Design of a narrow—band—pass IR filter with a long—wavelength pass band

B.J. Pond and C.K. Carniglia

S. Systems Corporation
Developmental Optics Facility
P0 Box 9316
Albuquerque, NM 87119

ABSTRACT

Narrow—band—pass (NBP) interference filters are commonly used in the infrared

(IR) spectral region. It may happen that such a filter is to be used in
conjunction with an optical system which must pass thermal radiation in the 8 to
12 m wavelength range. Thus the NBP filter must be designed in such a way that
it also transmits from 8 to 12 pm. This paper presents two design techniques for
achieving the required performance. In one technique two reflective stacks are
used, providing blocking on either side of the NBP region. Additional layers are
used to provide the transparency over the region 8 to 12 m. The second approach
involves using a multiple—cavity Fabry—Perot filter to achieve the NBP
performance. The long—wave--pass region can be achieved by varying the refractive
index of selected layers within the multilayer coating. Changing these indices
has a minimal effect on the performance in the pass band.

The above design techniques are applied to the NBP filter with the following
specifications:

Pass—band center: 4.0 m

Pass-band width: m
Pass—band transmittance: 80%

Pass—band edge slope: ( 0.05 im (5% to 95%)

Long-wave region: 8—12 m

Long—wave transmission: T 90%

One useful design trick that can be employed takes advantage of the fact that the
long—wave transmission region covers a range of wavelengths which are
approximately twice the wavelength of the NBP region. Thus layers with a halfwave
optical thickness of 4 pm can be added without affecting the NBP performance.
These layers will have an optical thickness close to a quarterwave over the 8 to
12 pm range and can be used to reduce the reflectance over this region.

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 1 . INTRODUCTION

Narrow—band--pass (NBP) filters are commonly used in optical systems to

transmit light of a specific range of wavelengths. Methods for designing such
filters are well known and are given in standard textbooks on thin film optics.'
The purpose of this paper is to explore, from a 'theoretical point of view, the
design of NBP filters with the additional spectral requirement that they transmit
light over a long—wavelength pass band.

For the purposes of discussion, consider the design of a filter that transmits
a narrow band of wavelengths centered at 4 m as well as the range of wavelengths
from 8—12 m. The additional spectral requirement necessitates modifications to
the standard designs. The design techniques presented here take advantage of the
fact that the long—wave--pass (LWP) region has approximately twice the wavelength
of the NBP region.

. 2. SPECIFIC SPECTRAL REQUIREMENTS

The NBP specifications are taken to be typical of a filter used in the near
infrared (NIR) spectral range:

Pass-band center: 4.0 m

Pass-band width: im
Pass—band transmittance: ) 80%
Pass-band edge slope: > 0.05 m
The edge slope is taken to be the range over which the transmittance goes from 5%
to 95% of the required pass—band transmittance of 80%.

The specifications of the LWP region correspond to the spectral range for
thermal radiation:

Long—wave region: 8-12 m

Long—wave transmission: T > 90%

Because this paper is only investigating certain theoretical aspects of the

design, additional blocking requirements will not be addressed. In particular,
the level of the blocking at wavelengths shorter than the NBP wavelength as well
as between the two spectral bands would be relevant to the final design.
Presumably, these blocking requirements could be met by using additional
multilayer filters on the second side of the substrate carrying the NBP filter, or
on additional substrates as necessary.

The number of materials available for a filter with these specifications is

somewhat limited. Various Il—VI compounds could be used, such as ZnS, ZnSe or
CdSe. These have refractive indices n of approximately 2.5 over the wavelength
ranges of interest. One of these materials could be combined with Ge as a
high—index material (n 4) or ThF4 as a low—index material (n 1.5). We will
adopt the latter approach, combining ZnS (n = 2.25) with ThF4. In the design
presented in the following sections, H is used to represent quarterwave (QW)
layers of ZnSe and L is used to represent QW layers of ThF4.

