Nonlinear Silicon Research Articles

Non-magnetic continuum quasi bound terahertz non-reciprocal device

The terahertz isolator breaks the Lorentz reciprocity and is a typical non-reciprocal unidirectional transmission device, which is an indispensable and important component in terahertz systems. Due to the loss of terahertz radiation in current non-reciprocal materials, terahertz non-reciprocal devices remain a significant challenge. By combining third-order nonlinearity with the out of plane asymmetry and in-plane breaking of device structures, a nonlinear silicon grating metasurface terahertz isolator is proposed. By controlling the quasi-bound state radiation linewidth of the continuum medium, the designed silicon grating metasurface structure has an isolation of 12.08 dB and an insertion loss of 4.7 dB under terahertz intensity of 0.5 MW/cm2. This device provides a new solution for the design of terahertz non-reciprocal devices and has great application prospects in terahertz integrated systems.

Effect of squared, cubic and quartic on-site potentials on heat conduction in a nonlinear silicon lattice

This paper explains the process of heat conduction in a nonlinear silicon lattice governed by squared, cubic and quartic on-site potentials along with squared and quartic interaction potentials. The tanh method is employed to construct solutions to the resulting nonlinear equations. The results show the transfer of heat in the form of solitary waves which are presented graphically.

Infrared imaging with nonlinear silicon resonator governed by high-Q quasi-BIC states

Nonlinear light-matter interactions have emerged as a promising platform for various applications, including imaging, nanolasing, background-free sensing, etc. Subwavelength dielectric resonators offer unique opportunities for manipulating light at the nanoscale and miniturising optical elements. Here, we explore the resonantly enhanced four-wave mixing (FWM) process from individual silicon resonators and propose an innovative FWM-enabled infrared imaging technique that leverages the capabilities of these subwavelength resonators. Specifically, we designed high-Q silicon resonators hosting dual quasi-bound states in the continuum at both the input pump and signal beams, enabling efficient conversion of infrared light to visible radiation. Moreover, by employing a point-scanning imaging technique, we achieve infrared imaging conversion while minimising the dependence on high-power input sources. This combination of resonant enhancement and point-scanning imaging opens up new possibilities for nonlinear imaging using individual resonators and shows potential in advancing infrared imaging techniques for high-resolution imaging, sensing, and optical communications.

A multigrid waveform relaxation method for solving the nonlinear silicon problem with relaxing boundary conditions

This paper introduces a multigrid FAS Waveform Relaxation method (FAS-MGWR) for solving a heat transfer model in a thin and homogeneous silicon bar with constant density and heat capacity. This method exhibits versatility, making it applicable to a range of problems including electronic device engineering, numerical simulation of nanofluids, among others. The Finite Difference Method with central differences (CDS) for spatial discretization and the Crank-Nicolson method for temporal approximation were utilized. Comparison with literature results and code verification demonstrated that irrespective of the combinations of physical and numerical parameters, the apparent order of discretization error converges to the theoretical asymptotic order. The study underscores the superior performance of the proposed FAS-MGWR method, notable for its parallel architecture, particularly in terms of computational time, compared to existing literature. Notably, the FAS-MGWR method was found to have excellent convergence factor and speed-up in relation to its singlegrid version, underscoring its efficiency and practical advantage in addressing complex thermal problems.

Raman amplification at 2.2 μm in silicon core fibers with prospects for extended mid-infrared source generation

Raman scattering provides a convenient mechanism to generate or amplify light at wavelengths where gain is not otherwise available. When combined with recent advancements in high-power fiber lasers that operate at wavelengths ~2 μm, great opportunities exist for Raman systems that extend operation further into the mid-infrared regime for applications such as gas sensing, spectroscopy, and biomedical analyses. Here, a thulium-doped fiber laser is used to demonstrate Raman emission and amplification from a highly nonlinear silicon core fiber (SCF) platform at wavelengths beyond 2 μm. The SCF has been tapered to obtain a micrometer-sized core diameter (~1.6 μm) over a length of 6 cm, with losses as low as 0.2 dB cm−1. A maximum on-off peak gain of 30.4 dB was obtained using 10 W of peak pump power at 1.99 μm, with simulations indicating that the gain could be increased to up to ~50 dB by extending the SCF length. Simulations also show that by exploiting the large Raman gain and extended mid-infrared transparency of the SCF, cascaded Raman processes could yield tunable systems with practical output powers across the 2–5 μm range.

