Slow-light Silicon Research Articles

Slow-light silicon modulator with 110-GHz bandwidth.

Silicon modulators are key components to support the dense integration of electro-optic functional elements for various applications. Despite numerous advances in promoting the modulation speed, a bandwidth ceiling emerges in practices and becomes an obstacle toward Tbps-level throughput on a single chip. Here, we demonstrate a compact pure silicon modulator that shatters present bandwidth ceiling to 110 gigahertz. The proposed modulator is built on a cascade corrugated waveguide architecture, which gives rise to a slow-light effect. By comprehensively balancing a series of merits, the modulators can benefit from the slow light for better efficiency and compact size while remaining sufficiently high bandwidth. Consequently, we realize a 110-gigahertz modulator with 124-micrometer length, enabling 112 gigabits per second on-off keying operation. Our work proves that silicon modulators with 110 gigahertz are feasible, thus shedding light on its potentials in ultrahigh bandwidth applications such as optical interconnection and photonic machine learning.

Application of slow-light engineered chalcogenide and silicon photonic crystal waveguides for double-dimensional microwave frequency identification

Four-wave mixing effect was utilized within short dispersion-engineered slow-light silicon and AMTIR1 chalcogenide photonic crystal waveguides with group velocities of c/33 and c/23, respectively, for simultaneous measurement of frequency and power level of an RF tone over a frequency range of 0.01–80 GHz. In our numerical simulations, we considered the impact of various nonlinear phenomena that affected the system outputs. An FWM conversion efficiency of approximately − 45 dB was achieved for a 10 mW continuous-wave pump and probe in an 80 µm AMTIR1 PhC waveguide. In our system, two orthogonal and independent outputs were generated simultaneously. These independent outputs were achieved using a microwave photonics Hilbert transformer implemented using the transversal filtering approach. Since the process was inherently incoherent, the nonlinearity of the four-wave mixing did not affect the resulting signals orthogonality. The ability to simultaneously identify both the RF frequency and the power level of a microwave signal would make this system a perfect candidate for various applications, such as instantaneous frequency measurement receivers.

Utilization of slow light enhancement of four-wave mixing within a silicon photonic crystal for microwave frequency measurement purposes

We report the demonstration of an instantaneous frequency measurement system based on the four-wave mixing (FWM) effect in short dispersion engineered slow-light silicon photonic crystal waveguides for RF frequency measurement purposes within a range of 10 MHz to 80 GHz. Three nonlinear media were investigated including 3 mm ridge waveguide, 80 µm nanowire, and 80 µm photonic crystal (PhC). The system size could thus be decreased, and as a result system integration would become possible. We have shown that the optical power required to excite FWM is low enough to remove any need for optical amplification, and hence the system noise floor will be kept low. Issues due to the amplifier saturation will also be resolved this way. As a result, no noise reduction system, like lock-in amplification, would be required. A better system latency will also be achieved accordingly. The system dynamic range would also be improved in two ways. First, due to the low noise floor, and second, because of removing any optical amplifier that possibly could become saturated at higher power levels. All three media behaviors were simulated by the split step Fourier method, and the results showed that the best medium to be used is PhC.

DAC-Less PAM-4 Slow-Light Silicon Photonic Modulator Providing High Efficiency and Stability

We report a slow-light silicon modulator that enables high-speed PAM operation without using an electrical digital-to-analogue converter (DAC). Bragg grating resonators, integrated into each arm of a Mach-Zehnder modulator, enhance the phase modulation through the slow light effect. The optical 4-level PAM signal is generated by driving directly the segmented phase shifter design with two binary signals. This modulator presents an ultra-compact footprint (L <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SL-MZM</sub> = 570 μm), low energy consumption (73 fJ/bit), large electro-optic bandwidth (>40 GHz). Up to 90 Gb/s is achieved over an nm-range spectral operation bandwidth (Δλ = 2 nm). Compared to other low-energy resonator-based modulators, such as micro-rings, this operating bandwidth confers higher stability with a potential operating temperature range of ΔT = 50 °C. We further examine the robustness of the proposed design to fabrication variations by measurements of spectral properties across the wafer. This modulator is of particular interest for applications, such as short-range data communications that require multiple compact and energy-efficient modulators on a single chip.

