Small-signal Modulation Response 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.

Impact of cavity design on the modulation properties of a GaAs-based VCSEL

GaAs-based vertical-cavity surface-emitting lasers (VCSELs) are commonly used as light sources for optical interconnects in short-range systems. Here, we analyse the impact of the cavity Q factor and the number of quantum wells in the active region on the small-signal modulation response of a GaAs-based VCSEL. By tuning the reflectivity of the mirror it is possible to obtain flat response curves with a high −3 dB bandwidth. It is also beneficial to increase the number of quantum wells in the active region.

Liquid-Crystal Spin-VCSEL with Electro-Optically Controllable Birefringence

We suggest a new construction of spin-VCSEL with an embedded nematic liquid crystal (LC) in a second cavity. We design such a coupled-cavity LC-VCSEL and develop a procedure for calculating its LC-voltage dependent polarization resolved resonant longitudinal modes and their quantum-well confinement factors. Using these characteristics, we are able to slightly modify the spin-flip VCSEL model to include the voltage dependent birefringence and anisotropy. Then, we show that such an LC-VCSEL can reach small signal modulation response with a 3dB cut off frequency of several hundreds of GHz.

Impact of Carrier Transport and Capture on VCSEL Dynamics

Using a vertical-cavity surface-emitting laser (VCSEL) equivalent circuit model based on two carrier rate equations to include effects of carrier dynamics, we study the impact of carrier transport and capture on the small- and large-signal modulation response of high-speed VCSELs. The model also accounts for parasitics, current-induced self-heating, and gain compression. A variation of the effective capture time from 1 to 15 ps is found to have a large impact on the small-signal modulation response, with the 3 dB bandwidth decreasing from 40 to 15 GHz and the response transitioning from under-damped to over-damped. This is primarily due to the increasing low frequency parasitic-like roll-off with increasing effective capture time. A significant effect on the optical waveforms produced by the VCSEL under 56 Gbit/s on-off keying (OOK) non-return-to-zero (NRZ) and pulse-amplitude modulation 4 (PAM4) modulation is observed, with a short effective capture time leading to horizontal eye closure caused by timing jitter (TJ) and intersymbol interference (ISI) and a long effective capture time leading to vertical eye closure caused by long rise- and fall-times. However, for high modulation speed, a short effective capture time is needed and the photon lifetime should be set for clear eye opening. We also show the impact of the effective capture time on the output power vs current characteristics and map the dependence of internal temperature, carrier densities, carrier escape and leakage rates, and spontaneous recombination rates on current for different effective capture times.

Small-signal modulation response and [formula omitted] bandwidth of reflective semiconductor optical amplifier based fiber cavity laser

In this paper we propose a small-signal model of a reflective semiconductor optical amplifier (RSOA) based fiber cavity laser (FCL), which can be used for determining the small-signal modulation response and the corresponding −3dB bandwidth. The model is encapsulated in a boundary value problem (BVP), which, through the boundary condition, accounts for the fiber cavity transfer function. Starting from the numerical solution of the BVP, we investigate the modulation response and the −3dB bandwidth of an RSOA-FCL. We show that, due to the round-trip group delay, the RSOA-FCL’s modulation response exhibits oscillatory behavior. The bandwidth of an RSOA-FCL is analyzed with respect to the RSOA’s bias current density and active region length, the distribution fiber length, and the spectral width of an optical band-pass filter. We find that, in case of significant fiber dispersion, the bandwidth of FCL is limited by the lower of the two bandwidths — RSOA’s or fiber’s, usually the latter one. In case of small or negligible fiber dispersion, the bandwidth of FCL can be improved by increasing the RSOA’s bias current or fiber length and/or selecting the optimal RSOA active region length, and is limited by the RSOA’s performance.

Temperature stability of small-signal modulation response of WGM microlasers with InGaAs/GaAs quantum well-dots in the active region

In this paper, results are presented on III-V quantum well dot microring diode lasers tested at elevated temperatures. To the best of our knowledge, the first uncooled microdisk lasers with diameter of 40 μm with 3-dB bandwidth above 2 GHz at 55°C are demonstrated.

