L-shape probability distributions are extremely non-Gaussian distributions that have been surprisingly successful in describing the frequency of occurrence of extreme events, ranging from stock market crashes and natural disasters, the structure of biological systems, fractals, and optical rogue waves. In this paper, we show that fluctuations in stimulated Raman scattering in silicon, as well as in coherent anti-Stokes Raman scattering, can follow extreme value statistics and provide mathematical insight into the origin of this behavior. As an example of the experimental observations, we find that 16% of the Stokes pulses account for 84% of the pump energy transfer, an uncanny resemblance to the empirical Pareto principle or the 80/20 rule that describes important observation in socioeconomics.
We report on the fabrication and characterization of photonic-based nanothermometers, a silicon photonic Bragg grating and photonic crystal cavity. When cladded with silicon dioxide layer the sensors have at least eight times better sensitivity compared to the sensitivity of conventional fiber Bragg grating sensors. We demonstrate that these photonic thermometers are a viable temperature sensing solution.
The Luneburg lens is an aberration-free lens that focuses light from all directions equally well. We fabricated and tested a Luneburg lens in silicon photonics. Our technique is sufficiently versatile for making perfect imaging devices on silicon platforms.
We report systematic studies of plasmonic and photonic guiding modes in large-area chemical-vapor-deposition-grown graphene on nanostructured silicon substrates. Light interaction in graphene with substrate photonic crystals can be classified into four distinct regimes depending on the photonic crystal lattice constant and the various modal wavelengths (i.e. plasmonic, photonic and free-space). By optimizing the design of the substrate, these resonant modes can magnify the graphene absorption in infrared wavelength, for efficient modulators, filters, sensors and photodetectors on silicon photo…
The majority of silicon photonics is built on silicon-on-insulator (SOI) wafers while the majority of electronics, including CPUs and memory, are built on bulk silicon wafers, limiting broader acceptance of silicon photonics. This discrepancy is a result of silicon photonics's requirement for a single-crystalline silicon (c-Si) layer and a thick undercladding for optical guiding that bulk silicon wafers to not provide. While the undercladding problem can be partially addressed by substrate removal techniques, the complexity of co-integrating photonics with state-of-the-art transistors and real…
Optical computing accelerators may help alleviate bandwidth and power consumption bottlenecks in electronics. We show an approach to implementing logarithmic-type analog co-processors in silicon photonics and use it to perform the exponentiation operation. The function is realized by exploiting nonlinear-absorption-enhanced Raman amplification saturation in a silicon waveguide.
We propose a scheme to realize controlled phase gate between two single photons through a single quantum dot in slow-light silicon photonic crystal waveguide. Enhanced Purcell factor and beta factor lead to high gate fidelity over broadband frequencies compared to cavity-assisted system. The excellent physical integration of this silicon photonic crystal waveguide system provides tremendous potential for large-scale quantum information processing.
We propose the use of silicon graphene waveguides to implement a tunable broadband microwave photonics phase shifte based on integrated ring cavities. Numerical computation results show the feasibility for broadband operation over 40 GHz bandwidth and full 360 degree radiofrequency phase-shift with a modest voltage excursion of 0.12 volt.
One dimensional nanobeam photonic crystal cavities are fabricated in silicon dioxide with silicon nanocrystals. Quality factors of over 9 x 10^3 are found in experiment, matching theoretical predictions, with mode volumes of 1.5(lambda/n)^3 . Photoluminescence from the cavity modes is observed in the visible wavelength range 600-820 nm. Studies of the lossy characteristics of the cavities are conducted at varying temperatures and pump powers. Free carrier absorption effects are found to be significant at pump powers as low as a few hundred nanowatts.
We report the observations of spontaneous Raman scattering in silicon photonic crystal waveguides. Continuous-wave measurements of Stokes emission for both wavelength and power dependence is reported in single line-defect waveguides in hexagonal lattice photonic crystal silicon membranes. By utilizing the Bragg gap edge dispersion of the TM-like mode for pump enhancement and the TE-like fundamental mode-onset for Stokes enhancement, the Stokes emission was observed to increase by up to five times in the region of slow group velocity. The results show explicit nonlinear enhancement in a silicon…
We show that fluctuations of Raman amplified pulses, in the presence of a noisy pump, follow extreme value statistics, and provide mathematical insight into the origin of this perplexing behavior.
