antireflection coatings for both visible and far-infrared spectral regions

Antireflection coatings for both visible andfar-infrared spectral regions

Li Li, J. A. Dobrowolski, J. D. Sankey, and J. R. Wimperis

Two methods are described for the design of antireflection coatings that act in two widely separatedspectral regions. Design results are presented for coatings on ZnS, ZnSe, and Ge substrates that reducethe reflectance in a broad region at 10 plm, as well as in a band of wavelengths in the visible ornear-infrared part of the spectrum.

1. Introduction

While antireflection (AR) coatings have importantapplications in the ultraviolet and visible spectralregions, they are particularly indispensable in infra-red instrumentation for which high refractive-indexsubstrates are often used. Without these AR coat-ings, the surface reflectances of optical componentswould be prohibitively high in this region.

Since the first book on this topic,' hundreds ofpapers have been written and patents issued dealingwith AR coatings. Excellent reviews of the topic canbe found in Refs. 2-5. However, relatively littleattention has been paid thus far to AR coatings thathave been designed to act simultaneously in morethan one spectral region. An exception to this arecoatings for optical components that are used forfrequency doubling or tripling.6 -8 In these in-stances, the wavelengths of interest are within afactor of 2 or 3 of each other. In general, however,there exists a requirement for AR coatings that act inwidely separated spectral regions. For example,whenever visible light is used in the alignment ofinfrared optics, the reflectances from ZnSe and Geoptics carrying far-infrared reflecting coatings can bequite troublesome. As another example, in our labo-ratory the 12.56-pm transition of a single barium ionis being investigated as a possible frequency stan-dard.9 10 The electronic state of this ion is deter-

L. Li and J. A. Dobrowolski are with the Institute for Microstruc-tural Sciences, National Research Council of Canada, Ottawa,Ontario KlA OR6, Canada. J. D. Sankey is with the Institute forNational Measurement Standards, National Research Council ofCanada, Ottawa, Ontario KlA OR6. J. R. Wimperis is withInteroptics, a Division of Lumonics, Inc., 14 Capella Court, Ne-

pean, Ontario K2E 7V6, Canada.Received 10 January 1992.

Experimental results are given for one system.

mined from the scattering of 0.493-pm radiation.For this experiment surfaces are required that have alow reflectance at 0.493 ,um combined with a hightransmittance at 12.56 pm. In both of these applica-tions the ratio of the two wavelength regions ofinterest is of the order of 20:1.

A simple solution to this problem is a single-layerAR coating for the infrared wavelength. Becausethe layer is thick, there will be many higher-orderminima in the visible part of the spectrum. It ispossible to adjust one of these minima to coincidewith the required visible wavelength without seri-ously affecting the infrared performance. Such coat-ings are available commercially, however, the lowreflection regions are narrow, especially in the visible.More elaborate coatings for this purpose, based onthe use of several layers, have been designed with theaid of refinement programs, but, to our knowledge,the systems have not been described in the openliterature."

In this paper we present two systematic methodsfor the design of broadband AR coatings for twowidely separated spectral regions (Section 2). Theresults of some numerical calculations are given inSection 3. The preparation and the experimentalperformance of one dual-band AR coating is describedin Section 4. This is followed by some generalcomments (Section 5).

2. Design Approach

The design of an AR coating with low reflectance inboth the far-infrared (AIR) and in the visible (XVIS)parts of the spectrum is rather difficult because oftheir wide separation. While it is relatively simple todesign AR coatings for each of the two regionsseparately, when the two multilayers are combinedon one substrate, interference effects between thetwo systems will occur and lead to a loss of perfor-

6150 APPLIED OPTICS / Vol. 31, No. 28 / 1 October 1992

mance. In the present case one would expect thedeterioration in the infrared not to be serious. Theratio IR/XVIs is 20:1 and hence the visible ARcoating is relatively thin in the infiraed-and-thereforeshould have little effect on the performance in thatregion. Unfortunately, the infrared AR coating willdefinitely affect the performance in the visible region.In this section we describe two approaches to thesolution of this problem. One is based on the elimi-nation of interface reflections, and the other is basedon the use of extended buffer layers. For the pur-pose of this problem they are equivalent, and both areillustrated with the aid of Fig. 1.

