Graphene Nanoribbon Waveguides Research Articles

Machine-learning design of graphene nanoribbon waveguide side-coupled absorber

Machine learning is emerging as a new approach that provides more options for solving complex problems involving electromagnetic phenomena. This paper evaluates the application of machine learning to the design of graphene-based absorbers, which is a research challenge. Five machine learning algorithms — [Formula: see text]-nearest neighbor regression (kNN), artificial neural network (ANN), decision tree (DT), extremely randomized trees (ETs) and random forest (RF) — are applied to realize the transmission spectrum prediction and reverse design of a graphene nanoribbon waveguide side-coupled absorber. The results show that all five algorithms are effective, with RF being the most accurate in the inverse design. Compared with previous work, the application of machine learning in the intelligent design of graphene absorbers is evaluated more comprehensively, providing a reference for the selection of machine learning algorithms for future inverse design problems.

Dynamically tunable multiband plasmon-induced transparency effect based on graphene nanoribbon waveguide coupled with rectangle cavities system

A dynamically tunable multiband plasmon-induced transparency (PIT) effect in a series of rectangle cavities coupled with a graphene nanoribbon waveguide system is investigated theoretically and numerically by tuning the Fermi level of the graphene rectangle cavity. A single-PIT effect is realized using two different methods: one is the direct destructive interference between bright and dark modes, and the other is the indirect coupling through a graphene nanoribbon waveguide. Moreover, dual-PIT effect is obtained by three rectangle cavities side-coupled with a graphene nanoribbon waveguide. Results show that the magnitude of the dual-PIT window can be controlled between 0.21 and 0.74, and the corresponding group index is controlled between 143.2 and 108.6. Furthermore, the triple-PIT effect is achieved by the combination of bright–dark mode coupling and the cavities side-coupled with waveguide mechanism. Thus, sharp PIT windows can be formed, a high transmission is maintained between 0.51 and 0.74, and the corresponding group index is controlled between 161.4 and 115.8. Compared with previously proposed graphene-based PIT effects, the size of the introduced structure is less than 0.5 μm2. Particularly, the slow light effect is crucial in the current research. Therefore, a novel approach is introduced toward the realization of optical sensors, optical filters, and slow light and light storage devices with ultra-compact, multiband, and dynamic tunable.

Plasmon induced transparency effect based on graphene nanoribbon waveguide side-coupled with rectangle cavities system

In order to reduce the size of the device and realize the ultrafast response time and dynamic tunableness, the single-band and dual-band plasmon induced transparency (PIT) effect are investigated based on graphene nanoribbon waveguide side-coupled rectangle cavity. The slow light properties of the model are analyzed numerically and theoretically by coupled mode theory and finite difference time domain method. With controlling the chemical potential of the graphene rectangle cavity, the tunability of the resonant wavelength and the transmission peak can be achieved simultaneously in single-band and dual-band PIT model. As the chemical potential of graphene increases, the resonant wavelength of each transmission window of PIT effect decreases gradually and presents the blue shift. In addition, through dynamically tuning the resonant wavelength of the graphene rectangle cavity, when the chemical potential of the graphene rectangle cavity increases from 0.41 to 0.44 eV, the group index of single PIT system is controlled to be between 79.2 and 28.3, and the tunable bandwidth is 477 nm. Moreover, the group index of dual PIT system is controlled to be between 143.2 and 108.6 when the chemical potentials of graphene rectangle cavities 1, 2, and 3 are 0.39–0.42 eV, 0.40–0.43 eV, and 0.41–0.44 eV, respectively. The size of the entire PIT structure is <0.5 μm<sup>2</sup>. The research results here in this work are of reference significance in designing and fabricating the optical sensors, optical filters, slow light and light storage devices with ultrafast, ultracompact and dynamic tunableness.

