THE high channel-to-channel crosstalk is a principal drawback

IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 40, NO. 5, MAY 2004 513 Detailed Model and Investigation of Gain Saturation and Carrier Spatial Hole Burni...
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IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 40, NO. 5, MAY 2004

513

Detailed Model and Investigation of Gain Saturation and Carrier Spatial Hole Burning for a Semiconductor Optical Amplifier With Gain Clamping by a Vertical Laser Field Chao-Yuan Jin, Yong-Zhen Huang, Senior Member, IEEE, Li-Juan Yu, and Shen-ling Deng

Abstract—A detailed model for semiconductor linear optical amplifiers (LOAs) with gain clamping by a vertical laser field is presented, which accounts the carrier and photon density distribution in the longitudinal direction as well as the facet reflectivity. The photon iterative method is used in the simulation with output amplified spontaneous emission spectrum in the wide band as iterative variables. The gain saturation behaviors and the noise figure are numerically simulated, and the variation of longitudinal carrier density with the input power is presented which is associated with the ON–OFF state of the vertical lasers. The results show that the LOA can have a gain spectrum clamped in a wide wavelength range and have almost the same value of noise figure as that of conventional semiconductor optical amplifiers (SOAs). Numerical results also show that an LOA can have a noise figure about 2 dB less than that of the SOA gain clamped by a distributed Bragg reflector laser. Index Terms—Gain clamping, linear optical amplifier (LOA), noise figure, rate equations, semiconductor optical amplifier (SOA).

I. INTRODUCTION

T

HE high channel-to-channel crosstalk is a principal drawback for using conventional semiconductor optical amplifiers (SOAs) in wavelength division multiplexing (WDM) applications. This problem can be overcome by using gain-clamped semiconductor optical amplifiers (GCSOAs), which run a continuous lasing mode throughout the cavity in order to provide a reservoir of photons to dampen gain fluctuations. Conventionally, the gain clamping was achieved by fabricating two distributed Bragg reflector (DBR) mirrors on both ends of the amplifier [1]–[3]. The attractive device characteristics of the GCSOA have received considerable attention and some numerical models were developed [4]–[6]. Recently, the linear optical amplifier (LOA) with integrated vertical lasers was introduced [7], which shows a remarkable linear amplification in the presence of power transients, and the wavelength conversion based on the LOA was demonstrated [8]. The transient behavior and noise characteristics were analyzed for the SOA with

the gain clamping by a vertical cavity laser [9]. However, most steady-state characteristics, especially the carrier distribution in the longitudinal cavity and its remarkable contribution to the gain clamping of the LOA, were not mentioned yet. In this paper, we numerically simulate the gain-clamping behaviors and associated carrier spatial hole burning in the LOA, and compare the noise figure for the LOA, SOA, and GCSOA. Because numerical simulation for SOA, especially for GCSOA, is a time consumption computation task, a powerful simulating technique is greatly demanded for thoroughly modeling the device characteristics. Recently, we shown that photon iterative method, which choose the output photon spectrum as the iteration variables for solving the rate equations, is a much faster and more efficient algorithm than the conventional approach with the carrier density distribution as iterative variables [10]. A detailed position dependent rate equation model is used to analyze the gain saturation and carrier spatial hole burning in the LOA based on the photon iterative method. The results show that the nearly constant distribution of carrier density is the main reason for the low noise figure and wideband gain clamping, which is better than the characteristics of the GCSOA. II. RATE EQUATIONS MODEL Gain clamping with a vertical laser can be realized by combing vertical-cavity lasers (VCLs) in the direction perpendicular to the amplifier cavity, as shown in Fig. 1. A detailed model of the LOA is described by four equations

Manuscript received November 6, 2003; revised January 20, 2004. This work was supported by the National Nature Science Foundation of China under Grant 60225011, the Major State Basic Research Program under Grant G2000036606, and the Project of “863” plan under Grant 2003AA311070. The authors are with the State Key Laboratory on Integrated Optoelectronics, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China. Digital Object Identifier 10.1109/JQE.2004.826427 0018-9197/04$20.00 © 2004 IEEE

(1)

(2)

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IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 40, NO. 5, MAY 2004

m s are used in the numerical and simulation. At the facets of the amplifier’s cavity, we use the following boundary conditions for the signal and ASE power: (8) (9) (10) (11)

Fig. 1. Schematic structure of the LOA with the vertical laser field.