Efficient high harmonic generation in nonlinear photonic moiré superlattice

Photonic moir\'e superlattice as an emerging platform of flatbands can tightly confine the light inside the cavity and has important applications not only in linear optics but also in nonlinear optics. In this paper, we numerically investigate the third- and fifth-order harmonic generation (THG and FHG) in photonic moir\'e superlattices fabricated by the nonlinear material silicon. The high conversion efficiency of THG and FHG is obtained at a relatively low intensity of fundamental light, e.g., the maximum conversion efficiency of THG and FHG arrives even up to be $10^{-2}$ and $10^{-9}$ at the fundamental intensity of 30 kW/m2, respectively, in the moir\'e superlattice of near flat band formed by the twist angle 6.01o. The results indicate the photonic moir\'e superlattice of a high-quality factor and flatbands is a promising platform for efficient nonlinear processes and advanced photonic devices.

Laser-Activated Second Harmonic Generation in Flexible Membrane with Si Nanowires.

Nonlinear silicon photonics has a high compatibility with CMOS technology and therefore is particularly attractive for various purposes and applications. Second harmonic generation (SHG) in silicon nanowires (NWs) is widely studied for its high sensitivity to structural changes, low-cost fabrication, and efficient tunability of photonic properties. In this study, we report a fabrication and SHG study of Si nanowire/siloxane flexible membranes. The proposed highly transparent flexible membranes revealed a strong nonlinear response, which was enhanced via activation by an infrared laser beam. The vertical arrays of several nanometer-thin Si NWs effectively generate the SH signal after being exposed to femtosecond infrared laser irradiation in the spectral range of 800-1020 nm. The stable enhancement of SHG induced by laser exposure can be attributed to the functional modifications of the Si NW surface, which can be used for the development of efficient nonlinear platforms based on silicon. This study delivers a valuable contribution to the advancement of optical devices based on silicon and presents novel design and fabrication methods for infrared converters.

Toward in-fiber nonlinear silicon photonics

Silicon core fibers (SCFs) offer an exciting opportunity to harness the nonlinear functionality of the semiconductor material within the excellent waveguiding properties of optical fiber systems. Over the past two decades, these fibers have evolved from a research curiosity into established components for use across a wide range of photonic applications. This article provides a comprehensive overview of the evolution of the SCFs, with a focus on the development of the fabrication and post-processing procedures that have helped unlock the nonlinear optical potential of this new technology. As well as reviewing the timeline of advancements in nonlinear performance, a perspective will be provided on the current challenges and future opportunities for in-fiber nonlinear silicon systems.

Classical imaging with undetected photons using four-wave mixing in silicon core fibers

Undetected-photon imaging allows for objects to be imaged in wavelength regions where traditional components are unavailable. Although first demonstrated using quantum sources, recent work has shown that the technique also holds with classical beams. To date, however, all the research in this area has exploited parametric down-conversion processes using bulk nonlinear crystals within free-space systems. Here, we demonstrate undetected-photon-based imaging using light generated via stimulated four-wave mixing within highly nonlinear silicon fiber waveguides. The silicon fibers have been tapered to have a core diameter of ∼ 915 nm to engineer the dispersion and reduce the insertion losses, allowing for tight mode confinement over extended lengths to achieve practical nonlinear conversion efficiencies ( ∼ − 30 dB ) with modest pump powers ( ∼ 48 mW ). Both amplitude and phase images are obtained using classically generated light, confirming the high degree of spatial and phase correlation of our system. The high powers ( > 10 nW ) and long coherence lengths ( > 4 km ) associated with our large fiber-based system result in high contrast and stable images.

Input-Output-Improved Reservoir Computing Based on Duffing Resonator Processing Dynamic Temperature Compensation for MEMS Resonant Accelerometer.

