JOURNAL OF THE OPTICAL SOCIETY OF AMERICA
`
`VOLUJME 37, NUMBER 10
`
`OCTOBER, 1947
`
`Practical Methods of Making and Using Multilayer Filters 1
`
`MARY BANNING
`Institute of Optics, University of Rochester, Rochester, New York
`(Received February 3, 1947)
`
`The general method of making an evaporated multiple-layer interference filter from two di-
`electrics is described for any desired wave-length range. The proper thickness of each layer to
`give maximum reflection in the desired region and at the desired angle of incidence is first
`computed, and next the visible reflectivity of such a film at normal incidence. This visible re-
`flectivity is used as the gauge to determine the proper thicknesses of the films and the point at
`which the evaporation of each layer should be stopped. Practical difficulties encountered in
`making these filters are also discussed with various ways of surmounting them.
`Several examples of special filters for particular purposes are reviewed in detail, including
`infra-red and polarizing filters.
`
`- - -
`
`A GREAT deal of material has been published
`during the last year on methods of com-
`puting the spectral reflection and transmission
`of multilayer films. 2-5 However, little has yet
`been said about the making of such filters and
`their practical applications. The present article
`describes methods of making multilayer filters
`and easy "rules of thumb" by which the proper
`film thicknesses may be computed. For lack of
`sufficient personal experience, no attempt is
`made to describe metallic-dielectric films such as
`are used to increase metallic reflection,6 or to
`form selective transmission filters,7 although the
`same problems occur in these cases. The exact
`
`A
`
`C
`
`r
`I
`
`[
`
`PHASE CHANGE
`ON REFLECTION
`
`~~41 A/
`
`I I
`
`In,t,
`
`Z n S
`
`I
`
`1 "t
`
`cryolite
`
`nat,
`
`1 Z n S
`
`LASS
`
`FIG. 1. Schematic diagram of three-layer filter.
`
`The work described here was carried out inwhole or in
`part under contract with Division 16 of the Office of
`Scientific Research and Development, at the University
`of Rochester.
`2 P. King and L. B. Lockhart, J. Opt. Soc. Am. 36, 513
`(1 946).
`3 D. L. Caballero, J. Opt. Soc. Am. 36, 710A (1946).,
`R. L. Mooney, J. Opt. Soc. Am. 36, 256 (1946).
`6 H. D. Polster, J. Opt. Soc. Am. 350A (1946).
`'A. F. Turner, J. Opt. Soc. Am. 36, 711A (1946).
`7 Such filters are now being commercially produced by
`the Farrand Optical Company, Inc., New York City.
`
`theoretical treatment of both metallic and di-
`electric multilayer films is given in a forthcoming
`article by H. D. Polster, whose work coincided
`with a large part of that described here.
`The first highly reflecting films of zinc sulfide
`were made by Pfund in 1933,8 and the first "non-
`reflecting" films of low index fluorides evaporated
`in 1935 by Strong;9 in 1939, Cartwright and
`Turner tried a combination of low and high
`index films and produced selective reflection.'0
`Since that time many laboratories have been
`working on this problem, but because of the war
`little has been published except for a short ac-
`count from the RCA Laboratories."
`
`SIMPLE FILTERS
`
`Development of multilayer filters at the Uni-
`versity of Rochester arose accidentally, in Sep-
`tember, 1942, from the need of producing a reflex
`plate that would reflect approximately 50 per-
`cent of the incident light and transmit the rest.
`A single coating of zinc sulfide, evaporated to an
`optical thickness of a quarter wave-length for
`green light, did not give sufficient reflection; if a
`plate of glass was coated on both sides, the re-
`flection was nearly satisfactory, but this necessi-
`tated exposing one of the soft coatings to rough
`handling and atmospheric conditions. Two plates
`coated on one side and mounted with their
`coated faces together were difficult to align per-
`
`8 A. H. Pfund, J. Opt. Soc. Am. 24, 99 (1934).
