Introduction

In this chapter, we will present the theory and analytical modeling of chirp in the Mach–Zehnder modulator (MZM) arising from optical and electrical asymmetries of the interferometric structure. Material-induced chirp will not be considered. In general, “chirp” refers to self-phase modulation during the light intensity modulation process, and is defined as the relative time variation of the optical phase relative to the normalized intensity change. Accordingly, chirp vanishes for small phase changes occurring during large relative intensity variations.

An ideal light intensity MZM does not show any phase changes as a consequence of the variation of the electric field amplitude. The modulator is biased at the quadrature point, where the intensity transfer characteristic has an inflection point. During modulation, the optical phasor moves in the complex plane in a straight-line path between the origin and the maximum amplitude point. During the transient of the electric field phasor amplitude, the phase remains constant and the chirp is zero. Although it might seem misleading, the ideal MZM also behaves as a phase modulator, just changing the bias point on the transfer characteristic. In this case, the MZM is biased at the null point, corresponding to the origin of the complex phasor plane. Again, ideal phase modulation occurs along a straight-line path. The amplitude of the phasor moves between opposite points along the path, symmetrically positioned relative to the origin. The phase remains constant during each half-path, switching instantaneously by π as the phasor crosses the origin. Accordingly, phase modulation is achieved through an ideal square wave profile of the phase function, independently of the wavefronts of the phasor amplitude. Since the phase remains constant during each half-path displacement, the chirp is still zero. The reader may argue that an ideal phase modulator should move along a circle in the phase plane, changing only the phase of the optical field while the amplitude remains constant. This is correct, of course, but is not achievable with a conventional MZM. However, the ideal phase modulator, as depicted above, describes a circular phase path, showing constant amplitude of the optical phasor during transients, while the phase continuously rotates by π, presenting infinite chirp.