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 3. METHOD 1: TWO REFLECTIVE STACKS

Following Macleod,' the first method considered is the use of two OW stack
reflectors, one on either side of the 4-pm pass band. There are two forms for the
reflective stack:

LWP: x(H/2 L H,2)m

and
SWP: x(L/2 H L/2)m

where SWP stands for short—wave pass. In this notation, x is the center
wavelength for the stack; i.e., the optical thicknesses of the layers H and L are
a QW at x. The power m indicates that the three—layer periods are repeated m
times. Note that the designations LWP and SWP are somewhat arbitrary since the
actual performance of the stacks depends on the substrate material.

To understand the performance of these designs, it is useful to plot the

Herpin-equivalent index (HEI).1 This is done in Fig. 1 and 2 for x = 4.64 m.
This center wavelength places the short wavelength cutoff just above 4 zm. The
dashed curves in the figures correspond to the HEI. The solid curves illustrate
the transmittance of the stacks on a ZnS substrate for the case m = 13.

Fig. 1 illustrates the HEI and transmittance for the LWP design. For
wavelengths longer than the rejection band, the HEI is less than 1.8, and crosses
through the value of 1.5 at about 7 m. This value corresponds to the index of
the ideal QW anti—reflection (AR) coating for the ZnS substrate. Note that (1.5)2
= 2.25, which is the refractive index assumed for ZnS. This fact is born out in
the transmittance curve in the long wavelength region where the peak values are
nearly 100%. The HE1 on the short wavelength side of the rejection band is quite
high. Note that over the NBP region at 4 m, the HEI is off the scale.

The SWP filter has the behavior shown in Fig. 2. In this case, the HEL in the
long wavelength region is greater than 1.8, thus not providing an AR. In fact the
index crosses through the substrate value of 2.25 at about 7 im and the ripples in
the transmittance curve are minimal at that wavelength. The HEI is quite low for
the short wavelength region, with a value of approximately 0.5 at 4 m.

To form the NBP filter, one of these stacks must be combined with a similar
stack centered at a wavelength shorter than 4 m to give the desired pass band.
The general form of the design is as follows:

air I (AR3) (Stack 2) (AR2) (Stack 1) (AR1) I sub.

Here, stacks 1 and 2 are of the form of the LWP or SWP stacks given above. One
stack must have a center wavelength of approximately 4.64 im and the other, a
center wavelength of approximately 3.37 to give the desired pass band at 4
m. The AR layers must increase the transmission over both the NBP region at 4 m
and the LWP region from 8 to 12 m.

Because both the LWP and SWP stacks have indices close to 1 .8 in the region
from 8—12 m, it is likely that an AR layer will be needed for this region. A QW
layer of L with center wavelength of 8 m can provide an AR for this region

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 13
4.64(H/2 L H/2)
100 5

80 4

LU
I
rn
U 0
z 60 3
z
I-
4E
I—
2
rn
0
U)
40 C
z
a:
I— 20 1

0 0

Wavelength (Microns)

Fig. 1 Transmittance (solid curve) and Herpin—equivalent index (dashed curve)

versus wavelength for the LWP design discussed in the text. The center
wavelength has been chosen to be 4.64 m to give a reflection band edge
of 4.1 m.
13
4.64(L/2 H L/2)
100 5

-.% 80 4

Li
Iri
60 3 -U
z
IIE 40
F— P1
0
2 C
za:
U) '-4

a:
I— 20 I

0 0

Wavelength (Microns)

Fig. 2 Same as Fig. 1 for the SWP design discussed in the text.

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 without affecting the NBP region at all. This is because the thickness of such a
layer is a HW at 4 m and thus has no effect (often referred to as absentee) at
this wavelength.

For the case that the SWP is chosen for stack 1 and LWP for stack 2, or vice
versa, the HEIs of these stacks will cross in the NBP region. Thus a specific AR
layer between the stacks is not needed. In the case that both stacks are LWP or
both are SWP, a QW of H or L (or some other material) centered at 4 m would make
a logical choice for AR2. Because the HEIs for the stacks are high, AR1 might not
be necessary. Thus a first try at the possible designs might be

air I 8(L) z(Stack 2) 4(V) x(Stack 1) I sub.