`9 J. Strong, J. Opt. Soc. Am. 26, 73 (1936).
`10 C. H. Cartwright and A. F. Turner, Phys. Rev. 55,
`1128A (1939).
`11 G. L. Dimmick, J. Soc. Mot. Pic. Eng. 38, 36 (1942).
`
`792
`
`Edmund Optics(cid:15)(cid:3)(cid:44)(cid:81)(cid:70)(cid:17)(cid:3)
`(cid:40)(cid:91)(cid:75)(cid:76)(cid:69)(cid:76)(cid:87)(cid:3)(cid:20)(cid:19)15(cid:3)
`
`0001
`
`

`

`MULTILAYER FILTERS
`
`793
`
`100.
`
`0
`
`,, 6C
`
`I 4
`
`X I4
`
`,0
`
`80
`
`i 6C
`
`40
`2
`
`,
`c ^
`
`4000
`
`4400
`
`4800
`
`6400
`
`6800
`
`7200
`
`7600
`
`5.600
`5200
`6000
`'WAVELENGTU
`I A
`FIG. 3. Second-order filters of seven layers. (1) ZnS to
`second magenta; (2) ZnS to second yellow; (3) ZnS to
`spcnd whit- () 7 nS t
`r-fi h,
`r.-n-1 hill
`holis
`-i-
`.--
`1 -
`-..-
`-
`-_-
`-E,-
`_.-
`
`4000
`
`4.800
`
`5600
`
`6400
`
`7200
`
`WAVE LENGTH
`
`IN A
`
`FIG. 2. Effect of addition of layers, first-order inter-
`ference. (1) 1 ZnS layer; (2) 2 ZnS and 1 cryolite; (3) 3
`ZnS and 2 cryolite; (4) 4 ZnS and 3 cryolite; (5) 5 ZnS and
`4 cryolite.
`
`fectly parallel and double images resulted, while
`cementing the two together decreased the re-
`flection too much.
`At the suggestion of J. W. Evans, a low index
`dielectric layer of cryolite was evaporated on top
`of the high index layer and followed by a second
`high index film,
`thus "substituting"
`for the
`intermediate air layer. It was soon found that
`the thickness of the low index layer was as
`critical as that of the high index layers and that
`best results were obtained when all three had an
`optical thickness of a quarter wave-length. Such
`a film showed 60 percent reflection for the middle
`portion of the visible spectra.
`The explanation of this is very simple. Figure 1
`shows a schematic three-layer filter. According
`to a convention adopted here, high index films
`are shown with greater length than low index
`films. Light reflected from all four interfaces,
`A, B, C, and D, must be in phase for maximum
`reflection. A phase change of
`/2 will take place
`whenever light is reflected from a high index
`medium into a lower index medium, or at sur-
`faces A and C in Fig. 1. The ray reflected at A
`suffers a phase change of
`/2. The ray from B
`goes 2n1i 1 farther than that from A and thus
`differs in phase by 2n1 1t plus X/2; now if n 1t,
`equals
`/4, the two rays differ by X and are in
`phase. The ray from C changes phase by 2n 1t1
`plus 2 2 t2 plus A/2 at reflection and is, therefore,
`2n2t2 plus X/2 out of phase with that from A;
`to be in phase n2 t2 must be
`/4. Similarly n3t3
`must be
`/4.
`
`In the case mentioned above, that of a reflex
`plate using visible light, the wave-length for
`which this must hold is approximately 5400A.
`The effect of adding more and more layers is
`shown in Fig. 2, with the maximum reflection
`becoming greater and the width of the reflection
`band becoming narrower. The graphs are shown
`as transmission values. The reflection is obtained
`by subtracting these values from 100 percent, as
`the absorption loss is negligible. This filter is the
`simplest to make, as the color changes are quite
`definite and easy to see. It is the fundamental
`first-order filter, with the optical thickness of all
`layers a quarter wave-length for green light. It
`is not advisable to put down more than four
`sulfide layers (with three of cryolite), as the
`total thickness becomes so great that the film
`tends to crackle off. This is even more pronounced
`with layers of greater thickness, as described
`below.
