Self-consistently determining mean field used in rate equations of semiconductor lasers

An analytical expression for the mean field has been derived from the traveling wave rate equations in terms of the geometric mean of the counter-propagating fields inside the cavity, and an implicit solution has been obtained for the geometric mean inside the laser. These lead to the establishment of the analytical relation between the mean field inside the cavity and the output field from the diode laser. It is hoped that this relation may provide a common reference for the evaluation of the injection coefficient when studies are made on the injected semiconductor lasers, whose nonlinear dynamic characteristics are critically dependent on the injection coefficient, with rate equations simplified by adopting the mean field approximation.     

连续波环形染料激光器的单向运转特性

本文讨论了连续波环形染料激光器的单向运转特性。采用改进的Ganiel速率方程模型,分析了在单向运转条件下泵浦光通量、染料分子密度等参量对激光光通量、激发单重态粒子集居数密度以及增益的影响;揭示了在连续波环形染料激光器中单向运转条件下存在粒子集居数密度的非对称性、激光光通量与激活介质内空间位置的相关性和增益峰值波长的扫描现象。本文给出了数值计算结果。     

三能级光纤激光器速率方程组的阈值解析解

 在考虑了泵浦损耗及激光损耗的情况下，解析求解了阈值泵浦下的三能级光纤激光器速率方程组，获得了泵浦功率阈值的显函数解析表达式，泵浦功率沿光纤变化的隐函数表达式，以及用功率变化表示的各个能级的粒子数密度随位置变化的显函数表达式。并利用这些表达式对光纤激光器的阈值特性进行了研究，研究表明：泵浦功率阈值随泵浦损耗系数增大而增大；激光上能级粒子数密度随归一化位置呈下降趋势，而下能级粒子数密度的变化与此相反；泵浦功率阈值越大(光纤长度越长),净增益系数随归一位置下降就越快。所获得的结果适用于单包层和双包层光纤激光器。     

Studying the Mode－Spectra Characteristics of An Above－Threshold Biased Semiconductor Laser

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Analytical and visual modeling of InGaN/GaN single quantum well laser based on rate equations

An analytical, visual and open source model based on solving the rate equations for InGaN/GaN single quantum well (QW) lasers has been carried out. In the numerical computations, the fourth-order Runge–Kutta method has been used for solving the differential rate equations. The rate equations which have been considered in this simulation include the two level rate equations for the well and separate confinement heterostructure (SCH) layers. We present a new and inexpensive modeling method with analytical, visual and open source capabilities to investigate and comprehend the QW laser characteristics such as time behavior of carriers in SCHs and QW, photon density, output power and gain, and also the output power versus current which presents the threshold current of the laser. The characteristics of the QW lasers, which include laser time response (P–t), turn-on delay time of lasing and output power–current (P–I) characteristic and related features such as threshold current and slope efficiency have been investigated. Our model accurately computes the P–t and P–I characteristics such as turn-on delay time, threshold current and slope efficiency, and also illustrates the effects of parameters such as the injection current and geometry.     

用行波速率方程组确定半导体激光器的输出场

为了解决在平均场近似速率方程中自洽地由激光器腔内平均场来确定输出场的问题,以半导体激光器为例,采用集总形式的端面反射率,通过求解行波速率方程组,得出了半导体激光器腔内平均光子数密度与输出光子数密度的解析关系式.结果表明,半导体激光器输出场与腔内平均场之比是一个与泵浦电流有关的量,把它当成常数是有偏见的.     

