Introduction

This chapter provides an analysis, with simulations and working examples, of the optical response of the optical coupler and the Mach–Zehnder interferometer (MZI). Due to the specific field interactions governing the behavior of these devices, we will identify these optical responses as interferometric optical responses. We have presented the coupled-mode theory of the directional optical coupler in Chapter 8, and we begin this chapter from those conclusions, developing the theory of the optical frequency response of an ideal optical coupler. Section 10.2 begins with a derivation of the frequency response matrices for the bar and cross paths of an ideal optical coupler. According to the coupled-mode field solutions, the transfer behavior of the field on the bar and cross paths is different, reflecting different frequency-response models. The modeling has been made as simple as possible, removing material-dependent parameters and related characteristics. We will analyze the optical response of the optical coupler as an idealized device, neglecting any dependence on the waveguide structure or the technology and focusing on the fundamental characteristics. As a result, the frequency transfer matrix applies to an idealized four-port optical device, highlighting its fundamental behavior. The impulse response matrix is easily deduced from this by means of the Fourier transform technique. The section proceeds with simulations of optical coupler responses to CW and modulated excitation, using various pulse models. These examples serve to verify quantitatively the operation of the optical coupler excited by a modulated optical field.

Section 10.3 illustrates the operation of a binary tree and a four-quadrant phase shifter as examples of cascaded optical coupler structures, retrieving the composite half-power transfer function.