Generally AWG devices serve as multiplexers, demultiplexers, filters, and add-drop
devices in optical WDM and DWDM applications. Figure 1 shows a schematic
representation of the MxN AWG. The device consists of two concave slab waveguide
star couplers (or free propagation zones/ranges, FSZ), connected by a dispersive
waveguide array with the equal length difference between adjacent array waveguides.
Generally, there are two kinds of AWG: 1xN (M=1) and NxN (M=N). The number of the wavelength channels N is selected with the exponent of 2 such as 16, 32, 64, and 128.
The number of the array waveguides P is not a dominant parameter in the AWG design
because the Δλ and N do not depend on it. Generally, P is selected so that the number of
array waveguides is sufficient to make the numerical aperture (NA), in which they form a
greater number than the input/output waveguides, such that almost all the light diffracted
into the free space region is collected by the array aperture. As a general rule, this number
should be bigger than four times the number of wavelength channels.
For example, you can have an AWG with M=1 (number of input ports), N=16 (number of output ports), P = 60 (number of array waveguides).