Multiple reflectors as narrow-band and broadband vacuum ultraviolet filters

Multiple reflectors as narrow-band and broadbandvacuum ultraviolet filters

Muamer Zukic and Douglas G. Torr

We report on the development of a new coating design for applications in the vacuum ultraviolet thatyields significantly higher reflectivity over selectable bandwidths. We demonstrate that the concept can beused to fabricate high-performance narrow-band and broadband reflection filters, whose spectralproperties can be greatly enhanced by utilizing several of these filters in tandem. For example, we havefabricated a narrow-band filter at the location of the 0 I 135.6-nm line with a 3.2-nm bandwidth, a peaktransmittance of 39.3%, and out-of-band wavelength blocking of better than 10' %. The principle of ourdesign approach is to use a combination of high (H) and low (L) refractive-index dielectric pairs so thatH + L X,/2, where HIL < 1. H and L designate the optical thicknesses of high- and low-index filmmaterials. This kind of choice for the high-low ratio reduces the effects of absorption for the H films forwhich the extinction coefficient in the vacuum ultraviolet is much higher than for the low-index filmmaterial MgF,. The reduced absorption of multilayers with HIL < 1 results in a significant increase inreflectivity compared with the classical quarter-wave stack for which HIL = 1.

I. Introduction

Narrow-band filters that are commercially availablein the vacuum ultraviolet (VUV) wavelength regionfrom 120 to 160Ynm have typical transmittances lessthan 15% and a full width measured at half of thetransmittance maximum (FWHM) of greater than 25nm. The peak transmittance of the filters that arecentered at the longer wavelengths from 160 to 230nm lie between 20 and 25% with FWHM 20 nm.1

Malherbe2 reported the design and the spectralperformance of a narrow-band filter that is centeredat the hydrogen Lyman-a line (121.6 nm) with a peaktransmittance of close to 15% and a FWHM of 9 nm.The filter transmittance is close to 7% at 126 nm andalmost 1% at 135 nm. This pass window renders thefilter not particularly useful for terrestrial imagingapplications if a spectral discrimination of the atomicoxygen lines at 130.4 and 135.6 nm is desired. Anarrow-band filter that is centered at 202.5 nm wasalso reported by the same author.3 The filter has apeak transmittance of greater than 85% and a FWHMof 2.5 nm. However, the filter blocking zone is very

The authors are with the Department of Physics, University ofAlabama in Huntsville, Research Institute C-10, Huntsville, Ala-bama 35899.

Received 17 August 1990.0003-6935/92/101588-09$05.00/0.e 1992 Optical Society of America.

short (- 10 nm), and the transmittance for wave-lengths that are longer than 220 nm becomes > 85%.

The calculated and experimental spectral perfor-mance of a Fabry-Perot-type narrow-band filter cen-tered at 179 nm was reported by Spiller.4 The theoret-ical calculation predicted a narrow-band filter with aresolution of XO/AX = 60 and a peak transmittance of25%, but the measured performance had a resolutionthat was almost four times smaller and a peaktransmittance that was much smaller. Discrepanciesbetween the theoretically predicted and experimen-tally obtained spectral curves have been ascribed tothe excitation of a surface plasma wave that travelsalong the surface of an aluminum film.

The variable bandwidth transmission filter thatwas reported by Elias et al.

5 had bandwidths from 7 to20 nm with peak transmittances from 20% to 40%,respectively. The filter was centered at 176 nm and,as in the case of other all-dielectric filters, sufferedfrom pass windows in the longer-wavelength region.

Narrow-band filters for the VUV wavelength rangefrom 120 to 230 nm with optical properties that aresimilar to those listed above have been reported byother authors. 9 The FWHM bandwidths of some ofthe filters that we developed recently" are smallerthan 5 nm with peak transmittances of > 25% cen-tered at wavelengths as low as 135 nm. Since theywere all-dielectric filters, the transmittance in thelonger-wavelength region provided insufficient block-ing for some applications.

1588 APPLIED OPTICS / Vol. 31, No. 10 / 1 April 1992

Currently available VUJV broadband filters withbandwidths of > 10 nm have relatively low transmit-tance, and the shape of the transmittance curve issimilar to that of Fabry-Perot-type filters.','," Formost applications a passband with a more rectangularshape and higher transmittance is required.

By taking all this into account it is clear that theVUV spectral range lacks high-quality narrow-bandand broadband filters such as are available in thevisible and infrared parts of the spectrum. Certainly alack of low absorbing film materials in the VUV forthe all-dielectric filters and the coupling of the inci-dent light into plasma surface waves of the metal formetal-dielectric filters are reasons for this.

