barrier shell which can interact by terahertz (THz) signal field is designed numerically. It is found that the phase variation of THz signal field imparts the tunability in the group velocity of the transmitted and reflected pulses through a dielectric slab.

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 (v_{g, min}) and the energy loss (L) as well as that between v_{g, 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.

In this paper, the linearized form of the nonlinear mild-slope equations derived by Isobe (1994) is considered and analyzed for the dispersion, group velocity and shoaling characteristics. It is found that the dispersion relation is just a Padé's expansion of that obtained by the small amplitude wave theory. The agreement of the dispersion relation, group velocity and gradient of shoaling coefficient with the small amplitude wave theory is good from shallow to deep water even with small numbers of terms of the series in the mild-slope equations. The dispersion relation is also examined for evanescent waves. Furthermore, the vertical distribution functions for progressive and evanescent waves are analyzed and compared with the small amplitude wave theory. Then, the water depth limitation corresponding to the number of terms in the even-order polynomial vertical distribution functions is suggested.

The following sections are included:

• Introduction
• Light (Plane Wave)
• Realization of Pulse: Result of Interference
• Representation of a Pulse under SVEA
• Brief Summary
• Definition of Intensity
• Intensity of Ultrafast Pulse
• The Gaussian Pulse: Field Envelope vs. Intensity Envelope
• Time-Bandwidth Product (TBP)
• Characteristics of Ultrafast Pulses: Experimental Aspects
• Further Reading