Abstract

In this third paper of our series, some consequences of the theories for the refractive and the rotatory dispersion are examined. It is shown that the Sellmeier-Drude and the Lorentz-Lorenz formulas for the dispersion of the refractive index are equivalent, and in fact are special cases of a more general equation. In a similar vein, the classical oscillator model of Vysin and the quantum calculations of Agranovich, for the rotatory dispersion, are shown to be equivalent for a nonmolecular crystal. This equivalence is used to analyze and interpret the Agranovich type of equation that we deduced from our measurements reported in the first two papers. It is found that the oscillator parameters specified by our data and this equation are reasonable in the light of completely unrelated experiments and considerations.

© 1979 Optical Society of America

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  1. P. Hennessey and K. Vedam, "Piezo- and thermooptical properties of Bi12GeO20. I. Optical rotatory dispersion," J. Opt. Soc. Am. 65, 436–441 (1975).
  2. K. Vedam and P. Hennessey, "Piezo- and thermooptical properties of Bi12GeO20. II. Refractive index," J. Opt. Soc. Am. 65, 442–445 (1975).
  3. M. Moffitt and A. Moscovitz, "Optical activity in absorbing media," J. Chem. Phys. 30, 648–660 (1959).
  4. W. Kuhn, "Quantitative Verhaltnisse und Beziehungen bei der natürlichen optischen Aktivität," Z. Phys. Chem. B4, 14–36 (1929).
  5. P. Hennessey, "Piezo- and Thermooptical Properties of Bismuth Germanium Oxide," Ph.D. Thesis, The Pennsylvania State University, 1972 (University Microfilms, Ann Arbor, Michigan, Order No. 72–33, 172).
  6. V. A. Kizel, Y. I. Krasilov, V. I. Burkov, V. A. Madii, and 2. M. Alikanova, "The gyrotropy of cubic crystals of uranyl compounds," Opt. Spectrosc. 27, 344–347 (1969).
  7. V. Vysin, "Note on the theory of the rotatory dispersion of crystals," Proc. Phys. Soc. 87, 55–60 (1966).
  8. P. Drude, Lehrbuch der Optik (Leipzig, 1900) (English translation, Dover, New York, 1959), Chap. VI.
  9. M. Born, "Uber die naturliche optische Aktivitat von Flussigkeiten und Gasen," Phys. Zeit. 16, 251 (1915); "Elecktronentheorie das naturlichen optischen Drehungsvermogens isotroper und anisotroper Flussigkeiten," Ann. Phys. 55, 177–240 (1918); Optik (Springer, Berlin, 1933), Sec. 84.
  10. W. Kuhn and K. Bein, "Beschaffenheit und raumliche Ausdehnung des Streumomentes bei optisch activen Molekülen," Z. Phys. Chem. B22, 406–422 (1933).
  11. S. Chandrasekhar, "Theoretical interpretation of the optical activity of quartz," Proc. Ind. Acad. Sci. 37A, 468–484 (1953); "Optical rotatory dispersion of crystals," Proc. R. Soc. 259A, 531–533 (1961).
  12. V. M. Agranovich, "Theory of the inherent optical activity of molecular crystals, I. Classical theory," Opt. Spectrosc. 1, 338–347 (1956); "Theory of the inherent optical activity of molecular crystals, II. Quantum theory," Opt. Spectrosc. 2, 738–746 (1957).
  13. C. W. Deutsche, "Theory of optical activity of crystalline benzil," J. Chem. Phys. 53, 1134 (1970).
  14. D. R. Penn, "Wave-number-dependent dielectric function of semiconductors," Phys. Rev. 128, 2093–2097 (1962).
  15. K. S. Krishnan and S. K. Roy, "The dispersion formulae and the polarization fields," Philos. Mag. 43, 1000 (1952).
  16. E. U. Condon, W. Altar, and H. Eyring, "One electron rotatory power," J. Chem. Phys. 5, 753 (1937).
  17. P. Hennessey, "Piezo- and thermo-optical properties of bismuth germanium oxide IV. The absorptive properties," J. Opt. Soc. Am. (to be published).
  18. S. C. Abrahams, P. B. Jamieson, and J. L. Bernstein, "Crystal structure of piezoelectric bismuth germanium oxide Bi12GeO20," J. Chem. Phys. 47, 4034–4041 (1967).
  19. K. Vedam and T. A. Davis, "Pressure and temperature variation of the optical rotatory power of α-quartz," J. Opt. Soc. Am. 11, 1451–1455 (1968).
  20. G. G. Douglas and R. N. Zitter, "Transport processes of photoinduced carriers in bismuth germanium oxide (Bi12GeO20)," J. Appl. Phys. 39, 2133–2135 (1968).
  21. R. F. Aldrich, S. L. Hou, and M. L. Harvill, "Electrical and optical properties of Bi12GeO20," J. Appl. Phys. 42, 493–494 (1971).

