Stokes Mueller Treatment of Artifacts in Natural Raman Optical Activity

Abstract

A description of Raman scattering based on the theory by Barron and on Stokes Mueller formalism was developed into a uniform mathematical calculus such that Raman scattering can now be easily represented by a simple phenomenological matrix. This matrix, the Mueller matrix of a modulator driven by a square-wave voltage, and the matrix for a laser regarded as a fictitious polarizer are presented for the first time. With the use of these three matrices and the ones for the analyzer, the polarizer, the linearly birefringent sample cell, the circularly birefringent sample, and the partially polarizing detector, the main reasons for the appearance of artifacts in Raman optical activity have been identified. On the basis of a calculation for right-angle scattering of an isotropic solution of chiral molecules, sources of artifacts appear to be the linear birefringence of the cell walls and of the modulator material. Phase-sensitive detection is found to observe Raman optical activity with a minimal number of artifacts.

Keywords

Stokes Mueller calculus Optical activity Vibrational optical activity Raman optical activity Raman spectroscopy Modulation spectroscopy Electro-optic modulation Phase-sensitive detection Instrumentation Scattering tensor Chirality Artifacts

Get full access to this article

View all access options for this article.

References

Barron

L. D.

Vrbancich

, in Topics in Current Chemistry, Boschke

F. L.

, Ed. (Springer, Berlin, 1984), Vol. 123, p. 151.

Nafie

L. A.

, in Advances in Infrared and Raman Spectroscopy, Clark

R. J. H.

Hester

R. E.

, Eds. (Heyden, London, 1984), Vol. 11, p. 49.

Nafie

L. A.

, in Vibrational Spectra and Structure, Durig

J. R.

, Ed. (Elsevier, Amsterdam, 1981), Vol. 10, p. 153.

Barron

L. D.

Buckingham

A. D.

, Mol. Phys. 20, 1111 (1971).

According to IUP AC [ Fassel

V.A.

, Pure Appl. Chem. 30, 651 (1972)] both the intensity of the detected (I^d) and incident radiation (Iⁱ) should be named radiance (W × sr⁻¹ × m⁻²) or irradiance (W × m⁻²). If one additionally takes into account the solid angle together with the surface element, or the surface element only, both quantities—the radiance and the irradiance, respectively—yield another quantity denned as radiant power or radiant flux (W).

Hug

Kint

Bailey

G. F.

Scherer

J. R.

, J. Amer. Chem. Soc. 97, 5589 (1976).

Waki

Higuchi

Tanaka

Sakayanagi

, Bunko Kenkyu 26, 271 (1977).

Hansen

H.-J.

Sliwka

H.-R.

Hug

, Hel. Chim. Acta 62, 1120 (1979).

Barron

L. D.

Buckingham

A. D.

, Ann. Rev. Phys. Chem. 26, 381 (1975).

10.

Hug

, Appl. Spectrosc. 35, 115 (1981).

11.

Barron

L. D.

Vrbancich

, J. Raman Spectrosc. 15, 47 (1984).

12.

Escribano

J. R.

, Chem. Phys. Lett. 121, 191 (1985). There is a misprint in that paper. The term sin³(Δβ/2) in equation 6 should read sin(Δβ/2) only.

13.

Oboodi

M. R.

Davies

M. A.

Gunnia

Blackburn

M. B.

Diem

, J. Raman Spectrosc. 16, 366 (1985).

14.

Barron

L. D.

Torrance

J. F.

Cutler

D. J.

, “A New Multichannel Raman Optical Activity Instrument,” accepted by J. Raman Spectrosc.

15.

A closer look at the symmetry properties of this “vector” reveals its quaternion-like behavior. See for example: Pawley

G. S.

, Mol. Phys. 43, 1321 (1981) and Ref. 36.

16.

Perrin

, J. Chem. Phys. 10, 415 (1942).

17.

Jones

R. C.

, J. Opt. Soc. Amer. 37, 107 (1947).

18.

Mueller

, J. Opt. Soc. Amer. 38, 661 (1948).

19.

Hecht

Jordanov

, unpublished research.

20.

Jones

R. C.

, J. Opt. Soc. Amer. 46, 528 (1956).

21.

Barron

L. D.

, Molecular Light Scattering and Optical Activity (Cambridge University Press, Cambridge, 1982).

22.

Barron

L. D.

, in Molecular Spectroscopy, Specialist Periodical Reports (The Chemical Society, London, 1976), Vol. 4, p. 96.

23.

Jensen

H. P.

Schellman

J. A.

Troxell

, Appl. Spectrosc. 32, 192 (1978).

24.

Richards

Wolf

, Proc. Roy. Soc. (London) 253, 358 (1959).

25.

Barron

L. D.

Buckingham

A. D.

, J. Amer. Chem. Soc. 101, 1979 (1979).

26.

Hecht

Jordanov

Schrader

, unpublished results.

27.

van de Hulst

H. C.

, Light Scattering by Small Particles (Wiley, New York, 1957).

28.

van de Hulst

H. C.

, Multiple Light Scattering (Academic Press, New York, 1980).

29.

Barron

L. D.

Johnston

C. J.

, J. Raman Spectrosc. 16, 208 (1985).

30.

Billings

B. H.

Land

E. H.

, J. Opt. Soc. Amer. 38, 819 (1948).

31.

Korte

E.-H.

, private communication.

32.

Data of the dichroic sheet polarizer 03FPG (Melles Griot GmbH, Darmstadt, FRG).

33.

Shindo

Ohmi

, J. Amer. Chem. Soc. 107, 91 (1985); (data of the Hamamatsu head-on photomultiplier R376).

34.

Based on the data of the Innova laser series (Coherent Corporation, Palo Alto, USA).

35.

Data of the Glan-Thompson calcite polarizer PGT18 (B. Halle Nachfl. Optische Werkstätten, Berlin, FRG).

36.

Schönhofer

Kuball

H.-G.

Puebla

, Chem. Phys. 76, 453 (1983).

37.

Born

Wolf

, Principles of Optics (Pergamon Press, Oxford, 1975).

38.

Based on the data of the Schlieren seed-free-quality fused-silica Dynasil®.

39.

Yariv

, Quantum Electronics (Wiley, New York, 1975), 2nd ed.

40.

Rees

C. S.

Shah

S. M.

Stanojevic

C. V.

, Theory and Applications of Fourier Analysis (Marcel Dekker, New York, 1981).

41.

Watson

G. N.

, A Treatise on the Theory of Bessel Functions (Cambridge University Press, Cambridge, 1966), 2nd ed.

42.

Gradshteyn

I. S.

Ryzhik

I. M.

, Table of Integrals, Series and Products (Academic Press, New York, 1980).

43.

Based on the data of the transverse modulator LM 0202, 4 × 45° y-cut ADP crystals (Gsänger Optische Komponenten GmbH, Planegg, FRG).

44.

Chiu

Y.-N.

, J. Chem. Phys. 52, 3641, 4950 (1970).