Orthogonal Signals and the Orthogonalization Procedure

Chapter 2 is dedicated to the principle of signal orthogonalization, because orthogonal signals are widely used in telecommunication theory and practice, like the carriers of baseband signals, subcarriers in orthogonal frequency division multiplexing systems, and the spreading sequences in spread-spectrum and code division multiple access (CDMA) systems. The orthonormal basis functions are defined and the procedure of the vector representation of signals is demonstrated. The Gram–Schmidt orthogonalization procedure and construction of the space diagram are presented in detail. Using orthonormal signals, signal synthesizers and analysers that can be used to form discrete-time transmitters and receivers are theoretically founded. Understanding of this chapter is a prerequisite for understanding Chapters 4–10, because the orthonormal signals defined in this chapter will be used throughout the book. The basis harmonic orthonormal functions will define the carriers in the discrete and digital communication systems.

Design of Silicon TE0/TE1 Mode Router Using Mach-Zehnder and Multimode Interferometers

This paper proposes a new design of two-mode three-port optical mode router for mode division multiplexing systems. The device consists of a Mach-Zehnder interferometer (MZI) and a multimode interferometer (MMI), which utilizes silicon material for photonic integrated circuits (PIC). By setting appropriate values for the two butterfly-shaped phase shifters (PSs) at MZI and MMI, the input mode, either transverse electric (TE) modes TE0 or TE1, can be routed to the desired output among the three output ports. The device is designed and optimized via three-dimensional beam propagation method (3D BPM). The proposed device achieves very low insertion loss and small cross-talk, which are less than 0.4 dB and -24.5 dB, respectively, over the whole C band.