Nonlinear Slab Research Articles

Saturation and absorption effects on the transmission properties of Kerr-type nonlinear layers

The effects of absorption and saturation on soliton states in Kerr-type nonlinear layers are theoretically investigated. In addition to the usual gray and bright soliton structures observed in nonlinear slabs, a flat soliton, i.e., a particular soliton excitation with electric field amplitude independent of the position within the layer, is researched in cases of self-defocusing and self-focusing nonlinearities. Effects caused by the combination of absorption and saturation, such as the shift and extinction of the flat soliton peak, the decrease in the amplitude of the electric field within the nonlinear layer, and the suppression of the multistable behavior of the transmission coefficient in the vicinity of the soliton peaks, are discussed. The present theoretical results are compared and found in good quantitative agreement with previous experimental measurements.Graphical

Easily variable and scalable terahertz pulse source based on tilted-pulse-front pumped semiconductors

A new type of terahertz source containing only two optical elements - a volume phase holographic grating, and a semiconductor nonlinear slab - is proposed. The setup does not require any microstructuring, has only one diffraction order, and can be scaled to large pump sizes without any principal limitations. Furthermore, it can be easily adapted to different pump wavelengths and THz phase-matching frequencies. The Fresnel loss at the boundary of the materials can be significant at conventional pump polarizations (s-pol), but a single-layer anti-reflection (AR) coating can reduce it. Pumping such a setup with polarization in the dispersion plane (p-pol, TM mode) can reduce the effective nonlinear polarization and consequently the terahertz generation efficiency. However, in the absence of AR coating, this reduction is overcompensated by the reduced Fresnel loss.

Degenerate spontaneous parametric down-conversion in nonlinear metasurfaces.

We propose a simple scheme of degenerate spontaneous parametric down-conversion (SPDC) in nonlinear metasurfaces or photonic crystal slabs with quasi-guided modes. It employs a band crossing between even- and odd-parity quasi-guided mode bands inside the light cone (above the light line) and a selection rule in the conversion efficiency of the SPDC. The efficiency can be evaluated fully classically via the inverse process of noncollinear second-harmonic generation (SHG). As a toy model, we study the SPDC and SHG in a monolayer of noncentrosymmetric spheres and confirm that the scenario works well to enhance the SPDC.

Deformation of multilayered physically nonlinear concrete slabs by quasi-static loads

Three-layer concrete slabs are considered where each layer is formed of its concrete grade. These slabs are widely used in the construction industry, particularly in the construction of agricultural buildings and structures; thus, calculating these slabs under the external loads and forces caused by their weight is an important and relevant task. It is assumed that the concretes are non-linearly formed, and the ratios between stresses and strains are taken as the third-order polynomials with different coefficients for the different grades of concrete. The slabs are supposed to be sufficiently thin, and the Kirchhoff-Lyav hypotheses are valid. The equations of the Genka-Ilyushin deformation theory are used as the equations for the state of phase materials of the considered hybrid slabs. The complete systems of resolving equations are obtained, the equations are solved by the Bubnov-Galerkin method, and the resulting systems of algebraic equations are solved numerically in the Maple mathematical package. The graphs of the slabs' deflection and the deformation values at each point of the slab are obtained. The significant difference is shown in the maximum deflections and deformations with and without considering the slab's weight.

Scalable microstructured semiconductor THz pulse sources.

In recent years several microstructured lithium niobate THz pulse source were suggested for high-energy applications. Two types of those, the reflective and the transmissive nonlinear slab are adopted here for semiconductors. These new sources are scalable both in THz energy and size. Furthermore, they can outperform the already demonstrated contact grating source in diffraction and THz generation efficiency. Compared to the lithium niobate sources, they are more feasible, thanks to the easier manufacturing and the longer pump wavelength. They can produce intense, nearly single-cycle THz pulses at higher frequencies. With 20 mJ pumping at 1.8 µm wavelength, 45 µJ THz energy, and 17 MV/cm focused peak electric field can be expected at 3 THz phase matching frequency from the transmissive nonlinear echelon slab setup consisting of a 4 mm thick structured plan-parallel gallium phosphide crystal.

