Saturable Nonlinear Media Research Articles

Switching behavior of a nonlinear Mach–Zehnder interferometer: Saturating nonlinearity

This paper uses the Beam Propagation Method to investigate numerically the switching behavior of a Nonlinear Mach–Zehnder Interferometer (NMZI). A saturating-type nonlinearity has been considered for the present investigations. It is shown that the input versus output characteristics change drastically when a Kerr type nonlinear medium is replaced by a saturating type nonlinear medium. In contrast to an NMZI with Kerr nonlinearity, where only quantitative behavior changes with NMZI length, quantitative as well as qualitative behaviors change in the case of a saturating nonlinearity. We propose an all-optical stabilizer and MZI with stable “ON” and “OFF” states on the basis of our investigation.

Spatial solitons in photonic lattices with large-scale defects**Project supported by the National Natural Science Foundation of China (Grant No. 10704067) and the Natural Science Foundation of Zhejiang Province, China (Grant No. Y6100381).

We address the existence, stability and propagation dynamics of solitons supported by large-scale defects surrounded by the harmonic photonic lattices imprinted in the defocusing saturable nonlinear medium. Several families of soliton solutions, including flat-topped, dipole-like, and multipole-like solitons, can be supported by the defected lattices with different heights of defects. The width of existence domain of solitons is determined solely by the saturable parameter. The existence domains of various types of solitons can be shifted by the variations of defect size, lattice depth and soliton order. Solitons in the model are stable in a wide parameter window, provided that the propagation constant exceeds a critical value, which is in sharp contrast to the case where the soliton trains is supported by periodic lattices imprinted in defocusing saturable nonlinear medium. We also find stable solitons in the semi-infinite gap which rarely occur in the defocusing media.

Broken ring solitons in Bessel optical lattices

We address the existence of ring solitons broken by several nodes in a defocusing saturable nonlinear medium with an imprinted Bessel optical lattice. Such a multipolelike soliton is composed of two or more arc patterns with opposite phase between the adjacent components. The width of existence domain is determined only by the saturation degree of medium. The maximum number of soliton components depends on the radius of the lattice ring, where they reside. Those novel solitons can be trapped entirely on any ring of the Bessel lattice provided that the lattice is modulated deep enough. This study offers a smooth transition from the multipole soliton to necklace soliton.

Mutual-focusing of two co-propagating beams and formation of trapped spatial breather pair in saturable nonlinear media

In this paper, using parabolic equation approach, coupled propagation of two coaxially co-propagating and mutually incoherent bright cylindrical beams in saturable nonlinear medium has been investigated. Considering the coupling coefficient equal to unity ( κ=1), a detailed account of formation of spatial soliton pair (i.e. both beams are stationary trapped) and spatial breather pair (i.e. width of each beam oscillates with the propagation distance) has been provided and existence of spatially trapped breather pair (i.e. average width of each breather of the pair does not change with the propagation distance) has been shown. Conditions of formation of trapped spatial breather pair and their existence line has also been revealed for arbitrary beam width ratio of the beams. It is revealed that spatial soliton pairs are just a special case of trapped breather pair. The regions (conditions) of mutual-focusing and mutual-defocusing of spatial soliton pair/breather pair have also been identified. Lastly, the law of trapped breather pair formation is proposed.

Exact bright and dark spatial soliton solutions in saturable nonlinear media

We present exact analytical bright and dark (black and grey) solitary wave solutions of a nonlinear Schrödinger-type equation describing the propagation of spatial beams in media exhibiting a saturable nonlinearity (such as centrosymmetric photorefractive materials). A qualitative study of the stationary equation is carried out together with a discussion of the stability of the solutions.

Modulated optical phase conjugation in rhodamine 110 doped boric acid glass saturable absorber thin films

The optical phase conjugation signal in nearly nondegenerate four wave mixing was studied using a rhodamine 110 doped boric acid glass saturable absorber nonlinear medium. We have demonstrated a narrow band optical filter (2.56±0.15Hz) using an optical phase conjugation signal in the frequency modulation of a weak probe beam in the presence of two strong counterpropagating pump beams in rhodamine 110 doped boric acid glass thin films (10−4m). Both the pump beams and the probe beam are at a wavelength of 488nm (continuous-wave Ar+ laser). The probe beam frequency was detuned with a ramp signal using a piezoelectric transducer mirror.

