Nonlinear Waveguide Research Articles

Wide-spectrum optical soliton solutions to the time-fractional cubic-quintic resonant nonlinear Schrödinger equation with parabolic law

The time-fractional cubic-quintic resonant nonlinear Schrödinger equation with parabolic law and its soliton solutions have significant implications to examine the dynamics of optical solitons, self-phase modulation, optical beam propagation in nonlinear media, pulse propagation in optical fibers, nonlinear waveguides, and signal transmission systems. This study focuses on the investigation of different soliton solutions related to various aspects of optical solitons, including their formation, propagation traits, and stability analysis of the mentioned equation. Soliton solutions are able to carry out long-distance transmission without frequent amplification and regeneration. We exploit an advanced mathematical technique, the (G′/G,1/G)-expansion method to descend and analyze the soliton solutions. As a result, a significant number of definitive and efficient solitons, such as compacton, bell-shaped, anti-peakon, breather, periodic, and singular solitons have resulted. The uniqueness of the obtained solutions is established by comparing them with previous results. Also, we discuss in detail the implications of fractional derivative and the application of the obtained solutions to optical fiber communication and other relevant fields. The findings of the present study provide valuable insights into the fundamental nature of optical solitons. These insights will contribute to the design and optimization of future optical networks, enabling the development of faster, more reliable, and higher-capacity communication systems.

Pair of optical solitons in parallel planar waveguides coupled by linear photonic crystal

We propose a simple optical model, which consists of two Kerr nonlinear parallel planar waveguides sandwiching a one-dimensional photonic crystal for demonstrating the phenomenon of spontaneous symmetry breaking in optics. We study the shape and stability of soliton pairs propagating in two planar waveguides and the spontaneous symmetry breaking of the power distribution of solitons in the two waveguides. The results of numerical simulation show that there is supercritical type of spontaneous symmetry breaking in this system. More optical power P and smaller refractive index of photonic crystals [Formula: see text] make soliton solutions more prone to spontaneous symmetry breaking bifurcation. Asymmetric soliton solutions and symmetric soliton solutions correspond to different dispersion relations. Under the given total power P, for the symmetric soliton solutions, the propagation constant k increases linearly with [Formula: see text], and for asymmetric soliton solutions, the propagation constant k decreases nonlinearly with [Formula: see text]. The minimum point of [Formula: see text] is just the demarkation between the symmetric soliton solutions and the asymmetric soliton solutions. If [Formula: see text] is fixed, the minimum point of the Hamiltonian of the system, [Formula: see text], is also the critical point of the two different kinds of soliton solutions. We also study stable and unstable distributions of two kinds of soliton solutions.

Present and future of terahertz integrated photonic devices

Photonic integrated circuits have benefited many fields in the natural sciences. Their nanoscale patterning has led to the discovery of novel sources and detectors from ultraviolet to microwaves. Yet terahertz technologies have so far leveraged surprisingly little of the design and material freedom provided by photonic integrated circuits. Despite photoconduction—the process in which light is absorbed above the bandgap of a semiconductor to generate free carriers—and nonlinear up- and down-conversion being by far the two most widespread approaches to generate and detect terahertz waves, so far, terahertz technologies have been mostly employed in bulk. In this perspective, we discuss the current state-of-the-art, challenges, and perspectives for hybrid optical-terahertz photonic chips. We focus, in particular, on χ(2) and χ(3) nonlinear waveguides and waveguide-integrated photoconductive devices. We highlight opportunities in the micro- and macroscale design of waveguide geometries and printed antennas for the optimization of emission and detection efficiencies of terahertz waves. Realizing complex functionalities for terahertz photonics on a single chip may come into reach by integration and miniaturization compatible with telecom and fiber technologies.