Differential gain and gain compression of an overdamped interband cascade laser

This work investigates the differential gain and gain compression factor of an interband cascade laser (ICL), through the analysis of the small-signal modulation response. The differential gain of the ICL is extracted to be 7.9 × 10−16 cm2, which is comparable to that of typical quantum well lasers. On the other hand, the gain compression factor is determined to be 5.1 × 10−15 cm3, which is two orders of magnitude higher than the latter. In addition, we demonstrate that the ICL is overdamped due to the strong gain compression effect. It is found that the K factor governed by the damping factor and the resonance frequency is as high as 31.4 ns.

Optimum thickness of GaAs top layer in AlGaAs‐based 850 nm VCSELs for 56 Gb/s PAM‐4 applications

We studied the influence of GaAs top-layer thickness on the small-signal modulation response and 56 Gb/s four-level pulse-amplitude modulation eye quality of 850 nm vertical-cavity surface-emitting lasers (VCSELs). We considered the proportionality of the gain-saturation coefficient to the photon lifetime. The simulation results that employed the transfer-matrix method and laser rate equations led to the conclusion that the proportionality should be considered for proper explanation of the experimental results. From the obtained optical eyes, we could determine an optimum thickness of the GaAs top layer that rendered the best eye quality of VCSEL. We also compared two results: one result with a fixed gain-saturation coefficient and the other that considered the proportionality. The former result with the constant gain-saturation coefficient demonstrated a better eye quality and a wider optimum range of the GaAs top-layer thickness because the resultant higher damping reduced the relaxation oscillation.

Generation of wideband chaos without time delay signature using the microlaser with dispersive optical feedback

We propose and numerically demonstrate a method of generating wideband chaos laser without time delay signature by using a circular-side hexagonal resonator (CSHR) microlaser with optical feedback from a chirped fiber Bragg grating (CFBG). The theoretical model of the circular-side hexagonal resonator microlaser with chirped fiber Bragg grating feedback is established according to the Lang-Kobayashi equations. The effects of bias current, feedback strength and CFBG dispersion on the bandwidth of the chaos laser and the feedback time delay signature are investigated. The results show that the CFBG-feedback CSHR microlaser can generate a wideband chaos without feedback time-delay signature under the condition of high bias current with a wideband and flat small-signal modulation response and the bandwidth can reach 14 GHz.

Theoretical analysis of carrier heating effect in quantum-dot semiconductor lasers based on a multi-level energy balance equations model

In this paper, we develop a self-consistent numerical approach for quantum-dot (QD) semiconductor lasers which enables us to dynamically describe the charge-carrier temperature in the wetting layer (WL) and within the QDs during the laser operation. The self-consistent analysis of the WL-QD system is performed using an asymmetric multi-population rate-equation model with a multi-level energy balance equations approach. An important aspect of the model is that the carrier scattering dynamics in the combined WL-QD system is described by Coulomb scattering rates, and these rates are incorporated into the laser dynamical equations as nonlinear functions of the electron and hole densities in the WL. Using the presented model, the impact of carrier heating on the steady-state, turn-on dynamics and small-signal modulation response of QD lasers is investigated. As a main result it is shown that the carrier temperature in the WL is sufficiently higher than the carrier temperature inside the QDs, because the WL is the main origin of all carrier–carrier collisions in the system and, it not only acts as a carrier reservoir for QDs but can also inhibit the carrier heating inside the QDs.

Numerical model for small-signal modulation response in vertical-cavity surface-emitting lasers

We present a numerical model allowing for simulations of small-signal modulation (SSM) response of vertical-cavity surface-emitting lasers (VCSELs). The model of SSM response utilizes only the data provided by a static model of continuous-wave operation for a given bias voltage. Thus the fitting of dynamic measurement parameters is not needed nor used. The validity of this model has been verified by comparing experimental SSM characteristics of a VCSEL with the results of simulations. A good agreement between experiment and simulations has been observed. Based on the results obtained in the simulations of the existing laser, the impact of the number of quantum wells in the active region on the modulation properties has been calculated and analyzed.

Generation of laser chaos with wide-band flat power spectrum in a circular-side hexagonal resonator microlaser with optical feedback.

We numerically demonstrate the generation of wide-band laser chaos with flat power spectrum in a 2D circular-side hexagonal resonator (CSHR) microlaser subject to long-cavity optical feedback. The bandwidth and flatness of the chaotic power spectrum are investigated under different bias currents and optical feedback rates. Under low bias current, the bandwidth under an optimized optical feedback rate increases obviously as raising bias current and the power spectrum flatten simultaneously. Under high bias current, the optimized bandwidth gradually tends toward stabilization, with corresponding flatness less than 5 dB. We compare the chaotic power spectra with small-signal modulation response (SSR) curves under different bias currents. It can be concluded that wide-band and flat SSR indicates wide-band and flat chaotic power spectrum. This work argues that we can enhance laser chaos by using a laser device with wide-band and flat SSR and simple optical feedback configuration, which is significantly beneficial to synchronization-based applications including chaos communication and key distribution.

