A Fourier-Fresnel integral-based transfer function model for a near-parabolic phase profile arrayed-waveguide grating

The near-parabolic phase profile arrayed-waveguide grating (AWG) is known to exhibit a broad yet flat passband response. However, to our knowledge, the near-parabolic phase profile solution was previously obtainable only by numerical methods. Here, we show how a novel, hidden-variable optimization of an even second-order approximation to the near-parabolic phase aperture function, allows the AWG spectral transfer function to be described using a Fourier-Fresnel transform. The Fresnel integral-based analytic expression obtained provides a good fit to within 2.15 dB across the 3-dB passband width compared with the exact solution.