Models of waveguides combining gradient and nonlinear optical layers

Objectives. Theoretical studies of the waveguide properties of interfaces between nonlinear optical and graded-index media are important for application in optoelectronics. Waveguides combining layers with different optical properties seem to be the most promising, since they can be matched to optimal characteristics using a wide range of control parameters. The paper aims to develop a theory of composite optically nonlinear gradedindex waveguides with an arbitrary profile, within which it is possible to obtain exact analytical expressions for surface waves and waveguide modes in an explicit form. The main feature of the theory proposed in this paper is its applicability for describing surface waves and waveguide modes, in which the field is concentrated inside the gradient layer and does not exceed its boundary, avoiding contact with the nonlinear layer.Methods. Analytical methods of the theory of optical waveguides and nonlinear optics are used.Results. A theoretical description of the waveguide properties of the interface between two media having significantly different optical characteristics is carried out. The formulated model of a plane waveguide is applicable to media having an arbitrary spatial permittivity profile. An analytical expression describing a surface wave propagating along the interface between a medium having stepwise nonlinearity and a gradient layer with an arbitrary permittivity profile is obtained. Additionally, analytical expressions for surface waves propagating along the interface between a medium with Kerr nonlinearity (both self-focusing and defocusing), as well as graded-index media characterized by exponential and linear permittivity profiles, are obtained.Conclusions. The proposed theory supports a visual description in an explicit analytical form of a narrowly localized light beam within such waveguides. It is shown that by combining different semiconductor crystals in a composite waveguide, it is possible to obtain a nonlinear optical layer on one side of the waveguide interface and a layer with a graded-index dielectric permittivity profile on the other.

100-Gbps per-channel all-optical wavelength conversion without pre-amplifiers based on an integrated nanophotonic platform

Abstract All-optical wavelength conversion based on four-wave mixing attracts intense interest in many areas, especially in optical fiber communications, due to the advantages of femtosecond response, modulation-format transparency, and high flexibility in optical network management. In this paper, we present the first optical translation of 32-GBaud 16QAM signals with an integrated Si3N4 nonlinear nanophotonic waveguide. An on-chip continuous-wave conversion efficiency of up to −0.6 dB from S band to C band is achieved in the dispersion-engineered low-loss Si3N4 nonlinear waveguide that is back-end compatible with complementary metal–oxide–semiconductor processes. The high conversion efficiency avoids the use of external optical amplifiers for signal demodulation. The converted idler is successfully received with a sensitivity penalty of less than 0.5 dB. Moreover, pre-amplifier-free multichannel wavelength conversion of over-100-Gbps coherent signals in C band is also demonstrated using the same Si3N4 nanophotonic waveguide via changing the pump wavelength, which shows good flexibility in all-optical signal processing. Additionally, wavelength conversion with a bandwidth over 100 nm can be expected by optimizing the current Si3N4 nanophotonic waveguide, which is promising for commercial coherent fiber communications and has bright prospects in various areas including optical signal processing, imaging, optical spectroscopy, and quantum optics.

An elastic luminescent organic single crystal with linear and nonlinear optical waveguide properties

In recent years, organic single crystals combining elastic and photoluminescent (PL) properties have attracted extensive attention due to their promising applications in many fields. However, elastic organic crystals with two-photon luminescence (2 PL) waveguiding properties are still rarely found, which is imperative for various applications, including near-infrared (NIR) bioimaging and nonlinear optical (NLO) photonic devices. This work reports an elastic single crystal with a long needle shape, anthracene-9,10-dicarbaldehyde (An-DC). Its crystal (100) face exhibits highly reversible bending by applying the mechanical force, which is facilitated by the van der Waals (C– H···π), H-bond (C–H⋯O), and π···π interactions among molecules. The crystal emits a strong orange-red fluorescence when excited by blue-violet light. Interestingly, it also exhibits excellent two-photon fluorescence emission when stimulated by near-infrared light. Based on these linear and nonlinear optical characteristics, the waveguide applications of the An-DC crystal were implemented. Notably, in the bending state, the luminescence performance and the crystal structure of the An-DC crystal are maintained well, which can be used as a low-loss material for linear and nonlinear optical waveguide devices, thus expanding the potential use of flexible organic crystals.

Propagation of the ordinary and extraordinary modulated optical pulses in a nonlinear Kerr-type birefringent optical waveguide: Analytical description

The purpose of this work is to describe theoretically the behavior of modulated pulses in nonlinear birefringent optical waveguides and particularly in the optical fibers, by taking into account the anisotropy of the medium as well as the orientation of the optical axis with respect to the propagation direction of an incoming pulse. Firstly, the multiple times scale method is used to describe the behavior of an optical pulse in the waveguide whose optical axis is perpendicular to the direction of propagation of the pulse. It appears that in the nonlinear regime, the optical pulse splits into two different modes in propagation namely an ordinary mode and an extraordinary mode which propagate with different group velocities. These modes are described by the different nonlinear Schrodinger (NLS) equations involving nonlinear Kerr-like responses. Next, we turn attention to the waveguide whose the optical axis is parallel to the direction of propagation of an incoming pulse and found that the two modes continue to exist, and are also described by different NLS equations. In addition, we show that for some parameter regime, the two modes become identical and described by the same NLS equation.

