Coupled-mode Equations Research Articles

Theory of Stimulated Brillouin Scattering in Fibers for Highly Multimode Excitations

Stimulated Brillouin scattering (SBS) is often an unwanted loss mechanism in both active and passive fibers. Highly multimode excitation of fibers has been proposed as a novel route toward efficient SBS suppression. Here, we develop a detailed, quantitative theory which confirms this proposal and elucidates the physical mechanisms involved. Starting from the vector optical and scalar acoustic equations, we derive appropriate nonlinear coupled mode equations for the signal and Stokes modal amplitudes and an analytical formula for the SBS (Stokes) gain with applicable approximations, such as the neglect of shear effects. This allows us to calculate the exponential growth rate of the Stokes power as a function of the distribution of power in a highly multimode signal. The peak value of the gain spectrum across the excited modes determines the SBS threshold—the maximum SBS-limited power that can be sent through the fiber. The theory shows that the peak SBS gain is greatly reduced by highly multimode excitation due to gain broadening and relatively weaker intermodal SBS gain. The inclusion of exact vector optical modes in the calculation is crucial in order to capture the incomplete intermodal coupling due to mismatch of polarization patterns of higher-order modes. We demonstrate that equal excitation of the 160 modes of a commercially available, highly multimode circular step index fiber raises the SBS threshold by a factor of 6.5 and find comparable suppression of SBS in similar fibers with a D-shaped cross section. Published by the American Physical Society 2024

Coupled modes analysis of stimulated Brillouin scattering in the regimes of nonlinear ion acoustic waves

The nonlinear saturation of stimulated Brillouin scattering (SBS) in long scale length plasmas is studied in detail through coupled mode equations. Our model incorporates harmonic and subharmonic generation of ion acoustic waves (IAWs), as well as nonlinear Landau damping and the nonlinear frequency shift of IAWs induced by particle trapping. Numerical simulations are carried out across various IAW wavenumbers (k a λ De ) and electron-ion temperature ratios (Z i T e /T i ) within different SBS instability regimes. The results demonstrate that our model can distinguish the importance of each effect contributing to the nonlinear behavior in SBS under different plasma conditions. Furthermore, we examine the scaling of SBS reflectivity with laser intensity under conditions relevant to inertial confinement fusion.

Coupled mode theory-based analytical model of a ring resonator refractive index sensor incorporating bending loss and dispersion

This paper presents an analytical model of a silicon nitride-based 2D ring resonator refractive index (RI) sensor using coupled mode theory (CMT). The proposed model decomposes the ring resonator into two coupling regions and employs coupled-mode equations to describe input and output amplitudes via scattering matrix analysis. The proposed sensor, operating with varying refractive indices in the background cladding, demonstrates a sensitivity of 218 nm/RIU and a total quality factor of 1198. A comprehensive analysis of the bending loss in the proposed sensor is conducted, elucidating its impact on sensitivity, coupling quality factor, and intrinsic quality factor. This analysis aids in the selection of optimal ring resonator parameters, including radius, width, and gap, to achieve superior sensing performance. Furthermore, the paper examines the effect of dispersion on sensitivity and quality and compares the results with those obtained from CMT-based silicon core ring resonator and disk resonator RI sensors. This study provides valuable insights for the design and optimization of high-performance silicon nitride-based RI sensors for various applications.

Bifunctional acoustic lossy coupler for broadband power splitting and absorption

In this work, we propose a bifunctional acoustic lossy coupler for broadband power splitting and absorption. Following the three-level system in quantum physics, the three-waveguide (WG) acoustic system is proposed to obtain efficient energy transfer behaviors. Given the agreement in form between Schr o¨ dinger equation and coupled mode equation, the time-dependent external fields are mapped into space-varying coupling actions between adjacent WGs. The propagation paths of the incident waves can be predicted by Schr o¨ dinger-like equation, which are verified by numerical simulations and experimental measurements. Owing to the different responses to lossy medium in WG B for WG A incidence and WG C incidence, the acoustic coupler can be considered as a broadband power splitter and muffler by selecting different input ports. Meanwhile, according to the reversibility of acoustic path, a switchable acoustic logic gate with functions of “OR” and “XOR” is constructed as well by taking advantage of the lossless adiabatic coupler, and the function can be controlled conveniently by reversing the phase of input waves from WG A or C. Our work provides a new scheme for the design of bifunctional acoustic coupler, which may have a profound impact on the development of non-resonance acoustic high-performance devices.

