The far infrared transmission of crystal quartz at 3 K

Injrared fhys. Vol. 27,No. 5,pp.305-308,1987 Printed in Great Britain. All rights reserved

0020-0891/87 $3.00 + 0.00 Copyright 0 1987 Pergamon Journals Ltd

THE FAR INFRARED TRANSMISSION QUARTZ AT 3 K LENNART Stockholm

NORDH

Observatory,

and

G~RAN

OF CRYSTAL

OLOFSSON

S-133 00 Saltsjiibaden,

Sweden

and OVE APPELBLADand LENNARTKLYNNING University

of Stockholm,

Institute

of Physics,

Vanadisvlgen

9, S-l 13 46 Stockholm,

Sweden

(Received 5 March 1987) Abstract-We present transmission measurements of Z-cut crystal quartz at 3 K in the wavenumber range 60-180 cm-‘. The results show that the absorption is extremely small and in fact on the average a factor of ten smaller than indicated by earlier measurements discussed in the literature. One consequence of our results is that crystal quartz is useful in the FIR as a substrate material for Fabry-Perot meshes used in cryogenic experiments.

1.

INTRODUCTION

A number of optical materials, like quartz, sapphire and germanium, are useful for transmission optics in the FIR. Furthermore, when these materials are cooled to cryogenic temperatures the transmission generally improves. (‘J) For this reason, transmission optics can be an attractive choice in certain low-temperature experiments. In particular, optical flats can be used as substrates for metallic Fabry-Perot meshes. The attractive property of optical flats in this application, compared to free-standing meshes, is more or less guaranteed flatness and rigidity, which is particularly important for space experiments. It is obvious, however, that any interior absorption in the substrate will affect the peak transmission of the filter. We have tested a number of Fabry-Perot meshes on crystal quartz substrates at cryogenic temperatures and the results are quite promising. These results will be presented in a forthcoming paper, but here we simply note that the transmission was better than expected from existing data on the absorption coefficient of crystal quartz. For this reason we found it justified to make a more accurate determination of the absorption coefficient of crystal quartz at liquid helium temperature. All measurements and results to be discussed below are restricted to the ordinary ray.

2. THE EXPERIMENT The output beam from a high-resolution Fourier transform spectrophotometer (Bomen DA3.002) was collimated and directed into the test cryostat cooled with liquid helium and pumped to a temperature of about 3 K. As dectector a stressed Ge : Ga photoconductor was used. In order to block NIR and MIR radiation, black polyethylene and teflon were used. This blocking, combined with the spectral sensitivity of the detector, gave a useful spectral coverage between 60 and 180 cm-‘. The test sample in the cryostat was a polished 10 mm thick, 25 mm diameter z-cut crystal quartz plate (from Infrared Laboratories Inc.). The quartz plate was slightly wedge-shaped (4.4 arcmin) which has to be kept in mind when analysing the data. The test plate could be inserted in the optical path by means of a mechanical feed-through. In order not to saturate the dectector, a metal mesh transmitting only about 1% of the light was placed in front of the test plate. This mesh was tilted in order not to give false fringes in combination with the test plate. The spectrometer was operated at various resolutions (from 0.03 to 1 cm-‘) and the interferograms were weighted by the Hamming function to give a clean instrument profile. 305

LENNARTNORDHet al

306

0.01 83

I

I

I

84

85

86

Wavenumber Fig.

J

87

(cm“)

1. A high resolution (A.a = 0.03 cm-‘) transmission tracing of crystal quartz (thickness 10 mm, ordinary ray) at a temperature of 3 K.

3. RESULTS

AND

ANALYSIS

The measurements made at a resolution of 0.03 cm-’ reveal, as expected, the fringes from the interference at the two surfaces of the test plate. Figure 1 shows a part of this transmission curve. In the spectral range 120-180 cm-’ the signal-to-noise ratio is insufficient for an identification of individual fringes. The low-resolution measurements (see Fig. 2) exhibit a good S/N ratio and have a reproducibility of f 1%. In the analysis below we will use the following notations: Transmission for light intensity at one surface = t, reflection for light intensity at one surface = r, absorption coefficient = k (cm-‘), index of refraction = n, plate thickness = D (cm), phase angle = 6 = 2nnD/A (normal incidence), wavelength in vacuum = A (cm), wave number = CT= l/A (cm-‘), fraction of transmitted intensity = T, attenuation coefficient a = e-kD. For the case of a plane-parallel plate with low absorption relations hold:‘3) t=l-r,

and placed in vacuum the following (1)

r = (n - 1)2/(11+ l)*,

(2)

T = at’/(l f r2a2 - 2ra cos 26).

(3)

I.(

p:

$ ; -_

0.:

E

e

I-

0.c

I

loa

Wavanumber (cm-‘)

Fig. 2. A low resolution (Au = 1cm-‘)

transmission tracing of the same sample as in Fig. I.

FIR

transmissionof crystal quartz at 3 K

307

P

x x

2.101

I

I

60

70

I 80

I 90

Wovenumber

I 100

x

I 110

I 120

I 130

CcmT1l

Fig. 3. A comparison between the values of the refractive index of crystal quartz derived by us (T = 3 K, open circles) and by Loewenstein et ul.(‘) (T = I.5 K, crosses).

