Gap solitons in a medium with third-harmonic generation (original) (raw)
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Three-wave gap solitons in waveguides with quadratic nonlinearity
Physical Review E, 1998
A model of the second-harmonic-generating ((2)) optical medium with a Bragg grating is considered. Two components of the fundamental harmonic ͑FH͒ are assumed to be resonantly coupled through the Bragg reflection, while the second harmonic ͑SH͒ propagates parallel to the grating, hence its dispersion ͑diffraction͒ must be explicitly taken into consideration. It is demonstrated that the system can easily generate stable three-wave gap solitons of two different types ͑free-tail and tail-locked ones͒ that are identified analytically according to the structure of their tails. The stationary fundamental solitons are sought for analytically, by means of the variational approximation, and numerically. The results produced by the two approaches are in fairly reasonable agreement. The existence boundaries of the soliton are found in an exact form. The stability of the solitons is determined by direct partial differential equation simulations. A threshold value of an effective FH-SH mismatch parameter is found, the soliton being stable above the threshold and unstable below it. The stability threshold strongly depends on the soliton's wave-number shift k and very weakly on the SH diffraction coefficient. Stationary two-soliton bound states are found, too, and it is demonstrated numerically that they are stable if the mismatch exceeds another threshold, which is close to that for the fundamental soliton. At kϽ0, the stability thresholds do not exist, as all the fundamental and two-solitons are stable. With the increase of the mismatch, the two-solitons disappear, developing a singularity at another, very high, threshold. The existence of the stable two-solitons is a drastic difference of the present model from the earlier investigated (2) systems. It is argued that both the fundamental solitons and two-solitons can be experimentally observed in currently available optical materials with the quadratic nonlinearity.
Proceedings of the 4th International Conference on Photonics, Optics and Laser Technology, 2016
The existence and stability of quiescent solitons in a dual core optical medium, where the one core has only Kerr nonlinearity while the other has Bragg grating and dispersive reflectivity are investigated. Three spectral gaps are identified in the systems linear spectrum, in which both lower and upper band gaps overlap with one branch of the continuous spectrum for all values of normalized group velocity c in the linear core; and, the central band gap remains a genuine bandgap. Soliton solutions exist only in the lower and upper gaps. In the absence of dispersive reflectivity, stable solitons are only found in the upper bandgap. However, introduction of dispersive reflectivity significantly alters the stability characteristics of solitons and results in the stabilization of solitons in a portion of the lower bandgap.
Families of Bragg-grating solitons in a cubic–quintic medium
Physics Letters A, 2001
We investigate the existence and stability of solitons in an optical waveguide equipped with a Bragg grating (BG) in which nonlinearity contains both cubic and quintic terms. The model has straightforward realizations in both temporal and spatial domains, the latter being most realistic. Two different families of zero-velocity solitons, which are separated by a border at which solitons do not exist, are found in an exact analytical form. One family may be regarded as a generalization of the usual BG solitons supported by the cubic nonlinearity, while the other family, dominated by the quintic nonlinearity, includes novel "two-tier" solitons with a sharp (but nonsingular) peak. These soliton families also differ in the parities of their real and imaginary parts. A stability region is identified within each family by means of direct numerical simulations. The addition of the quintic term to the model makes the solitons very robust: simulating evolution of a strongly deformed pulse, we find that a larger part of its energy is retained in the process of its evolution into a soliton shape, only a small share of the energy being lost into radiation, which is opposite to what occurs in the usual BG model with cubic nonlinearity.
Optical-parametric-oscillator solitons driven by the third harmonic
Physical Review E, 2004
We introduce a model of a lossy second-harmonic-generating (χ (2) ) cavity externally pumped at the third harmonic, which gives rise to driving terms of a new type, corresponding to a cross-parametric gain. The equation for the fundamental-frequency (FF) wave may also contain a quadratic self-driving term, which is generated by the cubic nonlinearity of the medium. Unlike previously studied phase-matched models of χ (2) cavities driven at the second harmonic (SH) or at FF, the present one admits an exact analytical solution for the soliton, at a special value of the gain parameter. Two families of solitons are found in a numerical form, and their stability area is identified through numerical computation of the perturbation eigenvalues (stability of the zero solution, which is a necessary condition for the soliton's stability, is investigated in an analytical form). One family is a continuation of the special analytical solution. At given values of parameters, one soliton is stable and the other one is not; they swap their stability at a critical value of the mismatch parameter. The stability of the solitons is also verified in direct simulations, which demonstrate that the unstable pulse rearranges itself into the stable one, or into a delocalized state, or decays to zero. A soliton which was given an initial boost C starts to move but quickly comes to a halt, if the boost is smaller than a critical value C cr . If C > C cr , the boost destroys the soliton (sometimes, through splitting into two secondary pulses). Interactions between initially separated solitons are investigated too. It is concluded that stable solitons always merge into a single one. In the system with weak loss, it appears in a vibrating form, slowly relaxing to the static shape. With stronger loss, the final soliton emerges in the stationary form.
