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[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. % V1 q+ x! o' p
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. 6 I: M+ z5 Q8 `9 }) W8 f
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. - ^0 S$ R& ^0 `; \+ U$ ~
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Here is the design with thicknesses given in nm:
' k t/ c# t. Z: JTIO2 75.13
" K* \4 a$ K, o. rSIO2 126.599 F3 _& L6 a# G5 L7 t
TIO2 78.97: s, ~ J1 y+ n; w5 F& Q' j; a0 _
SIO2 128.10. K$ @ n# v, M4 J( j
TIO2 79.51
0 p; f8 v3 G: d5 Y9 k5 kSIO2 200.03
- {4 a8 o; D, U6 l+ J* JTIO2 113.53
/ m9 E: f9 d5 W6 D" {7 _SIO2 153.01/ l' A" G9 Q. l, B
TIO2 43.45
, o5 p$ n+ B* PSIO2 20.85
5 a& V( G7 O3 z+ p+ ?$ M3 hTIO2 84.089 t6 @, ^5 ^1 y1 D6 O. i
SIO2 140.53
# R' [ n" o8 o4 lTIO2 19.379 B9 S6 Z( \8 P: Q$ N' K
SIO2 59.24
0 g* x- x, _8 ~TIO2 84.74
, P7 H+ G( s$ cSIO2 194.55
2 n0 j6 O4 Z, b+ }1 v; v$ y; QTIO2 122.32
# ^- m' a5 p) q4 D/ k# JSIO2 128.32% ]. J) z6 X& j9 I
TIO2 79.15
' y4 [% t; d( S- ASIO2 127.49; N8 z) B3 v _* W6 M" D9 @
TIO2 77.77
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