Symmetric Coupler Research Articles

Controllable combined Peregrine soliton and Kuznetsov–Ma soliton in $${\varvec{\mathcal {PT}}}$$ PT -symmetric nonlinear couplers with gain and loss

We investigate a (2+1)-dimensional-coupled variable coefficient nonlinear Schrodinger equation in parity time symmetric nonlinear couplers with gain and loss and analytically obtain a combined structure solution via the Darboux transformation method. When the imaginary part of the eigenvalue \(n\) is smaller or bigger than 1, we can obtain the combined Peregrine soliton and Akhmediev breather, or Kuznetsov–Ma soliton, respectively. Moreover, we study the controllable behaviors of this combined Peregrine soliton and Kuznetsov–Ma soliton structure in a diffraction decreasing system with exponential profile. In this system, the effective propagation distance \(Z\) exists a maximal value \(Z_m\) and the maximum amplitude of the KM soliton appears in the periodic locations \(Z_{i}\). By modulating the relation between values of \(Z_m\) and \(Z_i\), we realize the control for the excitation of the combined Peregrine soliton and Kuznetsov–Ma soliton, such as the restraint, maintenance, and postpone.

Discrete solitons and vortices on two-dimensional lattices of PT-symmetric couplers.

We introduce a 2D network built of PT-symmetric dimers with on-site cubic nonlinearity, the gain and loss elements of the dimers being linked by parallel square-shaped lattices. The system may be realized as a set of PT-symmetric dual-core waveguides embedded into a photonic crystal. The system supports PT-symmetric and antisymmetric fundamental solitons (FSs) and on-site-centered solitary vortices (OnVs). Stability of these discrete solitons is the central topic of the consideration. Their stability regions in the underlying parameter space are identified through the computation of stability eigenvalues, and verified by direct simulations. Symmetric FSs represent the system's ground state, being stable at lowest values of the power, while anti-symmetric FSs and OnVs are stable at higher powers. Symmetric OnVs, which are also stable at lower powers, are remarkably robust modes: on the contrary to other PT-symmetric states, unstable OnVs do not blow up, but spontaneously rebuild themselves into stable FSs.

A Novel Single-Layer Microstrip Coupler with Arbitrary Power Division Ratio and Harmonics Suppression

In this article, a novel symmetrical single-layer microstrip coupler with lumped inductors is proposed to achieve arbitrary power division ratio and enhanced harmonics-suppression performance simultaneously. It consists of four inductors and four transmission-line sections. By the classical even- and odd-mode analysis technique, closed-form and simple mathematical equations for the whole-circuit electrical parameters and scattering parameters are provided. The calculated results of two numerical examples show that this novel microstrip coupler can effectively suppress the second and third harmonics without affecting the operating-frequency performances. Finally, for experimental verifications, two practical examples with different power division ratios of k = 1 and k = 1.414 are designed, fabricated, and measured, respectively. The measurement results illustrate the good power division ratio at the operating frequencies (such as 800 and 900 MHz), implementing wide-band harmonics suppression.

Probability of breaking of the PJ symmetry at collision between breathers with random phases in the model of a PJ symmetric planar coupler

The interaction between breathers has been studied in the model of a nonlinear plane PJ-symmetric coupler. It has been shown that the dynamics of the interaction depends significantly on the relative phase of the breathers. The probability of breaking of the PJ symmetry in the collision of breathers having random initial phases has been estimated for various sets of parameters of the model and breathers. Various scenarios of collision of breathers have been described.

PT-symmetric coupler with a coupling defect: soliton interaction with exceptional point.

We study the interaction of a soliton in a parity-time (PT) symmetric coupler which has local perturbation of the coupling constant. This defect does not change the PT-symmetry of the system, but locally can achieve the exceptional point. We found that the symmetric solitons after interaction with the defect either transform into breathers or blow up. The dynamics of antisymmetric solitons are more complex, showing domains of successive broadening of the beam and of the beam splitting in two outward propagating solitons, in addition to the single breather generation and blowup. All the effects are preserved when the coupling strength in the center of the defect deviates from the exceptional point. If the coupling is strong enough, the only observable outcome of the soliton-defect interaction is the generation of the breather.

