Traveling Wave Model Research Articles

Photon balance in the fiber laser model

Abstract In this article, we present the results of the numerical study related to the balance of photons in a fiber laser simulated by the traveling wave model (TWM). This study is essential since the balance of photons is closely related to the fundamental physical law of conservation of energy. For generality, we consider that active ions of the gain fiber present excited state absorption at both the laser and pump wavelengths and the fiber background loss. We compare the results of simulation based on the TWM, in which the radial distributions of the populations of the energy levels of the active ions are accounted for, with those obtained when these distributions are omitted. We show that, in the first case, the balance of photons is wholly preserved, while in the second case, the balance of photons is disturbed by tens of percent. The physics behind this result is discussed.

Traveling wave mode analysis of a coherence collapse regime semiconductor laser with optical feedback

A highly developed traveling wave model for a semiconductor laser system supports sophisticated mode analysis of the coherence collapse regime in semiconductor lasers with delayed optical feedback. The concept of instantaneous optical modes is used. Time-frequency representations of chaotic trajectories are constructed and interpreted. This involves synthesizing the calculated optical modes with their corresponding steady states, analysis of the mode driving and coupling sources, and field expansion into modal components. The results support detailed physical interpretation of the optical and radiofrequency spectra throughout the coherence collapse regime. This includes simulation results for the transition out of coherence collapse at high optical feedback. Also key frequencies observed in the radiofrequency spectrum of the chaotic output are linked to the modes that mix to generate them.

Nonlinear dispersion analysis using dynamic traveling wave model in chemical kinetics

Nonlinear dispersion analysis using dynamic traveling wave model in chemical kinetics

Ultra-narrow-linewidth hybrid-integrated self-injection locked laser at 780 nm

Narrow-linewidth lasers are essential across a wide range of applications, including classical and quantum sensing, trapped ion systems, position/navigation/timing systems, optical clocks, and microwave frequency synthesizers. In the visible and near-visible spectrum, low-noise lasers are particularly important for laser trapping and cooling techniques, which are vital for trapped ion quantum computing, sensing, and atomic clocks. In this context, our work showcases a hybrid-integrated narrow-linewidth laser that operates at 780 nm, achieving a self-heterodyne linewidth of 105 Hz. To validate the experimental results, we performed a numerical analysis that combines insights from a many-body theory applied to the gain region with a travelling-wave model to capture the laser dynamics. Our investigation further delves into how the linewidth of the self-injection locked lasers is influenced by the parameters of micro-ring resonators, aiming to assess the potential for achieving Hz-level integrated laser linewidths at 780 nm. This work not only demonstrates the technical feasibility of Hz-level narrow-linewidth lasers but also lays the groundwork for future explorations in the field.

Theoretical analysis of passively mode-locked semiconductor ring lasers.

In this paper, the theoretical analysis of the passive mode-locked semiconductor ring lasers (PML-SRLs) is investigated based on a travelling wave model. It is found that both the optical confinement factor and the injection current make great contributions to the operation regime and the performance of PML-SRLs. All operation regimes of PML-SRLs are governed by the transient gain-loss balance. Such balance is closely associated with the relationship among the stimulated rate in the semiconductor optical amplifier (SOA), the carrier lifetime in the saturated absorber (SA), and the roundtrip time of the ring resonator. Furthermore, our investigation indicates that the mode-locked state of such PML-SRLs is independent of the passive waveguide, but the performance degrades with the increased waveguide loss or the shortened waveguide length, once the material bandwidth is wide enough. Another discovery is that it is possible to achieve the high energy pulse in the PML-SRL with shortening the passive length and narrowing the gain spectrum meanwhile. Overall, such investigations should benefit designing the required PML-SRLs and achieving the high performance.

Efficient and accurate parameter extraction for quantum-well DFB lasers: a comprehensive approach integrating multiple mathematical models

This study proposes an efficient and accurate method for parameter extraction of quantum well distributed feedback (DFB) lasers by combining the rate equation model, finite element method, transmission matrix method, and traveling wave model (TWM). By fabricating and measuring the companion Fabry-Perot (FP) lasers, material and structural parameters common with the target DFB laser are extracted efficiently. All the intrinsic parameters of the DFB laser are accurately extracted by integrating multiple mathematical models, and the possibility of multiple solutions is avoided. From the extracted parameters, the output characteristics of the DFB laser are simulated using the TWM. The simulation results agree closely with the experimental results, proving the feasibility and accuracy of the proposed method.

