Nonlinear Directional Coupler Research Articles

Solitons of the Twin-Core Couplers with Fractional Beta Derivative Evolution in Optical Metamaterials via Two Distinct Methods

The rapid advancements in metamaterial research have brought forth a new era of possibilities for controlling and manipulating light at the nanoscale. In particular, the design and engineering of optical metamaterials have created advances in the field of photonics, enabling the development of advanced devices with unprecedented functionalities. Among the myriad of intriguing metamaterial structures, the nonlinear directional couplers with beta derivative evolution have emerged as a significant avenue of exploration, offering remarkable potential for light propagation and manipulation. This study obtains the solitary wave solutions for twin-core couplers having spatial-temporal fractional beta derivative evolution by using two different methods, the Bernoulli method and the complete polynomial discriminant system method. By graphing some of the obtained solutions, the effect of the beta derivative has been shown. The findings would be beneficial to understand physical behaviours in nonlinear optics, particularly twin-core couplers with optical metamaterials.

Harnessing XPM effects in non-linear directional couplers for 4-bit gray code conversion and even parity verification

Abstract The all-optical switching phenomena in the non-linear directional coupler using cross-phase modulation (XPM) effect have been proposed. It is designed to generate an all-optical XOR functionality, considering the XOR logic gates as a basic module the design and analysis of an efficient all-optical 4-bit binary to gray code converter and 4-bit even parity checker circuit is proposed. The design methodology includes the switching of a weak continuous-wave (CW) signal, which is controlled by the combination of two controlled pump signals. In this paper, mathematical analysis of the coupled mode theory associated with optical directional couplers has been discussed. The switching characteristics of XPM effect based All-optical directional couplers have been examined for appropriate values of the controlled pump signals. Appropriate values of extinction ratio and corresponding controlled pump signal levels are investigated for an efficient generation of XOR logic gates. Further, the detailed analysis of layout generation and design aspects of All-optical 4-bit binary to gray code converter and 4-bit even parity checker circuits have been carried out. The proposed methodology is verified by the appropriate simulation results, which include the transmittivity, extinction ratio (Xratio) curve variation and dynamic time domain plot associated with proposed units.

Switching dynamics in adiabatically coupled PT-symmetric directional coupler consisting of three nonlinear waveguides

We design and numerically investigate the switching dynamics between two outer waveguides in parity-time (PT)-symmetric adiabatically coupled three waveguides nonlinear directional coupler (NLDC) system. The study is performed for different combinations of linear and nonlinear waveguides using coupled mode theory (CMT). Here, one of the outer waveguides has variable gain and the other has equal amount of variable loss while the middle waveguide is neutral. The merits of different configurations of PT-symmetric NLDC over the conventional NLDC are also discussed in detail. In particular, it has been noticed that the device provides switching even in case when middle waveguide is nonlinear, and the outer waveguides are linear for which conventional system behaves as linear coupler. In addition, we study the effect of loss to gain ratio on critical switching power. Further, the effects of launched light power and gain (loss) value on the transmitted power are investigated.

Design and analysis of all-optical half and full adder/subtractor using nonlinear asymmetric directional couplers

The utilization of nonlinear asymmetric directional couplers has emerged as a viable alternative to conventional systems for the execution of arithmetic operations using optical signals. The present study explores the utilization of a coupler-based framework for the development of an all-optical half- and full-adder/subtractor circuit designed with the basic logic gates (AND, OR, XOR) and a soliton pulse as input signals. Nonlinear asymmetric directional couplers have been analysed theoretically and numerically, including the detailed mathematics of coupled wave theory. The switching characteristics of XPM effect based All-optical directional couplers have been examined for appropriate values of the phase shift (∆φ). Appropriate values of ∆φ, extinction ratio (dB), and corresponding controlled pump signal levels and other parameters are investigated for an efficient generation of fundamental logic gates. Further, the detailed analysis of layout generation and design aspects of an all-optical half- and full-adder/subtractor circuit along with the basic logic gates circuits has been carried out. Simulation results are validated with the standard result. The research findings demonstrate that soliton pulses might potentially be useful for optical computing applications when used as the input signal to nonlinear asymmetrical directional couplers.

Dynamical behavior and modulation instability of optical solitons in nonlinear directional couplers

Dynamical behavior and modulation instability of optical solitons in nonlinear directional couplers

Sensitive Demonstration of the Twin-Core Couplers including Kerr Law Non-Linearity via Beta Derivative Evolution

