Input Soliton Research Articles

QKD and QDC via optical–wireless link for quantum mobile telephone network application

We propose a novel system of the simultaneous continuous variable quantum key distribution (QKD) and quantum dense coding (QDC) using a soliton pulse within the nonlinear micro-ring resonator devices. By using the appropriate soliton input power and nonlinear micro-ring parameters, the continuous signals are generated spreading over the spectrum. The polarized photons are formed by using the polarization control unit incorporating into the micro-ring system, which is allowed the different time slot entangled photon pair randomly formed. Results obtained have shown that the application of such a system for the simultaneous continuous variable quantum cryptography and dense coding within a single system is plausible, which is can be implemented within the mobile telephone hand set and networks.

Continuous variable quantum key distribution via a simultaneous optical-wireless up–down-link system

We propose a remarkably simple system of a continuous variable quantum key distribution using chaotic signals generated by a soliton pulse within a nonlinear micro-ring resonator system. By using the appropriate soliton input power and micro-ring parameters, continuous signals are generated spreading over the spectrum. Polarized photons are formed incorporating the polarization control unit into the micro-ring system, which allows different time slot entangled photons to be randomly formed. Two different frequency bands for up–down-link converters can be selected (filtered) and performed, which is available for the simultaneous up–down-link application in the telephone networks. Results obtained have shown that the application of such a system for continuous variable quantum cryptography via optical-wireless up–down-link converters within a single system is plausible.

Discrete light bullets in two-dimensional photonic lattices: Collision scenarios

We report systematic results of collisions between discrete spatiotemporal optical solitons in two-dimensional photonic lattices. We show that the outcomes of collisions strongly depend on the initial soliton parameters, such as their input amplitudes (energies) and their transverse velocities. Four generic outcomes are identified in the study of collisions between discrete light bullets located in the corner, at the edge, and in the center of the photonic lattice: (a) merger of both low and high amplitude solitons into a single one, at small values of the kick parameter (soliton transverse velocity), (b) spreading of low amplitude solitons at intermediate values of the kick parameter, (c) bouncing of high amplitude solitons at intermediate values of the kick parameter, which is accompanied by a sharp modification of input soliton transverse velocities, and (d) quasi-elastic (symmetric) interactions of both low and high amplitude solitons at large values of the kick parameter.

The use of NOLM for investigations of initial development of supercontinuum in fibers with anomalous dispersion

We performed a numerical study of the transmission through a nonlinear optical loop mirror (NOLM) of a sequence of solitons generated at the initial stage of the supercontinuum (SC) generation. We found that the NOLM exhibits a selective transmission that critically dependents on the amplitude of the input solitons and on the NOLM loop length. The results demonstrate that by properly selecting these parameters the NOLM behaves as an optically controlled switch that allows the transmission of solitons with similar amplitude and width. The results obtained by employing this method are reasonably good and can be used to analyze the soliton formation at the initial stage of SC generation.

Chaotic soliton switching generation using a nonlinear micro ring resonator for secure packet switching use

We propose a new design of the secure packet switching device using the nonlinear behaviors of soliton in a micro ring resonator, where the nonlinear penalty of light traveling in the device becomes beneficial. The chaotic signals are generated by a Kerr effects nonlinear type of the input soliton pulse in a micro ring resonator, where the control input power can be used to specify the output filtering signals. Some device parameters are chosen and simulated using the proposed model. The potential of using such a device for communication security is performed and discussed. For instance, the packet switching of the chaotic encoding data increases from the chaotic signal encoding of 100 bits −1. Results obtained have shown the potential of using such a proposed device for the tunable bandpass and band-stop filters, in which packet switching data can be performed and secured.

Oscillation of spatial solitons in a waveguide with a symmetrical refractive index profile

Dynamics of (1+1)D spatial solitons in a Kerr medium with a transversely symmetrical refractive index profile is investigated. Propagation of solitons is analysed theoretically by using an effective-particle approach. Analytical results show that the soliton oscillates periodically with a variable acceleration. The expression of oscillatory period is derived by introducing a concept of 'average acceleration'. Both acceleration and oscillatory period are determined by the parameters of the input soliton and the waveguide. Propagations of solitons are simulated numerically and good agreement is obtained between the theoretical and numerical results.

