Calibration of TLM Model for Semiconductor Optical Amplifier by Heuristic Parameters’ Extraction

The systemic behavior of a Semiconductor Optical Amplifier model was optimized through extensive simulations, reaching reasonable approximation to experimental obtained from commercial devices for the optical gain versus bias current, for different optical inputs powers (-25 up to 0 dBm), and for the gain saturation profile for different I-bias (0 up to 180 mA). For that, parameters such as active region thickness, confinement factor, linear gain coefficient, and the transparency current were adjusted by the presented method. The method can be applied for different SOAs, enabling more accurate numerical predictions for black-box devices.


I. INTRODUCTION
In recent years, the exponential increase in demand for network bandwidth keeps pushing the transmission rate growth in optical links.An attractive device to support the consequent requirement of low cost on this expansion can be the semiconductor optical amplifier (SOA), mainly regarding medium-range optical links.Several SOA applications have been proposed in linear and nonlinear regimes, such as wavelength converters [1]- [2], memory modules [3], optical buffers [4], optical space switches [5]- [8], and carrier wavelength reusing [9]- [10].In addition, some regenerators use SOA to process optical signals, in setups with Mach-Zehnder [11] or Sagnac [12] interferometers, being able to process phase-encoded signals such as DPSK (Differential Phase-Shift Keying) [13] and QPSK (Quadrature Phase-Shift Keying) [14].The authors have recently proposed a quasi-linear SOAbased amplifier, demonstrated in silico for 16-QAM (Quadrature Amplitude Modulation) signals with improvements for the intrinsic constellation's distortions [15].
The accurate modeling of this device can be useful to study the impact of nonlinear amplification of multilevel-encoding optical signals mentioned above.In this work, the SOA gain modeling is optimized by a calibration technique, where several intrinsic parameters are extracted heuristically.This technique is demonstrated using a commercial platform (Virtual Photonics Int, VPI [16]) that uses the Transmission Line Matrix (TLM) method to simulate the propagation of light through the The SOA-model calibration was performed by matching the experimental and simulated curves of optical gain vs. current and also optical gain vs. optical input power (P in ).The experimental curves were obtained from a commercial SOA (InPhenix, IPSAD1503).The SOA net optical gain was characterized by: 1) varying the bias current from 0 up to 180 mA and using two input optical powers, P in = -12 and -5 dBm; 2) varying the input power from -25 up to 0 dBm for bias currents of 40, 60, and 150 mA.

A. Experimental Setup
The experimental curves were obtained using the setup shown in Fig. 1: a CW laser (@1550 nm) is followed by an optical isolator to avoid back-propagation, and an OSA (Optical Spectrum Analyser) is used for optical output and noise measurements.The net optical gain is obtained by the difference between the output power and the input power (P out -P in ), in dB scale.Fig. 2(a) shows the gain vs.
current and Fig. 2(b) the gain vs. optical input power for the commercial SOA.The SOA active cavity's length was obtained from the distance between residual Fabry-Perot modes [17], which can be seen in the ASE spectrum for high bias current (~200 mA).The finite facet reflectivity produces spurious longitudinal modes, and from their spacing the longitudinal length can be obtained by [18]: where λ = 1550 nm is the central wavelength, n g = 3.86 is the effective refractive index for the active cavity, and Δλ = 0.48 nm is the ripples' wavelength spacing.