Dynamic behavior of injection-locked two-state quantum dot lasers

Quantum dot (QD) lasers with excited state (ES) emission exhibit superior characteristics compared with their ground state (GS) emission. Here, we have developed a model that predicts the small-signal modulation response and relative intensity noise (RIN) of a QD laser capable of emitting from both GS and ES resonance energies in free-running and also under optical injection-locking conditions. The GS resonance wavelength in the injection-locked laser benefits a considerable RIN reduction of ∼20 dB/Hz before a lasing threshold of ES emission, while the ES resonance wavelength is promoted more regarding the modulation bandwidth around the lasing threshold, which is almost doubled, especially at very low injection ratios. Contrary to the GS, the injected locked RIN is the poorest property of ES emission, which shows ∼10 dB/Hz enhancement at the lasing threshold and larger injection ratios. It was affirmed that the RIN response of ES emission can be significantly reduced at the cost of setup complexity through simultaneous injection locking of both wavelengths. A 3 dB modulation bandwidth of ∼18 GHz is achieved for ES emission, which is more than twice that of the free-running operation of ES emission.

Small-Signal Analysis of High-Performance VCSELs

In this paper, a comprehensive model to describe the small-signal modulation response of ultra-high performance single- and multi-mode vertical-cavity surface-emitting lasers (VCSELs), with modulation bandwidths exceeding 30 GHz, is presented. Traditionally, utmost simplified dynamic models are used to extract dynamic figures of merit from single-mode edge-emitting lasers. These methods are later on also applied to evaluate the dynamic performance of VCSELs, even though these devices have a very different geometrical layout and modal confinement. However, to understand the dynamic performance of high-speed VCSELs, a model supporting the transverse and longitudinal mode profile, and the driving current inhomogeneity in the active region, is needed. Therefore, multi-mode VCSEL rate equations are established here. Moreover, to access the dynamic figures of merit of these devices, a comprehensive analytical fitting function based on our carrier reservoir splitting approach is derived. Thus, because of the high carrier and photon densities inside these optimized VCSELs, the common carrier reservoir splits up as a result of numerous effects such as mode competition, carrier diffusion and spatial hole burning. These and other effects have a tremendous impact on the small signal modulation response shape and bandwidth, and also on the current distribution profile in the carrier reservoirs. Compared with our recently reported work, this novel model presented includes the effects of gain compression and inhomogeneous current injection between the different lasing modes. Consequently, it is found that the further tuning of our multi-mode VCSEL dynamic model, to include these effects, yields a more physical and consistent figures of merit of high-performance VCSELs.

Antiresonances and Ultrafast Resonances in a Twin Photonic Oscillator

We consider the properties of the small-signal modulation response of symmetry-breaking phase-locked states of twin coupled semiconductor lasers. The extended stability and the varying asymmetry of these modes allows for the introduction of a rich set of interesting modulation response features, such as sharp resonances and antiresonances as well as efficient modulation at very high frequencies exceeding the free running relaxation frequencies by orders of magnitude.

Understanding the Bandwidth Limitations in Monolithic 1.3 μm InAs/GaAs Quantum Dot Lasers on Silicon

In this paper, we present measurements and simulations of the small-signal modulation response of monolithic continuous-wave 1.3 μ m InAs/GaAs quantum dot (QD) narrow ridge-waveguide lasers on a silicon substrate. The 2.5 mm-long lasers investigated demonstrate 3 dB modulation bandwidths of 1.6 GHz, D -factors of 0.3 GHz/mA1/2, modulation current efficiencies of 0.4 GHz/mA1/2, and K -factors of 2.4 ns and 3.7 ns. Since the devices under test are not designed for high-speed operation due to their long length and hence long photon lifetime, the modulation response curves are used as a fitting template for numerical simulations with spatiotemporal resolution to gain insight into the underlying laser physics. The obtained parameter set is used to unveil the true potential of the laser material in an optimized device geometry by modeling the small-signal response at different cavity lengths, mirror reflectivities, and for different numbers of QD layers. The simulations predict a maximum 3 dB modulation bandwidth of 5 GHz to 7 GHz for a 0.75 mm-long cavity with 99% and 60% high-reflection coatings and ten QD layers. Modeling the impact of dislocations on the dynamic performance qualitatively reveals that enhanced non-radiative recombination in the wetting layer leaves the modulation bandwidth of QD lasers on silicon almost unaffected, while dislocation-induced optical loss does not pose a problem, as long as sufficient gain is provided by the QD active region.