Plasmon induced transparency effect based on graphene nanoribbon waveguide side–coupled with rectangle cavities system

为了减小器件尺寸、实现超快速响应和动态可调谐，研究了基于石墨烯纳米条波导边耦合矩形腔的单波段和双波段的等离子体诱导透明（PIT）效应，通过耦合模式理论和时域有限差分法从数值计算和模拟仿真两方面分析了模型的慢光特性。通过调节石墨烯矩形腔的化学势，同时实现了单波段、双波段PIT模型的谐振波长和透射峰值的可调谐性。当石墨烯的化学势增加时，各个波段PIT窗口的谐振波长逐渐减小，发生蓝移。此外，通过动态调谐石墨烯矩形腔的谐振波长，当石墨烯矩形腔的化学势为0.41 eV到0.44 eV时，单PIT系统的群折射率控制在79.2到28.3之间，可调谐带宽为477 nm；当石墨烯矩形腔1、2、3的化学势分别为0.39 eV到0.42 eV、0.40 eV到0.43 eV、0.41 eV到0.44 eV时，双PIT系统的群折射率控制在143.2到108.6之间。并且，整个系统的尺寸小于0.5 μm2。研究结果对于超快速、超紧凑型和动态可调谐的光传感、光滤波、慢光和光存储器件的设计和制作具有一定的参考意义。

Comb-Shaped Graphene Nanoribbon Bandpass Filter.

In this study, a novel comb-shaped graphene nanoribbon wideband bandpass filter for use at midinfrared frequencies is proposed. In addition, numerical investigation was carried outwith finite difference time-domain (FDTD) numerical simulations. The filter includes one graphene nanoribbon (GNR) waveguide laterally coupled to six perpendicular GNRs on each side. With a simple geometric shape, the transmission bandwidth and efficiency of waves within the structure can be tuned by altering the width or length of the GNR teeth. Moreover, the transmission spectra can be easily tuned within a broad frequency region by tuning the chemical potential of the graphene teeth, thanks to the electronic tunability of monolayer graphene. This work offers a promising method for developing ultra-compact tunable graphene devices and for designing integrated all-optical architectures.

Controllable graphene W-shaped three-port THz circulator

We propose a new graphene-based THz circulator. It consists of a circular graphene resonator and three graphene nanoribbon waveguides of W-geometry placed on a dielectric substrate. Surface plasmon-polariton waves propagate in the waveguides. The nanoribbon excites in the resonator dipole resonance. Nonreciprocity of the device is defined by nonsymmetry of the conductivity tensor of the magnetized graphene. Numerical simulation example present a circulator which operates at a central frequency of 7.5 THz has the bandwidth 4.25% for isolation −15 dB, insertion loss −2.5 dB. Applied DC magnetic field is 0.56 T and Fermi energy of graphene ϵF=0.15 eV. The frequency band of the circulator can be enlarged at the expense of higher DC magnetic field and its central frequency of operation can be tuned by varying resonator radius, nanostrips width, distance between the resonator and the waveguide. Fermi energy allows one to control dynamically the circulator responses.

Plasmonic Feynman Gate Based on Suspended Graphene Nano-Ribbon Waveguides at THz Wavelengths

In this paper, a plasmonic Feynman gate based on suspended graphene nano-ribbon waveguides at THz wavelengths is proposed and numerically investigated. The proposed plasmonic Feynman gate is composed of two cascaded microring resonators. The resonant states of microring resonators are flexibly controlled by tuning chemical potentials of graphene in rings, and thus, the logic operation results of Feynman gate can be performed successfully. Compared to the plasmonic Feynman gate based on graphene nano-ribbons deposited on the Si substrate and the plasmonic Feynman gate based on graphene nano-ribbons deposited on the SiO2/Si substrate, our designed plasmonic Feynman gate can have better extinction ratio and crosstalk. Calculation results exhibit that the extinction ratio is larger than 15.39 dB and the crosstalk is lower than −15.55 dB when input logic states of our designed device are ‘00’, ‘01’, ‘10,’ and ‘11’.