A. Method Based on the Elimination of InterfaceReflections

In Fig. 1(a) n, n, and nm are the refractive indices of athick layer, substrate, and medium, respectively.If ni differs substantially from either the substrate ormedium refractive index, the transmission spectrumwill exhibit the familiar maxima and minima that areassociated with interference of light in a single film.To eliminate or reduce the amplitude of these oscilla-tions, it is necessary to remove the reflection from oneof the two interfaces of this layer. For example, inFig. 1(b) the thicknesses and optical constants oflayers 1 to (i - 1) can be chosen such that the layers

(a)

n, n1 n2 ... n i,1n

~~1_ _

I (b)

nn n2 ...n. n+1 ..n nm

act as an AR coating I between two media of refractiveindices nm and ni. In the spectral region for whichthe AR coating is designed, only the interface betweenthe -layer n and the medium nm remains effective.The spectral reflectance of the complete system willbe constant and independent of the thickness of theith layer. Now if a second set of layers (i + 1) to I isadded to form an AR coating II for the secondinterface, the transmission will be close to unity inthe spectral region in which both AR coatings I and IIare effective [Fig. 1(c)]. The above principle wasapplied in 1955 to AR coat 5-p1m-thick ZnS layerswith a radial thickness variation for use in asphericoptical elements.12,' 3

This principle can also be used to design an ARcoating with a low reflectance in the far-infrared andin the visible parts of the spectrum. For this pur-pose layer i is chosen to have an optical thickness ofXIR/ 4 and a refractive index of n = (nsfnm) 1 2

. Thenext step is to surround this layer by suitable ARcoatings I and II for the visible part of the spectrum.These coatings may consist of one or more layers ofdifferent refractive indices and non-quarter-wave op-tical thicknesses.

B. Method Based on the Use of Extended Buffer Layers

Mouchart described the important concept of a bufferlayer whose thickness, at one wavelength, does notaffect the performance of a multilayer containing it.14Knittl used this additional degree of freedom tocontrol polarization effects in filters.15 Becausebuffer layers offer a powerful approach not only to thedesign of AR coatings for two widely separated spec-tral regions but also for the solution of other prob-lems, a brief review of the topic is given here.

The buffer layer concept can be readily explainedwith the aid of an admittance diagram (Fig. 2).Consider the system of Fig. 1(c). Let the admittanceof subsystem I be Y and let it correspond to point A inFig. 2. In this diagram the admittance locus of theith layer is a circle of diameter that depends on Y andthe refractive index n of the layer. Points A and B atthe intersection of the circle with the real axiscorrespond to optical thicknesses that are even andodd multiples of a quarter wavelength, respectively.Clearly the admittance of the system is not changedby the addition of multiples of half-wave layers, no

I (c) 1I

zc~

0 X/ ? 2 nm

1. Sc e m t(d ) Il IV

Fig. 1. Schematic representation of various multilayers and theirsubsystems (see text).

ni-i

ABREAL

n 4

Fig. 2. Representation of the concepts of absentee and bufferlayers on an admittance chart.

1 October 1992 / Vol. 31, No. 28 / APPLIED OPTICS 6151

matter what their refractive index. Such index-independent layers are therefore called absentee lay-ers. When the refractive index ni is equal to admit-tance Y, the diameter of the circle in the admittancediagram corresponding to the ith layer shrinks to apoint, and A and B coincide. The performance of anysystem containing such a layer will therefore notdepend on its thickness. (If there is absorption inlayer i, the above statement is true for reflectanceonly.) The term buffer layer is applied to such athickness-independent absentee layer.