Hunter' 2 achieved a measure of success in solvingthis problem by combining two or more reflectors in aseries to achieve the desired spectral performance forthe design of the VUV reflection polarizers andanalyzers. The idea is that, if sufficiently high reflec-tivity can be achieved within the passband, the in-band exponential loss of reflectivity with additionalreflective surfaces becomes insignificant comparedwith the net out-of-band exponential reflectance re-duction. However, for the approach to be viable, theratio of in-band to out-of-band reflectivity at eachsurface should be of the order of 10, e.g., 90% and10%, respectively. Two reflections, for example, thenreduce the in-band reflectivity to 81%, whereas theout-of-band reflectivity is reduced to 1% and so on.

In this paper we report the successful design andfabrication of narrow-band and broadband reflectionfilters with the desired 90% reflectance. These filtersare then combined into a multiple reflector to provideexcellent blocking for out-of-band wavelengths andthe desired spectral shape for both narrow-band andbroadband applications. For example, narrow-bandfiltering with a bandwidth of 3.2 nm and a through-put at the central wavelength (135.6 nm) of 39.3%was achieved. The blocking of out-of-band wave-lengths was better than 10-4 %. A multiple reflectorwas designed to illustrate the performance of abroadband filter that was centered at 175 nm. In thiscase a bandwidth of 11 nm and throughput of > 54%were realized. Out-of-band blocking was better than3 x 10-3%.

In Section II is a review of the theory of quarter-wave (QW) and other multilayer options that we call7r filters.'3 The design and spectral performance ofseveral narrow-band and broadband filters are pre-sented in Section III. Section IV deals with experimen-tal techniques that include thin-film deposition, sub-strate handling, and preparation. A summary is inSection V.

multilayer stack are given by'4

(M1 + M21s)o - (M2,1 + M22rS),(M11 + M1 2 %q)To + (M2,1 + M22qS)

= (M11 + M210)1o + (M2,1 + M221s)

(1)

(2)

where 0 and %s, which are the effective opticalfunctions of the incident medium and the substrate,are defined as

,o = no cos 00,

,qs = ns cos Os

for s polarization, and as

cos 00no

cos Os4s =-

(3)

(4)

(5)

(6)

for p polarization. Angles 00 and O. for light propaga-tion through the incident medium and the substrateare measured relative to the normal of the film plane.Thus no and ns are the refractive indices of theincident medium and the substrate, respectively. It isassumed that both the substrate and incident me-dium have negligible extinction coefficients and there-fore real optical functions. The terms Mij, i, j = 1, 2are the elements of the multilayer characteristicmatrix M, which is defined as the product of thematrices of the individual layers Ml, where

cos StMl = i-9, sin S1

- sin lc1

Cos t

The phase thicknesses of the films 8l are given by

261= X Nd, cos 0,

x0

(7)

(8)

where Xo is the vacuum wavelength of the incidentlight, N, is the optical function (usually referred to asthe optical constant) of the lth layer, defined as

N, = n,(1 + iK,) = nj + inlK = n + iki, (9)

K, = kI /n,, n, is the refractive index, k, is the extinctioncoefficient, d, is the physical thickness, and El is thecomplex angle of the light within the Ith film.

The reflection and transmission coefficients, r andt, are complex numbers of the form

11. Absorbing Multilayers

A. Reflectance Transmittance and Absorptance

The intensity reflection and transmission coefficientsfor a plane electromagnetic wave that is incident on a

(10)r = IrI exp(i4r),

t = t exp(i4,), (11)

where (, and at are the phase changes of reflectionand transmission. The intensity reflectance R, trans-

1 April 1992 / Vol. 31, No. 10 / APPLIED OPTICS 1589

mittance T, and absorptance A of a multilayer aregiven by

R = rr*, (12)

T = IS tt*, (13)

A = 1 - (R + T). (14)

B. Quarter-Wave-Tuned Multilayers

Multilayer stacks that are formed by high- and low-index materials alternating throughout a stack areusually referred to as tuned filters or tuned multilay-ers. The basic design of such a multilayer stack isgiven in either the symmetric [(HL)PH] or the asym-metric form [(HL)P]. Symmetric (LH)PL] and asym-metric [(LH)P] tuned multilayers represent anotherform of the basic design. H and L designate the opticalthickness of high and low refractive-index film mate-rials, respectively, and p is the number of HL pairs.The form and the symmetry of a stack are determinedby the refractive indices of the substrate and incidentmedium."