Fiber-coupled plug-and-play heralded single photon source based on Ti:LiNbO3 and polymer technology.

A reliable, but cost-effective generation of single-photon states is key for practical quantum communication systems. For real-world deployment, waveguide sources offer optimum compatibility with fiber networks and can be embedded in hybrid integrated modules. Here, we present what we believe to be the first chip-size fully integrated fiber-coupled heralded single photon source (HSPS) module based on a hybrid integration of a nonlinear lithium niobate waveguide into a polymer board. Photon pairs at 810 nm (signal) and 1550 nm (idler) are generated via parametric down-conversion pumped at 532 nm in the LiNbO3 waveguide. The pairs are split in the polymer board and routed to separate output ports. The module has a size of (2 × 1) cm2 and is fully fiber-coupled with one pump input fiber and two output fibers. We measure a heralded second-order correlation function of g h(2)=0.05 with a heralding efficiency of η h=3.5% at low pump powers.

Stabilizing solitons of the cubic–quintic nonlinear Schrödinger equation by frequency-dependent linear gain-loss and delayed Raman response

We demonstrate transmission stabilization against radiation emission by frequency-dependent linear gain-loss and perturbation-induced frequency shifting for solitons of the cubic–quintic nonlinear Schrödinger (CQNLS) equation. We consider soliton propagation in a nonlinear optical waveguide with focusing cubic nonlinearity, defocusing quintic nonlinearity, and dissipative perturbations due to weak frequency-dependent linear gain-loss, cubic loss, and delayed Raman response. The frequency shifting is induced by delayed Raman response. Our perturbation analysis and numerical simulations with the perturbed CQNLS equation show that transmission stabilization with CQNLS solitons is indeed possible, and in this way provide the first demonstration of the stabilization method for solitons of a nonintegrable nonlinear wave model. Moreover, we find that transmission stabilization with energetic CQNLS solitons is realized with significantly smaller frequency shifts and pulse distortion compared with stabilization with energetic solitons of the cubic nonlinear Schrödinger equation. Therefore, our study also demonstrates that stabilization of energetic solitons by the method is significantly improved by the presence of defocusing quintic nonlinearity.

At the threshold of distributed Kerr-lens mode-locking in a Cr:ZnS waveguide laser

We demonstrate feasibility of spatiotemporal mode-locking in a mid-IR Cr:ZnS waveguide laser based on the nonlinear spatial mode coupling. The experiment shows efficient power scaling with the excitation of intramode beatings, causing a pronounced Q-switching, which could result in nonlinear mode-coupling. The contribution of such multimode beatings and resulting Q-switching is confirmed numerically. We suggest that a particularly high nonlinearity in Cr:ZnS combined with multimode waveguide leads to a soft aperture induced by a pump beam. The numerical simulations demonstrate that such an aperture could provide an effective spatial mode control in a nonlinear multimode waveguide, which, thereby, opens the way to the birth of a spatiotemporal dissipative soliton, or light bullet, formation, thus forming the basis for the future distributed Kerr-lens mode locking in the energy-scalable solid-state waveguide (or yet unrealized fiber) laser.

Asymmetric modulation instability in nonlinear metamaterial waveguides

In this paper, we explore the formation of asymmetric modulation instability spectrum in the metamaterials as a result of the joined effect of self-steepening and intra-pulse Raman scattering. In general, the modulation instability gain spectrum is symmetric about the zero perturbation frequency. Here we observe asymmetric modulation instability gain spectrum and the asymmetry depends on the sign of the refractive index of the medium. When the refractive index of the medium is negative the band with high modulation instability gain is observed at positive detuning frequency regime in contrast to the case of positive refractive index regime where the band with high modulation instability gain is present at a negative detuning frequency regime. This preponderance is attributed to the opposite directionality of phase velocity and energy flow in a negative index material. Our study provides additional ways to tune soliton and ultrashort pulses utilizing engineering freedom of metamaterials.