Symmetric Few-Mode Fiber Couplers as the Key Component for Broadband Mode Multiplexing

All-fiber broadband mode multiplexers (MMUXs) for mode and wavelength division multiplexing transmission systems are designed and analyzed. The MMUXs are based on cascaded 2-D or 3-D symmetric few-mode fiber (FMF) couplers. The MMUXs are optimized for operation over the C band and multiplex modes LP $_{01}$ , LP $_{11a}$ , LP $_{11b}$ , LP $_{21a}$ , LP $_{21b}$ , and LP $_{02}$ with a nearly flat response and an average insertion loss around 1.6 dB, depending on the design approach. The operation of the FMF couplers and the MMUXs is analyzed numerically by means of a full-vectorial beam propagation method. If the two polarization states of each LP mode are further considered, such all-fiber MMUXs can be used to combine 12 spatial channels, supporting an order of magnitude capacity increase—compared to a single spatial channel system—in optical fiber transmission systems through space (mode and polarization) division multiplexing.

Quasi -symmetry in passive photonic lattices

The concept of quasi- symmetry in an optical wave-guiding system is elaborated by comparing the evolution dynamics of a -symmetric directional coupler and a passive directional coupler. In particular, we show that in the low-loss regime, apart from an overall exponentially damping factor that can be compensated via a dynamical renormalization of the power flow in the system along the propagation direction, the dynamics of the passive coupler fully reproduce the one in the -symmetric system.

Stochastic parity-time-symmetric coupler

We introduce a stochastic parity-time (PT)-symmetric coupler, which is based on dual-core waveguides with fluctuating parameters, such that the gain and the losses are exactly balanced in average. We consider different parametric regimes that correspond to the broken and unbroken PT symmetry, as well as to the exceptional point of the underlying deterministic system. We demonstrate that in all the cases the statistically averaged intensity of the field grows. This result holds for either linear or nonlinear coupler and is independent on the type of fluctuations.

Novel Dual-Band Quasi-0-dB Coupled-Line Coupler Using the Composite Right/Left-Handed Transmission Lines

A novel edge-coupled symmetric coupled-line coupler featuring the quasi-0-dB couplings at adjacently dual frequencies is presented based on the composite right/left-handed (CRLH) transmission lines. The fulfillment of dual-frequency quasi-0-dB couplings is derived from the complete backward and complete forward coupling phenomena at the higher and lower operating frequencies, respectively. To this end, the dispersion relations of the even and odd-mode CRLH lines have to be engineered in a particular manner so that: 1) the substantial attenuation level for each mode; 2) the 180° phase difference between the even and odd-mode reflection coefficients in the overlapped stopband region are obtained to accomplish the complete backward coupling; 3) the enabling curve intersection for the even and odd-mode Bloch impedances; and 4) the considerable difference between the even and odd-mode propagation constants in the left-handed regions are obtained to suppress the impedance coupling and attain strong forward coupling. Based on a thorough analysis on the even and odd-mode dispersion characteristics and Bloch impedances of the coupled lines, the operating principle and design procedure for the proposed coupler with dual-band complete couplings can be fully explained and greatly simplified. A symmetric CRLH coupled-line coupler consisting of seven coupled unit cells was experimentally developed and a shielding (metal) box was used to prevent radiation loss in the forward coupling band. Experimental results show that the maximum coupling levels are -1.3 and -0.9 dB, corresponding to the 3-dB fractional bandwidths of 15.8% and 10.8% at the lower and higher operating frequencies, respectively. Good agreement is obtained between the simulated and experimental results.

On PT Symmetry Systems: Invariance, Conservation Laws, and Reductions

An analysis of a PT symmetric coupler with “gain in one waveguide and loss in another” is made; a transformation in the PT system and some assumptions results in a scalar cubic Schrödinger equation. We investigate the relationship between the conservation laws and Lie symmetries and investigate a Lagrangian, corresponding Noether symmetries, conserved vectors, and exact solutions via “double reductions.”