If the optical thickness of a film (which is defined asa product of the physical thickness of a film and itsrefractive index) is equal to one quarter of somereference wavelength X, this film is referred to as aQW. Applications of QW multilayers are based on thefact that for an incident wavelength X = X,, thebeams reflected from the various interfaces will all bein phase, so that the reflectance obtained is a maxi-mum.

We have shown that at a zero angle of incidence,the maximum reflectance of a QW stack with absorb-ing film materials is achieved when the number of HLpairs p satisfies the following condition:

p P01= 4 tan-'i K K)j (15)

where

kH

nH (16)

nL = -X (17)

where nH and nL are refractive indices of high- andlow-index film materials, and k and kL are correspond-ing extinction coefficients. Values of p p0 corre-spond to numbers of HL pairs for which both theabsorptance and reflectance of the stack are constantand sum to unity, i.e.,

R +A-> 1, (18)

which results in a value for the stack transmittancethat is essentially equal to zero.

An alternative description of the optical propertiesof a QW stack with absorbing films might be given interms of the standing wave ratio (SWR).'6 The SWR

in general is the ratio of the maximum and minimumamplitudes in a standing wave. In multilayer theory itis the ratio of the maximum-to-minimum electric-field amplitude in the standing wave formed by theinterference of the incident and reflected electromag-netic waves. For a symmetrical QW stack

SWR = 1 + ,R1-vF (19)

where R is the intensity reflectance of the stack. TheSWR saturated level and therefore the maximumreflectance of a QW stack of the form [(HL)PH] isgiven by's

R-12 =kH + kL IRK 1 2.110nH2- nL

(20)

where RK, the ultimate reflectance, is usually referredto as the Koppelmann limit. Thus the reflectance of aQW stack R RK asp oc, if the film materials thatform the stack are absorbing. For nonabsorbing filmmaterials R - 1 asp o.

It should be emphasized that Eq. (20) was derivedwith some approximations, and it cannot replace anexact calculation of the maximum reflectance of a QWstack. Equation (20) provides an extremely simplerelationship between the maximum reflectance thatis obtainable with an absorbing QW stack and theoptical properties of film materials that form thestack. However, the value that was obtained for themaximum reflectance must be treated as an estimate.In addition RK is derived for the zero angle ofincidence, and it does not represent the ultimatereflectance for 00 0. Therefore we reference theexactly calculated reflectance [Eq. (12)] as the Koppel-mann limit for a QW stack at any angle of incidence.

The Koppelmann limit and how to extend it havebeen the subjects of a number of theoretical andexperimental studies.'1 2

1 Some approaches involvenumerical refinement of the film thicknesses to re-duce the electric-field amplitude in the high-indexmaterials that are close to the side of incidence. Otherauthors, by assuming values of the extinction coeffi-cient that are lower than 10-3, derived approximatingformulas for the thicknesses of an optimum (HL) pairthat would provide the maximum reflectance. -

BaF2 and LaF, are the only available VUV high-index film materials that are identified at this time.22

They both have values of the extinction coefficientthat are greater than 10-2 for wavelengths below 200nm. This means that most of the above-mentionedand referenced techniques for the improvement ofthe Koppelmann limit are not applicable to the VWwavelength range. Our approach to this problem is toutilize multilayer stacks with an optical thicknessratio HIL < 1 instead of standard QW stacks forwhich HIL = 1. MgF2 film material has values of theextinction coefficient of the order of 10-4 for almostthe entire VUXT wavelength region,22 and it is usedexclusively as the low-index film material for all


multilayer designs that are presented in this paper.Since the extinction coefficient of the high-indexmaterials (BaF2 and LaF3) is 100 times greater thanthat of MgF2, the stacks with HIL < 1 have lowerabsorption and therefore higher reflection than stackswith HIL = 1.

C. Third-Wave-Tuned Multilayers

The definition of the third-wave (TW) multilayers isnot standardized as in the case of the QW stacks. It isdefined here as a tuned multilayer that has onematerial with optical thickness that is equal to onethird of some reference wavelength, while the opticalthickness of the other material is equal to one sixth ofa reference wavelength, i.e.,

nHdH = 6'

A,

n~dL = 3

Since kH/kL 2 100 for the currently available high-and low-index materials in the VUV (LaF,, BaF,, andMgF2), the choice of which material should have theoptical thickness of Xr/6 is obvious.

