  Topological photonics have led to the robust optical behavior of the device,
which has solved the problem of the influence of manufacturing defects and
perturbations on the device performance. Meanwhile, temporal coupled-mode
theory (t-CMT) has been developed and applied widely. However, the t-CMT of
cascaded coupling cavities (CCC) system and its corresponding high-order filter
has yet to be established. Here the t-CMT of CCC system is established based on
the existing t-CMT. By combining the CCC with the topological waveguides, a
versatile design scheme of the high-order nonreciprocal add-drop filter (HONAF)
is proposed. The relationship between coupling effect of cavities and
transmission and filtering performance of HONAF is analyzed quantitatively,
then a method to improve the transmission efficiency and quality factor of the
filter is given. Based on the combination of gyromagnetic photonic crystals and
decagonal Penrose-type photonic quasicrystals, a HONAF is proposed. The
transmission and filtering performance of the HONAF are numerically analyzed,
which verifies the consistency between the theoretical prediction and the
numerical simulation. The t-CMT of CCC system established can be widely used in
the coupled resonator optical waveguides and their related systems. The
designed HONAF can also be applied and compatible to microwave communication
system.
