Saturable Media Research Articles

Dynamics of stable solitons of circular Pearcey Gaussian beams in a photorefractive strontium barium niobate crystal.

We explore the behavior of abruptly autofocusing (AAF) beams in a saturable nonlinear medium. Stable solitons with different distribution structures are found under different combinations of external electric field and light field structure. Furthermore, the evolution of circular Pearcey Gaussian (CPG) beams in a photorefractive strontium barium niobate crystal is investigated. In particular, we fixed the external electric field to discuss the nonlinear propagation dynamics versus the initial light power. As the light power increases, the number of foci increases, and the distance between the foci decreases. Our study uncovers a fascinating interplay between AAF beams and the saturable nonlinear medium. We are convinced that the outcomes of our study may find potential applications in the realms of optical communication and photonic-integrated devices.

Silent white light: Reduction of the second-order intensity correlation coefficient

We investigate the intrawaveguide statistics manipulation of broadband light by combining semiconductor quantum dot physics with quantum optics. By cooling a quantum dot superluminescent diode to the liquid nitrogen temperature of 77 K, Blazek [] have demonstrated a temperature-dependent reduction of the second-order intensity correlation coefficient from 2 for thermal amplified spontaneous emission light to g(2)(0,T=190K)≈1.33. Here, we model the broadband photon statistics assuming amplified spontaneous emission radiation in a pumped, saturable quantum dot gain medium. We demonstrate that, by an intensity increase due to the quantum dot occupation dynamics via the temperature-tuned quasi-Fermi levels, together with the saturation nonlinearity, a statistics manipulation from thermal Bose-Einstein statistics towards Poissonian statistics can be realized, thus producing “silent white light” with a reduced second-order correlation coefficient. Such intensity-noise-reduced broadband radiation is relevant for many applications such as optical coherence tomography, optical communication, or optical tweezers. Published by the American Physical Society 2024

Parabolic and rectangular self-similar evolution in saturable media

Parabolic and rectangular self-similar evolution in saturable media

Shock waves in semi-infinite photonic lattices

We investigate the existence, stability and propagation dynamics of shock waves existing in defocusing saturable media modulated by a semi-infinite photonic lattice. Such surface waves consist of modulationally stable pedestals in bulk media and decaying oscillatory tails in semi-infinite photonic lattices. Due to Bragg-type reflection, they are strongly localized at the edge of the optical lattice. The kink steepness, pedestal height and localization degree can be controlled by propagation constant, saturable degree and lattice depth. Two types of kinks, i.e., “out-of-phase” and two branches of “in-phase” shock waves are revealed. Out-of-phase shock waves are stable in a substantial part of their existence domain. While the lower-branch in-phase waves with low energy flow are stable in almost their whole existence domain, the higher-branch in-phase waves are completely unstable. We thus show the first example of stable in-phase shock waves in nonlinear optics. Our findings provide new insight into the dynamics of semi-localized nonlinear surface shock waves or kink solitons.

Anomalous interaction of Pearcey Gaussian pulse in saturable nonlinear media

The dynamics of the mutual interaction of two temporally separated Pearcey Gaussian (PG) pulses in a saturable nonlinear medium is investigated. According to the temporal separation, relative phase, and saturation coefficient of the two pulses, we observed attraction or repulsion between PG pulses. The attraction leads to the generation of breathing solitons whose period increases linearly with the saturation parameter. By adjusting the pulse separation, the change of the initial interference makes the two pulses transmit without mutual interference. We also find that the repulsion makes the two pulses separate, and the interval decreases with the saturable parameter. We also investigate the impact of quadratic chirp imposed on the input pulse on the interaction dynamics. Our results reveal a novel scenario for PG pulses interaction in the nonlinear Schrödinger equation and provide an alternative mechanism to control breather soliton generation.

Modulational instability in nonlinear saturable media with competing nonlocal nonlinearity.

