## 1 Introduction  
In current photonic networks, wavelength-division multiplexing (WDM), in which optical signals with different wavelengths are combined into one optical fiber and separated after transmission, is essential for large network capacity. Since its invention around 1980, the arrayed waveguide grating (AWG) has been globally applied for WDM as a wavelength multiplexer and demultiplexer [1; 2; 3]. AWGs have highly contributed to telecommunications growth in line with the progress in silica-based planar lightwave circuits (PLCs), which have other applications such as optical splitters, switches, and attenuators [4]. Figure 1a illustrates the configuration of an AWG, which is compared with the conventional prism-type spectrometer. The AWG is composed of input waveguides, an input slab waveguide, arrayed waveguides, an output slab waveguide, and output waveguides. The configuration and function are the same as that of the prism-type spectrometer. The arrayed waveguides correspond to a prism as a dispersive medium, and the input/output slabs correspond to collimating and focusing lenses. The AWG features compactness and uniform insertion loss owing to its wafer-process fabrication. A silica AWG on silicon or silica substrate has further benefits, including low loss, compatibility with silica-based optical fiber compared with other materials, an easily scalable and customizable channel number and spectral shape, cost-effective mass productivity, and high reliability under various mechanical and environmental conditions. There are a variety of AWGs with respect to their channel number, spacing, and so on. In the early 2000s, when Internet usage surged rapidly, a record large number of 400 channels and narrow spacing of 1 GHz were reported [5; 6]. Currently, the International Telecommunication Union (ITU) has standardized several channel spacing options, such as 12.5, 50, and 100 GHz [7]. A WDM system with less than 200-GHz spacing is called dense WDM (DWDM), which is widely used in commercial long-haul and metro networks. For example, 40 channels with 100-GHz spacing in the 1.5-m wavelength band (C-band) is one of the common allocations. In regards to other AWG characteristics, temperature compensation or thermalization have been adopted [8; 9]. Methods for reducing crosstalk between channels have also been reported [10]. Another essential characteristic is flat-top shaping, which will be covered in the next section in detail. Long-haul traffic has grown owing to the contribution of AWGs in DWDM line-side networks. However, data traffic in shorter reaches is becoming more and more important recently. The global trend in data traffic is summarized in Figure 1b. The solid line (black) represents data traffic on a logarithmic scale [11]. Since the remarkable increase after the millennium, traffic has continuously increased and will reach petabits per second soon after 2020. In the meantime, client-side interfaces have also progressed exponentially. The triangles and dashed line (blue) are the standardization year and extrapolated Ethernet growth, respectively, which indicate that Ethernet speed has increased by a factor of ten within about a seven-year period. The 100-gigabit Ethernet (100 GbE) and beyond have been standardized since 2010. Based on current technology trends, client-side networks such as those used in datacenters and for mobile links with the reach of 100 km or less will consume more data for local wireless traffic with the advent of self-driving vehicles, edge computing for artificial intelligence, and automation with the Internet-of-Things (IoTs). These developments will require real-time operation without latency, ensured security, and event-driven data processing. Accordingly, future networks should not only be cloud storage-based but also have distributed computing edges to accommodate a variety of data protocols other than TCP/IP.