To make the ith layer into a buffer layer it isnecessary to add layers to the substrate so that theequivalent admittance of the resulting substrate-layer combination will match refractive index ni atXvIs. In the following, such subsystems are referredto as matching layers. From the point of view ofreflectance, the matching layers behave like a visibleAR coating for the n, I ni interface. Buffer layer i willcontinue to act as a buffer layer even if a secondsubsystem II is deposited over it [Fig. 1(c)]. To makethe reflectance of the complete system equal to zero,the second subsystem II must also be a visible ARcoating. If layer i is chosen to be an AR coating forAIR, then the complete system will act as an ARcoating at both wavelengths.

The above conclusions are valid for the designwavelengths XvIs and AIR only. This may be suffi-cient for many applications. However, for the pur-pose at hand it is important that the AR coatings inthe visible part of the spectrum be sufficiently broad.To achieve this within the constraints of real coatingmaterials, AR coatings I and II consisting of morethan one layer may have to be used. In conjunctionwith such coatings, the buffer layer is effective notonly at the design wavelengths but also for a consider-able spectral range around it. This is what is meantby the term extended buffer layer.

The number of coating materials available for theinfrared part of the spectrum is rather limited, and asatisfactory performance may not be achieved with asingle layer of refractive index ni. There is no reasonwhy a multilayer solution should not be selected forthe infrared component as well. This is illustratedin Fig. 1(d), in which three layers of refractive indicesni, nj, and nk form an infrared AR coating centered atAIR. They are sandwiched between subsystems I, II,III, and IV that act as AR coatings at the appropriateinterfaces. In principle, a multilayer can include anynumber of extended buffer layers.

C. Design of the Infrared and Visible AR Coatings

Any one of the design approaches for AR coatingsdescribed in Refs. 1-5 can be employed to obtainsuitable solutions for the infrared or visible sub-systems. Alternatively, it is possible to use a thin-film synthesis program, such as those described inRef. 16. Note, however, that many infrared sub-strates and coating materials have large extinctioncoefficients in the visible. Therefore one has to solvefor the thicknesses of matching layers that do not

absorb in the visible and that remove the reflectancefrom the interface between two admittances Y, andY2. These admittances, Y = ( + il) and Y2 =

(a2 + i2), may correspond to the complex refractiveindices of media or coating materials or to the admit-tances of multilayers. This provides enough degreesof freedom even when the two media are both absorb-ing. The derivation of the expressions for the thick-nesses of a two-layer AR coating are given in Appen-dix A.

D. Refinement of the Primary Solution

Systems of the type shown in Figs. 1(c) and 1(d) canbe composed of the various subsystems obtained fromthe formulas for two-layer AR coatings or by othermeans. The resulting multilayer can then be usedas a starting design for numerical refinement withone of the many available optimization routines.' 7

An improvement in performance can be achieved inthis way. In the optimization calculations the disper-sion of the refractive indices and the extinctioncoefficients of the coating and substrate materialsmust be allowed for.

3. Results of Calculations

For this paper five AR coatings were designed (Table1). In this table material names of layers in theinfrared AR coatings are printed in bold charactersand are underlined. The spectral regions of thecoatings and the substrate materials are also listed inTable 1. Initial designs were obtained by the meth-ods described in Section 2 and were refined by usingthe damped-least-squares method. The followingmerit function (MF) was used:

(1)

where M is the number of wavelengths in the visibleand infrared spectral regions at which the target andcalculated reflectances RR and R are compared. Thetolerance AR on the reflectance was equal to 0.01.

The designs were based on ZnS and ThF4, and theoptical constants of ThF4 , Ge, ZnS, and ZnSe weretaken from Palik.'8 ,19 The calculated performancesof the systems are shown in Figs. 3(a)-3(e). For thesake of clarity the visible and infrared portions of thereflectance spectrum are plotted separately. Thedotted and solid curves in each diagram represent theperformance of the designs before and after refine-ment, respectively.