A Four-Port Ultra-Compact Terahertz Splitting Filter Based on Graphene Nanoribbon

A four-port ultra-compact plasmonic splitting filter based on graphene diamond ring resonator is proposed and investigated by using the finite-difference time-domain method. Numerical simulation results show that the transmission spectra can be affected by the structural parameters and the chemical potential of graphene. Especially, the resonant frequencies can be easily manipulated by changing bias voltage without changing the dimension parameters of the filter. The simple structure that consists of graphene nanoribbon waveguides and a graphene resonator shows both splitting and filtering capability. This compact intersection structure has potential applications in highly integrated optical circuits for terahertz frequency.

Ultra-compact graphene plasmonic filter integrated in a waveguide**Project supported by the National Basic Key Research Program of China (Grant No. 2015CB932400), the National Key Research and Development Program of China (Grant No. 2016YFA0201600), the National Natural Science Foundation of China (Grant Nos. 51372045, 11504063, and 11674073), the Key Program of the Bureau of Frontier Sciences and Education, Chinese Academy of

Graphene plasmons have become promising candidates for deep-subwavelength nanoscale optical devices due to their strong field confinement and low damping. Among these nanoscale optical devices, band-pass filter for wavelength selection and noise filtering are key devices in an integrated optical circuit. However, plasmonic filters are still oversized because large resonant cavities are needed to perform frequency selection. Here, an ultra-compact filter integrated in a graphene plasmonic waveguide was designed, where a rectangular resonant cavity is inside a graphene nanoribbon waveguide. The properties of the filter were studied using the finite-difference time-domain method and demonstrated using the analytical model. The results demonstrate the band-pass filter has a high quality factor (20.36) and electrically tunable frequency response. The working frequency of the filter could also be tuned by modifying the cavity size. Our work provides a feasible structure for a graphene plasmonic nano-filter for future use in integrated optical circuits.

Tunable plasmonic band-pass filter based on Fabry–Perot graphene nanoribbons

A plasmonic band-pass filter (BPF) structure is designed and proposed in this research. The filter structure includes two graphene nanoribbon (GNR) waveguides laterally coupled to three perpendicular GNRs that forms a Fabry–Perot resonator (FPR). The transmission spectrum of the proposed structure can be tuned in an efficient and flexible fashion by making adjustments on the overall geometrical structure and its chemical potential, as well. Geometry can be modified in the design step, even as a real-time controlling voltage can be applied as a chemical potential tuner. The coupling distances between GNR waveguides and GNRs of the FPR and also coupling distances among GNRs of FPR themselves strongly affect the transmission spectrum and bandwidth characteristics of the BPF. Transmission spectrum with one, two, or three peaks can be achieved by adjusting the distances between GNRs of the FPR, even as other geometrical adjustments and/or chemical potential tuning shifts the spectrum to the desired frequency range. The results achieved by 3D finite-difference time-domain (3D-FDTD) method verify the capability of the proposed structure to be applied in applications used in plasmonic and nano-optoelectronics devices.

An ultra-compact tunable intersection structure based on graphene nanoribbon

An ultra-compact plasmonic intersection structure with wavelength-tunable functionality is proposed and investigated using the finite-difference time-domain (FDTD) method. The structure consists of four symmetrical graphene nanoribbon waveguides and a graphene nanoring resonator, which exhibits the perfect cross transmission effect. Further investigation shows that the intersection wavelength of the proposed structure can be adjusted by related parameters, such as the chemical potential of the graphene nanoribbon, the radius of the nanoring, the thickness of the substrate and the width of the graphene nanoribbon. The simulation results are validated by the phase matching theory in the nanoring. Such a device may find applications in signal intersection and demultiplexing.