and are the power reflection coefficients at the where amplifier’s input and output facets with the value of , and is the input signal power. (3) III. GAIN AND SPONTANEOUS EMISSION (4) and are frequencies where is the photon frequency, of input signal and laser field of the VCL. The superscript ‘ ’ presents the signal and the spontaneous emission propagating in ans represent the forward and backward directions. the spontaneous emission coupled into the ASE and the vertical is the gain coefficient. Equation (1) is the laser field, position-dependent rate equation for the carrier density along the cavity, (2) is the spatially averaged rate equation for of the VCLs and the traveling-wave the photon rate [given equations in both directions for the injected signals by (3)] and the whole spectrum of amplified spontaneous [given by (4)]. In the carrier rate equation emission (ASE) (1), a uniform current injection into the active layer is assumed and the carrier transport effects in longitudinal direction are ignored. The reflectivity and the lasing wavelength of the VCL and nm, respectively. are chosen as mm, and the width and The length of the LOA is m and m, thickness of the active region are and respectively, with the optical confinement factor. the absorption loss cm , and the effective cavity m. is the group speed of the length of the VCL is signal with the group refractive index of 3.55. The threshold of the VCL can be defined as [11] gain

We simply take the material gain spectrum of bulk material for simulation [12], [13] as follows:

(12) and are the Fermi–Dirac distributions in the where conduction band and valence band, the radiative carrier recom, and is the bination lifetime is defined by bandgap energy with the following bandgap shrinkage [14]: (13) is taken to be where the bandgap shrinkage coefficient eVm. is the bandgap energy without the injected carrier. The effective masses of the electron and the heavy hole kg and are taken to be kg. The material gain can also be expressed as the stimulated emission minus stimulated absorption as follows: (14) and are the rates per unit length of stimulated where can be defined as emission and absorption, and (15)

(5)

From the Einstein relations, the spontaneous emission specis related to the stimulated emission by trum

Assuming that the VCL is perfectly confined laterally, the opof the VCL is given as tical confinement factor

(16)

(6)

Based on the derivation process of the spontaneous emission factor in [15], the spontaneous emission coupled into the ASE spectrum in the frequency range can be expressed as

where

is the propagation constant. The recombination rates are given by (7) (17)

is the defect and linear radiation recombination cowhere is the spontaneous radiation recombination coefficients, efficient, and is the Auger recombination coefficient. The s m s , values of

If

is small enough,

can be written as (18)

JIN et al.: DETAILED MODEL AND INVESTIGATION OF GAIN SATURATION AND CARRIER SHB FOR A SOA WITH GAIN CLAMPING

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and the spontaneous emission coupled into the lasing mode of the VCL can be approximately written as (19) where

is the longitudinal mode interval of the VCL. IV. SIMULATION RESULTS

In this section, the photon iterative method [10] is employed to numerically solve the above rate equations given above. In secthe simulation, the length of the LOA is split into tions. We assume that the carrier density is uniform and an independent VCL exists in each section. The spontaneous emission spectrum is divided into sections with frequency interval Hz, and the wavelength of the input signal is taken to be 1550 nm. The selection of between the lasing wavelength and maximum gain wavelength is very important, because an appropriate value of will give enough gain to the amplifier while ensuring the lasing of the VCLs. In the steady-state simulation, we solve the VCL photon density from (2) and insert it into (1), and then obtain the following steady-state carrier rate equation for each section:

Fig. 2. Total lasing mode power of the VCL and the LOA gain versus the injection current.

(20) First, we choose the output signal power and ASE spectrum as the iterative variables to solve the carrier density in each section from (20) with a set of initial values, then calculate the output signal power and ASE spectrum again according to (3) and (4) based on the obtained carrier density in each section. In the next iterative circle, we choose the average of the initial values and the calculated values of the output signal power and ASE spectrum as the new initial values for calculating the carrier density from (20) again [10]. Good convergence can be obtained by this photon iterative method with relative error less than after 15 iterative circles. In Fig. 2, the total output power of the VCL and LOA gain are plotted as functions of the injection current. The results show that the threshold current for the VCL is about 75 mA and the LOA gain is well clamped on a constant value by lasing mode. The carrier density distributions are plotted in Fig. 3 at the injection currents of 100, 120, 150, 300, and 500 mA. The carrier density is clamped by the threshold condition of the VCL and has nearly uniform distribution at high injection currents, which is greatly different from the carrier distribution in the GCSOA. In Fig. 4, we plot the fiber-to-fiber gain of the LOA versus the output signal power with the two-side optical fiber coupling loss of 6 dB. The gain saturation curve agrees very well with the experiment results [7]. The amplifier’s gain is well clamped until the lasing of the VCL is turned off by the input signal. At an injection current of 200 mA, the maximum gain is about 17 dB and the saturation output power is 15 dBm. At an injection current

Fig. 3. Variance of the carrier density distribution at the injection current of 100, 120, 150, 300, and 500 mA.

