Coupled Rate Equations Research Articles

High-peak-power narrow-pulsed linearly polarized laser at ∼3 µm

A hundred-watt-level peak-power linearly polarized Ho,Pr:GdScO3 laser with narrow pulses was first realized at ∼3 µm through a combination of theoretical simulation and experiment. This is the narrowest pulse width, and the highest peak power has been achieved in a passively pulsed Ho,Pr co-doped laser to date. We realized a linearly polarized narrow-pulsed laser at ∼3 µm, with a maximum peak power of 185 W and shortest pulse width of 42 ns. A further theoretical model was built by simulating the dynamic process of the mid-infrared (MIR) pulsed Ho,Pr:GdScO3 laser using coupled rate equations. The numerical simulation results were fundamentally in agreement with the experimental results, which verified the potential of Ho,Pr:GdScO3 crystals to produce sub-50-ns hundred-watt peak power MIR lasers. The results presented an effective way to achieve high-peak-power, narrow-pulse, and linearly-polarized lasers, which have significant research potential and promising applications in the MIR band.

Efficient general method for numerically modeling laser pulse propagation, overlap, and lifetime effects in amplifiers

An efficient numerical time-dependent general method is developed to address incoherent pulse overlap and lifetime effects in laser amplifiers. The alternating propagation-population laser energetics method (APPLE) has been validated against a semi-discrete coupled rate equation numerical method (SDRE) and analytic formalisms in bounding cases. APPLE is based on decoupled rates applied to a time-dependent framework where both space-time-dependent populations and pulse energetics are consistently updated in each time step. A significant advantage of APPLE lies in its conceptual simplicity, ease of implementation, and relatively small computational cost. SDRE tracks the populations through coupled rates and uses the method of lines to discretize the hyperbolic partial differential transport equations allowing for use of ordinary differential equation solvers. With reasonably sized mesh, we report both energetic and power pulse shape relative differences on the order of one percent between the models over a large range of initial conditions.

High-power idler-resonant intracavity KTA OPO driven by a dual-loss-modulated Q-switched mode-locked laser with AOM and Sb2Te3 nanosheets

By using Sb2Te3 nanosheets as saturable absorbers (SA) and an acousto-optic modulator (AOM), a laser-diode (LD) end-pumped idler-resonant KTiOAsO4 (KTA)-based intracavity optical parametric oscillator (IOPO) pumped by a dual-loss-modulated Q-switched mode-locked (QML) laser has been realized. The experimental results show that the pulse widths of the Q-switched envelope and the mode-locking pulse numbers underneath the Q-switched envelope decrease as the pump power increases. When the pump power reaches a certain value, only one mode-locking pulse underneath a Q-switched envelope exists, resulting in the generation of the subnanosecond mode-locking pulses of OPO with the repetition rate of AOM. The minimum mode-locking pulse durations of the signal and idler waves were measured to be 545 and 936 ps at an AOM frequency of 1 kHz and a diode pump power of 22.45 W, corresponding to the maximum peak powers of 648 and 185 kW, respectively. Furthermore, a set of coupled rate equations for the dual-loss-modulated QML laser-pumped intracavity idler-resonant OPO was formulated according to the Gauss distribution of intracavity photon density. The numerical simulations of these equations agree with the experimental results. These results collectively suggest the potential application of Sb2Te3 as a promising nanomaterial in the realm of optoelectronics.

Design and characterization of colloidal quantum dot photoconductors for multi-color mid-infrared detection