1975

1971

R. F. Aldrich, S. L. Hou, and M. L. Harvill, "Electrical and optical properties of Bi12GeO20," J. Appl. Phys. 42, 493–494 (1971).

1970

C. W. Deutsche, "Theory of optical activity of crystalline benzil," J. Chem. Phys. 53, 1134 (1970).

1969

V. A. Kizel, Y. I. Krasilov, V. I. Burkov, V. A. Madii, and 2. M. Alikanova, "The gyrotropy of cubic crystals of uranyl compounds," Opt. Spectrosc. 27, 344–347 (1969).

1968

K. Vedam and T. A. Davis, "Pressure and temperature variation of the optical rotatory power of α-quartz," J. Opt. Soc. Am. 11, 1451–1455 (1968).

G. G. Douglas and R. N. Zitter, "Transport processes of photoinduced carriers in bismuth germanium oxide (Bi12GeO20)," J. Appl. Phys. 39, 2133–2135 (1968).

1967

S. C. Abrahams, P. B. Jamieson, and J. L. Bernstein, "Crystal structure of piezoelectric bismuth germanium oxide Bi12GeO20," J. Chem. Phys. 47, 4034–4041 (1967).

1966

V. Vysin, "Note on the theory of the rotatory dispersion of crystals," Proc. Phys. Soc. 87, 55–60 (1966).

1962

D. R. Penn, "Wave-number-dependent dielectric function of semiconductors," Phys. Rev. 128, 2093–2097 (1962).

1959

M. Moffitt and A. Moscovitz, "Optical activity in absorbing media," J. Chem. Phys. 30, 648–660 (1959).

1952

K. S. Krishnan and S. K. Roy, "The dispersion formulae and the polarization fields," Philos. Mag. 43, 1000 (1952).

1937

E. U. Condon, W. Altar, and H. Eyring, "One electron rotatory power," J. Chem. Phys. 5, 753 (1937).

1933

W. Kuhn and K. Bein, "Beschaffenheit und raumliche Ausdehnung des Streumomentes bei optisch activen Molekülen," Z. Phys. Chem. B22, 406–422 (1933).

1929

W. Kuhn, "Quantitative Verhaltnisse und Beziehungen bei der natürlichen optischen Aktivität," Z. Phys. Chem. B4, 14–36 (1929).

Abrahams, S. C.

S. C. Abrahams, P. B. Jamieson, and J. L. Bernstein, "Crystal structure of piezoelectric bismuth germanium oxide Bi12GeO20," J. Chem. Phys. 47, 4034–4041 (1967).

Agranovich, V. M.

V. M. Agranovich, "Theory of the inherent optical activity of molecular crystals, I. Classical theory," Opt. Spectrosc. 1, 338–347 (1956); "Theory of the inherent optical activity of molecular crystals, II. Quantum theory," Opt. Spectrosc. 2, 738–746 (1957).

Aldrich, R. F.

R. F. Aldrich, S. L. Hou, and M. L. Harvill, "Electrical and optical properties of Bi12GeO20," J. Appl. Phys. 42, 493–494 (1971).

Alikanova, M.

V. A. Kizel, Y. I. Krasilov, V. I. Burkov, V. A. Madii, and 2. M. Alikanova, "The gyrotropy of cubic crystals of uranyl compounds," Opt. Spectrosc. 27, 344–347 (1969).

Altar, W.

E. U. Condon, W. Altar, and H. Eyring, "One electron rotatory power," J. Chem. Phys. 5, 753 (1937).

Bein, K.

W. Kuhn and K. Bein, "Beschaffenheit und raumliche Ausdehnung des Streumomentes bei optisch activen Molekülen," Z. Phys. Chem. B22, 406–422 (1933).

Bernstein, J. L.

S. C. Abrahams, P. B. Jamieson, and J. L. Bernstein, "Crystal structure of piezoelectric bismuth germanium oxide Bi12GeO20," J. Chem. Phys. 47, 4034–4041 (1967).

Born, M.

M. Born, "Uber die naturliche optische Aktivitat von Flussigkeiten und Gasen," Phys. Zeit. 16, 251 (1915); "Elecktronentheorie das naturlichen optischen Drehungsvermogens isotroper und anisotroper Flussigkeiten," Ann. Phys. 55, 177–240 (1918); Optik (Springer, Berlin, 1933), Sec. 84.

Burkov, V. I.