High Sensitivity Nanoplasmonic Sensor Based on Plasmon-Induced Transparency in a Graphene Nanoribbon Waveguide Coupled with Detuned Graphene Square-Nanoring Resonators

A novel nanoscale structure for high sensitivity sensing which consists of a graphene nanoribbon waveguide coupled with detuned graphene square-nanoring resonators (GSNR) based on edge mode is investigated in detail. By altering the Fermi energy level of the graphene, the plasmon-induced transparency (PIT) window from the destructive interference between a radiative square-nanoring resonator and a dark square-nanoring resonator can be easily tailored. The coupled mode theory (CMT) is used to show that the theoretical results agree well with the finite difference time domain (FDTD) simulations. This nanosensor yields a ultrahigh sensitivity of ∼2600 nm/refractive index unit (RIU) and a figure of merit (FOM) of ∼54 in the mid-infrared (MIR) spectrum. The revealed results indicate that the Fermi energy level of the graphene and the coupling distance play important roles in optimizing the sensing properties. Our proposed structure exerts a peculiar fascination on the realization of ultra-compact graphene plasmonic nanosensor in the future.

Switching terahertz waves with graphene-integrated split-ring resonator

In this paper, we design and numerically demonstrate an electrically controllable terahertz wave switch consisting of a graphene nanoribbon waveguide and three graphene split-ring resonators. By applying a bias voltage on the graphene split-ring resonators, this switch can dynamically control the amplitude of the transmitted terahertz wave at 9THz. Moreover, the calculated results show that the extinction ratio of this switch can be tuned from 30dB to 0.82dB when the chemical potential varies from 0.1eV to 0.2eV. The total size of the present device is only 3μm×2μm. This work may pave the ways for the further development of compact and integrated high-performance graphene-based terahertz wave devices.

Edge plasmons and cut-off behavior of graphene nano-ribbon waveguides

Graphene nano-ribbon waveguides with ultra-short plasmon wavelength are a promising candidate for nanoscale photonic applications. Graphene edge plasmons are the fundamental and lowest losses mode. Through finite element method, edge plasmons show large effective refractive index and strong field confinement on nanoscale ribbons. The edge plasmons follow a k1/2 dispersion relation. The wavelengths of the edge plasmons and center plasmons differ by a fixed factor. The width of edge plasmon is inversely proportional to wave vector of edge plasmon kedge. Edge defects associate with graphene nano-ribbon induce extra losses and reduce the propagation length. Cut-off width of edge plasmons reduces with increasing frequency. Cut-off width of center plasmon is enlarged by edge component but the enlargement effect diminishing with the increase of kedge. The results are important for the application of graphene plasmon towards ultra-compact photonic devices.

Plasmonic mode analysis of deep subwavelength graphene nanoribbon waveguides

Deep subwavelength plasmonic graphene nanoribbon waveguides for telecommunication frequencies are proposed. The mode properties of graphene nanoribbon waveguides with varied chemical potential are numerically investigated in terms of the effective indices and the propagation length of the plasmonic modes. A refractive index as high as 4980 is obtained on the plasmonic mode along the nanoribbon waveguide with a width of 3 nm at a frequency of 190 THz, and the normalized mode area on the scale of 10−8(1/λ0)2. An embedded graphene nanoribbon waveguide was also proposed and it is that the optical characteristic can be tuned by adjusting the chemical potential of graphene. The proposed structure can be a fundamental component of the future integrated plasmonic circuit system.

Dynamically tunable plasmon induced transparency in a graphene-based nanoribbon waveguide coupled with graphene rectangular resonators structure on sapphire substrate.

In this paper, we propose dynamically tunable plasmon induced transparency (PIT) in a graphene-based nanoribbon waveguide coupled with graphene rectangular resonators structure on sapphire substrate by shifting the Fermi energy level of the graphene. Two different methods are employed to obtain the PIT effect: one is based on the direct destructive interference between a radiative state and a dark state, the other is based on the indirect coupling through a graphene nanoribbon waveguide. Our numerical results reveal that high tunability in the PIT transparency window can be obtained by altering the Fermi energy levels of the graphene rectangular resonators. Moreover, double PITs are also numerically predicted in this ultracompact structure, comprising series of graphene rectangular resonators. Compared with previously proposed graphene-based PIT effects, our proposed scheme is much easier to design and fabricate. This work not only paves a new way towards the realization of graphene-based integrated nanophotonic devices, but also has important applications in multi-channel-selective filters, sensors, and slow light.