In this design, 8(L) represents the.QW AR in the 8—12 m and z and x represent the
stack centers, 4.64 and 3.37 .m, as discussed above. The layer 4(Y) represents
the QW AR necessary when stacks 1 and 2 are similar, and Y=H or L is used in the
initial designs.

It may be possible to use some insight from a knowledge of the HEIs for the
stacks to predict which of the combinations is best. It is not difficult to try
various combinations to see which offers the possibility for the best
performance. Table 1 lists all of the designs together with the minimum values of

Table 1. Comparison of Various Filter Designs

Stack 1 AR2 Stack 2 Minimum T (%)

# Center(x) Type V Center(z) Type NBP LWP

1 3.73 m SWP L 4.64 m SWP 67 88

2 3.73 m H 4.64 m 45 82

3 3.73 m LWP L 4.64 m LWP 12* 89

4 3.73 m H 4.64 m 20* 85

5 3.73 m SWP - 4.64 m LWP 25* 90

6 3.73 m LWP 4.64 m SWP 45 93

7 4.64 m SWP L 3.73 m SWP 20 92

8 4.64 m H 3.73 m 12* 95

9 4.64 m LWP L 3.73 m LWP 45 90

10 4.64 m H 3.73 m 70 84

11 4.64 SWP — 3.73 m LWP 45* 94

12 4.64 m LWP - 3.73 im SWP 25 90

* Pass band is significantly wider at the bottom.

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 the transmittance in the NBP region and the LWP. region. The designs are
identified in terms of the center wavelength x and z for the two stacks, the types
of stacks (LWP or SWP) and the intensity of a layer V if present between the
stacks.

None of the designs listed in Table 1 meets the transmission requirement of

80% in the NBP region, although some are not too far below this value. Several of
the designs exceed the 90% requirement over the 8-12 m range. As an example, the
transmittance of design 11 is illustrated in Fig. 3.

The final step in the design procedure is to refine some of the layer
thickness to attempt to meet or exceed the specifications in both spectral
regions. For example, the first design can be written in the following form:

air/8(L)4.64(aLbHcL)(L/2HL/2)(dLeHfL)4(L) 3.73(gLhHIL)(L/2HL/2)'2(jLkHmL)/sub

where a—ni are the multipliers of the thicknesses of the layers relative to
quarterwaves at the center wavelengths of 4.64 and 3.73 zm. These multipliers are
allowed to vary to give the optimum performance.

air/ 8(L) 3.37(LNP) 4.64(SWP) /sub

100 100

80 80

U
U 60 60
za:
F-
I-
1-4
40 40
U)
za:
c
F- 20 20

0 0
2 4 6 8 10 12

Wave length (Microns)

Fig. 3 The transmittance of NBP filter design 11 from Table 1. The + symbols in
the range of 4 m and the line at 90% from 8-12 m indicate the desired
performance levels. This design meets the LWP requirements but the
transmittance over the NBP region is low.

542 / SPIE Vol. 1307

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 The golden section method2 was used for optimization. Three passes were made
through the layers being refined. The results of optimizing the six most
promising designs are listed in Table 2. The design numbers listed correspond to
the designs in Table 1. In addition to listing the minimum transmission in the
pass bands, the RMS deviation of the transmission from 100% over the pass bands is
also given. For designs 1 and 9, an additional variable was considered. The
index of the spacer layer (V listed in generalized design) was also optimized.
The results for these designs are numbered la and 9b in the tables.

The optimum designs are la and 11. The actual optimized design 11 is as
follows:

air I 3.37(O.554H O.997L O.487H)(H/2LH/2)'2(O.479H O.928L O.448H)

464(O.527L l.057H O.587L)(L/2HL/2)'1(O.767L l.ll6H O.628L) I sub.

The optimized performance is illustrated in Fig. 4.

One could continue by refining more layers and refractive indices in the
designs. However, at this point a second design approach is presented.

Table 2. Comparison of Various Optimized Designs

Minimum T (%) RMS (100--T)%

NBP LWP

1 94 89 5.7
95 93 3.5
2 92 87 6.8

6 93 90 6.3

9 93 90 5.2
gb 93 93 4.0
10 90 87 7.0

11 95 93 3.5

a spacer index = 1.815

b spacer index = 1.545

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 Optimized: air/8(L) 3.73(LNP) 4.64(SNP) /sub
100 100

80 80
.\.

