Dual-core Waveguide Research Articles

Symmetry-breaking bifurcations of pure-quartic solitons in dual-core couplers.

We investigate spontaneous symmetry- and antisymmetry-breaking bifurcations of solitons in a nonlinear dual-core waveguide with the pure-quartic dispersion and Kerr nonlinearity. Symmetric, antisymmetric, and asymmetric pure-quartic solitons (PQSs) are found, and their stability domains are identified. The bifurcations for both the symmetric and antisymmetric PQSs are of the supercritical type (alias phase transitions of the second kind). Direct simulations of the perturbed evolution of PQSs corroborate their stability boundaries predicted by the analysis of small perturbations.

Symmetry-breaking bifurcations and excitations of solitons in linearly coupled NLS equations with PT-symmetric potentials

We address symmetry-breaking bifurcations (SBBs) in the ground state (GS) and dipole-mode (DM) solitons of the one-dimensional linearly coupled NLS equations, modelling the propagation of light in a dual-core planar waveguide with the Kerr nonlinearity and two types of P T -symmetric potentials. The P T -symmetric potential is employed to obtain different types of solutions. A supercritical pitchfork bifurcation occurs in families of symmetric solutions of both the GS and DM types. A novel feature of the system is interplay between breakings of the P T and inter-core symmetries. Stability of symmetric GS and DM modes and their asymmetric counterparts, produced by SBBs of both types, is explored via the linear-stability analysis and simulations. It is found that the instability of P T -symmetric solutions takes place prior to the inter-core symmetry breaking. Surprisingly, stable inter-core-symmetric GS solutions may remain stable while the P T symmetry is broken. Fully asymmetric GS and DM solitons are only partially stable. Moreover, we construct symmetric and asymmetric GS solitons under the action of a pure imaginary localized potential, for which the SBB is subcritical. These results exhibit that stable solitons can still be found in dissipative systems. Finally, excitations of symmetric and asymmetric GS solitons are investigated by making the potential’s parameters or the system’s coupling constant functions, showing that GS solitons can be converted from an asymmetric shape onto a symmetric one under certain conditions. These results may pave the way for the study of linear and nonlinear phenomena in a dual-core planar waveguide with P T potential and related experimental designs.

One-dimensional Townes solitons in dual-core systems with localized coupling.

The recent creation of Townes solitons (TSs) in binary Bose-Einstein condensates and experimental demonstration of spontaneous symmetry breaking (SSB) in solitons propagating in dual-core optical fibers has drawn renewed interest in the TS and SSB phenomenology in these and other settings. In particular, stabilization of TSs, which are always unstable in free space, is a relevant problem with various ramifications. We introduce a system which admits exact solutions for both TSs and SSB of solitons. It is based on a dual-core waveguide with quintic self-focusing and fused (localized) coupling between the cores. The respective system of coupled nonlinear Schrödinger equationsgives rise to exact solutions for full families of symmetric and asymmetric solitons, which are produced by the supercritical SSB bifurcation (i.e., the symmetry-breaking phase transition of the second kind). Stability boundaries of asymmetric solitons are identified by dint of numerical methods. Unstable solitons spontaneously transform into robust moderately asymmetric breathers or strongly asymmetric states with small intrinsic oscillations. The setup can be used in the design of photonic devices operating in coupling and switching regimes.

Light bullet solutions in a dual-core waveguide amplifier with different modulated coefficients and a varying source

Light bullet solutions in a dual-core waveguide amplifier with different modulated coefficients and a varying source

Trapping wave fields in an expulsive potential by means of linear coupling

We demonstrate the existence of confined states in one- and two-dimensional (1D and 2D) systems of two linearly coupled components, with the confining harmonic-oscillator (HO) potential acting upon one component and an expulsive anti-HO potential acting upon the other. The systems can be implemented in optical and BEC dual-core waveguides. In the 1D linear system, codimension-one solutions are found in an exact form for the ground state (GS) and dipole mode (the first excited state). Generic solutions are produced by means of the variational approximation and are found in a numerical form. Exact codimension-one solutions and generic numerical ones are also obtained for the GS and vortex states in the 2D system (the exact solutions are found for all values of the vorticity). Both the trapped and antitrapped components of the bound states may be dominant ones, in terms of the norm. The localized modes may be categorized as bound states in continuum, as they coexist with delocalized ones. The 1D states, as well as the GS in 2D, are weakly affected and remain stable if the self-attractive or repulsive nonlinearity is added to the system. The self-attraction makes the vortex states unstable against splitting, while they remain stable under the action of the self-repulsion.

