Nonlinear Optical Waveguides Research Articles

Enhanced optical Kerr nonlinearity of graphene/Si hybrid waveguide

In this work, we experimentally study the optical Kerr nonlinearities of graphene/Si hybrid waveguides with enhanced self-phase modulation. In the case of CMOS compatible materials for nonlinear optical signal processing, Si and silicon nitride waveguides have been extensively investigated over the past decade. However, Si waveguides exhibit strong two-photon absorption (TPA) at telecommunication wavelengths, which leads to a significant reduction of the nonlinear figure-of-merit (FOM). In contrast, a silicon nitride based material system usually suppresses the TPA but simultaneously leads to the reduction of Kerr nonlinearity by one order of magnitude. Here, we introduce a graphene/Si hybrid waveguide, which maintains the optical properties and CMOS compatibility of Si waveguides, while enhancing the Kerr nonlinearity, by transferring over to the top of the waveguides. The graphene/Si waveguides are measured to have an enhanced nonlinear parameter of 510 W−1 m−1, compared with that of the Si waveguide of 150 W−1 m−1. An enhanced nonlinear FOM of 2.48 ± 0.25 has been achieved, which is four times larger than that of the Si waveguide of 0.6 ± 0.1. This work reveals the potential application of graphene/Si hybrid waveguides with high Kerr nonlinearity and FOM for nonlinear all-optical signal processing.

Topology optimization of nonlinear optical waveguide devices considering output signal phase

A signal output of optical devices with multi-input ports, such as a logic gate, depends on the phase difference between input ports. In order to cascade optical devices, it is essential to design such devices considering not only desired output power but also desired output signal phase. We propose a topology optimization method for optical devices considering the output signal phase. In our approach, the beam propagation method (BPM) is employed as a numerical simulation method and the adjoint variable method (AVM) is used to calculate the sensitivity of output power and signal phase to design parameters. The validity and the effectiveness of our approach are verified through design examples of a three-branching waveguide with linear media and an all-optical logic gate utilizing nonlinear media.

Эволюция интенсивных световых импульсов в нелинейной среде с учетом эффекта Рамана

AbstractThe evolution of high-intensity light pulses in nonlinear single-mode optical waveguides, the dynamics of light in which is described by the nonlinear Schrödinger equation with a Raman term taking into account stimulated Raman self-scattering of light, is investigated. It is demonstrated that dispersive shock waves the behavior of which is much more diverse than in the case of ordinary nonlinear Schrödinger equation with a Kerr nonlinearity are formed in the process of evolution of pulses of substantially high intensity. The Whitham equations describing slow evolution of the dispersive shock waves are derived under the assumption of the Raman term being small. It is demonstrated that the dispersive shock waves can asymptotically assume a stationary profile when the Raman effect is taken into account. Analytical theory is corroborated by numerical calculations.

基于五氧化二钽集成非线性光波导的高重复频率宽带平坦相干光频率梳的产生

基于五氧化二钽集成非线性光波导的高重复频率宽带平坦相干光频率梳的产生

Symmetry breaking in competing single-well linear-nonlinear potentials

The combination of linear and nonlinear potentials, both shaped as a single well, enables competition between the confinement and expulsion induced by the former and latter potentials, respectively. We demonstrate that this setting leads to spontaneous symmetry breaking (SSB) of the ground state in the respective generalized nonlinear Schr\"{o}dinger (Gross-Pitaevskii) equation, through a spontaneous off-center shift of the trapped mode. Two different SSB bifurcation scenarios are possible, depending on the shape of the nonlinearity-modulation profile, which determines the nonlinear potential. If the profile is bounded (remaining finite at $|x|\rightarrow \infty $), at a critical value of the integral norm the spatially symmetric state loses its stability, giving rise to a pair of mutually symmetric stable asymmetric ones via a direct pitchfork bifurcation. On the other hand, if the nonlinear potential is unbounded, two unstable asymmetric modes merge into the symmetric metastable one and destabilize it, via an inverted pitchfork bifurcation. Parallel to a systematic numerical investigation, basic results are obtained in an analytical form. The settings can be realized in Bose-Einstein condensates and nonlinear optical waveguides.

Nonlinear planar optical waveguide sensors comprising metamaterial guiding films at terahertz frequencies

In this paper, we propose a metamaterial film bounded by a nonlinear cover and a dielectric substrate as a THz wave sensor. The dispersion characteristics and magnetic field profiles have been derived, computed and analyzed. Confinement of the light waves was found to increase with both nonlinearity and frequency. We believe our results can be used to design novel tunable future sensors.

