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THE EFFICIENCY OF BEAMSPLITTERS IN THE
FAR INFRA-RED MICHELSON INTERFEROMETER
D. James, J. Ring
To cite this version:
JOURNAL DE PHYSIQUE Colloque C 2, supplkment uu no 3-4, Tome 28, mars-avril1967, page C 2
-
150THE EFFICIENCY
OF
BEAMSPLITTERS IN THE FAR INFRA-RED
MICHEL SON INTERFEROMETER
D. J. JAMES and J. RING
Department of Applied Physics, University of Hull, England
Abstract. - The efficiency of thin film beamsplitters for Interferometers has been computed. The computations are repeated for various combinations of beamsplitters for cases where the thickness variations take place both within and outside the coherence area of the incident radiation. R6sum6. - L'efficacitB des separatrices a couches minces a ete etudiee. Les calculs ont BtB faits dans le cas de couches d'epaisseur variable, et dans les cas oh cette variation se produit soit B I'intBrieur soit A I'extBrieur de la zone de cohbrence du rayonnement incident.
The efficiency of a Michelson Interferometer beamsplitter is defined as the depth of modulation of the interference fringes
y(o) = 4 R T
where R is the intensity reflection coefficient and where T is the intensity transmission coefficient.
The beamsplitter most used in the far infra-red is a thin film of Melinex. This material transmits well throughout the spectral range except for an absorption band at 380 cm-I [I]. The average refractive index of the material in the far infra-red is 1.85 [2].
Neglecting absorption, T = 1
-
R andR is calculated from the Fresnel amplitude reflection
coefficients. (Figure 1). no cos4,
-
nl cos41
= - rzs rls = no cos4,
+
n, cos4,
no cos-
n1 cos +O rip = - - --
r z p , no cos4,
+
n1 cos4,Intensity reflection coefficients
2 r?,(l
-
cos 2 6)R, =
1
+
r%-
2 r:, cos 2 62 7L
where 6 =
-
a
n d cos4,
is the phase difference bet-FIG. 1. -Multiple reflection at a thin film interface. ween adjacent emerging beams, and subscripts s and p refer to the two planes of polarisation [3]. The effi- ciency function has been computed for an angle of incidence
41,
= 450 and the results are shown infigure 2. The average efficiency for a 6 y Melinex beamsplitter over the frequency range 10-500 cm-l is
44.8
%.
The efficiency is a periodic function of fre- quency with fairly strong polarisation characteristics. For unpolarised radiation, the two curves shown must be averaged. If high efficiency is required at low fre- quencies, this can only be attained by using a thicker beamsplitter, resulting in many cycles of the efficiency function within a small bandwidth.THE EFFICIENCY IN THE FAR INFRA-EUD MICHELSON INTERFEROMETER C 2
-
151FIG. 2. - Beamsplitter efficiency vs. frequency for a 6 p Melinex film.
In order to obtain low frequency efficiency without many cycles, the shape of the efficiency curve must be changed in such a way that the bandwidth is increased without decreasing the slope of the curve at the low frequency end. A thinner dielectric film will of course increase the bandwidth at the expense of low frequency efficiency, and the simplest way of improving this is to manufacture a beamsplitter with variations in thick- ness.
Considering the simplest case, in which there are only two thicknesses, d , and u', = 2 d l , there are only two limiting cases to consider :
(i) When the variations in thickness take place outside the coherence area of the illuminating radiation. The resulting efficiency is then the average of the two computed efficiency curves for d, and d,. The result of such averaging is shown in figure 3. It can be seen that the bandwidth is doubled, with some loss of efficiency at intermediate frequencies.
100 Efficiency %
t
(ii) When the variations in thickness occur within the coherence area of the illuminating radiation, the amplitude reflection coefficients must be averaged and the efficiency calculated for these. The result of this computation is shown in figure 4, for the perpen- dicular polarisation. A comparison curve for incohe- rent energy is also shown. The slope of the curve at low frequencies is almost the same, the peak is slightly shif- ted to low frequencies and there is an increase in band- width.
,V I I 8 1 , I I I , \ I
200 400 600 800 1000
Wovenumber cm4
FIG. 4.
-
Beamsplitter efficiency vs. frequency for incoherent and coherent combination of films.Metal meshes have also been used in beamsplitters in the far infra-red and microwave regions. Complex grids may also be used, and the same limiting condi- tions would apply. Figure 5 shows the result of incoherent averaging of meshes. Curve A is taken from
experimental measurements by P. Vogel and L. Gen- zel [4], and curve B and the averaged curve C have
been derived from this. The fluctuations in the effi- ciency curve are averaged out, and greater bandwidth is obtained.
01 I I t
0,s 1 2 3 4 5 1/d
FIG. 5. - Beamsplitter efficiency vs. I / d for metal meshes.
FIG. 3. - Beamsplitter efficiency vs. frequency for incohe- rent combination of films. Averaged over both planes of pola- rization.
C 2 - 1 5 2 D. J. JAMES AND J. RING
and the degree of mixing will vary with frequency. A
Michelson interferometer has been constructed t o investigate these effects experimentally. The manufac- ture of complex beamsplitters whose dimensions change within the coherence radius is feasible if the far infra-red since, using a conventional detecting system with f /l condensing optics with a 3 mm detector, the coherence radius is approximately 2 rnm at 1 = 100 y.
[l] WILLIS (H. A.) et al., Spectrochimica Acta, 1963, 19,
1957.
121 GEBBIE (H. A.) and STONE (N. B.), Infrared Physics,
1964, 4, 85.
[3] HEAVENS (0. S.), <( Optical Properties of Thin Solid Films )), Butterworth's London 1957.
[4] VOGEL (P.) and GENZEL (L.), Injrared Physics, 1964, 4, 257.
DISCUSSION
J. RING.
