## Black-box model for the complete characterization of the spectral gain and noise in semiconductor optical amplifiers

Optics Express, Vol. 14, Issue 4, pp. 1626-1631 (2006)

http://dx.doi.org/10.1364/OE.14.001626

Acrobat PDF (693 KB)

### Abstract

A Black Box Model for the quick complete characterization of the optical gain and amplified spontaneous emission noise in Semiconductor Optical Amplifiers is presented and verified experimentally. This model provides good accuracy, even neglecting third order terms in the spectral gain shift, and can provide cost reduction in SOA characterization and design as well as provide simple algorithms for hybrid integration in-package control.

© 2006 Optical Society of America

## 1. Introduction

2. K. Stubkjaer, “Semiconductor optical amplifier-based all-optical gates for high-speed optical processing,” IEEE J. Sel. Opt. Quantum Electron. **6**, 1428–1435 (2000). [CrossRef]

2. K. Stubkjaer, “Semiconductor optical amplifier-based all-optical gates for high-speed optical processing,” IEEE J. Sel. Opt. Quantum Electron. **6**, 1428–1435 (2000). [CrossRef]

4. J. Leuthold et.al., “Novel 3R regenerator based on semiconductor optical amplifier delayed-interference configuration,” IEEE Phontonics Technol. Lett. **13**, 860–862 (2001). [CrossRef]

5. N. C. Frateschi et.al., “Uncooled Performance of 10-Gb/s Laser Modules With InGaAlAs-InP and InGaAsP-InP MQW Electroabsorption Modulators Integrated With Semiconductor Amplifiers,” IEEE Phontonics Technol. Lett. **17**, 1378–1380 (2005). [CrossRef]

6. C.Y. Tsai et.al., “Theoretical modeling of the small-signal modulation response of carrier and lattice temperatures with the dynamics of nonequilibrium optical phonons in semiconductors lasers,” IEEE J. Sel. Top. Quantum Electron. **5**, 596–605 (1999). [CrossRef]

7. C. M. Gallep and E. Conforti, “Reduction of Semiconductor Optical Amplifier Switching Times by Pre-Impulse-Step Injected Current Technique,” IEEE Photon. Technol. Lett. **14**, 902–904 (2002). [CrossRef]

## 2. Theory

### 2.1Gain modeling

*λ*=

_{sh}*[λ*is the shift in the central frequency

_{0}- a_{4}(N - N_{tr})]*λ*,

_{0}*N*the transparency carrier density,

_{tr}*Γ*the confinement factor, and

*a*are gain parameters [8

_{1-4}8. C. M. Gallep and E. Conforti, “Simulations on picosecond nonlinear electro-optic switching using an ASE-calibrated semiconductor optical amplifier model,” Opt. Commun. **236**, 131–139 (2004). [CrossRef]

*N*being an averaged value of the electron-hole population density along the amplifier cavity. Thus,

*R, S, T*and

*W*depend only on the SOA internal and intrinsic parameters and, obviously, on the wavelength

*λ*. Now, if the cubic term in Eq. (3) is discarded (i.e.,

*T*= 0), Eq. (3) can be rewritten for three different wavelengths (

*λ*,

*λ*

_{1}and

*λ*

_{2}) and combined in order to eliminate

*N*and

*N*

^{2}, hence obtaining

*F*

_{1},

*F*

_{2}and

*F*

_{3}depend on

*R*,

*S*and

*W*, which are evaluated at

*λ*,

*λ*and

_{1}*λ*.

_{2}*λ*and

_{1}*λ*if the

_{2}*F*’s spectral functions are known. The main advantage in the BBM interpolation process is that these three spectral functions (

*Fs*) can be easily determined from the amplifier as a whole, including all penalties inherent to engineering mounts (packaging, gain polarization dependence, optical interconnections, etc). In fact,

*F*,

_{1}*F*and

_{2}*F*are obtained from three complete spectral gain curves, each one measured under different SOA’s bias currents (say

_{3}*A*,

*B*and

*C*). Writing Eq. (4) three times for these three different pump conditions, a set of equations are obtained which in a matrix form are:

*F*,

_{1}*F*and

_{2}*F*are obtained and so the gain spectra at any different pump condition can be determined by Eq. (4)

_{3}*by measuring the optical gain just at the two reference wavelengths λ*. If a reduction in device testing complexity is desired, one needs to measure the gain spectra for three bias currents and then, under any other operating condition, the optical gain at two fixed wavelengths to obtain the entire spectrum. In Section 3, experimental validation is presented. Now, it becomes important to evaluate an extension of the same approach to treat the ASE noise.

