Eigenmode Expansion Research Articles

Transfer Matrix Method with Gouy Phase Shift correction applied to a High Numerical Aperture fiber-to-fiber optical coupling analysis

In this paper, we present the transmittance and reflectance study of the optical coupling between two High Numerical Aperture (HNA) fibers using a new model based on the Transfer Matrix Method (TMM). The TMM is corrected by the effects of the Gouy phase shift and the mode overlap is used in the material between the fibers to calculate the coupling loss. The coupling is also simulated using the Eigenmode Expansion (EME) method, and these numerical results are compared with experimental ones. The Gaussian beam nonparaxial field equations are used to evaluate the phase of the light in the coupling region and to obtain the effective refractive index of the wave between the fiber facets. Our TMM approach produced results close to experimental ones. Our model is, at least, two orders of magnitude faster than a commercial solver, and easy to coding; highlighting this approach’s importance as a transmittance/reflectance simulation tool.

Single-Mode versus Multimode Fiber Bragg Grating Temperature Sensors: A Theoretical Study

This paper aims to enhance understanding regarding the impact of the geometrical parameters of the grating on the transmission spectrum of single-mode and multimode fiber Bragg grating sensors and to compare the performance of both sensors for temperature monitoring. Furthermore, we propose a novel design where we combine between phase shifted and tilted grating in MMFBG sensors to further enhance their sensitivity and make them more suited for temperature sensing applications. In this regard, a numerical simulation using the eigenmode expansion (EME) solver of Lumerical software is conducted. Analysis of the obtained results suggests that the multimode Fiber Bragg grating sensor has the potential to be used as a temperature sensor with good sensitivity when it is well designed.

Spectrum contrast enhancement of fiber fabry-perot sensor by coupling efficiency improvement

This paper investigates the impact of interface angles on the coupling efficiency of a fiber Fabry-Perot interferometer (FFPI) sensor using both simulation and experimental methods. The FFPI sensor, which consists of a single-mode fiber (SMF), hollow-core fiber (HCF), and diaphragm, has its coupling efficiency determined by the generalized scattering matrix of the cascaded fiber system. To obtain the interface angles of the FFPI sensor, a new on-line monitoring system is developed based on microscopic images of the FFPI cavity and an image processing algorithm using OpenCV. By combining the eigenmode expansion method (EME) model and the online interface angle measurement technique, the coupling efficiency and spectral contrast of the FFPI cavity are evaluated and improved. Additionally, the corresponding working point in the intensity demodulation based FFPI sensor can be quickly identified. Using this method, an FFPI sensor with a spectral contrast of over 35 dB is achieved, which is significantly higher than existing similar sensors, and its sensitivity also reaches 50.80 mV/MPa. This work also holds significance for controlling and enhancing the spectral characteristics of other cascaded fiber optic sensors.

Design of 16-wavelength high-power heterogeneous III-V/Si laser arrays with varying stripe width and grating period

Multi-wavelength laser array is currently one of the most attractive technologies to provide high density links for advanced optical communications and computing. The conventional scheme of varying grating period is almost impossible to achieve 8-wavelength or more. And, the optical output power of heterogeneously integrated quantum dot laser can hardly meet the commercial demand. In this paper, we report a 16-wavelength high-power heterogeneously integrated quantum dot distributed feedback laser array. To the best of our knowledge, this is the first heterogeneously integrated quantum dot laser array that tunes the lasing wavelength by combining the scheme of varying the stripe width and grating period of laser units. The effective refractive index of gratings is calculated by eigenmode expansion method. When the grating period is fixed at 198 nm, and the stripe widths of laser units are 2.00 μm, 2.25 μm, 2.60 μm and 3.15 μm, respectively, the corresponding lasing wavelengths are 1307.94 nm, 1308.49 nm, 1309.06 nm and 1309.63 nm, respectively, and the wavelength spacing of the adjacent laser units is about 100 GHz. By additionally adjusting the grating period between 196 nm and 202 nm with 2 nm spacing of grating period, a 16-wavelength QD DFB laser array is designed with the wavelength range from 1294.73 nm to 1336.09 nm. In addition, asymmetric distributed feedback grating is adopted to improve the optical output power at the front-end of laser arrays. The maximum ratio of the output power at the both end of laser units is 19.6 when the grating duty cycles of the front-end and the back-end of the λ/4 phase-shift is 0.7 and 0.5, respectively, and the grating lengths is 250 μm and 450 μm, respectively. This work will promote the performance improvement of heterogeneously integrated quantum dot lasers and develop the quantum dot lasers towards multi-wavelength.

