POLARIZATION PROPERTIES OF FAR INFRA-RED BEAMSPLITTERS

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POLARIZATION PROPERTIES OF FAR INFRA-RED

BEAMSPLITTERS

Ernest Loewenstein, Amos Engelsrath

To cite this version:

Ernest Loewenstein, Amos Engelsrath. POLARIZATION PROPERTIES OF FAR

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JOURNAL DE PHYSIQUE Colloque C 2, supplkment au no 3-4, Tome 28, mars-avril I967, page C 2

-

155

POLARIZATION PROPERTIES OF FAR INFRA-RED BEAMSPLITTERS

AFCRL (CROI) Bedford, Massachusetts, 01730 and AMOS ENGELSRATH

Block Engineering, Inc. 19 Blackstone Street Cambridge, Massachusetts, 02139, U. S. A.

Rkum6. -On calcule l'energie transmise par un interfkrom6tre dam le cas d'une skparatrice rkaliske avec un film mince sans support. La polarisation du faisceau incident sur le rkcepteur est donnke, et l'on montre qu'en pla~ant la dparatrice sous l'incidence Brewsterienne et non sous l'incidence habituelle de 4S0 un faisceau sortant compl6tement polarisk peut &tre obtenu avec trks peu de pertes d'knergie. On donne les rtsultats d'une cornparaison avec l'expkrience.

Abstract. - The energy throughput of an interferometer is calculated for the case where an unsupported thin film is used as a beamsplitter. The polarization of the beam toward the detector is calculated, and it is shown that by setting the beamsplitter at the Brewster angle rather than the usual 450, a completely polarized output beam may be expected, and at very little cost in energy. Comparison with experiment is given.

A) Introduction.

-

The Michelson interferometer used in the far infrared employs as a beamsplitter an unsupported thin film of mylar (polyethylene tereph- thalate). Since the reflection and transmission properties of thin films can be computed exactly in terms of their optical constants, it is possible to compute the throughput and polarization of the instrument much more simply than in the case of a beamsplitter deposi- ted on a substrate. While the optical constants of mylar are not well known it is possible to show both theoretically and experimentally that by setting the beamsplitter at the Brewster angle instead of the usual 450, the beam emerging toward the detector is almost completely polarized, perpendicular to the plane of incidence onto the beamsplitter. This is true despite the fact that mylar displays both birefringence and optical activity.

B) Energy Considerations for the Michelson Inter- ferometer. - Figure 1 illustrates a Michelson interferometer with an incident beam of unit amplitude. There are two emergent beams, one toward the detector, the other toward the source. If r and t denote respectively the amplitude reflection and transmission coefficients of the beamsplitter, then at zero path difference

1

2

E det = 4 8

IL

tl

FIG. 1. -Illustrating the incoming and outgoing beams of a Michelson interferometer at zero path difference. Ei = incom-

ing energy, E, = energy returning toward the source, E d e t =

energy going toward the detector; t and r are the complex amplitude reflection and transmission coefficients of the beamsplitter.

and

Esourcc =

I

r2

+

t2

I

. (2).

These equations illustrate the dissymmetry of the two beams. For the one travelling toward the detector the beams traversing the two arms each suffer one Edet = 4

1

rt (

'

(I) transmission and one reflection at the beamsplitter,

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C 2 - 1 5 4 ERNEST V. LOEWENSTEIN AND AMOS ENGELSRATH

while for the other case one beam is reflected twice We may rewrite ( 7 4 and (7b) in polar form :

and the other transmitted twice. If we let

r = y eie (30)

and

A = 2 nv(D2

-

D l )

(D,

-

D l ) = path difference the equations for the energy become :

In the case of a non absorbing beamsplitter, conserva- tion of energy requires that

While the beams of equations 4 and 5 are complemen- tary, the visibility of the fringes, for monochromatic light, is better in the beam travelling toward the detec- tor, unless r2 = t2 = 0.5.

C) Polarization Properties.

-

The amplitude reflection and transmission coefficients of a non absorbing dielectric film in vacuum are given by [ I ] :

6 = 4 nnvd cos 9, where

d = thickness of the medium

n = index of refraction of the medium v = wave number of the radiation

0, = angle between the normal and the ray inside the medium

R, T = Fresnel coefficients for the energy reflectance and transmittance of a single surface. If a wave of unit amplitude is incident upon the medium and we arbitrarily set the phase equal to zero at the point of incidence, then these equations give the amplitudes and phases of the reflected and transmitted waves at the point where each leaves the film. The phase change corresponding to the distance tra- versed through the film is included in t.

