Finite Difference Eigenmode Research Articles

Harnessing surface plasmon polaritons from nanogroove plasmonic lenses to enhance the EM fields around plasmonic nanoantennas

In this paper, we present a device—consisting of a bowtie nanoantenna surrounded by either an asymmetric plasmonic nanogroove or a symmetric plasmonic nanogroove—that allows improved excitation of the bowtie nanoantenna via interaction between the bowtie nanoantenna and the surface plasmon polaritons (SPPs) generated from the nanogrooves. We study the effect of both a linear plasmonic nanogroove as well as a circular plasmonic nanogroove (i.e., a circular nanogroove plasmonic lens) on the EM fields around a bowtie nanoantenna placed at a certain distance from the nanogroove. We show that the electric field enhancement of a bowtie nanoantenna can be significantly improved by the interaction between the bowtie nanoantenna and the SPPs generated from the nanogrooves. We employed FDTD simulations to calculate quantities such as the electric field enhancements and power coupling into SPPs as well as a finite difference eigenmode solution to obtain dispersion relation of the nanogrooves. The geometrical parameters of the symmetric nanogroove and asymmetric nanogroove were optimized to couple maximum light into SPPs. We show that the bowtie nanoantenna surrounded by a single asymmetric nanogroove plasmonic lens produces a SERS electromagnetic enhancement factor (EMEF) of 1010—even when the gap between the arms of the bowtie nanoantenna is as large as 10 nm—which is three orders of magnitude higher than SERS EMEF of a stand-alone bowtie nanoantenna and one order of magnitude higher than the SERS EMEF of a bowtie nanoantenna surrounded by a single symmetric nanogroove plasmonic lens. In addition, the effect of the radius of nanogroove plasmonic lenses is studied. The calculation of collection efficiencies of Raman signal from the proposed nanostructures shows that ∼62% Raman signal can be collected from the bowtie nanoantenna surrounded by a symmetric nanogroove plasmonic lens or an asymmetric nanogroove plasmonic lens (PL) compared to 10% Raman signal collected from only a bowtie nanoantenna on a silica substrate.

Enhancing modulation performance by design of hybrid plasmonic optical modulator integrating multi-layer graphene and TiO2 on silicon waveguides

A novel way to enhance modulation performance is through the design of a hybrid plasmonic optical modulator that integrates multi-layer graphene and TiO2 on silicon waveguides. In this article, a design is presented of a proposed modulator based on the use of the two-dimensional finite difference eigenmode solver, the three-dimensional eigenmode expansion solver, and the CHARGE solver. Leveraging inherent graphene properties and utilizing the subwavelength confinement capabilities of hybrid plasmonic waveguides (HPWs), we achieved a modulator design that is both compact and highly efficient. The electrical bandwidth f 3dB is at 460.42 GHz and it reduces energy consumption to 12.17 fJ/bit with a modulator that functions at a wavelength of 1.55 μm. According to our simulation results, our innovation was the optimization of the third dielectric layer’s thickness, setting the stage to achieve greater modulation depths. This synergy between graphene and HPWs not only augments subwavelength confinement, but also optimizes light–graphene interaction, culminating in a markedly enhanced modulation efficiency. As a result, our modulator presents a high extinction ratio and minimized insertion loss. Furthermore, it exhibits polarization insensitivity and a greater bandwidth. Our work sets a new benchmark in optical communication systems, emphasizing the potential for the next generation of chip-scale with high-efficiency optical modulators that significantly outpace conventional graphene-based designs.

Mirror-terminated Mach-Zehnder interferometer based on SiNOI slot and strip waveguides for sensing applications using visible light

In this work, a highly sensitive sensor based on silicon nitride (SiN) waveguide is proposed that can be used for gas sensing using visible light. The whole sensor waveguide uses a silicon dioxide (SiO2) cladding while the sensing arm uses a fluidic cladding such as water. The proposed device is based on loop-mirror terminated (LMT) Mach-Zehnder interferometer (MZI), where the reference arm is exposed to the reference SiO2 medium, while the sensing arm is exposed to the sensing medium leading to a change in the refractive index of the waveguide cladding. The sensor performance is overall optimized by optimizing the design performance of all the components of the structure one by one. The waveguide sensitivity of both strip and slot types is analyzed for gaseous medium in order to compare their sensitivities and select the dimensions of the waveguide that results in the highest device sensitivity. Transverse-electric (TE) polarization is considered in this study for strip waveguide, where a higher sensitivity is founded with respect to the transverse-magnetic (TM) polarization. The field confinement in the slot waveguide in the sensing region is investigated and verified with a mode solver, where the optimum dimensions are obtained using finite difference eigenmode and finite difference time domain solvers. With a sensing arm length of 150 μm only, the proposed sensor achieves a device sensitivity of about 1,320 nm/RIU and a figure-of-merit (FOM) as high as 641 RIU−1 at the wavelength of 650 nm, which is the highest reported FOM up to the author’s knowledge. Higher values of the FOM are possible by employing a longer sensing arm.

