Kit H. Chan

Demonstration of 20-Gb/s all-optical XOR gate by four-wave mixing in semiconductor optical amplifier with RZ-DPSK modulated inputs

We propose and demonstrate an all-optical XOR gate at 20 Gb/s using four-wave mixing in a semiconductor optical amplifier (SOA), with return-to-zero differential phase-shifted keying modulated input signals. With such constant intensity modulation format, the patterning-induced degradation in SOA is also alleviated. The proposed scheme is robust and feasible for optical logic operation at ultrahigh speeds.

An all-optical XOR logic gate for high-speed RZ-DPSK signals by FWM in semiconductor optical amplifier

All-optical exclusive-OR (XOR) logic gate is a basic and crucial element for optical signal processing. We propose and demonstrate a novel high-speed all-optical XOR gate based on four-wave mixing (FWM) in a semiconductor optical amplifier, with optical return-to-zero differential phase-shift keying (RZ-DPSK) input signals. With this constant-envelope modulation format, the patterning effect-induced signal degradation in semiconductor optical amplifier (SOA) is alleviated. The proposed XOR gate can accommodate both two-input and three-input logic operations, which offer better flexibility for cascaded all-optical processing. Experimental demonstrations at 10- and 20-Gb/s verified the logic integrity of the proposed XOR gate. In addition, the XOR output tolerance against temporal misalignment among the data inputs is also experimentally investigated

An all-optical packet header recognition scheme for self-routing packet networks

We proposed a serial-to-parallel conversion scheme for optical packet header processing. All-optical recognition of a three-bit packet header was demonstrated. The obtained parallel optical signal from the converter can be detected by low speed photodetector array, and can be used as switching control signal for the optical packet switch in a self-routing network node.

A Three-dimensional Spherical Nonlinear Interface Dynamo

A fully three-dimensional, nonlinear, time-dependent spherical interface dynamo is investigated using a finite-element method based on the three-dimensional tetrahedralization of the spherical system. The spherical interface dynamo model consists of four zones: an electrically conducting and uniformly rotating core, a thin differentially rotating tachocline, a uniformly rotating turbulent convection envelope, and a nearly insulating exterior. The four regions are coupled magnetically through matching conditions at the interfaces. Without the effect of a tachocline, the conventional nonlinear α2 dynamo is always stationary, axisymmetric, and equatorially antisymmetric even though numerical simulations are always fully three-dimensional and time dependent. When there is no tachocline, the azimuthal field is confined to the convection zone while the poloidal magnetic field penetrates into the radiative core. The effects of an interface dynamo with a tachocline having a purely axisymmetric toroidal velocity field are as follows: (1) the action of the steady tachocline always gives rise to an oscillatory dynamo with a period of about 2 magnetic diffusion units, or about 20 yr if the magnetic diffusivity in the convection zone is 108 m2 s-1; (2) the interface dynamo solution is always axisymmetric, selects dipolar symmetry, and propagates equatorward (for the assumed form of α) although the simulation is fully three-dimensional; (3) the generated magnetic field mainly concentrates in the vicinity of the interface between the tachocline and the convection zone; and (4) the strength of the toroidal magnetic field is dramatically amplified by the effect of the tachocline. Extensions of Cowlings theorem and the toroidal flow theorem to multilayer spherical shell regions with radially discontinuous magnetic diffusivities are presented.

Transcritical flow of a stratified fluid: The forced extended Korteweg–de Vries model

Transcritical, or resonant, flow of a stratified fluid over an obstacle is studied using a forced extended Korteweg–de Vries model. This model is particularly relevant for a two-layer fluid when the layer depths are near critical, but can also be useful in other similar circumstances. Both quadratic and cubic nonlinearities are present and they are balanced by third-order dispersion. We consider both possible signs for the cubic nonlinear term but emphasize the less-studied case when the cubic nonlinear term and the dispersion term have the same-signed coefficients. In this case, our numerical computations show that two kinds of solitary waves are found in certain parameter regimes. One kind is similar to those of the well-known forced Korteweg–de Vries model and occurs when the cubic nonlinear term is rather small, while the other kind is irregularly generated waves of variable amplitude, which may continually interact. To explain this phenomenon, we develop a hydraulic theory in which the dispersion ter...