Plasma-grating-based laser pulse compressor.

To avoid damage in high-power laser systems, a chirped plasma-based grating is proposed for compressing laser pulses that have been previously stretched and amplified. This chirped grating is generated through the interaction of chirped pump laser pulses in a plasma slab. Particle-in-cell (PIC) simulations demonstrate that the grating exists for a duration sufficient to be utilized in the final chirped pulse amplification (CPA) stage. The generation of the grating is quite flexible, as several parameters can be adjusted, such as plasma density, chirp, length, and intensity of the pump laser. To begin, the structure of the grating is analyzed in terms of ponderomotive effects of the pump laser pulses. The primary application of the chirped plasma-based grating lies in compressing laser pulses to large amplitudes and short durations after they have been stretched and amplified beforehand. The compression factor is explored in connection with potential grating parameters. Reflectivity and effective bandwidth of chirped plasma gratings are parameters to be optimized. However, the grating spectral bandwidth can only be increased at the expense of reflectivity. The PIC results are made understandable through model calculations based on coupled mode equations.

Composite photonic lattice with a broad channel to sustain topological interface states

In the field of topological photonics, one goal is to seek specialized structures with topological protection that can support the stable propagation of light. We have designed a topological configuration featuring a broad channel to sustain edge or interface states. The topological properties are elucidated by analyzing the energy spectrum, eigenstates, and winding numbers. Furthermore, the propagation characteristics of light within our structure are examined through the computation of intensities derived from the coupled mode equations. Our findings reveal that the structure is capable of confining light to the central region, facilitating stable and robust propagation for large-sized beams. Additionally, simulations conducted using commercial software have substantiated the theoretical analysis. Our finding may have significant implications for the modulation of structured light and the development of photonic devices with wide channel capabilities.

Simultaneous generation of first- to fourth-order OAM modes based on a cascaded preset-twist long-period fiber grating

Abstract We propose and demonstrate the simulation and fabrication of an all-fiber orbital angular momentum (OAM) mode converter capable of generating first- to fourth-order modes simultaneously, which is realized by inscribing a cascaded preset-twist long-period fiber grating (CPT-LPFG) in a six-mode fiber utilizing a CO2 laser. A new segmented Runge–Kutta method is proposed to simulate the preset-twist long-period fiber gratings. By calculating the twist angle and relative coupling coefficient for each pitch and then solving the coupled mode equations utilizing the Runge–Kutta algorithm. The simulation illustrates that the preset-twist method significantly improves the coupling coefficient of higher-order modes, thereby reducing coupling difficulty. In the experiment, by twisting the fiber at an angle of 1080° and fabricating cascaded gratings with periods of 745 μm, 310 μm, 204 μm, and 146 μm, it is feasible to generate first- to fourth-order OAM modes simultaneously, at wavelengths of 1635 nm, 1548 nm, 1460 nm, and 1334 nm, respectively. The insertion loss is less than 1 dB, and the mode purity is over 90 %. To the best of our knowledge, this is the first time that first- to fourth-order OAM modes are simultaneously generated utilizing a single long-period fiber grating.

Polymer free volume and its connection to the entanglement length and the plateau modulus via polymer mode-coupling theory and equation of state

Using a many-chain system of Gaussian chains interacting with each other through the Lennard-Jones (LJ) potential, we demonstrate that there exists a connection between polymer fractional free volume (f) and the entanglement chain length (Ne). Here, f is determined by the generic van der Waals (GvdW) equation of state using the intermolecular radial distribution function [g(r)] of the Gaussian chain generated by the polymer reference interaction sites model while Ne by the polymer mode-coupling theory (PMCT) for strongly coupled macromolecules. The key concept in PMCT is that intermolecular forces experienced by a bead in a chain surrounded by other chains are strongly coupled to the site specific intramolecular radial distribution function. The calculated Gp and η of polyethylene with chain lengths from 500 to 2000 interacting with one another through the LJ potential agree well with experiment and molecular dynamics simulation.