_{1}and λ_{2}### 2.2 Noise modeling

*L*indicates linear scale are used,

*N*is the so called noise factor where the rightmost term in Eq. (6) is valid for

_{sp}*G*≫1, as is usually the case in SO As. Now, one can write Eq. (6) in logarithmic scale and use Eq. (3) with T=0 to obtain:

^{L}^{dBm}is equal to

*N*in logarithmic scale (dBm), called ‘equivalent input noise term’ in order to stress that the ASE output power could be expressed as the amplification of this equivalent input noise. Now, Seq

_{sp}(λ)B^{dBm}depends on

*N*, the carrier population density, and so it can be expanded as a power series of

*N*. Assuming this expansion up to the quadratic term and rearranging the terms proportional to each power of

*N*in Eq. (7), one can proceed as in the derivation of Eq. (4) and write Eq. (7) for three different wavelengths, combining them to eliminate

*N*and

*N*

^{2}:

^{dBm}(

*λ*) and

*G*(

*λ*) in Eq. (7). Thus, Eq. (8) is an even more limited solution for the ASE output power than Eq. (4) is for the gain of the SOA. Nevertheless, as shown in the next Section, this equation provides excellent theoretical predictions for the ASE output power of a commercially available SOA.

## 3. Experimental validation

*Corning Inc.*) were measured with an Optical Spectrum Analyzer (

*Anritsu*, MS96A), using 400-point discretization for the acquired spectral span. The optical signals were directly collected from the SOA module with single-mode fiber cables with FC-APC (angled) connectors, avoiding spurious reflections. The SOA bias current was varied, in 50-mA steps, from 100mA to 450mA, and the typical ASE spectra are presented at Fig. 1(a).

*Fs*spectral functions. Then, at different pump conditions (bias currents), the ASE power is measured at the two chosen reference wavelengths,

*λ*and

_{1}*λ*, to predict the whole spectra through Eq. (8). In this example the curves corresponding to bias currents of 100mA, 250mA and 400mA were chosen to calculate the

_{2}*Fs*functions, and

*λ*= 1450 nm and

_{1}*λ*= 1550 nm as the reference wavelengths. The calculated curves are shown in Fig. 1(b). To better visualize the BBM accuracy, the relative error ((P

_{2}_{exp}- P

_{BBM})/ P

_{exp}) was calculated and is presented at Fig. 2, with good agreement between the BBM reconstruction and the experimental within 2% in all cases.

*Fs*functions, and the wavelengths 1530 nm and 1555 nm as the reference wavelengths. The BBM prediction for the SOA optical gain is presented at Fig. 3(b). A good accuracy was obtained as shown by the relative error presented in Fig. 4, as done before for the ASE case, where relative errors within 4% are shown. The 10% relative error point (out of the figure span) at the 150 mA curve was due to an experimental fluctuation in the laser optical power at 1520 nm. Therefore, the accuracy is similar for both ASE and gain.

*Fs*functions or when predicting the gain (ASE power) at the reference wavelengths. This happens by construction and is natural, since these measured curves are used to interpolate the other spectra. For instance, if in the right side of Eq.(5)

*λ*=

*λ*

_{1}is used, one will obtain

*F*

_{1}(

*λ*

_{1},

*λ*

_{1},

*λ*

_{2})=1 and

*F*

_{2}(

*λ*

_{1},

*λ*

_{1},

*λ*

_{2})=

*F*

_{3}(

*λ*

_{1},

*λ*

_{1},

*λ*

_{2})=0. Similarly, if

*λ*=

*λ*

_{2}is used, one will obtain

*F*

_{2}(

*λ*

_{2},

*λ*

_{1},

*λ*

_{2})=1 and

*F*

_{1}(

*λ*

_{2},

*λ*

_{1},

*λ*

_{2})=

*F*

_{3}(

*λ*

_{2},

*λ*

_{1},

*λ*

_{2})=0. In the same way, substituting in Eq. (4) the expression for the

*Fs*curves as a function of the measured gains A,B and C, given by the solution of Eq. (5), it is straightforward to show that Eq. (4) gives the trivial relations

*G*(

_{A,B,C}*λ*)=

*G*(

_{A,B,C}*λ*).

*μ*m. The noisy characteristic of this region in Fig. 1(b) is a consequence of the fluctuations also observed in the spectral curves used to calculate the Fs functions (Fig. 1(a)).

## 4. Discussion and conclusion

*three*energy levels are involved in the amplification process. The BBM presented in [9] is an extension for a

*tree-level*system of a model originally presented for erbium-doped amplifiers, i.e., for a

*two-level*system [10

10. E. V. Vanin, U. Person, and G. Jacobsen, “Spectral Functional forms for Gain and Noise Characterization of EDFAs,” IEEE J. Lightwave Technol. **20**, 243–249 (2002). [CrossRef]

## Acknowledgments

## References and links

1. | A. Rieznik et.al., “Spectral functional forms for modeling SOAs noise,” Proceedings of the SBMO/IEEE MTT-S International Microwave and Optoelectronics Conference 2005 (Brasília, DF, Brazil). |

2. | K. Stubkjaer, “Semiconductor optical amplifier-based all-optical gates for high-speed optical processing,” IEEE J. Sel. Opt. Quantum Electron. |

