The Effect of Optical Polarization on Reflection Spectra

Allan H. Reed and Ernest Yeager

The theoretical basis for polarization effects in reflection spectra are reviewed. It is shown that lightpolarized parallel to the plane of incidence interacts more strongly with the absorbing species than doeslight of perpendicular polarization except under conditions of internal reflection when the absorber is athin film between two nonabsorbing media. In this instance the relative degree of interaction is de-termined by the refractive indices of the three phases. Experimental results are presented which showthe predicted effects for internal reflection spectroscopy both when the absorbing medium is a solution of(CH3)4NCl in D 2 0 and when it is a monolayer of stearic acid.

Introduction

The effect of optical beam polarization is consideredin the derivation of the theoretical expressions for thereflectivity of an interface. Relatively few experi-mental data on such effects in reflection spectroscopy,however, have been reported. According to thetheories of both external' and internal 2 reflection, thecomponent of the light polarized parallel to the plane ofincidence should show the stronger absorption bands ina reflection spectrum; but the theoretical reasons aredifferent for the two types of reflection. The purposeof this paper is to compare experimental data on polar-ization effects with theory for internal reflection spec-troscopy.

Theory

For external reflection, the phase shift which the re-flected wave undergoes is very close to 1800 for the com-ponent polarized perpendicular to the plane of in-cidence, regardless of the angle of incidence. Thus theincident and reflected electric vectors near the surfacefor this polarization almost cancel each other. Lightpolarized parallel to the plane of incidence, however,undergoes much less phase change except near grazingincidence. From this it follows that a surface layershould produce relatively little absorption of lightpolarized perpendicular to the plane of incidence, butrelatively strong absorption of light of parallel polariza-tion. This theory' also predicts that the optimumangle of incidence will be high, but not grazing, e.g.,700 for light of parallel polarization.

The important factor in internal reflection is theinteraction of the field in the second medium with the

absorbing species in that medium. While the degree ofinteraction actually depends on the orientation of theabsorbing dipoles with respect to the reflecting surface,the theory2 developed from Maxwell's equations pre-dicts that the degree of coupling with a homogeneousmedium of randomly oriented dipoles is always greaterfor parallel polarization than for perpendicular polar-ization. The same type of treatment has been extendedto a medium having anisotropic optical properties. 3

The Fresnel coefficients for internal reflection whenthe second medium is absorbing can be expanded in apower series as4

(1)

where the subscript j refers to either parallel (p) orperpendicular (s) polarization, the Qj's are factors whichdepend on the angle of incidence and the refractive in-dex ratio, and K is the attenuation index. In all in-stances it can be shown that Q, > Q,. The greatercoupling of the parallel component of the field is equiv-alent to a greater effective thickness for parallel polar-ization than for perpendicular polarization. The effec-tive thickness is defined2 as the thickness of samplewhich would be required in transmission spectroscopyto give the same amount of light absorption as is ob-tained in a reflection spectrum of the same sample usingone reflection.

When the attenuation of the reflected light is smallso that the expansion of Eq. (1) to the first power isadequate, it may be written in a form analogous to theBeer-Lambert law:

(Rj° - Rj)/Rj° = ARj1R, = QjK. (2)

The authors are with the Chemistry Department, CaseWestern Reserve University, Cleveland, Ohio 44106.

Received 22 August 1967.

When a multiple reflection system of n reflections is usedand ARj/R30 << 1, one may write Eq. (2) as:

(I - Ij)/I'j = Aj/I'j = nQjK. (3)

March 1968 / Vol. 7, No. 3 / APPLIED OPTICS 451

R = Rj1(1 - QjK + ... ),

0.3Al

IO

0.1 0.2 0.3CONCENTRATION, MOLES/LITER

Fig. 1. A/I0 vs concentration for the 1486-cm-' band of(CH3)4NCl in D20 for polarized and unpolarized spectra at 450angle of incidence. A parallel polarization, * perpendicular

polarization, * no polarization.

From the definition of absorbance, it follows that

A = logio(Ij°/1i) _ nQjK/2.303. (4)

The treatment of a thin absorbing film between twononabsorbing media is more complicated in the caseof internal reflection spectroscopy. Harrick' gives theeffective thickness of thin isotropic films as

te = (4t n21 cos0)/(1 - n312), (5)

and

4t n2 l cosO[(1 + n324) sino - n3l2 6

p (1 - n31')[(1 + n312) sin2o -n,,] (6)

where t is the true thickness, 0 is the angle of incidence,and nab = na/nb with the subscript 2 in Eqs. (5) and (6)corresponding to the absorbing film between phases 1and 3. The ratio te,/tep is then given as

te = [(1/n312) + 1] sin2O - 1tep [(l/n 3 1

2) + (n322/fl 21 2)] sin2o - 1 (7)

From Eq. (7) it can be seen that t/te > 1 when n 3 2/n 21< 1 and te/tee < 1 when n 32 /n, > 1.

