Compensation for Nonlinear Distortion of Optical Transmitter with Predistortion

The paper studies the nonlinear distortion of direct modulated laser diode applying to AM-VSB lightwave CATV systems from the viewpoint of rate equations and designs a predistortion circuit in an easier way. It is shown that CSO and CTB in 60 PAL channels have been improved obviously.     

Second-order distortion of amplified intensity-modulated signalswith chirping in erbium-doped fiber

Second-order distortion produced in an erbium-doped fiber amplifier (EDFA) is investigated theoretically and experimentally. Rate equations for intermodulation products are led by the perturbation method. From numerical calculation, it is shown that optimum combinations of input power to EDFA and signal wavelength exist that give a distortion-free condition, Improvement of the composite second-order (CSO) distortion, which results from the cancellation of the laser distortion and the gain tilt induced distortion, was confirmed for VHF multichannel transmission. Furthermore, CSO distortion-free transmission in cascaded EDFA's has been demonstrated for a 42-channel AM-SCM signal by experimentally determining the optimum operating condition of the EDFA such that each amplifier generates no additive distortion     

A multidimensional laser simulator for edge-emitters includingquantum carrier capture

A multidimensional semiconductor laser simulator is presented which follows a rate equation approach for the coupling between optics and electronics. Capture and emission rates for the bound and free carriers are used for the quantum well. The electronic equations and the optical equations are solved in a self-consistent manner for one, two, and three dimensions. As an example, an InGaAs quantum-well ridge laser is analyzed, and the multidimensional simulation approach for Fabry-Perot device structures is discussed. A three-dimensional (3-D) simulation of a device with a truncated contact shows the applicability of the simulator to complex laser cavity designs     

副载波多路复用模拟光传输系统中激光器非线性畸变的分析

本文主要分析副载波多路复用模拟光传输系统中激光器的非线性畸变，提出一个激光器非线性失真分析的完整的数学模型，特别考虑了多路副载波情况下激光器的削波影响。认真分析了ＱｕｎＳｈｉ等人的论文，对他们提出的传输系统中ＣＳＯ和ＣＴＢ的计算公式进行了改进，考虑了高阶失真项的影响。理论推导已为实验所得多路光纤ＣＡＴＶ链路中的ＣＳＯ和ＣＴＢ结果所证实。     

Linear antenna array synthesis using cat swarm optimization

Antenna arrays with high directivity and low side lobe levels need to be designed for increasing the efficiency of communication systems. A new evolutionary technique, cat swarm optimization (CSO), is proposed for the synthesis of linear antenna arrays. The CSO is a high performance computational method capable of solving linear and non-linear optimization problems. CSO is applied to optimize the antenna element positions for suppressing side lobe levels and for achieving nulls in desired directions. The steps involved in the problem formulation of the CSO are presented. Various design examples are considered and the obtained CSO based results are validated by comparing with the results obtained using particle swarm optimization (PSO) and ant colony optimization (ACO). The flexibility and ease of implementation of the CSO algorithm is evident from this analysis, showing the algorithm's usefulness in electromagnetic optimization problems.     

Numerical simulation of intensity and phase noise from extracted parameters for CW DFB lasers

A self-consistent numerical approach is demonstrated to analyze intensity and phase noise from experimentally extracted parameters for a continuous-wave distributed feedback (DFB) laser. The approach takes into account the intrinsic fluctuations of the photon number, carrier number, and phase. Values for the parameters appearing in the rate equations are extracted from the measured relative intensity noise spectra and linewidth of the laser. The simulation of the frequency spectra of intensity and phase noise of the DFB laser are performed by fast Fourier transform and exhibit good agreement with experimental results. The model presented here can readily be extended for the purpose of system simulations.     