Evolutionary stability of antigenically escaping viruses.

Antigenic variation is the main immune escape mechanism for RNA viruses like influenza or SARS-CoV-2. While high mutation rates promote antigenic escape, they also induce large mutational loads and reduced fitness. It remains unclear how this cost-benefit trade-off selects the mutation rate of viruses. Using a traveling wave model for the coevolution of viruses and host immune systems in a finite population, we investigate how immunity affects the evolution of the mutation rate and other nonantigenic traits, such as virulence. We first show that the nature of the wave depends on how cross-reactive immune systems are, reconciling previous approaches. The immune-virus system behaves like a Fisher wave at low cross-reactivities, and like a fitness wave at high cross-reactivities. These regimes predict different outcomes for the evolution of nonantigenic traits. At low cross-reactivities, the evolutionarily stable strategy is to maximize the speed of the wave, implying a higher mutation rate and increased virulence. At large cross-reactivities, where our estimates place H3N2 influenza, the stable strategy is to increase the basic reproductive number, keeping the mutation rate to a minimum and virulence low.

Design of distributed feedback lasers grown on Si using time-domain traveling wave model combined with mode refractive index method

This paper proposes an optimization method combining the time-domain traveling wave model and the mode refractive index method, employed for characterizing both the transverse and longitudinal modes of quantum dot distributed feedback (DFB) lasers grown on Si. We use this method to optimize the overall performance of the Si-based DFB laser, and determine the material and chip structural parameters, including the ridge width, etching depth, grating thickness and grating position as optimization parameters. Here, the optimal DFB laser operating under fundamental transverse and single longitudinal mode is obtained. Its threshold current is as low as 5 mA, the slope efficiency is as high as 0.77 mW mA−1, and the side mode suppression ratio is up to 48 dB. When the injection current is 150 mA, the output power exceeds 100 mW. The corresponding ridge width, etching depth and grating thickness are 2 μm, 1.3 μm and 20 nm, respectively. The distance from the grating to the active region is 200 nm. Therefore, the novel method presented in this paper offers an effective scheme for the design of DFB lasers grown on Si with excellent performance.

Co-simulation of real-time electromagnetic transient and transient stability simulations using dynamic phasor T-Line model

This paper presents techniques to interface a Transient Stability Analysis (TSA) based model to an ElectroMagnetic Transient (EMT) based model running on a Real Time Digital Simulator. Practical challenges of implementing such an interface are discussed. The proposed TSA model can be simulated using a substantially larger time-step compared to the EMT model. The interface between the EMT model and the TSA model is implemented using a transmission line modeled using Dynamic Phasors (DP). Time-step delay is the primary cause of numerical instability in co-simulations. In this work, a traveling wave model of a transmission line is used to decouple the EMT and TSA networks. The interface requires that the propagation delay of the interfaced transmission lines be greater than the EMT time-step even though the TSA is simulated using a much larger time-step than the EMT model. The proposed technique is validated using the IEEE 39 bus system and a power system with 500 buses.

Ground strains induced by the 2022 Hunga-Tonga volcanic eruption, observed by a 1500-m laser strainmeter at Kamioka, Japan

In this study, we detected the horizontal ground strains induced by the atmospheric Lamb wave emitted from the 2022 eruption of the Tonga–Hunga Ha’apai undersea volcano, at an underground observatory in Kamioka, Japan. The observed strains were in the range of {10}^{-11}–{10}^{-10} and were measured precisely using a 1500-m laser strainmeter with a high resolution in the order of {10}^{-12}. This was one of the first observations of a Lamb wave using a laser strainmeter. The strainmeter was constructed in a tunnel of the KAGRA gravitational-wave telescope. Our observations demonstrate that strain and atmospheric pressure were clearly correlated, resulting in a regression coefficient of - left(2.3-3.7right)times {10}^{-10} strain/hPa. This finding was compared with the responses under regular pressure conditions and the estimations obtained using the local deformation and traveling wave models. The observed coefficients for the Lamb wave exhibited smaller magnitudes than those observed under regular conditions and take values between that of the two theoretical models. These results reflect the intermediate scale of the pressure distribution of the Lamb wave between the assumptions of the simple models. The strain variations were also found to have started earlier than the corresponding pressure changes at the observation site with characteristic time lags ranging from 25 to 155 s. In addition, several aspects related to the mechanism that created the time lags are discussed.Graphical