Giant second-harmonic generation in monolayer MoS2 boosted by dual bound states in the continuum.

Dielectric metasurfaces open new avenues in nonlinear optics through their remarkable capability of boosting frequency conversion efficiency of nonlinear optical interactions. Here, a metasurface consisting of a square array of cruciform-shaped silicon building blocks covered by a monolayer MoS2 is proposed. By designing the metasurface so that it supports optical bound states in the continuum (BICs) at the fundamental frequency and second harmonic, nearly 600× enhancement of the second-harmonic generation (SHG) in the MoS2 monolayer as compared to that of the same MoS2 monolayer suspended in air is achieved. To gain deeper insights into the physics of the metasurface-induced enhancement of nonlinear optical interactions, an eigenmode expansion method is employed to analytically investigate the main characteristics of SHG and the results show a good agreement with the results obtained via full-wave numerical simulations. In addition, a versatile nonlinear homogenization approach is used to highlight and understand the interplay between the BICs of the metasurface and the efficiency of the SHG process. This work suggests a promising method to enhance the nonlinear optical processes in two-dimensional materials, enabling the development of advanced photonic nanodevices.

Design of a 1 × 3 Power Splitter Based on Multimode Interference in a Parabolic-Type Slot-Waveguide Structure

Multimode interference (MMI) couplers based on silicon slot-waveguide structures have received widespread attention in recent years. The key issues that need to be addressed are the size and loss of such devices. This study introduces a 1 × 3 silicon-based slot-waveguide multimode interference power splitter. The device uses a gallium-nitride slot-waveguide structure to reduce the length of the coupling region and decrease additional losses. To reduce the width of the coupling region, the multimode interference coupling area is designed with a parabolic-shaped structure. The introduction of a tapered structure between the input/output waveguides and the coupling region improves additional losses and non-uniformity. Furthermore, we conducted an analysis of the fabrication tolerances of the coupling region. In this paper, we use mode solution to simulate the design of the device in the 1550 nm optical wavelength range. The eigenmode expansion method is used to simulate and optimize the parameters of the device. The device is simulated using the eigenmode expansion solver. The simulation results show that the total length of the coupling region for the device is only 4 μm. The normalized transmission of the device is 0.992, and its excess loss and imbalance are 0.036 dB and 0.003 dB, respectively. The proposed power splitter can be applied to integrated optical circuit design, optical sensing, and optical power measurement.

Interlayer coupled dual-layer metagratings for broadband and high-efficiency anomalous reflection

Recent progress in metagratings highlights the promise of high-performance wavefront engineering devices, notably for their exterior capability to steer beams with near-unitary efficiency. However, the narrow operating bandwidth of conventional metagratings remains a significant limitation. Here, we propose and experimentally demonstrate a dual-layer metagrating, incorporating enhanced interlayer couplings to realize high-efficiency and broadband anomalous reflection within the microwave frequency band. The metagrating facilitated by both intralayer and interlayer couplings is designed through the combination of eigenmode expansion (EME) algorithm and particle swarm optimization (PSO) to significantly streamline the computational process. Our metagrating demonstrates the capacity to reroute a normally incident wave to +1 order diffraction direction across a broad spectrum, achieving an average efficiency approximately 90% within the 14.7 to 18 GHz range. This study may pave the way for future applications in sophisticated beam manipulations, including spatial dispersive devices, by harnessing the intricate dynamics of multi-layer metagratings with complex interlayer and intralayer interactions.

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.