The modulational instability (MI) phenomenon is addressed in a nonlocal medium under controllable saturation. The linear stability analysis of a plane-wave solution is used to derive an expression for the growth rate of MI that is exploited to parametrically discuss the possibility for the plane wave to disintegrate into nonlinear localized light patterns. The influence of the nonlocal parameter, the saturation coefficient, and the saturation index are mainly explored in the context of a Gaussian nonlocal response. It is pointed out that the instability spectrum, which tends to be quenched by the high nonlocality parameter, gets amplified under the right choices of the saturation parameters, especially the saturation index. Via direct numerical simulations, confirmations of analytical predictions are given, where competing nonlocal and saturable nonlinearities enable the emergence of trains of patterns as manifestations of MI. The comprehensive parametric analysis carried out throughout the numerical experiment reveals the robustness of the obtained rogue waves of A- and B-type Akhmediev breathers, as the nonlinear signature of MI, providing the saturation index as a suitable tool to manipulate nonlinear waves in nonlocal media.

Modulational Instability of Optical Vortices in Engineered Saturable Media

Propagation of light beams in turbid media such as underwater environments, fog, clouds, or biological tissues finds increasingly important applications in science and technology, including bio-imaging, underwater and free-space communication technologies. While many of these applications traditionally relied on conventional, linearly polarized Gaussian beams, light possesses many degrees of freedom that are still largely unexplored, such as spin angular momentum (SAM) and orbital angular momentum (OAM). Here, we present nonlinear light–matter interactions of such complex light beams with “rotational” degrees of freedom in engineered nonlinear colloidal media. By making use of both variational and perturbative approach, we consider non-cylindrical optical vortices, elliptical optical vortices, and higher-order Bessel beams integrated in time (HOBBIT) to predict the dynamics and stability of the evolution of these beams. These results may find applications in many scenarios involving light transmission in strongly scattering environments.

Suppression of Nonlinear Optical Rogue Wave Formation Using Polarization-Structured Beams.

A nonlinear self-focusing material can amplify random small-amplitude phase modulations present in an optical beam, leading to the formation of amplitude singularities commonly referred to as optical caustics. By imposing polarization structuring on the beam, we demonstrate the suppression of amplitude singularities caused by nonlinear self-phase modulation. Our results are the first to indicate that polarization-structured beams can suppress nonlinear caustic formation in a saturable self-focusing medium and add to the growing understanding of catastrophic self-focusing effects in beams containing polarization structure.

Complex dynamics of perturbed solitary waves in a nonlinear saturable medium: A Melnikov approach

Objective:To investigate the nonlinear dynamics of a periodically perturbed second-order ordinary differential equation obtained by using traveling wave variables in the model of pulse propagation in a nonlinear medium with saturation. Method:The Melnikov function of the investigated system along its homoclinic and heteroclinic orbits is constructed. It is established that the necessary condition for the occurrence of Melnikov chaos is always met. By analogy with the well-known Duffing equation, a damping term is added to the system to control chaos. Using the numerical calculation of the Melnikov integrals, conditions are found on the parameters of the new system for which the Melnikov chaos takes place. To verify the results obtained by the Melnikov method, attraction basins of the system are constructed. Results:The results obtained by the Melnikov method go in agreement with the structure of the constructed basin boundaries.

Bistable soliton switching dynamics in a PT -symmetric coupler with saturable nonlinearity

We investigate the switching dynamics in a $\mathcal{PT}$-symmetric fiber coupler composed of a saturable nonlinear material as the core. In such a saturable nonlinear medium, bistable solitons may evolve due to the balance between dispersion and saturable nonlinearity, which we extend in the context of the $\mathcal{PT}$-symmetric coupler. Our investigations of power-controlled and phase-sensitive switching show richer soliton switching dynamics than the currently existing conventional counterparts, which may lead to ultrafast and efficient all-optical switching dynamics at very low power owing to the combined effects of $\mathcal{PT}$ symmetry and saturable nonlinearity. In addition to the input power, the relative phase of the input solitons and saturable coefficient are additional controlling parameters that efficiently tailor the switching dynamics. Also, we provide a suitable range of system and pulse parameters that would be helpful for the practical realization of the coupler to use in all-optical switching devices and photonic circuits. Finally, we develop a variational approach to analytically investigate the switching dynamics in such $\mathcal{PT}$-symmetric couplers that excellently predicts the numerical findings.