The two H and L films in a QW multilayer form anHL pair with total optical thickness equal to Xr/2,which corresponds to a total phase thickness of the8 = rr pair. Similarly an HL pair of a TW multilayerhas an overall optical thickness that is equal to X,/2,which again corresponds to a total phase thickness ofthe pair that is equal to rr. Thus the principle of highreflectance at a reference wavelength of a TW-tunedmultilayer is similar to that of a QW stack. Theconcept of the TW multilayer leads to other kinds ofmultilayer, which are discussed in the next section.

D. rr Multilayers

We define a rr multilayer as one whose basic HL pairhas a total optical thickness of Xr/2. The opticalthicknesses of individual H and L films that form apair satisfy the following condition:

H + L = 2" (21)2~~~~~~(1where Xr is the reference wavelength of the multi-layer. The total phase thickness of the pair is equal to'r, i.e., 5

H + 5L = 'r. Thus QW and TW stacks are the

special cases of Tr multilayers. In a QW stack the lightthat is reflected from all interfaces is in phase, whilein a TW and other 1r multilayers the light that isreflected from each HL pair is in phase. Obviously,QW stacks with low-absorbing film materials (whichare available in the visible and infrared parts ofspectrum) provide higher reflectance with fewer lay-ers than other 7r stacks. However, in the VUV wherelow-absorbing high-index film materials do not exist,a 'r multilayer with a smaller physical thickness of Hrelative to L can provide lower absorptance andtherefore higher reflectance of the stack.

0

0

0

2

100

98

96

94

92

90

88

86

84

820 0. 1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

H/L

Fig. 1. Maximum reflectance of the Tr stack calculated for the zeroangle of incidence at 145 nm. The diamonds represent 99-layerstacks, triangles 55-layer stacks, and squares 35-layer stacks: H isLaF, and L is MgF2. The Koppelmann limit is 90.8%.

Figure 1 illustrates how the Koppelmann limit canbe easily extended for the zero angle of incidence. Itshows the maximum reflectances that are calculatedfor the 99-, 55-, and 35-layer 7r stacks that are plottedagainst the ratio of the optical thicknesses of high-and low-index film materials (HIL). The referencewavelength is 145 nm, with MgF, as the high-indexmaterial, LaF3 as the low-index material, and fusedsilica as the substrate. The Koppelmann limit is RK =

90.8%. The 99-layer filter has a maximum reflectanceof 96.5% when the ratio of optical thicknesses HIL =1/4. This ratio corresponds to the optical thicknessesofH = Xr/ 10 and L = 4A,/10. The 55-layer 'r stack hasa maximum reflectance of 95.3% for HIL = 1/3,which corresponds to optical thicknesses of H = Xr/8and L = 3rI/8. The HIL = 1/2 ratio provides amaximum reflectance of 93.6% for the 35-layer 'rstack. From Fig. 1 it follows that, at the zero angle ofincidence, stacks with the HIL < 1 ratio provide asignificant improvement in maximum reflectance overwhat can be achieved with QW stacks for whichHIL= 1.

Figures 2 and 3 show maximum reflectances andbandwidths (full width measured at half of the reflec-tance maximum), respectively, that are calculated at00 = 450 for the 99-, 55-, and 35-layer Tr stacks andplotted against the ratio of the optical thicknesses ofhigh- and low-index material (HIL). The referencewavelength is 135.6 nm with MgF2 as the low-indexmaterial, LaF3 as the high-index material, and fusedsilica as the substrate. The Koppelmann limit for theQW stack is RK = 89.5%, 00 = 450 at the angle ofincidence. The 99- and 55-layer 'r multilayers (Fig. 2)have a maximum reflectance of 93.0 and 92.7%,respectively, when the ratio of the optical thicknessesis HIL = 1/3. This corresponds to optical thicknessesof high- and low-index film materials:

8

3A,8


I I

1 1.1

0C.)

U3

._

10:2

100

98

96

94

92

90

88

86

84

820 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

20

18

3

E-C:

M

1 1.1

H/'L

Fig. 2. Maximum reflectance of the 7r stack calculated for a 450angle of incidence at 135.6 nm. The diamonds represent 99-layerstacks, triangles 55-layer stacks, and squares 35-layer stacks. H isLaF2 , and L is MgF,. The Koppelmann limit is 89.5%.

The 35-layer 'r stack (Fig. 1) has a maximum reflec-tance of 91.4% forH/L = 1/2. The optical thicknessesfor this H to L ratio of the Fr multilayer are given by

H = '6

L = 3

16

14

12

10

8

6

4

2

00 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1

H/LFig. 3. Full width at half of the reflectance maximum of the rstacks calculated for a 450 angle of incidence. The maximumreflectance of the stacks as a function of the HIL ratio is shown inFig. 2.

reflectance peak of 88.4%. The measured bandwidthof 7.2 nm agrees with the theoretical predictions.