Forced response analysis of the rotor blade rows with the ROM-based aeroelastic model

Forced response is one of the aeroelastic problems which lead to the blade damage. The energy method based on the hypothesis of a conventional travelling wave model and direct numerical simulation are used usually to analyze the problem. However, energy method cannot cover the fluid-structure coupling effect, while numerical simulation needs large computational cost. A rapid method, based on the reduced order model (ROM), is developed to analyze the forced response of the rotor blades. The unsteady aerodynamic force acting on blades is divided into two parts according to the source. One part is due to the blade vibration. An unsteady aerodynamic force model is built to simulate it and then an aeroelastic model is built by coupling the structural equation. The other part is due to rotor-stator interaction (RSI), which is regarded as the excitation of the aeroelastic model. Then the forced response of the rotor blade rows is transferred to calculate the response of the aeroelastic model under the RSI excitation, which requires one to two orders of magnitude less computational time than direct numerical method and could study the effect of the structural parameters conveniently. Results show that the effect of fluid-structure coupling is crucial to the low-mass-ratio structure. Besides, the structural frequency is not exactly coincident with the excitation frequency when the response amplitude reaches its peak.

Cable Modeling for Very Fast Transient Simulation Studies Using One-Sided Voltage Transfer Function Measurements

A novel measurement-based method for high-frequency modeling of shielded cables is introduced for use in very fast transient simulation studies. The method requires measurements on one cable end only, thereby being applicable to installed cable systems. Three frequency sweep voltage transfer measurements are performed at one cable end using a vector network analyzer (VNA) with gain-phase setup, two voltage probes and one series resistor. From the measurements is calculated the cable 2 × 2 admittance matrix as function of frequency where a sign arbitrariness is removed using a local rational model that is swept along the frequency samples. The resulting admittance matrix can be fitted by a lumped-parameter rational model, or be subjected to modeling by a frequency-dependent traveling wave model which also permits to change the cable length. Application to a 150 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> single core cable of 252 m length demonstrates that the model reproduces measured cable high-frequency damping effects that result in sub-microsecond voltage rise times. A classical modeling approach based on skin effect formulae gives too little damping.

Analysis of the Local Dynamics of Interictal Discharge Propagation Using a Traveling Wave Model

Analysis of the Local Dynamics of Interictal Discharge Propagation Using a Traveling Wave Model

Implementation of Traveling Wave Models of Grating-Based Integrated Optical Devices for Circuit Simulation

This paper presents the development and use of a traveling wave model of waveguide-based grating devices for use as a compact model in a circuit-level simulator. Both passive and active devices are modeled, with the grating being characterized by coupling coefficients for the two counter-propagating waves. It is shown how the implicit carrier frequency can be offset from the Bragg frequency using two possible methods: either by the static detuning of the model or introducing a phase modulation into the coupling coefficients. Other physical aspects of the model are addressed such as dispersion and energy conservation. A comparison to a 1D Yee-cell model is used to verify the applicability of the traveling wave model. As an example of the circuit simulation of a passive device, an optical code generating application is used and it is noted that for a passive device the interface between the compact model and the circuit simulator is not a concern. Using traveling-wave-based laser simulations of grating-based laser structures it is demonstrated that the model captures the complex behaviour of the devices. In particular the lasing frequency is naturally produced from the model and the introduction of delay elements into the structure can be used to restrict the laser to single mode operation. A number of examples are used to illustrate important aspects of its use as a compact model. Firstly, it is shown that an operating point for either of the laser configurations can be constructed and detuning used to produce an un-modulated output, allowing for much more efficient simulations. A final example uses a directly modulated laser to illustrate the effect of back reflection on the stability of the laser simulation.

Calculation of the steady states in dynamic semiconductor laser models

We discuss numerical challenges in calculating stable and unstable steady states of widely used dynamic semiconductor laser models. Knowledge of these states is valuable when analyzing laser dynamics and different properties of the lasing states. The example simulations and analysis mainly rely on 1(time)+1(space)-dimensional traveling-wave models, where the steady state defining conditions are formulated as a system of nonlinear algebraic equations. The performed steady state calculations reveal limitations of the Lang-Kobayashi model, explain nontrivial bias threshold relations in lasers with several electrical contacts, or predict and explain transient dynamics when simulating such lasers.