Highly coherent supercontinuum generation in circular lattice photonic crystal fibers using low-power pulses

Two structures of circular lattice Photonic Crystal Fibers (PCFs) based on Ge20Sb15Se65 (GSS) material have been proposed for a highly coherent broadband supercontinuum generation (SCG) in the mid-infrared region. Numerical studies using the Finite Difference Eigenmode (FDE) solver on both structures show that the fundamental modes are well confined in the core while the confinement losses are very low. Also, the high nonlinear coefficient of 22.01 W−1m−1 and 17.99202 W−1m−1 for the two structures ensure that these structures can accomplish high nonlinear activity. It has been found that broadband supercontinuums (SCs) spanning from 0.45 μm to 5.3 μm and 0.48 μm to 6.5 μm can be generated using a hyperbolic secant pulse of 0.5 kW. The proposed structures also show very good structural tolerance to optical properties that prevents any radical shift in SC spectra owing to potential fabrication mismatch.

High-sensitivity slot Bragg grating sensor based on chalcogenide glasses

In this study, the finite difference eigenmode approach was used to conduct a theoretical investigation and analysis of the chalcogenide slot waveguide. Maximum power confinement factors of 36.3 % and 56.7 % were found for the slot and cladding areas, respectively. The bidirectional eigenmode expansion approach was then used to develop the chalcogenide slot Bragg grating (SBG) sensor, which was manufactured by electron beam lithography and inductively coupled plasma etching. The chalcogenide SBG has a minimum feature size of 150 nm, which makes it easier to manufacture than silicon photonics Bragg grating devices. Measurement results show a high sensitivity of 325 nm/RIU compared to the conventional evanescent field waveguide sensor in the sensing experiment.

Sub-wavelength tunneling barrier in rib waveguide microring modulators with vanishing bending losses.

Silicon photonics ring resonators in rib waveguide configuration are among the most important components for wavelength-division-multiplexed communication networks. While the rib waveguide enables simple electrical connectivity in microring modulators and add-drop multiplexers, it also results in unacceptable bending losses once the circumference is shrunk below a few micrometers, limiting achievable free spectral ranges and resonant enhancements. We introduce a sub-wavelength tunneling barrier at the critical radius at which the conformally mapped effective index of the slab exceeds that of the waveguide in order to suppress these bending losses, while increasing the resonator's resistance only slightly. The fundamental working principle is explained and illustrated with a design study based on the finite difference eigenmode method. Three-dimensional finite difference time domain simulations verify the design and a proof-of-concept microring modulator is modeled based on the novel geometry.

Detection of volatile organic compounds using mid-infrared silicon nitride waveguide sensors

Mid-infrared (mid-IR) sensors consisting of silicon nitride (SiN) waveguides were designed and tested to detect volatile organic compounds (VOCs). SiN thin films, prepared by low-pressure chemical vapor deposition (LPCVD), have a broad mid-IR transparent region and a lower refractive index (nSiN = 2.0) than conventional materials such as Si (nSi = 3.4), which leads to a stronger evanescent wave and therefore higher sensitivity, as confirmed by a finite-difference eigenmode (FDE) calculation. Further, in-situ monitoring of three VOCs (acetone, ethanol, and isoprene) was experimentally demonstrated through characteristic absorption measurements at wavelengths λ = 3.0–3.6 μm. The SiN waveguide showed a five-fold sensitivity improvement over the Si waveguide due to its stronger evanescent field. To our knowledge, this is the first time SiN waveguides are used to perform on-chip mid-IR spectral measurements for VOC detection. Thus, the developed waveguide sensor has the potential to be used as a compact device module capable of monitoring multiple gaseous analytes for health, agricultural and environmental applications.

