A unified circuit model for static and dynamic analyses of semiconductor optical amplifiers and laser diodes

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A uniﬁed circuit model for static and dynamic analyses

of semiconductor optical ampliﬁers and laser diodes

Jau-Ji Jou

a,*

, Cheng-Kuang Liu

b

, San-Liang Lee

b

a_{Department of Electronic Engineering, National Kaohsiung University of Applied Sciences, 415, Chien-Kung Road, Kaohsiung 807, Taiwan, ROC} b_{Department of Electronic Engineering, National Taiwan University of Science and Technology, 43, Keelung Road., Sec. 4, Taipei 106, Taiwan, ROC}

Received 6 March 2006; received in revised form 5 January 2007; accepted 31 January 2007

The review of this paper was arranged by Prof. Y. Arakawa

Abstract

Semiconductor optical amplifiers (SOAs) and laser diodes (LDs) are important components for optical systems. The structure and principle of SOAs and LDs are similar. In this paper, we have proposed a unified equivalent circuit model, which includes time delay circuit and different boundary conditions, for the simulations of traveling wave (TW) SOAs, Fabry–Perot (FP) SOAs and LDs. The effect of amplified spontaneous emission on FP-SOAs is also taken into account. Using this circuit model, our simulation results are in good agreement with published results for SOAs. This model has also been applied to analyze the static and dynamic behavior in LDs. A good agreement between our simulated results and the theoretical calculations is observed for LDs.

Keywords: Semiconductor optical ampliﬁer; Laser diode; Circuit model

1. Introduction

Semiconductor optical amplifiers (SOAs) are important components for optical networks. They are very attractive for their wide gain spectrum, and capability of integration with other devices. In the linear regime, they can be used for both booster and in-line amplifiers [1–3]. Also, much research activities have been done on all-optical signal pro-cessing with SOAs [4,5]. Laser diodes (LDs) are similar devices to SOAs, and they also are the key components for various applications ranging from end and high-speed (i.e. fiber communications, and compact-disc play-ers) to low-end and low-speed (i.e. laser pointers, and laser displays) systems.

There are two primary types of SOAs: traveling wave (TW) SOAs and Fabry–Perot (FP) SOAs. The principle of TW-SOA and FP-SOA is identical, i.e. intrinsic

stimu-lated light amplification. The difference between TW-SOA and FP-TW-SOA is reflectivity of cavity facets. The internal reflectivity of FP-SOA is higher than TW-SOA. Actually, an FP-SOA can be regarded as a FP-LD that is biased below the threshold current. The active layer of an SOA has a positive medium gain but not large enough for laser emission.

Electrical equivalent circuit models for optical compo-nents are useful as they allow existing, well-developed circuit simulators to be used in design and analysis of opto-electronic devices [6–8]. A circuit simulator also allows integration with electrical components (package parasitic, laser driver circuit, etc.). Equivalent circuit models have been separately reported for LDs [9–11] and SOAs [12– 14]. However, the principles of SOAs and LDs are extre-mely similar. In this paper, we ﬁrst present a uniﬁed equiv-alent circuit model for SOAs and LDs.

Our circuit model is described in Section2. In Sections3 and 4, this model is validated by the simulations of other workers for SOAs, and the static and dynamic behavior

*

Corresponding author. Tel.: +886 7 3814526; fax: +886 7 3811182. E-mail address:jjjou@cc.kuas.edu.tw(J.-J. Jou).

www.elsevier.com/locate/sse Solid-State Electronics 51 (2007) 360–365

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fp ¼ 1 2p tgatot RspðNthÞ Nth I=Ith 1 1 N0=Nth 0:5 ð13Þ The peak frequency as a function of bias current is shown inFig. 6b. The circle keys exhibit our simulations and the results of Eq.(13)are represented by the solid curve. Our simulations are in good agreement with the results of this formula.

We also have analyzed the transient responses of laser diodes during the switching of current. The feature of relaxation oscillation and turn-on delay can be observed in our simulation, as shown in Fig. 7a. When the turn-on current is higher, the relaxation frequency becomes higher and turn-on delay time is shorter. The turn-on delay time and the relaxation frequency can be formularized as [19], td¼ Nth RspðNthÞ giI=ðqV Þ giI=ðqV Þ RspðNthÞ ð14Þ fr¼ 1 2p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð2pfpÞ 2 a2 q ð15Þ where a¼1 2 dRsp dN N¼Nth þ1 2tgatotð2pfpÞ 2 . As shown in

Fig. 7b, the circle keys and the square keys represent our simulations for the turn-on delay time and the relaxation frequency, respectively. The solid curves are the results of Eqs.(14) and (15). Our simulations are in agreement with the results of these formulas.

5. Conclusions

We have proposed a unified equivalent circuit model of semiconductor optical amplifiers and laser diodes. Through the aid of SPICE circuit simulator, it is convenient to implement our model. The model has been verified by ana-lyzing (1) the gain against input signal power in FP-SOAs and TW-SOAs and (2) the L–I curve, small signal response, and pulse response in laser diodes. The simulation results of our model showed a good agreement with the published results. It can be extended to include other effects or devices such as modulators, fibers, multiplexers, and parasitic com-ponents. The model may be of great value for integrated circuit designers requiring an equivalent circuit model for the optical source or amplifier of the optical communica-tion systems in order to simulate accurately the mixed pho-tonic/electronic modules.

Acknowledgements

This work was supported by the National Science Council, Taipei, Taiwan, ROC, under project Nos. NSC-93-2215–E-151-004, NSC-95-2219–E-011-005, and NSC-95-2219–E-011-002. The authors would like to thank Chip Implementation Center for providing the simulation software.

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