Four-Wavelength Bandpass Filter

[size=+3]Four-Wavelength Bandpass Filter
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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.
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+ |$ ~  p# S1 k3 R2 c Here is the design with thicknesses given in nm:
TIO2      75.13
# N1 b; M7 d: m5 G; j. @. I# ^SIO2     126.59
# ?, C: s0 K# u! ~5 ~' A/ r; `TIO2      78.97
- a2 a, c/ k/ g! n. H/ ESIO2     128.10
9 K* a  a9 e) Q$ G- x. eTIO2      79.51
6 ?8 E/ o6 u( Q* t6 Z1 X1 FSIO2     200.03
0 {1 b# Q7 ~, V/ sTIO2     113.53
SIO2     153.01
3 A4 k0 x0 Z2 A0 y/ ?( Y& KTIO2      43.45
5 G; k4 v) V6 W3 ^" i  D/ h5 ^SIO2      20.85
' o* k( h; C" }  @TIO2      84.08
SIO2     140.53
TIO2      19.37
3 o/ |% p; S/ d6 g5 OSIO2      59.24
. o+ Z0 C1 v6 bTIO2      84.74
SIO2     194.55
TIO2     122.32
5 l) P( N6 H# `  a" }+ S' nSIO2     128.32
TIO2      79.15
SIO2     127.49
' u# g2 W' x7 h2 cTIO2      77.77