## 3 SiN for Coarse Wavelength Division Multiplexing (CWDM) Optical Transceivers in the O-Band
### CWDM SiN Echelle Grating Multiplexer  
Echelle gratings (EG) are diffraction grating spectrometers whose principle is based upon phase matching the light reflected from neighboring facets. Using a slab waveguide as a free propagation region (FPR), we describe a simple grating on a classic Rowland mounting using the following equation [39]:  
\[d(\sin\theta_{i}+\sin\theta_{m})=\frac{m\lambda}{n_{eff}(\lambda)}\]  
where \(\theta_{i}\) (70\({}^{\circ}\)) and \(\theta_{m}\) (88\({}^{\circ}\)) are the angles of incidence and diffraction of the \(m\)th (3 rd) diffraction order, \(\lambda\) is the wavelength in free space, \(d\) (1.76 \(\upmu\)m) is the spacing of the grating teeth, and \(n_{eff}\) (1.748) is the effective index of the slab mode at 1310 nm, while the Rowland mounting radius is 55 \(\upmu\)m. In particular, the input access waveguide to the FPR was tapered from 700 nm up to 2.4 \(\upmu\)m in order to minimize the scattering losses at the entrance of the slab region due to the modal propagation mismatch between the effective indices of the slab and the rib. Concerning the output, an array of multimode waveguides (MMWs) 2.2 \(\upmu\)m in width ensures wide channel bandwidth and low insertion losses, while maintaining high interchannel isolation. In addition, the grating teeth were blazed, chirped and oriented to focus the light into the selected diffraction order, and dimensioned according to the proximity of the neighboring teeth in order to reduce cross-shadowing, thus enhancing performance.  
Optical and scanning electron microscope (SEM) images of the EGs (de-)multiplexers are illustrated in Figure 3a,b, respectively. A close to 90% reflectivity of the EG facets is ensured through the use of 1 st-order DBRs with a 50% fill factor and 422-nm periodicity (Figure 3b). For this device, a slightly different fabrication process was used to show the full potential of SiN Echelle Multiplexer: Dose-optimized 8-inch VISTEC variable-shape e-beam lithography was used for the SiN patterning. A 300-nm-thick PECVD-grown SiO\({}_{2}\) layer over the SiN layer was used as a hard mask for protecting the waveguides from ion bombardment during encapsulation, as well as to ensure optimum pattern transfer from the e-beam resist to the nitride layer.  
The results are shown in Figure 3c. The measurements reveal insertion losses averaging 1.5 dB across the four transmission channels, an average interchannel isolation above 30 dB (when determined at the center of the transmission channel), and a precise channel spacing of nearly 20 nm. A \(-\)1 dB channel bandwidth varying between 7 and 9 nm and a channel-to-channel non-uniformity of 1.4 dB were found. As well as that, phase errors arising from local facet imperfections or non-verticality both have an impact on the defocusing of the image spot at the output, impinging slightly on insertion losses.  
The thermal chromatic dispersion (i.e., the temperature-related wavelength shift) of the device itself when operating at increasing temperature is also important, as it impacts the flexibility of the device when operating in radically different environments, especially at the receiver side of the optical link. Recently, state-of-the-art SiN Mach-Zehnder multiplexers have been realized, with a reported thermal chromatic dispersion of 18.5 pm/\({}^{\circ}\)C [17]. Similar measurements were carried out on the SiN EGs presented in this paper, indicating an even lower thermal detuning coefficient, measured at below 13 pm/\({}^{\circ}\)C, as shown in the inset of Figure 3c. This is possible thanks to the EG operating over a slab FPR instead of rib/strip waveguides. In fact, the effective index variation of a slab waveguide is noticeably lower compared to those of strip or rib waveguides, making SiN EGs an attractive solution on the path toward quasi-athermal behavior.