-

( 1

-

R ) sin 6

exp

[

i arctan

( 1

+

R ) (1

+

cos 6 )

It is noted that the arguments of the exponentials satisfy eqn (6) because their tangents are negative reciprocals of each other.

Substituting ( 8 4 and (8b) into (4), and setting the path difference equal to zero we have for the energy in the beam toward the detector of the interferometer, for unit incident energy :

8 R T ~ ( ~

-

cos 6)

Edet =

(1

+

R2

-

2 R cos 6 ) '

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Since R and T, the Fresnel coefficients, are dependent upon polarization, an unpolarized incident beam will be polarized to some degree by passage through the interferometer. We define percentage polarization by

Es and Ep are respectively the energies in the polariza- tion perpendicular and parallel to the plane of incidence for the detector beam. It is noted that the pola- rization can be 100

%

if Ep = 0 , which does occur at the Brewster angle.

EXPERIMENTAL RESULTS. We have measured the polarization of the detector beam of an interferometer using a 6 micron thick beamsplitter at two angles of incidence : 450 and 600. As a polarizer we used a pile of polyethylene sheets, described by Mitsuishi et al. [2]. In addition, we have computed the polarization, using eqn (9) with n = 1.75, which is approximately the refractive index of mylar over a broad range of the far infra-red 131.

Our results are summarized in figure 2, which shows the measured polarization at 45O and 60° angles of incidence and the computed polarization at 450. It is seen that there is reasonable agreement between the calculated and observed polarization at 45O between

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POLARIZATION PROPERTIES OF FAR INFRA-RED BEAMSPLITTERS C 2

-

155

100 2 0 0

W A V E N U M B E R crn-'

POLARIZATION OF EMERGENT BEAM 100 ; A A A * ' A ~ A A A ~ A ~I

FIG. 2. - Calculated and observed polarization of the bezm toward the detector. Solid line : calculated polarization at 45" angle of incidence ; crosses : observed polarization at 450 angle of incidence ; triangles : observed polarization at 600 angle of incidence (Brewster angle). The dropoff below 100 cm-1 and the dip between 400 and 500 cm-1 are artifacts of the beamsplitter.

90

numbers and a cc line )) or dip between 400 and

500 cm-l. These features are artifacts introduced by the channel spectrum characteristic of the polarizer plates, which are about 9 microns thick.

A L O B S E R V E D FOR 60a A -

-

A A WAVENUMBERS (cm-'I a I- 4 0 -

FIG. 3. -Observed energies in the parallel and perpendicular polarizations (defined with respect to the plane of incidence onto the beamsplitter) at 600 angle of incidence.

Figure 3 shows the energies in the parallel and perpendicular polarizations at 600 angle of incidence. The two peaks in the parallel polarization are due to the above mentioned polarizer characteristic. The line at 380 cm-I is the strongest absorption line of mylar in the far infra-red, but no change in polarization is observed at this wavelength. Calculations show that the polarization is quite insensitive to changes in either index or absorption coefficient, so it will not be possible

to derive optical constants of beamsplitter materials from polarization measurements. It may, with very precise measurements, be possible to determine diffe- rences of index for a birefringent material, but no investigation has been made of this point (Mylar itself is birefringent).

CALCULATED BEAMSPLITTER EFFICIENCY

100 I 1 I 3

"0 100 2 0 0 3 0 0 400 5 0 0 W A V E N U M B E R cm-'

FIG. 4. -Computed energy in the detector beam at 450 and

600 angle of incidence. Solid line 45O, dashed line 600.

Finally, we see in figure 4 that there is very little cost in energy when the interferometer is set at 600 instead of

450. The total intensity at the peak decreases by 30 %,

but the pass band broadens. Furthermore, the only energy lost is that in the parallel polarization, so if polarized light is to be used, there is no loss whatever in setting up the interferometer at 600 in the first place.

D) Conclusion.

-

We have derived equations for the energy in the output beams of a Michelson interferometer using an unsupported thin film as a beamsplitter. We have shown both theoretically and experimentally that it is possible to produce nearly completely polarized radiation in the beam travelling toward the detector by letting the incoming radiation strike the beamsplitter at the Brewster angle.

E) Acknowledgements. - The authors thank Mr. Robert'L. Morgan who operated and maintained the interferometer and detector. The digital computa- tions were handled by Mr. John Dolan.

[I] BORN (M.) and WOLF (E.), ((.Principles of Optics ))

(New York, The MacM~llan Company, 1964,

2nd Edition), pp. 323 ff.

[2] MITSUISHI (A.) et al., 3. Opt. Soc. Am., 1960, SO, 433.