3. | E. Conforti, C.M. Gallep, and A.C. Bordonalli, “Decreasing Electro-Optic Switching Time in Semiconductor Optical Amplifiers by Using Pre-Pulse Induced Chirp Filtering,” Optical Ampl. Applications 2003 TOPS ,
J. Mørk and A. Srivastava ed.. (OSA Publications) |

4. | J. Leuthold et.al., “Novel 3R regenerator based on semiconductor optical amplifier delayed-interference configuration,” IEEE Phontonics Technol. Lett. |

5. | N. C. Frateschi et.al., “Uncooled Performance of 10-Gb/s Laser Modules With InGaAlAs-InP and InGaAsP-InP MQW Electroabsorption Modulators Integrated With Semiconductor Amplifiers,” IEEE Phontonics Technol. Lett. |

6. | C.Y. Tsai et.al., “Theoretical modeling of the small-signal modulation response of carrier and lattice temperatures with the dynamics of nonequilibrium optical phonons in semiconductors lasers,” IEEE J. Sel. Top. Quantum Electron. |

7. | C. M. Gallep and E. Conforti, “Reduction of Semiconductor Optical Amplifier Switching Times by Pre-Impulse-Step Injected Current Technique,” IEEE Photon. Technol. Lett. |

8. | C. M. Gallep and E. Conforti, “Simulations on picosecond nonlinear electro-optic switching using an ASE-calibrated semiconductor optical amplifier model,” Opt. Commun. |

9. | A.A. Rieznik et.al., “Black Box Model for Thulium Doped Fiber Amplifiers,” Proc. of the Optical Fibers Conference2003 (Atlanta, Georgia, USA), 627–628 |

10. | E. V. Vanin, U. Person, and G. Jacobsen, “Spectral Functional forms for Gain and Noise Characterization of EDFAs,” IEEE J. Lightwave Technol. |

**OCIS Codes**

(140.3280) Lasers and laser optics : Laser amplifiers

(250.5980) Optoelectronics : Semiconductor optical amplifiers

**ToC Category:**

Optoelectronics

**History**

Original Manuscript: October 28, 2005

Revised Manuscript: December 23, 2005

Manuscript Accepted: February 13, 2006

Published: February 20, 2006

**Citation**

Cristiano Gallep, Andrés Rieznik, Hugo Fragnito, Newton Frateschi, and Evandro Conforti, "Black-box model for the complete characterization of the spectral gain and noise in semiconductor optical amplifiers," Opt. Express **14**, 1626-1631 (2006)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-4-1626

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### References

- A. Rieznik et al., "Spectral functional forms for modeling SOAs noise," Proceedings of the SBM O/IEEE MTT-S International Microwave and Optoelectronics Conference 2005 (Brasília, DF, Brazil).
- K. Stubkjaer, "Semiconductor optical amplifier-based all-optical gates for high-speed optical processing," IEEE J. Sel. Opt. Quantum Electron. 6, 1428-1435 (2000). [CrossRef]
- E. Conforti, C.M. Gallep, A.C. Bordonalli, "Decreasing Electro-Optic Switching Time in Semiconductor Optical Amplifiers by Using Pre-Pulse Induced Chirp Filtering," Optical Ampl. Applications 2003 TOPS, J. Mørk, and A. Srivastava ed.. (OSA Publications) 92, 111-116 (2003).
- J. Leuthold et al., "Novel 3R regenerator based on semiconductor optical amplifier delayed-interference configuration," IEEE Phontonics Technol. Lett. 13, 860-862 (2001). [CrossRef]
- N. C. Frateschi et al., "Uncooled Performance of 10-Gb/s Laser Modules With InGaAlAs-InP and InGaAsP-InP MQW Electroabsorption Modulators Integrated With Semiconductor Amplifiers," IEEE Phontonics Technol. Lett. 17, 1378-1380 (2005). [CrossRef]
- C.Y. Tsai et al., "Theoretical modeling of the small-signal modulation response of carrier and lattice temperatures with the dynamics of nonequilibrium optical phonons in semiconductors lasers," IEEE J. Sel. Top. Quantum Electron. 5, 596-605 (1999). [CrossRef]
- C. M. Gallep and E. Conforti, "Reduction of Semiconductor Optical Amplifier Switching Times by Pre-Impulse-Step Injected Current Technique," IEEE Photon. Technol. Lett. 14, 902 -904 (2002). [CrossRef]
- C. M. Gallep and E. Conforti, "Simulations on picosecond nonlinear electro-optic switching using an ASE-calibrated semiconductor optical amplifier model," Opt. Commun. 236, 131-139 (2004). [CrossRef]
- A.A. Rieznik et al., "Black Box Model for Thulium Doped Fiber Amplifiers," Proc. of the Optical Fibers Conference 2003 (Atlanta, Georgia, USA), 627-628.
- E. V. Vanin, U. Person, and G. Jacobsen, "Spectral Functional forms for Gain and Noise Characterization of EDFAs," IEEE J. Lightwave Technol. 20, 243-249 (2002). [CrossRef]

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