Journal of Nonlinear Optical Physics & Materials

This special issue presents a collection of experimental and theoretical research in nonlinear waves, with emphasis on nonlinear optics, which were presented at the conference Nonlinear Guided Waves VIII held at the Hotel Victoria, Oaxaca, Mexico in April 2016. This preface provides a short history of the conference series Nonlinear Guided Waves and short introductions to the contributed papers which puts them in context.

Novel photonic structures such as multicore fibers and graphene based arrays present unique opportunities to manipulate and control the propagation of light. Here, we discuss nonlinear dynamics for structures with a few (2–6) elements for which linear and nonlinear properties can be tuned. Specifically, we show how nonlinearity, coupling, and parity–time (${𝒫}{𝒯}$) symmetric gain/loss relate to existence, stability and in general, dynamical properties of nonlinear optical modes. The main emphasis of our presentation will be on systems with few degrees of freedom, most notably couplers, trimers and generalizations thereof to systems with six nodes.

A highly nonlocal optical response in space has been shown to heal several shortcomings of beam self-action in nonlinear optics. At the same time, nonlocality is often connected to limits and constraints in both temporal and spatial domains. We provide a brief and rather subjective review of what we consider the main benefits and some drawbacks of a highly nonlocal response in light localization through nonlinear optics, with several examples related to reorientational soft matter, specifically nematic liquid crystals.

A dispersive shock wave (DSW), with a circular geometry, is studied in a colloidal medium. The colloidal particle interaction is based on the repulsive theoretical hard sphere model, where a series in the particle density, or packing fraction is used for the compressibility. Experimental results show that the particle interactions are temperature dependent and can be either repulsive or attractive, so the second term in the compressibility series is modified to allow for temperature dependent effects, using a power-law relationship. The governing equation is a focusing nonlinear Schrödinger-type equation with an implicit nonlinearity. The initial jump in electric field amplitude is resolved via a DSW, which forms before the onset of modulational instability. A semi-analytical solution for the amplitude of the solitary waves in a DSW of large radius, is derived based on a combination of conservation laws and geometrical considerations. The effect of temperature and background packing fraction on the evolution of the DSW and the amplitude of the solitary waves is discussed and the semi-analytical solutions are found to be very accurate, when compared with numerical solutions.

We study shelf-like breathers and dispersive shock phenomena in a discrete nonlinear Schrödinger (DNLS) equation with a nonlocal nonlinearity. The system models laser light propagation in waveguide arrays made from a nematic liquid crystal substratum. Shelf-like breathers are studied in the regime of small linear intersite coupling, and we report some new theoretical existence and stability results. We also study numerically the evolution from nearby dam-break and more general jump initial conditions for stronger linear intersite coupling. In the defocusing case, we see rarefaction and shock wave profiles, superposed with oscillations. Some of the hyperbolic features of the observed profiles are described approximately by continuous NLS hydrodynamics. Nonlocality is seen to lead to some smoothing of the rapid oscillations seen in the local DNLS.

The all-optical control of the trajectory of a nonlinear optical beam propagating in a nematic liquid crystal cell is studied using a combination of modulation theory and full numerical solutions of the governing nematic equations. In detail, the output position of a signal beam is controlled via its interaction with a second, co-propagating control beam. The input positions of both the signal and control beams are fixed, with the output position of the signal beam determined by the input angle of the control beam. A simple modulation theory based on treating the optical beams as mechanical particles in a potential well is found to give only adequate agreement with numerical solutions. However, extending this modulation theory to include the detailed profiles of the beams, so that the beams are treated as rigid bodies moving in a potential well, leads to simple, extended equations which determine the input angle of the control beam required for a given output position of the signal beam. The predictions of this extended particle theory, or rigid body theory, are compared with full numerical solutions of the nematic equations and excellent agreement is found.

We study the evolution of a quantum discrete nonlinear Schrödinger (DNLS) system using as initial conditions coherent states corresponding to points in the vicinity of breather solutions of the classical system. We consider various examples of stable and unstable breathers and examine the distance between exactly evolved states and coherent states with parameters that evolve according to classical dynamics. Initial conditions near stable breathers and their vicinity are seen to lead to recurrences to small distances between the two evolving states. Similar recurrences are not observed for initial conditions near unstable breathers.

The nonlinear optical properties of different samples of dielectric nanocolloids and their application to generate optical spatial solitons in two transverse dimensions are investigated. Each sample is constituted by a suspension of polystyrene nanospheres in water, and we analyze four cases with two different particle sizes (62nm and 77nm in diameter) and concentrations (0.5% and 1.0% solids). The z-scan technique is used to evaluate and compare the nonlinear refractive index of the nanocolloids. A detailed experimental study on the formation of soliton-like beams as a function of different parameters is also presented. Importantly, the generated solitons propagate along distances exceeding by one order of magnitude the propagation distances observed previously in the same kind of media.

