Laser Rate Equations Research Articles

Analysis of the temporal and spectral output properties of a mode-locked andQ-switched laser oscillator with a nonlinear mirror based on stimulated Brillouin scattering

The emission dynamics of a mode-locked laser oscillator with a nonlinear mirror based on stimulated Brillouin scattering (SBS) has been investigated with regard to its spectrum and to its intensity distribution. The investigation was carried out experimentally as well as by numerical simulations. The laser yields trains of pulses with measured durations of $410\phantom{\rule{0.3em}{0ex}}\mathrm{ps}$ and energies of the single pulse of up to $2\phantom{\rule{0.3em}{0ex}}\mathrm{mJ}$. Two theoretical models describing the complex emission dynamics of a mode-locked SBS-laser oscillator are introduced. The first model consists of spectrally resolved laser rate equations and thus describes the mode locking in the frequency domain by the superposition of the longitudinal resonator modes. The SBS-$Q$-switch is incorporated by a phenomenological description of the time dependent SBS reflectivity. Numerical simulations based on this model yield the evolution of a few 100 longitudinal laser modes and the corresponding intensity distribution during the course of a $Q$-switch pulse with $10\text{\ensuremath{-}}\mathrm{ps}$ resolution. The influences of the different components on the spectrum and thus on the pulse duration will be discussed. The second model describes all occurring dynamics in the time domain providing easy access to the study of misalignment on the output dynamics. Results of numerical simulations of both models and measurement results are compared.

Analytical solutions to rate equations of fiber lasers containing three-energy-level ions

A 980-nm wave pumped erbium-doped single-clad fiber laser has been studied by using rate equations for three-energy-level ions. A closed-form expression for the output laser power has been deduced and the output characteristics of the fiber laser have been analytically quantified. The effects of the input pump power and the fiber length on the ratio of the exit pump power to the input pump power have been discussed. In addition, the variations of the averaged population densities on each energy-level with the fiber length have been studied.

Stability of semiconductor injection lasers in the framework of the model described by rate equations

The stability of semiconductor injection lasers is studied on the basis of the analysis of the first Lyapunov exponent and the characteristic parameters of the laser rate equations.

Modelling of Tm3+-doped LiNbO3 Waveguide Lasers

In this work, CW laser operation of Tm3+-doped LiNbO3 channel waveguides has been modelled. The model is based on time dependent laser rate equations coupled with the laser signal and pump photon flux equations. Steady state solutions for the population densities, pump and signal powers are obtained by using finite difference discretization of the active volume. The effects of spectroscopic parameters such as concentration dependent cross-relaxation and excess waveguide loss have been analyzed. We demonstrate good agreement with experimental data previously reported in Zn-diffused LiNbO3:Tm3+ channel waveguide lasers. It is shown also that laser performance can be substantially improved by optimizing the cavity length.

Nonlinear dispersive three-dimensional finite-difference time-domain analysis for photonic-crystal lasers

The three-dimensional finite-difference time-domain method that can handle dispersive and dynamic nonlinear-gain media is proposed and realized. The effect of carrier diffusion is included through the laser rate equations. Through this three-dimensional nonlinear gain FDTD method, rich laser-dynamics behaviors, such as the lasing threshold, the relaxation oscillation, and the spatial hole burning, are directly observed from a hexapole mode.

Application of shannon's entropy to classify emergent behaviors in a simulation of laser dynamics

Laser dynamics simulations have been carried out using a cellular automata model. The Shannon's entropy has been used to study the different emergent behaviors exhibited by the system, mainly the laser spiking and the laser constant operation. It is also shown that the Shannon's entropy of the distribution of the populations of photons and electrons reproduces the laser stability curve, in agreement with the theoretical predictions from the laser rate equations and with the experimental results.