Nanophotonics: An Emerging and Promising Approach for COVID-19 Diagnostic Technology

The public health crisis initiated by the emergence of the COVID-19 pandemic emphasizes the need for rapid and accurate diagnostic tests to monitor large populations through community mass testing. Many testing techniques have been implemented to prevent disease spread, critical to pandemic control. Polymerase chain reaction (PCR) tests for detecting viral RNA and immunoassay tests for detecting SARS-CoV-2 antibodies are currently used to diagnose COVID-19. PCR tests are time-consuming, with a 24–48 hours turnaround time. Samples undergoing PCR detection must also be sent to a laboratory to be processed by highly specialized workers, preventing a point-of-care diagnosis from being provided. Popular immunoassay tests have drawbacks as well. Enzyme-linked immunosorbent assays (ELISAs) are extremely labor-intensive and expensive, whereas lateral flow assays (LFAs) are primarily used for antigen detection. In this work, we propose a photonic SARS-CoV-2 detection method based on a ring resonator. We calculate the sensor performance using the finite-difference eigenmode (FDE) method. The sensor sensitivity in ring resonator resonance frequency is 29 nm/RIU, with an intrinsic detection level (iLOD) of 6.89 × 10-5 RIU. We envision ring resonator-based lab-on-chip devices being widely used for applications such as early diagnosis, with the added benefit of being ultra-compact and easily handled by non-specialists.

Optimization of Silicon Nitride Waveguide Platform for On-Chip Virus Detection.

This work presents a rigorous and generic sensitivity analysis of silicon nitride on silicon dioxide strip waveguide for virus detection. In general, by functionalizing the waveguide surface with a specific antibodies layer, we make the optical sensor sensitive only to a particular virus. Unlike conventional virus detection methods such as polymerase chain reaction (PCR), integrated refractive index (RI) optical sensors offer cheap and mass-scale fabrication of compact devices for fast and straightforward detection with high sensitivity and selectivity. Our numerical analysis includes a wide range of wavelengths from visible to mid-infrared. We determined the strip waveguide’s single-mode dimensions and the optimum dimensions that maximize the sensitivity to the virus layer attached to its surface at each wavelength using finite difference eigenmode (FDE) solver. We also compared the strip waveguide with the widely used slot waveguide. Our theoretical study shows that silicon nitride strip waveguide working at lower wavelengths is the optimum choice for virus detection as it maximizes both the waveguide sensitivity (Swg) and the figure of merit (FOM) of the sensor. The optimized waveguides are well suited for a range of viruses with different sizes and refractive indices. Balanced Mach–Zehnder interferometer (MZI) sensors were designed using FDE solver and photonic circuit simulator at different wavelengths. The designed sensors show high FOM at λ = 450 nm ranging from 500 RIU−1 up to 1231 RIU−1 with LMZI = 500 µm. Different MZI configurations were also studied and compared. Finally, edge coupling from the fiber to the sensor was designed, showing insertion loss (IL) at λ = 450 nm of 4.1 dB for the design with FOM = 500 RIU−1. The obtained coupling efficiencies are higher than recently proposed fiber couplers.

Compact Gas Sensor Using Silicon-on-Insulator Loop-Terminated Mach–Zehnder Interferometer

In this paper, we propose a compact optical gas sensor based on the widespread silicon-on-insulator (SOI) technology, operating in the near-infrared (NIR) region around the 1.55 µm wavelength. The sensor employs a loop-terminated Mach–Zehnder interferometer (LT-MZI) with a slot waveguide and a strip waveguide for the sensing arm and the reference arm, respectively. For the same arm length, the LT-MZI can achieve a detection limit two times lower than that of the conventional MZI. Different sensor components were designed, and the optimum dimensions were obtained using finite-difference eigenmode (FDE) and finite-difference time-domain (FDTD) solvers. With a sensing arm length of only 150 μm, our sensor achieves a device sensitivity of 1070 nm/RIU and a figure-of-merit (FOM) as high as 280.8 RIU−1 at the 1.55 μm wavelength. Higher values of FOM can be attained by employing a longer sensing arm. The whole sensor is subjected to air cladding; thus, there is no need for oxide deposition and a further lithography step for sensing-area patterning. The sensor is well suited for low-cost fabrication and large-scale production. Finally, the same LT-MZI device with strip and slot arms but with oxide cladding was fabricated and characterized. The measurements were in good agreement with the electromagnetic (EM) simulation results, ensuring the reliability of our proposed design.