对数饱和非线性介质中的自洽多模高斯孤子解

对数饱和非线性介质中的自洽多模高斯孤子解

A numerical method for finding multiple co-existing solutions to nonlinear cooperative systems

In this paper, a local min-orthogonal method is developed to solve cooperative nonlinear elliptic systems for multiple co-existing solutions. A characterization of co-existing critical points of a dual functional is established and used as a mathematical justification for the method. The method is then implemented to numerically solve two coupled nonlinear Schrödinger equations which model spatial vector solitons propagating in a saturable bulk nonlinear medium for multiple co-existing solutions.

Optical transmittance of plane-parallel-faces saturable nonlinear media

The transmittance of saturable nonlinear media under plane-wave excitation is analyzed for a Fabry-Perot geometry. The medium response is studied in terms of both a squared-field amplitude modulus and a time-averaged Poynting vector modulus. It was observed that both cases provide similar transmittance for the parameter range considered. For the nonlinearity proportional to the time-averaged Poynting vector modulus, a simple analytical expression for transmittance is derived as an Airy-type pattern. This allows us to perform a global analysis on the optical properties in terms of the nonlinear parameters and medium thickness. Several types of behavior were found at different parameter regions. Bistability happens only for excitation intensities around the saturation value. Finally, some possible implications of our results for bistable solitons are proposed.

Interactions of partially incoherent spatial solitons in logarithmic saturable nonlinear media

The interactions of two partially incoherent spatial solitons in logarithmic saturable nonlinear media are investigated numerically based on the coherent density approach. Numerical simulations show that the interaction through cross-phase modulation (XPM) result in attraction, with the solitons going through each other, and these interactions are insensitive to their initial relative phase. Two equal-width solitons with different incoherence may repel each other and exchange energy. If the two equal-width solitons propagate collinearly they can linearly superpose and fuse into a steady composite partially incoherent spatial soliton. The interactions through self-phase modulation (SPM) are very sensitive to their initial relative phase and coherence, and can be changed from attraction to repulsion or vice versa. Some interesting numerical examples are presented to show how these interactions can be controlled by these parameters.

Propagation of a Mixture of Modes of a Laser Beam in a Medium with Saturable Nonlinearity

Propagation of a mixture of modes of a laser beam through a saturable nonlinear medium has been studied using JWKB method and the paraxial ray approximation. Two second order nonlinear coupled differential equations for the beam width parameters resembling equations of coupled nonlinear oscillators of unit mass are obtained. A scalar potential of the system has been formulated whose analysis yields some valuable information like existence of two critical values of the potential within which bound state of the system exists. From the stability analysis it has been found that the stable beam propagation depends on the ratio of intensities of the two modes. A threshold of power is defined. When beam power is above the threshold value the propagation is stationary.

Coupled spatial-soliton pairs in saturable nonlinear media

We present a simple and straightforward approach to investigate coupled spatial-soliton pairs of two copropagating mutually incoherent (i.e., both beams are fully spatially and temporally coherent, but are incoherent with respect to one another) light beams in saturable nonlinear media. The approach provides a deeper understanding of coupled spatial-soliton pairs and reveals many interesting features, including the entire existence curve of such solitons.

Interaction of noncollinear spatial solitons in a nonlinear optical medium

The effects caused by nonresonant nonlinear interaction between noncollinear self-focusing beams are considered in two-dimensional optical samples by use of multiscale analysis. An analytical expression for beam trajectory shifts that are due to mutual interaction is derived, and the range of parameters is given, beyond which the mentioned consideration fails. We compare our results with the naive geometrical-optics model. It is shown that these two approaches give the same results. This justifies use of the geometrical-optics approach to describe elastic and almost-elastic collision processes both in Kerr and saturable nonlinear media. The results we obtained could be useful for the design of phase independent nonlinear photonic switches and all-optical logic elements.

Single- and double-vortex vector solitons in self-focusing nonlinear media

We study two-component spatial optical solitons carrying an angular momentum and propagating in a self-focusing saturable nonlinear medium. When one of the components is small, such vector solitons can be viewed as a self-trapped vortex beam that guides either the fundamental or first-order guided mode, and they are classified as single- and double-vortex vector solitons. For such composite vortex beams, we demonstrate that a large-amplitude guided mode can stabilize the ringlike vortex beam which usually decays due to azimuthal modulational instability. We identify different types of these vector vortex solitons and demonstrate both vortex bistability and mutual stabilization effect.

Theory of incoherent optical solitons: beyond the mean-field approximation.