Li
U 60 60
za:
I.-
I—

40 40
U,
za:
I- 20 20

0 0
2 4 6 8 10 12

Wavelength (Microns)

Fig. 4 Same as Fig. 3 for the optimized version of design 11.

4. METHOD 2: FABRY—PEROT FILTER

The second type of NBP filter suitable for this application is the Fabry-
Perot (F—P) filter, also discussed in Ref. 1. The standard F—P filter consists
of two reflective QW stacks separated by a HW spacer. Such a design produces an
extremely narrow pass band. If one uses fewer layers in the QW stack reflectors,
the pass band becomes wider at the expense of the rejection level; i.e., the
blocking on either side of the pass band is not as good. The usual solution is
to repeat the F—P filter several times, resulting in a design with multiple HW
spacer layers. This design is often referred to as the multiple-cavity F—P
filter.

For the application at hand, a three-cavity design is most appropriate. By

choosing the number of layers in the QW stack reflectors, the width of the pass
band can be adjusted. The basic design is of the form

air I (HL) 2H L(HL)21 2H L(HL)2n+l 2H L(HL) I sub.

In this design the 2H layers are the HW spacers. The group of the form L(HL)r j5
the QW stack reflector and the groups L(HL)2n+l represent two QW stacks with an H
phase—adjusting layer between them. Note that the first QW stack does not have
the extra L layer. The resulting number of L layers is odd, providing an AR
coating at the design wavelength.

Fig. 5 illustrates the performance of the design for a center wavelength of 4

m for three values of n. The "+"s in the figure represent the design goals for
the NBP region of the filter. The design for n 2 is close, but slightly

544 / SPIE Vol. 1307 Electro-Optical Materials for Switches, Coatings. Sensor Optics, andDetectors (1990)

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 (HL)n2HL(HL)2nl2HL(HL)2n2HL(HL)5ITh
100

80

Id
U
za: 60

I—
II
I—
40
(J
z
a:
I— 20

0
3.4 3.6 3.8 4 4.2 4.4 4.6
Wavelength (Microns)
Fig. 5 Transmittance versus wavelength in the NBP region for several F—P
designs. The s- symbols illustrate the performance goals. The parameter
n determines the number of periods in the reflector stacks.

narrower than the specified width. If the designer could affect the
specifications, he might be able to determine that the narrower pass band was
satisfactory for the application. However, if the exact value of the band width
is important, one is forced to use the case n = 1 and further adjust the width.

The band width is also affected by the thickness of the spacer layer, which must
be an integer HW multiple. Thus a design of the form

air I HL mH LHLHLHL mH LHLHLHL mH LHL I sub

is investigated. This is similar to the previous design with n = 1, but with

spacer layers of thickness mH where m is an even integer. Fig. 6 illustrates the
performance of this design for three values of m. The value m 6 gives the
closest fit to the desired specifications.

The techniques employed so far are commonly known to designers of multilayer

filters. They allow one to adjust the width of the pass band consistent with the
desired rejection level. We now turn to the LWP region of the filter. This is
illustrated in Fig. 7, which is a plot of the transmittance versus wavelength for
the design to this point:

air / HL 6H LHLHLHL 6H LHLHLHL 6H LHL / sub.

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 HL mH LHLHLHL mH LHLHLHL mH LHL/sub
100

80

Li
U 60
za:
F-
F-
II 40
U)
z
a:
F- 20

0
3.4 3.6 3.8 4 42 4.4 4.6
Wave'ength (Microns)

Fig. 6 Same as Fig. 5. In this figure the parameter m determines the thickness
of the spacer layer.

HL 6H LHLHLHL 6H LHLHLHL 6H LHL/sub

l00

80

Li
U 60
z
a:
1—
F-
'-4
40
U)
za:
F— 20

0
2 4 6 8 10 12

Navelenyth (Microns)

Fig. 7 Transmittance versus wavelength over the full spectral range of interest
for the optimum design selected from Fig. 6.