`Reference to Fig. 1 shows that if all the films
`are made twice as thick (nt=X/2), the ray from
`
`,00
`
`1OC_~~~~~~~~;-
`
`z6 e~
`
`\
`
`/
`
`4C -
`
`4000
`
`4400
`
`4800
`
`5200
`5600
`6200
`WAVELENGTH
`IN A
`
`6400
`
`68O0
`
`7200
`
`FIG. 4. Effect of changing the order of cryolite in a
`three-layer filter. ZnS always first order. (1) cryolite first
`order; (2) cryolite second order; (3) cryolite third order.
`
`0002
`
`

`

`794
`
`MARY BANNING
`
`TABLE I. Colors of different thickness of zinc sulfide and
`cryolite films as seen by reflection at normal incidence.
`
`Color
`
`ZnS
`bluish white
`white
`yellow
`magenta
`blue
`greenish white
`yellow
`magenta
`blue
`green
`
`Cryolite
`yellow
`magenta
`blue
`white
`yellow
`magenta
`blue
`greenish white
`yellow
`magenta
`
`Optical Thickness for Green Light
`
`X/4, first order maximum
`
`X/2, first order minimum
`3X/4, second order maximum
`
`X, second order minimum
`
`5X/4, third order maximum
`
`time consumed is much greater than if all layers
`are deposited in the same vacuum. A small test
`piece, shielded from evaporating materials ex-
`cept for a small area, can be placed beside the
`actual sample and rotated slightly after each
`layer to present a clean surface for observation.
`The cryolite and zinc sulfide are placed in cru-
`cibles side by side on the bottom of the evaporat-
`ing chamber and the sample centered above
`them.
`If the sample is large, it can be rotated during
`evaporation about an axis perpendicular to its
`face, and the crucibles offset from the center to
`provide an even coating. The proper crucible
`
`90
`
`SC
`
`'C
`
`, -o
`
`E0\ MULTI L AYER
`~:- FILTER
`
`/
`/
`
`K
`'
`
`_0.
`
`'.
`
`.
`
`b
`
`/ l
`
`I
`
`JO~
`
`ORIGINAL
`
`t
`
`0~
`
`t
`
`j
`
`C
`
`BRODE
`FILTER
`M 8 I N A r
`
`W IX
`
`COMBINATION
`
`60
`
`50
`
`4C
`
`30
`
`20
`
`lO
`
`z 0 I
`
`n I
`
`In
`
`z I
`
`- z
`
`z
`
`-
`
`0
`
`4n
`
`w4C,
`
`4000
`
`4400 4800 5200 5600 6000 6400
`IN A
`WAVELENGTH
`
`FIG. 5. Multilayer filter designed to distinguish
`betwveen the emission of two phosphors.
`
`A will tend to cancel that from B, while that
`from C will cancel the one from D. Thus there
`will be very little reflection of green light. How-
`ever, light of twice this wave-length, about 1.1
`microns, will find the optical thickness equal to
`1 of its wave-length, and will be strongly re-
`flected. This filter has been found useful as a
`reflex plate for stimulating and observing infra-
`red phosphors which have a maximum sensitivity
`to radiation of 1.1 microns, and emit in the green.
`Now if the films are made even thicker so that
`the four rays will again be in phase
`t= 4X,
`and again green light will be strongly reflected.
`This is called a second-order filter, several of
`which (of 7 layers) are shown in Fig. 3, for light
`of various wave-lengths. It can be seen that the
`reflection band is much narrower than is the one
`of a first-order filter. Going to the third order,
`or ~--thickness, gives an even sharper band,
`useful when only a short spectral range is to be
`considered. In some cases it is desirable to com-
`bine cryolite layers of first order with second-
`order zinc sulfide layers, or vice versa. The effect
`of changing the cryolite order while holding that
`of the sulfide constant is shown for a three-layer
`filter in Fig. 4.