The infrared AR coating for ZnSe in Fig. 3(a)consists of a single layer of ThF4 and therefore cannotreduce the reflectance to zero at X = 12.56 pmbecause the index of this material is not equal to(nsnm)1/2. Notice, however, that the visible AR coat-ing does reduce the reflection to zero at X = 0.493 ,um.By using a two-layer infrared AR design for theinfrared, the reflectance in both spectral regions canbe reduced to small values [Fig. 3(b)]. These ARcoatings are suitable for optics for the frequency


i M T - R 2 12

MF = 1 8R

Table 1. Construction Parameters

Example A B C D E

Wavelength Xv,,=0

.49 3 Xv,=0.493 Xvis=0.6328 XvIs=0.6 328

xl~.0(ji) XrR =12.56 , I= 1 2.56 ~ Jn 10.60 XIR =1 060 ________=8__12 _

Substrate ZnSe ZnSe I ZnSe Germanium IZnS

Metric Material Metric Metric Metric Thickness Metric

Layer No. Material Tik s tmThcns Lr)material Thcns(t)Material Matal e 4mStarting Final Starting Final Starting Final Starting Final Ll starting FinalDesign Design Design Design Design Design Design Design ____ Design Design

Substrate ZnSe _ ZnSe _ Ge ZnS _ ___

1 ThF, 0.0193 0.0179 ThF4 0.0193 0.0187 ThF4 0.0282 0.0264 ZnS 0.0607 0.0669 ThF, 0.0429 0.0337

2 ZnS 0.0227 0.0235 ZnS 0.0227 0.0234 ZnS 0.0278 0.0292 ThF, 0.1079 0.02 ZnS 0.0281 0.0550

3 ThF4 2.4039 2.2906 ThF4 1.1202 1.1578 ThF4 0.9724 0.8932 ZnS 1.0355 0.8111 TF 0.3418 0.2970

4 ZnS 0.0145 0.0142 ZnS 0.0164 0.0135 ZnS 0.0218 0.0196 ThF4 0.0338 0.0433 ZnS 0.0281 _

5 ThF4 0.1087 0.1083 ThF4 0.0262 0.0326 ThF4 0.0338 0.0390 ZnS 0.0218 0.0152 ThF4 0.0429 _

6 Air ZnS 0.3970 0.3138 ZnS 0.3163 0.2604 ThF, 0.9496 0.7664 ,ZnS 0.5082 0.4812

7 1ThF 4 0.0637 0.0819 ThF, 0.0894 0.0905 ZnS 0.0207 0.0241 ThF, 0.0429 0.0264

8 ZnS 0.0049 _ ZnS 0.0043 0.0023 ThF4 0.1388 0.1331 ZnS 0.0281 0.0288

9 ~~~~~~ ~~ ~~~Air _ _ Air Air - - hF4 1. 9471 1.6002

10 ZnS 0.0278 0.0279

11 _ _ _ __ _ _ _ _ ___ _ _ _ _ _ __ _ _ ThF, 0.1749 0.1736

Medium Air

E t) (jm 2.569112.4545 1.6704 1.641 1.494011.36062.3 3688 1.942313.2 2128.7238Merit Fnton 2.098 j1.469 0.608 J022J1.071 0.240 J - J4.269 1.013 j1.208 0.20

standard based on the single barium-ion transitionmentioned in Section 1. Figure 3(c) shows similarresults for an AR coating on a ZnSe substrate thatwas designed for 0.6328- and 10.6-pLnm laser wave-lengths.

The next AR coating was for a Ge substrate [Fig.3(d)]. Unlike the ZnSe substrate above, this mate-rial has a strong absorption coefficient in the visiblepart of the spectrum. The design of an AR coatingby conventional methods is not so straightforward.However, the application of the equations given inAppendix A yields a good starting design. Numericalrefinement results in a further improvement of theperformance both in the visible and infrared parts ofthe spectrum.