High Contrast Optical “OR” Logic Gates Using a Photonic Crystal Fiber Modulated by PAM-ASK

In this work, we present a numerical study of an all-optical logical gate based in a symmetric nonlinear directional coupler (NLDC) in Photonic Fiber Crystals (PCFs) PCFs operating with two ultrashort fundamental soliton pulses of 100 fs, modulated by PAM-ASK with binary amplitude modulation to represent the logical level 1 and 0. The performance of a symmetric dual core NLDCPCF to execute two-input logical functions is examined. We evaluate the effect resulting from an increment in the PAM coding parameter offset (ε), considering the anomalous Group Velocity Dispersion (GVD), third-order dispersion (β3) and nonlinear effects Self Phase Modulation (SPM), Self-Steepening (SS), lntrapulse Raman Scattering (IRS) in a lossless configuration. Our results indicate that is possible to get logical operations for the cores 1 or 2 using a phase control to the input pulse in one of the fibers.

All-optical switching in a symmetric three-waveguide coupler with phase-mismatched absorptive central waveguide

All-optical switching operation based on manipulation of absorption in a three-waveguide directional coupler is theoretically investigated. The proposed structure consists of one absorptive central waveguide and two identical passive side waveguides. Optically induced absorption change in the central waveguide effectively controls the coupling of light between the two side waveguides, leading to optical switching action. The proposed architecture alleviates the fabrication challenges and waveguide index matching conditions that limit previous demonstrations of similar switching schemes based on a two-waveguide directional coupler. The proposed device accommodates large modal index difference between absorptive and passive waveguides without compromising the switching extinction ratio.

Stability boundary and collisions of two-dimensional solitons inPT-symmetric couplers with the cubic-quintic nonlinearity

We introduce one- and two-dimensional (1D and 2D) models of parity-time (PT)-symmetric couplers with the mutually balanced linear gain and loss applied to the two cores and cubic-quintic (CQ) nonlinearity acting in each one. The 2D and 1D models may be realized in dual-core optical wave guides in the spatiotemporal and spatial domains, respectively. Stationary solutions for PT-symmetric solitons in these systems reduce to their counterparts in the usual coupler. The most essential problem is the stability of the solitons, which become unstable against symmetry breaking with the increase of the energy (norm) and retrieve the stability at still larger energies. The boundary value of the intercore-coupling constant, above which the solitons are completely stable, is found by means of an analytical approximation, based on the cw (zero-dimensional) counterpart of the system. The approximation demonstrates good agreement with numerical findings for the 1D and 2D solitons. Numerical results for the stability limits of the 2D solitons are obtained by means of the computation of eigenvalues for small perturbations, and verified in direct simulations. Although large parts of the soliton families are unstable, the instability is quite weak. Collisions between 2D solitons in the PT-symmetric coupler are studied by means of simulations. Outcomes of the collisions are inelastic but not destructive, as they do not break the PT symmetry.

PT-symmetric coupler withχ(2)nonlinearity

We introduce the notion of a ${\cal PT}$-symmetric dimer with a $\chi^{(2)}$ nonlinearity. Similarly to the Kerr case, we argue that such a nonlinearity should be accessible in a pair of optical waveguides with quadratic nonlinearity and gain and loss, respectively. An interesting feature of the problem is that because of the two harmonics, there exist in general two distinct gain/loss parameters, different values of which are considered herein. We find a number of traits that appear to be absent in the more standard cubic case. For instance, bifurcations of nonlinear modes from the linear solutions occur in two different ways depending on whether the first or the second harmonic amplitude is vanishing in the underlying linear eigenvector. Moreover, a host of interesting bifurcation phenomena appear to occur including saddle-center and pitchfork bifurcations which our parametric variations elucidate. The existence and stability analysis of the stationary solutions is corroborated by numerical time-evolution simulations exploring the evolution of the different configurations, when unstable.

Blow-up regimes in thePT-symmetric coupler and the actively coupled dimer

In the actively coupled (AC) pair of waveguides, the growth of small perturbations is saturated by the focusing nonlinearity that couples the linearly growing mode to the linearly damped mode. On the other hand, in the $\mathcal{PT}$-symmetric coupler, the focusing nonlinearity promotes the blow-up of stationary light beams. The purpose of this study is to compare the nonlinear dynamics and explain the opposite effect of the same nonlinearity in the two systems. We show that, while the blow-up regimes are stable in the $\mathcal{PT}$-symmetric pair of waveguides, they are unstable and hence cannot be observed in the AC dimer.