A self-consistent analysis of semiconductor laser rate equations for system simulation purpose

A procedure for extraction of the rate-equation parameters of semiconductor laser diodes is presented. Using small signal measurements, we have formulated a complete set of equations, which can be resolved analytically to obtain a solution for a combination of parameters that constitute a modified rate-equation model and is presented here for the first time. The proposed method does not necessitate at, or below threshold measurements, which require high sensitivity from the measuring equipment. Furthermore, without the need for any optimization, the solution to the rate equations is completely self-consistent since the parameters are linked together through functional relationships. With this new method, the determination of all the necessary rate-equation parameters to carry out large signal simulation is exclusive of the measurements for signal chirp, and as such computation of the chirp parameter is not included here. Comparison between large signal measurements and simulations from the computed parameters show very good agreement for a range of above threshold bias currents.

Numerical Investigation of Optical Chaotic Multiplexing Communications

A novel chaotic multiplexing communication system based on a one-way coupled map lattice configuration is proposed and numerically investigated with semiconductor laser rate equations that include the Langevin noise source. Calculations show that dual synchronization and duplex communication can be achieved under an ideal condition in which no wavelength and phase differences between lasers exist. The impact of the wavelength and phase differences between lasers on synchronization is discussed briefly.

Numerical solution of Boltzmann tranport equation for TEA CO 2 laser having nitrogen-lean gas mixtures to predict laser characteristics and gas lifetime

Selective laser isotope separation by TEA CO 2 laser often needs short tail-free pulses. Using laser mixtures having very little nitrogen almost tail free laser pulses can be generated. The laser pulse characteristics and its gas lifetime is an important issue for long-term laser operation. Boltzmann transport equation is therefore solved numerically for TEA CO 2 laser gas mixtures having very little nitrogen to predict electron energy distribution function (EEDF). The distribution function is used to calculate various excitation and dissociation rate of CO 2 to predict laser pulse characteristics and laser gas lifetime, respectively. Laser rate equations have been solved with the calculated excitation rates for numerically evaluated discharge current and voltage profiles to calculate laser pulse shape. The calculated laser pulse shape and duration are in good agreement with the measured laser characteristics. The gas lifetime is estimated by integrating the equation governing the dissociation of CO 2. An experimental study of gas lifetime was carried out using quadrapole mass analyzer for such mixtures to estimate the O 2 being produced due to dissociation of CO 2 in the pulse discharge. The theoretically calculated O 2 concentration in the laser gas mixture matches with experimentally observed value. In the present TEA CO 2 laser system, for stable discharge the O 2 concentration should be below 0.2%.

A rate equation model of asymmetric multiple quantum-well lasers

This paper gives a description of a rate equation model to simulate the steady-state and frequency response characteristics of asymmetric multiple quantum well (AMQW) lasers using several different methods. AMQW lasers consist of several quantum wells of different widths or compositions designed to achieve a broad net gain profile for improved wavelength tuning. The position of the quantum wells relative to the p-side of the device plays an important role in the steady-state characteristics due to a significant nonuniform carrier distribution across the active region. Simulations of the carrier distribution and the onset of simultaneous lasing for certain structures are demonstrated using this model. Appropriate values for the distributed material loss and tunneling times were determined here by fitting the model output to measurements of the transition cavity length for a number of AMQW lasers. As well, comparison of different calculation methods demonstrates it is more appropriate to use a numerical analysis of the laser rate equations rather than analytic equations when modeling the frequency response of these structures. However, an analytic equation for the resonance frequency was found that fit well with numerical simulations of several different AMQW laser structures.