Volterra series analysis of semiconductor laser diode

Theoretical models for laser nonlinearities are analyzed. Volterra transfer function G/sub n/ are calculated from the laser rate equations using an output-to-input approach. Nonlinear models for second-harmonic, third-harmonic, and two-tone third-order intermodulation distortions are calculated from G/sub n/. The transfer function-based models are simplified and a new equation for intermodulation distortion is developed. Comparisons with previous results are presented. It is suggested that this analytical technique offers a valuable tool for the performance analysis of future broadband optical communication systems.<>     

Transverse-mode competition effects observed in the numericalsimulation of transients in gain-guided semiconductor laser arrays

A numerical analysis of transient turn-on in a gain-guided semiconductor laser array is presented. The self-consistent approach, valid in the strong-coupling limit, treats the array as a single waveguide laser with a transversely varying refractive index. The program first solves for the modes of this system without considering stimulated emission. The overall modal gain is then inserted into the rate equations in order to calculate a photon density; this results in a new spatial gain distribution, which in turn causes changes to the modal intensity profiles. This analysis is used to find both steady-state results and instabilities which result from mode competition. The approach is to solve instantaneous eigenvalue equations     

Computer simulation of laser photon fluctuations: Theory of single-cavity laser

This paper is the first of a series devoted to theoretical studies of photon fluctuations in the light output of semiconductor injection lasers. Statistics on laser photon fluctuations are collected by means of a simulation of the dynamic behavior of the laser based on numerical solutions of noise driven laser rate equations. This first paper in the series introduces the noise driven rate equations for a single-cavity laser, explains the method used for their numerical solution, and discusses some approximate analytical results. The second paper presents results of photon counting statistics for the single-cavity laser collected from numerical solutions of the time dependent equations. Additional papers in this series will concentrate on coupled-cavity and distributed feedback lasers. Comparison of these statistical results will show clearly the advantage of coupled-cavity and distributed feedback laser designs over conventional single (Fabry-Perot) cavity injection lasers.     

Feedback sensitivity and coherence collapse threshold of semiconductor DFB lasers with complex structures

A general method for evaluating the feedback sensitivity of semiconductor lasers is proposed based on Green's functions approach. The rate equations derived in this paper generalize works already published to any type of laser cavities such as those with axially varying parameters. The variation of the lasing frequency occurring under external optical feedback is then used to predict the coherence collapse threshold. The approach is validated for conventional DFB lasers by comparing the calculated feedback sensitivity with those obtained from analytical expressions. Both feedback sensitivity and coherence collapse thresholds are then calculated and analyzed for DFB lasers with a chirped grating. A remarkable agreement on the critical feedback level between simulations and measurements is obtained for all the lasers under study.     

Nonlinear circuit analysis of harmonic and intermodulationdistortions in laser diodes under microwave direct modulation

A microwave nonlinear circuit analysis technique which can account for all known steady-state responses has been developed and applied to the large-signal characterization of directly modulation laser diodes. An equivalent circuit derived from the rate equations is used to model the laser diode. The proposed technique is based on a harmonic balance algorithm which represents two-tone inputs by describing frequencies. Second-harmonic and third-order intermodulation distortion results for a single-mode GaAlAs diode have been compared with corresponding measured data to validate the method. Aperiodic responses are detected by means of bifurcation theory prior to the harmonic balance analysis and are simulated in the time domain. Simulated results are shown to agree well with published measurements, and indicate the capability of using this approach for the computer-aided design of microwave fiber-optic transmitters     

Frequency- and time-dependent gain characteristics of dye lasers

The approach used by McCumber for treating phonon-terminated lasers is applied to investigate the gain properties of dye lasers and is extended to include effects arising from population buildup in the triplet-level system and associated triplet-triplet absorptive losses. The gain is expressed in terms of time-dependent excited-state populations and spectral emission and/or absorption functions. For a given optical-pump pulse, a computer program is used to solve rate equations for the populations up to threshold and to calculate the gain as a function of time and frequency. The gain varies with frequency over the broad fluorescence bands characteristic of dye molecules and with time until the threshold for laser action is reached. Experiments using rhodamine 6G verify the predicted dependence of the laser frequency and time of threshold on cavityQand demonstrate laser frequency tuning by adjusting the opening time of an intracavityQswitch. No variation of laser frequency is expected for fluorescing molecules exhibiting large Stokes shifts; this is observed for 7-hydroxycoumarin. Computer calculations of the gain for anthracene and rhodamine B illustrate the dependence of gain properties on the rate of intersystem crossing and triplet-triplet absorption. An estimate of the rate of intersystem crossing for rhodamine B in methanol is obtained from a comparison of predicted and observed laser threshold conditions. Requirements for achieving flashlamp-pumped laser action are shown to depend upon both flashlamp and dye properties and are analyzed using the above approach.     