An effort was conducted to numerically determine, using the Nonlinear Schrodinger Split-Step Fourier method, if using cross phase modulation could cause temporal soliton pulse propagation in a silicon slow-light photonic crystal waveguide shorter than a millimeter. The simulations demonstrated that due to the higher powers and shorter scales of photonic crystals, two-photon absorption would cause an optical soliton pulse to be extremely dissipative. The model demonstrated, however, that by utilizing cross-phase modulation, it is possible to sustain a compressed soliton pulse within a silicon p…
We outline the design for a photonic crystal resonator made in a hybrid Silicon/Lithium Niobate material system. Using the index contrast between silicon and lithium niobate, it is possible to guide and confine photonic resonances in a thin film of silicon bonded on top of lithium niobate. Quality factors greater than $10^6$ at optical wavelength scale mode volumes are achievable. We show that patterning electrodes on such a system can yield an electro-optic coupling rate of 0.6 GHz/V (4 pm/V).
The spectra of silicon integrated waveguides are tailored to process analog computing (i.e.,differential and integral) in optical domain with huge bandwidth.With the theory of signal and system, we design some silicon integrated devices to implement photonic differentiator and optical differential equation solver. The basic principle is to tailor the spectra of silicon integrated waveguides to meet the requirements of analog computing circuits. These analog photonic integrated circuits are very promising in future computing systems with high speed, low cost, and compact size. We also plan to e…
Optical isolation is a long pursued object with fundamental difficulty in integrated photonics. As a step towards this goal, we demonstrate the design, fabrication, and characterization of on-chip wavelength-scale optical diodes that are made from the heterojunction between two different silicon two-dimensional square-lattice photonic crystal slabs with directional bandgap mismatch and different mode transitions. The measured transmission spectra show considerable unidirectional transmission behavior, in good agreement with numerical simulations. The experimental realization of on-chip optical…
In this work we show theoretically that it is possible to design a large band gap in the infrared range using a one-dimensional Photonic Crystal heterostructure made of porous silicon. Stacking together multiple photonic crystal substructures of the same contrast index, but of different lattice periods, it is possible to broad the narrow forbidden band gap that can be reached by the low contrast index of the porous silicon multilayers. The main idea in this work is that we can construct a Giant Photonic Band Gap -as large as desired- by combining a tandem of photonic crystals substructures by …
On-chip optical isolators play a key role in optical communications and computing based on silicon integrated photonic structures. Recently there have raised great attentions and hot controversies upon isolation of light via linear and passive photonic structures. Here we analyze the optical isolation properties of a silicon photonic crystal slab heterojunction diode by comparing the forward transmissivity and round-trip reflectivity of in-plane infrared light across the structure. The round-trip reflectivity is much smaller than the forward transmissivity, justifying good isolation. The consi…
We demonstrate the first functional signal processing device based on stimulated Brillouin scattering in a silicon nanowire. We use only 1 dB of on-chip SBS gain to create an RF photonic notch filter with 48 dB of suppression, 98 MHz linewidth, and 6 GHz frequency tuning. This device has potential applications in on-chip microwave signal processing and establishes the foundation for the first CMOS-compatible high performance RF photonic filter.
We demonstrate a fully coherent supercontinuum spectrum spanning 500 nm from a silicon-on-insulator photonic wire waveguide pumped at 1575 nm wavelength. An excellent agreement with numerical simulations is reported. The simulations also show that a high level of two-photon absorption can essentially enforce the coherence of the spectral broadening process irrespective of the pump pulse duration.
We experimentally demonstrate phase sensitive amplification (PSA) in a silicon photonic crystal waveguide based on pump-degenerate four-wave mixing. An 11 dB phase extinction ratio is obtained in a record compact 196 μm nanophotonic device due to broadband slow-light, in spite of the presence of two-photon absorption and free-carriers. Numerical calculations show good agreement with the experimental results.