Phase sensitivity of light dynamics in PT-symmetric couplers

We study the sensitivity of light dynamics to the internal phase of propagating pulses in the two types of \(\mathcal {PT}\)-symmetric models. The first is a waveguide array with an embedded pair of waveguides with gain and loss, called \(\mathcal {PT}\)-coupler, and the second is a planar coupler which models a chain of \(\mathcal {PT}\)-symmetric couplers. For the first model we investigate the soliton scattering on the mode localized on the coupler, while for second model we study the collision of two breathers. For both models we find that the light dynamics is sensitive to the internal phases of the interacting pulses. Particularly, the \(\mathcal {PT}\)-symmetry breaking can take place or not, depending on the internal phases of two signals having identical other parameters.

Analysis of tem three‐section symmetrical directional couplers with tandem‐connected center section

ABSTRACTThe analysis of TEM three‐section symmetrical directional couplers with tightly coupled section realized as a tandem connection of two coupled‐line sections has been shown. The design equations allowing for calculating the required even‐mode characteristic impedances of coupled‐line sections for arbitrarily chosen coupling coefficient and coupling ripple have been derived. The proposed method has been utilized for analysis of three‐section 3‐dB symmetrical couplers with different coupling ripple and the results are given in a tabular form. The theoretical analysis has been confirmed by measurements of a 3‐dB three‐section symmetrical coupler, in which coupled‐line sections constituting a tightly coupled section have been miniaturized to for better fitting to the coupler's structure. © 2013 Wiley Periodicals, Inc. Microwave Opt Technol Lett 55:2578–2582, 2013

Graphical Approach for Nonlinear Optical Switching by PANDA Vernier Filter

Nonlinear response of light such as bistability, the Ikeda instability and the dynamics of light within InGaAsP-InP-modified add-drop resonator (PANDA Vernier resonator) is studied. The signal flow graph method is used to obtain the optical transfer function. Invariant and symmetric coupling coefficients k <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> = k <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</sub> = 0.25 for indirect couplers are applied and the effect of changing symmetric direct couplers (K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> = K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ) for two different resonant mode numbers is studied. The minimum drop port switching time of 2.83 ps and 2.87 ps for resonant mode numbers of 7;5;5 and 4;3;3 are achieved, respectively. The simulated results introduce the PANDA Vernier system as a proper optical device for future optical communication and signal processing systems.

The C-Band accelerating structures for SPARC photoinjector energy upgrade

The use of C-Band structures for electron acceleration and production of high quality beams has been proposed and adopted in several linac projects all over the world. The two main projects that adopted such type of structures are the Japanese Free Electron Laser (FEL) project in Spring-8 and the SwissFEL project at Paul Scherrer Institute (PSI). Also the energy upgrade of the SPARC photo-injector at LNF-INFN (Italy) from 150 to more than 240 MeV will be done by replacing a low gradient S-Band accelerating structure with two C-band structures. The structures are Traveling Wave (TW) and Constant Impedance (CI), have symmetric axial input couplers and have been optimized to work with a SLED RF input pulse. The paper presents the design criteria of the structures, the realization procedure and the low and high power RF test results on a prototype. The high power tests have been carried out by the Frascati INFN Laboratories in close collaboration with the Japanese Laboratory KEK. Experimental results confirmed the feasibility of the operation of the prototype at 50 MV/m with about 10−6 breakdowns per pulse per meter. Such high gradients have not been reached before in C-Band systems and demonstrated the possibility to use C-band accelerators, if needed, at such high field level. The results of the internal inspection of the structure after the high power test are also presented.

Novel injection methods for substitution of irradiation under different coupling routes of electromagnetic interference

At present, the maximum electromagnetic radiated field strength which can be simulated is not able to satisfy the requirements of electromagnetic environment effects tests on electronic systems. To broaden the effective frequency range of the current injection technique, new current injection methods were put forward for substitution of the radiation. A wide-band current injection device was designed based on the symmetric directional coupler principle. With a typical antenna receiving system under test, the validity of the methods were analyzed by theory and verified by experiments when the Equipment Under Test (EUT) had different coupling routes of electromagnetic interference (EMI). The results indicate that: firstly, the relationship between radiated fields and injected voltage is linear, even if the responses of the system are non-linear; secondly, the method is valid even if the test frequency is up to gigahertz; thirdly, the novel methods of current injection are able to substitute for irradiation effectively when the antenna and the interconnected cable are the main coupling routes of EMI respectively.