# Construction of Nonblocking Wavelength/Space Switches with AWGs and WSSes
## 1 Introduction  
WDM (wavelength-division-multiplexing) optical networks have been widely deployed. About 100 wavelength channels can be packed into a fiber and each channel can support a data rate of up to 100 Gb/s [1]. An optical cross-connect (OXC) [2; 3; 4; 5] is a key component in such a network. An OXC is a switch involving switching in both the wavelength and the space domain [6; 7; 8; 9; 10; 11]. In this paper, we will show how to use two technologies, AWG (arrayed-waveguide grating) and WSS (wavelength selective switches), to design such a nonblocking optical cross-connect.  
An AWG is a passive device and can route multiple wavelengths to different destinations simultaneously. Each input of an \(N\times N\) AWG can send in \(N\) signals, each destined for a different output, of different wavelengths simultaneously. An \(N\times N\) AWG can forward all \(N^{2}\) signals without blocking [12]. The multi-wavelength capability makes it more attractive for constructing a nonblocking optical OXC than other switching technologies, such as SOA (semiconductor optical amplifiers) [13; 14; 15].  
This capability of AWGs has been exploited in many works [7; 8; 9; 10; 11; 12; 16; 17; 18; 19]. To design a scalable AWG-based nonblocking wavelength/space switch, one has to overcome two limitations. One is that the number of wavelengths available is limited and the other is that the size of the AWGs that can be constructed today is still limited. These issues are discussed in [11]. To meet the design goals, [11] uses a decomposition technique that is carried out in the original switch/wavelength topology. This decomposition technique is complicated and the values of the space and wavelength parameters are quite rigid in the discussion of [11]. In the paper, we show a decomposition technique for designing an AWG-based nonblocking wavelength/space switch. The decomposition is carried out in a transformed space network. This new technique is simpler and more flexible in designing switches of different sizes and wavelength numbers than given in [11].  
In addition to AWG, WSS [4; 5; 20; 21; 22] is another commercially available technology for constructing nonblocking space/wavelength switches. We will present a different decomposition technique for designing WSS-based nonblocking optical cross-connects. The resulting nonblocking optical cross-connects derived from the two approaches, AWG-based and WSS-based, display quite different characteristics. The former requires tunable WCs, while the latter does not; the former requires no optical space switching, while the latter does. They also put different constraints on switch sizes. We intend to compare two in terms of the scalability, switch size constraint, and number of WCs (wavelength converters) required.  
The rest of the paper is organized as follows. In Section 2, we introduce how to dilate the AWG-based switch in the space domain and present a new decomposition technique for designing an AWG-based nonblocking wavelength/space switch. In Section 3, we present how to use WSSes to design a switch with the same nonblocking wavelength/space property. In Section 4, we study the space-wavelength tradeoffs between AWG-based and WSS-based switches. Section 5 concludes our discussion.