Figure 5 shows the measured and calculated reflec-tance at a 450 angle of incidence for a 29-layer Fr stackwith BaF2 as the high-index material and fused silicaas the substrate. The ratio HIL = 1/3 and the opticalthicknesses are

nHdH = A,

The lowest decrease in the maximum reflectanceoccurs for the QW stack when the number of films isdecreased from 99 to 35. This result is certainlyexpected since the saturation level of the SIR de-creases with an increase in the multilayer absorption.Of all the multilayers the physical thickness of thehigh-index material (LaF3 in this particular case)within the multilayer is the greatest for the QWstack. Therefore, the SWR saturation level for theQW stacks is achieved with fewer layers comparedwith other r stacks. As should be expected thebandwidth decreases with a decrease in the H/L ratio.It is 17 nm for the QW stack and 6.9 nm for the stackwithH/L = 1/5 (Fig. 3).

From Figs. 2 and 3 it follows that, for the design ofa narrow-band reflector that is centered at 135.6 nm,the r stack with H/L = 1/4 seems to be the mostfeasible choice. The 35-layer stack with this ratio hasoptical thicknesses of

XnHdH = -

4XnLdL = T -

3A,,,LdL =8- (23)

The measured reflectance maximum at X, = 135.6 nmis 86.0% with a bandwidth of 7.2 nm. The theorypredicts an 86.9% maximum reflectance and a 6.8-nmbandwidth.

E. Higher-Order rr Multilayer Stacks

The first-order QW stacks have a wider high-reflectance zone than other r multilayers. The widthof the high-reflection zone (AX)H.R of a QW multilayer

100

80

3

zE-)

a)-U)

(22)

The calculated value of the maximum reflectance isRma, = 88.4% at 135.6 nm, and the FWHM is 7.2 nm.Figure 4 shows the measured and calculated reflec-tance of this stack with fused silica as the substratematerial. The measured values of the peak reflectanceat 135.6 nm is 88.3%, while the theory predicts the

60

40

20

140 160 180 200 220 240 260 280 300 320WAVELENGTH [nm]

Fig. 4. Measured (squares) and calculated (diamonds) reflectanceof the 35-layer r stack for a 450 angle of incidence centered at 135.6nm. The optical thickness ratio HIL = 1/4, where H is LaF2 and Lis MgF,.


I I I I I I I I I I

- I I I I I I I I I

I I I I I I I I I I

I I I I I I I I

0 120

100

80

a)

C-zZ)

a),

60

40

20 fI

120 140 160 180 200 220 240 260 280 300 320WAVELENGTH [nm]

Fig. 5. Measured (squares) and calculated (diamonds) reflectanceof the 29-layer mr stack for 450 angle of incidence centered at 135.6nm. The optical thickness ratio HIL = 1/3, where H is BaF, and Lis MgF2.

with nonabsorbing film materials is given by23

1 4Xr, . 1nH -nL\-sin- )' (24)(XH 2(m - 1) + 1 Ir T + nL(

where m is the order of the 'r multilayer. For absorb-ing film materials the width of the high-reflectionzone is smaller than that calculated by using Eq. (24).Thus Eq. (24) gives a maximum width for a high-reflectance zone that is obtainable for materials withrefractive indices n, and nL, Thus an alternativeapproach for the design of the narrow-band reflectorsis to utilize the QW or other Tr stacks with higher-order m. However, an increase in the order of a Trstack from 1 to say m changes the total phasethickness of an HL pair from r -> m'r. The totaloptical thickness of an HL pair is increased by Xr/2when the order of a 7r stack is increased by unity. Theincreased physical thickness of both high- and low-index film materials results in increased absorptanceand therefore lower reflectance of the stack. Figure 6shows the calculated and experimentally obtainedreflectance of the second-order QW stack centered at

100

80

z

a.

a)

60

40

20

0 I |120 130 140 150 160 170 180 190 200 210 220 230

WAVELENGTH [nm]

Fig. 6. Measured (squares) and calculated (diamonds) reflectanceof the 35-layer second-order QW stack for a 45° angle of incidencecentered at 135.6 nm. H is BaF,, and L is MgF2 .