`
`DEPOSITION OF LAYERS
`Before taking up more complicated filters,
`the method of deposition should be mentioned.
`It is not at all necessary to break the vacuum in
`an evaporator during the making of a filter;
`although this does no harm to the filter, the total
`
`1.0
`
`1.1
`
`.2
`1.3
`1.4
`I.5)
`WAVELEN GTH
`IN MICRONS
`FIG. 6. Multilayer filter designed to sharpen the cut-off
`of another infra-red filter.
`
`1.6
`
`1.7
`
`0003
`
`

`

`MULTILAYER FILTERS
`
`795
`
`positions are found by successive approxima-
`tions. Circular filters of 7-inch diameter have
`been made in this manner, showing only 1 per-
`cent variation in reflectivity over their surfaces.
`This can be done with crucibles only nine inches
`below the level of the plate, in a 12-inch di-
`ameter bell jar. A small hole drilled in the center
`of the disks allows access to a test piece sup-
`ported just above the large sample.
`The evaporators used. here have large flat
`glass tops for viewing purposes.12 Thicknesses of
`the layers are judged by watching, at as near to
`normal incidence as possible, the changing colors
`reflected from
`the sample or test piece. A
`fluorescent lamp hung over the chamber pro-
`vided a good white light source. Both the back
`of the sample and the inside of the glass top are
`coated with mineral oil to prevent deposition on
`these surfaces in the form of a reflecting film and
`consequent confusion in viewing the reflected
`light.
`As the evaporation of zinc sulfide proceeds, it
`first shows a bluish white reflection, then as it
`gets thicker it reflects a brilliant white (optical
`thickness of X/4 for green light), yellow, magenta,
`blue, greenish white, etc. The third "white" is a
`definite green, as even a single layer shows a
`much narrower reflection band in the third order.
`Finally the color changes alternately from pink
`to green as the orders progress. Cryolite starts
`with a faint yellow, hard for a novice to see,
`then turns magenta (X/4 for green light), blue,
`white, deep yellow, deep magenta, blue, green,
`etc. Table I shows the colors seen at various
`thicknesses for both the sulfide and fluoride. If a
`plate is to be used at an angle of incidence other
`than normal, the colors should be viewed at that
`angle, since at high angles they will differ con-
`siderably from those shown at normal incidence.
`
`MORE COMPLICATED FILTERS
`If a wide band filter reflecting yellow light is
`desired, zinc sulfide
`is deposited
`to the first
`yellow reflection, and cryolite to the first blue.
`A narrower band as shown in Fig. 3 can be made
`with the second yellow and the second blue.
`Other visible light filters can be made by fol-
`lowing the same law; zinc sulfide to the color
`
`12 M. Banning and F. W. Paul, Rev. Sci. Inst. 15, 152
`(1944).
`
`FIG. 7. Schematic diagram of a polarizing beam splitter.
`
`desired to be reflected and cryolite to the com-
`plementary color.
`For example, a problem arose involving two
`different phosphors with separate but close
`emission peaks. The complete emission bands
`overlapped to such an extent that distinction
`between the two was difficult. A filter was de-
`sired that would cut out the common region be-
`tween the two bands and at the same time pre-
`serve as much as possible of the rest of the emis-
`sion. Figure 5 shows the two emission bands and
`the curve of the filter designed to distinguish
`them. A green reflection was desired, so white
`sulfide and magenta cryolite were
`indicated.
`Since a very sharp cut-off was needed, it was
`decided to use third-order cryolite and first-
`order sulfide. The filter curve shown is the result
`of the first attempt.
`Filters such as these cannot be made for the
`ultraviolet except for the region very close to
`the visible spectrum, as zinc sulfide begins to
`have an appreciable absorption around 3650A.