An MEMS resonant accelerometer is a temperature-sensitive device because temperature change affects the intrinsic resonant frequency of the inner silicon beam. Most classic temperature compensation methods, such as algorithm modeling and structure design, have large errors under rapid temperature changing due to the hysteresis of the temperature response of the accelerometer. To address this issue, we propose a novel reservoir computing (RC) structure based on a nonlinear silicon resonator, which is specifically improved for predicting dynamic information that is referred to as the input-output-improved reservoir computing (IOI-RC) algorithm. It combines the polynomial fitting with the RC on the input data mapping ensuring that the system always resides in the rich nonlinear state. Meanwhile, the output layer is also optimized by vector concatenation operation for higher memory capacity. Therefore, the new system has better performance in dynamic temperature compensation. In addition, the method is real-time, with easy hardware implementation that can be integrated with MEMS sensors. The experiment's result showed a 93% improvement in IOI-RC compared to raw data in a temperature range of -20-60 °C. The study confirmed the feasibility of RC in realizing dynamic temperature compensation precisely, which provides a potential real-time online temperature compensation method and a sensor system with edge computing.

Harmonic generation from silicon membranes at visible and ultraviolet wavelengths.

Nonlinear silicon photonics offers unique abilities to generate, manipulate and detect optical signals in nano-devices, with applications based on field localization and large third order nonlinearity. However, at the nanoscale, inefficient nonlinear processes, absorption, and the lack of realistic models limit the nano-engineering of silicon. Here we report measurements of second and third harmonic generation from undoped silicon membranes. Using experimental results and simulations we identify the effective mass of valence electrons, which determines second harmonic generation efficiency, and oscillator parameters that control third order processes. We can then accurately predict the nonlinear optical properties of complex structures, without introducing and artificially separating the effective χ(2) into surface and volume contributions, and by simultaneously including effects of linear and nonlinear dispersions. Our results suggest that judicious exploitation of the nonlinear dispersion of ordinary semiconductors can provide reasonable nonlinear efficiencies and transformational device physics well into the UV range.

Designing a single-mode anomalous dispersion silicon core fiber for temporal multiplet formation.

A highly nonlinear single-mode anomalous dispersion silicon core fiber (SCF) is suitably designed and optimized to generate a high repetition rate pulse train in the temporal domain from a single input pulse at a sufficiently shorter optimum length in comparison to silica-based standard fibers used for the same purpose. The large amount of Kerr-induced nonlinearity of a SCF is effectively utilized here such that input Gaussian pulses or pulse trains transform into a highly repetitive temporal multiplet. The effects of free-carrier generation-induced change in absorption and dispersion are included while studying the nonlinear pulse propagation through the SCF. To declare the generated pulse as a superior-graded triplet, a Q parameter, as a function of relative pulse parameters of the individual pulses of a triplet, is defined for the first time, to the best of our knowledge. Different pulse parameters are thoroughly optimized as well as the effect of external gain is examined from the perspective of requirement of shorter fiber length and development of quality triplets. Finally, the work is further extended for the formation of quadruplet pulses by the same type of SCF. It is to be mentioned here that such a methodical study for the generation of a temporal multiplet using a semiconductor core fiber has not been reported earlier.

One-Phototransistor-One-Memristor Array with High-Linearity Light-Tunable Weight for Optic Neuromorphic Computing.

The recent advances in optic neuromorphic devices have led to a subsequent rise in use for construction of energy-efficient artificial-vision systems. The widespread use can be attributed to their ability to capture, store, and process visual information from the environment. The primary limitations of existing optic neuromorphic devices include nonlinear weight updates, cross-talk issues, and silicon process incompatibility. In this study, a highlylinear, light-tunable, cross-talk-free, and silicon-compatible one-phototransistor-one-memristor (1PT1R) optic memristor is experimentally demonstrated for the implementation of an optic artificial neural network (OANN). For optic image recognition in the experiment, an OANN is constructed using a 16×3 1PT1R memristor array, and it is trained on an online platform. The model yields an accuracy of 99.3% after only ten training epochs. The 1PT1R memristor, which shows good performance, demonstrates its ability as an excellent hardware solution for highly efficient optic neuromorphic and edge computing.