Spatiotemporal optical solitons in a dual-core waveguide amplifier with inter modal dispersion

We obtain spatiotemporal optical solitons in a dual-core waveguide amplifier with inter modal dispersion, which can be described by a (3+1)-dimensional generalized nonlinear Schrödinger equation with modulated coefficients and a varying source. Two types of specific media of physical interest are considered to show the propagation behaviors of solutions. We find that the structures of these spatiotemporal optical soliton solutions can be controlled by tuning the dispersion, nonlinearity, gain, and the source parameters.

Solitons in [formula omitted]-symmetric systems with spin–orbit coupling and critical nonlinearity

We construct families of one-dimensional (1D) stable solitons in two-component PT-symmetric systems with spin–orbit coupling (SOC) and quintic nonlinearity, which plays the critical role in 1D setups. The system models light propagation in a dual-core waveguide with skewed coupling between the cores. Stability regions for the solitons are identified in the system’s parameter space. They include the main semi-infinite gap, and an additional finite annex gap. Stability boundaries are identified by means of simulations of the perturbed evolution, which agree with results produced by the linear-stability analysis for small perturbations. Distinct evolution scenarios are identified for unstable solitons. Generally, they suffer blowup or decay, while weakly unstable solitons transform into breathers. Due to a regularizing effect of SOC, stationary solitons are also found beyond the exceptional point, at which the PT symmetry breaks down, but they are unstable. Interactions between adjacent solitons are explored too, featuring rebound or merger followed by blowup. Slowly moving (tilted) solitons develop weak oscillations, while fast ones are completely unstable. Also considered is the reduced diffractionless system, which creates only unstable solitons.

Construction of a dual-core hollow waveguide for visible and mid-infrared light transmission based on PTFE tubing and UV gel

This work proposes a facile approach to fabricate a dual-core hollow waveguide based on two common and low-cost raw materials, namely polytetrafluoroethylene (PTFE) tube and ultraviolet (UV) gel. A silica glass tube is nested inside a heat-shrinkable PTFE tube. After heat treatment at 350 °C, the PTFE tube shrinks and then transforms into the low-index polymer on the outside of the silica tube. The PTFE-coated silica glass tubing is filled with UV gel followed by inserting a typical Ag/AgI mid-infrared (IR) hollow optical fiber. The UV gel is cured by UV radiation, forming a solid low-index layer between the PTFE-coated silica glass tubing and the Ag/AgI hollow optical fiber. A visible laser beam can be transmitted at a loss of 0.4 dB/m through the silica annulus between the low-index PTFE and UV gel layer. A 10.6-μm-wavelength CO2 laser beam is delivered through the Ag/AgI hollow optical fiber (core size 530 μm) and the transmission loss goes up from 1.63 to 3.22 dB/m as the bending angle increases from 0° to 90°.

Fractional quantum couplers

Fractional quantum coupler, a new type of quantum couplers that is composed of arrays of two coupled waveguides or a dual-core waveguide with intermodal coupling, within which the light waves diffraction is of the fractional-order differentiation, is put forward in the territory of fractional quantum mechanics. The modelling equations of such fractional couplers are derived in the framework of coupled nonlinear fractional Schrödinger equations with the space derivative of fractional order denoted by Lévy index α, and localized wave solutions as spatial optical solitons of these equations are constructed and their nonlinear propagation properties are discussed. Linear perturbation method based on linear stability analysis, and direct simulations are conducted to identify the stability and instability regions of the predicted solitons.

Stabilization of one-dimensional Townes solitons by spin-orbit coupling in a dual-core system

It was recently demonstrated that 2D Townes solitons (TSs) in two-component systems with cubic self-focusing, which are normally made unstable by the critical collapse, can be stabilized by linear spin-orbit coupling (SOC), in Bose-Einstein condensates and optics alike. We demonstrate that 1D TSs, realized as optical spatial solitons in a planar dual-core waveguide with dominant quintic self-focusing, may be stabilized by SOC-like terms emulated by obliquity of the coupling between cores of the waveguide. Thus, SOC offers a universal mechanism for the stabilization of (quasi-) TSs. A combination of systematic numerical considerations and analytical approximations identifies a vast stability area for skew-symmetric solitons in the system’s main (semi-infinite) and annex (finite) bandgaps. Tilted (”moving”) solitons are unstable, spontaneously evolving into robust breathers. For broad solitons, diffraction, represented by second derivatives in the system, may be neglected, leading to a simplified model with a finite bandgap. It is populated by skew-antisymmetric gap solitons, which are nearly stable close to the gap’s bottom.

Controllable propagation of chirped self-similar waves in tapered grating dual-core waveguide amplifiers

We study the controllable propagation of chirped self-similar waves to a generalized nonlinear Schrödinger equation in tapered grating dual-core waveguide amplifiers. We find that the W- and bell-shaped solitons and elliptic function solutions can exist under some constraint conditions. The propagation of these self-similar wave solutions can be controlled by appropriately choosing the system parameters. The compression and broadening behaviors of the self-similar waves are discussed in details.

