Abstract

This paper introduces a method for synthesis of optical thin-film coatings aimed at both simplicity and versatility. Implementation of the method in a computer program allows the designer to build a multilayer interactively by successive construction of special four-layer modules. Each added module effects an exact transformation at a single wavelength from an initial point in the complex reflectance plane to a desired target point. The computational algorithm is practical for use on a small computer yet yields good results without the need for starting designs. Several synthesis examples are presented.

© 1983 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. P. Borgogno, E. Pelletier, J. Opt. Soc. Am. 68, 964 (1978).
    [CrossRef]
  2. A. L. Bloom, Appl. Opt. 20, 66 (1981). (A brief survey of refinement methods is given in this paper.)
    [CrossRef] [PubMed]
  3. J. A. Dobrowolski, Appl. Opt. 4, 937 (1965);Appl. Opt.9, 1396 (1970);Appl. Opt.20, 74 (1981).
    [CrossRef] [PubMed]
  4. J. F. Tang, Q. Zheng, J. Opt. Soc. Am. 72, 1522 (1982).
    [CrossRef]
  5. P. H. Berning, A. F. Turner, J. Opt. Soc. Am. 47, 230 (1957).
    [CrossRef]

1982 (1)

1981 (1)

1978 (1)

1965 (1)

1957 (1)

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (9)

Fig. 1
Fig. 1

Multilayer structure of N − 1 layers illustrating the use of complex reflection and transmission coefficients.

Fig. 2
Fig. 2

Four steps depicting the addition of one layer to an N − 1 layer system.

Fig. 3
Fig. 3

Addition of two nonabsorbing layers to an N′ + 2 layer system, transforming reflectance rN′+2 into rN′+4.

Fig. 4
Fig. 4

Synthesis with a four-layer module. The first addition is composed of two layers; these materials may be absorbing.

Fig. 5
Fig. 5

Theoretical performance of three-layer antireflection coatings on germanium. Curve 1 is the first synthesis attempt; curve 2 is the final result from refinement of layer thicknesses. Design details are given in Table I.

Fig. 6
Fig. 6

Theoretical performance of two antireflection designs from Table II. The substrate material is glass, index 1.52.

Fig. 7
Fig. 7

Broadband reflectance obtained from thickness variations of four film layers on germanium. The target reflectances leading to curves 1 and 2 were 81% and 95%, respectively. Curve 3 is the spectral response of a quarterwave stack centered at 10 μm. See Table III for design parameters.

Fig. 8
Fig. 8

High reflector coating on germanium with antireflection notch filtering. Design parameters are given in Table III.

Fig. 9
Fig. 9

Spectral characteristics of a nineteen-layer induced transmission filter design. Aluminum is the metal film, thickness 10 nm. See Table IV for details.

Tables (4)

Tables Icon

Table I Optical Description of a Three-Layer Antireflection Coating for Germanium (Target Reflectance at 3.2-μm Wavelength, λmin = 3.0 μm, λmax = 5.8 μm, Nλ = 8)

Tables Icon

Table II Optical Description of Two Antireflection Coatings for Glass (Target Reflectance at 450-nm Wavelength, λmin = 400 nm, λmax = 680 nm, Nλ = 8)

Tables Icon

Table III Broadband, High Reflectors for the 8–12- μm Wavelength Region

Tables Icon

Table IV Optical Description of an Induced Transmission Filter (Target Reflectance at 500-nm Wavelength, λmin = 520 nm, λmax = 600 nm, Nλ =5)

Equations (35)

Equations on this page are rendered with MathJax. Learn more.

r N = f N ( 1 ɛ N 2 ) + ( ɛ N 2 f N 2 ) r N 1 ( 1 f N 2 ɛ N 2 ) + f N ( 1 ɛ N 2 ) r N 1 ,
t N = n ̂ N τ N 2 ɛ N ( 1 f N 2 ɛ N 2 ) + f N ( 1 ɛ N 2 ) r N 1 ,
f N = ( n ̂ N 1 ) / ( n ̂ N + 1 ) , τ N = 2 / ( n ̂ N + 1 ) ,
ɛ N = exp ( i 2 π n ̂ N d N / λ ) .
p N = ( f N + r N 1 ) / ( 1 + f N r N 1 ) ,
q N = n ̂ N τ N t N 1 / ( 1 + f N r N 1 ) ,
r N = ( f N + z N ) / ( 1 f N z N ) ,
t N = τ N ɛ N q N / ( 1 f N z N ) ,
p N = ( α N + z N 1 ) / ( 1 + α N z N 1 ) ,
α N = ( f N f N 1 ) / ( 1 f N f N 1 ) ,
z N = ɛ N 2 p N .
t N = ɛ N ( 1 f N p N ) t N 1 / ( 1 f N z N ) .
p 3 = ( f 3 + r 2 ) / ( 1 + f 3 r 2 ) ,
| p 3 | 2 = ( xp 3 ) 2 + ( yp 3 ) 2 .
z 4 = ( f 4 + r 4 ) / ( 1 + f 4 r 4 ) ,
| z 4 | 2 = ( xy 4 ) 2 + ( yz 4 ) 2 .
| z 4 | = | p 4 | = | ( α 4 + z 3 ) / ( 1 + α 4 z 3 ) | .
xz 3 = | z 4 | 2 | p 3 | 2 α 4 2 ( 1 | z 4 | 2 | p 3 | 2 ) 2 α 4 ( 1 | z 4 | 2 ) .
yz 3 = ± [ | p 3 | 2 ( xz 3 ) 2 ] 1 / 2 .
p 4 = ( α 4 + z 3 ) / ( 1 + α 4 z 3 ) .
ɛ j 2 = z j / p j = z j p j * / | p j | 2 .
cos ( 4 π n j d j / λ ) = [ ( xz j ) ( xp j ) + ( yz j ) ( yp j ) ] / | p j | 2 ,
sin ( 4 π n j d j / λ ) = [ ( yz j ) ( xp j ) ( xz j ) ( yp j ) ] / | p j | 2 ,
MF = λ | r 4 ( λ ) r T ( λ ) | 2 ,
MF = λ | R 4 ( λ ) R T ( λ ) | .
Δ λ = ( λ max λ min ) / ( N λ 1 ) .
2 u 2 = [ ( n 2 k 2 γ 2 ) 2 + 4 n 2 k 2 ] 1 / 2 + ( n 2 k 2 γ 2 ) ,
2 υ 2 = [ ( n 2 k 2 γ 2 ) 2 + 4 n 2 k 2 ] 1 / 2 ( n 2 k 2 γ 2 ) ,
n ̂ = β ̂ / ( 1 γ 2 ) 1 / 2 , s polarization ,
n ̂ = ( n + ik ) 2 ( 1 γ 2 ) 1 / 2 / β ̂ , p polarization .
f = ( n ̂ 1 ) / ( n ̂ + 1 ) ; τ = 2 / ( n ̂ + 1 ) ,
ɛ = exp ( i 2 π β ̂ d / λ ) .
R = | r | 2 , s - or p polarization ,
T = ( u o / n i cos Θ i ) | t | 2 , s polarization ,
T = real part of [ ( n 0 + ik 0 ) 2 / β ̂ 0 ] ( n i / cos Θ i ) | t | 2 , p polarization .

Metrics