Positive Kerr Nonlinearity Research Articles

The phase of darkness – measuring the phase of a dark pulse

Dark optical solitons are solutions to the nonlinear Schrödinger equation in normal dispersion media with positive Kerr nonlinearity, exhibiting a discrete π phase jump. These solitons are valuable to applications within telecommunication. Recent advancements have demonstrated the generation of two-colour bright-dark soliton pairs through cross-amplitude modulation in laser cavities, resulting in mode locking. In this study we present for the first time full field characterization of the electric field of a dark pulse. We achieved this by performing Blind Frequency Resolved Optical Gating measurements using the synchronous bright pulse as the gate pulse. The retrieved dark pulse verifies the existence of the expected π phase jump in the phase of the dark pulse, confirming theoretical predictions.

A thin-film waveguide problem with positive Kerr nonlinearity and its TM standing wave solution

In the previous work [1], we applied the scattering-type TM standing wave solution to a slab waveguide with negative Kerr nonlinearity. In this work, we analyzed a waveguide problem with positive Kerr nonlinearity. In our formalism, fields are expressed through the value of a dielectric function and a constant of non-flow integral of motion. We formulated the necessary boundary condition for both boundaries with no reference to a film thickness. The condition binds a dielectric function to have two equal or two different values at boundaries leading to the existence of symmetrically and asymmetrically fit wave pieces. Families of such standing wave solutions were constructed. The satisfactory boundary condition is implemented when we start to apply a film thickness to family data. The family of symmetrically fit wave pieces turned out to have a relatively complex structure due to two singularities in a dielectric function and three regions had to be analyzed separately. To look for matches within the data we presented two simple criteria that completely define the length-form and the number of standing wave solutions within a film. Afterward, a calculation of fitted solutions is straightforward.

Theory for the interaction of pure-quartic solitons

We theoretically studied the interaction of pure-quartic solitons resulting from the balance between the positive Kerr nonlinearity and the negative quartic dispersion. Based on the Hamiltonian of the nonlinear Schrödinger equation, we derived the analytic expression of the interaction potential, which plays a key role in predicting the evolution of the interacting pure-quartic solitons. The potential curve can be divided into several regions, in each of which it is easy to judge whether the interacting solitons are attracting, repealing, oscillating, or forming equilibrium bound states according to the curve shape therein.

Generalized self-similar propagation and amplification of optical pulses in nonlinear media with high-order normal dispersion

We investigate theoretically and numerically the self-similar propagation of optical pulses in the presence of gain, positive Kerr nonlinearity, and positive (i.e., normal) dispersion of even order $m$. Starting from a modified nonlinear Schr\"odinger equation, separating the evolution of amplitude and phase, we find that the resulting equations simplify considerably in the asymptotic limit. Exact solutions to the resulting equations indicate that the temporal intensity profile follows a $1\ensuremath{-}{T}^{m/(m\ensuremath{-}1)}$ function with an $m$-dependent scaling relation, with a ${T}^{1/(m\ensuremath{-}1)}$ chirp, where $T$ is the pulse's local time. These correspond to a triangle and a step function, respectively, as $m\ensuremath{\rightarrow}\ensuremath{\infty}$. These results are borne out by numerical simulations, although we do observe indications of nonasymptotic behavior.

Surface Waves at the Interface of a Photorefractive Crystal and a Medium with Positive Kerr Nonlinearity

The types of nonlinear surface waves with extraordinary polarization arising at the interface between a photorefractive crystal and a medium with positive Kerr nonlinearity are described. It has been shown that nonlinear surface waves of two types with an asymmetric profile can exist in such a system. Waves of the first type damp when moving away from the interface into the depth of the photorefractive and Kerr crystals without oscillations, while waves of the second type damp into the depth of a photorefractive crystal with oscillations. Dispersion relations have been obtained and the conditions for the existence of all described types of waves have been written depending on the optical characteristics of the crystals.

Поверхностные волны на границе фоторефрактивного кристалла и среды с положительной керровской нелинейностью

The types of nonlinear surface waves of extraordinary polarization that occur at the interface between a photorefractive crystal and a medium with positive Kerr nonlinearity are described. It is shown that nonlinear surface waves of an asymmetric profile of two types can exist in such a system. The waves of the first type decay when moving away from the interface without oscillations both in the depth of the photorefractive crystal and in the Kerr crystal, and the waves of the second type decay in the depth of the photorefractive crystal with oscillations. Dispersion relations are obtained, and the conditions for the existence of all the described types of waves are indicated depending on the optical characteristics of the crystals.