On fluid motion in librating ellipsoids with moderate equatorial eccentricity

The motion of a homogeneous fluid of viscosity nu confined in a librating ellipsoidal cavity with semi-axes a and moderate equatorial eccentricity E is investigated. The ellipsoid rotates with an angular velocity Omega(0)(1 + d delta sin (omega) over capt), where Omega(0) is the mean rate of rotation, (omega) over cap is the libration frequency and Omega(0)delta represents the amplitude of longitudinal libration. When delta << E(2) and E(1/2) << E(2) << 1, where E is the Ekman number defined as E = nu/(a(2)Omega(0)), an explicit analytical solution describing fluid motion in librating ellipsoids is derived for any size of the libration frequency (omega) over cap. Three-dimensional numerical simulations of the same problem are also performed, revealing the generation of mean zonal flow in librating ellipsoidal cavities and showing a satisfactory agreement between the asymptotic and numerical analyses.

Mitigation of pattern-induced degradation in SOA-based all-optical OTDM demultiplexers by using RZ-DPSK modulation format

In this letter, we propose and demonstrate to employ return-to-zero differential phase-shifted-keying (RZ-DPSK) modulation format in optical time-division-multiplexing (OTDM) systems so as to mitigate the pattern-induced degradation in semiconductor optical amplifier-based all-optical demultiplexers. Experimental results prove that RZ-DPSK can effectively alleviate such impairment with negligible induced power penalty, and thus, is more robust than the conventional RZ ON-OFF keying modulation format in OTDM systems.

A routing loop control scheme in optical layer for optical packet networks

In future optical label switching (OLS) network, optical layer routing loop control is crucial for maintaining the network stability. In this paper, an optical loop control scheme using optical time to live (TTL) count down is proposed and experimentally demonstrated for the first time. Asynchronous TTL count-down up to 24 bits for 20-Gb/s packets is demonstrated.

Spherical Interface Dynamos: Mathematical Theory, Finite Element Approximation, and Application

Stellar magnetic activities such as the 11-year sunspot cycle are the manifestation of magnetohydrodynamic dynamo processes taking place in the deep interiors of stars. This paper is concerned with the mathematical theory and finite element approximation of mean-field spherical dynamos and their astrophysical application. We first investigate the existence, uniqueness, and stability of the dynamo system governed by a set of nonlinear PDEs with discontinuous physical coefficients in spherical geometry, and characterize the system by a saddle-point type variational form. Then we propose a fully discrete finite element approximation to the dynamo system and study its convergence and stability. For the astrophysical application, we perform some fully three-dimensional numerical simulations of a solar interface dynamo using the proposed algorithm, which successfully generates the equatorially propagating dynamo wave with a period of about 11 years similar to that of the Sun.

A nonlinear vacillating dynamo induced by an electrically heterogeneous mantle

This paper reports the first spherical numerical dynamo based on a three-dimensional finite element method. We investigate a nonlinear dynamo in a turbulent electrically conducting fluid spherical shell of constant electric conductivity surrounded by an electrically heterogeneous mantle. Magnetic fields in the form of a three-dimensional azimuthally traveling dynamo wave are generated by a prescribed time-dependent α in the fluid shell. In the inner sphere, we assume that there is a solid electrical conductor with the same conductivity as that of the fluid shell. Equilibration of the generated magnetic fields is achieved by the nonlinear process of α-quenching. We show for the first time that finite element methods can be effectively and efficiently employed to simulate three-dimensional dynamos in spherical systems. We also show that an electrically heterogeneous mantle can modulate the core dynamo, leading to a vacillating dynamo whose amplitude depends upon the relative phases between the generated magnetic field and the heterogeneous mantle.