B. Simulations
The TLM approach is widely used to model the light amplification inside the SOA [19]- [21].In such approach the behavior of each TLM section must be considered as an interplay between the optical and the electronic populations [16].Such modelling can be useful for numerical prediction on optical networks, but it requires proper calibrationotherwise non-realistic predictions appear easily.
So, the device characterization must be properly designed and performed, and be equally validated for different models of commercial, black-box SOAs.
Before starting the model calibration, the SOA length must be determined, as shown above (Eq.1).
After, the parameters listed in Table I are changed individually to observe and analyze their impact over the aforementioned optical gain curves.In order to do this, parameter sweep is performed for a range of values below and above a default start, preconfigured in the numerical model.These parameters are used in the rate equations and applied to the wave equations which are used to model the propagation of the optical signal within the SOA active region.The solutions of these equations are obtained numerically using the TLM method [16].First, the optical confinement factor and the cavity's transversal sizes are parameters of greatest interest.Therefore, those parameters should are the first to be tested.The confinement factor is related to the portion of the optical field within the active region and depends on the cavity thickness.The relationship of the three size dimensions, ie.total volume, to the confinement also determines the SOA output saturation power [22].
To analyze the mutual relationship between those, a parallel sweep was performed combining the confinement factor and the width and thickness of the active cavity and, thus, find the best match to the experimental data for the profiles of gain vs current and of gain vs P in .Figure 3 shows a case where good approximation is reachedoptimized at 2.5 µm, 100 nm, and 0.17, respectively.But a better adjust is still needed for the 40-80 mA range, where simulated and experimental curves differs substantially.Some preconfigured parameters may have their default value out of the actual value, and this may depend on factors such as the SOA dimensions (length, width, and thickness), the semiconductor material (InGaAsP, InGaAs, etc.), SOA structure (bulk, MQW, QD, guided index, and guided gain), etc.For that, the other parameters of  The CDT refers to the density of carriers to reach transparency, i.e. when the optical gain surpasses all losses (gain = 0 dB).The ICD refers to the device's intrinsic carrier's density.The amplifier optical gain is linearly dependent on the electronic carrier's density, with parabolic shaped spectra, and with effective bandwidth as function of the electronic density; the parameter N ref models the reference carrier density for that.The amplifier gain is also a function of the differential gain (dg/dN) [23], adjusted by G coeff .The parameter ε contributes to the amplifier gain compression since the gain saturation occurs at very high photon density.The physical origin of this nonlinear gain coefficient is mainly the spectral hole burning [16].
The parameter A recomb represents the nonradiative recombination process of carriers by crystal defects (traps), that may occur in the active region during SOA fabrication and also when the device suffers aging.Carriers near those traps recombine non-radiatively, with no photon emission.This linear effect is known as linear recombination coefficient, being significant for low current injection [23].
The parameter B recomb models the interaction of two carriers, an electron in the conduction band and a hole in the valence band, meeting and recombining to produce light by spontaneous emission, whose small portion is coupled to the active waveguide [23].The C recomb models the most important nonradiative recombination, the so called Auger, involving three particles that exchange energy without irradiation.
The parameter I coeff designates the portion of the SOA injected current reaching the active region.
This current may partially deviates around the SOA electric contact, reducing so its contribution to the excited carriers' population in the conduction band.The parameter OCE, by its very name, represents the portion of optical power that is coupled to the amplifier coming from an optical fiber.
The parameter ILC also plays an important role in the effective optical gain, so that internal losses are due to Rayleigh scattering of light, absorption of photons by material resonances, and non-uniform distribution of the optical field in the waveguide [24].The parameter ILCD changes by carriers lateral spreading and non-radiative electron-hole recombination (phonons) [19].
The capture time refers to the capture of carriers by the quantum well, after these carriers cross the SCH region.The escape time of carriers on the active region occurs through the thermionic emission of these carriers.

III. RESULTS AND DISCUSSIONS
The adjustments for the gain vs. current and gain vs. P in profiles were done based on the model behavior, as presented in the previous section.The Fig. 4 and Fig. 5 show the experimental and numerical results after our calibration procedure.
The calibrated parameters (Table I) differ from default ones as explained: the active region was found thicker (100 nm) than the standard value (40 nm), correction based on the transparency current (see Fig. 2(a)), greater than the default set.The confinement factor differs from the standard value (0.07 to 0.165) because it is proportional to the cross-sectional area of the active region.Thus, for an increase in thickness, an increase in the confinement factor is expected.The injection efficiency coefficients (I coeff ) models the fact that only part of the injected carriers reaches the active region, while some diffuse around the metal contact and the semiconductor, and so the calibrated value is lower than the ideal.The internal loss coefficient (ILC) of the calibrated model (4000 m -1 ) is also bigger than default (3000 m -1 ), since the internal loss is higher in thicker active regions.The fiber-towaveguide coupling is not perfect, and so the optical coupling efficiency (OCE) is lower than 100%, ranging from 20% to 70% [16].
The linear gain coefficient (G coeff ) varied from 3x10 -20 m 2 to 8.7x10 -20 m 2 due to the strong dependence on the number of quantum wells, generally equal to or greater than 12 [25].As mentioned above, the transparency current increases with the thickness of the amplifier, consequently the density of carriers in the transparency (CDT) increased from 1.5x10 24 m -3 to 1.7x10 24 m -3 .The initial carrier density (ICD) can be used to converge the gain/current curve.Thus, the ICD value for the calibrated SOA was lower than default for convergence at low currents.
The Linear Recombination (A recomb ) is proportional to defects during fabrication or to the SOA operation time (aging), and is significant at low currents.Thus, it was set at 5x10

TABLE I .
PARAMETERS FOR SOA MODEL -DEFAULT AND CALIBRATED