For the maxima and the minima of the fringe pattern we find: T,,, = at2/( 1 - ~a)‘,

(4)

Tmln= at’/{ 1 + ra)‘.

(5)

The transmission can also be expressed as a Fourier series; T

=

1

at2

(1 + 2ra cos 2S + 2r2a2 cos 46 + 2r3a3 cos 66 + . . .).

This implies that the mean transmission will be given by: 2n

T = (l/271)

T(6) dd = at’/{1 - r2a2).

s0

(7)

3.1. The refra~t~ue index In order to derive the absorption coefficient we need to know the refractive index. The fringe maxima occur for 6, = A%, where iV is the order of interference. Using the measured positions of two arbitrarily chosen maxima the mean refractive index can be calculated: n, = (iv, - N2)/2D(o, - fr*).

(8)

We use a spacing between the measured maxima of 50 orders, which approximately corresponds to 11.3 cm-‘. Since individual fringes are difficult to identify in the wavenumber range 120-180 cm-‘, we can derive the refractive index only for the range 60-120cm-‘. The result is shown in Fig. 3, where we have also plotted the values obtained by Loewenstein et al.‘*’ whose values agree well with those published by Alvarez et al. 14)This shows a clear difference between the two determinations, in particular when approaching the absorption band, starting at 126 cm-‘. As our measurements were made in collimated light, the interpretation of the fringes is straightforward, The error bars in Fig. 3 are dominated by the uncertainty in defining the fringe positions. Any systematic source of error that we can think of-like the thickness determination-is less than An = 0.002, so we cannot explain the discrepancy. 3.2. The absorption coeficient Once the refractive index is known, there are in principle two ways in which the absorption coefficient can be determined, by using either equations (4) and (5) or equation (7). Combining equations (4) and (5) gives:

Tmax/Tmi, = (1 +

ra)2/(1 - ra)*,

(9)

which can be applied directly for calculating the absorption coefficient. The advantage of this method is that the result would be insensitive to a possible non-linear response of the detector. This is due to the fact that there is no need for an accurate absolute transmission measurement. The

LENNARTNORDH et al

308 Table

I. The absorption coefficient of crystal quartz at 3 K Absorution

Wavenumber 60cm 70 80 90 100 110 120 130 140 I50 160 170 I80

’

0.05 * 0.06 i 0.08 i 0.09 + 0.08 f 0.08 i 0. I I i -(absorption 0.32 0.17 0.30 0.26 0.3 I

+ + * + i

coefficient

0.03 cm 0.03 0.03 0.03 0.03 0.03 0.03

’

band saturated) 0.04 0.04 0.04 0.04 0.04

disadvantage of this method is that a high resolution and a good S/N ratio are needed. For this reason and because our test plate was slightly wedge-shaped (which means that the fringes were not fully in phase across the 12 mm diameter illuminated area) we could not use this method. It should be noted, however, that neither the fringe periods nor the mean transmission are affected by the wedge shape. We are thus restricted to the second method based on equation (7) and our low-resolution transmission measurements. In order to calculate t and r we use equations (1) and (2) and the n-values given in Fig. 3. For the wavenumber range 140-l 80 cm-’ we use the n-values given in Ref. (2) increased by A, = 0.02, which is the difference between the two sets of values in the range 70-90 cm-‘. It should be noted, however, that this small modification of the refractive index does not result in a significantly different absorption coefficient. The result is given in Table 1. In order to estimate the precision of the derived absorption coefficients, we have to consider the possible non-linearity of the detector when changing the background radiation level by 30% (which results from inserting the test plate in the light-path). In a separate test we found that the deviation from linearity was less than 3% which means that our transmission measurements should be reliable to the same precision. Therefore the errors given in Table 1 refer to this uncertainty, except for the wavenumber range 140-180 cm--‘, where a small error of a statistical nature has been included. The absorption coefficients are on average a factor of ten smaller than those given in Ref. (2). Even if we take into account the errors quoted by these authors, f 0.2 cm-‘, there remains a large systematic difference. Since we used quite a thick test sample, the expected transmission, using the absorption coefficients given in Ref. (2), would have been at least a factor of two smaller than that actually measured. In conclusion we find that crystal quartz, due to its low absorption, is a useful optical material at liquid helium temperature for wavenumbers smaller than 120 cm-‘. In particular it can be used as substrate for metallic Fabry-Perot meshes. Acknowledgement-This Dr 24/86.

research

is supported

by the Swedish Board for Space Activities

through

grants

REFERENCES 1. A Handi, J. Claudel, E. Decamps, X. Gerbaux and P. Strimer, C. r. Acad. Sci. 255, 1595 (1962). 2. E. V. Loewenstein, D. R. Smith and R. L. Morgan, Appl. Opt. 12, 398 (1973). 3. M. Born and E. Wolf, Principles of Opfics. Pergamon Press, Oxford (1959). 4. J. A. Alvarez, R. E. Jennings and A. F. M. Moorwood, Infrared Phys. 15, 45 (1975).

No. Dr 21/85 and