Compact Low Loss Ribbed Asymmetric Multimode Interference Power Splitter

Optical power splitters (OPSs) are utilized extensively in integrated photonic circuits, drawing significant interest in research on power splitters with adjustable splitting ratios. This paper introduces a compact, low-loss 1 × 2 asymmetric multimode interferometric (MMI) optical power splitter on a silicon-on-insulator (SOI) platform. The device is simulated using the finite difference method (FDM) and eigenmode expansion solver (EME). It is possible to attain various output power splitting ratios by making the geometry of the MMI central section asymmetric relative to the propagation axis. Six distinct optical power splitters are designed with unconventional splitting ratios in this paper, which substantiates that the device can achieve any power splitter ratios (PSRs) in the range of 95:5 to 50:50. The dimensions of the multimode section were established at 2.9 × (9.5–10.9) μm. Simulation results show a range of unique advantages of the device, including a low extra loss of less than 0.4 dB, good fabrication tolerance, and power splitting ratio fluctuation below 3% across the 1500 nm to 1600 nm wavelength span.

Optimization of the reflection in the optical coupling between high numerical aperture fibers and photonic integrated circuits

The optical coupling in silicon Photonic Integrated Circuits (PICs) remains one of the main topics in the improvement of the performance of these devices. Highly demanding parameter specifications, such as loss, reflection, and bandwidth, drive the continuous search for optimization. The use of High Numerical Aperture Fibers (HNA fibers) to couple light in small diameter mode edge couplers, is one of the existing technologies that address the coupling challenge. We demonstrate, using Eigenmode Expansion (EME) and Transfer Matrix Method (TMM) simulations, that the Optical Return Loss (ORL) of this coupling approach can be made as low as −45 dB for both Transverse Electric (TE) and Transverse Magnetic (TM) polarizations, simultaneously. The results from our TMM model agree well with a commercial solver one and are faster (six orders of magnitude) and more computationally efficient. It is shown that the refractive index in the TMM should be corrected to compensate for the Gouy phase shift in the non-guided sections of the optical coupling. Additionally, the reflection pattern, as a function of the gap between the fiber and the PIC, provides a way to control the distance of the fiber to avoid packaging-related problems.

Nonlinear beat wave decay of Kelvin/diocotron waves on a two-dimensional vortex

We describe theory and experiments investigating nonlinear beat wave decay of diocotron modes on a nonneutral plasma column (or Kelvin waves on a vortex). Specifically, a Kelvin/diocotron pump wave varying as Ap exp [i(lpθ−ωpt)] decays into two waves: a Kelvin/diocotron daughter wave with exponentially growing amplitude Ad(t), mode number ld<lp, and frequency ωd; and an exponentially growing “beat wave” with mode number lb and frequency ωb. Nonlinear wave–wave coupling requires lb=lp−ld and ωb=ωp−ωd. The new theory simplifies and extends a previous weak-turbulence theory for the exponential growth rate of this instability, by instead using an eigenmode expansion to describe the beat wave as a wavepacket of continuum (Case/van Kampen) modes. The new theory predicts the growth rate, the nonlinear frequency shift (both proportional to Ap2), and the functional form of the beat wave, with amplitude proportional to ApAd*(t). Experiments observe beat wave decay on electron plasma columns for a range of mode numbers up to lp=5 and ld = 4, with results in quantitative agreement with the theory, including the ld = 1 case for which measured growth rates are negligible, as expected theoretically.

Analysis of High-Order Surface Gratings Based on Micron Lasers on Silicon

High-quality silicon-based lasers are necessary to achieve full integration of photonic and electronic circuits. Monolithic integration of III–Vmicron lasers on silicon by means of the aspect ratio trapping (ART) method is a promising solution. To obtain sufficient optical feedback to excite the laser without introducing complex fabricating processes, we have designed a high-order surface grating on micron lasers which was epitaxially grown by the ART method and can be fabricated by common UV lithography. The performance of the grating was analyzed by the finite-difference time-domain (FDTD) method and eigenmode expansion (EME) solver. After simulation optimization, the etching depth was set to 0.6 μm to obtain proper reflection. The width of the slots and the slot spacing were selected to be 1.12 μm and 5.59 μm, respectively. Finally, we obtained results of 4% reflectance and 82% transmittance at a 1.55 μm wavelength at 24 periods.