(Invited) Two-color soliton meta-atoms and molecules

We present a detailed overview of the physics of two-color soliton molecules in nonlinear waveguides, i.e. bound states of localized optical pulses which are held together due to an incoherent interaction mechanism. The mutual confinement, or trapping, of the subpulses, which leads to a stable propagation of the pulse compound, is enabled by the nonlinear Kerr effect. Special attention is paid to the description of the binding mechanism in terms of attractive potential wells, induced by the refractive index changes of the subpulses, exerted on one another through cross-phase modulation. Specifically, we discuss nonlinear-photonics meta atoms, given by pulse compounds consisting of a strong trapping pulse and a weak trapped pulse, for which trapped states of low intensity are determined by a Schr\"odinger-type eigenproblem. We discuss the rich dynamical behavior of such meta-atoms, demonstrating that an increase of the group-velocity mismatch of both subpulses leads to an ionization-like trapping-to-escape transition. We further demonstrate that if both constituent pulses are of similar amplitude, molecule-like bound-states are formed. We show that z-periodic amplitude variations permit a coupling of these pulse compound to dispersive waves, resulting in the resonant emission of Kushi-comb-like multi-frequency radiation.

Chirp-induced chaotic self-trapped patterns and power controllable interactions in nonlocal nonlinear system with oscillatory responses

We introduced a class of chaotic self-trapped patterns (CSTPs) in nonlocally nonlinear system with sine-oscillatory response, which are induced by the linear chirps. Such chirp-induced CSTPs can exist under a general nonlocality condition, and can be produced by optical beams of any profiles. The CSTPs exhibit both the soliton property and the chaotic property. The mechanism for generating the CSTPs in the nonlinear system with sine-oscillatory response is the multi-reflections by the optical self-induced nonlinear refractive index waveguide, and the multi-interferences between the beams and their reflected counterparts. The interactions of two linearly chirped beams were investigated, which can be controlled by the optical power. We can realize the “ON” and the “OFF” states of light fields by only changing the optical power, and could present a method in the optical switching.

Custom Nonlinearity Profile for Integrated Quantum Light Sources

Heralded single-photon sources are a fundamental building block for optical quantum technologies. These sources need to be unfiltered and integrated to have good scalability and avoid unnecessary losses. To attain this goal, it is necessary to control the effective nonlinearity seen by the fields as they mix and propagate in a waveguide source. In this paper, we introduce a method to design nonlinear waveguides with arbitrarily shaped effective nonlinearity profiles. The method takes advantage of the fact that the second-order nonlinear response is a tensor quantity and thus the local effective nonlinearity of a material depends on the propagation direction of the fields participating in the interaction. Thus, by locally changing the propagation direction of the fields we can modulate the wave-mixing process. Our method allows for the waveguide fabrication process to be significantly simplified. The material structure of the waveguide is made by a single crystal, no longer needing oriented patterning or periodic poling. We use our method to design waveguides with a nonlinearity profile that is Gaussian in the propagation length, allowing the generation of perfectly pure heralded single photons.

Adiabatic light propagation in nonlinear waveguide couplers with longitudinally varying detunings via resonance-locked inverse engineering

We investigate the adiabatic evolution of light in nonlinear waveguide couplers via resonance-locked inverse engineering based on stimulated Raman adiabatic passage (STIRAP). The longitudinal varying detunings of the propagation coefficients are designed to eliminate dynamically the nonlinear effect, which induce the non-adiabatic oscillations. We show that different light evolutions such as complete light transfer, light split and light return can be realized adiabatically with appropriate choices of the detunings even in the nonlinear regime. The features open new opportunities for the realization of all-optical nonlinear devices with high fidelity in integrated optics.

Very-large-scale integrated quantum graph photonics

Graphs have provided an expressive mathematical tool to model quantum-mechanical devices and systems. In particular, it has been recently discovered that graph theory can be used to describe and design quantum components, devices, setups and systems, based on the two-dimensional lattice of parametric nonlinear optical crystals and linear optical circuits, different to the standard quantum photonic framework. Realizing such graph-theoretical quantum photonic hardware, however, remains extremely challenging experimentally using conventional technologies. Here we demonstrate a graph-theoretical programmable quantum photonic device in very-large-scale integrated nanophotonic circuits. The device monolithically integrates about 2,500 components, constructing a synthetic lattice of nonlinear photon-pair waveguide sources and linear optical waveguide circuits, and it is fabricated on an eight-inch silicon-on-insulator wafer by complementary metal–oxide–semiconductor processes. We reconfigure the quantum device to realize and process complex-weighted graphs with different topologies and to implement different tasks associated with the perfect matching property of graphs. As two non-trivial examples, we show the generation of genuine multipartite multidimensional quantum entanglement with different entanglement structures, and the measurement of probability distributions proportional to the modulus-squared hafnian (permanent) of the graph’s adjacency matrices. This work realizes a prototype of graph-theoretical quantum photonic devices manufactured by very-large-scale integration technologies, featuring arbitrary programmability, high architectural modularity and massive manufacturing scalability.