135.6 nm at a 450 angle of incidence. BaF2 is used asthe high-index material and fused silica as the sub-strate. The calculated value of the maximum reflec-tance is 83.1%, while the measured value is 69.9%.Discrepancies between the theory and experimentmay be explained by the presence of physical factorsthat are neglected in the theoretical calculation, suchas the surface and volume scattering, film and sub-strate contaminations, and film inhomogeneity. Theagreement between the theoretical prediction and theexperimentally obtained results is much better forthe first-order filters (Figs. 4 and 5) than for thesecond-order QW stack. This may indicate that thickerfilms in the QW stack are more affected by thephysical factors that are neglected in the multilayertheoretical calculation.

Ill. Multiple Reflection Filters

A. Narrow Band

The reflection filters that are shown in Figs. 4 and 5have measured reflectances at the central wavelengthof 86.0 and 88.3%, respectively. They both haverelatively high reflectance in the shorter-wavelengthregion and an average reflectance of the order of 10%for the longer wavelengths. The reflectance outsidethe filter's pass zone and the bandwidth of the passzone can be reduced by means of multiple reflectionsfrom two or more reflection filters on which light isincident at an angle of 45°. The overall transmissionsof combinations of four and six 29-layer filters areshown in Figs. 7 and 8, respectively.

The maximum throughput of the four-filter combi-nation at the central wavelength X = 135.6 nm is53.7% and the bandwidth is 4.3 nm. The blocking forshorter wavelengths is better than 0.7%, and forlonger wavelengths it is better than 10-2 %. If furtherimprovement in the blocking for wavelengths outsidethe pass zone is required, six or more filters can becombined. However, adding more filters will reducethe overall transmittance of the combination. Themaximum throughput of the six-filter combination atthe central wavelength is 39.3% with a bandwidth of

60

50 _

40 _

10

.0

0

30 _

20 L

10 _

OL120 140 160 180 200 220 240 260 280 300 320

WAVELENGTH [nm]

Fig. 7. Transmittance of the combination of the four 29-layerfilters shown in Fig. 5. The bandwidth is 4.3 nm, and a peaktransmittance at 135.6 nm is 53.7%.


I I I Il I I I I I

-- J L I I I I I I I

60

50

E-

0

._

v0

40

30

20

10 l l l l I l l l 1120 140 160 180 200 220 240 260 280 300 320

WAVELENGTH [nm]

Fig. 8. Transmittance of the combination of the six 29-layerfilters shown in Fig. 5. The bandwidth is 3.2 nm, and a peaktransmittance at 135.6 nm is 39.3%.

3.2 nm. The blocking outside the pass zone is betterthan 10-4% for longer wavelengths and better than0.07% for shorter wavelengths. If a 4-mm-thick MgF2window is placed at the entrance of the combination,the transmittance of shorter wavelengths may be lessthan 10-4%.

B. Broadband

The pass zone of a broadband filter is bounded bylower and upper wavelengths. Ideally the spectralcomponents of the incident light, with wavelengthsthat are shorter than the lower wavelength andlonger than the upper wavelength of the filter, to-gether referred to as the out-of-band spectrum, arerejected. In the design examples that follow, wave-lengths of the out-of-band spectrum are rejected bymeans of the multiple reflections from QW stacks.The rejection at shorter wavelengths might be im-proved by a suitable choice of window material, whichis placed at the entrance of a multireflector combina-tion. Windows made of BaF2 and CaF2 absorb wave-lengths of less than 135 and 125 nm, respectively,while fused silica and A12 03 may be used for broad-band filters with a lower pass limit above 145 nm.3'24

Because of the narrower high-reflection zone the rmultilayers with H/L < 1 are not suitable for thedesign of broadband reflectors. The QW stacks forwhich H/L = 1 are a better choice for the design andfabrication of these filters. Figure 9 shows the mea-sured and calculated reflectance at a 450 incidentangle for the 25-layer QW stack. The reference wave-length is 175 nm, LaF3 is used as the high-indexmaterial, and fused silica is used as the substrate. Themeasured peak value of the reflectance is 90.3%, andthe bandwidth measured at half of the reflectancemaximum is 19 nm. The average reflectance for theout-of-band wavelengths is of the order of 10%. TheKoppelmann limit for LaF3 and MgF2 at this wave-length is RK = 94.4%, and the theoretically predictedvalue of the peak reflectance is 91.6%.

The agreement between the theory and the experi-ment is much better than for the second-order QWstack (Fig. 6). Again this may indicate that thicker

80

vWU

U

a))I

a)

60

4020 ,120 130 140 150 160 170 180 190 200 210 220 230

WAVELENGTH [nm]

Fig. 9. Measured (squares) and calculated (diamonds) reflectanceof the 25-layer QW stack for a 45° angle of incidence centered at 175nm. H is LaF2 and L is MgF,.

films in the second-order QW stack are more affectedby the physical factors that are neglected in themultilayer theoretical calculation.