`However, the infra-red region is still open to
`exploration, the only limit imposed is that of the
`necessary thickness of the layers. Since "colors"
`in the infra-red cannot be detected easily during
`
`0004
`
`

`

`796
`
`MARY BANNING
`
`to calculate what
`evaporation it is necessary
`color of visible light will be reflected at the proper
`thickness for the infra-red, and watch for this.
`Although the resulting filter may not be perfect
`the first time, it is usually close enough to pre-
`dict what minor changes must be made. A spe-
`cific example of this occurred when it became
`desirable to sharpen up the cut-off of another
`kind of filter, a gel filter made at Ohio State
`University by Dr. Wallace Brode. As shown in
`Fig. 6, this was opaque from 0.6 to 1.0 micron
`and then slowly rose in transmission to 60 per-
`cent from 1.3 to 1.6. However, it was to be used
`for a purpose in which radiation of 1.3 microns
`was not desired but that of 1.4 microns was
`necessary.
`This called for a second-order filter with maxi-
`mum reflection at 1.3/i. Since second-order films
`at 1.31i are very thick, it was decided to compro-
`mise on first-order sulfide and second-order cryol-
`ite. To find the wave-length reflected by the sul-
`fide in the visible, the following formula is used:
`nt = X/4 = 3x/ 4 ,
`where X is the wave-length in the infra-red and
`x is the wavelength in the visible. In this case the
`region around 4300A, or second-order blue, is
`reflected. Thus the sulfide must be evaporated
`until it reflects second-order blue.
`The cryolite is to be second order in the infra-
`red; to find what color it will reflect in the visible,
`the appearance of the sulfide, if evaporated to
`second order at 1.3 microns, is first calculated.
`In this case the formula is
`nt = 3X/4 = 5x/4 = 7y/4 = 9z/4.
`Supplementary maxima are seen to be at 7800,
`5570, and 4300A of third, fourth, and fifth orders,
`respectively. This would, with sulfide, probably
`appear to be the fourth blue just before the fourth
`green. The complementary cryolite color is the
`fourth yellow. The curve obtained with second
`blue sulfide and fourth yellow cryolite is shown
`in Fig. 6 along with the resultant curve of the
`two filters.
`Another method for making these high order
`filters is to compute the color of the sulfide, and
`then find the cryolite color by trial and error; a
`good guess is usually approximately right. Once
`the proper colors are found, they are not at all
`
`*hard to duplicate. A second person, once shown
`the colors, can reproduce a filter so that the
`curves made by two different operators are nearly
`indistinguishable.
`If the filter is to be used at an angle of in-
`if for some
`cidence other than normal, and
`reason it cannot be watched at this angle during
`evaporation, a simple calculation gives the color
`it will reflect at normal incidence. In this case the
`optical thickness is no longer nt but nt cos0,
`where 0 is the angle of refraction in the film.
`01, the angle of refraction in the sulfide, and 02,
`the angle in the fluoride, are computed from the
`known angle of incidence and refractive indices
`by Snell's law. Thus
`
`nt=
`
`x
`4 cos
`
`x'
`4
`
`where X is the wave-length reflected at the angle
`of incidence and X' is the wave-length reflected
`normally (X' > X).
`
`POLARIZING BEAM SPLITTERS
`In January, 1943 we observed marked polariza-
`tion by reflection from multilayer films on glass
`plates. In March, 1943 a request was made by
`Dr. S. M. MacNeille, of Eastman Kodak Com-
`pany, for the development of polarizing beam
`splitters made by the deposition of multilayer
`filters on glass prisms which, as he pointed out,
`would permit light to enter the film at the po-
`larizing angle. These have been made and found
`to work quite satisfactorily. Films are deposited
`on the hypotenuse faces of two 45-90 prisms
`which are then cemented to form a cube, as
`shown in Fig. 7. Half of the incident light is
`reflected and half transmitted, each part being
`plane polarized to more than 98 percent, over a
`small angle of incidence.