Simulation and Analysis of Microring Electric Field Sensor Based on a Lithium Niobate-on-Insulator

With the increasing sensitivity and accuracy of contemporary high-performance electronic information systems to electromagnetic energy, they are also very vulnerable to be damaged by high-energy electromagnetic fields. In this work, an all-dielectric electromagnetic field sensor is proposed based on a microring resonator structure. The sensor is designed to work at 35 GHz RF field using a lithium niobate-on-insulator (LNOI) material system. The 2.5-D variational finite difference time domain (varFDTD) and finite difference eigenmode (FDE) methods are utilized to analyze the single-mode condition, bending loss, as well as the transmission loss to achieve optimized waveguide dimensions. In order to obtain higher sensitivity, the quality factor (Q-factor) of the microring resonator is optimized to be 106 with the total ring circumference of 3766.59 μm. The lithium niobate layer is adopted in z-cut direction to utilize TM mode in the proposed all-dielectric electric field sensor, and with the help of the periodically poled lithium niobate (PPLN) technology, the electro-optic (EO) tunability of the device is enhanced to 48 pm·μm/V.

A Three-Core Hybrid Plasmonic Polarization Splitter Designing Based on the Hybrid Plasmonic Waveguide for Utilizing in Optical Integrated Circuits

In this research, by using the theory of the surface plasmon polaritons and the plasmonic hybrid components, a new symmetric three-core hybrid plasmonic splitter is proposed at the communication wavelength range. The design consists of two silicon external waveguides with the same dimensions and features, and a centered hybrid waveguide. The centered hybrid waveguide simulated with two silver metal layers and a core silicon waveguide. The plasmonic hybrid coupler supports three supermodes and directly couples the transverse magnetic (TM) mode to the second external waveguide. In contrast, the transverse electric (TE) mode passes through the first external waveguide without coupling. The essential features of the proposed design were studied thoroughly. The most significant parameters of the structure, including propagated modes in the waveguides, extinction ratio (ER), insertion loss (IL), and power transfers, were evaluated using the finite-difference eigenmode (FDE) and eigenmode expansion (EME) methods. The results show that the ERs for the external waveguides are greater than 38 dB for the first external waveguide and 40 dB for the second external waveguide. The ILs of the TE and TM modes are less than 0.1 dB and 0.5 dB at the 1550 nm telecommunication wavelength, respectively.

Graphene oxide integrated silicon photonics for detection of vapour phase volatile organic compounds

The optical response of a graphene oxide integrated silicon micro-ring resonator (GOMRR) to a range of vapour phase Volatile Organic Compounds (VOCs) is reported. The response of the GOMRR to all but one (hexane) of the VOCs tested is significantly higher than that of the uncoated (control) silicon MRR, for the same vapour flow rate. An iterative Finite Difference Eigenmode (FDE) simulation reveals that the sensitivity of the GO integrated device (in terms of RIU/nm) is enhanced by a factor of ~2, which is coupled with a lower limit of detection. Critically, the simulations reveal that the strength of the optical response is determined by molecular specific changes in the local refractive index probed by the evanescent field of the guided optical mode in the device. Analytical modelling of the experimental data, based on Hill-Langmuir adsorption characteristics, suggests that these changes in the local refractive index are determined by the degree of molecular cooperativity, which is enhanced for molecules with a polarity that is high, relative to their kinetic diameter. We believe this reflects a molecular dependent capillary condensation within the graphene oxide interlayers, which, when combined with highly sensitive optical detection, provides a potential route for discriminating between different vapour phase VOCs.

Straight Long-Range Surface Plasmon Polariton Waveguide Sensor Operating at l0 = 850 nm.

A bulk refractive index sensor based on a straight long-range surface plasmon polariton (LRSPP) waveguide is theoretically designed. The waveguide sensor consists of an Au stripe that is embedded in ultraviolet sensitive polymer SU-8. The geometric parameters are optimized by finite difference eigenmode method at the optical wavelength of 850 nm. The sensitivity of 196 dB/RIU/mm can be obtained with a 1.5 μm wide, 25 nm thick Au stripe waveguide. Straight LRSPP waveguides are fabricated by a double layer lift-off process. Its optical transmission is characterized to experimentally prove the feasibility of the proposed design. This sensor has potential for the realization of a portable, low-cost refractometer.

Polarization-independent directional coupler and polarization beam splitter based on asymmetric cross-slot waveguides.