A behavioral approach to model thermal sensitivity of semiconductor lasers

A new method is proposed in this paper to model the effects of temperature on the steady state and large signal response of single mode edge emitting semiconductor laser. Traditionally, a separate thermal rate equation, in conjunction with the laser rate equation model is used to describe the thermal behavior [IEEE J. Quant. Electron., 31(10) (1995); J. Lightwave Technol., 17(9) (1999)] or, temperature dependence of the rate equation parameters is explicitly defined through their respective characteristic temperatures to model thermal behavior [IEEE Proc. J., 140(4) (1993); IEEE J. Quant. Electron., 4 (1968) 119; IEEE Photon. Technol. Lett., 1 (1989) 356]. However, these methods introduce a number of additional parameters that necessitate new measurements and rigorous numerical computations for their determination and impart more complexity to the model. In the work presented here, a new thermal threshold is defined for the external laser slope efficiency together with an output feedback function obtained through the rate equations-time dynamics. This inherently introduce the dominant thermal mechanisms into the model with the parameters extracted from steady state measurements in a self-consistent manner, providing considerable reduction in computation complexity. The resulting modified rate equations also account for high power gain saturation effects, which is otherwise only possible through higher-level (1D–3D) modeling methods. Measured results from two commercial single mode lasers have shown excellent conformance with simulations, using this approach.

Computational Simulation of Laser Dynamics as a Cooperative Phenomenon

The different kinds of behavior exhibited by the system in a laser dynamics simulation using a cellular automata model are analyzed. Three distinct types of behavior have been found: laser constant operation, laser spiking and a complex behavior showing irregular oscillations. In the last case, the power spectrum follows a power law of the type 1/f−β with exponent close to β = 2. In the laser spiking regime, the dependence of the decay rate of the oscillations is found to be in good agreement with the predictions of the theoretical laser rate equations and the experimental phenomenology. In our model the system components evolve under local rules which reproduce the physics of the laser system at the microscopic level, and the laser properties appear as cooperative emergent phenomena associated to these rules.

Transition from laser-off to laser-on through on–off intermittency in a gain-modulated CO_2 laser

We observe the route from laser-off to laser-on in a CO2 laser. On the route, on–off intermittency appears, which is caused by discharge instability near the laser threshold. By analyzing the probability distribution of a laminar phase near the onset of the intermittency, we confirm that what we have observed is on–off intermittency. We reproduce the intermittency through a numerical simulation of the laser rate equations.

Self-consistent rate equations of self-assembly quantum wire lasers

We describe a detailed model for the dynamical and spectral properties of quantum dash (quantum wire assembly) lasers. We use a self-consistent semiclassical theory for a multimode laser field which interacts with an inhomogeneously broadened assembly of quantum wires via the quantum mechanical radiation-matter interaction. Our comprehensive coupled equations are spectrally resolved enabling to study accurately the effect of the gain inhomogeneity. Carrier-carrier and carrier-phonon scattering are also included. We highlight the effective capture rate which is determined by the ratio between the number of states in the reservoir and in the assembly, the energetic region into which carriers are captured and the width of the inhomogeneously broadened gain. Specifically, we demonstrate that a large number of states ratio lowers both the linear optical differential gain and the nonlinear gain coefficient. We show that gain suppression dominates when a realistic energy range into which capture takes place is considered as well as for small number of states ratios. In addition, we show that the width of the inhomogeneous broadening plays a relatively small role. We conclude that the differential gain and nonlinear damping can not be optimized simultaneously. These results point therefore to the clear advantages offered by laser structures which employ non conventional carrier injection schemes such as tunnelling barrier or n-type /spl delta/-doping regions.

Alternative formulation of carrier transport in spatially-dependent laser rate equations

The level of accuracy of the conventional implementation of carrier transport into the quantum wells in spatially-dependent rate equations appears too high compared to the overall precision of rate equations. The dynamic description of the normalized carrier profile in the barrier region is of little use, since no stimulated interactions with the optical field occur in this region. Furthermore, it is only described by transverse diffusion and effects such as transport through the graded heterostructures formed by the mirror layers are neglected, which makes its accuracy disputable. Finally, this implementation nearly doubles the time required to solve the carrier rate equations. We propose therefore a more consistent model that still considers the dynamic evolution of the carrier population while assuming a time-invariant profile at the interface between the barrier and the quantum wells. This simplification both removes the requirement for unavailable parameters (such as the ambipolar diffusion coefficient in the barrier) and improves the numerical efficiency of the algorithm since only one additional ordinary differential equation needs be solved. The model is still capable of reproducing the influence of longitudinal transport on the modal distribution and high-frequency behavior of diode lasers.