Asymmetric Localization of Light by Second-Harmonic Generation

We introduce a nonlinear photonic system that enables asymmetric localization and unidirectional transfer of an electromagnetic wave through the second-harmonic generation process. Our proposed scattering setup consists of a noncentrosymmetric nonlinear slab with nonlinear susceptibility ${\ensuremath{\chi}}^{(2)}$ placed to the left side of a one-dimensional periodic linear photonic crystal with an embedded defect. We engineered the linear lattice to allow the localization of a selected frequency $2{\ensuremath{\omega}}_{\ensuremath{\star}}$ while frequency ${\ensuremath{\omega}}_{\ensuremath{\star}}$ is in the gap. Thus in our proposed scattering setup, a left-incident coherent transverse electric wave with frequency ${\ensuremath{\omega}}_{\ensuremath{\star}}$ partially converts to frequency $2{\ensuremath{\omega}}_{\ensuremath{\star}}$ and becomes localized at the defect layer while the unconverted remaining field with frequency ${\ensuremath{\omega}}_{\ensuremath{\star}}$ exponentially decays throughout the lattice and gets reflected. For a right-incident wave with frequency ${\ensuremath{\omega}}_{\ensuremath{\star}}$ there will not be any frequency conversion and the incident wave gets fully reflected. Our proposed structure will find application in designing optical components such as optical sensors, switches, transistors, and logic elements.

Uniformly scalable lithium niobate THz pulse source in transmission geometry.

A novel THz source, based on optical rectification in LiNbO3 using the tilted-pulse-front technique, is proposed and experimentally demonstrated. The pulse-front tilt is introduced by a volume phase holographic grating, efficiently used at perpendicular incidence in transmission, and the THz pulses are produced in a LiNbO3 plane-parallel nonlinear echelon slab, arranged parallel to the grating. As a unique feature, the entire setup has a plane-parallel, transmission-type configuration, which straightforwardly enables distortion-free scaling to large sizes, high pulse energies and high THz field strengths. The possibility of operating the setup at cryogenic temperature for increased THz generation efficiency is also investigated. Calculations predict efficiencies of 95% for diffraction and 2% for THz generation at room temperature with a refractive-index-matching liquid between the grating and the echelon slab.

Resonance-forbidden second-harmonic generation in nonlinear photonic crystals

Abstract Second harmonic generation through nonlinear nano-photonic structures is important in both classical and quantum applications. It is commonly expected that the second harmonic frequency can always be generated as long as appropriate quadratic nonlinearity is provided by the material and the phase-matching condition is satisfied. Here, we present an anomaly to this common wisdom by showing that second-harmonic dipoles generated in a nonlinear photonic crystal slab can be completely nonradiative. As a result, no energy is transferred from the fundamental frequency to the second harmonic even when the phase-matching condition is satisfied – a phenomenon we call “resonance-forbidden second-harmonic generation”. Through numerical simulation, we identify two mechanisms that can achieve this phenomenon: symmetry protection and parameter tuning. The finite-size effect and the topological origin of this phenomenon are also discussed.

Tunable optical bistability at microwave frequency based on 1D sandwich photonic structure consisting of a nonlinear dielectric slab and two magnetized cold plasma layers

In this paper, tunable optical bistability that denotes the relationship between input intensity and output intensity is numerically investigated in the microwave frequency region based on the one-dimensional (1D) sandwich photonic structure consisting of a Kerr-type nonlinear material slab and two magnetized cold plasma layers. Results show that, in the case of TM-polarized electromagnetic wave, width and switching thresholds of the bistability loops are dependent on the working frequency, initial incidence angle, layer thickness, plasma density, and external magnetic field, which should be judiciously selected to obtain a required bistability behavior. Compared to the case of switch-down threshold, the switch-up threshold in the bistability loop is more sensitive to the changes of parameters. Through this study, the suggested 1D sandwich photonic structure is beneficial to the all-optical signal processing.

