Various efforts have been made to get a wellestablished laser models such as a rate equationbased model and a finitedifferencetimedomain fdtd based model for oeic design however, the difficulty of extracting. Comparison of numerical methods for modeling laser mode locking with saturable gain. Laser pumpprobe techniques a variation on flash photolysis used to study very fast processes. The laser diode rate equations model the electrical and optical performance of a laser diode. Simple rate equations in a two level laser system by gibson december 22, 2004 introduction laser is an acronym for light ampli. Ianno for over ve decades, laserinduced damage and breakdown in optical materials has been an active eld of research. Walker atk aerospace group, brigham city, ut, 84302 a unique numerical method has been developed for solving onedimensional ablation. Laser pumping and population inversion steady state laser pumping and population inversion 4level laser 3level laser laser gain saturation upperlevel laser transient rate equations upperlevel laser threelevel laser solve rateequations in steadystate introduce the upperlevel model solve rateequations under transients.
This tool allows a user to alter the parameters in the laser rate equations, while plotting three unique graphs. From the above equation we see, for a twolevel atomic system, the incident signal will make the population difference. By introducing a thermally dependent empirical offset current into the rate equations, we are able to model in a. Extraction of semiconductor laser rate equation parameters. Jacobsa,c introduction diodeendpumped solidstate lasers are very popular because of their high efficiency, excellent beam quality, compactness and robustness. We present a set of rate equations for the modal amplitudes and. A laser medium a collection of atoms, molecules, etc.
We present a rateequation model for twophoton lasers that, despite its simplicity, captures the essential physics of their behavior and affords an intuitive understanding of their novel threshold and stability behavior. Rate equations analysis of phaselocked semiconductor laser. Laser rate equations university of california, davis. Rate equation model for multimode semiconductor lasers with spatial hole burning daan lenstra1, and mirvais yousefi2 1photonic integration group, department of electrical engineering, eindhoven university of technology, eindhoven, netherlands 2photonic sensing solutions, amsterdam, netherlands d.
Introduction chemical reaction kinetics deals with the rates of chemical processes. The laser is a light source that exhibits unique properties such as directionality, monochromaticity and coherence eleccion, 1972. In this chapter, we will setup laser rate equations using the fabryperot optical cavity as a model. Ode45 problem of solving laser rate equation physics. Chapter 7 lasers after having derived the quantum mechanically correct suszeptibility for an inverted atomic system that can provide gain, we can use the twolevel model to study the laser and its dynamics. In this paper, we present a simple thermal model of verticalcavity surfaceemitting laser vcsel lightcurrent li characteristics based on the rateequation.
Chapter 11 basics of semiconductor lasers cornell university. Any chemical process may be broken down into a sequence of one or more singlestep processes known either as elementary processes, elementary reactions, or elementary steps. We derive a novel rate equation system for a laser consisting of two coupled cavities arranged in tandem. Laser rate equationode simulation problem physics forums. The analytical expressions for the threshold current density and the output power are derived using the model and the thermal behaviour of these parameters is examined. Sebastian wieczorek, applied mathematics, university college cork october 21, 2015 1 introduction lets consider a laser which consist of an optical resonator lled with an active medium excited atoms, electrons or molecules. A heat coupled laser rate equation model was developed to investigate the effects of heat generation on lasing performance. Our model considers thermal depopulation of laser levels when the system is pumped by 1480 nm. Rateequation model for multimode semiconductor lasers with spatial hole burning daan lenstra1, and mirvais yousefi2 1photonic integration group, department of electrical engineering, eindhoven university of technology, eindhoven, netherlands 2photonic sensing solutions, amsterdam, netherlands d. Our ecsl model is a threemirror cavity laser as in 5, shown in i. During this work and for the entire laboratory measurements we used a commercial semiconductor distributed feedback dfb laser, with a central wavelength of 1550 nm. Modeling of modelocked fiber laser by combining of rate. Extended rate equations model for describing the dynamics of the.
It is found that both strong injection level and positive optical frequency detuning increase the modulation bandwidth. Chapter 4 laser dynamics single mode before we start to look into the dynamics of a multimode laser, we should recall the technically important regimes of operation of a singlemode laser. Spontaneous and stimulated processes einstein a and b coefficients rate equation analysis gain saturation. The derivation of the photon rate equations is based on classical electromagnetic theory, while the rate equations for the electrons are written down heuristically in analog with the. The rate law or rate equation for a chemical reaction is an equation that links the initial or forward reaction rate with the concentrations or pressures of the reactants and constant parameters normally rate coefficients and partial reaction orders.
Verticalcavity surfaceemitting lasers vcsels are a new generation of semiconductor lasers that have many advantages. I used ode45 to solve this problem, but the result was not agreed with the reference. Rate equation model of a coupledcavity laser abstract. This rate equation is used to investigate selfstarting, steadystate pulse energy, stability, pulse quantization, simultaneous cw and pulse operation, hysteresis in mode locking, multiplepulse operation, relaxation oscillations, and noise behavior. Modified rate equation model including the photonphoton resonance antti laakso and mihail dumitrescu optoelectronics research centre tampere university of technology tampere, finland abstractwhen the longitudinal confinement factor in an edgeemitting laser with two dominant longitudinal modes is treated as. A similar rate equation can be derived for the photon density d dt. Spontaneous and stimulated processes einstein a and b. Pdf even with the use of variable transformations, quantumwell qwlaser models based on the standard rate equations and a linear gainsaturation. The value of the material gain that satisfies the lasing condition, 2 1 1 2 r r e ag l.