Figure 10 shows the transmittance of combinationsof four and six of these reflectors. The four-reflectorcombination has a peak transmittance of 66.3% and abandwidth of 11.5 nm. The rejection of the out-of-band spectrum up to 300 nm is better than 0.1%. If a4-mm-thick fused silica parallel plate is used as thewindow, the rejection of the shorter wavelengths ofthe out-of-band spectrum is better than 10-3%. Thesix-reflector combination has a peak transmittance of54.04% with a bandwidth of 11 nm. This combinationprovides much better rejection for out-of-band wave-lengths. The transmittance of the combination forout-of-band wavelengths is less than 3 x 1-3%. If a4-mm-thick fused silica is used as the window, thetransmittance of the combination for shorter wave-lengths of the out-of-band spectrum is less than10-5%.

IV. Experimental Arrangement

All depositions are made onto 12.7-mm-diameter by2-mm-thick MgF2 fused silica substrates with a rms

100

80

a)0E)

rQ.

0U

60

40

20

0 l I , I / I I ' 1 I I I120 130 140 150 160 170 180 190 200 210 220 230

WAVELENGTH [nm]

Fig. 10. Transmittance of combinations of the four (solid curve)and six (dashed curve) 25-layer QW stacks shown in Fig. 9.


100

roughness of less than 1 nm. The substrates arecleaned by the supplier (Acton Research Corporation,Acton, Mass.) by using the following procedure: opti-cal soap wash, water rinse, ethanol soak then ultra-sonic bath, fresh ethanol rinse, and finally a Freonrinse. The substrates are packed in a clean-roomenvironment in Delrin holders. They are removedfrom Delrin holders immediately prior to mounting inthe substrate holder for deposition. Mounting in thesubstrate holder is done in a laminar flow bench.During the transport from the bench to the vacuumchamber the substrate is kept in a flow of drynitrogen. All depositions are made at the Universityof Alabama in Huntsville, Optical Aeronomy Labora-tory and spectrophotometric measurements are madeat the Atomic Physics Branch of the NASA/ MarshallSpace Flight Center.

The vacuum system consists of a cryopump and asorption pump that gives an oil-free environment forall depositions and therefore provides a low probabil-ity of hydrocarbon contamination of the films. Thefilms are deposited with low deposition rates of0.18-0.20 nm/s upon substrates that are heated to200'C. The predeposition pressure is 7.5 x 10', whilethe deposition pressure varies between 1.7 and 2.3 x10' for all coating materials. The temperature ismonitored with a Chromel-Alumel thermocouple thatis attached to an aluminum ring substrate holder.The substrate and the ring holder are placed in thecenter of a 40-mm-diameter by 6-mm-thick stainless-steel plate. A quartz crystal is used for the filmthickness and deposition rate monitoring. The deposi-tions are made with an electron gun. The gun has afixed voltage of 10 kV, and low-power depositions aremaintained by supplying low current to the filament.The source-to-substrate distance is 500 mm, and thesource-to-monitor distance is 350 mm.

V. Summary

The idea of utilizing multiple reflections from 7rmultilayer reflection filters on which the light isincident at a 450 angle constitutes the basis of ournarrow-band and broadband filters. The multi-reflector combinations provide a superior spectralperformance for both the narrow-band and the broad-band filters over what is currently available.

The high-reflective multilayer coatings for the nar-row-band reflection filters are designed by using Trmultilayer stacks with H/L < 1 instead of theclassical QW stacks for which H/L = 1. It is shownthat the r stacks with H/L < 1 have a higherreflectance and a smaller bandwidth than the QWstacks and are therefore more suitable for the designof narrow-band reflection filters. It is demonstratedthat the QW stack maximum reflection limit at both00 = 00 (Koppelmann limit) and 00 = 450 can be easilyextended for the coating materials that are availablein the VUV. A peak reflectance of more than 96% for azero angle of incidence can be achieved for wave-lengths that are as low as 135.6 nm when Fr stacks

with the ratio H/L < 1 are utilized. Stacks with morethan 99 layers can provide further improvements inthe maximum reflectance, but the lowest value of theH/L ratio is limited by the smallest feasible thicknessof the high-index films. Furthermore, Fr multilayerswith H/L < 1 are not suitable for broadband reflec-tors, since the width of their high-reflectance zone isgenerally not as wide as the QW stacks.