Analysis and Design of Low-Loss and Fast All-Optical Switch Elements on Silicon Nitride for Integrated Quantum Photonics

Fast and ultra-low loss single-photon switching and routing are essential for photonic quantum computation and communication. To address this need in a scalable fashion, all-optical switches that can be fabricated in an ultra-low loss and mature Si <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_{3}$</tex-math></inline-formula> N <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$_{4}$</tex-math></inline-formula> photonic integrated circuit (PIC) foundry platform are designed and optimized for sub-ns switching times suitable for deterministic quantum-dot single-photon sources. The working principle relies on cross-phase modulation (XPM) of the single photons with a 1550-nm pump pulse and is enhanced by a ring resonator. Two different designs of the primary switch element are theoretically studied, namely a ring resonator intensity switch (RRIS) based on resonance shifting due to XPM and a ring resonator phase switch (RRPS) acting as an all-optical phase shifter in a Mach–Zehnder interferometer. As a novel approach to speed up the switching, chirped pre-emphasis and wipe sections for the pump pulses are utilized. A design tool is established from analytical expressions and serves as starting point for further optimization using a dedicated travelling-wave model (TWM). The TWM demonstrates the feasibility of both designs to be driven by either the proposed pre-emphasis pulse shape or a train of chirped Gaussian pulses. While the RRPS turns out to require less pump energy, its operation is more sensitive to pump-power fluctuations. Insertion losses below 0.1 dB and a power consumption below 5 nJ at 1 GHz switching rates for both configurations prove the potential of this concept for scalable quantum photonic applications.

Parameter Extraction For Quantum Well DFB Lasers Based on 1D Traveling Wave Model

Extracting the parameters of a laser from the measured results is critical for laser design, modeling and optimization. This work presents a parameter extraction method for quantum well distributed feedback (DFB) lasers based on the one-dimensional traveling wave model (1D TWM). Facet reflectivities, grating coupling coefficient and the other parameters can be extracted by fitting the lasing spectrum, light-current (L-I) curve, intensity modulation (IM) response and large-signal chirp. During the extraction progress, the 1D TWM is simplified to improve the extraction efficiency. The feasibility of this extraction method is verified by extracting parameters from preset simulation results and experimental results, respectively. The 1D TWM can reflect the physical properties of the laser profoundly and the parameter extraction method based on 1D TWM will be a valuable tool for laser design, optimization or processing improvement.

Coherent Potts machine based on an optical loop with a multilevel phase-sensitive amplifier

The Potts model is an extended version of the Ising model that has been intensively studied for applications in physical computers solving combinatorial optimization problems. This study proposes a coherent Potts machine (CPM), named after the coherent Ising machine (CIM), which is a type of Ising-model-based physical computer. A phase-sensitive amplifier (PSA) used in a CIM based on an optical loop with a measurement feedback system is replaced with a multilevel PSA, owing to which the optical pulses in the loop behave as Potts spins of multivalued discrete states. The operation of the proposed CPM was analyzed and numerically simulated using a traveling-wave model, demonstrating its capability to solve a graph coloring problem.

Stochastic nonlinear model of the dynamics of actively Q-switched lasers.

In this paper, we present a novel stochastic and spatially lumped multi-mode model to describe the nonlinear dynamics of actively Q-switched lasers and random perturbations due to amplified spontaneous emission. This model will serve as a basis for the design of (nonlinear) control and estimation strategies and thus a high value is set on its computational efficiency. Therefore, a common traveling-wave model is chosen as a starting point and a number of model-order reduction steps are performed. As a result, a set of nonlinear ordinary differential equations for the dynamic behavior of the laser during a switching cycle is obtained. A semi-analytic solution of these differential equations yields expressions for the population inversion after a switching cycle and for the output energy, which are then used to formulate a nonlinear discrete-time model for the pulse-to-pulse dynamics. Simulation studies including models with different levels of complexity and first experimental results demonstrate the feasibility of the proposed approach.

Traveling-wave model of coherent Ising machine based on fiber loop with pulse-pumped phase-sensitive amplifier

A coherent Ising machine (CIM) is an optical system that physically solves combinatorial optimization problems based on the Ising model. This paper presents an analytical model describing the operation of a CIM using a long fiber loop with a phase-sensitive amplifier. Instead of the conventional analytical model based on the mean-field approximation in a cavity, a traveling-wave model, which traces the state evolution of each pulse circulating along the loop, was applied. A difference equation for the state of a pulse moving around the loop was derived, and simulations were performed. These results reflect the CIM operation reasonably well.