Parametric amplification in coupled nonlinear waveguides: The role of coupling dispersion

We present the theory of parametric amplification in coupled nonlinear waveguides considering the frequency dependency of the coupling strength. We show that coupling dispersion can indeed compensate for the uncoupled individual waveguides dispersion enabling a substantial tailoring of the gain spectrum. Our theory describes both phase-sensitive and phase-insensitive operational modes, it can be straightforwardly generalized to include arbitrary higher-order waveguide and coupling dispersion and its predictions agree very well with numerical simulations both in the presence and in the absence of waveguide losses. It provides a tool for the design of novel versatile parametric amplifiers based both on coupled integrated waveguides and dual-core fibers too.

Optical analog to coherent population return in coupled nonlinear waveguides

In this paper, we investigate the optical analog to coherent population return (CPR) in coupled nonlinear waveguides. The nonlinearity sometimes plays a negative role in classical simulations of quantum adiabatic passages in waveguides. Nevertheless, it is interesting to note that the nonlinearity here helps simulating the adiabatic CPR technique. The CPR can still occur when the detuning (difference of the propagation constants) between the two nonlinear waveguides is moderate, which is a typical requirement of the technique. Moreover, the adiabatic process can appear when the detuning is small or zero. This is done by simply adjusting the incident light power, which is easy and of high accuracy compared with modulating the propagation constants. Therefore, the requirements towards the propagation constants of the waveguides are further relaxed in the nonlinear case. Finally, we point out that the CPR in nonlinear waveguides can be extended to design achromatic beam splitters.

Crystal packing and photoelectric property of bis(2-picolyl)amine-functionalized triarylborane and its complexes

Organic crystalline materials are attracting increasing interest due to their promising applications in the fields of nonlinear optics (NLO), organic lasers, optical waveguides, and light-emitting transistors. In this paper, a photoelectric molecule QB was constructed through combining an electron-withdrawing unit, a triarylborane, and a metal-ligand unit of bis(2-picolyl)amine. The crystallization behavior and crystalline photoelectric properties of QB and its complexes were thoroughly studied. This compound exhibited polymorphism, and a green emitting block-like crystal and blue-emission lamellar crystal were obtained, respectively. Their different photoluminescence mechanisms were clarified through X-ray crystallographic analysis and theoretical calculations. Furthermore, the single-crystal structures of the complexes of QB coordinating with KCN and Zn(ClO4)2 were also determined. Crystal QB-KCN emitted strong blue fluorescence at 445 nm, owing to the formation of rigid 2-to-2 adduct, which could effectively suppress non-radiative transitions. Crystal QB-Zn(ClO4)2 showed very weak cyan emission due to its loose molecular packing. The electrochemical results illuminated that the metal coordination can effectively affect the electron-withdrawing ability of conjugated triarylborane, and further affect the monomolecular luminescent properties due to the intramolecular charge transfer. We believe that polymorphism and metal coordination are available means to obtain excellent crystalline photoelectric materials.

Parametric amplification based on intermodal four-wave mixing between different supermodes in coupled-core fibers.

Parametric amplifiers relying on the nonlinear four-wave mixing process are known for their signature symmetric gain spectrum, where signal and idler sidebands are generated on both sides of a powerful pump wave frequency. In this article we show analytically and numerically that parametric amplification in two identically coupled nonlinear waveguides can be designed in such a way that signals and idlers are naturally separated into two different supermodes, hence providing idler-free amplification for the supermode carrying signals. This phenomenon is based on the coupled-core fibers analogue of intermodal four wave-mixing occurring in a multimode fiber. The control parameter is the pump power asymmetry between the two waveguides, which leverages the frequency dependency of the coupling strength. Our findings pave the way for a novel class of parametric amplifiers and wavelength converters, based on coupled waveguides and dual-core fibers.