田學農，高建軍

(1．蘇州科技學院電子與信息工程學院，江蘇蘇州215009;2．華東師范大學信息科學技術學院，上海200241)

TIAN Xuenong1，GAO Jianjun2*

(1．College of Electronic and Information Engineering，Suzhou University of Science and Technology，Suzhou Jiangsu 215009，China;2．School of Information Science and Technology，East China Normal University，Shanghai200241，China)

Modeling of semiconductor lasers is crucial for the designers of opto-electrical systems such as radio over fiber links［1－3］．Various circuit models for semiconductor lasers have been proposed to reflect the characteristics of lasers in the simulation．Although the models proposed so far can meet the requirements to some extent in the engineering design，they are always only valid under some constraint conditions and always have errors with the measurement results．The development of more accurate and comprehensive model is necessary［4－6］．

Some earlier models for semiconductor lasers have errors for reflection coefficient of semiconductor lasers in low frequency domain with the measurement results．Prof．Gao Jianjun proposed a new model which introduce a diode at the input port of lasers and the optical part and electrical part of the model is separated［7］．Using Gao’s model the simulation results of the reflection coefficient at low frequency domain agree better with the measurement results than conventional models．However，that model is only verified with small signal circuit model of lasers and the large signal simulation with Tucker’s circuit model of the laser is not converged at some bias currents．In this paper we verified Gao’s idea with a SDD(Symbolic Defined Devices)based model in ADS(Advanced Design Systems)．The convergence of the model is more robust and it can accurately simulate the low frequency reflection coefficient of semiconductor lasers in large signal simulation．

1 Model Development

The improved model proposed by Gao is shown in Fig．1． Compared with conventional models for semiconductor lasers，an independent Schockley diode DScand a current source IINare added．The diode DScis used to simulate the input electrical characteristic．IINis the current injected into the active region of the lasers and is equal to the current passed through the diode DSc．With this new model the electrical part and the optical part of the lasers are separated．

Fig．1 Improved model of semiconductor lasers

The modeling of intrinsic laser is based on the rate equations and is implemented using SDD component in ADS．To improve the convergence of the model，the following transformation is taken for the rate equations．

Where N is the carrier density，S is the photon density，V is the voltage across the laser，η is the diode ideality factor，k is Boltzmann constant，T is the laser’s temperature，Neis the equilibrium carrier density，m is a new variable for the transformation，δis a small constant to improve the convergence，Snis the normalization constant，and Г is the optical confinement factor．

After the transformation，the following equations are obtained

Fig．3 Simulation of the improved model of semiconductor lasers

Whereτnis the carrier recombination lifetime，τpis the photo lifetime，β is the spontaneous emission coupling coefficient，ε is the gain compression factor，Nomis the carrier transparency density，IAis the current injected into the laser，g0is the gain coefficient．

Equations(3)and(4)are written into the SDD component of ADSas shown in Fig．2．

Fig．2 SDD implementation of the intrinsic semiconductor lasers

2 Simulation Results

The simulation setup is shown is Fig．3．The DC，AC characteristics and S parameters of the lasers can be simulated with the setup．

Using the proposed model above，the input characteristics of a laser is simulated and analyzed in ADS．The intrinsic and parasitic parameters of the lasers are taken from Ref．［8］．The modeled and simulated I－V performance of the input port of the laser is shown in Fig．4．

Fig．4 Measued and simulated I－V characteristics

Fig．5 compares the modeled and measured reflection coefficient for the laser in the frequency range 0．1 GHz－30 GHz under the bias current of 20 mA．It can be found that the improved model is more accurate than the conventional models，especially for the magnitude of the reflection coefficient in the low frequency range．

Fig．5 Comparison of modeled and measured reflection coefficient for the laser

Fig．6 Comparison of the reflection coefficient for the laser at different bias conditions

Fig．6 shows the variation of the magnitude of the reflection coefficient of the laser with different bias currents using the proposed model in this paper．It is shown that the magnitude of the reflection coefficient increases with the increasing of the bias currents．

3 Conclusions

An implementation of the laser model proposed by Gao is realized using the SDD component in ADS．The convergence of the implementation is more robust than conventional counterpart．Simulation results show that the model agrees well with the measured results and the reflection coefficient of the lasers in low frequency range can be more accurately simulated than conventional models．It is the first published result of the large signal verification of Gao’s model as we know．The proposed implementation would be helpful for the characterization of the semiconductor lasers and the design of opto-electrical systems such as radio over fiber applications．

Acknowledgement

This work was supported by the State Key Laboratory of Advanced Optical Communication Systems and Networks，Shanghai Jiao Tong University，China．

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