This report paves the way for low cost, multi-color, room-temperature, and easily-feasible mid-IR photodetector with distinct output currents. The proposed device is designed and simulated to be fabricated by the solution-process technology thanks to its simplicity and fabrication ease, room-temperature operation capability, low production cost, and excellent photoelectric properties. In this approach, the proposed structure is composed of an array of n × n pixels, where each pixel is designed to enable multi-wavelength detection. The absorber layer consists of different sized quantum dots that absorb distinct wavelengths simultaneously through interband transitions in the mid-infrared region. Selective energy contacts based on quantum well structures are designed to be deposited on interdigitated contacts as a means of extracting the stimulated carriers from the absorber layers to the metal contacts. Through resonant tunneling, the excited carriers are transferred, which generates the output photocurrent and significantly reduces the dark current. In order to model the designed multi-color photoconductor, coupled rate equations and three-dimensional Schrodinger-Poisson equations have been developed and solved self-consistently. As a way of demonstrating the validity of the introduced model, a experimentally fabricated photoconductor and a theoretically modeled photodetector using the nonequilibrium Green’s function (NEGF) model have been simulated; the comparison between the simulation results is quite satisfactory. In order to simplify the theoretical model, two different sizes of InSb/ZnSe core/shell quantum dots have been considered in the theoretical model to detect two MIR wavelengths (3 µm and 4 µm) of the incident light. Simulation results indicate that the peak responsivities are about 3.3(A/W) and 6(A/W), and the high specific detectivities D* are about 9 × 1010(cm.Hz1/2W−1) and 15 × 1010(cm.Hz1/2W−1) for the wavelengths of 4 µm and 3 µm, respectively.

Optical properties of meso-tetra(sulphonatophenyl) porphyrins (TPPS 4) and their Fe 3+, Mn 3+, Zn 2+ complexes with different pH values studied using by picosecond pulse trains

Applying picosecond pulse trains propagating in meso-tetra(sulphonatophenyl) porphyrins and their Fe 3+, Mn 3+, Zn 2+ complexes, we studied the nonlinear dynamics at different pH values. The pulse train at wavelength 532nm is comprised of 20 subpulses with 70ps width and 13ns spacing. We simplified the energy structures of porphyrins and metalloporphyrins to five-level models. In solving coupled rate equations and two-dimensional paraxial field, we used Crank-Nicholson numerical method to do the calculations. The results revealed that in irregular metalloporphyrins with central paramagnetic ion Mn 3+ or Fe 3+, the central ion would act as electron acceptor, which leads to charge transfer of unpaired metal electron to the porphyrin ring π conjugated system, and strengthen the spin–orbit coupling of electronic systems and weaken the transition prohibition between electronic states in porphyrins. However regular metalloporphyrins with central diamagnetic ion Zn 2+ has similar optical properties to free base porphyrins, and Zn 2+ TPPS 4 has much longer excited state lifetimes and slower intersystem crossing. In solutions, hydrogen bond would be formed to porphyrin, which can change the transitions of π electrons and thus the charge transfer can be strengthened in the porphyrin ring. In weak intensity region with linear absorption, nonprotonated porphyrins with high pH value show better optical limiting (OL) effect. Conversely in high intensity region, protonated porphyrins with low pH value show better OL effect. Besides, increasing interaction distances of porphyrins and metalloporphyrins with laser pulses is another important factor to raise the OL effects.

Investigations on saturable absorption characteristic of PdS2 and its application to high-peak-power sub-nanosecond intracavity OPO

In this work, a unique pentagonal TMD material, palladium disulfide (PdS2) nanosheets were fabricated by the liquid-phase exfoliation (LPE) process, and the physical characteristics were also investigated. The nonlinear transmittance is measured by the power scanning method and the modulation depth is fitted to be 15.3%. Based on the transmittance curve, the saturable absorption parameters of PdS2 are calculated, including 5.85 × 10−19 cm2 ground-state absorption cross-section, 1.63 × 10−19 cm2 excited-state absorption cross-section, and 683.5 μs excited-state lifetime. By employing both PdS2 as a saturable absorber (SA) and an acousto-optic modulator (AOM), a doubly Q-switched and mode-locked (QML) laser-pumped intracavity KTiOPO4 (KTP) optical parametric oscillator (OPO) was realized. The pulse energy and the pulse width of the Q-switched envelope for signal wave have been measured. At higher pump power, the high-peak-power low-repetition-rate sub-nanosecond mode-locking pulse of signal wave is generated, in which there is only one mode-locked pulse underneath a Q-switched envelope. The measured shortest signal pulse duration is 530 ps, corresponding to a peak power of 337 kW, at an incident pump power of 9.81 W and an acousto-optic modulator (AOM) repetition rate of 1 kHz. In addition, by considering the Gauss distribution of intracavity photon density, a set of coupled rate equations for a doubly QML laser-pumped intracavity OPO was given and the numerical simulations agreed with the experimental results. These results indicate that PdS2 is a promising nonlinear optical material for optical applications in the near-infrared (NIR) region.