The agreement between theoretical and experimen-tal results is much better for first-order filters (Figs. 4and 5) than for the second-order QW stack (Fig. 6)and for QW stacks that are centered at longer wave-lengths (Fig. 9). This may indicate that thicker filmsin the QW stack are more affected by the physicalfactors that are neglected in the multilayer theoreti-cal calculation such as surface and volume scattering,film inhomogeneity, and film contamination.

References1. Optical Filters Catalog (Acton Research Corporation, Acton,

Mass., 1989).2. A. Malherbe, "Interference filters for the far ultraviolet,"

Appl. Opt. 13, 1275-1276 (1974).3. A. Malherbe, "Multidielectric components for the far

ultraviolet," Appl. Opt. 13, 1276-1276 (1974).4. E. Spiller, "Interference filters for the ultraviolet and the

surface plasmon of aluminum," Appl. Opt. 13, 1209-1215(1974).

5. L. R. Elias, R. Flach, and W. M. Yen, "Variable bandwidthtransmission filter for the vacuum ultraviolet: La1.,CeF 3,"Appl. Opt. 12, 138-139 (1973).

6. E. T. Fairchild, "Interference filters for the VUV (1200-1900A)," Appl. Opt. 12, 2240-2241 (1973).

7. B. K. Flint, "Special application coatings for the vacuumultraviolet (VUV)," Opt. Eng. 18, 92-97 (1979).

8. B. K. Flint, "Recent developments in ultraviolet filters andcoatings," Adv. Space Res. 2, 135-142 (1983).

9. W. R. Hunter, "Review of vacuum ultraviolet optics," inOptical Coatings: Applications and Utilization II, G. W. DeBell and D. H. Harrison, eds., Proc. Soc. Photo-Opt. Instrum.Eng. 140, 122-130 (1978).

10. M. Zukic, D. G. Torr, J. F. Spann, and M. R. Torr, "VUV thinfilms. Part 2: Vacuum ultraviolet all-dielectric narrowbandfilters," Appl. Opt. 29, 4293-4302 (1990).

11. E. Spiller, "Multilayer interference coatings for the vacuumultraviolet," in Space Optics, Proceedings of the Ninth Interna-tional Congress of the International Commission for Optics,B. J. Thompson and R. R. Shannon, eds. (National Academy ofSciences, Washington, D.C., 1974), pp. 581-597.

12. W. R. Hunter, "Design criteria for reflection polarizers andanalyzers in the vacuum ultraviolet," Appl. Opt. 17, 1259-1270 (1978).

13. M. Zukic and D. G. Torr, "VUV thin films," in Thin Films,K. H. Guenther, ed., Springer Topics in Applied Physics,(Springer-Verlag, Berlin, 1991), Chap. 7.

14. M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford,1983), Chap. 1.

15. H. A. Macleod, Thin-Film Optical Filters (Macmillan, NewYork, 1986), Chaps. 2, 5, 6.

16. L. Young, "Prediction of absorption loss in multilayer interfer-ence filters," J. Opt. Soc. Am. 52, 753-761 (1962).

17. C. K. Carniglia and J. H. Apfel, "Maximum reflectance ofmultilayer dielectric mirrors in the presence of slightabsorption," J. Opt. Soc. Am. 70, 523-534 (1980).


18. G. Koppelmann, "On the theory of multilayers consisting ofweakly absorbing materials and their use as interferometermirrors," Ann. Phys. Leipzig 5, 388-396 (1960).

19. J. H. Apfel, "Optical coatings design with reduced electric fieldintensity," Appl. Opt. 16, 1880-1885 (1977).

20. P. H. Lissberger, "The ultimate reflectance of multilayerdielectric mirror," Opt. Acta 25, 291-298 (1978).

21. M. Sparks and M. Flannery, "Simplified description of multi-layer dielectric reflectors," J. Opt. Soc. Am. 69, 993-1006(1979).

22. M. Zukic, D. G. Torr, J. F. Spann, and M. R. Torr, "VUV thinfilms. Part 1: Optical constants of BaF2 , CaF2 , LaF3, MgF2,A120,, HfO2 , and SiO2 thin films," Appl. Opt. 29, 4284-4292(1991).

23. P. Yeh, Optical Waves in Layered Media (Wiley, New York,1988), Chaps. 6 and 7.

24. D. F. Heath and P. A. Sacher, "Effects of a simulatedhigh-energy space environment on the ultraviolet transmit-tance of optical materials between 1050 A and 3000 A," Appl.Opt. 5, 937-943 (1966).


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Multiple reflectors as narrow-band and broadband vacuum ultraviolet filters