Directly modulated quantum dot lasers on silicon with a milliampere threshold and high temperature stability

Microring lasers feature ultralow thresholds and inherent wavelength-division multiplexing functionalities, offering an attractive approach to miniaturizing photonics in a compact area. Here, we present static and dynamic properties of microring quantum dot lasers grown directly on exact (001) GaP/Si. Effectively, a single-mode operation was observed at 1.3 μm with modes at spectrally distant locations. High temperature stability with T0∼103 K has been achieved with a low threshold of 3 mA for microrings with an outer ring radius of 15 μm and a ring waveguide width of 4 μm. Small signal modulation responses were measured for the first time for the microrings directly grown on silicon, and a 3 dB bandwidth of 6.5 GHz was achieved for a larger ring with an outer ring radius of 50 μm and a ring waveguide width of 4 μm. The directly modulated microring laser, monolithically integrated on a silicon substrate, can incur minimal real estate cost while offering full photonic functionality.

Tunnel injection transistor laser for optical interconnects

Transistor laser (TL) is already an established potential candidate for high speed optical interconnects and present day optical communication networks. This paper investigates theoretically the possibility of having lower base threshold current density and enhanced modulation bandwidth by inserting a tunnel injection structure in a TL having multiple quantum wells (MQW) in the base of the heterojunction bipolar transistor. Transfer of injected charge carriers from bulk to low dimensional nano-structure is assumed to occur via virtual energy states, which contributes to the terminal current. Small signal modulation response is obtained by solving the Statz–De Mars laser rate equations. The optimum threshold base current, confinement of carrier, light power outputs etc. are estimated for three QWs positioned at distances of 39, 59, and 79 nm from the emitter-base junction across the base. Incorporation of tunneling structure substantially lowers the base threshold current and increases the modulation bandwidth as compared to usual MQW transistor laser structure. The changes are more prominent with increasing tunneling probability.

Theoretical study of laser-mode competition in quantum-dot semiconductor lasers using a self-consistent electro-opto-thermal model

We present a new model for quantum-dot (QD) semiconductor lasers which includes the self-consistent treatment of electrical, optical, and thermal interactions. The approach is developed from the energy balance equation to incorporate the carrier temperature and a three-level rate equation to describe the carrier and photon dynamics within the QD active region operating simultaneously on two longitudinal modes: via ground-state (GS) and first-excited-state (ES) transitions. Using the presented model, the steady-state, small-signal modulation response and transient device characteristics are calculated and analyzed. Similar to the situation of mode competition of laser modes, it is found that the light output power of the GS mode enters the roll-off regime, while the power of the ES mode increases. The model also predicts the negative temperature dependency of the power threshold for the ES mode, which can be understood from the negative temperature-dependent behavior of incomplete clamping of the ES population above the GS threshold. The simulated results are in good agreement with experimental data from the devices reported earlier.

Temperature performance analysis of intersubband Raman laser in quantum cascade structures

In this paper we investigate the effects of temperature on the output characteristics of the intersubband Raman laser (RL) that integrated monolithically with a quantum cascade (QC) laser as an intracavity optical pump. The laser bandstructure is calculated by a self-consistent solution of Schrodinger-Poisson equations, and the employed physical model of carrier transport is based on a five-level carrier scattering rates; a two-level rate equations for the pump laser and a three-level scattering rates to include the stimulated Raman process in the RL. The temperature dependency of the relevant physical effects such as thermal broadening of the intersubband transitions (ISTs), thermally activated phonon emission lifetimes, and thermal backfilling of the final lasing state of the Raman process from the injector are included in the model. Using the presented model, the steady-state, small-signal modulation response and transient device characteristics are investigated for a range of sink temperatures (80–220K). It is found that the main characteristics of the device such as output power, threshold current, Raman modal gain, turn-on delay time and 3-dB optical bandwidth are remarkably affected by the temperature.