Fig. 4. Gain of the LOA versus output signal power at different injection currents and reflectivities.

of 100 mA, the maximum gain keeps the same, but the saturation output power is descend to 9.5 dBm. The detailed relationship between the saturation output power and applied current is plotted in Fig. 5, as the saturation output power is increased with the increasing applied current. In Fig. 4, we also plot amplifier

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IEEE JOURNAL OF QUANTUM ELECTRONICS, VOL. 40, NO. 5, MAY 2004

Fig. 5. Saturation output power versus the injection current.

gain versus output power for an LOA with a larger VCL reflectivity of 0.996, which corresponds to the VCL threshold current of 65 mA. The amplifier gain decreases to 13.2 dB due to the decrease of the VCL threshold gain, but the saturation output power maintains the same value as is the case with the VCL reflectivity of 0.994 and the same current of 200 mA. The VCL is usually turned off as the output power reaches the saturation output power. Thus, the saturation output power is negligbly affected by the threshold gain of the VCL. In Fig. 6, the longitudinal carrier density profiles are plotted under different input signal powers for the LOA with an injection current of 200 mA. When the input power is larger than 10 dBm, the carrier density near the output facet begins to fall below threshold. Fig. 6(b) shows the detailed variation of carrier density under low input power. When the VCL lasing mode does not turn off, the carrier density keeps a nearly constant value of m . With the increase of the input signal, the carrier density in the output side first drops below the threshold carrier density. The range of low carrier density increases with the further increase of the input signal, and the carrier density finally approaches the transparent carrier density. Output power distributions of VCLs along the amplifier’s cavity are shown in Fig. 7 for the LOA with an injection current of 200 mA and the input signal of , and 15 dBm. The output power of the VCL decreases from 40 to about 10 W/ m with the increase of the input signal. The output ASE spectra of the LOA at mA and the input signal power of , and 10 dBm are plotted in Fig. 8. The output ASE decreases with the increase of input power slowly as the input signal power is less than the saturating input power, which is about 10 dBm, and then the output ASE decreases quickly as the input signal power increases from 10 to 5 dBm. Finally, we calculate the noise figure for the LOA and compare the results with conventional SOAs and GCSOAs. The noise figure can be expressed as [16] (21) is the bandwidth of the ASE where is the device gain and filter in front of the detector, which is taken to be nm. Fig. 9(a) shows the noise figure and gain versus the input signal

Fig. 6. (a) Longitudinal carrier density profiles at I = 200 mA and input signal power P = 30; 10; 5; 0; 5; 10, and 15 dBm. (b) The detailed distribution of carrier density at I = 200 mA and input signal power P = 30; 20, and 15 dBm.

0 0 0

0 0

Fig. 7. I

0

Distribution of output power of VCLs along the amplifier’s cavity at P = 30; 10; 5; 0; 5; 10, and

= 200 mA and input signal power

15 dBm.

0 0 0

power for the LOA at mA. The noise figure keeps constant until the input signal power is larger than 0 dBm. Fig. 9(b) shows the gain saturation curves of [10] and the corresponding noise figures for the GCSOA at mA and a conventional SOA at mA. For the LOA, the noise figure first

JIN et al.: DETAILED MODEL AND INVESTIGATION OF GAIN SATURATION AND CARRIER SHB FOR A SOA WITH GAIN CLAMPING

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Fig. 8. Spectral density of output ASE for the LOA at I = 200 mA and input signal power P = 30; 10; 5; 0, and 10 dBm.

0 0 0

Fig. 10. (a) Gain spectra and (b) the noise figure versus wavelength for the LOA at injection currents of 50, 70, 80, and 200 mA.