Improving Low-Dispersion Bandwidth of the Silicon Photonic Crystal Waveguides for Ultrafast Integrated Photonics

We design a novel slow-light silicon photonic crystal waveguide which can operate over an extremely wide flat band for ultrafast integrated nonlinear photonics. By conveniently adjusting the radii and positions of the second air-holes rows, a flat slow-light low-dispersion band of 50 nm is achieved numerically. Such a slow-light photonic crystal waveguide with large flat low-dispersion wideband will pave the way for governing the femtosecond pulses in integrated nonlinear photonic platforms based on CMOS technology.

Efficiency-Speed Tradeoff in Slow-Light Silicon Photonic Modulators

The purpose of this paper is twofold. First, we discuss the efficiency-speed tradeoff in slow-light (SL) silicon photonic (SiP) modulators. For this, a comprehensive model for the electro-optic (EO) response of lumped-electrode SL Mach-Zehnder modulators (SL-MZMs) is presented. The model accuracy is verified by comparing it to experiments. Our analysis shows that slowing down the optical wave helps to enhance efficiency by increasing the interaction time between the optical wave and the uniform voltage across lumped electrodes, but at the cost of limiting the EO bandwidth. Then, we investigate SL-MZMs with traveling-wave (TW) electrodes whose dynamic interaction is predicted using a distributed circuit model. Having been solved by the finite-difference time-domain (FDTD) method, the model shows that TW SL-MZMs are capable of improving both efficiency and speed under an optimized SL effect. We also compare SL-MZMs with conventional MZMs (C-MZM) considering a figure of merit (FOM) that combines key parameters such as efficiency, loss, and EO bandwidth. We show that the additional loss of SL waveguides significantly impacts the preferred modulator choice at different baudrates. The second aim of this paper is to examine different design strategies to reduce Vπ of C-MZMs in order to meet the requirement of COMS driver using 1) a longer phase shifter, 2) higher doping densities, and 3) the SL effect. It is shown that the SL effect provides the best overall performance among the three. Indeed, only the SL effect offers simultaneous improvement in Vπ, footprint, and EO bandwidth; the other approaches provide Vπ reduction but at the cost of reduced speed or enlarged footprint (or even both).

Double-layer graphene on photonic crystal waveguide electro-absorption modulator with 12 GHz bandwidth

Abstract Graphene has been widely used in silicon-based optical modulators for its ultra-broadband light absorption and ultrafast optoelectronic response. By incorporating graphene and slow-light silicon photonic crystal waveguide (PhCW), here we propose and experimentally demonstrate a unique double-layer graphene electro-absorption modulator in telecommunication applications. The modulator exhibits a modulation depth of 0.5 dB/μm with a bandwidth of 13.6 GHz, while graphene coverage length is only 1.2 μm in simulations. We also fabricated the graphene modulator on silicon platform, and the device achieved a modulation bandwidth at 12 GHz. The proposed graphene-PhCW modulator may have potentials in the applications of on-chip interconnections.

Analysis of Kerr nonlinearity enhancement in silicon nitride waveguides using one-dimensional slow light structure

A corrugated based slow-light silicon nitride waveguide is studied numerically to enhance Kerr nonlinearity by increasing the group index of the waveguide at the band edge. The structure is optimized taking into account the limitations existing in CMOS-compatible platforms. Bandwidth limitations of the structure are investigated at different wavelengths for various slow-down factors. Finite size realizations of the structure are studied using transfer matrix method to obtain the desired transmission and group velocity at the band edge. Optical loss corresponding to slow-light effect is modeled, and the limitations imposed by the slow-light loss on the nonlinear phase shift saturation are considered. It is shown that by employing slow-down factor of 3, the nonlinear phase shift is improved by a factor of 5. Also, in comparison with a straight waveguide, shorter corrugated waveguides (up to nine times) can provide the same accumulated nonlinear phase shift.

Slow-light-enhanced energy efficiency for graphene microheaters on silicon photonic crystal waveguides

Slow light has been widely utilized to obtain enhanced nonlinearities, enhanced spontaneous emissions and increased phase shifts owing to its ability to promote light–matter interactions. By incorporating a graphene on a slow-light silicon photonic crystal waveguide, here we experimentally demonstrate an energy-efficient graphene microheater with a tuning efficiency of 1.07 nmmW−1 and power consumption per free spectral range of 3.99 mW. The rise and decay times (10–90%) are only 750 and 525 ns, which, to the best of our knowledge, are the fastest reported response times for microheaters in silicon photonics. The corresponding figure of merit of the device is 2.543 nW s, one order of magnitude better than results reported in previous studies. The influence of the length and shape of the graphene heater to the tuning efficiency is further investigated, providing valuable guidelines for enhancing the tuning efficiency of the graphene microheater.