We present a general theory of partially coherent optical solitons in slow-responding nonlinear media that takes into account intensity fluctuations of the light sources generating such solitons. If intensity fluctuations of the source are negligible, the theory reduces to the previously reported mean-field theory of partially coherent solitons. However, when such fluctuations are significant, our theory shows that the properties of partially coherent solitons in saturable nonlinear media can be qualitatively different from those predicted by the mean-field theory.

Stable vortex and dipole vector solitons in a saturable nonlinear medium.

We study both analytically and numerically the existence, uniqueness, and stability of vortex and dipole vector solitons in a saturable nonlinear medium in (2+1) dimensions. We construct perturbation series expansions for the vortex and dipole vector solitons near the bifurcation point, where the vortex and dipole components are small. We show that both solutions uniquely bifurcate from the same bifurcation point. We also prove that both vortex and dipole vector solitons are linearly stable in the neighborhood of the bifurcation point. Far from the bifurcation point, the family of vortex solitons becomes linearly unstable via oscillatory instabilities, while the family of dipole solitons remains stable in the entire domain of existence. In addition, we show that an unstable vortex soliton breaks up either into a rotating dipole soliton or into two rotating fundamental solitons.

Spatial optical (2+1)-dimensional scalar- and vector-solitons in saturable nonlinear media

(2+1)-dimensional optical spatial solitons have become a major field of research in nonlinear physics throughout the last decade due to their potential in adaptive optical communication technologies. With the help of photorefractive crystals that supply the required type of nonlinearity for soliton generation, we are able to demonstrate experimentally the formation, the dynamic properties, and especially the interaction of solitary waves, which were so far only known from general soliton theory. Among the complex interaction scenarios of scalar solitons, we reveal a distinct behavior denoted as anomalous interaction, which is unique in soliton-supporting systems. Further on, we realize highly parallel, light-induced waveguide configurations based on photorefractive screening solitons that give rise to technical applications towards waveguide couplers and dividers as well as all-optical information processing devices where light is controlled by light itself. Finally, we demonstrate the generation, stability and propagation dynamics of multi-component or vector solitons, multipole transverse optical structures bearing a complex geometry. In analogy to the particle-light dualism of scalar solitons, various types of vector solitons can - in a broader sense - be interpreted as molecules of light.

Spatial optical (2+1)‐dimensional scalar‐ and vector‐solitons in saturable nonlinear media

Abstract(2+1)‐dimensional optical spatial solitons have become a major field of research in nonlinear physics throughout the last decade due to their potential in adaptive optical communication technologies. With the help of photorefractive crystals that supply the required type of nonlinearity for soliton generation, we are able to demonstrate experimentally the formation, the dynamic properties, and especially the interaction of solitary waves, which were so far only known from general soliton theory. Among the complex interaction scenarios of scalar solitons, we reveal a distinct behavior denoted as anomalous interaction, which is unique in soliton‐supporting systems. Further on, we realize highly parallel, light‐induced waveguide configurations based on photorefractive screening solitons that give rise to technical applications towards waveguide couplers and dividers as well as all‐optical information processing devices where light is controlled by light itself. Finally, we demonstrate the generation, stability and propagation dynamics of multi‐component or vector solitons, multipole transverse optical structures bearing a complex geometry. In analogy to the particle‐light dualism of scalar solitons, various types of vector solitons can ‐ in a broader sense ‐ be interpreted as molecules of light.

Internal oscillations and instability characteristics of (2+1)-dimensional solitons in a saturable nonlinear medium.

Two related problems on scalar (2+1)-dimensional solitons in a saturable nonlinear medium are investigated. The first one is the internal oscillations of fundamental (single-hump) solitons. Internal modes which cause these oscillations, both with and without angular dependence, are discovered. The visual effect of angle-dependent internal modes on the soliton can be a rotation or spatially uneven breathing of the perturbed soliton. These internal oscillations are very robust and persist for a very long distance. The second problem is the instability of double-hump and radially symmetric solitons. Unstable eigenmodes of these solitons are presented. Contrary to intuition, the instability growth rates decrease to zero when the soliton power becomes high. Thus the instability is strongly suppressed at high powers. This phenomenon is corroborated by our direct numerical simulations.

Generation of lattice structures of optical vortices

We demonstrate experimentally the generation of square and hexagonal lattices of optical vortices and reveal their propagation in a saturable nonlinear medium. If the topological charges of the vortices are of the same sign the lattice exhibit rotation, while if alternative, we observe stable propagation of the structures. In the nonlinear medium the lattices induce periodic modulation of the refractive index. Diffraction of a probe beam by this nonlinearity-induced periodic structure is observed.