Coherent Soliton Research Articles

Twisted Gaussian Schell-model solitons.

We show that a certain class of spatially partially coherent solitons, namely, twisted Gaussian Schell-model solitons, exists in a logarithmically saturable nonlinear medium with a noninstantaneous temporal response. Unlike previously reported Gaussian Schell-model solitons, those discussed here carry a position-dependent twist phase, which vanishes in the fully coherent limit. We demonstrate that the presence of the twist phase provides an opportunity for controlling the degree of spatial coherence of such solitons without affecting their intensity.

Exact soliton solutions, shape changing collisions, and partially coherent solitons in coupled nonlinear Schrödinger equations.

We present the exact bright one-soliton and two-soliton solutions of the integrable three coupled nonlinear Schrödinger equations (3-CNLS) by using the Hirota method, and then obtain them for the general N-coupled nonlinear Schrödinger equations ( N-CNLS). It is pointed out that the underlying solitons undergo inelastic (shape changing) collisions due to intensity redistribution among the modes. We also analyze the various possibilities and conditions for such collisions to occur. Further, we report the significant fact that the various partially coherent solitons discussed in the literature are special cases of the higher order bright soliton solutions of the N-CNLS equations.

Coherence enhancement of spatially incoherent light beams through soliton interactions

We show that the spatial coherence of a partially incoherent light beam can be greatly enhanced through an energy-conserving interaction with an incoherent or a coherent dark spatial soliton. Computer simulations show that during this process a portion of the incoherent beam is trapped within the dark notch of the dark soliton, thus forming a sharp intensity spike. In this region the correlation length dramatically increases by at least 2 orders of magnitude.

Unified model for partially coherent solitons in logarithmically nonlinear media

We investigate the propagation of a partially coherent beam in a nonlinear medium with logarithmic nonlinearity. We show that all information about the properties of the beam, as well as the condition for formation of incoherent solitons, can be obtained from the evolution equation for the mutual coherence function. The key parameter is the detuning $\ensuremath{\Delta}$ between the effective diffraction radius and the strength of the nonlinearity. Stationary partially coherent solitons exist when $\ensuremath{\Delta}=0$ and the nonlinearity exactly compensates for the spreading due to both diffraction and incoherence. For nonzero detunings the solitons are oscillating in nature, and we find approximate solutions in terms of elliptic functions. Our results establish an elegant equivalence among several different approaches to partially coherent beams in nonlinear media.

Asymmetric partially coherent solitons in saturable nonlinear media

We investigate theoretically properties of partially coherent solitons in optical nonlinear media with slow saturable nonlinearity. We have found numerically that such a medium can support spatial solitons which are asymmetric in shape and are composed of only a finite number of modes associated with the self-induced waveguide. It is shown that these asymmetric spatial solitons can propagate many diffraction lengths without changes, but that collisions change their shape and may split them apart.

Partially coherent solitons of variable shape in a slow Kerr-like medium: exact solutions.

We carry out a theoretical investigation of the properties of partially coherent solitons for media which have a slow Kerr-like nonlinearity. We find exact solutions of the Nth-order Manakov equations in a general form. These describe partially coherent solitons (PCSs) and their collisions. In fact, the exact solutions allow us to analyze important properties of PCSs such as stationary profiles of the spatial beams and effects resulting from their collisions. In particular, we find, analytically, the number of parameters that control the soliton shape. We present profiles which are symmetric as well as those which are asymmetric. We also find that collisions allow the profiles to remain stationary but cause their shapes to change.

Collision-induced shape transformations of partially coherent solitons

We present experimental results related to collisional properties of partially coherent solitons (PCSs). In experiments with a photorefractive crystal we show that collisions in nonlinear media cause the PCS comprised of few mutually incoherent soliton components to change its shape.

Partially Coherent Solitons on a Finite Background

We have found a new class of exact solutions for multicomponent partially coherent solitons in photorefractive media with a drift mechanism of nonlinear response. Their novel feature is that the composite $M$-component sech-shaped soliton is located on a constant-background plane wave. The solutions are characterized by two free parameters and these are related to the maximum intensity of the composite soliton and to the amplitude of the background.

Interaction of spatial photorefractive solitons

We present a review of our recent theoretical and experimental results on the interaction of two-dimensional solitary beams in photorefractive SBN crystals. We show that the collision of coherent solitons may result in energy exchange, fusion of the interacting solitons, the birth of a new solitary beam or the complete annihilation of some of them, depending on the relative phase of the interacting beams. In the case of mutually incoherent solitons, we show that the photorefractive nonlinearity leads to an anomalous interaction between solitons. Theoretical and experimental results reveal that a soliton pair may experience both attractive and repulsive forces, depending on their mutual separation. We also show that strong attraction leads to periodic collision or helical motion of solitons depending on initial conditions.