On the Hamiltonian form of cross-mode modulation in nonlinear optical waveguides.

It is commonly believed that the Hamiltonian approach applies only to linear systems, or nonlinear systems with proper linearization procedures. In this Letter, we show that the Hamiltonian approach based on linear coupled-mode theory applies very well for cross-mode modulation, i.e., field variation of the probe light induced by a strong co-propagating pump light in a degenerate mode group. By deriving eigenvalues and eigenvectors of the nonlinear system, evolution of the probe light can be obtained, which agrees with numerical simulations of multimode nonlinear Schrödinger equations. Using the Hamiltonian approach, a simple approach for determining the pump mode for realizing arbitrary mode conversion is discussed. Two concrete scenarios of the optically induced vector mode conversions within the LP11-mode group are further exemplified.

Design and fabrication of nonlinear optical waveguides for far-detuned wavelength conversion to the mid-infrared

Abstract Highly nonlinear gain media that are optically pumped by rare-earth doped sources have become a promising approach for the fabrication of all-fiber mid-infrared laser sources. This article focuses on the recent progresses of highly nonlinear chalcogenide microwires as practical gain media for far-detuned wavelength conversion towards the mid-infrared.

Transmission stabilization in soliton-based optical-waveguide systems by frequency-dependent linear gain-loss and the Raman self-frequency shift

We study transmission stabilization against radiation emission in soliton-based nonlinear optical waveguides with weak linear gain-loss, cubic loss, and delayed Raman response. We show by numerical simulations with perturbed nonlinear Schr\"odinger propagation models that transmission quality in waveguides with frequency independent linear gain and cubic loss is not improved by the presence of delayed Raman response due to the lack of an efficient mechanism for suppression of radiation emission. In contrast, we find that the presence of delayed Raman response leads to significant enhancement of transmission quality in waveguides with frequency dependent linear gain-loss and cubic loss. Enhancement of transmission quality in the latter waveguides is enabled by the separation of the soliton's spectrum from the radiation's spectrum due to the Raman-induced self-frequency shift and by efficient suppression of radiation emission due to the frequency dependent linear gain-loss. Further numerical simulations demonstrate that the enhancement of transmission quality in waveguides with frequency dependent linear gain-loss, cubic loss, and delayed Raman response is similar to transmission quality enhancement in waveguides with linear gain, cubic loss, and guiding filters with a varying central frequency.

Nonlinear optical waveguides inscribed by fs-laser in organic crystal for broadband second harmonic generation of UV pulses

Optical waveguides are main components for the development of integrated photonic devices, not only for allowing light guidance but also for their ability to act as nonlinear optical elements. Direct laser writing with ultrashort pulses has provided considerable advances in the fabrication of 3D waveguides and the improvement of its optical properties. Nonetheless, such progresses have been achieved for waveguides designed in inorganic materials and little attention has been devoted to organic crystals, which offer new perspectives for the field. In this direction, this paper describes the fs-laser inscription of cladding waveguides in an amino acid crystal, with guiding losses on the order of 0.5 dB/mm at visible and infrared regions. Such waveguides are able to act as active nonlinear optical elements, supporting broadband second harmonic generation centered at 377 nm, with a normalized power conversion efficiency of (10.3 ± 0.4) % (MW cm2)−1. Its normalized intensity conversion efficiency was greater than the one for the crystal itself, probably due to the influence of the waveguide dispersion contribution on the phase matching condition.

Stability band structure for periodic states in periodic potentials

A class of periodic solutions of the nonlinear Schrödinger equation with non-Hermitian potentials are considered. The system may be implemented in planar nonlinear optical waveguides carrying an appropriate distribution of local gain and loss, in a combination with a photonic-crystal structure. The complex potential is built as a solution of the inverse problem, which predicts the potential supporting required periodic solutions. The main subject of the analysis is the spectral structure of the linear (in)stability for the stationary spatially periodic states in the periodic potentials. The stability and instability bands are calculated by means of the plane-wave-expansion method, and verified in direct simulations of the perturbed evolution. The results show that the periodic solutions may be stable against perturbations in specific Floquet–Bloch bands, even if they are unstable against small random perturbations.