Gap solitons under competing local and nonlocal nonlinearities
Physical Review A, 2011
We analyze the existence, bifurcations, and shape transformations of one-dimensional gap solitons (GSs) in the first finite bandgap induced by a periodic potential built into materials with local self-focusing and nonlocal self-defocusing nonlinearities. Originally stable on-site GS modes become unstable near the upper edge of the bandgap with the introduction of the nonlocal self-defocusing nonlinearity with a small nonlocality radius. Unstable off-site GSs bifurcate into a new branch featuring single-humped, double-humped, and flat-top modes due to the competition between local and nonlocal nonlinearities. The mechanism underlying the complex bifurcation pattern and cutoff effects (termination of some bifurcation branches) is illustrated in terms of the shape transformation under the action of the varying degree of the nonlocality. The results of this work suggest a possibility of optical-signal processing by means of the competing nonlocal and local nonlinearities.
Vibrations and Oscillatory Instabilities of Gap Solitons
Physical Review Letters, 1998
Stability of optical gap solitons is analyzed within a coupled-mode theory. Lower intensity solitons are shown to always possess a vibration mode responsible for their long-lived oscillations. As the intensity of the soliton is increased, the vibration mode falls into resonance with two branches of the long-wavelength radiation producing a cascade of oscillatory instabilities of higher intensity solitons. [S0031-9007(98)
Quiescent Gap Solitons in Coupled Nonuniform Bragg Gratings with Cubic-Quintic Nonlinearity
Applied Sciences
We study the stability characteristics of zero-velocity gap solitons in dual-core Bragg gratings with cubic-quintic nonlinearity and dispersive reflectivity. The model supports two disjointed families of gap solitons (Type 1 and Type 2). Additionally, asymmetric and symmetric solitons exist in both Type 1 and Type 2 families. A comprehensive numerical stability analysis is performed to analyze the stability of solitons. It is found that dispersive reflectivity improves the stability of both types of solitons. Nontrivial stability boundaries have been identified within the bandgap for each family of solitons. The effects and interplay of dispersive reflectivity and the coupling coefficient on the stability regions are also analyzed.
Interaction Dynamics of Gap Solitons in Dual-Core Bragg Gratings With Cubic-Quintic Nonlinearity
IEEE Journal of Quantum Electronics, 2016
Interactions between quiescent gap solitons in dualcore Bragg gratings with cubic-quintic nonlinearity are systematically investigated. In a previous work it was found that the model supports symmetric and asymmetric soliton solutions. For each of these categories there exist two disjoint families of quiescent gap solitons. One family can be regarded as the generalization of the quiescent gap solitons in dual-core Bragg gratings with Kerr nonlinearity (called Type 1). On the other hand, the other family is found in the region where the quintic nonlinearity is dominant (called Type 2). The interactions of in-phase Type 1 asymmetric solitons result in a range of outcomes, namely, fusion into a single zero-velocity soliton, asymmetrical separation of solitons, symmetrical separation of solitons, formation of three solitons, and the destruction of solitons. In the case of symmetric solitons, interactions of in-phase Type 1 solitons may lead to fusion in the form of a quiescent soliton, asymmetrically separating solitons, or the formation of three solitons. It is also found that interaction of in-phase asymmetric Type 2 solitons results in their destruction. Also, the effects of the quintic nonlinearity, coupling coefficients, initial separation, and initial phase difference on the outcomes of the interactions are analyzed. Also, in the case of asymmetric solitons, the outcomes of the soliton-soliton interactions for specular-symmetric and cross-symmetric initial configurations are compared.
Proceedings of the 8th International Conference on Photonics, Optics and Laser Technology, 2020
The interaction of quiescent gap solitons in coupled fiber Bragg gratings with dispersive reflectivity and cubicquintic nonlinearity in both cores is investigated. It has been found that with low to moderate dispersive reflectivity the interactions have similar characteristics to the nonlinear Schrodinger solitons i.e. in-phase solitons always attract each other and out-of-phase solitons repel. It is found that the interaction of in-phase solitons may result in a number of outcomes such as formation of a quiescent soliton, generation of two separating solitons and formation of a quiescent and two moving solitons. For strong dispersive reflectivity, the interaction outcomes depend on the initial separation.