# Lossless WDM PON Photonic Integrated Receivers Including SOAs
## 3 SOA Design, Modelling and Analysis  
Due to unavoidable non-perfect mode matching at the interface between the spot-size converter and the SOA, the usual travelling-wave assumption for the amplifier is no longer strictly valid, and even small reflections need to be taken into account. In this work we consider a nearly traveling wave (NTW) semiconductor optical amplifier [30] design for 16.5 dB gain at peak wavelength, large  
Figure 1: Lossless WDM PON architecture with proposed photonic integrated receiver. All link, coupling and on-chip losses are compensated by twin parallel integrated SOAs in the receiver. OLT: optical line terminal, ODN: optical distribution network, ONT: optical network terminal, TF: tunable filter. gain bandwidth of around 150 nm, and \(<\)1 dB gain ripple. Both steady state and dynamic analysis is performed for optimum SOA design using a parabolic gain model. Under proper forward biasing of the device, amplification occurs in the active region of the SOA, so that the signal experiences a single pass gain \(G_{sp}=\exp(gL)\), where g is the net gain per unit length which includes the material gain coefficient per unit length \(g_{m}=a(n-n_{0})-a_{2}(\lambda-\lambda_{p})^{2}\), being \(a\) and \(a_{2}\) the differential gain coefficient and gain constant, respectively, \(n\) and \(n_{0}\) the injected and transparency carrier densities, respectively, and \(\lambda_{p}\) the peak gain wavelength [31]. The amplification factor for a resonant amplifier is defined by [30; 32]:  
\[G=\ \frac{(1-R_{1})(1-R_{2})G_{sp}}{\left(1-G_{sp}\sqrt{R_{1}R_{2}}\right)^{2}+ 4G_{sp}\sqrt{R_{1}R_{2}}\ sin^{2}(\phi)} \tag{1}\]  
where \(\varphi\) is the total single-pass (carrier-dependent) phase shift, and \(R_{1}\) and \(R_{2}\) are facet reflectivities. The NTW regime of operation for the amplifiers is defined as the condition for which the gain ripples \(\Delta\)G are below 3 dB, which requires residual facet reflectivities (RFR) such that \(G_{sp}\sqrt{R_{1}R_{2}}\leq 0.17\)[30]. Figure 2 shows the simulated spectral characteristic of the amplifier gain, for which the gain ripples due to residual facet reflectivities are within about 0.3 dB. In this simulation, the SOA single pass gain \(G_{sp}\) is about 16.5 dB, and facet reflectivities are \(R_{1}=R_{2}=4\times 10^{-4}\). The RFR is such that \(G_{sp}\times R=0.017\), corresponding to \(\Delta G=0.3\) dB, which is in good agreement with the experimentally measured gain profile. In order to extrapolate relevant parameters to be used in the simulation, we performed measurements from a real device. In particular, the active region length has been obtained from the measured free-spectral range (FSR) of the ASE ripples as [33]:  
\[L=\frac{\lambda_{0}^{2}}{2\overline{n}\Delta\lambda} \tag{2}\]  
where \(\lambda_{0}\) is the central wavelength (1500 nm), \(\overline{n}\) is the average semiconductor refractive index and \(\Delta\lambda\) is the FSR (0.2 nm). Since the ASE is proportional to the amplifier gain (\(G\)), the gain ripple can be directly measured on the ASE spectrum [34]. The active region length was obtained by measuring the wavelength spacing between two maxima of the ASE spectrum ripples. The gain profile is shown in Figure 3 together with the simulated one; the peak gain of 16.5 is measured at 1500 nm and the gain at 1550 nm is around 15 dB. The simulated curve is in good agreement with the measured one in the region above the peak wavelength (i.e., around the operating wavelength of 1550 nm), whereas there is little  
Figure 2: Simulated semiconductor optical amplifier (SOA) gain profile, with inset showing a magnified ripple in the center part of gain profile with gain ripple (\(\Delta G\)) of 0.3 dB, and FSR (\(\Delta\lambda\)) of 0.2 nm. difference between the measured and simulated gain profile below the peak wavelength. Besides the obvious approximation introduced by the parabolic model, this mismatch is also ascribed to the gain tilting effect in the SOA under the broadband light injection used for the measurement.