Modelling of passively Q-switched lasers with intracavity Raman conversion

We present a model of passively Q-switched Raman lasers by utilizing the rate equations. The intracavity fun-damental photon density, Raman photon density and the initial population-inversion density of the gain medium are assumed to be of Gaussian spatial distributions. These rate equations are normalized by introducing some synthetic parameters and solved numerically, and a group of general curves are generated. Prom these curves we can understand the dependence of the Raman laser pulse characteristics on the parameters about the pumping, the gain medium, the Raman medium and the resonator. An illustrative calculation for a passively Q-switched Nd^3＋：GdVO4 self-Raman laser is presented to demonstrate the usage of the curves and related formulas.[第一段]     

掺铒光纤放大器中抽运问题的理论分析

依据掺铒光纤放大器的速率方程和光传输方程,在不计放大自发辐射的情况下,得出了抽运功率和信号增益在放大器中沿光纤分布的隐函形式的解析表达式,并利用数值模拟对三种抽运方式下的放大器特性进行了分析。     

解二维时间相关光子扩散方程的交替方向隐式法

研究了应用交替方向隐式法求解非均匀生物组织中的二维时间相关光子扩散方程,并同解析解以及Monte Carlo模拟的结果作了比较,数值结果表明,该方法具有较好的稳定性和较高的精度.     

Spherical gravitational collapse with photon emission and a generalized Schwarzchild interior solution

The general dynamical equations for perfect fluid filled spheres with an outward flux of photons are derived. The vital role played by the energy density of the free gravitational field in accelerating photon production has been emphasized. It is pointed out that even when the material energy density is finite, the energy density of the free gravitational field can take infinitely large values resulting in vanishing surface area of the star. A generalized Schwarzschild interior solution with conformally flat geometry but with photon emission has been obtained. It is pointed out that the interior conformal coordinate system bears a strong resemblance to the exterior Krushkal coordinates. It is shown that for spherical star the invariant velocity of the fluid particles, falling towards the centre, is proportional to its radius suggesting that the outer envelopes collapse at a faster rate than the core part. It is shown that the interior radiating solution can be matched with generalized Schwarzchild exterior solution.     

Numerical stability for laser radiation computations

The numerical stability for solving the coupled differential equations for laser radiation intensity and gain is investigated. Simplified lasing conditions are considered under which a closed-form solution is obtained and numerical stability can be determined. The analytical solution illustrates the effect of the important physical parameters, and it provides a basis for evaluation of numerical methods. It is shown that the explicit numerical procedure is inherently unstable, and that stability requires an implicit approach. Partially-implicit methods, which are conditionally stable, are also discussed.     

Laser-diode side-pumped actively Q-switched eye-safe intracavity optical parametric oscillator

Eye-safe laser of 1573 nm wavelength from a laser-diode (LD) side-pumped actively Q-switched Nd:YAG/KTP intracavity optical parametric oscillator (IOPO) with acousto-optic (AO) modulator is presented. The dependences of the average output power, the pulse width, pulse energy, and the peak power on incident pump current for the generated-signal-light pulses are obtained. By considering the Gaussian spatial distributions of the pump light in laser medium, the photon densities of the fundamental, the signal, and the idle waves as well as the initial population-inversion density and the coupled rate equations of this IOPO are described, in which the influence of the pump rate, the thermal effect in the gain medium and the change of the photon density along the cavity axis have been also taken into account. These coupled equations are solved numerically, and the theoretical calculations are consistent with the experimental results.     

An improved transmission line laser model for multimode laser diodes incorporating thermal effects

An improved transmission line model to study the thermal effects in semiconductor laser diodes is reported in this paper. The temperature effects in the laser characteristics are obtained by incorporating temperature dependent gain and carrier density equations for the laser cavity. These primary factors are introduced in the regular transmission line laser model to estimate the static and dynamic characteristics of an 1.3μm InGaAsP double heterostructure laser diode. The results show good agreement with the experimental observation and solution of rate equations referred in the literature. The key feature of this model is that it provides the laser spectra at various temperatures. Based on the model, time dependent evolution of optical spectrum, temperature dependent optical output and frequency chirp are evaluated. Further the distribution of photon and electron density within the cavity is also determined.     