声光调QCO_2激光器的理论计算和实验研究

采用谐振腔内插入声光调制器的方法进行了小型CO2激光器的调Q实验,并根据影响激光器输出的诸多因素,利用调Q脉冲激光器速率方程对该激光器输出的主要技术参数进行了理论计算,据此提出了声光调QCO2激光器优化设计的途径和方法。设计制成的声光调QCO2激光器获得峰值功率超过4000 W,激光脉冲宽度为180 ns,与理论计算基本一致。激光器脉冲重复频率调节范围1 Hz~100 kHz。理论分析和实验结果均证明,调Q晶体中超声场的渡越时间并不会影响输出激光的脉冲宽度,因此无需在腔内插入光学透镜进行光束直径的压缩变换;渡越时间的影响只是体现在延长了激光脉冲的建立时间上;激光器的最佳工作频率在1 kHz左右,这与CO2分子0001能级大约1 ms的辐射寿命相匹配,当频率超过1 kHz时,激光的脉冲宽度随着频率的增加而开始加宽。激光器通过光栅选线的设计方式实现了9.2~10.8μm的全波段波长调谐,测得激光输出谱线超过60条。     

Calculating the CSO/CTB spectrum of CATV amplifiers and opticalreceivers

The discrete CSO/CTB intermodulation distortion has a big influence on the CATV net quality. This article describes a new method to calculate the composite second order (CSO) and composite triple beat (CTB) intermodulation distortion spectrum for the full frequency range of a coaxial cable CATV amplifier for any input frequency plan. The calculation takes into account the output level ripple and preemphasis, using frequency dependent intermodulation coefficients. These coefficients have been established through CSO/CTB measurements on multichannel test systems for standard frequency plans at 5-8 intermodulation frequencies or on distortion arrays for the two (three) oscillator measuring test system. The defined intermodulation coefficients are unrelated to the frequency plan and the input/output level ripple. It is also possible to calculate the CSO/CTB spectrum caused by analogue channels within digital QAM channels. The results equally apply to optical CATV receivers. Simulation results have been verified using extensive data from multichannel measurement systems     

Dynamic behaviors of semiconductor lasers under strong sinusoidalcurrent modulation: modeling and experiments at 1.3 μm

The theoretical analysis is based on rate equations including gain-compression effects. General criteria are established to predict the existence of irregular behaviors. Experiments are performed on a single-mode buried-heterostructure InGaAsP laser at 1.3 μm. An original method is proposed to evaluate the parameters of the rate equations. Fully optical measurements are used. The nonlinear gain coefficient and the electrical response of the packaged laser are simultaneously determined from small-signal characteristics. Time-domain measurements show the three behaviors achieved with the laser, i.e., simple periodic, periodic with multiple spikes, and periodic doubling. Excellent agreement is found between experiments and calculations. Frequency-domain measurements are focused on distortions in periodic regimes. A quantitative limit of perturbation theories is given which corresponds to a second-order harmonic level exceeding -15 dB     

Time-dependent modeling of erbium-doped waveguide lasers in lithiumniobate pumped at 980 and 1480 nm

We have developed a rigorous phenomenological model for analyzing rare-earth doped waveguide lasers. The model is based on time-dependent laser rate equations for an arbitrary rare-earth-doped laser host with multiple energy levels. The rate equations are coupled with the laser signal and pump photon flux equations that have time-dependent boundary conditions. The formulation results in a large and stiff set of transcendental and coupled differential equations that are solved using finite difference discretization and the method of lines. Solutions for the laser signal power, pump power, and populations of ion energy levels as functions of space and time are obtained for waveguide lasers. We have used the model to predict the CW characteristics and Q-switched performance of waveguide lasers in lithium niobate pumped by a 980-nm source. Our analysis shows that hole burning can occur in erbium-doped lithium niobate lasers because of the intensity variation across guided transverse modes. We have predicted that Q-switch pulse peak powers can exceed 1 kW with pulsewidths less than 1 ns. Moreover, we have compared the CW and Q-switched performance of 980-nm pumped waveguide lasers and 1480 nm pumped waveguide lasers. An analysis of the effects of host- and fabrication-dependent parameters on CW 980-nm pumped lasers is included. These parameters include cooperative upconversion, excited state absorption, doping concentration, excess waveguide loss, cavity length, and mirror reflectance values. We demonstrate good quantitative agreement with waveguide laser experimental data obtained in our laboratory and with results from the literature     

