Laser modeling software requires minimal parameter knowledge
JIGESH K. PATEL, PABLO V. MENA, and ENRICO GHILLINO
Optical light sources and the transmission medium are two of the most important elements in modeling a fiber-optic system, each having a significant impact on receiver design and system performance. Singlemode optical fiber, the most popular choice of transmission medium, affects the quality of data transmission through linear-, nonlinear-, and polarization-related effects that are commonly modeled with the nonlinear Schrödinger equation.1
In the majority of cases, fiber manufacturers provide sufficient information such as wavelength-dependent attenuation and dispersion characteristics, the area and nonlinear index of the core, and the polarization mode dispersion coefficient to enable the prediction of transmission impairments with very good accuracy.2 Unfortunately, the same cannot be said about optical sources such as edge-emitting semiconductor lasers and vertical-cavity surface-emitting lasers (VCSELs). Even when datasheets provide a number of useful parameters, manufacturing variances make it very difficult, if not impossible, to accurately model laser behavior.
If the model of the laser is flawed, design of the driver circuit and estimation of system performance are very likely flawed as well. As a result, Synopsys focuses on the accurate system-level characterization and modeling of semiconductor lasers. First, we outline a mixed-level design flow, starting with device-level laser modeling and using it to estimate system behavior. Next, we discuss a datasheet-based approach to describe a physical laser. Finally, we detail the modeling of laser behavior based on measured characteristics.
Mixed-level modeling
RSoft LaserMOD is a commercial semiconductor-laser modeling tool used by companies that manufacture their own lasers in-house or have access to all data on the laser geometry and material characteristics.3 In this case, LaserMOD provides a parametric computer-aided design (CAD) interface for the layout and simulation of active photonic devices such as Fabry-Perot, distributed feedback, and distributed Bragg reflector semiconductor lasers, as well as VCSELs and silicon modulators.
LaserMOD accounts for the optical, electrical, and thermal properties of these devices, including complex effects such as spatial hole burning and self-heating. If desired, parasitic effects can be included to account for packaging. Results from device modeling in LaserMOD can be used for the generation and extraction of system-level model parameters that can then be used for end-to-end fiberoptic system simulation in the commercial system simulator RSoft OptSim, as well as generation of an analog circuit representation for laser-driver design (see Fig. 1).4
One of the advantages of this grounds-up approach is that the system designer has full device-level knowledge of the laser and does not need to rely on third-party datasheets. Therefore, the designer can build Monte Carlo performance boundaries for the whole system based on stochastic variations in the geometrical and physical properties of the laser.
Datasheet-driven laser modeling
Within OptSim, different types of semiconductor lasers are modeled by using rate equations.5 Solving these equations requires knowledge of a large number of physical parameters to accurately model the electrical and optical behaviors of the laser. While mixed-level simulation is an excellent approach for obtaining these parameters, system designers often only have access to laser datasheets from component vendors. Furthermore, these datasheets do not report many of the parameters specific to a rate-equation model. The Best Fit Laser Toolkit is a built-in utility within OptSim that helps bridge this gap by extracting the physical parameters required to solve the rate equations using a limited number of datasheet parameters.
For the Best Fit Laser Toolkit's parameter fitting process, a designer starts with a laser datasheet and inserts the electrical and optical parameters (such as slope efficiency and threshold current) found in the datasheet into the Toolkit (see Fig. 2).6 Using the methodology discussed in the next section, and taking into account the accuracy settings defined by the user, the Toolkit then performs numerical optimization to determine the physical parameters required by the laser rate equations. These parameters can then be used to model the laser within an OptSim simulation, or the Toolkit may be used to generate an equivalent circuit model that includes the p-n junction and packaging effects.
Measurement-driven laser modeling
There may be cases when none of the above approaches can help a system designer in modeling a laser of interest. Sometimes, for example, the laser design is unknown or a datasheet is not available. Furthermore, even when physical parameters are known, there can be wide variations in the performance of lasers within the same batch due to imperfections in the laser manufacturing process. As a result, the behavior of a laser model parameterized from device-level simulation or datasheets may differ from the measured behavior of a particular fabricated device. In these cases, measured characteristics of the laser can be used to extract model parameters and accurately reproduce device performance within OptSim.