Sub-nanosecond single mode-locking pulse generation in an intracavity KTP optical parametric oscillator with a few-layer Bi2Te3 topological insulator saturable absorber

By utilizing the ultrasound-assisted liquid phase exfoliation process, Bi2Te3 nanosheets are synthesized and deposited onto a quartz plate to form a saturable absorber (SA), in which nonlinear absorption characteristics around 1 μm are investigated with a home-made Q-switched laser. With the as-prepared Bi2Te3 SA employed, a sub-nanosecond KTiOPO4 (KTP) based intracavity optical parametric oscillator (IOPO) pumped by a dual-loss-modulated Q-switched and mode-locked (QML) laser is successfully realized. With a short duration of sub-nanosecond and a repetition rate of several kilohertz (kHz), the signal wave’s single mode-locking pulse existed underneath a Q-switched envelope can be formed. At an incident pump power of 8.92 W and an acousto-optic modulator (AOM) repetition rate of 2 kHz, a signal wave’s single mode-locking pulse underneath a Q-switching envelope with a measured minimum pulse duration of 520 ps is accomplished. It is the first demonstration of such Bi2Te3 SA utilized in a solid-state QML IOPO laser, to the best of our knowledge. According to the experimental results, this provides an efficient and straightforward approach to acquire sub-nanosecond OPO signal wave pulses. Additionally, the relevant coupled rate equations are established, and the simulation results match the experimental results, revealing the potential of Bi2Te3 as a nanomaterial for optoelectronic applications.

Simulation and design of dual-wavelength all-optical semiconductor optical amplifier with solution-processed quantum dots

All-optical semiconductor optical amplifiers (SOAs) present a cost-effective and highly efficient solution for long-distance WDM networks. In this study, the investigation of a dual-wavelength all-optical SOA incorporating two distinct sizes of solution-processed InAs/AlAs core/shell quantum dots (QDs), operating at 1.31 and 1.55 μm wavelengths, both simultaneously and individually, has been proposed. To comprehensively evaluate the optical performance of our proposed dual-wavelength all-optical SOA, the modified coupled rate equations governing carriers dynamics and the optical photon propagation equations have been solved numerically while taking into account both homogeneous and inhomogeneous broadening, as well as fluorescence or förster resonance energy transfer (FRET) effects. This computational approach provides valuable insights into the optical behavior of dual-wavelength all-optical SOA. In our proposed structure, cost-effective solution-based methods for implementing QDs of varying sizes offer flexibility to adjust QD size across a broad range, from as small as 0.1 nm to meet specific requirements. This adjustment is made with meticulous consideration of appropriate synthesis techniques.

Identifying the origin of delayed electroluminescence in a polariton organic light-emitting diode.

Modifying the energy landscape of existing molecular emitters is an attractive challenge with favourable outcomes in chemistry and organic optoelectronic research. It has recently been explored through strong light-matter coupling studies where the organic emitters were placed in an optical cavity. Nonetheless, a debate revolves around whether the observed change in the material properties represents novel coupled system dynamics or the unmasking of pre-existing material properties induced by light-matter interactions. Here, for the first time, we examined the effect of strong coupling in polariton organic light-emitting diodes via time-resolved electroluminescence studies. We accompanied our experimental analysis with theoretical fits using a model of coupled rate equations accounting for all major mechanisms that can result in delayed electroluminescence in organic emitters. We found that in our devices the delayed electroluminescence was dominated by emission from trapped charges and this mechanism remained unmodified in the presence of strong coupling.