Interaction of Nonlinear Ekman Pumping, Near-Inertial Oscillations, and Geostrophic Turbulence in an Idealized Coupled Model

AbstractA new coupled model is developed to investigate interactions among geostrophic, Ekman, and near-inertial (NI) flows. The model couples a time-dependent nonlinear slab Ekman layer with a two-layer shallow water model. Wind stress forces the slab layer and horizontal divergence of slab-layer transport appears as a forcing in the continuity equation of the shallow water model. In one version of the slab model, self-advection of slab-layer momentum is retained and in another it is not. The most obvious impact of this explicit representation of the surface-layer dynamics is in the high-frequency part of the flow. For example, near-inertial oscillations are significantly stronger when self-advection of slab-layer momentum is retained, this being true both for the slab-layer flow itself and for the interior flow that it excites. In addition, retaining the self-advection terms leads to a new instability, which causes growth of slab-layer near-inertial oscillations in regions of anticyclonic forcing and decay in regions of cyclonic forcing. In contrast to inertial instability, it is the sign of the forcing, not that of the underlying vorticity, that determines stability. High-passed surface pressure fields are also examined and show the surface signature of unbalanced flow to differ substantially depending on whether a slab-layer model is used and, if so, whether self-advection of slab-layer momentum is retained.

Seismic response of reinforced concrete wall buildings with nonlinear coupling slabs

Reinforced concrete (RC) structural walls are widely used in high-rise buildings as the lateral force resisting system because of their inherent economy, stiffness, and strength. The floor plan configuration of residential buildings in Chile consists mainly in assemblies of large longitudinal walls and shorter transverse walls coupled by floor slabs. The coupling effect of the slabs has affected the response and the observed damage of RC buildings in recent earthquakes. The main objective of this article is to assess the seismic response of a RC structural wall building with coupling slabs. Additionally, the effect of the amount of slab reinforcement on the seismic response of the building is evaluated. To achieve the proposed objectives, seven three-dimensional models of a case study building were developed using shell-type elements in DIANA. The first four models aim to evaluate the effect of using elastic slabs with reduced (i.e. cracked) moment of inertia. The last three models consider nonlinear behavior for both walls and slabs. The response of the building was estimated using nonlinear static analysis and the seismic performance is evaluated from the results of roof displacement and shear, moment, and axial forces of the walls. Additionally, the seismic performance is evaluated from the strain demands of concrete and steel in both walls and slabs. Relevant conclusions about the building behavior, slab demands, and failure mode are drawn.

Frequency conversion in nano-waveguides using bound-state-in-continuum.

Optical frequency conversion in semiconductor nanophotonic devices usually imposes stringent requirements on fabrication accuracy and etch surface roughness. Here, we adopt the concept of bound-state-in-continuum (BIC) for waveguide frequency converter design, which obviates the limitations in nonlinear material nano-fabrication and requires to pattern only a low-refractive-index strip on the nonlinear slab. Taking gallium phosphide (GaP) as an example, we study second-harmonic generation using horizontally polarized pump light at 1.55 µm phase matching to vertically polarized BIC modes. A theoretical normalized frequency conversion efficiency of 1.1×104 % W -1 c m -2 is obtained using the fundamental BIC mode, which is comparable to that of conventional GaP waveguides.

