Wide Infrared Bandpass Filter

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This coating is for light at normal incidence on a germanium substrate (index 4). The requirements are: A. Transmittance < 0.1% for wavelengths 2000-3000 nm B. Transmittance > 99% for wavelengths 3300-5000 nm C. Transmittance < 0.1% for wavelengths 5500-7000 nm The two coating materials are Ge and ZnS (indices 4.2 and 2.2). Although this coating could be designed by "brute force" (just input the optimization targets and let needle/tunneling find a design), a faster approach for wide bandpass filters is to (1) design short and long wave pass filters, (2) append the two filters, and (3) reoptimize. The procedure is illustrated here. First, starting with a single thin layer, the needle/tunneling method was used to create a 31-layer long-wave pass filter using requirements A and B. The transmission in requirement A was reduced to 0.01% so that the final design can meet the 0.1% requirement. The performance is shown below. Second, starting with a single thin layer, the needle/tunneling method was used to create a 17-layer short-wave pass filter using requirements B and C. The performance is shown below. Third, experience shows that it is best to place the short-wave pass filter closest to the substrate and then to append the long-wave pass filter. (The needle/tunneling method "discovers" this fact when the brute-force approach is used.) Before optimizing, the performance is: After optimizing this design, the final performance is: Here are the designs, with the first layer closest to the substrate and thickness given in nm. With a little more work, it may be possible to eliminated some thin layers. Short Long Bandpass ZnS 83.39 97.33 Ge 48.25 48.60 ZnS 756.31 761.47 Ge 403.51 412.85 ZnS 710.33 720.06 Ge 377.93 382.28 ZnS 696.05 705.03 Ge 370.17 370.42 ZnS 696.91 709.26 Ge 365.05 358.23 ZnS 705.00 718.52 Ge 361.44 353.08 ZnS 719.03 724.86 Ge 360.53 360.01 ZnS 751.56 710.47 Ge 328.61 398.52 ZnS 369.01 158.71 564.95 Ge 124.38 40.79 ZnS 260.14 224.72 Ge 78.55 125.31 ZnS 149.33 133.58 Ge 102.25 98.28 ZnS 235.97 268.21 Ge 145.53 138.25 ZnS 279.07 238.01 Ge 128.80 125.48 ZnS 196.52 232.65 Ge 67.11 68.54 ZnS 159.26 168.55 Ge 132.16 150.14 ZnS 271.50 254.28 Ge 144.32 125.25 ZnS 281.93 307.19 Ge 149.33 165.16 ZnS 278.65 256.22 Ge 140.79 133.04 ZnS 271.93 289.60 Ge 147.16 147.63 ZnS 276.89 266.04 Ge 138.39 134.34 ZnS 271.52 265.60 Ge 152.12 156.86 ZnS 291.92 294.15 Ge 135.69 123.17 ZnS 249.93 250.12 Ge 166.98 178.96 ZnS 553.73 528.64

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