Phase fluctuations of linearly chirped solitons in a noisy optical fiber channel with varying dispersion, nonlinearity, and gain

The phase fluctuations of arbitrarily nonlinearity- and dispersion-managed solitons propagating in a noisy fiber channel are studied both analytically and numerically. We begin by discussing the stability problem of such linearly chirped solitons with a full linear stability analysis. It is shown that these sophisticated solitons possess an enhanced stability against perturbations and therefore hold promise for applications in optical telecommunications. We then make an approach to the phase statistics of these solitons, which stems from an inevitable random walk in phase evolutions due to amplified spontaneous emission noise. By using the variational approach together with impulse-response (Green) functions, an elegant closed-form expression for the phase variance is derived based on an unconstrained self-similar soliton ansatz in which the effect of chirp fluctuations has been critically taken into account as well as the dispersive and nonlinear effects. An inspection of the intriguing subtleties of the interplay among these effects reveals that the chirp fluctuations effect does play an important role in the control of nonlinear phase noise via fiber dispersion, independently of whether the input solitons are initially chirped or not. Our analytical result also offers many possibilities of optimally manipulating nonlinear phase noise with engineered fiber parameters that may lead to the steady pulse propagation, broadening, or compression under favorable parametric conditions. Last, we demonstrate our result by several convincible examples and show an excellent agreement between analytical predictions and numerical simulations.

Higher-order soliton compression with pedestal suppression in nonlinear optical loop mirrors constructed from dispersion decreasing fibers

Compression of higher-order solitons in nonlinear optical loop mirrors (NOLMs) constructed from dispersion decreasing fibers (DDFs) is investigated numerically. Results show that when compared to a soliton-effect pulse compressor in which only a piece of DDF is used, a NOLM constructed from a DDF not only suppresses pulse pedestals but also significantly reduces frequency chirps of the compressed pulse. Furthermore, since both compression and pedestal suppression are realized in the same loop, the novel compressor not only is simpler and more compact but also less affected by higher-order effects as compared with the recently reported techniques based on DDF. For a given input pulse, there is an optimum loop length at which the best trade-off among the compression factor, pulse quality, and output peak power can be obtained. The proposed scheme works well for a broad range of input soliton orders.

Bistable soliton states and switching in doubly inhomogeneously doped fiber couplers

Switching between the bistable soliton states in a doubly and inhomogeneously doped fiber system is studied numerically. Both the cases of lossless as well as lossy couplers are considered. It is shown that both up-switching (from the low state to the high state) and down-switching (from the high state to the low state) of solitons between bistable states are realizable, if the amplification of the input soliton for up-switching and the extraction of energy from it for down-switching are suitably adjusted.

Switching between bistable states of a soliton in a doubly inhomogeneously doped fiber coupler

Switching of bistable solitons in a recently proposed doubly and inhomogeneously doped fiber system [Phys. Rev. E58, 5021 (1998)] is studied numerically. It is shown that both upswitching and downswitching of solitons between bistable states are realizable in the given model if the amplification of the input soliton for upswitching and the extraction of energy from it for downswitching are suitably adjusted.

Split-step solitons in long fiber links

We consider a long fiber-optical link consisting of alternating dispersive and nonlinear segments, i.e., a split-step model (SSM), in which the dispersion and nonlinearity are completely separated. Passage of a soliton (localized pulse) through one cell of the link is described by an analytically derived map. Multiple numerical iterations of the map reveal that, at values of the system's stepsize (cell's size) L comparable to the pulse's dispersion length z D, SSM supports stable propagation of pulses which almost exactly coincide with fundamental solitons of the corresponding averaged nonlinear Schrödinger (NLS) equation. However, in contrast with the NLS equation, the SSM soliton is a strong attractor, i.e., a perturbed soliton rapidly relaxes to it, emitting some radiation. A pulse whose initial amplitude is too large splits into two solitons; however, splitting can be suppressed by appropriately chirping the initial pulse. On the other hand, if the initial amplitude is too small, the pulse turns into a breather, and, below a certain threshold, it quickly decays into radiation. If L is essentially larger than z D, the input soliton rapidly rearranges itself into another soliton, with nearly the same area but smaller energy. At L still larger, the pulse becomes unstable, with a complex system of stability windows found inside the unstable region. Moving solitons are generated by lending them a frequency shift, which makes it possible to consider collisions between solitons. Except for a case when the phase difference between colliding solitons is ≲0.05π, the interaction between them is repulsive. We also simulate collisions between solitons in two-channel SSM, concluding that the collisions are strongly inelastic: even if the solitons pass through each other, they suffer a large reduction of the amplitude.