Partially Coherent Solitons of Variable Shape

We present analytical and numerical results related to partially coherent solitons (PCS) of a novel class. In effect, there is freedom to choose the shape of a PCS as it is governed by $2N\ensuremath{-}1$ parameters, where $N$ is the number of linear modes contributing to the soliton. In particular, we show that a PCS may have an asymmetric shape. The PCS shape becomes arbitrary in the limit of complete incoherence. Another remarkable new feature of a PCS is that collisions in Kerr-like media cause the PCS to change its shape, although each beam remains a stationary soliton after the collision.

Coherent exciton solitons in nonlinear lattices

Coherent soliton states are analysed using the equivalent Boson Hamiltonian for excitons. This equivalent Hamiltonian includes the exciton concentrations corresponding to the Tyablikov approximation in the theory of magnetism. Soliton spectra were derived depending on the intensity oflight source that creates solitons. Increased exciton concentration enhances the soliton stability.

Phase Transitions and the Internal Noise Structure of Nonlinear Schrödinger Equation Solitons

We predict phase-transitions in the quantum noise characteristics of systems described by the quantum nonlinear Schr\"odinger equation, showing them to be related to the solitonic field transition at half the fundamental soliton amplitude. These phase-transitions are robust with respect to Raman noise and scattering losses. We also describe the rich internal quantum noise structure of the solitonic fields in the vicinity of the phase-transition. For optical coherent quantum solitons, this leads to the prediction that eliminating the peak side-band noise due to the electronic nonlinearity of silica fiber by spectral filtering leads to the optimal photon-number noise reduction of a fundamental soliton.

Observation of a Raman-induced interpulse phase migration in the propagation of an ultrahigh-bit-rate coherent soliton train

Coherent soliton packets generated in a passively mode-locked fiber laser are transmitted through 23km of dispersion-decreasing fiber. We observe a shift of the phase difference between solitons that is due to intrapulse Raman scattering. We attribute the stability in propagation of these trains to a trade-off between minimizing soliton-soliton interactions by reduction of the pulse width and minimizing this Raman-induced phase migration, which can force the solitons into a deleterious attractive phase relationship. We are thus able to demonstrate the propagation of 177-Gbit/s soliton packets over a distance of 123 soliton periods.

Quantum statistics of fundamental and higher-order coherent quantum solitons in Raman-active waveguides.

The quantum dynamics of coherent optical pulses are studied using a nondiagonal coherent-state generalized $P$ representation including photon-phonon interactions. Photon-number squeezing of coherent quantum solitons using spectral filtering is theoretically predicted. It is shown that Raman noise does not significantly reduce photon-number squeezing produced by spectral filtering of 1-ps fundamental coherent quantum solitons in optical fibers. Coherent $Nsech$ pulses with $N>1$ can show a larger reduction in photon-number fluctuations even at room temperature. The reduction in quantum noise for $N>1$ is not restricted to photon number and an improvement of more than 3 dB is also found for the quadrature-phase squeezed soliton experiments using a fiber Sagnac interferometer at 77 K.

Bifurcation in a cw-pumped Brillouin fiber-ring laser: Coherent soliton morphogenesis.

Stability analysis allows the understanding of experimental steady and pulsed regimes observed in cw-pumped Brillouin fiber-ring lasers. The instantaneous acoustic response model proves to be singular, while the coherent stimulated-Brillouin-scattering (SBS) three-wave model yields a well-behaved Hopf bifurcation for a critical value of the feedback (several percent in intensity). The computed nonlinear dynamics shows self-organization of asymptotically stable Brillouin pulses, not depending on the initial noise. Further experiments support the bifurcation.

Status of R&D on optical fiber communications systems in China

Research and development in China on optical fiber communications systems, including traditional high bit rate, coherent, and optical soliton systems is described. Their potential for telecommunications systems applications are outlined.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Soliton mechanism of optical anisotropy photoinduction in Langmuir-Blodgett films

Nonlinear excitations (kinks and vortices) in layered molecular structures are investigated. Attention is paid to the role of interaction between orientational and translational degrees of freedom. A theoretical interpretation of the influence of linearly polarized light on ordering in Langmuir-Blodgett films is given. It is shown that changes in the interaction between molecules in the excited state with respect to the ground state cause their rearrangement in the layer. Intermolecular orientational and translational interactions provide a coherent and cooperative soliton character of the arrangement.

Weak-pulse-activated coherent soliton switching in nonlinear couplers

An optical-fiber nonlinear coupler may permit all-optical switching of a soliton pulse by a much weaker control pulse. The sharp switching characteristics of the entire soliton energy that are obtained by varying the peak power or the phase of the weak pulse do not critically depend on the exact values of the soliton power or relative phase.

Coherent states and solitons in alpha-helix

The applicability of Glauber's coherent states to the theory of solitons in molecular chains with exciton-phonon interaction is critically studied. The results of the analysis are applied to the particular case of alpha-helix.

Time dependence of quantum fluctuations in solitons

We investigate quantum fluctuations in coherent solitons propagating in a dispersive nonlinear waveguide. Optimal squeezing or noise reduction occurs for a local oscillator width near the soliton width in time, i.e., the quantum fluctuations are localized.