Snakelike similaritons in combined harmonic-lattice potentials with a varying source

We study the dynamics of snakelike similaritons to the nonlinear Schrodinger equation in combined harmonic-lattice potentials with a varying source term. Using the self-similar and Mobius transformations, we construct a large number of analytical solutions which generate many types of novel snakelike similaritons under some constraint conditions, such as the W- and bell-shaped breathing similaritons and the elliptic function solutions. Then, four specific examples of physical interest are considered in details to show the dynamical behaviors of the similaritons. Especially, the compression effect of snakelike similaritons is demonstrated in dispersion-decreasing media with Bessel modulated nonlinearity. We find that the structures of snakelike similaritons can be controlled by tuning the coefficient parameters, the combined harmonic-lattice potentials, and the source term. The stability of the solutions has also been performed by numerical simulations. Our results may have potential applications in the dual-core fiber waveguides and Bose–Einstein condensates in the presence of an inhomogeneous source.

Nonlinear tunneling effect of snakelike self-similar waves in a grating dual-core waveguide amplifier

We study on the nonlinear tunneling effect of snakelike self-similar waves of the nonlinear Schrödinger equation with gains in an asymmetric dual-core waveguide amplifier with a long-period grating. Using the self-similar transformation we find the bright and dark snakelike self-similar waves with W-, U-, and bell-shaped profiles. As an application, we investigate the nonlinear tunneling effect of these optical structures under some constraint conditions. The results show that the snakelike self-similar waves can similarly pass through the nonlinear barrier or well and can be effectively controlled by adjusting the source amplitude and the long-period grating. Our results may have potential applications for improving channel capacity in the graded-index dual-core waveguide amplifiers with a long-period grating.

Efficient supercontinuum generation enabled by dispersion engineering in a dual-core waveguide

A compact dual-core waveguide is proposed for efficient supercontinuum generation, in which the use of Si-rich nitride and titanium dioxide provides a large enough index contrast for dispersion engineering. Strong anomalous group velocity dispersion is obtained over a wide bandwidth of 1860 nm which greatly reduces the dispersion length. The nonlinear length can also be significantly decreased due to high nonlinear Kerr index of Si-rich nitride. As a consequence, it could facilitate octave-spanning supercontinuum generation from 1160 to 2385 nm in a greatly reduced propagation distance, as short as 165μm. It is more than one order of magnitude shorter than those previously reported and can be further reduced to 70μm. This compact broadband source is promising not only for on-chip applications but also for applications in tiny environments such as nano-scale spectroscopic probing and study of biological molecules, cells and tissues.

Snakelike similaritons in tapered grating dual-core waveguide amplifiers

We present a physical model that describes bright and dark snakelike similaritons propagating in an asymmetric dual-core waveguide amplifier by considering self-focusing and self-defocusing Kerr nonlinearities. The asymmetric dual-core waveguide is composed of two adjoining, closely spaced, upper and lower cores, in which the upper one is an active tapered graded-index waveguide with a long-period grating along the medium while the lower one is a passive step-index waveguide. For different choices of tapered index profile, novel exact analytical similariton solutions undergoing a self-compression are obtained. Our results show that these optical structures can be effectively controlled by adjusting the long-period grating and amplitude of the source. Besides, the stability and interaction of two neighboring bright similaritons are discussed by means of numerical simulations. These results may simulate the possibility of experiments related to tapered grating dual-core waveguide amplifiers.

Slot-slot waveguide with negative large and flat dispersion covering C+L+U waveband for on-chip photonic networks.

A novel, to the best of our knowledge, dual-core slot-slot waveguide with extreme high dispersion is proposed. The high dispersion value at the desired wavelength is obtained based on strong resonance coupling between two slot-waveguide modes. The properties of dispersion magnitude and bandwidth are numerically analyzed by using the finite-difference time-domain method with a perfectly matched layer boundary. All numerical simulation results reveal that for the optimized geometrical parameters of H1=350 nm, L1=569 nm, S1=31.3 nm, La=1062.39 nm, H2=427 nm, L2=137.4 nm, and S2=63.5 nm, the maximum dispersion of negative 3.645×105 ps·nm-1·km-1 and dispersion full width at half-maximum of 6.3nm at 1550nm have been obtained. By cascading the slot-slot waveguides with varying width and height, a large and flattened dispersion of -3.5×105 ps·nm-1·km-1 covering the C+L+U waveband is obtained. Dispersion compensation of a 100Gbit/s return-to-zero on-off-keying optical time-division multiplexing signal after 50km full spectrum single-mode optical fiber transmission with five different central wavelengths is demonstrated through simulation for the first time. In addition, fabrication tolerance of the proposed slot-slot waveguide is analyzed. Such a waveguide is compatible with complementary metal-oxide-semiconductor technology and has potential applications in next-generation large-scale photonic integrated circuits.