The Study on the Spectral Analysis of Fiber Bragg Grating (FBG) as a Strain Sensor

Abstract: By adjusting the grating length and refractive index change, parameters of the Fibre Bragg grating which are the effective refractive index, Bragg wavelength, grating period, and strain-optic constant are provided and discussed, along with the characterization of the grating, including strain, Bragg wavelength shift, spectral response, and bandwidth. The coupled mode equations form the basis for data analysis and acquisition. This research uses a high-level computer language, such as GNU Octave software, to simulate FBG spectral responses.

Transverse mode distribution in multimode diode-pumped Raman fiber laser

Raman lasers based on multimode graded-index fibers may generate high-quality (M2∼2) Stokes beams when pumped by highly multimode (M2>30) laser diodes. Here we, examine, both experimentally and theoretically, the energy distribution of the output Stokes beam across the principal quantum mode number n in a bent multimode fiber operating well above the Raman threshold. In contrast to Kerr spatial beam cleaning, leading to a Rayleigh–Jeans mode power distribution, in a multimode Raman fiber laser, we find that the output mode powers approach an exponential distribution. We introduce a coupled-mode equations model, including random linear coupling between neighboring mode groups, and obtain a good agreement between numerical simulations and experimental results. The model shows that, for typical mode coupling coefficients, the randomization of the mode power distribution is compensated by both nonlinear (Raman and Kerr) effects and linear filtering from the fs-inscribed fiber Bragg grating, both acting on the Stokes beam over successive round trips. When random coupling becomes the dominating factor, the mode power distribution of the Stokes beam tends to equipartition, similar to what is observed with large-size highly multimode beams of low intensity (and nonlinearity) in the absence of any filtering.

Analytical model of direct-Bragg, exchange-Bragg, and evanescent coupling in a dual-waveguide structure and its application to single-mode lasing

Single-mode distributed-feedback lasing is explored for an asynchronous dual-waveguide uniform-grating structure that exhibits exchange-Bragg and evanescent coupling between optical modes of the two waveguides as well as direct-Bragg coupling between optical modes within each waveguide. Coupled-mode equations governing all coupling processes are presented and solved, yielding an analytical solution that is applicable to a variety of single-mode lasing mechanisms. We leverage this solution to elucidate the lasing mechanism in which the photonic bandgap (PBG) due to exchange-Bragg coupling is aligned to and suppresses a degenerate lasing mode associated with the direct-Bragg PBG of the active waveguide. PBG alignment and mode suppression are achieved for a range of values of Henry’s alpha, direct-Bragg coupling, exchange-Bragg coupling, and evanescent coupling that yield at-threshold gain margin and longitudinal power flatness superior to those of the benchmark λ/4-shifted DFB lasing structure. Such performance includes a gain margin ΔαL=0.88 for a minimum flatness F=0.0006, enabled by the power-transfer action of evanescent coupling. The dual-waveguide geometry and superior predicted performance make the structure compelling for both III-V and heterogeneous III-V-on-silicon platforms.

A stochastic approach to phase noise analysis for microwaves generated with Kerr optical frequency combs

Kerr optical frequency combs are expected to play a major role in photonic technology, with applications related to spectroscopy, sensing, aerospace, and communication engineering. Most of these applications are related to the metrological performance of Kerr combs, which is ultimately limited by their noise-driven fluctuations. For this reason, it is of high importance to understand the influence of random noise on the comb dynamics. In this communication, we theoretically investigate a model where Gaussian white noise is added to the coupled-mode equations governing the comb dynamics. This stochastic model allows us to characterize the noise-induced broadening of the spectral lines. Moreover, this study permits to determine the phase noise spectra of the microwaves generated via comb photodetection. In this latter case, our analysis indicates that the low-frequency part of the spectra is dominated by pattern drift while the high-frequency part is dominated by pattern deformation. The theoretical results are found to be in excellent agreement with numerical simulations.