Controlling Three-Color Förster Resonance Energy Transfer in an Optical Fabry–Pérot Microcavity at Low Mode Order

We study three-color Förster resonance energy transfer (triple FRET) between three spectrally distinct fluorescent dyes, a donor and two acceptors, which are embedded in a single polystyrene nanosphere. The presence of triple FRET energy transfer is confirmed by selective acceptor photobleaching. We show that the fluorescence lifetimes of the three dyes are selectively controlled using the Purcell effect by modulating the radiative rates and relative fluorescence intensities when the nanospheres are embedded in an optical Fabry–Pérot microcavity. The strongest fluorescence intensity enhancement for the second acceptor can be observed as a signature of the FRET process by tuning the microcavity mode to suppress the intermediate dye emission and transfer more energy from donor to the second acceptor. Additionally, we show that the triple FRET process can be modeled by coupled rate equations, which allow to estimate the energy transfer rates between donor and acceptors. This fundamental study has the potential to extend the classical FRET approach for investigating complex systems, e.g., optical energy switching, photovoltaic devices, light-harvesting systems, or in general interactions between more than two constituents.

Computation and Verification of Spatial Rate Equations for an Electro-Optically Q-Switched Laser-Diode Side-Pumped Nd:YAG Laser

In a side-pumped laser module, we simulate the pumping power distribution across the cross-section of Nd:YAG rods at varying diameters. The coupled rate equations with the spatial overlap efficiency for a four-level actively Q-switched side-pumped laser are considered complete. After a Q-switched pulse terminates, the expressions of laser output parameters are derived. We assess the single pulse energy, pulse width, and peak power using the analysis function. The 200 Hz Q-switched side-pumped Nd:YAG laser with a peak power of 103 kW and beam quality factors M2 = 1.67 is developed to the validity of theoretical models.

Ultrafast time-resolved carrier dynamics in tellurium nanowires using optical pump terahertz probe spectroscopy.

We report carrier relaxation dynamics in semiconducting tellurium nanowires (average diameter ∼ 10 nm) using ultrafast time-resolved terahertz spectroscopy. After photoexcitation using an 800 nm pump pulse, we observed an initial increase in the THz conductivity due to the absorption of THz radiation by photoexcited carriers. The time evolution of the differential conductivity (Δσ(τpp) = σpump on(τpp) - σpump off) shows a bi-exponential relaxation with the initial fast decay time scale of τ1 ∼ 25 ps followed by a longer relaxation time constant of τ2 ∼ 100 ps. Interestingly, the two time scales depend on the amount of the capping agent present on the surface of TeNWs, showing a faster relaxation of the photoexcited carriers as the percentage of capping decreases. This is physically interpreted as the surface state mediated relaxation mechanism of the photo-pumped carriers depending on the density of available surface states. A quantitative understanding is obtained using a coupled rate equation model taking into account the decay mechanisms determined from the surface mediated relaxation rate (DS) and direct recombination rate (DR) of the electron-hole pairs. Furthermore, the measured lattice temperature (TL) dependent dynamics, showing a faster relaxation at lower temperature, is understood using the same rate equation model, giving a power law dependence of the electron-hole recombination rate (DR) on TL as DR ∝ TL-1/2. This is explained by estimating DR using the van Roosbroeck-Shockley theory taking into account the density of states () of one-dimensional nanowires. Furthermore, to understand the measured frequency-dependent THz photoconductivity, we model Δσ(ω) using the Boltzmann transport equation taking into account the energy-dependent scattering rates showing the dominant role of short range (Γsr) and Coulomb scattering (ΓC) rates in the relaxation process, which further provides a measure of the charged and neutral impurity concentrations.