Recently, a silicon micromachining method to produce tetrahedral silicon particles was discovered. In this report we determine, using band structure calculations, the optical properties of diamond-lattice photonic crystals when assembled from such particles. We show that crystal structures built from silicon tetrahedra are expected to display small stop gaps. Wide photonic band gaps appear when truncated tetrahedral particles are used to build the photonic crystals. With truncated tetrahedral particles a band gap with a width of 23.6% can be achieved, which is more than twice as wide compared …
One dimensional nano-beam photonic crystal cavities fabricated in silicon dioxide are considered in both simulation and experiment. Quality factors of over 10^4 are found via simulation, while quality factors of over 5*10^3 are found in experiment, for cavities with mode volumes of 2.0 cubic wavelengths (in oxide) and in the visible wavelength range (600-716nm). The dependences of the cavity quality factor and mode volume for different design parameters are also considered.
We have studied the reflectivity of CMOS-compatible three-dimensional silicon inverse woodpile photonic crystals at near-infrared frequencies. Polarization-resolved reflectivity spectra were obtained from two orthogonal crystal surfaces corresponding to 1.88 pi sr solid angle. The spectra reveal broad peaks with high reflectivity up to 67 % that are independent of the spatial position on the crystals. The spectrally overlapping reflectivity peaks for all directions and polarizations form the signature of a broad photonic band gap with a relative bandwidth up to 16 %. This signature is supporte…
We propose a practical and efficient solution for the coupling of light from integrated single-mode waveguides to supercollimating planar photonic crystals on conventional silicon-on-insulator platforms. The device consists of a rib waveguide, designed to sustain spatially extended single-modes and matched to a supercollimating photonic crystal, which has been truncated at its boundary to improve impedance matching between the two photonic components. Three-dimensional simulations show transmission efficiencies up to 96 % and reflections below 0.2 % at wavelengths close to 1.55 microns. This a…
As photonics breaks away from today's device level toward large scale of integration and complex systems-on-a-chip, concepts like monitoring, control and stabilization of photonic integrated circuits emerge as new paradigms. Here, we show non-invasive monitoring and feedback control of high quality factor silicon photonics resonators assisted by a transparent light detector directly integrated inside the cavity. Control operations are entirely managed by a CMOS microelectronic circuit, hosting many parallel electronic read-out channels, that is bridged to the silicon photonics chip. Advanced f…
We propose a new type of bistable device for silicon photonics, using the self-electro-optic effect within an optical cavity. Since the bistability does not depend on the intrinsic optical nonlinearity of the material, but is instead engineered by means of an optoelectronic feedback, it appears at low optical powers. This bistable device satisfies all the basic criteria required in an optical switch to build a scalable digital optical computing system.
Besides being the foundational material for microelectronics, in optics, crystalline silicon has long been used for making infrared lenses and mirrors. More recently, silicon has become the key material to achieve large-scale integration of photonic devices for optical interconnect and telecommunication. For optics, silicon has significant advantages: it offers a very high refractive index and is highly transparent in the spectral range from 1.2 to 8 micron. To fully exploit silicon's superior performance in a remarkably broad range and to enable new optoelectronic functionalities, here we des…
We present a new approach to long range coupling based on a combination of adiabatic passage and lateral leakage in thin shallow ridge waveguides on a silicon photonic platform. The approach enables transport of light between two isolated waveguides through a mode of the silicon slab that acts as an optical bus. Due to the nature of the adiabatic protocol, the bus mode has minimal population and the transport is highly robust. We prove the concept and examine the robustness of this approach using rigorous modelling. We further demonstrate the utility of the approach by coupling power between t…
We present the design, fabrication and preliminary experiments of two-dimensional photonic crystal cavities made in nanoporous silicon luminescent at 700-800 nm. Enhancement in photoluminescence extraction efficiency at the resonant wavelength is expected due to Purcell effect and directed radiation pattern defined by the cavity. Such cavities should also enhance nonlinearities exhibited by porous Si beyond what is observed in one-dimensional distributed Bragg reflection cavities due to their small mode volumes and modest quality factors. This design aligns itself well to integration with conv…
We demonstrate the dynamics of stimulated Raman scattering in designed high-Q/Vm silicon photonic band gap nanocavities through the coupled-mode theory framework towards optically-pumped silicon lasing. The interplay of other chi(3) effects such as two-photon absorption and optical Kerr, related free-carrier dynamics, thermal effects, as well as linear losses such as cavity radiation and linear material absorption are included and investigated numerically. Our results clarify the relative contributions and evolution of the mechanisms, and demonstrate the lasing and shutdown thresholds. Our stu…
We demonstrate the efficient coupling (99.5%) of a silica whispering gallery mode microresonator directly with a silicon chip by using a silicon photonic crystal waveguide as a coupler. The efficient coupling is attributed to the small effective refractive index difference between the two devices. The large group index of the photonic crystal waveguide mode also contributes to the efficient coupling. A coupling Q of 2.68*10^6 is obtained, which allows us to achieve the critical coupling of a silica whispering gallery mode with an intrinsic Q of close to 10^7 with a Si chip.
