Optical nonlinearity enhancement with graphene-decorated silicon waveguides

Spatially resolved multimode excitation for smooth supercontinuum generation in a SiN waveguide

We propose a method of supercontinuum light generation enhanced by multimode excitation in a precisely dispersion-engineered deuterated SiN (SiN:D) waveguide. Although a regularly designed SiN-based nonlinear optical waveguide exhibits anomalous dispersion with the fundamental and first-order multimode operation, the center-symmetric light pumping at the input edge has so far inhibited the full potential of the nonlinearity of SiN-based materials. On the basis of numerical analysis and simulation for the SiN:D waveguide, we intentionally applied spatial position offsets to excite the fundamental and higher-order modes to realize bandwidth broadening with flatness. Using this method, we achieved an SNR improvement of up to 18 dB at a wavelength of 0.6 µm with an offset of about 1 µm in the Y-axis direction and found that the contribution was related to the presence of dispersive waves due to the excitation of TE₁₀, and TE₀₁ modes.

Pulsed Four-Wave Mixing at Telecom Wavelengths in Si3N4 Waveguides Locally Covered by Graphene

Recently, the nonlinear optical response of graphene has been widely investigated, as has the integration of this 2D material onto dielectric waveguides so as to enhance the various nonlinear phenomena that underpin all-optical signal processing applications at telecom wavelengths. However, a great disparity continues to exist from these experimental reports, depending on the used conditions or the hybrid devices under test. Most importantly, hybrid graphene-based waveguides were tested under relatively low powers, and/or combined with waveguide materials that already exhibited a nonnegligible nonlinear contribution, thereby limiting the practical use of graphene for nonlinear applications. Here, we experimentally investigate the nonlinear response of Si3N4 waveguides that are locally covered by submillimeter-long graphene patches by means of pulsed degenerate four-wave mixing at telecom wavelength under 7 W peak powers. Our measurements and comparison with simulations allow us to estimate a local change of the nonlinearity sign as well as a moderate increase of the nonlinear waveguide parameter (γ∼-10 m^-1W^-1) provided by graphene. Our analysis also clarifies the tradeoff associated with the loss penalty and nonlinear benefit afforded by graphene patches integrated onto passive photonic circuits, thereby providing some guidelines for the design of hybrid integrated nonlinear devices, coated with graphene, or, more generally, any other 2D material.

Enhanced Spectral Broadening of Femtosecond Optical Pulses in Silicon Nanowires Integrated with 2D Graphene Oxide Films

We experimentally demonstrate enhanced spectral broadening of femtosecond optical pulses after propagation through silicon-on-insulator (SOI) nanowire waveguides integrated with two-dimensional (2D) graphene oxide (GO) films. Owing to the strong mode overlap between the SOI nanowires and the GO films with a high Kerr nonlinearity, the self-phase modulation (SPM) process in the hybrid waveguides is significantly enhanced, resulting in greatly improved spectral broadening of the femtosecond optical pulses. A solution-based, transfer-free coating method is used to integrate GO films onto the SOI nanowires with precise control of the film thickness. Detailed SPM measurements using femtosecond optical pulses are carried out, achieving a broadening factor of up to ~4.3 for a device with 0.4-mm-long, 2 layers of GO. By fitting the experimental results with the theory, we obtain an improvement in the waveguide nonlinear parameter by a factor of ~3.5 and in the effective nonlinear figure of merit (FOM) by a factor of ~3.8, relative to the uncoated waveguide. Finally, we discuss the influence of GO film length on the spectral broadening and compare the nonlinear optical performance of different integrated waveguides coated with GO films. These results confirm the improved nonlinear optical performance of silicon devices integrated with 2D GO films.

A generic model for the study of supercontinuum generation in graphene-covered nanowires

We study supercontinuum (SC) generation in graphene-covered nanowires based on a generic model that correctly accounts for the evolution of the photon number under Kerr and two-photon absorption processes, and the influence of graphene is treated within the framework of saturable photoexcited-carrier refraction. We discuss the role of the various effects on the generation of SC by a thorough analysis of short-pulse propagation in two different kinds of graphene-covered nanowires, one made of silicon nitride and the other made of silicon. Finally, we discuss the effect of stacking graphene layers as a means to enhance SC generation with pulse powers compatible with those in integrated optical devices.

Enhancing Si3N4 Waveguide Nonlinearity with Heterogeneous Integration of Few-Layer WS2

The heterogeneous integration of low-dimensional materials with photonic waveguides has spurred wide research interest. Here, we report on the experimental investigation and the numerical modeling of enhanced nonlinear pulse broadening in silicon nitride waveguides with the heterogeneous integration of few-layer WS2. After transferring a few-layer WS2 flake of ∼14.8 μm length, the pulse spectral broadening in a dispersion-engineered silicon nitride waveguide has been enhanced by ∼48.8% in bandwidth. Through numerical modeling, an effective nonlinear coefficient higher than 600 m-1 W-1 has been retrieved for the heterogeneous waveguide indicating an enhancement factor of larger than 300 with respect to the pristine waveguide at a wavelength of 800 nm. With further advances in two-dimensional material fabrication and integration techniques, on-chip heterostructures will offer another degree of freedom for waveguide engineering, enabling high-performance nonlinear optical devices, such as frequency combs and quantum light sources.