Large stable oscillations due to Hopf bifurcations in amplitude dynamics of colliding soliton sequences

We demonstrate that the amplitudes of optical solitons in nonlinear multisequence optical waveguide coupler systems with weak linear and cubic gain-loss exhibit large stable oscillations along ultra-long distances. The large stable oscillations are caused by supercritical Hopf bifurcations of the equilibrium states of the Lotka–Volterra (LV) models for dynamics of soliton amplitudes. The predictions of the LV models are confirmed by numerical simulations with the coupled cubic nonlinear Schrödinger (NLS) propagation models with 2 ≤ N ≤ 4 pulse sequences. Thus, we provide the first demonstration of intermediate nonlinear amplitude dynamics in multisequence soliton systems, described by the cubic NLS equation. Our findings are also an important step towards realization of spatio-temporal chaos with multiple periodic sequences of colliding NLS solitons.

Solitary wave for a nonintegrable discrete nonlinear Schrödinger equation in nonlinear optical waveguide arrays**Project supported by the National Natural Science Foundation of China (Grant Nos. 11671255 and 11701510), the Ministry of Economy and Competitiveness of Spain (Grant No. MTM2016-80276-P (AEI/FEDER, EU)), and the China Postdoctoral Science Foundation (Grant No. 2017M621964).

We study a nonintegrable discrete nonlinear Schrödinger (dNLS) equation with the term of nonlinear nearest-neighbor interaction occurred in nonlinear optical waveguide arrays. By using discrete Fourier transformation, we obtain numerical approximations of stationary and travelling solitary wave solutions of the nonintegrable dNLS equation. The analysis of stability of stationary solitary waves is performed. It is shown that the nonlinear nearest-neighbor interaction term has great influence on the form of solitary wave. The shape of solitary wave is important in the electric field propagating. If we neglect the nonlinear nearest-neighbor interaction term, much important information in the electric field propagating may be missed. Our numerical simulation also demonstrates the difference of chaos phenomenon between the nonintegrable dNLS equation with nonlinear nearest-neighbor interaction and another nonintegrable dNLS equation without the term.

Design and Analysis of Dispersion Engineered Rib Waveguides for On-Chip Mid-Infrared Supercontinuum

A highly nonlinear optical rib waveguide structure with various core-shape profiles in As2Se3 chalcogenide glass has been reported for on-chip supercontinuum sources in the mid-infrared region. The reported rib waveguide structure offers the ultrabroadband mid-infrared spectral broadening spanning 1000–10 900 and 1000–11 880 nm for rectangular-core and triangular-core profiles, respectively, using 497-fs hyperbolic laser pulses of a peak power of 6.4 kW at 2800 nm. To the best of our knowledge, such an ultrabroadband supercontinuum spectrum has been reported for the first time using the triangular-core profile of waveguide in chalcogenide glass. The reported rib waveguide devices generating mid-infrared supercontinuum will be applicable in various important applications such as security, noninvasive early disease detection, defense, and spectroscopy.

Towards on-chip photon-pair bell tests: Spatial pump filtering in a LiNbO3 adiabatic coupler

Nonlinear optical waveguides enable the integration of entangled photon sources and quantum logic gates on a quantum photonic chip. One of the major challenges in such systems is separating the generated entangled photons from the pump laser light. In this work, we experimentally characterize double-N-shaped nonlinear optical adiabatic couplers designed for the generation of spatially entangled photon pairs through spontaneous parametric down-conversion, while simultaneously providing spatial pump filtering and keeping photon-pair states pure. We observe that the pump photons at a wavelength of 671 nm mostly remain in the central waveguide, achieving a filtering ratio of over 20 dB at the outer waveguides. We also perform classical characterization at the photon-pair wavelength of 1342 nm and observe that light fully couples from an input central waveguide to the outer waveguides, showing on chip separation of the pump and the photon-pair wavelength.

Impact of loss on the light propagation in 1D optical waveguide array in the presence of Kerr-type nonlinearity

The interplay between radiation loss (diagonal and off-diagonal) and Kerr-type nonlinearity on the light propagation in 1D array of nonlinear dissipative optical waveguides are investigated numerically. Our results show that, at low nonlinear parameters, the diagonal loss only reduces the light intensity in the guides and does not affect the ballistic regime of light spreading. However, for nonlinear parameters above a critical value, the transition from the localized to the ballistic regime can be observed, after certain propagation distance. The study of the interplay between off-diagonal loss term and Kerr type nonlinearity, demonstrates that the results depend mainly to the nonlinear parameter strength. In this case, and for low strength of nonlinearity, the transition from ballistic to diffusive regime is observed after a critical propagation distance, while, spreading from localized to diffusive regime occurs at high nonlinear parameters (above the critical one). In addition, we have examined the impact of the both diagonal and off-diagonal losses in highly nonlinear optical lattices. In this case, by increasing the propagation distance, three different regimes of light spreading (from localized to the ballistic, and then, from ballistic to the diffusive) can be observed. Both critical propagation distances in which these transitions occur increase by the magnitude of the nonlinear parameter, while, decrease by the enhancement of the loss coefficients.