Suppression of self-focusing for few-cycle pulses

Intense beams of light propagating through a medium with a positive Kerr nonlinearity can undergo self-focusing provided that their average power is larger than a certain critical power determined by the wavelength and material properties of the medium. Here, we show that for pulses comprising only a few optical cycles, this self-focusing can be inhibited by the presence of significant (normal) dispersion. We derive simple expressions to quantify the threshold power for self-focusing in the presence of dispersion. In addition, we show that under certain conditions, this threshold power can be larger than conventional critical power (for a dispersionless case) by a factor as large as several hundred.

Stationary and dynamical properties of pure-quartic solitons.

We numerically solve a generalized nonlinear Schrödinger equation and find a family of pure-quartic solitons (PQSs), existing through a balance of positive Kerr nonlinearity and negative quartic dispersion. These solitons have oscillatory tails, which can be understood analytically from the properties of linear waves with quartic dispersion. By computing the linear eigenspectrum of the solitons, we show that they are stable, but that they possess a nontrivial internal mode close to the radiation continuum. We also demonstrate evolution into a PQS from Gaussian initial conditions. The energy-width scaling of PQSs differs strongly from that for conventional solitons, opening up possibilities for PQS lasers.

Effect of long-range correlated disorder on the transverse localization of light in 1D array of optical waveguides

In this paper, the effects of the long-range correlated diagonal disordered optical waveguide arrays in the presence and absence of the positive Kerr nonlinearity are analyzed numerically. The calculated inverse localization length shows that the long-range correlation in a disordered system causes a decrease in the transverse localization in linear optical waveguide arrays. In the presence of positive Kerr nonlinearity, the inverse localization length is increased by increasing the nonlinear parameters in long-range correlated disordered systems in comparison with the uniform distribution disordered systems. This means that the long range correlation causes an enhancement of transverse localization in nonlinear waveguides in contrast with linear waveguide arrays. The calculated participation ratio and effective beamwidth confirm these results for linear and nonlinear systems.

Nonlinear light propagation in the defect band of one-dimensional defective structures

In this paper we numerically investigate the nonlinear propagation of defect state in one-dimensional structures with defects. We investigate the nonlinear transmission spectra and the bistable response for defective structures with different index gradients. The results show that positive Kerr nonlinearity can suppress the Wannier–Stark localization. And the nonlinear response of defect states band exhibits an optical switch behavior, which may be applied to all-optical devices. And the gap solitons from these defect states are presented.

Self-guiding multimode interference threshold switch

We propose a new passive optical thresholding device that combines the principles of multimode interference (MMI) with self-guiding. The multimode region is composed of a nonlinear optical material that will support a self-guided beam (i.e., a material with a positive Kerr nonlinearity). The device operates by switching between the MMI mode of operation and the self-guiding mode of operation, depending on the input light intensity. We describe the basic principles of a self-guiding MMI device, simulate the device, and discuss design issues associated with these optically controlled optical switches.

Near two-photon resonance short pulse compression in atomic noble gases

We simulate a pulse compression mechanism based on a near two-photon resonance (NTPR) transition contribution to the nonlinear refractive index of atomic Noble gas filled hollow waveguides. The negative refractive index contribution in the normal dispersive gas waveguide plays a similar role as in the case of soliton compression with positive Kerr nonlinearity and anomalous dispersion in optical fibers. The self-pulse compression to ∼15 fs can be achieved at moderate peak powers (∼MW) for 100 fs pulses in the spectral range 100–245 nm. We present simulated data concerning pulse and spectral shapes for xenon as a case study. The total throughput of the propagated pulse energy is >90%, mostly determined by the linear attenuation of the hollow waveguide propagation mode while two-photon absorption and the corresponding enhanced three-photon photo-ionization does not significantly reduce the pulse energy.

Nonlinear refraction and optical limiting in [quotation mark]thick[quotation mark] media

We experimentally and theoretically investigate optical beam propagation in nonlinear refractive materials having a thickness greater than the depth of focus of the input beam (i.e., internal self-action). A simple model based on the constant shape approximation is adequate for analyzing the propagation of laser beams within such media under most conditions. In a tight focus geometry, we find that the position of the sample with respect to the focal plane, z, is an important parameter in the fluence limiting characteristics of the output. The behavior with z allows us to perform a sample Z-scan from which we can determine the sign and magnitude of the nonlinear refraction index. In CS2, we have used this method to independently measure the negative thermally induced index change and the positive Kerr nonlinearity with nanosecond and picosecond CO2 laser pulses, respectively. We have experimentally examined the limiting characteristics of thick CS2 samples that qualitatively agree with our analysis for both positive and negative nonlinear refraction. This analysis is useful in optimizing the limiting behavior of devices based on self-action.