Transmission of electromagnetic waves through a nonlinear over-dense plasma slab

A study on the transmission of the electromagnetic waves from a structure consisting of an over-dense plasma layer with nonlinear effects is undertaken. The applied nonlinearity is presented due to the series expansion of the polarization in the medium. The nonlinear plasma layer is supposed to be placed between two linear dielectric layers. The transparency conditions are investigated for the p-polarized obliquely incident waves. It is shown that the formation of the surface waves can eventuate to the transmission of the incident waves. This fact has already be seen in the case of the linear over-dense plasma, but, here, it is examined in the presence of the nonlinear effects. To determine the propitious conditions for the surface wave excitation, the exact solutions of the electromagnetic field equations are used in all regions. The transmission, the reflection, and the dissipation rates of the electromagnetic waves from the entire structure are obtained, and the effects of the main parameters on them are discussed.

Tilted‐Pulse‐Front Schemes for Terahertz Generation

AbstractHigh energy single‐ to few‐cycle terahertz pulses enable the exploration of electron acceleration, strong‐field physics, and nonlinear terahertz spectroscopy. One important method of generating such terahertz pulses is using the tilted‐pulse‐front (TPF) technique. However, the needed angular dispersion leads to a spatial and temporal break‐up of the optical pump, reducing the generation efficiency and the electric field quality of the terahertz pulses. To decrease the effects caused by angular dispersion, multiple schemes with discrete pulse‐front‐tilt are suggested. Based on a 2D+1 numerical model, a systematic comparative study of the conventional TPF scheme, three discrete TPF schemes, and a scheme with spatio‐temporally chirped (STC) optical pulses is performed. Smaller optimal interaction lengths and conversion efficiencies are predicted compared to 1D models. For small pump beam sizes, it is concluded that the STC scheme delivers spatially homogeneous terahertz pulses with the highest conversion efficiency, and for short interaction lengths, the discrete TPF schemes cannot outperform the continuous ones. However, for large pump sizes, the nonlinear echelon slab delivers the spatially most homogeneous terahertz beams and has the unique potential of generating high energy terahertz pulses. In general, this work gives guidance to choose the most appropriate setup for a given terahertz experiment.

Tunable terahertz optical bistability and multistability in photonic metamaterial multilayers containing nonlinear dielectric slab and graphene sheet

In this study, optical bistability and multistability phenomena are numerically investigated in the terahertz frequency domain based on the quasiperiodic photonic metamaterial multilayers, in which both the regular positive index and special negative index materials are artificially arranged, according to the interesting Fibonacci sequence structure. In order to obtain the tunable bistability and multibistability behaviors, the Kerr-type nonlinear dielectric layer and graphene sheet are sandwiched between two Fibonacci quasiperiodic one-dimensional photonic crystals. Results show that the intensity-dependent hysteresis curves including bistability and multistability are thoroughly discussed by judiciously changing the systematical parameters such as the frequency of incident wave, thickness of each layer, incident angle, as well as the chemical potential of graphene which can produce strong influences on the switch-up/down threshold values and widths of hysteresis loops.

Tunable Tamm states at the interface of a 1D graphene-based photonic crystal and a nonlinear dielectric slab

We investigate the dispersion of the Tamm states at the interface of a 1D graphene-based photonic crystal and a nonlinear dielectric slab. We use the nonlinear transfer matrix method to obtain the dispersion of the Tamm states in both the graphene induced and Bragg gaps in the terahertz region. We explore the spectral tunability of the surface modes by adjusting parameters such as the thickness of the nonlinear slab, the intensity of the surface modes, and the chemical potential of graphene layers. We reveal that the penetration depth of the graphene induced bandgap modes in the uniform environment is several times greater than that of the conventional Bragg gap modes. Also, it is shown that we can improve the penetration depth of the surface modes by adjusting the thickness of the nonlinear slab, the intensity of the Tamm states, or the chemical potential of the graphene layers.