Reconfigurable Generation of PAM-4 Signal Based on Fano Effect for Optical Interconnect Systems

We present a novel low-power architecture for the generation of multilevel pulse amplitude modulation (PAM-4) signal generation. A new structure of a micro-ring resonator based on a 4´4 MMI (Multimode interference) coupler is proposed to control the coupling coefficient and Fano shapes. Based on this structure, a high linearity of the transmission is created, compared with the Mach Zehnder Interferometer (MZI) conventional structure. Here, instead of using directional couplers and MZI as shown in the previous reports, in our method only two 4´4 multimode interference structures on silicon on insulator (SOI) waveguides has been used. The new design is compatible and suitable for the current CMOS fabrication technology. In this work, the special design is as follows: one of two MMI couplers is used to be a micro-ring resonator and two segmented phase shifters are used in the micro-ring resonator to generate 4 levels of the PAM-4 signal. The micro-ring resonator is controlled to work at the over-coupled region, so the Fano effect can be generated. This proposed PAM-4 architecture uses the generated Fano effect, therefore an extreme reduction in power consumption can be achieved. A large fabrication tolerance of ±500 nm and a compact footprint of 10´500 µm2 can be carried-out. The device is simulated and optimally designed using the FDTD (finite difference time domain) and EME (Eigenmode Expansion). This architecture can be useful for optical interconnects and data center network applications.

Distributed curvature sensing using long period fiber grating and machine learning numerical analysis.

In this numerical study, we propose a fiber distributed curvature sensor based on the analysis of the spectral transmission of a long period fiber grating (LPG) with a neural network. A simulation of the optical transmissions of a proposed 6-cm LPG structure for different curvature profiles is first performed using EigenMode Expansion and a coupled-mode theory algorithm. Both fiber curvature profiles and their corresponding optical transmission spectra are then injected into a four dense layer neural network which, after training, leads to a 0.40% relative median estimation error in the bending profiles. This paper demonstrates the efficiency of neural network-based optical sensors to analyze non-uniform perturbations, while also revealing long-period gratings to be promising candidates for such systems.

Synthesis of Near-Field Arrays Based on Electromagnetic Inner Products

Near-field antennas have been successfully adopted in several wireless applications. To exploit the high reconfigurability of array antennas, multiple synthesis techniques for arrays operating in the near-field region have been proposed. Building upon previous works on eigenmode expansions of the radiated fields, two synthesis methods for the excitations of near-field arrays based on the definition of an inner product on the electromagnetic fields are investigated: the "maximum norm" and "minimum error field norm" methods. The "maximum norm" method computes the array excitations that maximize either the active power flow through a target surface or the electric/magnetic energy stored in an assigned volume, depending on the adopted inner product. The performance of the maximum active power flow method is compared with the one of the simpler conjugate phase method. Furthermore, the limit solution achieved when the target surface reaches the far-field region is compared against the "maximum Beam Collection Efficiency" method. The "minimum error field norm" method allows to synthesize a given target field. As an example, the latter method is used to find the optimal excitation of a Plane Wave Generator with a spherical quiet zone. The effectiveness and performance of the discussed synthesis methods are validated through numerical simulations.

Homogenized transition conditions for plasmonic metasurfaces

The present study aims to model the optical response of plasmonic metasurfaces made of a periodic arrangement of metallic particles with arbitrary shape and subwavelength dimensions. By combining homogenization with quasistatic plasmonic eigenmode expansion, the metasurface is replaced by a zero-thickness interface associated with frequency-dependent effective susceptibilities. The resulting discontinuities of the fields are responsible for strong interaction with the incoming light at the resonances when the complex permittivity of the metal passes close to the real permittivity of an eigenmode. Our modeling provides a physical picture of resonances in plasmonic metasurfaces, and it allows for a huge decrease in the numerical cost of their computations. In addition, comparisons with direct numerics in two dimensions evidence its predictive force at any incidence, particle shape, and arrangement.