低增益准分子激光最佳透射率的研究

对于激光系统性能而言,谐振腔最佳透射率具有非常重要的作用。低增益、宽带脉冲准分子激光的最佳透射率条件与其激光抽运脉冲引起的增益脉宽有密切关系。提出了在激光四能级系统速率方程的基础上模拟低增益准分子激光的跃迁行为。并利用合理的近似,研究低增益脉冲准分子激光谐振腔的最佳透射率。给出了其在不同增益脉宽情况下统一的最佳透射率条件,并分析了以小信号增益系数为函数的最佳透射率变化规律。所得到的结论为：低增益、宽带脉冲准分子激光的最佳透射率情况和连续激光器有所不同。而是取决于增益脉宽和光子寿命之间的关系。上述结论得到了相应实验研究结果的证实。     

Quantum information transmission between two qubits through an intermediary photon gas

The theory of the quantum information transmission between two semiconductor two-level quantum dots as two qubits through an intermediary photon gas in a cavity is presented. The reduced density matrix of each two-level quantum dot is the quantum information encoded into this qubit. The quantum information exchange between two distant qubits imbedded in the photon gas is performed in the form of the mutual dependence of their reduced density matrices due to the interaction between the electrons in the qubits and the photon gas. The system of rate equations for the reduced density matrix of the two-qubit system is derived. From the solution of this system of equations it follows the mutual dependence of the reduced density matrices of two distant qubits.     

LD泵浦Nd:GdVO4晶体Cr4+:YAG被动调Q激光特性研究

考虑腔内光子数密度的空间高斯分布以及晶体热效应的影响,给出了LD泵浦Nd:GdVO₄ 晶体Cr⁴⁺:YAG被动调Q 1.06 μm激光的耦合速率方程组.数值求解该方程组获得了输出激光的脉冲宽度、重复率、峰值功率以及单脉冲能量随泵浦功率的变化特性,其理论值与实验结果相符.     

Direct numerical simulation of quasi-three-level passive Q-switched laser

The Runge-Kutta method is used to solve numerically the rate equations of quasi-three-level passive Q-switched laser directly without any approximate treatment of these differential equations. The 946 nm self-Q-switched Cr,Nd:YAG laser is chosen for example to describe the details. The time-dependence of intra-cavity photon density is obtained and its detailed real-time changing process is reproduced in numerical solution. The curves of laser output parameters such as average output power, pulse width, repetition rate, pulse energy and peak power changing with different cavity conditions such as pump power, output coupler reflectivity, Cr,Nd:YAG crystal length, Nd³⁺ ion and Cr⁴⁺ ion concentrations are simulated according to direct numerical solution rather than analytical expressions. This direct numerical simulation method can be widely used to describe and optimize the quasi-three-level passive Q-switched laser theoretically.     

Effect of a small dispersion on self-focusing in a spatially one-dimensional case

The effect of a small dispersion on the self-focusing of solutions of equations of nonlinear geometric optics in a spatially one-dimensional case has been studied. This effect in the leading order is described by a universal special solution of the nonlinear Schrödinger equation, k]which is isomonodromic. The analytical and asymptotic properties of this universal solution have been considered.     

A hybrid multilevel method for high-order discretization of the Euler equations on unstructured meshes

Higher order discretization has not been widely successful in industrial applications to compressible flow simulation. Among several reasons for this, one may identify the lack of tailor-suited, best-practice relaxation techniques that compare favorably to highly tuned lower order methods, such as finite-volume schemes. In this paper we investigate solution algorithms in conjunction with high-order Spectral Difference discretization for the Euler equations, using such techniques as multigrid and matrix-free implicit relaxation methods. In particular we present a novel hybrid multilevel relaxation method that combines (optionally matrix-free) implicit relaxation techniques with explicit multistage smoothing using geometric multigrid. Furthermore, we discuss efficient implementation of these concepts using such tools as automatic differentiation.     

Control of the pulse width in a diode-pumped passively Q-switched Nd:YVO<Subscript>4</Subscript>/KTP green laser with GaAs saturable absorber

By varying the positions of the saturable absorber in the laser axis and the pump beam waist in the gain medium, respectively, we have theoretically and experimentally studied the control of the pulse width in a diode-pumped passively Q-switched Nd:YVO₄/KTP green laser with GaAs saturable absorber. A rate equation model is introduced, in which the intracavity photon density is assumed to be Gaussian spatial distribution, the longitudinal variation of the intracavity photon density and the pump beam spatial distribution are also considered. The experimental results are consistent with the numerical calculations of the rate equations.