Model Of Vertical-cavity Surface-emitting Lasers Research Articles

Particle swarm optimization-assisted approach for the extraction of VCSEL model parameters.

We propose a direct particle swarm optimization (PSO) method for extracting the parameters of a physical model describing the behavior of vertical-cavity surface-emitting lasers (VCSELs), starting from the light-current (L-I) characteristics and the small signal modulation (S21) responses, at different currents and temperatures. With an optimal choice of hyperparameters of the algorithm, the method is able to predict parameters that accurately reproduce the behavior of the device. Its prediction capabilities are compared to those of two commonly used nonlinear optimizers (Interior Point and Levenberg-Marquardt), to benchmark its performances.

40.1-GHz sub-freezing 850-nm VCSEL: microwave extraction of cavity lifetimes and small-signal equivalent circuit modeling.

We present an 850-nm vertical-cavity surface-emitting laser (VCSEL) constructed for a wide operating temperature range from 25°C to -50°C sub-freezing temperature, demonstrating 40.1-GHz at -50°C. The optical spectra, junction temperature, and microwave equivalent circuit modeling of a sub-freezing 850-nm VCSEL between -50°C and 25°C are also discussed. Reduced optical losses, higher efficiencies, and shorter cavity lifetimes at sub-freezing temperatures are the leading causes of the improved laser output powers and bandwidths. The e-h recombination lifetime and the cavity photon lifetime are shortened to 113 and 4.1 ps, respectively. Could potentially supercharge VCSEL-based sub-freezing optical links for applications in frigid weather, quantum computing, sensing, aerospace, etc.

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.

Large-Signal Equivalent Circuit for Datacom VCSELs – Including Intensity Noise

Optical interconnects (OIs) continue to require more and more sophisticated driver and receiver electronics as higher baud rates are pushed in datacom, mainly due to the bandwidth stagnation of the optoelectronic components such as the vertical-cavity surface-emitting laser (VCSEL) in the transmitter as well as the photodetector (PD) in the receiver. Another important focus is maintaining high energy efficiency for the OIs. For both cases, a reliable equivalent circuit model for high-speed VCSELs is required for link optimization. This work is an extension of our previously presented large-signal VCSEL equivalent circuit model, where noise is added to the physical processes that the VCSEL model is based on. Thus, a new step is taken in the strive of developing an even more accurate physics-based large-signal VCSEL equivalent circuit model for datacom applications. Following a detailed description of the VCSEL noise modelling, a presentation is given on simulated results of VCSEL relative intensity noise (RIN) spectrum and eye diagrams under 28 Gbaud on-off keying (OOK) and pulse-amplitude 4 (PAM4) modulation, and that are compared with corresponding measurement results. Good agreement is found over a wide range of VCSEL driving conditions and temperatures. A 28-GHz-bandwidth VCSEL is applied for the demonstration, and the presented noise extended VCSEL equivalent circuit model was implemented in Verilog-A, and the simulations were performed using Cadence Spectre.

Modeling of surface grating-loaded VCSEL with slowing light

We propose single-mode vertical cavity surface-emitting lasers (VCSEL) based on the surface grating with various cavity lengths ranging from 10 μm to 1 cm. We present the modeling of surface grating-loaded VCSEL based on the coupled-mode theory with slowing light. Thanks to the low effective index caused by the slow-wave propagation, a shallow surface grating of a few tens nm provides large optical feedback. A narrow stop band in the surface grating-loaded VCSEL waveguide appears because of the large waveguide dispersion of slow-waves. The numerical results on coupling coefficient, mode selectivity and threshold gain are given for single-mode, long-cavity and short-cavity grating-loaded VCSELs with different grating parameters. A wide range of grating coupling strength enables a short cavity of 10 μm and a long cavity of 1 cm with a single-mode operation. The proposed VCSEL structure may open up new VCSEL platforms for low-power consumption and high-power applications.

Spectral-dependent electronic-photonic modeling of high-speed VCSEL-MMF links for optimized launch conditions.

We present spectral-dependent electronic-photonic modeling of vertical-cavity surface-emitting laser (VCSEL)-multimode fiber (MMF) links for next-generation high-speed interconnects. The beam coupling processes, between the VCSEL and the MMF and between the MMF and the photodetector (PD), are discussed, with spectral-dependent three-dimensional launch conditions analyzed. The model accounts for fiber effects on the transmission performance, specifically modal attenuation, dispersion, mode mixing, and mode partition noise. An advanced split-step small-segment (4-S) method simulates the signal evolution over the MMF with high accuracy and high efficiency. Experimental validation at 25 Gbps confirms the high accuracy of the VCSEL-MMF link model. The model reveals that larger radial offsets can further excite lower-order mode groups reducing the power distributed to higher-order groups when a tilted beam couples to the input fiber facet. With an optimized misalignment launch, the modal bandwidth is greatly improved by 3.8-fold compared to the conventional center launch. The model helps determine the optimum launch condition to improve link performance metrics such as transmission reach.