Cantor set fractals from solitons

We show how a nonlinear system that supports solitons can be driven to generate exact (regular) Cantor set fractals. As an example, we use numerical simulations to demonstrate the formation of Cantor set fractals by temporal optical solitons. This fractal formation occurs in a cascade of nonlinear optical fibers through the dynamical evolution from a single input soliton.

Transmission Characteristics of Multi-Soliton Train in Twin-Core Fiber

Transmission characteristics of multisoliton train are analyzed by numerical simulation in twin-core fiber. It is shown that stable transmission of multisoliton train requires some difference of initial relative phase and enough initial relative separation between input solitons under strong coupling between two cores.

Time Jitters in Multiple-Core Fiber of Ring Structure

Property of soliton propagation is analyzed by using self-companying operator method in multiple-core fiber of ring structure. The results show that the time jitters of soliton transmission in every core relate to the relative amplitude among the input solitons in the multiple-core fiber.

Time Jitters in Multiple-Core Fiber

Property of soliton propagation is analyzed by using self-companying operator method in every core of multiple-core fiber. The results show that the time jitters of soliton transmission in every core relate to the relative phase among the input solitons in multiple-core fiber.

SOLITON TRANSMISSION IN TWIN-CORE FIBER

Property of soliton propagation is analyzed by using self-companying operator method in twin-core fiber. The results show : Property of soliton transmission does some thing with the amplitude and relative phase of input solitons, and energy exchange is of periodicity, or non- periodicity.

Soliton amplification and reshaping by a second-harmonic-generating nonlinear amplifier

We have systematically investigated soliton amplification and reshaping by a nonlinear optical amplifier consisting of an active second-harmonic-generating element and a piece of passive dechirping fiber with a dispersion different from that in the system fiber. In the active element the fundamental harmonic is damped by enhanced losses, whereas the second harmonic is amplified through the external pumping. By selecting the length of the dechirping fiber we find it possible to achieve practically ideal soliton amplification, viz., low-power input (fundamental) solitons are amplified and then released into the system fiber as virtually unchirped high-power fundamental solitons. We have found that a power gain for the soliton of as much as 20–25 dB can be readily achieved; the length or the dispersion of the dechirping fiber is not critical for the degree of soliton amplification. The dispersion of this fiber can be merely twice that of the standard system fiber, and its length can be <10 km. Moreover, we have found that the dechirping fiber is not always needed, although the effective power gain in these cases is smaller, 10–12 dB. We have further investigated the influence of a random amplitude noise added to the input soliton. We found that the soliton amplification and reshaping scheme proposed is reasonably stable against this noise, especially when the dechirping fiber is not used.

Long-range soliton interactions in dispersion-managed links

A numerical analysis of soliton propagation in a dispersion-compensated transmission system reveals the presence of a small dispersive-wave contribution to the propagating soliton that increases dramatically whenever the input soliton energy is detuned from its optimal value. A straightforward consequence of the dispersive-wave emission is an unexpectedly strong contribution to the long-range soliton-soliton interaction. We show that the combination of long- and short-range interactions induces soliton timing jitter that grows larger than that which arises from the Gordon-Haus effect.

Reduction of the dispersive wave in periodically amplified links with initially chirped solitons

It is shown that a prechirping of the input solitons can reduce the dispersive wave created by the focal mismatch between linear and nonlinear effects on a link with large amplifier spacing (Z/sub A//spl ges/50 km) and a small dispersion length (Z/sub c/<Z/sub A/). This technique is shown to be compatible with the chirped (bandwidth limited) amplification and to increase its domain of application.

Gaussian beam to spatial soliton formation in Kerr media

We present a detailed analysis of the generation and propagation of bright spatial soliton beams in nonlinear Kerr media, in which an input beam is assumed to be of a Gaussian or hyperbolic secant form. The problem is solved by the use of the inverse-scattering transform (IST). The analysis of the discrete spectrum obtained from the direct-scattering problem gives exact information about the parameters of the generated soliton. A condition of soliton appearance in the spectrum as a function of the complex width of the initial Gaussian beam is given numerically. The similarities and differences between the hyperbolic secant and Gaussian beams entering the Kerr medium are analyzed in detail. A case is found in which almost all (approximately 99.5%) the total intensity of the Gaussian beam entering the Kerr medium is transformed into the soliton beam. However, this analogy to the self-trapping of soliton beams occurs for higher total-intensity values than in the case of the soliton input profile. The evolution from the Gaussian to the soliton envelope is studied and the condition of self-trapping in the near field is found. The numerical method based on the IST of the solution to the nonlinear Schrödinger equation is refined.