Transient Super‐/Sub‐Linear Nonlinearities in Silicon Nanostructures

AbstractNonlinear silicon nano‐photonics has recently attracted significant attention due to the plethora of electric and magnetic Mie resonances that offer substantial enhancement of optical nonlinearities. Conventionally, the characterization of nonlinearity and its transient nature rely on intensity‐scan methods (z‐scan) in the spatial domain and pump‐probe techniques in the temporal domain. However, most studied ultrafast nonlinear effects are instantaneous, that is, strongest at zero pump‐probe delay, and have a solitary nonlinear power dependency (square, cubic, etc.). Here the authors found that when relaxation lifetime is dependent on pump fluence, transient nonlinearity appears. The effect is exemplified via Auger‐based nonlinear carrier dynamics of a nano‐silicon Mie‐resonator. The Auger‐induced transient nonlinearity not only locates at the time delay of several tens of picoseconds, but also displays diverse nonlinearities, including sub‐linear, super‐linear, and surprisingly full saturation, which features a “crossing point” where the probe scattering is pump‐fluence independent. The crossing point exists when the relaxation lifetime is inversely dependent to second power of carrier density. Combining confocal intensity‐scan (x‐scan) and pump‐probe temporal scan, the authors demonstrate that sub‐linearity and super‐linearity lead to swelled and reduced full‐width‐at‐half‐maximum (FWHM) of single‐nanostructure images, further confirming the nonlinearity as well as the potential of sub‐diffraction microscopy. The results open up a new avenue in nonlinear silicon nano‐photonics by adding new degrees of freedom in temporally tuning the types of transient nonlinearities, which are valuable in all‐optical signal processing and nano‐imaging.

Towards harmonic generation enhancement on silicon

Nowadays, nanostructures are routinely fabricated and integrated in different photonic devices for a variety of purposes and applications. For instance, nonlinear silicon photonics is an area of interest due to its high compatibility with CMOS technology, offering structure sizes down to 10nm at low cost. When the nanoscale is reached, light-matter interactions can display new phenomena, conventional approximations may not always be applicable, and new strategies must be sought in order to study and understand light-matter interactions at the nanoscale. In this work, we report a comparative experimental and theoretical study of second and third harmonic generation from silicon with the aim of explaining the nonlinear optical properties of this material at the nanoscale. We measure second and third harmonic efficiencies as a function of angle of incidence, polarization and pump wavelength. We compare these measurements with numerical simulations based on a microscopic hydrodynamic model which accounts for different possible contributions to the nonlinear polarization. This way, we have the ability to explain properly the SH and TH signals arising from different silicon samples. Once we have this knowledge, we are able to design more complex structures, such as silicon nanowires, where higher conversion efficiencies can be achieved.

Second Harmonic Generation in Germanium Quantum Wells for Nonlinear Silicon Photonics

Second-harmonic generation (SHG) is a direct measure of the strength of second-order nonlinear optical effects, which also include frequency mixing and parametric oscillations. Natural and artificial materials with broken center-of-inversion symmetry in their unit cell display high SHG efficiency, however, the silicon-foundry compatible group IV semiconductors (Si, Ge) are centrosymmetric, thereby preventing full integration of second-order nonlinearity in silicon photonics platforms. Here we demonstrate strong SHG in Ge-rich quantum wells grown on Si wafers. Unlike Si-rich epilayers, Ge-rich epilayers allow for waveguiding on a Si substrate. The symmetry breaking is artificially realized with a pair of asymmetric coupled quantum wells (ACQW), in which three of the quantum-confined states are equidistant in energy, resulting in a double resonance for SHG. Laser spectroscopy experiments demonstrate a giant second-order nonlinearity at mid-infrared pump wavelengths between 9 and 12 μm. Leveraging on the strong intersubband dipoles, the nonlinear susceptibility χ(2) almost reaches 105 pm/V, 4 orders of magnitude larger than bulk nonlinear materials for which, by the Miller’s rule, the range of 10 pm/V is the norm.