An accurate rate-equation description for DFB lasers and someinteresting solutions

Starting from the coupled-wave equations, we have derived an alternative set of rate equations which are valid for most single-section distributed feedback (DFB) lasers. These rate equations are in many respects more useful than the conventional rate equations and have also been used to derive the influence of spatial hole burning on characteristics such as the chirp, the linewidth, or the harmonic distortion. Numerical results are presented for a DFB laser with both facets cleaved, AR-coated, and for a λ/4-shifted DFB laser     

Assessment of laser noise influence on direct-detection transmission system performance

A new semi-analytical method of estimating the influence of laser noise on directly modulated direct-detection transmission system performance is proposed. Its accuracy is assessed for different propagation situations and receiver noise type dominance using rigorous mixed semi-analytical simulation. Two different relative intensity noise (RIN) powers at receiver input associated with the two laser currents of the binary levels are considered, and not just a single one corresponding to the laser average current as in other published works. It is shown that, to perform rigorous simulation, suitable methods of solving stochastic laser rate equations should be used, and a number of samples high enough in order to stabilize the sensitivity estimator should be considered. It has been found that, for power penalties of about 1 dB, more than 150 samples may be necessary. For a power penalty due to laser noise of about 4.5 dB, discrepancies not exceeding 0.4 dB are observed between the results obtained using the new semi-analytical approach and using the rigorous simulation. It is shown that the new semi-analytical approach gives more precise results than other approach currently used. For a power penalty due to laser noise not exceeding 2 dB, the discrepancies between the two approaches can reach roughly 1 dB. It is shown that these discrepancies can increase with the laser linewidth. Explicit expressions for system power penalty due to the RIN at the fiber output are presented, for both signal-independent and -dependent noise dominance. It is shown that these expressions give good upper bounds of the real power penalties.     

Rate equation model of a coupled-cavity laser

We derive a novel rate equation system for a laser consisting of two coupled cavities arranged in tandem. 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 conventional laser rate equations. This paper discusses the initial numerical evaluation of our coupled-cavity laser model which indicates that the laser tends to oscillate more readily in a single longitudinal mode than a single-cavity laser of comparable length. The enhanced mode selectivity stems from the constructive and destructive interference of the fields in the two coupled cavities. Suppression of secondary longitudinal modes by more than 20 dB is readily obtainable. The coupled-cavity laser maintains single-wavelength operation even if the peak of the gain profile shifts over a certain wavelength range. However, when it finally responds to a sufficiently large shift of the gain profile, it does so by jumping discontinuously to a new (single) operating wavelength. Further investigations of frequency tuning by means of the injection current as well as studies of the frequency instability due to temperature and refractive index variations will be reported in a separate publication.     

A Novel Approach of Modeling Cladding-Pumped Highly Er–Yb Co-Doped Fiber Amplifiers

We present a new modeling method for cladding-pumped highly Er-Yb co-doped fiber amplifiers. The method combines the beam propagation method (BPM) for the field propagation and nonlinear rate equations for the laser medium. The pump absorption, which is obtained numerically from the nonlinear rate equations, is used in BPM calculations of the field propagation. As a result, our method can effectively deal with difficult issues such as the multimode nature of cladding pumped schemes even in complicated structures, as well as strong nonlinearities in highly Er-Yb-doped fiber amplifiers. The simulation results are in very good agreement with experiments having different structures and different concentrations of Er-Yb. The method is particularly well suited to active fibers with low amplified spontaneous emission power, but it can also be developed further for more general cases.