Nano-resonator integrated with two-dimensional materials (e.g. transition metal dichalcogenides) have recently emerged as a promising nano-optoelectronic platform. Here we demonstrate resonatorenhanced second-harmonic generation (SHG) in tungsten diselenide using a silicon photonic crystal cavity. By pumping the device with the ultrafast laser pulses near the cavity mode at the telecommunication wavelength, we observe a near visible SHG with a narrow linewidth and near unity linear polarization, originated from the coupling of the pump photon to the cavity mode. The observed SHG is enhanced by…
Optical fiber tapers are used to collect photoluminescence emission at ~1.5 um from photonic crystal cavities fabricated in erbium doped silicon nitride on silicon. Photoluminescence collection via fiber taper is enhanced 2.5 times relative to free space, with a total taper collection efficiency of 53%. By varying the fiber taper offset from the cavity, a broad tuning range of coupling strength is obtained. This material system combined with fiber taper collection is promising for building on-chip optical amplifiers.
We report an optical link on silicon using micrometer-scale ring-resonator enhanced silicon modulators and waveguide-integrated germanium photodetectors. We show 3 Gbps operation of the link with 0.5 V modulator voltage swing and 1.0 V detector bias. The total energy consumption for such a link is estimated to be ~120 fJ/bit. Such compact and low power monolithic link is an essential step towards large-scale on-chip optical interconnects for future microprocessors.
Strongly enhanced third-harmonic generation (THG) by the topological localization of an edge mode in a Su-Schrieffer-Heeger (SSH) chain of silicon photonic crystal nanocavities is demonstrated. The edge mode of the nanocavity chain not only naturally inherits resonant properties of the single nanocavity, but also exhibits the topological feature with mode robustness extending well beyond individual nanocavity. By engineering the SSH nanocavities with alternating strong and weak coupling strengths on a silicon slab, we observe the edge mode formation that entails a THG signal with three orders …
We examine the cavity resonance tuning of high-Q silicon photonic crystal heterostructures by localized laser-assisted thermal oxidation using a 532 nm continuous wave laser focused to a 2.5 mm radius spot-size. The total shift is consistent with the parabolic rate law. A tuning range of up to 8.7 nm is achieved with ~ 30 mW laser powers. Over this tuning range, the cavity Q decreases from 3.2\times10^5 to 1.2\times10^5. Numerical simulations model the temperature distributions in the silicon photonic crystal membrane and the cavity resonance shift from oxidation.
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.
Resistance thermometry is a time-tested method for taking temperature measurements. In recent years fundamental limits to resistance-based approaches spurred considerable interest in developing photonic temperature sensors as a viable alternative. In this study we demonstrate that our photonic thermometer, which consists of a silicon waveguide integrated with a Bragg grating, can be used to measure temperature changes over the range from 5 C to 160 C with a combined expanded uncertainty [k = 2 ; 95% confidence level] of 1.25 degree C. The computational modeling of the sensor predicts the reson…
Silicon is now firmly established as a high performance photonic material. Its only weakness is the lack of a native electrically driven light emitter that operates CW at room temperature, exhibits a narrow linewidth in the technologically important 1300- 1600 nm wavelength window, is small and operates with low power consumption. Here, an electrically pumped all-silicon nano light source around 1300-1600 nm range is demonstrated at room temperature. Using hydrogen plasma treatment, nano-scale optically active defects are introduced into silicon, which then feed the photonic crystal nanocavity…
We have demonstrated an up to seven-fold enhancement of photoluminescence from silicon-rich silicon nitride film due to a single photonic crystal cavity. The enhancement is partially attributed to the Purcell effect. Purcell factor predicted by FDTD calculations is 32 for a linear three-defect cavity mode with computed quality factor of 332 and mode volume of 0.785 cubic wavelengths. Experimentally measured cavity quality (Q) factors vary in the range of 200 to 300, showing excellent agreement with calculations. The emission peak can be tuned to any wavelength in the 600 to 800 nm range.
