Theoretical investigation of a notch filter using a long-period grating based on the sampling theorem

A notch filter using a different grating scheme is investigated theoretically. The grating is the thermo-optic index change induced by individually controllable heaters that are periodically arranged on the filter surface. If the index change pattern induced by the heaters is in the form of sampling a periodic index change, the transmission spectrum of the filter has the same resonance band as that generated by the periodic index change. Simulation results show that the attenuation, bandwidth, and center wavelength of a resonance band are independently adjustable. In addition, it is shown that the transmission spectrum may be tailored to arbitrary predictable shapes. Finally, the realization of the filter is discussed.