Intensity-dependent Dispersion Research Articles

Stability of Black Solitons in Optical Systems with Intensity-Dependent Dispersion

Stability of Black Solitons in Optical Systems with Intensity-Dependent Dispersion

Interplay between intensity-dependent dispersion and Kerr nonlinearity on the soliton formation.

A generalized nonlinear Schrödinger equation is studied with the interplay between Kerr nonlinearity and intensity-dependent dispersion. The supported soliton solutions are characterized analytically in different families by the pseudo-potential method, in terms of Maimistov and Cuspon solitons for different ratio between the intensity-dependent dispersion and Kerr nonlinearity. Direct numerical simulations also agree with our analytical formulas. In addition to the well-studied Kerr-type nonlinearity, our results reveal an unexplored scenario with the introduction of the nonlinear corrections to wave dispersion.

Solitary waves with intensity-dependent dispersion: variational characterization

A continuous family of singular solitary waves exists in a prototypical system with intensity-dependent dispersion. The family has a cusped soliton as the limiting lowest energy state and is formed by the solitary waves with bell-shaped heads of different lengths. We show that this family can be obtained variationally by minimization of mass at fixed energy and fixed length of the bell-shaped head. We develop a weak formulation for the singular solitary waves and prove that they are stable under perturbations which do not change the length of the bell-shaped head. Numerical simulations confirm the stability of the singular solitary waves.

Localization in optical systems with an intensity-dependent dispersion

We address the nonlinear Schrodinger equation with intensity-dependent dispersion which was recently proposed in the context of nonlinear optical systems. Contrary to the previous findings, we prove that no solitary wave solutions exist if the sign of the intensity-dependent dispersion coincides with the sign of the constant dispersion, whereas a continuous family of such solutions exists in the case of the opposite signs. The family includes two particular solutions, namely cusped and bell-shaped solitons, where the former represents the lowest energy state in the family and the latter is a limit of solitary waves in a regularized system. We further analyze the delicate analytical properties of these solitary waves such as the asymptotic behavior near singularities, the spectral stability, and the convergence of the fixed-point iterations near such solutions. The analytical theory is corroborated by means of numerical approximations.

Solitons supported by intensity-dependent dispersion.

Soliton solutions are studied for paraxial wave propagation with intensity-dependent dispersion. Although the corresponding Lagrangian density has a singularity, analytical solutions, derived by the pseudo-potential method and the corresponding phase diagram, exhibit one- and two-humped solitons with almost perfect agreement to numerical solutions. The results obtained in this work reveal a hitherto unexplored area of soliton physics associated with nonlinear corrections to wave dispersion.

Comparison of asymptotic and transfer matrix approaches for evaluating intensity-dependent dispersion in nonlinear photonic and phononic crystals

This paper analyzes intensity dependent dispersion of acoustic and electromagnetic waves in nonlinear one-dimensional (1D) periodic media. Media considered include layered 1D crystals characterized by constitutive laws with cubic strain nonlinearities (phononic), and by cubic time-dependent Kerr nonlinearities (photonic). A recently presented perturbation approach is generalized such that it can be successfully applied to the analysis of wave propagation in weakly nonlinear elastic and electromagnetic systems. In both, the analysis predicts amplitude-dependent dispersion leading to tunable bandgaps. These predictions are compared with those obtained from a simplified analysis conducted by linearizing the governing equations about an assigned field intensity followed by application of the transfer matrix method, as is commonly done in nonlinear photonic crystal studies. Comparison of the two methods generally shows good dispersion agreement; however, in phononic systems the transfer matrix analysis does not accurately capture high-strain behavior that occurs for some configurations, such as those with thin nonlinear layers, and may even predict erroneous bandgaps. Numerical predictions resulting from a finite-element analysis of the nonlinear media confirm the improved accuracy of the perturbation approach, suggesting its continued use for predicting intensity-dependent dispersion in 2D and 3D nonlinear phononic and photonic crystals.

Intensity-dependent dispersion under conditions of electromagnetically induced transparency in coherently prepared multistate atoms

Interest in lossless nonlinearities has focussed on the the dispersive properties of $\Lambda $ systems under conditions of electromagnetically induced transparency (EIT). We generalize the lambda system by introducing further degenerate states to realize a `Chain $ \Lambda $' atom where multiple coupling of the probe field significantly enhances the intensity dependent dispersion without compromising the EIT condition.

Measurement of third order nonlinear susceptibilities by surface plasmons

We have developed a novel technique which utilizes the intensity-dependent dispersion relation of surface plasmons to study the third order nonlinear susceptibility coefficient χ(3). This new technique yields information about both the magnitude and the sign (with respect to χ(1)) of χ(3). Experimental results are reported for GaAs and Si at input wavelengths of 1.05 and 1.11 μm, respectively.