Four-Wavelength Bandpass Filter
This idea came from a graduate student who needed a bandpass filter for detecting light at
four wavelengths: 630, 690, 760, and 885 nm. Between these wavelengths the filter is allowed
to transmit 10%. The filter is to be coated on glass having index 1.52. The filter operates
at normal incidence. So that the demo version of TFCalc can be used to design this filter,
we use SIO2 and TIO2 as the two coating materials.
We use a total of nine optimization targets: eight discrete targets of 100% transmission at each of the four desired wavelengths ±1 nm and one continuous target asking for less than 10% transmission from 600 to 950 nm. Although it may seem contradictory to have a continuous target that includes the eight discrete targets, it works in TFCalc because each discrete target has the same weight as the entire continuous target.
There is no theory for a bandpass filter of this type. Hence we use TFCalc's needle/tunneling optimization to design the filter from "scratch". That is, we start with one thin layer of TIO2 and have TFCalc grow that layer into a filter meeting the requirements. After a few minutes, TFCalc finds a 21-layer design having the transmission curve shown below.
Here is the design with thicknesses given in nm:
TIO2 75.13 SIO2 126.59 TIO2 78.97 SIO2 128.10 TIO2 79.51 SIO2 200.03 TIO2 113.53 SIO2 153.01 TIO2 43.45 SIO2 20.85 TIO2 84.08 SIO2 140.53 TIO2 19.37 SIO2 59.24 TIO2 84.74 SIO2 194.55 TIO2 122.32 SIO2 128.32 TIO2 79.15 SIO2 127.49 TIO2 77.77
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