Finely engineered slow light photonic crystal waveguides for efficient wideband wavelength-independent higher-order temporal solitons.

By orthogonally dual-shifting the air-hole rows in the triangular photonic crystal waveguide, a novel finely engineered slow light silicon photonic crystal waveguide is designed for higher-order temporal solitons and ultrashort temporal pulse compression with a large fabrication tolerance. The engineering of dispersion provides the waveguide with a wide wavelength range with only low anomalous dispersion covering, which makes the compression ratio wavelength-independent and stable even under ultralow input pulse energy. The simulation results are based on nonlinear Schrödinger equation modeling, which demonstrates that the input picosecond pulses in the broad wavelength range with ultralow pJ pulse energy can be stably compressed by a factor of 6 to higher-order temporal solitons in a 250 μm short waveguide.

Unambiguous demonstration of soliton evolution in slow-light silicon photonic crystal waveguides with SFG-XFROG.

We demonstrate the temporal and spectral evolution of picosecond soliton in the slow light silicon photonic crystal waveguides (PhCWs) by sum frequency generation cross-correlation frequency resolved optical grating (SFG-XFROG) and nonlinear Schrödinger equation (NLSE) modeling. The reference pulses for the SFG-XFROG measurements are unambiguously pre-characterized by the second harmonic generation frequency resolved optical gating (SHG-FROG) assisted with the combination of NLSE simulations and optical spectrum analyzer (OSA) measurements. Regardless of the inevitable nonlinear two photon absorption, high order soliton compressions have been observed remarkably owing to the slow light enhanced nonlinear effects in the silicon PhCWs. Both the measurements and the further numerical analyses of the pulse dynamics indicate that, the free carrier dispersion (FCD) enhanced by the slow light effects is mainly responsible for the compression, the acceleration, and the spectral blue shift of the soliton.

Enhanced four-wave mixing in graphene-silicon slow-light photonic crystal waveguides

We demonstrate the enhanced four-wave mixing of monolayer graphene on slow-light silicon photonic crystal waveguides. 200-μm interaction length, a four-wave mixing conversion efficiency of −23 dB is achieved in the graphene-silicon slow-light hybrid, with an enhanced 3-dB conversion bandwidth of about 17 nm. Our measurements match well with nonlinear coupled-mode theory simulations based on the measured waveguide dispersion, and provide an effective way for all-optical signal processing in chip-scale integrated optics.

Integrated optical auto-correlator based on third-harmonic generation in a silicon photonic crystal waveguide

The ability to use coherent light for material science and applications is linked to our ability to measure short optical pulses. While free-space optical methods are well established, achieving this on a chip would offer the greatest benefit in footprint, performance and cost, and allow the integration with complementary signal-processing devices. A key goal is to achieve operation at sub-watt peak power levels and on sub-picosecond timescales. Previous integrated demonstrations require either a temporally synchronized reference pulse, an off-chip spectrometer or long tunable delay lines. Here we report a device capable of achieving single-shot time-domain measurements of near-infrared picosecond pulses based on an ultra-compact integrated CMOS-compatible device, which could operate without any external instrumentation. It relies on optical third-harmonic generation in a slow-light silicon waveguide. Our method can also serve as an in situ diagnostic tool to map, at visible wavelengths, the propagation dynamics of near-infrared pulses in photonic crystals.

Four-wave mixing in slow light photonic crystal waveguides with very high group index.

We report efficient four-wave mixing in dispersion engineered slow light silicon photonic crystal waveguides with a flat band group index of n(g) = 60. Using only 15 mW continuous wave coupled input power, we observe a conversion efficiency of -28 dB. This efficiency represents a 30 dB enhancement compared to a silicon nanowire of the same length. At higher powers, thermal redshifting due to linear absorption was found to detune the slow light regime preventing the expected improvement in efficiency. We then overcome this thermal limitation by using oxide-clad waveguides, which we demonstrate for group indices of ng = 30. Higher group indices may be achieved with oxide clad-waveguides, and we predict conversion efficiencies approaching -10 dB, which is equivalent to that already achieved in silicon nanowires but for a 50x shorter length.

