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 t o exhibit a broad yet flat passband response. However, to our knowledge, th e near-parabolic phase profile solution was previously obtainable only-by n umerical methods. Here, we show how a novel, hidden-variable optimization o f an even second-order approximation to the near-parabolic phase aperture f unction, allows the AWG spectral transfer function to be described using a Fourier-Fresnel transform. The Fresnel integral-based analytic expression o btained provides a good fit to within 2.15 db across the 3-dB passband widt h compared with the exact solution.