The last example, for a ZnS substrate, was chosento illustrate that it is also possible to design widebandAR coatings for the infrared spectral region from 8.0to 12.0 pim [Fig. 3(e)]. Here the infrared componentconsists of three layers. It is important to mentionthat it is not always necessary to add visible ARcoatings at all the interfaces (see Table 1, example E).This is especially true when the reflection from theinterface is small or when there are many layers (and,hence, parameters) available to reduce the reflectionin the visible spectral region.

The performances of the starting designs are closeto the required performances, especially in the visiblespectral region in which the infrared layers act asbuffer layers. The slight shift of the infrared reflec-tance curve toward longer wavelengths is due to the

incorporation of the visible AR layers in the system.The greater the ratio f XIR/XVIS, the smaller thisdisplacement will be. It is possible to compensatefor it by reducing the optical thicknesses of theinfrared layers. This was done for the example ofFig. 3(c). As a result, the performance of this partic-ular starting design was quite good in both the visibleand infrared spectral regions.

4. Experimental Results

To verify the above calculations we produced the ARcoating in Fig. 3(c). The substrate was a 3.0-mm-thick ZnSe piece polished flat to within 2 Xv~s and withplane-parallel surfaces to within 0.10. The deposi-tion system was a 500-mm bell jar equipped with afour-pocket Temescal electron-beam gun source.The base pressure of this system was 2 10-6 Torr,and the pressure did not exceed 3 x 10-5 Torr duringthe deposition process. The substrate was notheated. Optical monitoring with visible light wasused to control the thicknesses of the layers. Thecoating was deposited onto one side of the substrate.

Before the reflectance was measured, the uncoatedsurface of the substrate was roughened and paintedblack to prevent second surface reflection. The visi-ble reflectance measurements were performed on aPerkin-Elmer Lambda 9 spectrophotometer. Theinfrared reflectance was measured on a Perkin-ElmerModel 1310 Fourier-transform spectrophotometer.In Fig. 4 the experimental results are compared withthe calculated performance and with the reflectance


REFLECTANCE - VISIBLE

-(a)

0.46 0.48 0.50 0.52 0.54

(b)

. - -I -.- . -

0.46 0.48 0.50 0.52 0.54

0.60 0.65 0.70 0.75

0.70 0.75 0.80 0.85 0.90

REFLECTANCE - INFRARED

10.0

10.0

8.0

8.0

8.0 10.0 12.0

WAVELENGTH (gm) WAVELENGTH (gm)

Fig. 3. Calculated performance of various AR coatings: (a), (b) ZnSe substrate, XIR = 12.56 Wim, XvIs = 0.493 jim; (c) ZnSe substrate,

XIR = 10.6 jim, XvIS = 0.6328 jim; (d) Ge substrate, XIR = 10.6 jim, XvIs = 0.6328 jim; (e) ZnS substrate, XIR = 8-12 jim, XvIS = 0.8000 jim.

The dotted and solid curves represent the calculated performance before and after numerical refinement. The broken curve in (c) is the

modified starting design (see text).

of an uncoated surface. The difference in wave- dispersion of the optical constants of the coatinglength between the experimental and calculated curves materials, to monitoring errors, and/or to a change inin the infrared and the slight distortion of the visible sticking coefficients of the ZnS with a change incurve are probably due to an uncertainty in the substrate temperature.


0.10

0.06 _

11TNW I

14.0I I I I I I I

I I11.0 12.0 13.0 14.0

0.02t

0.10

0.06

0.02

0.10

0.06

0.02

0.10

0.06 1

0.02 1

0.10

0.06

0.02

I I I

I ~ ~ ~ ~ ~ -4

1412.010.0

(d) I I

I ii1� . .

I I . .... L. I I I

I I I I I

X '""' X~~~~~~

_ \ '-", /~I,I"

50.60 0.65 0.70 0.7g

(e)I I I I

_~~ \%/_

I I I I I I

, I lS I --- -- -- -- .1..