Maximization of Gain in Slow-Light Silicon Raman Amplifiers

We theoretically study the problem of Raman gain maximization in uniform silicon photonic-crystal waveguides supporting slow optical modes. For the first time, an exact solution to this problem is obtained within the framework of the undepleted-pump approximation. Specifically, we derive analytical expressions for the maximum signal gain, optimal input pump power, and optimal length of a silicon Raman amplifier and demonstrate that the ultimate gain is achieved when the pump beam propagates at its maximum speed. If the signal’s group velocity can be reduced by a factor of 10 compared to its value in a bulk silicon, it may result in ultrahigh gains exceeding 100 dB. We also optimize the device parameters of a silicon Raman amplifier in the regime of strong pump depletion and come up with general design guidelines that can be used in practice.

Wideband group velocity independent coupling into slow light silicon photonic crystal waveguide

We experimentally demonstrate efficient optical coupling into a slow light photonic crystal waveguide (PCW) that is independent of the group velocity of the guided mode. With a group index taper to match the group velocity between a strip waveguide and a PCW, the optical coupling efficiency is nearly constant throughout the spectrum of the defect-mode, including the slow light region near the band edge. Compared to strip-PCW butt-coupling without a group index taper, our measurement results show a 20 dB enhancement in coupling efficiency with 5 dB less Fabry–Perot fluctuations. The measurements show excellent agreement with two-dimensional finite-difference time domain simulations.

Four-wave mixing in slow light engineered silicon photonic crystal waveguides

We experimentally investigate four-wave mixing (FWM) in short (80 μm) dispersion-engineered slow light silicon photonic crystal waveguides. The pump, probe and idler signals all lie in a 14 nm wide low dispersion region with a near-constant group velocity of c/30. We measure an instantaneous conversion efficiency of up to -9dB between the idler and the continuous-wave probe, with 1W peak pump power and 6 nm pump-probe detuning. This conversion efficiency is found to be considerably higher (>10 × ) than that of a Si nanowire with a group velocity ten times larger. In addition, we estimate the FWM bandwidth to be at least that of the flat band slow light window. These results, supported by numerical simulations, emphasize the importance of engineering the dispersion of PhC waveguides to exploit the slow light enhancement of FWM efficiency, even for short device lengths.

Observation of four-wave mixing in slow-light silicon photonic crystal waveguides

Four-wave mixing is observed in a silicon W1 photonic crystal waveguide. The dispersion dependence of the idler conversion efficiency is measured and shown to be enhanced at wavelengths exhibiting slow group velocities. A 12-dB increase in the conversion efficiency is observed. Concurrently, a decrease in the conversion bandwidth is observed due to the increase in group velocity dispersion in the slow-light regime. The experimentally observed conversion efficiencies agree with the numerically modeled results.

Nonlinear loss dynamics in a silicon slow-light photonic crystal waveguide

We directly investigate both experimentally and numerically the influence of optical nonlinear loss dynamics on a silicon waveguide based all-optical device. The dynamics of these nonlinear losses are explored through the analysis of optical limiting of an amplitude distorted 10 Gbit/s signal in a slow-light silicon photonic crystal waveguide. As the frequency of the distortion approaches the free-carrier recombination rate, free-carrier absorption reaches a steady state, leaving two-photon absorption the dominant dynamic nonlinear loss. Our results highlight the importance of engineering the free-carrier lifetime in silicon waveguides for high speed all-optical processing applications.

Investigation of phase matching for third-harmonic generation in silicon slow light photonic crystal waveguides using Fourier optics

Using Fourier optics, we retrieve the wavevector dependence of the third-harmonic (green) light generated in a slow light silicon photonic crystal waveguide. We show that quasi-phase matching between the third-harmonic signal and the fundamental mode is provided in this geometry by coupling to the continuum of radiation modes above the light line. This process sustains third-harmonic generation with a relatively high efficiency and a substantial bandwidth limited only by the slow light window of the fundamental mode. The results give us insights into the physics of this nonlinear process in the presence of strong absorption and dispersion at visible wavelengths where bandstructure calculations are problematic. Since the characteristics (e.g. angular pattern) of the third-harmonic light primarily depend on the fundamental mode dispersion, they could be readily engineered.