Unidirectional beam splitting in acoustic metamaterial governed by double fractional stimulated Raman adiabatic passage

In this work, we take fractional stimulated Raman adiabatic passage (f-STIRAP) for the design of functional acoustic waveguide (WG) coupler into account. Assisted by the agreement in the form between Schrödinger equation in quantum mechanics and the coupled-mode equation of classical waves, the quantum three-level system is mapped onto the acoustic three-WG system with space-varying coupling actions between composing WGs. The output port of the coupler can be selected by adopting different superposition forms of incident waves, which is utilized to build a one-way acoustic mode converter based on double f-STIRAP. By further constructing a functional acoustic metamaterial arrayed by mode converters, a desired beam splitting behavior can be generated unidirectionally in a broadband. Our work bridges f-STIRAP and the design of acoustic metamaterial, which may have profound impacts on exploring quantum technologies for promoting advanced acoustic functional devices with simple configuration and excellent performance.

Formal Derivations of Mode Coupling Equations in Underwater Acoustics: How the Method of Multiple Scales Results in an Expansion over Eigenfunctions and the Vectorized WKBJ Solution for the Amplitudes

In this study formal derivation of mode coupling equations in underwater acoustics is revisited. This derivation is based on the method of multiple scales from which modal expansion of the field emerges, and the vectorized WKBJ equation for the coefficients in this expansion are obtained in an automatic way. Asymptotic analysis accomplished in this work also establishes a connection between coupled mode parabolic equations in three-dimensional case and the generalized WKBJ solution that emerges as its two-dimensional counterpart. Despite the fact that similar mode coupling equations can be found in literature, in our study a new systematic and formalized approach to their derivation is proposed. A theorem that guarantees asymptotic conservation of the energy flux in the considered two-dimensional waveguide is also proven.

Spiking Behaviour in Laterally-Coupled Pairs of VCSELs With Applications in Neuromorphic Photonics

We report a theoretical study on laterally-coupled pairs of vertical-cavity surface-emitting lasers (VCSELs) operated under conditions that generate or suppress high-speed optical spiking regimes, and show their potential in exemplar functionalities for use in photonic neuromorphic computing systems. The VCSEL numerical analysis is based on a system of five coupled mode equations, which, for the case of weak coupling, are reduced to a set of three equations that predict the saddle-node stability boundary in terms of device parameters and operating conditions. These results guide numerical simulation to demonstrate multiple neuron-like dynamics, including single- and multiple-spike emission, spiking inhibition, and rebound spiking directly in the optical domain. Importantly, these behaviours are obtained at sub-nanosecond rates, hence multiple orders of magnitude faster than the millisecond timescales of biological neurons. The mechanisms responsible are explained by reference to appropriate phase portraits. The coupled VCSELs model is then used for demonstration of high-speed, all-optical digital-to-spiking encoding and for representation of digital image data using rate-coded spike trains.

One-way acoustic beam splitting in spatial four-waveguide couplers designed by adiabatic passage

In this work, we introduce quantum-mechanical adiabatic passage into the design of spatial acoustic four-waveguide (WG) couplers. Thanks to the agreement in form between the Schrödinger equation in quantum mechanics and the coupled-mode equation of classical wave, the behavior of propagating wave in coupled WGs is capable of mapping to quantum states driven by external fields. By coupling the input and output WGs with a mediator WG in space, an apparent beam splitting is realized and the ratio of intensity can be customized arbitrarily by altering the space-dependent coupling strengths. Moreover, a one-way propagation feature is exhibited in the spatial coupler when an appropriate loss is introduced in the mediator WG owing to the existence of dark state. This work builds a bridge between quantum adiabatic technology and acoustic beam splitter, which may have potential applications in acoustic communication, filtering and detection.

Study of resonant mode coupling in the transverse-mode-conversion based resonator with an anti-symmetric nanobeam Bragg reflector.