To obtain new solitary wave solutions for non-linear directional couplers using optical meta-materials, a new extended direct algebraic technique (EDAT) is used. This model investigates solitary wave propagation inside a fiber. As a result, twin couplers are the subject of this study. Kerr law is the sort of non-linearity addressed there. Because it offers solutions to problems with large tails or infinite fluctuations, the resulting solution set is more generalized than the current solution because it is turned into a fractional-order derivative. Furthermore, the found solutions are fractional solitons with spatial–temporal fractional beta derivative evolution. In intensity-dependent switches, these nonlinear directional couplers also serve as limiters. Non-linearity alters the transmission constants of a system’s modes. The significance of the beta derivative parameter and mathematical approach is demonstrated graphically, with a few of the extracted solutions. A parametric analysis revealed that the fractional beta derivative parameter has a significant impact on the soliton amplitudes. With the aid of the advanced software tools for numerical computations, the categories of semi-dark solitons, singular dark-pitch solitons, single solitons of Type-1 along with 2, intermingled hyperbolically, trigonometric, and rational solitons were established and evaluated. We also discussed sensitivity analysis, which is an inquiry that determines how sensitive our system is. A comparative investigation via different fractional derivatives was also studied in this paper so that one can easily understand the correlation with other fractional derivatives. The findings demonstrate that the approach is simple and efficient and that it yields generalized analytical results. The findings will be extremely beneficial in examining and comprehending physical issues in nonlinear optics, specifically in twin-core couplers with optical metamaterials.

Energy- and time-controlled switching of ultrashort pulses in nonlinear directional plasmonic couplers.

We propose an ultracompact nonlinear plasmonic directional coupler for switching of ultrashort optical pulses. We show that this device can be used to control the routing of ultrashort pulses using either the energy or the duration of each individual pulse as switching parameters. The coupler is composed of two cores of a nonlinear dielectric material embedded into metallic claddings. The intricate nonlinear spatiotemporal dynamics of the system is simulated by the finite-difference time-domain technique.

Study on modulational instability in three-core nonlinear directional saturated coupler with septic nonlinearity

Study on modulational instability in three-core nonlinear directional saturated coupler with septic nonlinearity

Inelastic soliton interactions for nonlinear directional couplers in optical metamaterials with Kerr nonlinearity modulation stability

A directional coupler is made up of two parallel monolayer wave guides filled with high nonlinear optical metamaterial. The model equations of the directional twin-core couplers, which are coupled nonlinear Schrödinger equations (CNLSEs), were proposed in the literature. These equations have received the attention of a variety of works. The results found, therein, show mainly dark, bright or singular soliton solutions. The objective of this work is to search for different soliton geometric structures, which show novel patterns. To this issue a novel transformation, with complex amplitude, is introduced. It allows to inspect the waves produced via soliton periodic wave collision. The collision is elastic whenever the waves generated are, everywhere, smooth. Otherwise it is inelastic. Here, the unified method is used to find the traveling wave solutions of the CNLSEs. The solutions obtained are evaluated numerically and they are used to display the amplitude and the real part of the optical field in figures. These figures exhibit super-lattices, zig-zag soliton with rhombus modulation and graded solitons with blow up. These behaviors occur due to inelastic collisions. The contour plots show lattice waves with gap (region of blow up) or without gap. Also, ripples that occur currently in optical cables are observed. Furthermore, it is found that modulation instability (MI) is triggered for positive nonlinear phase shift coefficients or in the case when the coupling coefficients exceed a critical value. As far as MI holds, this leads to traveling waves blow up and gaps.

Logic gates through three core and dual core nonlinear directional couplers operating in continuous wave mode

Logic gates through three core and dual core nonlinear directional couplers operating in continuous wave mode

Multi-functional all-optical photonic crystal logic gate using nonlinear directional coupler

Multi-functional all-optical photonic crystal logic gate using nonlinear directional coupler

Supermode-based second harmonic generation in a nonlinear interferometer.

We demonstrate supermode-based second harmonic generation in an integrated nonlinear interferometer made of linear and nonlinear directional couplers. We use a fully-fibered pump shaper to demonstrate second harmonic generation pumped by the symmetric or anti-symmetric fundamental spatial modes. The selection of the pumping mode and thus of a specific SHG spectral profile is achieved through the selection of the fundamental wavelength and via a robust phase setting scheme. We use two methods: either post-selecting or actively setting the pumping mode. Such modal phase matching paves the way for classical and quantum applications of coupled nonlinear photonic circuits, where multimode excitation, encoding and detection are a route for multiplexing and scaling up light-processing.

Analysis of Kerr type nonlinear single-mode triangular index fiber directional coupler by a simple method

We present the coupling characteristics of directional coupler comprising two identical single-mode triangular index fibers both in the presence and the absence of Kerr nonlinearity. Triangular index fibers of some typical V numbers are chosen for our investigation. Our analysis is based on the simple series expression for the fundamental modal field for triangular index fiber developed by Chebyshev technique. Analytical expression of the coupling length in the absence as well as in the presence of Kerr nonlinearity is prescribed. Using the said expression of coupling length, we apply a method of iteration to evaluate the said coupling parameter in the presence of Kerr nonlinearity. We also show that our results match excellently with the exact results obtainable by rigorous finite-element technique. The execution of our formalism requires little computation. Thus our simple but accurate formalism to study the triangular index directional coupler will prove a suitable alternative to the existing rigorous methods in the field of nonlinear optics. This user-friendly method will prove beneficial to the scientists and technologists working in the field of nonlinear optics.