Modeling of generating ultra-high frequency oscillations in VCSEL integrated with cascaded transverse coupled cavities

We report on the design and modeling of vertical-cavity surface-emitting laser (VCSEL) integrated in the lateral direction with a cascade of multiple passive cavities. The scheme is proposed to increase the bandwidth of the VCSEL in the mm-waveband to generate ultra-high-frequency oscillations with low-frequency chirp. The model treats the transverse feedback induced by the cascaded transverse coupled cavities (TTCs) as time delay of the transverse slow light due to round trips in these cavities. The simulation is based on numerical integration of the modified time-delay rate equations of the intensity and phase of the electric field. The simulation results are used to optimize the TCCs parameters, including the coupling ratio and TCC length, for generating ultra-high-frequency signals with high intensity, low chirping and low distortion. The obtained results show that the proposed structure could achieve 300% enhancement of the modulation bandwidth of the C-VCSEL due to either extended carrier-photon resonance (CPR) frequencies of photon–photon resonance (PPR). Signals with frequencies as high as (40–49 GHz) with second-harmonic distortion lower than − 30 dB are presented.

Differential Electro-Optical Equivalent Circuit Model of a Vertical-Cavity Surface-Emitting Laser for Common-Mode Rejection Ratio Estimation

Vertical-cavity surface-emitting lasers (VCSEL) can be used to achieve galvanic isolation of systems operating in environments with high levels of electromagnetic noise. A small-signal differential electro-optical equivalent circuit model of a VCSEL is presented, in contrast to the usual single-ended models. The electro-optical and opto-electrical conversion of the signal is modelled, as well as the electrical characteristics of the VCSEL chip. The circuit model is based on an approach combining Y-parameters and mixed-mode S-parameters. Compared to conventional models that are aimed at describing the internal laser dynamics, the presented model is primarily focused on modelling the asymmetric parasitics in a differential VCSEL configuration. The parasitics between the 5-lead VCSEL TOSA package and the test printed circuit board are modelled. The impact of the asymmetry of the parasitics from the laser anode and cathode towards the ground is examined. The differential VCSEL model is used to estimate the transfer coefficients for both differential-mode and common-mode input signals. The ratio between the wanted and unwanted signal is expressed as the common-mode rejection ratio (CMRR). The model covers the frequency bandwidth up to 4 GHz required for integrated circuit EMC and ESD measurements.

VCSEL-Based In-Circuit Status-Monitoring and Effects-Diagnosis Method for HPEM Susceptibility Test on Digital Electronic Equipment

This paper proposes the method of using bias-free vertical-cavity surface-emitting lasers (VCSELs) for in-circuit monitoring and effects-diagnosis of digital electronic equipment undertaking HPEM susceptibility test. A circuit level model for typical single mode VCSEL and standard I/O buffer information specification model for I/O ports of digital ICs are built to simulate VCSEL's load effects to the digital IC from specific logic families, as well as VCSEL's light output. Simulation results show that VCSELs connected in parallel to IC's I/O ports can be lighted up and its light output can achieve remote status-monitoring of I/O ports’ states in real time, while its load effects to the I/O ports are light enough not to deteriorate its signal integrity or disturb the circuit's normal operation. An experiment is performed on commercial mini sized drone to validate this study and demonstrate this method's feasibility and advantages in equipment level HPEM susceptibility test.

Comprehensive vertical-cavity surface-emitting laser model for optical interconnect transceiver circuit design

Directly modulated vertical-cavity surface-emitting lasers (VCSELs) are commonly used in short-reach optical interconnect applications. To enable efficient optical interconnect transceiver systems operating at data rates up to 25 Gb/s and beyond, cosimulation environments, which allow for the optimization of driver circuitry with accurate compact VCSEL models, are necessary. A comprehensive VCSEL model, which captures thermally dependent electrical and optical dynamics and provides direct current, small-, and large-signal simulation capabilities with self-consistency, is presented. The device’s electrical behavior is described with an equivalent circuit, which captures both large-signal operation and electrical parasitics, while the optical response is captured with a rate-equation-based model. Bias and temperature dependencies are incorporated into both key electrical and optical model parameters. Experimental verification of the model is performed at 25 Gb/s with a 990-nm VCSEL to study the impact of bias current level and substrate temperature.