Experimental

The spectra for this study were obtained on a Perkin-Elmer model 621 ir spectrophotometer with a WilksScientific model 18 internal reflection modification re-placing the original source optics. The polarizer (Per-kin-Elmer part 186-0185) was a wire grid of goldvapor-deposited on a silver chloride substrate placed inthe common optical beam of the spectrophotometer infront of the entrance slit of the monochromator. Thispolarizer has a very high efficiency.6 The use of doublebeam mode of operation with germanium plates in bothbeams minimizes complications caused by differences inintrinsic response of the grating monochromator de-tector system to parallel and perpendicular componentsof the light. The introduction of the polarizer de-creases the total energy reaching the detector by ap-

proximately a factor of two, thus decreasing the signal-to-noise ratio. The spectrum obtained with lightpolarized parallel to the plane of incidence, however,will be relatively more intense than that with un-polarized light, because the more weakly interactingcomponent of the radiation no longer strikes the de-tector (see Fig. 1). The germanium internal reflectionplates were 50 mm long and 1 mm thick and had anangle of incidence of 45° which allowed forty-nine re-flections. In the measurements made with a liquid asthe second medium, only forty-three of these reflectionswere from the germanium-liquid interface because ofthe geometry of the cell confining the liquid.

Results and DiscussionIt can be shown4 that at a 450 angle of incidence, the

value of Q, is twice that of Q,. A plot of AIj/Ij or Aj asa function of concentration should be linear and theslope for parallel polarization should be twice that ofthe perpendicular polarization plot. This has been ob-served experimentally for the 1486-cm- 1 band of(CH3)4NCl. Figure 1 shows AljlIj for this band as afunction of the salt concentration in D20.

Figure 2 shows the spectra obtained for both paralleland perpendicular polarization of the C-H stretching re-gion for a monolayer of stearic acid deposited on agermanium reflection plate bya Langmuir-Blodgett tech-nique7 and then placed in contact with D20. The ratio(AI,/I')/Q.\I/I °) obtained from these measurements is0.54. Figure 3 shows the polarized spectra of the sameregion for a germanium-stearic acid monolayer-airinterface. The ratio (AI/I 0 )/(IpI ) in this case is0.83.

< 9 4

a 9 2z02 9

)

= 88

t. = 86

84

3100 3000 2900 2800 3100 3000WAVE NUMBER, GM-'

2900 2800

Fig. 2. Polarized spectra of a stearic acid monolayer on a ger-manium reflection plate with D20 as the third medium. (a)perpendicular polarization, (b) polarallel polarization. Curves I-with stearic acid monolayer, curves II-without monolayer.

452 APPLIED OPTICS / Vol. 7, No. 3 / March 1968

I I I I

98 -

961-

I

A

I I I I

o _

3 _

B

I I I I I I

2900 2800 31CWAVE NUMBER, CM-'

Fig. 3. Polarized spectra of a stearic acid monolayer on a ger-manium reflection plate with air as the third medium. (a) per-pendicular polarization, (b) parallel polarization. Curves I-with stearic acid monolayer, curves II-without monolayer.

The ratio te/tee calculated from Eq. (7) for a ger-manium-stearic acid-D 20 interface at 450 angle of in-cidence is 0.58. This calculation uses the values of4.0, 1.43, and 1.33 for the refractive indices of ger-manium, stearic acid, and D20, respectively. Thisratio calculated for the germanium-stearic acid-airinterface is 0.84. The use of a bulk property such as re-fractive index in a situation involving a monolayer is

certainly open to question, but in this case satisfactoryresults were obtained. It is possible that the length ofthe stearic acid molecule is great enough that even alayer one molecule thick approximates bulk propertiessince the C-H portion of the molecule could present arelatively uniform optical environment. Cautionshould be exercised, however, in the extension of thistreatment to monolayers of smaller molecules.

Conclusion

This work demonstrates the utility of a polarizer inreflection spectroscopy as a means of increasing therelative intensity of a reflection spectrum. It also showsthat experimental data can be obtained which are insatisfactory agreement with those predicted by theory.

This research was partially supported by the Office ofNaval Research.

References1. R. C. Greenler, J. Chem. Phys. 44, 310 (1966).2. N. J. Harrick, J. Opt. Soc. Am. 55, 851 (1965).3. P. A. Flournoy and W. J. Schaffers, Spectrochim. Acta 22,

5 (1966).4. W. N. Hansen, Spectrochim. Acta 21,815 (1965).5. N. J. Harrick, and F. K. DuPr6, Appl. Opt. 5, 1739 (1966).6. The Perkin-Elmer Corp., Norwalk, Conn. Instrument News

16, No. 3, p. 5 (1966).7. K. Blodgett, J. Am. Chem. Soc. 57, 1007 (1935).

Robert E. Hufnagel has been named director of research of theOptical Group at the Perkin-Elmer Corporation.

March 1968 / Vol. 7, No. 3 / APPLIED OPTICS 453