Richard S. Tasgal

Solitons in a nonlinear optical coupler in the presence of the Raman effect

Abstract Using both an approximation and numerical simulations, we examine solitons in a dual-core nonlinear optical fiber in which the Raman effect acts. We find that the Raman effect restabilizes the symmetric soliton at large energies. It also allows quasi-stable asymmetric solitary waves to exist at smaller energies.

Creating very slow optical gap solitons with a grating-assisted coupler.

We show that optical gap solitons can be produced with velocities down to 4% of the group velocity of light using a grating-assisted coupler, i.e., a fiber Bragg grating that is linearly coupled to a non-Bragg fiber over a finite domain. Forward- and backward-moving light pulses in the non-Bragg fiber(s) that reach the coupling region simultaneously couple into the Bragg fiber and form a moving soliton, which then propagates beyond the coupling region. Two of these solitons can collide to create an even slower or stopped soliton.

Continuous-wave solutions in spinor Bose-Einstein condensates

We find analytic continuous wave (cw) solutions for spinor Bose-Einstein condenates (BECs) in a magnetic field that are more general than those published to date. For particles with spin F=1 in a homogeneous one-dimensional trap, there exist cw states in which the chemical potential and wavevectors of the different spin components are different from each other. We include linear and quadratic Zeeman splitting. Linear Zeeman splitting, if the magnetic field is constant and uniform, can be mathematically eliminated by a gauge transformation, but quadratic Zeeman effects modify the cw solutions in a way similar to non-zero differences in the wavenumbers between the different spin states. The solutions are stable fixed points within the continuous wave framework, and the coherent spin mixing frequencies are obtained.

THE RAMAN EFFECT AND SOLITONS IN AN ELLIPTICAL OPTICAL FIBER

We derive a general system of coupled nonlinear Schrodinger equations, describing light in a bimodal optical fiber, taking into account the quasi-instantaneous Raman effect, group-velocity birefringence, phase-velocity birefringence, and optical activity, and for light with general ellipticity. The Raman coefficients prove to obey a relation which depends on the ellipticity. When group-velocity birefringence and optical activity are both non-zero, polarization couples to the changing frequency, so soliton polarization cannot be held constant in this case. Without optical activity, there are solitons with constant polarization either entirely in one polarization (“simple”) or equally divided between the two polarizations (“vector”). At ellipticity angle 0° to 35.3°, the simple solitons are stable and the vector solitons are unstable, and vice versa for ellipticity angle 35.3° to 90°. With optical activity, the polarization can be constant, but with a rather more complex form. Stability is also examined, and bistability is found in some circumstances.

Gap-Acoustic Solitons: Slowing and Stopping of Light

Solitons are paradigm localized states in physics. We consider here gapacoustic solitons (GASs), which are stable pulses that exist in Bragg waveguides, and which offer promising new avenues for slowing light. A Bragg grating can be produced by doping the waveguide with ions, and imprinting a periodic variation in the index of refraction with ultraviolet light. The Bragg grating in an optical waveguide reflects rightward-moving light to the left, and vice versa, and creates a gap in the allowed frequency spectrum of light. Nonlinearities, though, add complications to this simple picture. While low intensity light cannot propagate at frequencies inside the band gap, more intense fields can exist where low-intensity fields cannot. An optical gap soliton is an intense optical pulse which can exist in a Bragg waveguide because the intensity and nonlinearity let it dig a hole for itself inside the band gap, in which it can then reside. Far from the center of the pulse, the intensity is weak, and drops off exponentially with distance from the center. The optical gap soliton structure can be stable, and can have velocities from zero (i.e., stopped light) up to the group-velocity of light in the medium. When one also considers the system’s electrostrictive effects, i.e., the dependence of the index of refraction on the density of the material, which is a universal light-sound interaction in condensed matter, one obtains GASs. These solitons share many of the properties of standard gap solitons, but they show many fascinating new characteristics. GASs have especially interesting dynamics when their velocities are close to the speed of sound, in which range they interact strongly with the acoustic field. GASs which are moving at supersonic velocities may experience instabilities which leave the GAS whole, but bring the velocity abruptly to almost zero. Furthermore, GASs may be made to change velocity by collision with acoustic pulses. Moving GASs may be retarded by the phonon viscosity, as well as by interaction with high wave number (Brillouin) acoustic waves. Thus, the opto-acoustic interactions provide the basis for a set of tools with which light in the form of a GAS can be slowed down and controlled. In contrast with other forms of slow or stopped light, GASs can exist at room temperature, in relatively unexotic materials. This makes the GAS an attractive form in which to create and work with slow and stopped light.

The Raman effect and solitons in an optical fibre with general ellipticity

We derive equations for the quasi-instantaneous Raman effect in a nonlinear bimodal optical fibre with arbitrary (linear, circular or mixed) ellipticity. A balance-equations approach using an appropriate ansatz for the solitons shape yields a set of ordinary differential equations which approximate the dynamics of the soliton in such an arbitrary ellipticity fibre with group-velocity birefringence, phase-velocity birefringence and linear cross-coupling. The latter two effects are the most general Hamiltonian linear terms without derivatives in the underlying partial differential equations and are identical in form to the terms which describe a periodic twist. When group-velocity birefringence and linear cross-coupling are both nonzero, the soliton cannot hold a constant polarization. If linear cross-coupling is zero, there are solitons with constant polarizations and . As the only term which couples the inter-mode phase difference to the other parameters, linear cross-coupling is a singular perturbation. With zero group-velocity birefringence and nonzero linear cross-coupling, a solitons polarization may be constant at up to four different values, depending on the soliton and fibre parameters. Regarding stability of the polarization angle: without linear cross-coupling, at ellipticity angles from (linear ellipticity) to , the and polarization solitons are stable and the soliton is unstable and vice versa for ellipticity angles between and (circular ellipticity). With nonzero linear cross-coupling, the behaviour is analogous, but only approximately; the solitons which transform continuously to polarizations and are stable when the ellipticity is to , but at more than the polarization cannot be constant in the first place. The soliton with polarization tends to be but is not always unstable for ellipticity angles of to and at greater than there is always a solution with a stable polarization. This implies the possible coexistence of two different types of solitons, both stable, thus opening a new avenue to bistability of optical solitons.

Vibration Modes of a Vector Soliton in a Nonlinear Optical Fiber

We analyze the dynamics of a vector soliton governed by a nearly integrable system of coupled nonlinear Schrodinger equations. Positing a Gausssian ansatz, we find a continuous family of solutions which approximate vector solitons with arbitrary polarization. We find three small vibrational eigenmodes, of which only two were previously known. At 45° polarization the new internal oscillation consists of antisymmetric oscillations of the soliton. At arbitrary polarization all three eigenmodes are given in an implicit form. We find, additionally, a threshold of the relative velocity of the two polarizations that leads to splitting of the arbitrarily polarized vector soliton.