`In order for this to be true, the incident light
`must strike each interface of the multiple film at
`the polarizing angle, and the total reflectivity of
`the film must be such that all of the light polar-
`ized perpendicular to the plane of incidence is
`reflected. It is also desirous that the light path
`be normal to the entrance and exit faces of the
`cube.
`The index of refraction of the glass, as well as
`those of the two evaporated substances, is very
`
`0005
`
`

`

`MULTILAYER FILTERS
`
`797
`
`important in assuring that the reflection takes
`place at the critical angle. As shown in Fig. 7,
`ne, n, and n are the indices of refraction of the
`glass, sulfide, and fluoride, respectively; while so,
`xl and x2 are the angles of incidence at the glass-
`sulfide,
`the sulfide-fluoride and the fluoride-
`sulfide interfaces. From Brewster's and Snell's
`law the following equation must hold for the
`polarizing angle.
`
`nbi= 2nf nai/(nfi+nS2)
`
`Assuming that zinc sulfide has an index of 2.3
`and cryolite of 1.25 (evaporated close to 10-3
`mm Hg), the index of the glass prisms as com-
`puted from this formula must be 1.55. Another
`factor to be taken into account is the V-number
`of the glass. Zinc sulfide has a high dispersion
`with a V-number of 17. Thus in order to make
`certain that all wave-lengths reach the sulfide-
`fluoride interfaces at approximately the polariz-
`ing angle, the dispersion of the glass must be
`carefully chosen. It can easily be proved that
`for the ideal case, assuming the dispersion of
`cryolite is negligible:
`V=n(nf2 +n 2 ) V(n,-1)/ns(2nf2fifl)(n_l).
`
`Substituting
`in
`the equation gives V,7 = 48.5.
`Fortunately, either extra light flint or light
`barium crown will do for the purpose, with the
`first alternative being by far the best.
`Once the best indices of materials and glass
`(the same process can be repeated for different
`evaporated materials) are chosen,
`the proper
`thickness of the two films remains to be found.
`A broad reflection maximum, or first-order green,
`is desired, to cover as much of the visible spec-
`trum as possible. Because total reflection will
`take place at the hypotenuse faces before the
`prisms are cemented together, it is impossible
`to view the prisms at the polarizing angle while
`
`evaporating. Therefore, it is desirable to know
`what color will be reflected at approximately
`normal incidence if a film of proper thickness is
`deposited. This is done by computing the angles
`xi and x2 and using the cosine formula given
`above. Roughly, the high index film will appear a
`faint first yellow and the low index film the first
`greenish white. With extra light flint, zinc sulfide,
`and cryolite, the ratios of the undesired to de-
`sired polarized components are shown in Table
`II, for both beams and three different colors,
`
`TABLE II. Ratio of undesired to desired components
`of sample polarizing prism.
`
`Reflected beam
`Transmitted beam
`
`Red
`.0035
`.0138
`
`Green
`.0065
`.0031
`
`Blue
`.0103
`.0545
`
`taken normal to the cube faces. This beam
`splitter was made with three zinc sulfide layers
`on each prism. The polarization for white light
`remains greater than 98 percent over 5 degrees
`on each side of the normal entrance.
`There is no reason why equally good polarizers
`cannot be made for the infra-red.
`Although only zinc sulfide and cryolite are
`mentioned here, it is solely for the purpose of
`simplicity. Any high or low index materials will,
`in general, act the same way. The advantage of
`sulfide-cryolite films is that they are easy to
`evaporate and give a large index difference, in-
`suring a large reflection at each interface. How-
`ever, they are soft and sensitive to atmospheric
`changes.
`The author wishes
`to express her special
`gratitude to Dr. J. W. Evans for his constant
`encouragement and advice on all this work, and
`to Mr. Robert Hills, Jr., for his assistance during
`most of the development.
`
`0006
`
`