We apply the moment method to nonlinear pulse propagation in silicon waveguides in the presence of two-photon absorption, free-carrier dispersion and free-carrier absorption. The evolution equations for pulse energy, temporal position, duration, frequency shift and chirp are obtained. We derive analytic expressions for the free-carrier induced blueshift and acceleration and show that they depend only on the pulse peak power. Importantly, these effects are independent of the temporal duration. The moment equations are then numerically solved to provide fast estimates of pulse evolution trends i…
Silicon is an excellent material for microelectronics and integrated photonics with untapped potential for mid-IR optics. Despite broad recognition of the importance of the third dimension, current lithography methods do not allow fabrication of photonic devices and functional microelements directly inside silicon chips. Even relatively simple curved geometries cannot be realized with techniques like reactive ion etching. Embedded optical elements, like in glass, electronic devices and better electronic-photonic integration are lacking. Here, we demonstrate laser-based fabrication of complex 3…
Large port count spatial optical switches will facilitate flexible and energy efficient data movement in future data communications systems, especially if they are capable of nanosecond-order reconfiguration times. In this work, we demonstrate an 8x8 microring-based silicon photonic switch with software controlled switching. The proposed switch architecture is modular as it assembles multiple identical components with multiplexing/demultiplexing functionalities. The switch is fully non-blocking, has path independent insertion loss, low crosstalk and is straightforward to control. A scalability…
Silicon photonics promises to address the challenges for next-generation short-reach optical interconnects. Growing bandwidth demand in hyper-scale data centers and high-performance computing motivates the development of faster and more-efficient silicon photonics links. While it is challenging to raise the serial line rate, further scaling of the data rate can be realized by, for example, increasing the number of parallel fibers, increasing the number of wavelengths per fiber, and using multi-level pulse-amplitude modulation (PAM). Among these approaches, PAM has a unique advantage because it…
Silicon has attracted attention as an inexpensive and scalable material system for photonic-electronic, system-on-chip development. For this, a platform with both photodetectors and modulators working at high speeds, with excellent cross-wafer uniformity, is needed. We demonstrate an optical-lithography, wafer-scale photonics platform with 25 Gb/s operation. We also demonstrate modulation with an ultra-low drive voltage of 1 Vpp at 25 Gb/s. We demonstrate attractive cross-wafer uniformity, and provide detailed information about the device geometry. Our platform is available to the community as…
Silicon photonics lacks a second-order nonlinear optical response in general because the typical constituent materials are centro-symmetric and lack inversion symmetry, which prohibits second-order nonlinear processes such as second harmonic generation (SHG). Here, for the first time, we realize efficient SHG in a silicon-based optical microresonator by combining a strong photo-induced effective second-order nonlinearity with resonant enhancement and perfect-phase matching. We show a record-high conversion efficiency of 2,500 %/W, which is 2 to 4 orders of magnitude larger than previous works.…
Hyperuniform disordered networks belong to a peculiar class of structured materials predicted to possess partial and complete photonic bandgaps for relatively moderate refractive index contrasts. The practical realization of such photonic designer materials is challenging however, as it requires control over a multi-step fabcrication process on optical length scales. Here we report the direct-laser writing of hyperuniform polymeric templates followed by a silicon double inversion procedure leading to high quality network structures made of polycrystalline silicon. We observe a pronounced gap i…
Silicon photonics promises to alleviate the bandwidth bottleneck of modern day computing systems. But silicon photonic devices have the fundamental problem of being highly sensitive to ambient temperature fluctuations due to the high thermo-optic (TO) coefficient of silicon. Most of the approaches proposed to date to overcome this problem either require significant power consumption or incorporate materials which are not CMOS-compatible. Here we demonstrate a new class of optical devices which are passively temperature compensated, based on tailoring the optical mode confinement in silicon wav…
