A Frequency Domain Systems Theory Perspective for Semiconductor Optical Amplifier - Mach Zehnder Interferometer Circuitry in Routing and Signal Processing Applications

1.1 SOAs as nonlinear elements in Mach-Zehnder Interferometers Although SOAs have been initially introduced as integrated modules mainly for optical amplification purposes, they have been widely used in all optical signal processing applications, like all-optical switching and wavelength conversion, utilizing the exhibited nonlinearities such as gain saturation, cross-gain (XGM) and cross-phase modulation (XPM). These nonlinear effects that present the most severe problem and limit the usefulness of SOAs as optical amplifiers in lightwave systems can be proven attractive in optically transparent networks. The origin of the nonlinearities lies in the SOA gain saturation and in its correlation with the phase of the propagating wave, since the carrier density changes induced by the input signals are affecting not only the gain but also the refractive index in the active region of the SOA. The carrier density dynamics within the SOA are very fast (picosecond scale) and thus the gain responds in tune with the fluctuations in the input power on a bit by bit basis even for optical data at 10 or 40 Gb/s bit-rates (Ramaswami & Sivarajan, 2002). If more than one signal is injected into the SOA, their nonlinear interaction will lead to XPM between the signals. However, in order to take advantage of the XPM phenomenon and create functional devices, the SOAs have to be placed in an interferometric configuration such as a Mach-Zehnder Interferometer (MZI) that converts phase changes in the signals to intensity variations at its output exploiting interference effects. Semiconductor Optical Amplifier-based Mach-Zehnder Interferometers (SOA-MZIs) have been widely used in the past years as all-optical high speed switches for signal conditioning and signal processing, mainly due to their low switching power requirements and their potential for integration (Maxwell, 2006). Using this type of switch, a set of processing operations ranging from demultiplexing (Duelk et al.,1999) to regeneration (Ueno et al., 2001) and wavelength