1412.010.0

.0

.0

.014

1

thicknesses t1 and t2:

F cos~~1 . sin 81 sin 2]tB = Cos 81 i n, 1COS 82 in 1

C .in, sin 1 cos8 1 cin2sin 2 cos 82

X l i2 ] (Al)0.60 0.65 0.70 0.75

8.0 9.0 10.0 11.0

WAVELENGTH (pm)

where the quantities 81 and 82 are given by

2 1r8 = 7 nt,

27r°2 = - n2t2

12.0

Fig. 4. Comparison of the calculated (dotted curves) and experi-mental (solid curves) results in the visible (a) and infrared (b)spectral regions for the AR coating in Fig. 3(c). The reflection ofthe uncoated substrate is represented by the dashed curves.

(A2)

and is the wavelength of light. If the two layers areto act as a matching coating between ( + ) and(a2 + i2), the equivalent admittance Y must also beequal to the complex admittance ( + i):

CY= B= Yl +Y 2 = al + il.

5. Conclusions

It has been shown theoretically and experimentallythat it is possible to construct AR coatings on infraredsubstrate materials that operate in widely separatedspectral regions. Fairly wide AR regions in thevisible and in the infrared can also be achievedsimultaneously. This improves the chances of asuccessful manufacture of the coating. The use ofthese more complex designs does not materially affectthe overall deposition time and therefore should notsubstantially increase the cost of infrared AR coat-ings.

Equations for the thicknesses of two-layer ARsubsystems have been presented that are suitable forsubstrates and infrared coating materials with largeextinction coefficients in the visible part of the spec-trum. The starting designs need only a little refine-ment to achieve the desired performance.

The methods described in this paper can be appliedto other substrates and spectral regions.

It can be readily shown that Eqs. (Al) and (A3) yieldthe following expressions:

alxy + bix + cly + di = 0a2xy + b2x + c2y + d2 = 0' (A4)

where the various constants are defined as follows:

= tan °1

1Y = tan 82 '

X

Appendix A

Expressions for the thicknesses of a two-layer ARcoating for nonabsorbing substrates have been given,for example, by Catalan.20 We present here thecorresponding expressions for an interface betweentwo equivalent media with admittances ( + il)and ( 2 + i 2). These admittances may correspondto the complex refractive indices of media or coatingmaterials or to the admittances of multilayers.

Consider the characteristic matrix of a two-layersystem of refractive indices n and n2 and metric

(a,aln 2 a 2n,nl n2

b, 1132 a 2 13

nl ni

c _ Y1 f32 +a 2 13 1

n 2 n2

d = t2 -

a2 =

jb2 =

C2 = n2

P3n 2 132 n,

nl n2

oa1at2 131 132nl --+nl nl (A5)

a a 2 131 132_ +n2 n2

K = 132 - 31

Equations (A4) can be rewritten as follows:

Iy= ex + f

|ax2 + bx + c = Depending on whether the constants a, a2 are zero,four different definitions of the constants a, b, c, e,

(A6)


(a)' ' ' ' '

…

0.2

0.1

An Iu.V _

0.55

w0z0w-jLLw

0.2(-) . . . . I - I -

_ _ _ _.__ _

0.1

0.0

- l

(A3)

a=oa = 0 1~fa = 0b = C2bl - clb2 if a oC= c2 d - d2

a = a2e

b = a 2 f+ b2 + 2 e

C = C2 f+ d2

a= aleb = alf + b + cle

c=clf+ dl

a2 b1 - alb 2

a2C - aC2

a2d1- ad2a2C1 - aC 2

if a1= 0a2 ;d O

if (a1 O 0a2 = 0

a= aleb = alf+b +clec = clf + d

if ( 1•0 (A10)

It is therefore possible to solve Eq. (A6) first for x,then fory, and, hence, for t1 and t2-

This work was first reported at the Annual Meetingof the Optical Society of America, November 1991, inSan Jose, Calif. The authors are grateful to B. T.Sullivan for his comments.

References and Notes1. I. V. Grebenshchikov, ed., Prosuetlenie Optiki (Antireflection

Coating of Optical Surfaces) (State Publishers of Technical &Theoretical Literature, Moscow, 1946).