Punching in two-way RC flat slabs with openings and L section columns

PurposeThis study aims to contribute to a better understanding of the influence of the position of openings around L cross-section columns in reinforced concrete flat slabs through a nonlinear computational analysis compared to experimental results.Design/methodology/approachTests on four reinforced concrete flat slabs of 1800 x 1800 x 120 mm3 were carried out under symmetrical punching; one slab was referenced (without hole) and three had square holes of 100 x 100 mm2 close to columns and with centroid on the critical perimeter at 0.5 d and 2.0 d of the loaded area. A nonlinear analysis of the slabs was performed to aid the interpretation and preview of the experimental results, and to estimate the ultimate loads and failure modes. These estimates followed recommendations of ACI 318, Eurocode 2, NBR 6118, MC 2010 and critical shear crack theory.FindingsThe results showed that the presence of holes in the analyzed regions does not influence significantly the behavior of the slabs, leading to conservative structural design once the ultimate load estimates are low, while the computational results adequately estimated the slabs’ behavior.Research limitations/implicationsA few limitations were observed on how to implement the correct modeling system for computational nonlinear simulation.Practical implicationsAll design codes underestimated failure loads and the theoretical method was not much better. The nonlinear computational simulations were satisfactory, presenting results close to experimental ones (97 per cent accuracy). Computational simulation also showed that the presence of holes does not significantly influence the load-vertical displacement behavior or failure loads.Social implicationsStructural and civil engineers and designers can observe with better details the punching phenomenon and make take secure decisions to building projects. They can preview accurate cases that are not cited in design codes and literature.Originality/valueThis is a very rare subject in literature that interests the entire scientific community and especially reinforced concrete designers. Presenting a new methodology to nonlinear flat slab with openings modeling to punching shear provoked by L cross section columns, case that is not cited in literature and design codes.

Formation of hot image for attenuation-typed scatterer in laser beam through a defocusing nonlinear negative index medium slab

For high-power laser beams modulated by a small-scale attenuation-typed scatterer, the nonlinear imaging propagation where the imaging medium is a negative index medium slab with Kerr nonlinearity is investigated. The analytical solution of the propagation is presented under the plane wave approximation and thin-medium approximation. As a result, the formation of the hot image of the scatterer is demonstrated and the corresponding quantitative expressions for the intensity and on-axis position of image are obtained. It is found that the intensity of hot image is closely related to the value of the variable linear magnetic permeability of the negative index medium. Due to the negative nonlinearity of the medium, in the downstream area of the hot image plane, the beam intensity distribution is contrary to the conventional Kerr medium case, and the intense hot image fringe develops into a broad bright band. Besides, this paper also discusses in detail the differences between the intensity and on-axis position of hot image and their counterparts in the conventional Kerr medium case and shows some other beam propagation properties.

Nonlinear surface TM waves in a Kerr defocusing nonlinear slab sandwiched between photorefractive crystals

We consider the three-layered symmetric structure consisting of inner layer with Kerr type defocusing nonlinearity sandwiched by photorefractive crystals with diffusion nonlinearity mechanism. We describe theoretically the nonlinear surface TM electromagnetic waves with symmetrical field distribution arising in such a structure. Even and odd solutions of the boundary value problem formulated correspond to the surface waves of two types existing in different ranges. Each of these types of waves attenuates both without oscillations and with oscillations. We analyze the conditions of their existence depending on the Kerr and photorefractive crystals optical characteristics. We obtain the dependence of propagation constant of the surface wave damping monotonically in explicit form.

Demonstration of a tilted-pulse-front pumped plane-parallel slab terahertz source

A new type of tilted-pulse-front pumped terahertz (THz) source has been demonstrated, which is based on a LiNbO3plane-parallel slab with an echelon structure on its input surface. Single-cycle pulses of 1μJ energy and 0.30THz central frequency have been generated with 5×10-4 efficiency from such a source. One order-of-magnitude increase in efficiency is expected by pumping a cryogenically cooled echelon of increased size and thickness with a Ti:sapphire laser. The use of a plane-parallel nonlinear optical crystal slab enables straightforward scaling to high THz pulse energies and the production of a symmetric THz beam with a uniform pulse shape for good focusability and high field strength.