Nonlinear Slab Waveguide Research Articles

Numerical investigation of tunable Fano-based optical bistability in coupled nonlinear gratings

In this paper, we numerically report the optical bistability based on tunable Fano resonances in photonic structures consisting of two coupled nonlinear slab waveguide gratings facing to each other. Quality factor (Q-factor) and asymmetric factor (q-factor) of Fano resonance of the coupled grating structure can be tuned by changing the gap-distance and horizontal shifted-alignment. The switching intensity not only depends on the Q-factor, but also strongly depends on the q-factor of the resonance. Considering strong coupling coefficients and optimizing the gap-distance between two gratings, the Fano resonance with high Q-factor and optimal q-factor can be excited. It is found that the horizontal shifted-alignment of the system provides high-order resonant mode having higher Q-factor and thus reduces the switching intensity than that of the perfect alignment system. Depending on the wavelengths of operation and q-factors of Fano resonances, the optical bistabilities will provide various switching intensities.

Optical bistability based on Fano resonances in single- and double-layer nonlinear slab waveguide gratings

In this paper, we numerically investigate all-optical bistable switching at low input intensity based on Fano resonances available in nonlinear slab waveguide gratings with narrow slits. Fano resonances with various quality factors (Q-factors) in the single- and double-layer slab waveguide gratings are designed and their characteristics are studied by the finite-difference time-domain method. Dependencies on wavelengths of operation, various switching intensities, contrast, and bandwidth of all-optical bistabilities are observed. Comparing nonlinear characteristics of single- and double-layer grating configurations, the latter provides more bistable efficiency with the low input intensities needed and high contrast with high Q-factors at certain operating wavelengths. Both grating configurations in this work provide interesting venues for highly efficient Fano resonance-based all-optical bistable switching devices.

Propagation characteristics of nonlinear waveguides with complex refractive index using a transmission line model

The transmission line model for the nonlinear slab waveguides has been modified in order to tackle the guidance of nonlinear waves by slab waveguides with a complex refractive index. A detailed description of the modified method is presented for both TE and TM waves and for arbitrary nonlinearities. In order to demonstrate the potential use of the proposed method, we have examined the problem of nonlinear waveguiding in the presence of losses. Numerical results for the power-dependent attenuation coefficients are obtained for small and strong losses, in various configurations, and also compared with results from previous works.

Propagation of an Electromagnetic Beams in Non-Linear Dielectric Slab Wave Guides

Propagation of an Electromagnetic Beams in Non-Linear Dielectric Slab Wave Guides

Modes on a bent nonlinear waveguide: solutions based upon the method of perturbations

The changes to the field profile and propagation constant for guided modes travelling around a continuously bent nonlinear slab waveguide are investigated analytically by using a first-order perturbation theory. As with the linear case, the field profile shows a shift of the field maximum in the plane of curvature, but the mathematical description of the nonlinear waveguide is very different. We provide analytic solutions for the fields and propagation constants of even and odd symmetry.

Complete modulational-instability gain spectrum of nonlinear quasi-phase-matching gratings

We consider plane waves propagating in quadratic nonlinear slab waveguides with nonlinear quasi-phase-matching gratings. We predict analytically and verify numerically the complete gain spectrum for transverse modulational instability, including hitherto undescribed higher-order gain bands.

Examination of the core field uniformity for 3-layer power-law nonlinear slab waveguides

Uniform electric field in waveguide core may have some importance in application for various waveguide devices. It has been shown that uniform electric field can occur in and only in nonlinear waveguide structures with Kerr-like or saturable media. In this paper, three-layer slab optical waveguide for which the nonlinear permittivity of film and claddings take the same power-law form ε∼| E| δ , where E is the local electric field intensity and δ can be an arbitrary positive number ( δ=2 for Kerr-like media), has been analyzed to find out the structures in which the core electric field profile can become uniform at appropriate optical power. It is shown that there are five kinds of such structures. Numerical calculations for electric field profiles at different optical powers for various δ are made and the results are plotted for several realistic waveguide models. The results show that stronger nonlinearity is beneficial for occurrence of uniform core field at a lower optical power.

Plane waves in periodic, quadratically nonlinear slab waveguides: stability and exact Fourier structure

We consider the propagation of broad optical beams through slab waveguides with a purely quadratic nonlinearity and containing linear and nonlinear long-period quasi-phase-matching gratings. An exact Floquet analysis on the periodic, plane-wave solution shows that the periodicity can drastically alter the growth rate of the modulational instability but that it never completely removes the instability. The results are confirmed by direct numerical simulation, as well as through a simpler, approximate theory for the averaged fields that accurately predicts the low-frequency part of the spectrum.

Amplitude-identical core field of TE 0 modes in three-layer slab waveguides with nonlinear claddings

Uniform electric field exists only in nonlinear waveguide structures. Theoretical analysis and numerical results for typical examples are presented for three-layer nonlinear slab waveguides to find the appropriate structures in which the core electric field can become uniform at appropriate optical power. It is shown that there are five kinds of such structures. The electric field profiles are plotted for five typical examples. We notify that the occurrence of uniform field in a waveguide core may perhaps have prospective applications in waveguide, opto-electronic and photonic devices.

