Analysis on robustness of thickness of narrowband filters for far infrared

Due to the random fluctuation of thickness of layers in the deposition process, the robustness of thickness of narrowband filters for far infrared is calculated. The results show that the omnidirectional band gap and the gap ratio of the narrowband filter change little in accordance with the value of random degree less than 0.05. However, the transmission ratio can only reach to about 1/3 of the original one in the defect layer. Both the omnidirectional band gap and the gap ratio of the narrowband filter decrease with the increase of random fluctuation of thickness when the random degree is over 0.1. The first omnidirectional band gap disappears while the second one obviously transfers to the shortwave direction when the value of random degree reaches to 0.2. Meanwhile, the transmission ratio also reaches to about 1/3 of the original one in the defect layer.The two omnidirectional band gaps disappear totally when the value of random degree reaches to 0.5. A kind of narrowband filter for far infrared is prepared, and the results preferably demonstrate the effect of random fluctuation of thickness on the narrowband filter.