Stochastic bursting due to frequency drift in an injected fibre laser

The joint influence of stochastic frequency drift and optical injection on the dynamical behaviour of a rate-equation laser model is studied. When the autocorrelation time of the frequency fluctuations is larger than the typical timescales of the system's dynamics, and the amplitude of the frequency drift is larger than the injection locking range, the laser exhibits bursting behaviour at irregular times, each burst being followed by relaxation oscillations towards the unlocked state. The conditions under which this type of phenomenon occurs are fulfilled in fibre lasers. Accordingly, numerical simulation results of the model agree satisfactorily with the experimentally observed behaviour of an injected fibre ring laser.

Numerical approach to field fluctuations and spectral lineshape in InGaAsP laser diodes

AbstractThis paper reports on a numerical approach to model the field fluctuations, spectral lineshape and linewidth in semiconductor lasers. The approach is based on numerical solution of the laser rate equations augmented by Langevin noise sources that account for fluctuations in the lasing field. The paper newly examines contributions of intensity and frequency noises to the spectral characteristics of the lineshape and its linewidth over a wide range of injection current. The model is applied to InGaAsP lasers emitting in a wavelength of 1.5 μm as the most representative light sources in optical communication systems. Accuracy of approximated models of calculating linewidth from low‐frequency components of the frequency noise is checked. Effect of non‐linear gain suppression on the lineshape is also explored. The spectral lineshape promotes and the linewidth decreases as the laser is injected far from the near‐threshold region. The lineshape changes mainly with changes in the frequency noise spectrum while the linewidth is sensitive to variation in the low‐frequency levels of both intensity and frequency noises. Copyright © 2004 John Wiley & Sons, Ltd.

An improved analysis of semiconductor laser dynamics under strong optical feedback

We present an improved theoretical model to analyze dynamics and operation of semiconductor lasers under optical feedback (OFB). The model is applicable for arbitrary strength of OFB ranging from weak to very strong. The model has been applied to investigate the dynamics and operation of lasers over wide ranges of OFB and injection current. An improved set of modified rate equations of lasers operating under OFB were proposed. We introduced a theoretical model to determine the power emitted from both the laser back facet and external reflector. The results showed that the operation of semiconductor lasers is classified into continuous wave, chaotic, and pulsing operations, depending on the operating conditions. The light versus current characteristics were examined in the operating regions of the classified operations. Under strong OFB, we predicted for the first time pulsing operation of lasers at injection currents well above the threshold. We observed the pulsing operation in experiments in good correspondence with the simulated results.

A coupled-mode model for the Fabry-Perot semiconductor laser kink instability

This paper derives a coupled-mode Fabry-Perot semiconductor laser model from the longitudinal-mode laser rate equations with parabolic gain dispersion. Truncating the full coupled-mode model permits stability analysis of the Fabry-Perot laser kink instability, which is a mode hop with increasing current. Two mechanisms contribute to the mode hop: the Silberberg-Bar-Joseph instability transports energy from higher frequencies to lower frequencies and gain dispersion stops the energy transport. Numerical simulations have shown that higher order carrier modes are excited during intervals of energy transport among the optical modes. These numerical results suggest that modes greatly detuned from the peak gain affect the laser dynamics.

Sensitivity enhancement in erbium-doped fiber laser intra-cavity absorption sensor

The sensitivity of an erbium-doped fiber laser intra-cavity loss sensor is investigated theoretically and experimentally. The laser rate equations are modified to analyze the output characteristics of fiber laser under different pump powers and intra-cavity losses. Theoretical analysis shows that high sensitivity can be achieved when pump power is reduced to close to threshold value. The general trends of experimental results agree with the theoretical predictions.