Rib waveguide in Ga-Sb-S chalcogenide glass for on-chip mid-IR supercontinuum sources: Design and analysis

Recently, highly nonlinear Ga-Sb-S chalcogenide glasses have been reported for promising mid-infrared applications such as thermal imaging, nonlinear optics, and infrared lasers. However, the nonlinear optical fiber and waveguide geometries in Ga-Sb-S chalcogenide glasses have not been reported to date. In this paper, we numerically investigate the design of the dual zero dispersion engineered rib waveguide in Ga8Sb32S60 chalcogenide glass by employing MgF2 glass as a lower and upper cladding material. The waveguide structure possesses nonlinearity as high as 24 100 W−1 Km−1 and 14 000 W−1 Km−1 at 2050 and 2800 nm, respectively. The reported waveguide is able to generate a mid-infrared supercontinuum spectrum spanning from 1000 to 7800 nm when it pumped with 97 femtosecond laser pulses of a peak power of 1 kW at 2050 nm. We have also showed that the supercontinuum spectrum can be extended to the spectral range of 1000–9700 nm using pumping with 497 fs pulses of a peak power of 6.4 kW at 2800 nm. To the best of our knowledge, the proposed rib waveguide structure in Ga8Sb32S60 chalcogenide glass has been reported first time for nonlinear applications. Such a dispersion engineered rib waveguide structure has potential applications for the low-cost, power efficient, and compact on-chip mid-infrared supercontinuum sources and other nonlinear photonic devices.

Nonlinear photonics on-a-chip in III-V semiconductors: quest for promising material candidates.

We propose several designs of nonlinear optical waveguides based on quaternary III-V semiconductors AlGaAsSb and InGaAsP. These semiconductor materials have been widely used for laser sources. Their nonlinear optical properties, however, yet remain unexplored, while the materials definitely hold promise for nonlinear photonics on-a-chip. The latter argument is based on the fact that III-V compounds tend to exhibit high values of the nonlinear optical susceptibilities, while the nonlinear absorption in these materials can be minimized in the wavelength range of interest through a proper selection of the material composition. We present the modal analysis for the designed waveguide structures and show that the effective mode area much less than 1 μm2 can be achieved through a design optimization in each of the two compounds. We also present specific waveguide designs that demonstrate zero dispersion at the wavelengths of interest. The designed AlGaAsSb and InGaAsP waveguides are thus expected to demonstrate high values of the nonlinear coefficient and efficient nonlinear optical interactions.

Effects of the third-order dispersion on continuous waves in complex potentials

A class of constant-amplitude (CA) solutions of the nonlinear Schrodinger equation with the third-order spatial dispersion (TOD) and complex potentials are considered. The system can be implemented in specially designed planar nonlinear optical waveguides carrying a distribution of local gain and loss elements, in a combination with a photonic-crystal structure. The complex potential is built as a solution of the inverse problem, which predicts the potential supporting a required phase-gradient structure of the CA state. It is shown that the diffraction of truncated CA states with a correct phase structure can be strongly suppressed. The main subject of the analysis is the modulational instability (MI) of the CA states. The results show that the TOD term tends to attenuate the MI. In particular, simulations demonstrate a phenomenon of weak stability, which occurs when the linear-stability analysis predicts small values of the MI growth rate. The stability of the zero state, which is a nontrivial issue in the framework of the present model, is studied too

Engineering temporal-mode-selective frequency conversion in nonlinear optical waveguides: from theory to experiment.

Quantum frequency conversion (FC) in nonlinear optical media is a powerful tool for temporal-mode selective manipulation of light. Recent attempts at achieving high mode selectivities and/or fidelities have had to resort to multi-dimensional optimization schemes to determine the system's natural Schmidt modes. Certain combinations of relative-group velocities between the relevant frequency bands, medium length, and temporal pulse widths have been known to achieve good selectivities (exceeding 80%) for temporal modes that are nearly identical to pump pulse shapes, even for high conversion efficiencies. Working in this parameter regime using an off-the-shelf, second-harmonic generation, MgO:PPLN waveguide, and with pulses on the order of 500 fs at wavelengths around 800 nm, we verify experimentally that model-predicted Schmidt modes provide the high temporal-mode selectivity expected. The good agreement between experiment and theory paves the way to the implementation of a proposed two-stage FC scheme that is predicted by the present theory to reach near-perfect (100%) selectivity.