Silicon Photonics: Fundamentals and Devices

12.3 AWG Characteristics

12.3.1 Tuning and Free Spectral Range

We now consider the operation of the AWG in detail by using Figure 12.5. Following the notation given by Okamoto [11, 12], the input waveguide separation in the first waveguide is D₁, the array waveguide separation is d₁, and the radius of curvature is f₁. We consider first the general situation in which the parameters for the first and second slab regions are different. Thus in the second slab region the output waveguide separation, the array waveguide separation, and the radius of curvature are denoted by D, d, and f, respectively. The position in the input waveguide is measured counterclockwise from the center. The light input at the x₁ position is radiated into the first slab, and then all the guides in the array are excited. The excited field amplitude in ith guide of the array is a_i (i = 1 − N), where N is the total number of waveguides. The amplitude profile for a_i is usually Gaussian in nature. After propagating through the arrayed waveguide, the light beams constructively interfere into one focal point x in the second slab, where x is again measured counterclockwise from the center of the output waveguides. The position of this focal point depends on the signal wavelength, as already explained.

Figure 12.5 Schematic configuration of an AWG multiplexer. Reproduced with permission from [12]. Copyright (1999) Institute of Physics.

Figure 12.6 gives an expanded view of the second slab region. Let us consider ...