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 The performance in the LWP region is actually not too bad, dipping below the
specification in only two places.

The first step toward improving the performance in the LWP region might be
the addition of an AR coating consisting of a HW layer of L on the outside of the
design. Recall that this HW layer has no effect on the performance over the NBP
region, but can be an AR over the LWP region where its thickness is approximately
a QW. The design now looks like

air I 2L HL 6H LHLHLHL 6H LHLHLHL 6H LHL I sub

and the performance is illustrated in Fig. 8. There is a significant improvement

in performance in the LWP region.

As a further step, a HW layer can be added between the F—P design and the
substrate. In addition, the refractive indices of several layers can be adjusted
with minimal impact on the performance over the pass band. The general form of
this design is

air I 2A HL 6B LHLCLHL 6B LHLCLHL 6B LHL 2D I sub,

where the indices of layers A, B, C and D are to be optimized to provide maximum

transmittance over the range 8-12 m.

For the optimization, the refractive indices of the layers A—D were
constrained to lie between 1.5 (ThF4) and 4 (Ge). The indices of each of the
four materials were allowed to vary independently over this range. The index of
A was found to be the same as L, while the indices of B, C and 0 were in the
range of 2 to 2.1. The effect of the index of the spacers on the final
performance was found to be minimal and a simplified design of the following form
was adopted:

air I 2L HL 6H LHLMLHL 6H LHLMLHL 6H LHL 2M I sub.

The optimum value for M was found to be 2.05 and the final performance is shown
in Fig. 9.

5. DISCUSSION

The design based on two QW stacks has the following advantages over the F—P
design:

I Broader blocking regions

. Blocking level independent of band width

. Best design requires only two coating materials

A difficulty with this design is that there are two stack centers to control to
establish the pass band. In addition, it involves a number of non—QW layers.

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 2L HL 6H LHLHLHL 6H LHLHLHL 6H LHL/sub
100

80

Li
U 60
zcc
I-
I—
40
zcc
u-i

I— 20

0
6 8

Navelength (Microns)

Fig. 8 Same as Fig. 7 for the same design with an added HW layer.

2L HL 6H LHLMLHL 6H LHLMLHL 6H LHL 2M/sub

100

80

U
z 60
Li

cc

40
z
In

cc
I—
20

0
2 4 6 8 10 12

Navelength (Microns)

Fig. 9 Same as Fig. 7 for the final optimized F—P design.

548 / SPIE Vol. 1307 Electro-Optical Materials for Switches, Coatings, Sensor Optics, and Detectors (1990)

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 The F-P design has the following advantages over the QW—stack design.

I There is only one stack center to control

I The layers are all QWs or multiples at the central wavelength

I The band width of the NBP region is fixed by the design and
materials

However, the F-P approach has several problems:

I The tolerance on the thickness of the three spacer layers is

extremely tight

S There are only certain possible band widths that can be achieved

I The best designs require materials with intermediate refractive

indices

Both of these designs might require additional blocking. A design based on

the QW—stack approach, with a wider pass band, could be used to provide blocking
over a wider spectral region.

6. SUMMARY

Two design techniques have been investigated from a theoretical point of view
for a NBP filter with a LWP pass band. A design feature of both designs was the
use of a halfwave layer at the NBP region which provided a reduction in
reflection in the LWP region. Additional layers were identified in the F—P
design for which the performance in the NBP region was independent of refractive
index. The intermediate indices in some of the final designs may not correspond
to real materials. However, they might be achievable with mixtures of standard
materials.

7 . ACKNOWLEDGEMENTS

The coating performance and optimization calculations were carried out on a

program provided by Thin Film Designer Software.

This work was sponsored by the Air Force Weapons Laboratory, Air Force
Systems Command, United States Air Force, Kirtland AFB, New Mexico, 87117.

8. REFERENCES

1. H.A. Macleod, Thin—Film Optical Filters (Macmillan, NY, 1986), 2nd Ed.,
Chap. 7.

2. C. Holm, "Optical thin—film production with continuous reoptimization of

layer thickness," Appl. Opt. 18, 1978—1982 (1979).

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