Optical soliton and weierstrass elliptic function management to parabolic law nonlinear directional couplers and modulation instability spectra

Optical soliton and weierstrass elliptic function management to parabolic law nonlinear directional couplers and modulation instability spectra

The fractional comparative study of the non-linear directional couplers in non-linear optics

A new extended direct algebraic method is applied to extract new traveling wave solutions for non-linear directional couplers with the optical meta-materials. This model studies light distribution from the main fiber into other branch fibers, which can be one or more than one. So, for this reason, twin couplers and multiple core couplers are studied in this paper. Further two cases in multiple core couplers namely multiple core couplers near the neighbor and multiple core couplers with a complete neighbor are exhaustively discussed. The non-linearity type that is considered here is Kerr Law. The obtained solutions set is more generalized than the existing solution as it is transformed into fractional-order derivative because it gives the solutions of problems with heavy tails or infinity fluctuations. Furthermore, the obtained solutions contain almost all types of solitons such as dark, bright, dark-bright, rational, periodic, breather, and singular soliton solutions, etc. Moreover, the obtained solutions are fractional solitons with Atangana-Baleanu and modified Riemann–Liouville fractional operator. These non-linear directional couplers also act as limiters in intensity-dependent switches. The propagation constants of the modes of a system are changed by non-linearity. In order to discuss the physical nature of couplers, 2D and 3D figures are also shown.

Solitons in nonlinear directional couplers with optical metamaterials by unified Riccati equation approach

The unified Riccati equation approach identifies soliton solutions to couplers in optical metamaterials. A spectrum of soliton solutions with their respective existence criteria are recovered. Both, twin-core and multiple-core couplers are studied in this work.

Quantum Kerr nonlinear coupler: analytical versus phase-space method

The generation of squeezed states of light in a two-mode Kerr nonlinear directional coupler (NLDC) was investigated using two different methods in quantum mechanics. First, the analytical method, a Heisenberg-picture-based method where the operators are evolving in time but the state vectors are time-independent. In this method, an analytical solution to the coupled Heisenberg equations of motion for the propagating modes was proposed based on the Baker–Hausdorff (BH) formula. Second, the phase space method, a Schrödinger-picture-based method in which the operators are constant and the density matrix evolves in time. In this method, the quantum mechanical master equation of the density matrix was converted to a corresponding classical Fokker–Planck (FP) equation in positive-P representation. Then, the FP equation was converted to a set of stochastic differential equations using Ito rules. The strengths and weaknesses of each method are discussed. Good agreement between both methods was achieved, especially at early evolution stages and lower values of linear coupling coefficient. On one hand, the analytical method seems insensitive to higher values of nonlinear coupling coefficients. Nevertheless, it demonstrated better numerical stability. On the other hand, the solution of the stochastic equations resulting from the phase space method is numerically expensive as it requires averaging over thousands of trajectories. Besides, numerically unstable trajectories appear with positive-P representation at higher values of nonlinearity.

Optical switch based on Graphene clad two surface plasmonic polariton mode coupler

Graphene exhibits both surface plasmonics and non linear optical property. Considering these properties, an optical controlled compact graphene clad surface plasmonic polariton two modes interference (GCSPPTMI) structure with silicon waveguide core has been presented for all optical switching. The cross and bar state power of the device are obtained by introducing an additional phase between the excited SPP modes in silicon coupling region through nonlinear refractive index modulation of graphene clad with incidence of very low optical pulse energy of 0.82 pJ and width of 4 ps. The coupling length of the proposed device is ∼21.6 times less than that of existing all optical switch based on SPP modes. The degradation of power imbalances of the Graphene clad SPPTMI with fabrication tolerances (±) of both width and thickness is less than that of multimode interference based nonlinear directional coupler due to having less of device parameters. Our results promise to achieve high speed and compact optical switch.

Traveling wave with beta derivative spatial-temporal evolution for describing the nonlinear directional couplers with metamaterials via two distinct methods

This work is reported the analytical solutions for describing the nonlinear directional couplers with metamaterials by including spatial–temporal fractional beta derivative evolution. The auxiliary ordinary differential equation method and the generalized Riccati method with the properties of beta derivative are implemented to secure such solutions. The solutions are obtained in the new forms by involving of some useful mathematical functions. The constraint conditions among the traveling wave parameters are evaluated. Some of the obtained solutions are presented graphically to illustrate the effectiveness of beta derivative parameter and mathematical techniques. It is investigated that the amplitudes of soliton are increased with the increase of fractional beta derivative parameter. The obtained results would be very useful to examine and understand the physical issues in nonlinear optics, especially in twin-core couplers with optical metamaterials.

Dark soliton steering in PT-symmetric couplers with third-order and intermodal dispersions

We demonstrate steering dynamics of dark solitons in a parity–time ( P T )-symmetric nonlinear directional coupler (NLDC) in the presence of third-order dispersion (TOD) and intermodal dispersion (IMD). A complete switch with an excellent efficiency at a very low critical power, even lower compared to the bright soliton switching, has been observed. The numerical results show that both TOD and IMD have no effect on soliton steering in P T -symmetric couplers with coupling length π / 2 . But, as we increase the coupling length to 2 π , IMD shows marginal effects for dark soliton steering in P T -symmetric couplers, while TOD shows no impact. Additionally, we have also studied the phase-controlled switching in P T -symmetric couplers with two different coupling lengths and demonstrated its advantage over the power-controlled one.