Investigation of self-trapped excitonic dynamics in hematite nanoforms through non-degenerate pump–probe transmission spectroscopy

Non-degenerate pump–probe transmission spectroscopy is used to examine the ultrafast dynamics of photo-excited carriers in hematite nanoforms at various pump fluences. Using coupled rate equations, the kinetics of self-trapped exciton (STE) formation and its interaction with free excitons resulting in exciton annihilation were studied. It is shown from this model that the majority of the excitons were trapped by polaronic trap states to form self-trapped excitons within ∼3.5 ps. The findings indicate that free excitons and STEs interact non-linearly, similar to trap-assisted bi-molecular Auger recombination to annihilate one another. It is observed that there is substantial dependence of kinetics of STE formation and exciton decay on photo-excited exciton density, and the nature of this dependence indicates the reduced screening of electron–phonon interaction. Using the screening model applied to the rate constants of STE formation and decay, we estimate the saturation exciton density to be ∼3.3 × 1017 cm−3 and the average STE density to be ∼3.8 × 1018 cm−3 in the hematite nanoforms. We also noticed that doping K and Ni to hematite nanoforms up to 5% did not remarkably change the nature of the exciton dynamics.

Generalized Modeling of Photoluminescence Transients

Time‐resolved photoluminescence (TRPL) measurements and the extraction of meaningful parameters involve four key ingredients: a suitable sample such as a semiconductor double heterostructure, a state‐of‐the‐art measurement setup, a kinetic model appropriate for the description of the sample behavior, and a general analysis method to extract the model parameters of interest from the measured TRPL transients. Until now, the last ingredient is limited to single curve fits, which are mostly based on simple models and least‐squares fits. These are often insufficient for the parameter extraction in real‐world applications. The goal of this article is to give the community a universal method for the analysis of TRPL measurements, which accounts for the Poisson distribution of photon counting events. The method can be used to fit multiple TRPL transients simultaneously using general kinematic models, but should also be used for single transient fits. To demonstrate this approach, multiple TRPL transients of a GaAs/AlGaAs heterostructure are fitted simultaneously using coupled rate equations. It is shown that the simultaneous fits of several TRPL traces supplemented by systematic error estimations allow for a more meaningful and more robust parameter determination. The statistical methods also quantify the quality of the description by the underlying physical model.

Synthesis of core-shell polyhedron ZIF-8@ZIF-67 as saturable absorber for passive Q-switching operation in Tm:YAP laser at 3H4→3H5 transition

In this paper, we synthesized a novel core-shell polyhedron ZIF-8@ZIF-67 nanocomposites with a size of around 150 nm. Then the core-shell structure ZIF-8@ZIF-67 as a saturable absorber to passively Q-switch the Tm:YAP laser was demonstrated for the first time at 2.3 μm based on the Tm3+3H4 → 3H5 transition. ZIF-8@ZIF-67 possessed the excellent nonlinear optical absorption features with a large modulation depth of 6.7% at 2.3 μm. The obtained stable shortest pulse width was 208 ns with a repetition rate of 128 kHz. Moreover, to fully understand the nonlinear optical properties of the core-shell ZIF-8@ZIF-67 nanocomposites, the coupled rate equations were setup to simulate the 3H4→3H5 Q-switching operation. The numerical simulation results agreed well with the experimental results. It demonstrated that the ZIF-8@ZIF-67 core-shell nanocomposites feature great potential as saturable absorber candidate for the mid-infrared pulse generation.

Making a meta-surface soliton-ready

Abstract Metamaterials attracted significant attention due to their unprecedented properties in the electromagnetic domain. However, they are facing challenges while putting for applications due to the strong dispersion associated with the resonant responses and high losses. In this communication, we present a path to overcome these problems by turning the propagating electromagnetic wave into a soliton wave that can sustain dispersion and loss. For theoretical demonstration, we considered a hybrid 2D metamaterial that consists of arrays of split-ring resonators on a graphene layer. We identified the parametric region that ensures dispersion and loss less propagation of electromagnetic wave in form of a dissipative soliton. This approach can be applied to a large variety of metamaterials and metasurfaces for which a set of coupled rate equation is available.