Thermally-tuning silicon micro-cavities are versatile and beneficial elements in low-cost large-scale photonic integrated circuits (PICs). Traditional metal heaters used for thermal tuning in silicon micro-cavities usually need a thick SiO2 upper-cladding layer, which will introduce some disadvantages including low response speed, low heating efficiency, low achievable temperature and complicated fabrication processes. In this paper, we propose and experimentally demonstrate thermally-tuning silicon micro-disk resonators by introducing graphene transparent nano-heaters, which contacts the sili…
Encapsulation layers are explored for passivating the surfaces of silicon to reduce optical absorption in the 1500-nm wavelength band. Surface-sensitive test structures consisting of microdisk resonators are fabricated for this purpose. Based on previous work in silicon photovoltaics, coatings of SiNx and SiO2 are applied under varying deposition and annealing conditions. A short dry thermal oxidation followed by a long high-temperature N2 anneal is found to be most effective at long-term encapsulation and reduction of interface absorption. Minimization of the optical loss is attributed to sim…
We observe experimentally optical bistability enhanced through Fano interferences in high-Q localized silicon photonic crystal resonances (Q ~ 30,000 and modal volume ~ 0.98 cubic wavelengths). This phenomenon is analyzed through nonlinear coupled-mode formalism, including the interplay of chi(3) effects such as two-photon absorption and related free-carrier dynamics, and optical Kerr as well as thermal effects and linear losses. Our experimental and theoretical results demonstrate for the first time Fano-resonance based bistable states with switching thresholds of 185 micro-Watt and 4.5 fJ in…
We present an accurate and fast 3D simulation scheme for out-of-plane grating couplers, based on two dimensional rigorous (finite difference time domain) grating simulations, the effective index method (EIM), and the Rayleigh-Sommerfeld diffraction formula. In comparison with full 3D FDTD simulations, the rms difference in electric field is below 5% and the difference in power flux is below 3%. A grating coupler for coupling from a silicon-on-insulator photonic integrated circuit to an optical fiber positioned 0.1 mm above the circuit is designed as example.
We present a new resonant behavior based on bound states in the continuum in a guided wave silicon platform. The continuum has the form of a collimated beam of light which is confined vertically in a TE mode of a silicon slab. The bound state is a discrete TM mode of a ridge on the silicon slab. The coupling between the slab and ridge modes results in a single sharp resonance at the wavelength where they phase match. We experimentally demonstrate this phenomenon on a silicon photonic chip using foundry compatible parameters and interface it on-chip to standard single mode silicon nanowire wave…
We report and characterize low-temperature, plasma-deposited deuterated silicon nitride thin films for nonlinear integrated photonics. With a peak processing temperature less than 300$^\circ$C, it is back-end compatible with pre-processed CMOS substrates. We achieve microresonators with a quality factor of up to $1.6\times 10^6 $ at 1552 nm, and $>1.2\times 10^6$ throughout $λ$ = 1510 -- 1600 nm, without annealing or stress management. We then demonstrate the immediate utility of this platform in nonlinear photonics by generating a 1 THz free spectral range, 900-nm-bandwidth modulation-instabi…
Topological protection in photonics offers new prospects for guiding and manipulating classical and quantum information. The mechanism of spin-orbit coupling promises the emergence of edge states that are helical; exhibiting unidirectional propagation that is topologically protected against back-scattering. We directly observe the topological states of a photonic analogue of electronic materials exhibiting the quantum Spin Hall effect, living at the interface between two silicon photonic crystals with different topological order. Through the far-field radiation that is inherent to the states' …
We report the observation of a large-angle self-collimation phenomenon occurring in photonic crystals composed of nanorods. Electromagnetic waves incident onto such photonic crystals from directions covering a wide-range of incident angles become highly localized along a single array of rods, which results in narrow-beam propagation without divergence. A propagation length of 0.4 mm is experimentally observed over the wavelength range of 1540 nm to 1570 nm, even in the large incident angle case, which is a very considerable length scale for on-chip optical interconnection.
Optical isolators are an important building block in photonic computation and communication. In traditional optics, isolators are realized with magneto-optical garnets. However, it remains challenging to incorporate such materials on an integrated platform because of the difficulty in material growth and bulky device footprint. Here, we propose an ultracompact integrated isolator by exploiting graphene's magneto-optical property on a silicon-on-insulator platform. The photonic nonreciprocity is achieved because the cyclotrons in graphene experiencing different optical spin exhibit different re…
