[size=+3]Broadband Antireflection Graded-Index Coating
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" Z. s4 w3 ^: w3 d0 `* QIn an important 1962 paper, 0 h0 o" d) {* N; u5 r1 y; j9 n
Peter H. Berning, "Use of Equivalent films in the design of infrared multilayer antireflection coatings", Journal of the Optical Society of America, Vol. 52(4), pp. 431-436 (April 1962).
1 p7 H- c% ~: P, n& o- L" _) F7 bone of the coatings discussed by the author is a step-graded-index antireflection coating for germanium. This coating consists of 20 quarter-wave layers whose indices vary linearly from 1.35 (the lowest practical index available) to 4 (the index of germanium), as illustrated below.
; f9 A, i& P! ^7 Y5 x+ I2 a" S+ n% F3 }/ E# ~
The coating has a very broad wavelength range over which the reflectance is low. The question arises: is the linear profile the best possible? We can use optimization to explore this problem. Here we use a feature unique to TFCalc -- the capability of optimizing the reflective index while keeping the optical thickness fixed. We use one continuous optimization target: R=0 for 3-20 microns. To make the reflectance as flat as possible, we set the power in the merit function to 16. Surprisingly, the resulting index profile looks like part of a sine curve: ' ?) F, @2 H0 p/ r4 V; x
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The performance of the optimized design is significantly better. The reflectances of the two designs are shown below. $ N/ R# g; f% F; R
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+ J1 z( q* q, z# ?$ I( p
Here is the list of refractive indices in the optimized design, starting with the layer closest to the germanium substrate:
: K6 R4 W. C3 L2 J% x5 S( ^ 1 3.93568 S6 ^1 S* A* v5 {$ b. ?. E! O
2 3.7482- I5 x" a9 `$ ~/ b
3 3.3986
: y+ }4 @4 ?0 ~1 p, c7 S9 g 4 2.9121
3 w1 L! _, a2 S0 g0 n( q$ M 5 2.3790* o' O5 K: o5 o" Z; M
6 1.9044& b3 I F( M2 F
7 1.5598, m$ p1 f0 Z! p( n. k
8 1.3726
$ o; b- ~" t7 U/ k( r2 e' M$ [ 9 1.3500. |; ^2 k( U- ]
10 1.50424 s, a8 V1 U+ y6 M+ W2 N9 F
11 1.86062 E3 u8 b9 K! H: [0 r
12 2.4315* v7 Q1 B, J1 \$ ?7 [$ ?3 o# d
13 3.1456% R' u" q* _8 f( j' e4 p+ U! P
14 3.7738) L ^- a/ L) Q1 ?' f" `$ Z" z
15 4.0000
6 ?# m- n- o3 q* Q* j$ a 16 3.6871
1 r' b9 R8 ]/ I* J& h. Z 17 3.0181
3 X0 |+ w! _/ e 18 2.3016
+ q: c: m a5 @2 O8 V# E 19 1.7310! X2 N$ ]8 o! V, B; ?2 v0 q
20 1.35004 r2 c8 r8 u& I. Q8 h
The reference wavelength for the quarter-wave optical thickness is 5.217 microns, which is the midpoint, in the frequency scale, between 3 and 20 microns.
3 [9 Y T4 _( P# VNote: by using more layers, designs with more cycles of the sine curve can be found. However, the additional cycles do not improve the performance as dramatically as above. 8 y: i @/ I0 Z- i8 B
Download DesignYou may download the Berning design and watch how TFCalc optimizes it. You will need a real copy (i.e., not a demo) of TFCalc. Click here for the Windows or Macintosh file. This design assumes that you have a substrate called G whose index is 4. The G substrate was installed with the TFCalc software. $ U0 G. L# M4 i R
Windows users, when they download this file, will have to save it to disk. Be sure to save it with extension ".TFD". |