Performance tunable passively Q-switched fiber laser based on single-walled carbon nanotubes

Passively Q-switched fiber laser (PQFL) has great potential applications in remote sensing, ranging, and optical communications. However, the PQFLs were seldom studied in view of both theory and experiment. This paper is dedicated to make up for this shortcoming. On the one hand, by describing the coupling rate equations of the PQFL system, the Q-switched pulse output with a modulation frequency of 17.61 kHz and a modulation period of 56.8 μs was obtained at 140 mW pump power. On the other hand, an erbium-doped PQFL whose performance is tunable by controlling the pump power and polarization state was constructed by using a single-walled carbon nanotube (SWCNT) as the saturable absorber (SA). The Q-switched pulse with a repetition rate of 17.61 kHz and a signal-to-noise ratio of 50.2 dB was output at a pump power of 140 mW. The theoretical simulation results were in good agreement with the experimental results. It was also verified from such two aspects that the repetition rate of the output pulse of PQFL was approximately proportional to the pump power. This research promotes the theory and design of PQFL.

Mapping synchronization properties in a three-element laterally coupled laser array

We numerically study the synchronized chaos (SC) and spatiotemporal chaos (STC) in a three-element laterally-coupled laser array in the case of four waveguiding structures. The coupled rate equations are used to analyze the dynamics of the laser array, where spatiotemporal dynamic maps are generated to identify regions of SC, STC, and non-chaos in the parameter space of interest. First, we show that the key parameters of the laser array, i.e., the laser separation ratio, pump rate, linewidth enhancement factor, and frequency detuning play important roles in the array dynamics and synchronization properties. Then we show that the laser array composed of the purely real index guiding exhibits more obvious boundaries between SC and STC in wider parameter space with respect to these composed of either the positive index guiding with gain-indexing, the pure gain guiding, or the index antiguiding with gain-guiding. Finally, we show that the proposed laser array allows for two scenarios of parallel random bit generation (PRBG) by applying the same post-processing on chaos sources based on SC and STC dynamic states. Hence, our results provide a comprehensive study on the collective dynamics in the three-element laterally-coupled laser array and pave the way for PRBG based on laser arrays.

Effect of linewidth enhancement factor on the generation of optical vortices in a class-A degenerate cavity semiconductor laser.

The dynamical behavior of a one-dimensional ring array of lasers generated in a class-A degenerate cavity semiconductor laser is numerically investigated. The class-A behavior of the laser is obtained by considering a low-loss vertical external cavity surface emitting laser (VECSEL), in which a telescope and a mask allow us to control the geometry and the linear nearest-neighbour coupling between the lasers. The behavior of the lasers is simulated using coupled rate equations, taking the influence of the Henry factor into account. It is shown that the ring array of lasers exhibits multistability. Moreover, by comparison with a class-B semiconductor laser, it is proved that the class-A nature of the laser makes it more robust to the increase of the Henry factor when it comes to generating topological charge carrying arrays of lasers, thus opening new perspectives of application for such lasers.

Thermionic graphene/silicon Schottky infrared photodetectors

Optical communications, imaging, and biomedicine require efficient detection of infrared radiation. Growing demand pushes for the integration of such detectors on chips. It is a challenge for conventional semiconductor devices to meet these specs due to spectral limitations arising from their finite band gap, as well as material incompatibilities. Single layer graphene (SLG) is compatible with complementary metal-oxide-semiconductor (CMOS) Si technology, while its broadband (UV to THz) absorption makes the SLG/Si junction a promising platform for photodetection. Here we model the thermionic operation of SLG/Si Schottky photodetectors, considering SLG's absorption, heat capacity, and carrier cooling dependence on temperature and carrier density. We self-consistently solve coupled rate equations involving electronic and lattice temperatures, and nonequilibrium carrier density under light illumination. We use as an example the infrared photon energy of 0.4 eV, below the threshold for direct photoemission over the Schottky barrier, to study the photothermionic response as a function of voltage bias, input power, pulse width, electronic injection, and relaxation rates. We find that device and operation parameters can be optimized to reach responsivities competitive with the state of the art for any light frequency, unlike conventional semiconductor-based devices. Our results prove that the SLG/Si junction is a broadband photodetection platform.