## 2 MM-AWG and Optical Coupling  
Insertion loss and transmission bandwidth are the essential parameters in AWG design. In general, both are apt to be in a trade-off relationship. For example, parabola shaping is a simple solution to increase bandwidth by adding a taper structure at slab waveguides, though the loss increases [22]. To overcome the tradeoff, synchronic configurations have been proposed [23; 24], which consist of a cascading Mach-Zehnder interferometer (MZI) and AWG that provide low loss and a wide-band filter shape. This is a sophisticated approach, however, requiring high process uniformity for phase matching and a large chip for the cascading layout. Therefore, those types of AWGs have mainly been applied for high-spec networks with a large number of channels. As mentioned before, WDM is more important in client-side optics. Currently, for instance, WDM-based Ethernet specifications have already been standardized for 40 and 100 Gb/s and beyond [25; 26]. As the client-side demultiplexer, free-space optics with thin-film filters (TFFs) has been used, especially in coarse WDM (CWDM) systems with a small number of wavelengths [27; 28]. However, this optics has drawbacks. One is the need for complex and precise assembly in building an optical block using TFFs and collimating lenses. Furthermore, it is more difficult to configure for denser or larger-scale WDM. Hence, an alternative demultiplexer based on a PLC is a very promising candidate, which has also been widely implemented in optical transceivers. In our study, we used the MM-AWG, a low-loss flat-top demultiplexer, to build WDM photoreceivers with total bit rates of 10, 40, 100 Gb/s, and beyond. In contrast to the conventional AWG with single-mode output waveguides, the MM-AWG with multimode output waveguides provides a flat-top passband with low loss [29; 30]. We describe the procedure for estimating the spectral shape of MM-AWG using Figure 2. The design condition exemplified here is based on a silica PLC for the 1.3-\(\upmu\)m band with an index difference between the core and cladding of 2%, which is utilized in our 100-Gb/s photoreceiver (described later in Section 5). First, as shown in Figure 2a, the effective index of a waveguide is calculated as function of waveguide width. A vector finite difference mode solver was used to estimate the effective index in each mode order [31]. Parameter \(m\) is the mode order. The more the width of the output waveguides is enlarged, the higher the modes that are generated. In this case, a total of six modes, including the fundamental one (\(m=0\)), exist within the waveguide width of 15 \(\upmu\)m. Second, as shown in Figure 2b, the spectral shapes of the AWG are calculated for each mode and combined. The spectral flatness is determined by the number of modes taken into account, or by the waveguide width. The more modes taken into account, the flatter the spectral shape becomes, together with a reduction of insertion loss. Here, we explain the layout design and typical spectrum of the MM-AWG. The design condition is based on a silica PLC for the 1.5-\(\upmu\)m band, which is used in our 10-Gb/s receiver (presented in the next section). Figure 3a shows a schematic of the design of the AWG chip and a cross-sectional view of the waveguide. This silica-based MM-AWG has eight output ports consisting of single-mode-input and multimode-output waveguides. All the output channels are designed on the CWDM grid with the channel spacing of 20 nm. The MM-AWG has a gull-wing shape, and the chip size is 11 mm \(\times\) 65 mm, using the index difference of 0.75%. The core sizes of the input and output waveguides are 6 \(\times\) 6 and 6 \(\times\) 30 \(\upmu\)m, respectively. Note that the chip size is dependent on the index difference. Since the curvature or bending radius decreases as the index difference increases, the AWG layout shrinks and the chip size decreases for larger index differences. In addition, core size also depends on the index difference. A higher index provides a smaller core.