Tunable optical isolator using Graphene-photonic crystal-based hybrid system

In this article, an optical isolator is designed and simulated based on a hybrid configuration of the photonic crystal (PhC) and graphene. The PhC membrane is a hexagonal lattice of air holes arranged in a nonlinear silicon substrate. To provide a nonreciprocal transmission (optical isolator), breaking the symmetry of the light propagation path (the forth and back routes) is an essential condition. Here, the asymmetrical round trip of the light propagation and the Kerr-nonlinear effect are employed to obtain asymmetric propagation. The isolator structure includes a PhC waveguide that asymmetrically side-coupled to a specific embedded cavity. Then, to attain a tunable asymmetric transmission, a Nano-layer of graphene is located on the top of the mentioned PhC configuration. By altering the chemical potential of graphene one can control the isolation rate, frequency, and bandwidth of offered structure and thus possess a tunable optical isolator. The simulation results show that a 0.5 nm frequency shift can attain by the graphene chemical potential alterations from 0.45 eV to 0.65 eV in which it is suitable for Dense Wavelength Division Multiplexing (DWDM) communication and integrated optical circuits. Furthermore, as another advantage, a high forward normalized transmission (0.6) has resulted in a large average isolation rate of 32.5 dB due to low losses of the proposed structure.

Free-Space Nonreciprocal Transmission Based on Nonlinear Coupled Fano Metasurfaces

Optical nonlinearities can enable unusual light–matter interactions, with functionalities that would be otherwise inaccessible relying only on linear phenomena. Recently, several studies have harnessed the role of optical nonlinearities to implement nonreciprocal optical devices that do not require an external bias breaking time-reversal symmetry. In this work, we explore the design of a metasurface embedding Kerr nonlinearities to break reciprocity for free-space propagation, requiring limited power levels. After deriving the general design principles, we demonstrate an all-dielectric flat metasurface made of coupled nonlinear Fano silicon resonant layers realizing large asymmetry in optical transmission at telecommunication frequencies. We show that the metrics of our design can go beyond the fundamental limitations on nonreciprocity for nonlinear optical devices based on a single resonance, as dictated by time-reversal symmetry considerations. Our work may shed light on the design of flat subwavelength free-space nonreciprocal metasurface switches for pulsed operation which are easy to fabricate, fully passive, and require low operation power. Our simulated devices demonstrate a transmission ratio >50 dB for oppositely propagating waves, an operational bandwidth exceeding 600 GHz, and an insertion loss of <0.04 dB.

Nonlinear silicon photonics on CMOS-compatible tellurium oxide

Silicon photonics is coming of age; however, it is still lacking a monolithic platform for optical sources and nonlinear functionalities prompting heterogeneous integration of different materials tailored to different applications. Here we demonstrate tellurium oxide as a complementary metal oxide semiconductor silicon photonics platform for nonlinear functionalities, which is already becoming an established platform for sources and amplifiers. We show broadband supercontinuum generation covering the entire telecom window and show for the first time to our knowledge third-harmonic generation in its integrated embodiment. Together with the now-available lasers and amplifiers on integrated TeO 2 this work paves the way for a monolithic TeO 2 -based nonlinear silicon photonics platform.

Four-wave mixing of topological edge plasmons in graphene metasurfaces.

We study topologically protected four-wave mixing (FWM) interactions in a plasmonic metasurface consisting of a periodic array of nanoholes in a graphene sheet, which exhibits a wide topological bandgap at terahertz frequencies upon the breaking of time reversal symmetry by a static magnetic field. We demonstrate that due to the significant nonlinearity enhancement and large life time of graphene plasmons in specific configurations, a net gain of FWM interaction of plasmonic edge states located in the topological bandgap can be achieved with a pump power of less than 10 nW. In particular, we find that the effective nonlinear edge-waveguide coefficient is about γ ≃ 1.1 × 1013 W-1 m-1, i.e., more than 10 orders of magnitude larger than that of commonly used, highly nonlinear silicon photonic nanowires. These findings could pave a new way for developing ultralow-power-consumption, highly integrated, and robust active photonic systems at deep-subwavelength scale for applications in quantum communications and information processing.