All-optical graphene-on-silicon slot waveguide modulator based on graphene's Kerr effect

All-optical graphene-based optical modulators have recently attracted much attention because of their ultrafast and broadband response characteristics (bandwidth larger than 100 GHz) in comparison with the previous graphene-based optical modulators, which are electrically tuned via the graphene Fermi level. Silicon photonics has some benefits such as low cost and high compatibility with CMOS design and manufacturing technology. On the other hand, graphene has a unique large nonlinear Kerr coefficient, which we calculate using graphene's tight-binding model based on the semiconductor Bloch equations. Its real and imaginary parts are negative at the wavelength of 1.55 µm and E_F=0.1eV. To simultaneously use the benefits mentioned above, we present an all-optical, CMOS-compatible, and graphene-on-silicon slot (GOSS) waveguide extinction and phase modulator that consists of two different geometries. The first one consists of a one-stage GOSS waveguide with a single layer of graphene. To increase the light-graphene interaction and consequently enhance the modulation efficiency (ME), another stage of the GOSS waveguide is placed over the first one. This two-stage configuration is called a graphene-on-silicon double-slot (GOSDS) waveguide. The ME, insertion loss (IL), and modulation depth (MD) for a 12.5 µm GOSDS waveguide modulator with a double layer of graphene can reach 0.241 dB/µm, 1.31 dB, and 77%, respectively, at optical pump intensities about 9MWcm^-2. Our design has a smaller waveguide length (17.6 times) than the previous all-optical graphene-on-silicon ribbon waveguide extinction modulator and high MD (about 2 times) in comparison with a graphene-clad microfiber all-optical extinction modulator. Compared with an all-optical Mach-Zehnder interferometer phase modulator, our design has short graphene coated waveguide length (≈0.1 times) and low local optical intensities (≈0.043 times) needed for π phase shift. This study may promote the design and realization of high-performance, wideband, compact, and all-optical control on a single chip with a reasonable contrast level.

Quantum Noise in Fibers with Arbitrary Nonlinear Profiles

In this Letter we introduce a novel equation addressing the effect of quantum noise in optical fibers with arbitrary frequency-dependent nonlinear profiles. To the best of our knowledge, such an endeavor has not been undertaken before despite the growing relevance of fiber optics in the design of new quantum devices. We show that the stochastic generalized nonlinear Schrödinger equation, derived from a quantum theory of optical fibers, leads to unphysical results such as a negative photon number and the appearance of a dominant anti-Stokes sideband when applied to this kind of waveguides. Starting from a recently introduced master-equation approach to propagation in fibers, we derive a novel stochastic photon-conserving nonlinear Schrödinger equation suitable for modeling arbitrary nonlinear profiles, thus greatly enhancing the study of fiber-based quantum devices.

Enhanced Kerr Nonlinearity and Nonlinear Figure of Merit in Silicon Nanowires Integrated with 2D Graphene Oxide Films

Layered two-dimensional (2D) graphene oxide (GO) films are integrated with silicon-on-insulator (SOI) nanowire waveguides to experimentally demonstrate an enhanced Kerr nonlinearity, observed through self-phase modulation (SPM). The GO films are integrated with SOI nanowires using a large-area, transfer-free, layer-by-layer coating method that yields precise control of the film thickness. The film placement and coating length are controlled by opening windows in the silica cladding of the SOI nanowires. Owing to the strong mode overlap between the SOI nanowires and the highly nonlinear GO films, the Kerr nonlinearity of the hybrid waveguides is significantly enhanced. Detailed SPM measurements using picosecond optical pulses show significant spectral broadening enhancement for SOI nanowires coated with 2.2 mm long films of 1-3 layers of GO and 0.4 mm long films with 5-20 layers of GO. By fitting the experimental results with theory, the dependence of GO's Kerr nonlinearity on layer number and pulse energy is obtained, showing interesting physical insights and trends of the layered GO films from 2D monolayers to quasi bulk-like behavior. Finally, we show that by coating SOI nanowires with GO films, the effective nonlinear parameter of SOI nanowires is increased 16-fold, with the effective nonlinear figure of merit (FOM) increasing by about 20 times to FOM > 5. These results reveal the strong potential of using layered GO films to improve the Kerr nonlinear optical performance of silicon photonic devices.

Evaluation of graphene optical nonlinearity with photon-pair generation in graphene-on-silicon waveguides

We evaluate the nonlinear coefficient of graphene-on-silicon waveguides through the coincidence measurement of photon-pairs generated via spontaneous four-wave mixing. We observed the temporal correlation of the photon-pairs from the waveguides over various transfer layouts of graphene sheets. A simple analysis of the experimental results using coupled-wave equations revealed that the atomically-thin graphene sheets enhanced the nonlinearity of silicon waveguides up to ten-fold. The results indicate that the purely χ ⁽³⁾-based effective nonlinear refractive index of graphene is on the order of 10^-13 m ²/W, and provide important insights for applications of graphene-based nonlinear optics in on-chip nanophotonics.

Graphene's nonlinear-optical physics revealed through exponentially growing self-phase modulation

Graphene is considered a record-performance nonlinear-optical material on the basis of numerous experiments. The observed strong nonlinear response ascribed to the refractive part of graphene's electronic third-order susceptibility χ⁽³⁾ cannot, however, be explained using the relatively modest χ⁽³⁾ value theoretically predicted for the 2D material. Here we solve this long-standing paradox and demonstrate that, rather than χ⁽³⁾-based refraction, a complex phenomenon which we call saturable photoexcited-carrier refraction is at the heart of nonlinear-optical interactions in graphene such as self-phase modulation. Saturable photoexcited-carrier refraction is found to enable self-phase modulation of picosecond optical pulses with exponential-like bandwidth growth along graphene-covered waveguides. Our theory allows explanation of these extraordinary experimental results both qualitatively and quantitatively. It also supports the graphene nonlinearities measured in previous self-phase modulation and self-(de)focusing (Z-scan) experiments. This work signifies a paradigm shift in the understanding of 2D-material nonlinearities and finally enables their full exploitation in next-generation nonlinear-optical devices.