High-Density and Low-Crosstalk Multilayer Silicon Nitride Waveguide Superlattices With Air Gaps

High-density and low-crosstalk waveguide arrays are critical components in optical phased arrays (OPAs) and are widely used in solid-state light detection and ranging (LiDAR). In this work, silicon nitride waveguide superlattices with air gaps are proposed and analyzed theoretically. Mode analysis shows that the introduced air gaps beside the waveguide help shorten the skin depth of the evanescent field and increase the effective index range of the waveguide under single mode conditions. Lower crosstalk is demonstrated between a pair of waveguides with air gaps compared with those without air gaps. On this basis, a waveguide superlattice with air gaps is designed by combining the eigenmode expansion method and particle swarm optimization. The crosstalk of the waveguide superlattice is optimized to −24.3 dB when the waveguide pitch is 0.9 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mu \text{m}$</tex-math></inline-formula> , the propagation length is 1 mm, and the wavelength is 905 nm. The crosstalk is still below −22.4 dB under the typical process variations and over the wavelength range of 890 nm–920 nm. Therefore, the proposed air-gap waveguide superlattices with high density and low crosstalk offer opportunities to improve the beam steering performance of OPA chips in the near-infrared (NIR) waveband.

Plasmon coupling using eigenmode expansion and its sensing applications

Plasmonic nanostructures providing enormous diversified applications are always a boon for the nanomaterial researchers. The light-matter interaction additionally provides various plasmonic modes, which are studied, in general, with the optical spectra along with the near field enhancement plots. Further, to visualize all the hybrid plasmonic modes between any two coupled nanostructures, the eigenmode expansion is employed as it’s an analytical calculation for optical response of interacting nanostructures. Herein, we have simulated the optical spectra for various morphology of Au nanostructures and also the Au-Au dimer nanospheres using MATLAB based Boundary element method (BEM), which requires less computing space and time. Different plasmonic modes and their respective coupling decay was calculated by modifying the interparticle gap and incident angle of the plane wave. These modes were further overviewed using the eigenmode determination which provides the properties of plasmonic lattices. The refractive index sensing was also analyzed, representing the individual sensitivity for the corresponding nanostructures.

Механическое взаимодействие метаемого тела со стенками канала рельсового электромагнитного ускорителя. Тестовая задача

The vibration of the accelerator rails under the action of electromagnetic forces is considered. The armature and with it the right boundary of electromagnetic forces application moves along the barrel bore from the breach to muzzle. The rail accelerator is simply considered as a Bernoulli-Euler beam of finite length, lying on a viscoelastic foundation, with cantilever support from the side of the accelerator breech. The rail vibration is described by a differential equation in partial derivatives of the fourth order in coordinate and the second order in time. Using the eigenmode expansion method an analytical solution of the equation is obtained taking into account the change in the armature speed along the length of the barrel. Taking into account the peculiarities of the expression for natural vibration modes for this problem made it possible to simplify the calculations and take into account appropriate number of harmonics along the entire trajectory of the armature, which is difficult in the traditional application of the method, and thereby increase the accuracy of predicting the amplitude and nature of rail vibrations during the shot. The proposed approach allows testing and debugging numerical methods for solving complex problems, as well as more correctly designing the barrel of a rail accelerator.

Analysis of First-Order Gratings in Silicon Photonic Waveguides

A simple thin film effective index analysis for first-order gratings in Si photonic waveguides is shown to provide highly accurate results for reflected and transmitted power spectrums as long as the waveguide remains single mode and non-radiating. A cover layer can be added to the grating region of a Si photonic waveguide to increase the strength of the grating, modify transition losses from the input waveguide to the grating waveguide region, and/or modify the width of the reflectivity spectrum. For a given grating period, the peak reflection and spectral width of the reflectivity decrease as the duty cycle is decreased or increased from ∼50%. For both radiating and multimode structures, the coupling between all modes, power radiated towards the superstrate (upwards), power radiated downwards (substrate) and transmitted power analyzed by Floquet-Bloch, Eigenmode Expansion and Finite Difference Time Domain methods show excellent agreement. Coupling coefficients calculated using analytic formulas are shown to be accurate only for shallow grating depths.