General IIR optical notch filter based on Michelson Gires–Tournois interferometer

A general IIR optical notch filter design is presented from a digital filter design perspective for Michelson Gires–Tournois Interferometer structure. Optical notch filter with arbitrary notch frequency, notch point number, and 3 dB rejection bandwidth can be designed easily. According to the spectral requirement of desired notch filter, in frequency domain we firstly calculate the transfer function of desired allpass filter. Then the numbers of reflectors in Gires–Tournois etalon can be determined. We calculate the transfer function of this multi-cavity Gires–Tournois etalon by using Z-transform. By making the transfer function of allpass filter in frequency domain equal to that of the multi-cavity Gires–Tournois etalon, the notch filter can be directly realized. Different design examples are given in detail in the paper. The change of output spectrum is also investigated for the reflectance of the reflectors and the distance between the reflectors deviating from the ideal value. The results show that the notch filter has the tunability of notch frequency and 3 dB rejection bandwidth. The chromatic dispersion characteristic of the notch filter is analyzed finally. It shows that the notch filter has excellent chromatic dispersion characteristic.