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.
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