The polarization dependence of a directional coupler (DC) based on asymmetric cross-slot waveguides is investigated. Due to structural birefringence, the coupling behaviors of the quasi-TE and quasi-TM modes in the DC vary with the waveguide geometry. A polarization-independent directional coupler (PIDC) and polarization beam splitter (PBS) are proposed by tailoring the ratio of the coupling length for quasi-TE and quasi-TM modes. The simulated results show that the coupling lengths of the designed PIDC and PBS are 8 and 28.25μm, respectively. Both the PIDC and PBS show an insertion loss (IL) <0.7 dB on a bandwidth over 100nm. The extinction ratios are ∼20 dB for PIDC and ∼14 dB for PBS. The fabrication-error tolerance of the practical devices is also discussed. In this study, we employ a commercial software tool for finite difference eigenmode and three-dimensional finite difference time domain methods to perform the numerical simulations.

A systematic study of linear and nonlinear properties of photonic crystal fibers

In this paper, linear and nonlinear properties of photonic crystal fiber (PCF) are studied in terms of wavelength for triangular and square lattices to investigate the effects of changing the fiber dimensions including air-hole diameter, pitch size and the number of air-hole rings on the dispersion profile and its nonlinear parameter. A chalcogenide based PCF is proposed in this paper and modeled in TCAD environment of Mode Solution software related to Lumerical package. The finite difference eigenmode solver numerical method is utilized in the modeling and anisotropic perfectly matched layers (PML) are assumed as absorbing boundaries to be positioned outside the outer-most ring of the air-holes. Accordingly, the effects of changing each of aforementioned parameters on the value and slope of dispersion and loss profiles as well as on its nonlinear parameter are systematically determined. For instance, numerical results achieved by the simulation results show that both the value and slope of dispersion profile are reduced by considering the diameter of air holes with a constant value and increasing the pitch size of the fiber. Moreover, considering a fixed value for the pitch size and increasing the air hole diameters lead to an increase of dispersion profile in terms of wavelength. Additionally, the numerical results show that an increase in the diameter of the air holes results in an increase in the nonlinear parameter. Further, the input source’s wavelength increase will result in the reduction of the nonlinear parameter.

Electrically injected ultra-low threshold room temperature InGaN/GaN-based lateral triangular nanowire laser

We have demonstrated an electrically injected ultra-low threshold (8.9 nA) room temperature InGaN/GaN based lateral nanowire laser. The nanowires are triangular in shape and survived naturally after etching using boiling phosphoric acid. A polymethyl methacrylate (PMMA) and air dielectric distributed mirror provide an optical feedback, which together with one-dimensional density of states cause ultra-low threshold lasing. Finite difference eigen-mode (FDE) simulation shows that triangular nanowire cavity supports single dominant mode similar to TE01 that of a corresponding rectangular cavity with a confinement factor of 0.18.

Acceleration of FDTD mode solver by high-performance computing techniques

A two-dimensional (2D) compact finite-difference time-domain (FDTD) mode solver is developed based on wave equation formalism in combination with the matrix pencil method (MPM). The method is validated for calculation of both real guided and complex leaky modes of typical optical waveguides against the bench-mark finite-difference (FD) eigen mode solver. By taking advantage of the inherent parallel nature of the FDTD algorithm, the mode solver is implemented on graphics processing units (GPUs) using the compute unified device architecture (CUDA). It is demonstrated that the high-performance computing technique leads to significant acceleration of the FDTD mode solver with more than 30 times improvement in computational efficiency in comparison with the conventional FDTD mode solver running on CPU of a standard desktop computer. The computational efficiency of the accelerated FDTD method is in the same order of magnitude of the standard finite-difference eigen mode solver and yet require much less memory (e.g., less than 10%). Therefore, the new method may serve as an efficient, accurate and robust tool for mode calculation of optical waveguides even when the conventional eigen value mode solvers are no longer applicable due to memory limitation.

Yee-mesh-based finite difference eigenmode solver with PML absorbing boundary conditions for optical waveguides and photonic crystal fibers

Eigenvalue equations for solving full-vector modes of optical waveguides are formulated using Yee-mesh-based finite difference algorithms and incorporated with perfectly matched layer absorbing boundary conditions. The established method is thus able to calculate the complex propagation constants and the confinement losses of leaky waveguide modes. Proper matching of dielectric interface conditions through the Taylor series expansion of the fields is adopted in the formulation to achieve high numerical accuracy. The method is applied to the study of the holey fiber with triangular lattice, the two-core holey fiber, and the air-guiding photonic crystal fiber.