Modeling and optimization of single-mode vertical cavity surface emitting lasers

Vertical cavity surface emitting laser (VCSEL) plays a vital role in optical network. The present investigation reports the performance comparison of the modeling of single-mode VCSELs at room temperature for continuous wave operation. VCSEL for the study consists of InGaAsP-based cavity or active region sandwiched between GaAs/AlGaAs top mirror and GaAs/AlAs bottom mirrors with the aim of increasing the power conversion efficiency (PCE), lasing power, and decreasing the threshold current. It is observed that VCSELs with lower diameter are most suitable to achieve energy-efficient operation. The PCE obtained is ∼50% for the proposed single-mode VCSELs. The proposed VCSELs are suitable for short-reach optical interconnects such as chip-to-chip and board-to-board communication in high-performance computers.

Vector cavity solitons in broad area Vertical-Cavity Surface-Emitting Lasers.

We report the experimental observation of two-dimensional vector cavity solitons in a Vertical-Cavity Surface-Emitting Laser (VCSEL) under linearly polarized optical injection when varying optical injection linear polarization direction. The polarization of the cavity soliton is not the one of the optical injection as it acquires a distinct ellipticity. These experimental results are qualitatively reproduced by the spin-flip VCSEL model. Our findings open the road to polarization multiplexing when using cavity solitons in broad-area lasers as pixels in information technology.

Asymmetric dwell-time statistics of polarization chaos from free-running VCSEL.

We experimentally report on asymmetric dwell-time statistics of polarization chaos dynamics generated from free-running vertical-cavity surface-emitting lasers (VCSELs). Theoretically, we explain this behavior by introducing a misalignment between the phase and amplitude anisotropy within the spin-flip model for VCSELs. It induces an asymmetry in the VCSEL polarization behavior which is then responsible for significant changes in the statistics of the chaotic mode-hopping with an increase in the average residence time and an inversion of the dominant mode.

Photonic Generation of Microwave Signals Using a Single-Mode VCSEL Subject to Dual-Beam Orthogonal Optical Injection

We experimentally and theoretically investigate the photonic generation of microwave signals using a long-wavelength single-transverse-mode vertical-cavity surface-emitting laser (VCSEL) subject to two-frequency orthogonal optical injection. We study if a significant reduction of the linewidth is achieved in the double injection locking regime. In this regime, the VCSEL is subject to optical injection by two master lasers in such a way that stable locking is also observed if only light from one of the master lasers is injected. Our model includes the effect of the injected light reflected at the VCSEL's mirror generalizing previous modeling of reflection-mode optical injection-locked VCSELs. Our model also describes the high coherence associated to stable injection locking states and takes into account phase fluctuations in both master lasers. We observe no significant reduction of the linewidth in the double injection locking regime because the linewidth is mainly determined by the phase fluctuations of the two master lasers.

Temperature-dependent investigation of carrier transport, injection, and densities in AlGaAs-based multi-quantum-well active layers for vertical-cavity surface-emitting lasers

The electro-optical efficiency of vertical-cavity surface-emitting lasers (VCSELs) strongly depends on the efficient carrier injection into the quantum wells (QWs) in the laser active region. Carrier injection degrades with increasing temperature, which limits VCSEL performance in high-power applications where self-heating imposes high-operating temperatures. In a numerical model, we investigate the transport of charge carriers in an 808-nm AlGaAs multi-quantum-well structure with special attention to the temperature dependence of car- rier injection into the QWs. Experimental reference data were extracted from oxide-confined, top-emitting VCSELs. The transport simulations follow a drift-diffusion-model complemented by an energy-resolved car- rier-capture model. The QW gain was calculated in the screened Hartree-Fock approximation. With the combi- nation of the gain and transport model, we explain experimental reference data for the injection efficiency and threshold current. The degradation of the injection efficiency with increasing temperature is not only due to increased thermionic escape of carriers from the QWs, but also to state filling in the QWs initiated from higher threshold carrier densities. With a full opto-electro-thermal VCSEL model, we demonstrate how changes in VCSEL properties affecting the threshold carrier density, like mirror design or optical confinement, have con- sequences on the thermal behavior of the injection and the VCSEL performance. © 2015 Society of Photo-Optical