Bistable reflection and beam shifts with excitation of surface plasmons in a saturable absorbing medium.

We investigate the nonlinear reflection of a light beam from a Kretschmann configuration with saturable absorbing medium. The absorption of medium has direct influence on the intrinsic loss of the system, thus affecting the reflectivity and the phase variation when the surface plasmons are resonantly excited. As the incident power changes, the reflectivity can be switched between high and low values and exhibits absorptive optical bistability as a result of the inherent positive feedback by the intensity-dependent saturation effect. The Goos-Hänchen and the Imbert-Fedorov shifts of the reflected beam have the same bistable behavior as the reflectance. The effects of the thickness of metal film and the linear absorption coefficient on the hysteresis loop are analyzed in detail by considering the system losses and the saturated absorption. The bistable reflection and beam shifts may have applications in all-optical devices, such as optical switching.

The evolution of the solitons in periodic photonic moiré lattices controlled by rotation angle with saturable self-focusing nonlinearity media

We explored the evolution and stability of solitons formed by a Gaussian beam excited on-site in periodic photonic moiré lattices controlled by an angle with saturable self-focusing nonlinearity medium of lower applied bias, which makes use of the square lattices as a reference. When we introduce the rotation angle (), which satisfies the Pythagorean theorem and is commensurable, it will create a new lattice structure by rotating and superimposing two square lattices of the same period, which we called periodic photonic moiré lattices. Its energy band structure is special, which includes the flat band, and even opens the higher band-gap compared with square lattices. On the other hand, when we reduce the applied bias of the crystal, periodic photonic moiré lattices can still suppress the diffraction behaviour of Gaussian beam effectively and realize light localization by contrast with square lattices. Moreover, we proved the stability of the solitons formed by the Gaussian beams excited on-site in periodic photonic moiré lattices and revealed that the solitons could keep stable, but their stability regimes depend on the rotation angle shrinks and belong to the different bandgap. The discovery of the photonic moiré lattice provides a fresh approach for suppressing the diffraction behaviour of light and reduces the requirement for nonlinearity, which is beneficial for the diversity of our crystal material selection, and also provides a new way to manufacture high-efficiency optoelectronic devices.

Bright and dark solitons in a nonlinear saturable medium

The generalized nonlinear Schrödinger equation for description of optical solitons in a saturable medium is studied. The transformation variables are used for finding solitary wave solutions. Optical solitons for the description of pulse propagation are obtained in the form of implicit functions. Analytical solutions of the generalized nonlinear Schrödinger equation obtained for bright and dark solitons in a saturable medium are demonstrated.

Interaction of Airy Beams and Soliton in Saturable Nonlinear Medium

Interaction of Airy Beams and Soliton in Saturable Nonlinear Medium

Optical solitons in a saturable nonlinear medium in the presence of an asymmetric complex potential

We report on the existence of families of stable spatial solitons in a saturable nonlinear medium characterized by a refractive index with asymmetric distribution of gain and loss. The properties of the nonlinear modes bifurcating from the eigenvalue of the underlying linear problem are thoroughly investigated. The eigenvalue ranges in the power-eigenvalue diagrams for different gain/loss profiles are inspected. We find that the saturable nonlinearity severely restricts these ranges, as the eigenvalues tend to move quite fast to an asymptotic profile, as power increases. Numerical simulations of the wave equations are carried out and examples of the dynamics of the asymmetric solitons obtained exhibit a remarkable agreement with the analytic stability results.