2. J. T. Cox and G. Hass, "Antireflection coatings for optical andinfrared optical materials," Phys. Thin Films 2, 239-304(1964).

3. A. Mussett and A. Thelen, "Multilayer antireflection coatings,"in Progress in Optics, E. Wolf, ed. (Pergamon, New York,

1970), Vol. 8, pp. 203-237.4. J. A. Dobrowolski, "Coatings and filters," in Handbook of

Optics, W. G. Driscoll and W. Vaughan, eds. (McGraw-Hill,New York, 1976), Chap. 8, pp. 8-44-8-58.

5. H. A. Macleod, Thin Film Optical Filters, 2nd ed. (McGraw-

Hill, New York, 1986), pp. 71-136.6. P. W. Baumeister, R. Moore, and K. Walsh, "Application of

linear programming to antireflection coating design," J. Opt.Soc. Am. 67, 1039-1045 (1977).

7. V. R. Costich, "Multilayer dielectric coatings," in Handbook of

Lasers, R. J. Pressley, ed. (CRC, Cleveland, Ohio, 1981), pp.

155-170.8. J. Mouchart, "Thin film optical coatings. 3: Two-wave-

length antireflection coatings," Appl. Opt. 16, 3001-3008(1977).

9. A. A. Madej and J. D. Sankey, "Quantum jumps and the singletrapped barium ion: determination of collisional quenchingrates for the 5d2D5/2 level," Phys. Rev. A 41, 2621-2630(1990).

10. K. J. Siemsen, A. A. Madej, J. D. Sankey, J. Reid, and G.Magerl, "Stable 1

5NH3 laser for cooled, single ion Ba+ fre-

quency standard," in Proceedings of Laser Spectroscopy IX(Academic, Orlando, Fla., 1989), pp. 292-294.

11. P. Baumeister and A. Bloom, Coherent, Inc., 2301 Lindbergh

Street, Auburn, Calif. 95603 (personal communication, Novem-ber 1991).

12. J. A. Dobrowolski, "Optical aspherisingby vacuum deposition,"Ph.D. dissertation (University of London, London, 1955).

13. W. Weinstein and J. A. Dobrowolski, "Production of asphericsurfaces by vacuum deposition," in Astronomical Optics andRelated Subjects, Z. Kopal, ed. (North-Holland, Amsterdam,1956), pp. 360-365.

14. J. Mouchart, "Thin film optical coatings. 5: Buffer layertheory," Appl. Opt. 17, 72-75 (1978).

15. Z. Knittl, "Control of polarization effects by internalantireflection," Appl. Opt. 20, 105-110 (1981).

16. L. Li and J. A. Dobrowolski, "Computation speeds of different

optical thin film synthesis methods," Appl. Opt. 31, 3790-3799 (1992).

17. J. A. Dobrowolski and R. A. Kemp, "Refinement of opticalmultilayer systems with different optimization procedures,"Appl. Opt. 29,2876-2893 (1990).

18. R. F. Polter, "Germanium (Ge)," pp. 465-478; E. D. Palik andA. Addamiano, "Zinc sulfide (ZnS)," pp. 597-622, in Hand-book of Optical Constants of Solids," E. D. Palik, ed. (Aca-demic, Orlando, Fla., 1985).

19. L. Ward, "Zinc selenide (ZnSe)," pp. 737-760; I. Ohidal and K.

Navratil, "Thorium fluoride (ThF4)," pp. 1049-1058, in Hand-book of Optical Constants of Solids II, E. D. Palik, ed.(Academic, Boston, Mass., 1991).

20. L. A. Catalan, "Some computed optical properties of antireflec-

tion coatings," J. Opt. Soc. Am. 52, 437-440 (1962).


and f hold:

b1e-Cl

f cldi

biC1

C1

Cl

b2e = 2

C2

d2

antireflection coatings for both visible and far-infrared spectral regions

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