Dynamical control of solitons in a parity-time-symmetric coupler by periodic management

We consider a dual-core nonlinear waveguide with the parity-time (PT) symmetry, realized in the form of equal gain and loss terms carried by the coupled cores. To expand a previously found stability region for solitons in this system, and explore possibilities for the development of dynamical control of the solitons, we introduce “management” in the form of periodic sinusoidal variation of the loss-gain (LG) coefficients, along with synchronous variation of the inter-core coupling (ICC) constant. This system, which can be realized in optics (in the temporal and spatial domains alike), features strong robustness when amplitudes of the variation of the LG and ICC coefficients keep a ratio equal to that of their constant counterparts, allowing one to find exact solutions for PT-symmetric solitons. A stability region for the solitons is identified in terms of the management amplitude and period, as well as the soliton’s amplitude. In the long-period regime, the solitons evolve adiabatically, making it possible to predict their stability boundaries in an analytical form. The system keeping the Galilean invariance, collisions between moving solitons are considered too. Slowly moving solitons undergo multiple collisions, but eventually separate.

Snakelike self-similar solutions in a graded-index grating waveguide amplifier with an external source

We present a series of snakelike self-similar solutions to the nonlinear Schrodinger equation with a gain in the presence of an external source through asymmetric dual-core waveguide amplifiers with a long-period grating. The asymmetric dual-core waveguide is composed of two adjoining, closely spaced, upper and lower waveguides, in which the upper one is an active graded-index waveguide with a long-period grating along the medium, while the lower one is a passive step-index waveguide. The results show that: (1) the self-similar optical structures can be generated and effectively controlled by modulating the amplitude of the source; (2) the long-period grating can change the motion of the solutions and preserve their shapes. These results may raise the possibility of some experiments and potential applications in the graded-index grating waveguide amplifier with an external source.

Solitons in a chain of charge-parity-symmetric dimers

We consider an array of dual-core waveguides, which represent an optical realization of a chain of dimers, with an active (gain-loss) coupling between the cores, opposite signs of discrete diffraction in the parallel arrays, and a phase-velocity mismatch between them (which is necessary for the stability of the system). The array provides an optical emulation of the charge-parity ($\mathcal{CP}$) symmetry. The addition of the intracore cubic nonlinearity gives rise to several species of fundamental discrete solitons, which exist in continuous families, although the system is non-Hermitian. The existence and stability of the soliton families are explored by means of analytical and numerical methods. An asymptotic analysis is presented for the case of weak intersite coupling (i.e., near the anticontinuum limit), as well as weak coupling between cores in each dimer. Several families of fundamental discrete solitons are found in the semi-infinite gap of the system's spectrum, that have no counterparts in the continuum limit, as well as a branch which belongs to the finite band gap and carries over into a family of stable gap solitons in that limit. One branch develops an oscillatory instability above a critical strength of the intersite coupling, others being stable in their entire existence regions. Unlike solitons in conservative lattices, which are controlled solely by the strength of the intersite coupling, here fundamental-soliton families have several control parameters, one of which, viz., the coefficient of the intercore coupling in the active host medium, may be readily adjusted in the experiment by varying the gain applied to the medium.

Design of Low-loss and Highly Birefringent Porous-Core Photonic Crystal Fiber and Its Application to Terahertz Polarization Beam Splitter

We present the design of a porous-core PCF with elliptical holes in the core that achieved low loss, high birefringence, and flattened dispersion for guiding terahertz waves. The finite element method is used to study the properties of the designed waveguide in detail: effective material loss, birefringence, confinement losses, and dispersion. Simulation results show that the proposed structure exhibits simultaneously high modal birefringence of $1.32 \times 10 ^{-2}$ and a flattened dispersion over a broadband of 1.28 THz. Then, polarization splitters, based on both symmetric and asymmetric porous-core PCF structures, are designed and evaluated at 1 THz. We show that this kind of device exhibits a strong polarization-dependent coupling behavior. Numerical results show that the configuration based on dual-core waveguide with asymmetric cores can achieve a 10.9 cm long splitter with a broadband of 0.306 THz for x -polarization and 0.23 THz for y -polarization. Finally, this paper offers an effective method to design an ultrawideband polarization beam splitter to operate in the THz region, which might be relevant for future applications in technical areas, such as spectroscopy, sensing, and high-speed data transmission.