The process of extracting model parameters from measured data is well known and typically consists of the following elements (this same procedure is used for extracting model parameters from device simulation or datasheets). First, you obtain a set of measured device characteristics that you want to replicate in simulation. You then define error functions that quantify the differences between these device characteristics and their equivalent simulation results as a function of the model parameters. Finally, you optimize the model parameters such that these errors, and hence the differences between simulation and experiment, are minimized.
As an example, consider a multiple quantum well (MQW) laser. OptSim has a custom model that implements a MQW laser via a set of coupled rate equations, the parameters of which are automatically obtained by fitting file-based measurement data for the laser being used in the optical transmitter design.7 Measured curves that can help OptSim extract rate-equation parameters include the power-vs.-current (P-I) curve, small-signal amplitude modulation (AM) curves, small-signal frequency modulation curves, relative intensity noise curves, fiber transfer-function curves (AM curves with dispersive fiber), and a laser-linewidth curve. For an accurate model of a laser, measured P-I and AM data are essential; other curves from the above list are helpful but not absolutely mandatory.
In comparison, VCSELs are more complicated devices due to their thermal and spatial characteristics. The VCSEL model implemented within OptSim consists of a set of rate equations that take into account thermally dependent gain and carrier leakage, the spatial dependence of the carrier distribution, and self-heating.8 The model also includes expressions for the cavity current-voltage (I-V) relationship as well as electrical parasitics.
Because of its thermal behavior, extraction of the VCSEL model parameters requires measured data at different ambient temperatures. P-I curves at different temperatures allow for the modeling of the threshold current's temperature sensitivity as well as thermal rollover, while the laser's S-parameter small-signal modulation response (S21) at different bias currents and temperatures enables the modeling of dynamic characteristics, including relaxation frequency, 3 dB bandwidth, and overshoot. For example, excellent agreement can be achieved in these cases between simulation and experiment using the OptSim VCSEL model for two different devices based on published extracted model parameters (see Fig. 3).9-11
When the VCSEL must be modeled in the context of a laser-driver design, electrical terminal characteristics, such as I-V data at different temperatures, are required. Finally, additional data such as output-wavelength versus temperature (for estimating thermal impedance) and large-signal characteristics such as turn-on delay can allow a more accurate extraction of model parameters.
The laser is a critical component in fiber optic transmitters and has a direct effect on the quality of transmitted data. Furthermore, manufacturing processes are not perfect and can give wide variations in laser performance. With these issues in mind, users have various approaches for modeling a laser in the context of system-level simulation using RSoft OptSim. The choice of the most useful approach depends upon whether the designer has access to device-level simulation tools, datasheets, or measured characteristics. In the latter case, the availability of more detailed device characteristics from manufacturers or in-house measurements would undoubtedly help designers more optimally and efficiently develop and deploy their systems.
ACKNOWLEDGEMENT
LaserMOD and OptSim are trademarks of Synopsys.
REFERENCES
1. G. P. Agrawal, Nonlinear Fiber Optics, 2nd Edition, Academic Press, San Diego, CA (1995).
2. See http://bit.ly/17mMKYa.
3. See http://bit.ly/19tiJbp.
4. See http://bit.ly/13z4D8Y.
5. G. P. Agrawal and N. K. Dutta, Semiconductor Lasers, 2nd Edition, Van Nostrand Reinhold, New York, NY (1993).
6. See http://bit.ly/13WkxJ1.
7. M. M. Freire and H. J. A. da Silva, "Estimation of multiple-quantum well laser parameters for simulation of dispersion supported transmission systems at 20 Gbit/s," IEE Proc. Optoelectron., 146, 93–98 (April 1999).
8. P. V. Mena et al., J. Lightwave Technol., 17, 12, 2612–2632 (December 1999).
9. M. H. Crawford et al., "Visible VCSELs: Recent advances and applications," 1997 Digest of the LEOS Summer Topical Meetings-Vertical-Cavity Lasers, 17–18 (1997).
10. M. H. Crawford et al., "InAlGaP vertical cavity surface emitting lasers (VCSELs): Processing and performance," Proc. Int. Conf. InP Rel. Mater., 32–35 (1997).
11. B. J. Thibeault et al., IEEE Photon. Technol. Lett., 9, 1, 11–13 (January 1997).
Jigesh K. Patel is a senior application engineer and Pablo V. Mena and Enrico Ghillino are R&D engineers for the Optical Solutions Group at Synopsys, 400 Executive Boulevard, Suite 100, Ossining, NY 10562; email: [email protected]; www.synopsys.com.