A hybrid implicit-explicit FDTD scheme for nonlinear optical waveguide modeling

A hybrid implicit-explicit finite-difference time-domain (FDTD) method for solving the wave equation in nonlinear optical waveguiding structures is proposed. The new scheme combines the computational simplicity of the explicit scheme in linear medium regions with the superior stability property of the partially implicit scheme in regions of nonlinear materials, thus eliminating potential problems of instability associated with nonlinearity. Simulation results for Kerr-type nonlinear slab waveguides and corrugated waveguides are presented and compared with those obtained using the conventional noniterative FDTD scheme.

Analytical expressions of cut-off wavenumbers of TM modes in a Kerr-like nonlinear slab waveguide

A very simple analytical expression of cut-off wavenumbers for TM waves in a nonlinear MQW slab waveguide with Kerr-like nonlinearity is presented for the first time using a perturbation technique.

Dark and grey spatial solitary waves in non-linear slab waveguides

Propagation of dark and grey spatial solitary waves in slab waveguides using self-defocusing non-linear media is studied and an exact analytical solution is obtained.

Temporal modulation of nonlinear surface waves and soliton emission at nonlinear slab waveguides

The propagation of pulsed Gaussian beams end-firing the fundamental mode of a linear thin film covered with a nonlinear medium has been analysed by means of a variational method. Fundamental parameters for soliton emission and nonlinear surface wave propagation, such as critical power and film thickness, have been calculated. The role of the pulse shape has been investigated by comparing the behaviour of Gaussian and hyper-Gaussian pulses. The variational expressions obtained for the evolution of the beam width and trajectory are shown to be in good agreement with numerical simulations.

Full vectorial analysis of a nonlinear slab waveguide based on the nonlinear hybrid vector finite-element method

We propose a new nonlinear hybrid vector f inite-element method to study the propagation of an optical beam in a nonlinear waveguide in three space dimensions. The new method is a combination of the edge-element and f inite-difference methods; the former applies to the waveguide cross section and the latter to the propagation direction. To validate our method, a planar nonlinear waveguide (consisting of a linear substrate, a linear film, and a Kerr-type cladding) that is end-fire excited by the TE(0) and TM(0) modes is studied numerically. We demonstrate that the external excitation of a nonlinear slab waveguide can produce sequential threshold behavior by means of multisoliton emission from the waveguide.

Two-dimensional gap solitons in a nonlinear periodic slab waveguide

We present a three-dimensional analysis of counterpropagating waves in a periodic nonlinear slab waveguide. The analysis reveals the existence of two-dimensional gap solitons, whose stability depends on their total power’s being above (unstable) or below (stable) a critical power. Numerical experiments validate the analytical results.

Gaussian-beam excitation and stability of three-dimensional nonlinear guided waves

The propagation of stationary three-dimensional nonlinear guided waves and of Gaussian beams in a slab waveguide in which the cladding displays both Kerr-law and saturable instantaneous self-focusing nonlinearities is simulated numerically. The numerical analysis supports the hypothesis that the stationary three-dimensional nonlinear guided waves are stable on propagation for propagation constants corresponding to the ascending branches of the nonlinear dispersion curves. The numerical simulations of the Gaussian-beam propagation in the nonlinear slab waveguide illustrate both diffraction and nonlinear effects such as solitary-wave emission. The transparent-boundary condition, which employs no adjustable parameters and is easily incorporated into a Crank–Nicolson finite-difference scheme, was used in the three-dimensional calculations.

Guided transverse-magnetic waves supported by a weakly nonlinear slab waveguide

Guided TM waves in a slab waveguide that consists of a weakly Kerr-type nonlinear dielectric film bounded by semi-infinite linear dielectrics are analyzed by the singular perturbation technique with multiple space scales. The analytical expressions of the nonlinear guided TM waves are derived explicitly. Numerical results are presented for the effect of the power on the effective index and the field distributions. It is shown that the effective index for the nonlinear TM waves is a function of the power of the linear wave, which is the zero-order solution, and that the fields are confined in the film region as the power increases.

Evolution of nonlinear guided waves along a bent planar waveguide

AbstractOptical field propagation in a nonlinear bent slab waveguide with a Kerr‐like nonlinear cladding medium is presented. With increasing input power, the self‐focusing effect significantly disturbs the original waveguide configuration, and a nonstationary evolution behavior is found. It is shown that the onset and the direction of soliton emission are sensitive to the guiding capability of the initial waveguide. In particular, a novel result is observed when the waveguide supports more than one mode. © 1993 John Wiley & sons, Inc.

Dark solitons in nonlinear optics

Recent theoretical and experimental results on propagation of dark-pulse solitons in nonlinear optical media are reviewed. Using an analytical approach based on the nonlinear Schrodinger equation, the authors describe properties of dark solitons, features of their generation by different input pulses, and the dynamics of dark solitons in the presence of perturbations. They also briefly discuss experimental results which show the possibility of dark-soliton propagation in optical fibers (temporal dark solitons), laser beams passed through a sodium vapor and nonlinear slab waveguides (spatial dark solitons), and demonstrate that theoretical predictions and experimental data are in good agreement.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Calculations on nonlinear dielectric slab waveguides by the iterative eigenfunction expansion method

A new treatment for the behavior of both TE and TM nonlinear waves in an arbitrary nonlinear material is given. The treatment is based on a recently developed method, the iterative eigenfunction expansion method (IEEM). Compared with the results of the finite element method (FEM), this scheme has proven very successful. It is also easily extendable to other nonlinear behavior in varying geometries.