Four-Wavelength Bandpass Filter

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0 I3 x: s/ M( h) I: N[size=+3]Four-Wavelength Bandpass Filter

$ ^- b: W6 y2 c; d8 u, p$ [- IThis 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.

& x- E5 d; v2 D" k( _) u Here is the design with thicknesses given in nm:
TIO2      75.13
  e. R$ p/ q* ?" vSIO2     126.59
: u8 I4 I/ H$ s. D% tTIO2      78.97
SIO2     128.10
$ @4 g' J! `2 gTIO2      79.51
5 j8 r: l6 c" |- y# GSIO2     200.03
+ b5 q& o9 [$ b9 a) E& `: j& mTIO2     113.53
SIO2     153.01
# d2 g2 J7 K3 _TIO2      43.45
" f) j0 d) s" T. W/ YSIO2      20.85
TIO2      84.08
- o, L" k" [( K6 ~9 X$ hSIO2     140.53
$ Y/ I; N1 t' Y" ATIO2      19.37
6 y' m! \6 w) w1 _SIO2      59.24
2 B9 q1 h5 t# N0 z0 y; P. {TIO2      84.74
" Y$ C1 D& u; L1 H1 Z  bSIO2     194.55
- A# x1 p1 U; L+ UTIO2     122.32
SIO2     128.32
TIO2      79.15
SIO2     127.49
TIO2      77.77

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