Fig. 9. (a) The gain and noise figure of the LOA versus input signal power at I = 200 mA. (b) Device gain and noise figure versus input signal power for the GCSOA at I = 100 mA and the conventional SOA at I = 32 mA. The results of the GCSOA and SOA are plotted as squares and circles, respectively.

decreases from 6.29 to 6.27 dB as the input power increases from 20 to 5 dBm, and then increases as the input power further increases with the noise figure of 6.5 and 9.1 dB at the

input power of 5 and 15 dBm. The noise figure of the conventional SOA decreases from 6.28 to 6.0 dB with the increase of the input power, and then increases with the input power, as it is larger than 15 dBm. The results show that the LOA has almost the same value of the noise figure as the conventional SOA in a low input signal range. The noise figure of the GCSOA decreases from 8.5 to 6.6 dB as the input power increases from 20 to 10 dBm, and then again increases with the increase of the input power. The GCSOA shows a higher noise figure due to the remarkable longitudinal carrier spatial hole burning, which affects the ASE greatly [5]. When the gain clamping is turned off, the GCSOA’s noise figure is similar to that of the conventional SOA. But, for the LOA, before the turn-off of the VCL, there is little longitudinal spatial hole burning, and after the turn-off, the carrier density was changed consecutively and slowly along the longitudinal direction. Also, the noise figure of the LOA is similar to that of the conventional SOA rather than that of the GCSOA. The noise figure of the GCSOA is 2.2 dB larger than that of the conventional SOA and the LOA at low input power, which is in agreement with the results of [17], where the effect of DBR waveguide on the input signal was also considered. In Fig. 10, we plot the gain spectra and noise figure versus wavelength at the injection currents of 50, 70, 80, and 200 mA

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for the LOA. The gain is very low at a current of 50 mA, and the corresponding noise figure has a minimum value of about 7.34 dB at a wavelength of 1598 nm, which is larger than that at the higher injection current. The gain spectra are well clamped in a wide spectrum range as the current increases from 80 to 200 mA, which is better than the performance of the GCSOA. The wideband gain clamping is due to the stable carrier distribution in the longitudinal direction. In the GCSOA, the carrier distribution can only keep the average carrier density close to an approximate constant value, but for different wavelengths, under different applied currents, the remarkable longitudinal spatial hole burning will bring small changes to device gain [5]. The results also show that the noise figure increases with the decrease of wavelength because the gain spectrum decreases much faster than the ASE spectrum in the short-wavelength side. V. CONCLUSION We have introduced a detailed model for analyzing SOAs with gain clamping by a vertical laser field. The photon iterative method [10] is used in the numerical simulation, which can provide accurate results in a short computing time. The gain saturation and associated longitudinal spatial hole burning for carrier density are analyzed for the LOA. The noise figure is also calculated for the LOA and compared with that of the conventional SOA and the GCSOA. The LOA can be gain clamped over a wide wavelength range and demonstrates a low noise figure compared to conventional GCSOAs. REFERENCES [1] B. Bauer, F. Henry, and R. Shimpe, “Gain stabilization of a semiconductor optical amplifier by distributed feedback,” IEEE Photon. Technol. Lett., vol. 6, pp. 182–185, Feb. 1994. [2] J. C. Simon, P. Doussierre, P. Lamouler, I. Valiente, and F. Riou, “Travelling wave semiconductor optical amplifier with reduced nonlinear distortions,” Electron. Lett., vol. 30, no. 1, pp. 49–50, Jan. 1994. [3] L. F. Tiemeijer, P. J. A. Thijs, T. V. Dongen, J. J. M. Binsma, E. J. Jansen, and H. R. J. R. van Helleputte, “Reduced intermodulation distortion in 1300 nm gain-clamped MQW laser amplifiers,” IEEE Photon. Technol. Lett., vol. 7, pp. 284–286, Mar. 1995. [4] J. Sun, G. Morthier, and R. Baets, “Numerical and theoretical study of the crosstalk in gain clamped semiconductor optical amplifiers,” IEEE J. Select. Topics Quantum Electron., vol. 3, pp. 1162–1167, Oct. 1997. [5] J. L. Plummekers, M. A. Dupertuis, T. Hessler, P. E. Selbmann, S. Haacke, and B. Deveaud, “Longitudinal spatial hole burning and associated nonlinear gain in gain-clamped semiconductor optical amplifiers,” IEEE J. Quantum Electron., vol. 34, pp. 879–886, May 1998. [6] G. Giuliani and D. D’Alessandro, “Noise analysis of conventional and gain-clamped semiconductor optical amplifiers,” J. Lightwave. Technol., vol. 18, pp. 1256–1263, Sept. 2000. [7] D. A. Francis, S. P. Dijaili, and J. D. Walker, “A single-chip linear optical amplifier,” in Proc. Optical Fiber Communication Conf. (OFC2001), Anaheim, CA, Mar. 2001. paper: PD13. [8] J. Lwuthold, K. Dreyer, G. van den Hoven, and J. Lambe, “Linear all-optical wavelength conversion based on linear optical amplifiers,” in Proc. Optical Fiber Communication Conf. (OFC2002), Anaheim, CA, Mar. 2002. paper: ThDD5. [9] J. Oksanen and J. Tulkki, “On crosstalk and noise in an optical amplifier with gain clamping by vertical laser field,” J. Lightwave Technol., vol. 21, pp. 1914–1919, Sept. 2003.