The traveling-wave like Fabry-Perot (F-P) resonators based on transverse-mode-conversion have been extensively studied as on-chip filters. However, the incomplete transverse mode conversion will lead to the coupling between two degenerated resonant modes, which brings additional loss and may further induce the resonance splitting. In this paper, we take the transverse-mode-conversion based resonator with anti-symmetric nanobeam Bragg reflector as an example and study the resonant mode coupling in both the direct-coupled and side-coupled resonators. The coupled mode equations are used to model the incomplete transverse mode conversion of Bragg reflector. The resonant mode coupling can be effectively suppressed by carefully designing the phase shifter length and adding the tapered holes. The insertion loss of less than -1 dB can be achieved in the simulation using the two methods. This work is believed to benefit the design of mode-conversion based resonators with low insertion loss and non-splitting line shape.

Conversion and Active Control between Electromagnetic Induced Transparency and Absorber in Terahertz Metasurface

In this study, we use a phase-changing material vanadium dioxide (VO2) to design a multilayer metasurface structure to achieve the transition from an electromagnetically induced transparency(EIT) device to an absorber. The structure consists of a gold layer, a polyimide spacer layer, a VO2 layer, and a sapphire substrate. The top layer consists of one cut wire and two split-ring resonators with the same parameters. When the VO2 layer is in its insulating phase at room temperature, the peak of the EIT device will appear near 1.138 THz. When the VO2 layer is in the metallic state, two absorption peaks above 99.5% appear separately at 1.19 and 1.378 THz, respectively. To the best of our knowledge, this is the first time that a coupled mode equation is used to perform theoretical calculations for EIT devices and perfect absorbers simultaneously, and this is also the first time that coupled mode equations are used for the theoretical calculations of two absorption peaks in an absorber. The proposed metasurface combines the advantages of terahertz absorption, EIT and active device control, which will provide more ideas for the design of future terahertz devices and is also significant for the design and development of radomes for future stealth aircraft.

Enhanced Backscatter Fibers for Sensing in Telecom Networks

We discuss the application of enhanced backscattering fiber in telecom networks. Such fibers can greatly increase the potential of telecom networks to be used as sensors of network health and its surrounding environment. We describe the effects of increased attenuation and multipath interference (MPI) observed in such fibers as the fiber length and backscattering enhancement increases. For MPI we apply both a well known, approximate three bounce treatment as well as a full solution using coupled mode equations, and we verify the validity of the approximate solution. Our analysis allows us to obtain a sensor reach as a function of the backscattering enhancement level and apply this to interrogation schemes for which the minimum required signal power level and the maximum allowable MPI noise level are known. To show that the backscattering enhancement in our fiber does not interfere with telecom signals, we measure the penalty for signals propagating within and near the enhancement bandwidth in a 10 km length of continuously enhanced backscattering fiber. We find that signals only a few nm away from the enhancement bandwidth can propagate without OSNR penalty.

Simulation of Fiber Bragg Grating Using Different Physical Parameters for Investigating the Effectiveness on Strain Sensor Measurements

Abstract: This microstructure can be etched into the core of the single mode fibre by photo-inscribing it, and it has a length of a few millimetres. By illuminating the fibre with a UV laser beam and employing a phase mask to create an interference pattern in its core, this is achieved. For a variety of engineering measurements, including temperature, strain, pressure, tilt, displacement, acceleration, load, and the presence of numerous chemical and biological compounds in static and dynamic modes using Fiber Bragg Gratings (FBGs), these sensor elements are deemed outstanding. Mostly, researchers uses FBG to investigate its effectiveness in detecting physical parameters. Some people conduct research using applications and some people conduct research with simulation. For this project, the strain response of the optical FBG sensor is measured using Optiwave software with different parameters. It is shown that the various parameters represent one of the critical parameters in contributing to a high-performance fiber Bragg grating sensor. The simulated fiber gratings with different parameters were analysed and designed by calculating reflection and transmission spectra. Such simulations are based on solving coupled mode equations that describe the interaction of guided modes. It is affirmed that this model system can be used as the simulation results satisfy the previous research