Tunable plasmonic Bragg reflector with different graphene nanoribbon widths

We propose and numerically analyze a Bragg reflector composed of periodically arranged graphene nanoribbon waveguides with different widths. Because of the unique property of the graphene edge mode, the effective index contrast used for the reflector can be obtained by designing graphene nanoribbons with different widths without changing the dielectric substrate structure. Good band stop filtering characteristics are shown at the band gap of the transmission spectrum by numerical simulation. The performance of the proposed Bragg reflector is analyzed in terms of different parameters, such as the chemical potential, the number of periods, and the size of the unit cell. The proposed Bragg reflector will be expected to have important potential applications in the highly integrated SPP-based photonic devices.

Rigorous calculation of nonlinear parameters in graphene-comprising waveguides

We describe a rigorous formalism for the calculation of the nonlinear parameter of arbitrary three-dimensional nanophotonic graphene-comprising waveguides. Graphene is naturally implemented as a zero-thickness conductive sheet, modeled solely by complex linear and nonlinear surface conductivity tensors, whose values are extracted from theoretical models. This representation is compared to the more commonly employed equivalent bulk-medium representation and is found superior. We numerically calculate the nonlinear parameters of several optical waveguide archetypes overlaid with infinite graphene monolayers, including silicon-wire and plasmonic metal-slot and metal-stripe configurations. The metal-slot configuration offers the most promising performance for Kerr-type nonlinear applications. Finally, we apply the same formalism to probe the potential of graphene nanoribbon waveguide nonlinearity in the terahertz band.

Graphene nano-ribbon waveguides of record-small mode area and ultra-high effective refractive indices for future VLSI

Electronics circuits keep shrinking in dimensions, as requested by Moore's law. In contrast, photonic waveguides and circuit elements still have lateral dimensions on the order of the wavelength. A key to make photonics have a microelectronics-like development is a drastic reduction of size. To achieve this, we need a low-loss nanoscale waveguide with a drastically reduced mode area and an ultra-high effective refractive index. For this purpose, we propose here several low-loss waveguide structures based on graphene nano-ribbons. An extremely small mode area (~10(-7)λ(0)(2), one order smaller than the smallest mode area of any waveguide that has ever been reported in the literature; here λ(0) is the operating wavelength in vacuum) and an extremely large effective refractive index (several hundreds) are achieved. As a device example, a nano-ring cavity of ultra-small size (with a diameter of ~10(-2)λ(0)) is designed. Our study paves the way for future VLSI (very-large-scale integration) optoelectronics.

Mid-infrared active graphene nanoribbon plasmonic waveguide devices

Doped graphene emerges as a strong contender for active plasmonic material in the mid-infrared wavelengths due to the versatile external-control of its permittivity-function and also its highly-compressed graphene surface plasmon (GSP) wavelength. In this paper, we design active plasmonic waveguide devices based on electrical-modulation of doped graphene nanoribbons (GNRs) on a voltage-gated inhomogeneous dielectric layer. We first develop figure-of-merit (FoM) formulae to characterize the performance of passive and active graphene nanoribbon waveguides. Based on the FoMs, we choose optimal GNRs to build a plasmonic shutter, which consists of a GNR placed on top of an inhomogeneous SiO$_2$ substrate supported by a Si nanopillar. Simulation studies show that for a simple 50nm-long plasmonic shutter, the modulation contrast can exceed 30dB. The plasmonic shutter is further extended to build a 4-port active power splitter and an 8-port active network, both based on GNR cross-junction waveguides. For the active power splitter, the GSP power transmission at each waveguide arm can be independently controlled by an applied gate-voltage with high modulation contrast and nearly-equal power-splitting proportions. From the construct of the 8-port active network, we see that it is possible to scale up the GNR cross-junction waveguides into large and complex active waveguide networks, showing great potential in an exciting new area of mid-infrared graphene plasmonic integrated nanocircuits.