Analyses of the time-delay signature and bandwidth of the chaotic output from a master-slave vertical-cavity surface-emitting laser dynamical system

The time-delay signature (TDS) and the bandwidth (BW) are two important performance indexes to assess the chaos signal from a delayed laser system. Based on the spin flip model of vertical-cavity surface-emitting laser (VCSEL), we numerically investigate the characteristics of chaos dynamics in a master-slave VCSEL system, where a chaotic signal generated by a master VCSEL (M-VCSEL) under external optical feedback is unidirectionally injected into a slave VCSEL (S-VCSEL). The influences of injection strength, frequency detuning between M-VCSEL and S-VCSEL, and feedback strength of M-VCSEL on chaos TDS (including intensity TDS (I-TDS) and phase TDS (P-TDS)) and BW are investigated. The results show that by adjusting the injection strength and the frequency detuning, both I-TDS and P-TDS of two polarization components (referred to as X-PC and Y-PC respectively) of the chaotic output from the system can be suppressed simultaneously. Through further analyzing the influences of the injection strength and frequency detuning on the BW of chaotic signal, we find that the BWs of both X-PC and Y-PC of chaotic outputs can simultaneously exceed 30 GHz within a large negative frequency detuning range. Furthermore, by combining the evolution characteristics of the TDS and BW of chaotic outputs in the parameter space of injection strength and frequency detuning, the parameter region for generating the chaotic signals with wide BW and low TDS can be determined. In addition, by reasonably adjusting feedback strength, the quality of chaotic signal from the system can be further optimized.

Phase-bistable patterns and cavity solitons induced by spatially periodic injection into vertical-cavity surface-emitting lasers

Spatial rocking is a kind of resonant forcing able to convert a self-oscillatory system into a phase-bistable, pattern forming system, whereby the phase of the spatially averaged oscillation field locks to one of two values differing by $\ensuremath{\pi}$. We propose the spatial rocking in an experimentally relevant system---the vertical-cavity surface-emitting laser (VCSEL)---and demonstrate its feasibility through analytical and numerical tools applied to a VCSEL model. We show phase bistability, spatial patterns, such as roll patterns, domain walls, and phase (dark-ring) solitons, which could be useful for optical information storage and processing purposes.

High Power Single Mode Multi-Oxide Layer VCSEL with Optimized Thicknesses and Aperture Sizes of Oxide Layers

A novel multi-oxide layer structure for vertical cavity surface emitting laser (VCSEL) structures is proposed to achieve higher single mode output power. The structure has four oxide layers with different aperture sizes and thicknesses. The oxide layer thicknesses are optimized simultaneously to reach the highest single mode output power. A heuristic method is proposed for plotting the influence of these variable changes on the operation of optical output power. A comprehensive optical-electrical thermal-gain self-consistent VCSEL model is used to simulate the continuous-wave operation of the multi-layer oxide VCSELs. A comparison between optimized VCSELs with different structures is presented. The results show that by using multi-oxide layers with different thicknesses, higher single-mode optical output power could be achieved in comparison with multi-oxide layer structures with the same thicknesses.

Equivalent Circuit Model of High Speed VCSEL Implemented in Circuit Simulators

Optical interfaces have been recently standardized as the main physical layer interfaces for most short length optical communication systems, such as IEEE802.3ae, OIF-VSR, and the Fiber Channel. As interface speed increases, the requirements for forecasting the optical characteristics of direct modulated laser diodes (LDs) also increase because those standards define the specifications for physical layers with optical domains. In this paper, a vertical-cavity surface-emitting laser (VCSEL) equivalent electronic circuit model is described with which designers can simulate the I-L-V, S-parameter, and transient characteristics of LDs on a circuit simulator by improving convergence. We show that the proposed VCSEL model can model an 850-nm bandwidth VCSEL with 10-Gbps operation.

Optimizing Optical Output Power of Single-Mode VCSELs Using Multiple Oxide Layers

The influence of using multiple oxide layers with different positions and aperture sizes on vertical-cavity surface-emitting laser (VCSEL) performance is analyzed to show their effects on the optical output power, single-mode operation, and threshold current. The number of oxide layers, their positions, and aperture sizes are optimized to emit the maximum optical output power and transversally single-mode operation. A comprehensive 3-D optical-electrical thermal-gain self-consistent VCSEL model is used to simulate the continuous-wave operation of the multilayer oxide VCSELs. A comparison between optimized VCSELs possessing for different numbers of oxide layers is proposed. The results show that by using multilayer oxides, high-power single-mode VCSELs could be achieved.