[10] C. Y. Jin, W. H. Guo, Y. Z. Huang, and L. J. Yu, “Photon iterative numerical technique for steady-state simulation of gain-clamped semiconductor optical amplifiers,” IEE Proc. Optoelectron., vol. 150, no. 6, pp. 503–507, Dec. 2003. [11] L. A. Coldren and S. W. Corzine, Diode Lasers and Photonic Integrated Circuits. New York: Wiley, 1995. [12] A. Yariv, Optical Electronics. New York: HWR Int., 1985. [13] M. J. Connelly, “Wideband semiconductor optical amplifier steady-state numerical model,” IEEE J. Quantum Electron., vol. 37, pp. 439–447, Mar. 2001. [14] S. Adachi, GaAs and Related Materials, Singapore: World Scientific, 1994. [15] K. Petermann, “Calculated spontaneous emission factor for double-heterostructure injection lasers with gain-induced waveguiding,” IEEE J. Quantum Electron., vol. QE-15, pp. 566–570, July 1979. [16] H. Haus, “The noise figure of optical amplifiers,” IEEE Photon. Technol. Lett., vol. 10, pp. 1602–1604, Nov. 1998. [17] D. Wolfson, S. L. Danielsen, C. Joergensen, B. Mikkelsen, and K. E. Stubkjaer, “Detailed theoretical investigation of the input power dynamic range for gain-clamped semiconductor optical amplifier gates at 10 Gb/s,” IEEE Photon. Technol. Lett., vol. 10, pp. 1241–1243, Sept. 1998.

Chao-Yuan Jin was born in Shanxi Province, China, in 1978. He received the B.Sc. degree in physics from Nanjing University, Nanjing, China, in 2000, and the M.Sc. degree in microelectronics and solid-state electronics from the Chinese Academy of Sciences, Beijing, in 2003. Since 2003, he has been with the Institute of Semiconductors, Chinese Academy of Sciences, working on material growth by metal–organic chemical vapor deposition and the fabrication and simulation of semiconductor optical amplifiers.

Yong-Zhen Huang (M’95–SM’01) was born in Fujian Province, China, in 1963. He received the B.Sc., M.Sc., and Ph.D. degrees in physics from Peking University, Beijing, China, in 1983, 1986, and 1989, respectively. In 1989, he joined the Institute of Semiconductors, Chinese Academy of Sciences, Beijing, China, where he worked on the tunneling time for quantum barriers, asymmetric Fabry–Perot cavity light modulators, and vertical-cavity light-emitting lasers (VCSELs). In 1994, he was a Visiting Scholar at BT Laboratories, Ipswich, U.K., where he was involved in the fabrication of the 1550-nm InGaAsP VCSEL. Since 1997, he has been a Professor with the Institute of Semiconductors, Chinese Academy of Sciences, and is the Director of the Optoelectronic R&D center. His current research interests involved microcavity lasers, semiconductor optical amplifiers, and photonic crystals.

Li-Juan Yu was born in Heilongjiang Province, China, in 1963. She received the B.S. and M.Sc. degrees in solid physics from Jilin University, Changchun, China, in 1986 and 1989, respectively, and the Ph.D. degree in microelectronics from Xi’an Jiaotong University, Xi’an, China, in 2000. She joined the Institute of Semiconductors, Chinese Academy of Sciences, Beijing, China, in 2000, working on material growth by metal–organic chemical vapor deposition and the fabrication process of semiconductor optical amplifiers. She is currently an Associate Research Professor with the Institute of Semiconductors, Chinese Academy of Sciences, with research interests in material growth and process techniques for optoelectronic devices.

Sheng-ling Deng was born in Hubei Province, China, in 1979. He received the B.Sc. degree in physics from Nanjing University, Nanjing, China, in 2002, and is currently working toward the M.Sc. degree at the Institution of Semiconductors, Chinese Academy of Sciences, Beijing, China. His current research interest is the simulation of semiconductor optical amplifiers and quantum dot lasers.

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