- We propose a layer peeling algorithm with the eigenvalue problem to design optical IIR allpass filters with an equiripple phase response in the Chebyshev sense. The layer peeling algorithm is used to determine the coupling coefficients of the optical IIR allpass filter structures from the transfer function in the z-transform domain. The eigenvalue problem is used to design the transfer function with the optimal phase response of the optical IIR allpass filter. To verify the proposed method, we design a Hilbert transformer, which is useful in optical communications and signal processing. 1989-2012 IEEE.