Formation of dispersive shock waves in a saturable nonlinear medium.

We use the Gurevich-Pitaevskii approach based on the Whitham averaging method for studying the formation of dispersive shock waves in an intense light pulse propagating through a saturable nonlinear medium. Although the Whitham modulation equations cannot be diagonalized in this case, the main characteristics of the dispersive shock can be derived by means of an analysis of the properties of these equations at the boundaries of the shock. Our approach generalizes a previous analysis of steplike initial intensity distributions to a more realistic type of initial light pulse and makes it possible to determine, in a setting of experimental interest, the value of measurable quantities such as the wave-breaking time or the position and light intensity of the shock edges.

Blow-up and bounded solutions for a semilinear parabolic problem in a saturable medium

The present paper is on the existence and behaviour of solutions for a class of semilinear parabolic equations, defined on a bounded smooth domain and assuming a nonlinearity asymptotically linear at infinity. The behavior of the solutions when the initial data varies in the phase space is analyzed. Global solutions are obtained, which may be bounded or blow-up in infinite time (grow-up). The main tools are the comparison principle and variational methods. In particular, the Nehari manifold is used to separate the phase space into regions of initial data where uniform boundedness or grow-up behavior of the semiflow may occur. Additionally, some attention is paid to initial data at high energy level.

Comparison of Lambert W function with Adomian decomposition method for wave propagation in saturable absorption medium

We present a comparative study to examine the performances of both the Lambert W function method and Adomian decomposition method (ADM) for solving the nonlinear optical beam propagations in a saturable absorption (SA) medium for two distinct SA models. The SA-I model describes a fast saturable absorber (in which the relaxation time is much shorter than the pulse duration of the incident laser beam and no excited state absorption occurs) for a three-level system, while the SA-II model depicts a four-level system or two-photon absorption saturation. We derive the explicit analytic solutions based on the Lambert W function as well as ADM without using thin-sample approximation, and without weak saturation limit. The two different approaches to solve the nonlinear optical wave equation for two distinct SA models are compared and discussed in detail, and show excellent agreement with each other. Finally, to validate the theoretical analysis, we provide some experimental data for nonlinear optical transmission in methyl orange-doped PVA films, revealing excellent agreement with the theory of the SA-II model.

Gap solitons supported by two-dimensional parity-time-symmetric optical lattices in saturable media with fourth-order diffraction

The existence and the stability of in-phase dipole gap solitons in two-dimensional (2D) parity-time (PT)-symmetric optical lattices with defocusing saturable nonlinearity and a fourth-order diffraction property are investigated. When different values are used for the coupling constant of the fourth-order diffraction, the critical threshold of the 2D PT-symmetric optical lattices remains unchanged. The in-phase dipole solitons exist in the first finite gap and are shown to be stable in the moderate power region. The existence and stability of dipole solitons with different fourth-order diffraction coupling constants and different saturation parameters are therefore studied. We also investigate the transverse power-flow vector of these gap solitons.

Effect of nanoparticles’ diameter and concentration on the optical pulse formation in nanosuspensions

ABSTRACT We investigate the effect of nanoparticles’ diameter and concentration on the nonlinear absorption/refractive index in non-metallic nanosuspensions remarking that the results are in contrast to the colloidal metal nanoparticles. We then consider the nanosuspension as a saturable absorptive medium. Assuming a simple solution for Haus equation, we investigate the effect of diameter on optical pulse width and minimum energy required for pulse formation. We indicate that the pulse width will decrease for non-metallic nanosuspension if the diameter decreases while the pulse width will increase for metal nanoparticles conversely due to appearing the Local Field Enhancement (LFE). However, we show that the minimum-required energy is minimised for a certain value of nanoparticles’ diameter in both metal and non-metallic nanosuspensions. The potency of modulating the nonlinearity and the subsequent pulse-shaping feature presented in this study can be grounded for designing the novel all-optical/electro-optical components using the colloidal nanoparticles.