This paper experimentally demonstrated a ring cavity multi-wavelength Brillouin fiber laser employing fiber Bragg grating (FBG) that operated in the C-band region. The FBG plays a significant role to reflect signals and filter selected wavelengths. A number of generated Brillouin Stokes (BS) signals and tuning range ability were investigated. A 9km length of single mode fiber was utilized to provide a Brillouin gain medium for generating stimulated Brillouin scattering effect. In this work, at optimum output coupling ratio of 90% and Brillouin pump (BP) wavelength of 1550nm, up to a maximum of 26 BS signals were recorded by injecting 63.1mW of amplified BP powers. The BS signals were also tunable within the ranges of 1544–1556nm in accordance with the FBG properties at 3dBm bandwidth of 5nm.

We study the nonlinear (NL) absorption and refraction of 5,10,15,20-tetraphenyl-21H, 23H-porphin cobalt(II) (CoTPP) and 5,10,15,20-tetrakis(4-methoxyphenyl)-21H, 23H-porphin cobalt(II) (MCoTPP). The measurements were carried out in solutions prepared with chlorobenzene applying the D4$\sigma$-Z-scan technique with a laser delivering single pulses in the picosecond regime at 532nm. For each compounds, the NL coefficients were measured for three concentrations. The results show that these materials with unfilled $d$ shell exhibit a saturable absorption (SA), where they have been compared to the basic structure tetraphenylporphyrin (TPP) and zinc tetraphenylporphyrin (ZnTPP) with filled $d$ shell metal in order to see the influence of the central metal ion on the NL absorption (NLA) behavior.

A fully analytical approach to the problem of TE wave propagation in an open lossless waveguide filled with Kerr medium is suggested. It is shown that the waveguide supports two physically interesting guided regimes in the focusing case. In each of the regimes, there exists an infinite number of guided waves that do not have linear counterparts. It is also shown that in the defocusing case only one regime arises with a finite number of guided waves; all these solutions have linear counterparts. Numerical illustrations and discussion of the found results are presented.

An organic nonlinear optical (NLO) single crystal of L-methioninium picrate (LMP) has been grown by slow evaporation solution technique (SEST) at a constant temperature of $40^{\circ }$C. Formation of nucleation and growth kinetics of the crystal were observed using an optical microscope for different durations and it was found that the shape of nucleation is similar to the grown large size single crystals of the same material. The characterization techniques such as powder X-ray diffraction (PXRD) analysis, UV–Vis NIR, Vickers microhardness, piezoelectric d${}_{33}$ coefficient, photoconductivity and etching studies have been performed. The crystal system and lattice parameters of the grown crystal were determined by PXRD analysis. The spectroscopic properties of the synthesized compound were confirmed by Fourier transform infrared (FTIR) analysis. The UV–Vis NIR analysis was performed on the grown single crystal to find the optical absorption in the entire visible region. Attempts have been made to investigate the mechanical properties of LMP crystal using Vickers diamond pyramid indenter. In addition piezoelectric, photoconductivity and etching studies were carried out to study the d${}_{33}$ coefficient, photoconducting nature and surface properties respectively.

Spatial distribution and quantum trajectory control of the molecular harmonic spectra from H${}_2^{+}$ are theoretically investigated through the combination of a few-cycle 800nm pulse and a half-cycle pulse. Results show that by properly adding the half-cycle pulse, the harmonic cutoffs from the recombination process are extended, and the harmonic intensities from the positive-$x$ direction are suppressed. Moreover, as the internuclear distance increased, the modulations on the harmonic spectra are reduced. The time-dependent wave function and the time-frequency analyses of the harmonic spectra are shown to explain the above physical mechanism. Further, by adding the laser pulse to the bowtie-shaped gold nanostructure separated by an air gap $g=18$nm, much higher harmonic cutoff order can be obtained in the positive-$x_0$ region. Finally, two isolated attosecond pulses with the full width at half maximum of 34as and 31as are obtained.

The dynamics of a polystyrene bead linking to a $\lambda$-phage deoxyribonucleic acid (DNA) molecule under single optical tweezers using CW laser beam is analyzed by the full normalized Langevin equation with elastic and Brownian forces. The obtained results show that the stable time and stable position of polystyrene bead depend on its beginning position, laser beam waist, and laser beam power. The oscillation of polystyrene beads at stable position is observed with different parameters of optical tweezers. Finally, the conditions to stabilize the bead and to stretch the $\lambda$-phage DNA by single laser beam optical tweezers are discussed.