N1iph, then we can set n1 0and obtain only a rate equation for the upper laser level dt d n2 21 n2. Rate equation model e 2, n 2, g 2 e 1, n 1, g 1 cu q a bu population of states. Rate equation modeling get started with rate equation modeling. Modulation characteristics of semiconductor lasers mod see. A new approach to model cw co 2 laser using rate equations. Arnold abstract lasers provide the ability to accurately deliver large amounts of energy into con. Improved rate equations for external cavity semiconductor. Improved rate equations for external cavity semiconductor lasers. Theoretical model of the bistable semiconductor laser. Lets consider a laser which consist of an optical resonator filled with an active medium. Rate equation model of bulk optical damage of silica, and. We use the model to investigate the steadystate behavior of the laser, explore the stability of the steadystate solutions. Laser rate equations are written and solved in the frequency domain for homogeneous as well as for inhomogeneous gain.
The combined numerical model is compared with the pure dynamic rate equation for the amplification of a nanosecond. A rate law is a differential equation that describes the rate of change of a reactant or product concentration with time. The software rp fiber power can solve rate equations not only for simple gain systems with a single metastable level, but even for userdefined energy level schemes involving arbitrary optical and nonradiative transitions and energy transfers, where the rate. Modified rate equation model including the photonphoton. Rate equation analysis versus microscopic theory m. Abstract even with the use of variable transformations, quantumwell qw laser models based on the standard rate equations and a linear gainsaturation. The simplest way to analyze and understand laser dynamics is using rate equations. In this paper, we present a vcsel model, based on the standard laser rate equations, that meets the above requirements. Rate equation simulation of temporal characteristics of a. This system of ordinary differential equations relates the number or density of photons and charge carriers in the device to the injection current and to device and material parameters such as carrier lifetime, photon lifetime, and the optical gain the rate equations may be solved by. A singleelement planewave solidstate laser rate equation model e. Rate equation analysis of injectionlocked quantum cascade. We present a set of rate equations for the modal amplitudes and carrier inversion moments that describe the deterministic multimode dynamics of a. Comparison of numerical methods for modeling laser mode.
E 2, n 2, g 2 e 1, n 1, g 1 a decay of an excited state numbers in 106 s1 in the absence of a radiation field. Dynamical systemthe equations that describe the rate of change of laser photons is given below dq dt gnq. Complete rate equation modelling of quantum cascade lasers. Two popular methods to analyse the operation of cw co 2 lasers use the temperature model and the rate equation model. In general, the partial differential equation pde that is usedto model the system will haveaterm that is both nonlinear, due to the gain saturation, and stiff, due to the. Rateequation model for multimode semiconductor lasers with. Modulation characteristics of semiconductor lasers mod. The effect of temperature on the dynamics of a gaasbased quantum cascade laser qcl is analysed using a complete rate equation model. On the basis of combining the rate equation and nls equation, we have developed a novel modelocked fiber laser model, which can not only describe the dispersion and nonlinear effect of fiber, but also take consideration of the reciprocity of. Rateequation model for multimode semiconductor lasers. An iterative procedure is designed for the repetition rate pulse sequence. For many reactions the initial rate is given by a power law such as where a and b express the concentration of the species a and. Petermann, laser diode modulation and noise, kluwer academic, 1991 12.
We propose a combined model of the laser rate equation and the ginzburglandau equation for simulation of the amplification of the ultrashort pulse in an ytterbiumdoped fiber amplifier. Pdf rateequationbased laser models with a single solution regime. Chapter 4 fundamentals of lasermaterial interaction and. Rate equation model of bulk optical damage of silica, and the influence of polishing on surface optical damage of silica arlee smith, binh do laser, remote sensing, plasma and complex system science department sandia national laboratories, albuquerque, new mexico rod schuster, david collier. The modulation properties of optical injectionlocked quantum cascade lasers qcls are investigated theoretically via a simple low dimensional rate equation model. Light amplification by stimulated emission of radiation light could mean anything from microwaves to xrays essential elements. Among the two, the latter model directly calculates the population densities in the various vibrational levels connected with the lasing action, and provides a clearer illustration of the processes involved. Theoretical modeling of laser induced absorption phenomena in optical materials chris ferris, m. Rate equation modeling is a method of modeling the dynamics of laser gain media with differential equations for level populations.
Rp photonics encyclopedia rate equation modeling, gain. The analytical value10 for the slope efficiency was 48% and the rate equation model predicted a corresponding value of 44 %. Wideband and scalable equivalent circuit model for. Equation 1 1 can be verified by the experiment in 171 where the field. One main advantage of using the rate equation model instead of analytical solutions is that the populationdynamicsofthelasercrystalcanalsobeinvestigated fig. Here, rp is the equilibrium upper state population. Osa combined numerical model of laser rate equation and. Mathematical model using the rate equations in this section a mathematical model of the lightcurrent characteristics is derived and was justified by comparison to the experimentally measured data obtained by biv method. Heat transfer and fluid flow during laser spot welding of. A timedependent, twodimensional in space rate equation model of a transverselypumped pulsed dye laser oscillator, which incorporates transverse pump intensity variation in the presence of intracavity dye laser radiation, is proposed to understand and predict its temporal behaviour. A rate equation for pulse energy is obtained from the master equation of mode locking. Pumping and population inversion laser amplification.
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