V. A. Kizel, Y. I. Krasilov, V. I. Burkov, V. A. Madii, and 2. M. Alikanova, "The gyrotropy of cubic crystals of uranyl compounds," Opt. Spectrosc. 27, 344–347 (1969).

Chandrasekhar, S.

S. Chandrasekhar, "Theoretical interpretation of the optical activity of quartz," Proc. Ind. Acad. Sci. 37A, 468–484 (1953); "Optical rotatory dispersion of crystals," Proc. R. Soc. 259A, 531–533 (1961).

Condon, E. U.

E. U. Condon, W. Altar, and H. Eyring, "One electron rotatory power," J. Chem. Phys. 5, 753 (1937).

Davis, T. A.

K. Vedam and T. A. Davis, "Pressure and temperature variation of the optical rotatory power of α-quartz," J. Opt. Soc. Am. 11, 1451–1455 (1968).

Deutsche, C. W.

C. W. Deutsche, "Theory of optical activity of crystalline benzil," J. Chem. Phys. 53, 1134 (1970).

Douglas, G. G.

G. G. Douglas and R. N. Zitter, "Transport processes of photoinduced carriers in bismuth germanium oxide (Bi12GeO20)," J. Appl. Phys. 39, 2133–2135 (1968).

Drude, P.

P. Drude, Lehrbuch der Optik (Leipzig, 1900) (English translation, Dover, New York, 1959), Chap. VI.

Eyring, H.

E. U. Condon, W. Altar, and H. Eyring, "One electron rotatory power," J. Chem. Phys. 5, 753 (1937).

Harvill, M. L.

R. F. Aldrich, S. L. Hou, and M. L. Harvill, "Electrical and optical properties of Bi12GeO20," J. Appl. Phys. 42, 493–494 (1971).

Hennessey, P.

P. Hennessey and K. Vedam, "Piezo- and thermooptical properties of Bi12GeO20. I. Optical rotatory dispersion," J. Opt. Soc. Am. 65, 436–441 (1975).

K. Vedam and P. Hennessey, "Piezo- and thermooptical properties of Bi12GeO20. II. Refractive index," J. Opt. Soc. Am. 65, 442–445 (1975).

P. Hennessey, "Piezo- and thermo-optical properties of bismuth germanium oxide IV. The absorptive properties," J. Opt. Soc. Am. (to be published).

P. Hennessey, "Piezo- and Thermooptical Properties of Bismuth Germanium Oxide," Ph.D. Thesis, The Pennsylvania State University, 1972 (University Microfilms, Ann Arbor, Michigan, Order No. 72–33, 172).

Hou, S. L.

R. F. Aldrich, S. L. Hou, and M. L. Harvill, "Electrical and optical properties of Bi12GeO20," J. Appl. Phys. 42, 493–494 (1971).

Jamieson, P. B.

S. C. Abrahams, P. B. Jamieson, and J. L. Bernstein, "Crystal structure of piezoelectric bismuth germanium oxide Bi12GeO20," J. Chem. Phys. 47, 4034–4041 (1967).

Kizel, V. A.

V. A. Kizel, Y. I. Krasilov, V. I. Burkov, V. A. Madii, and 2. M. Alikanova, "The gyrotropy of cubic crystals of uranyl compounds," Opt. Spectrosc. 27, 344–347 (1969).

Krasilov, Y. I.

V. A. Kizel, Y. I. Krasilov, V. I. Burkov, V. A. Madii, and 2. M. Alikanova, "The gyrotropy of cubic crystals of uranyl compounds," Opt. Spectrosc. 27, 344–347 (1969).

Krishnan, K. S.

K. S. Krishnan and S. K. Roy, "The dispersion formulae and the polarization fields," Philos. Mag. 43, 1000 (1952).

Kuhn, W.

W. Kuhn and K. Bein, "Beschaffenheit und raumliche Ausdehnung des Streumomentes bei optisch activen Molekülen," Z. Phys. Chem. B22, 406–422 (1933).

W. Kuhn, "Quantitative Verhaltnisse und Beziehungen bei der natürlichen optischen Aktivität," Z. Phys. Chem. B4, 14–36 (1929).

Madii, V. A.

V. A. Kizel, Y. I. Krasilov, V. I. Burkov, V. A. Madii, and 2. M. Alikanova, "The gyrotropy of cubic crystals of uranyl compounds," Opt. Spectrosc. 27, 344–347 (1969).

Moffitt, M.

M. Moffitt and A. Moscovitz, "Optical activity in absorbing media," J. Chem. Phys. 30, 648–660 (1959).

Moscovitz, A.

M. Moffitt and A. Moscovitz, "Optical activity in absorbing media," J. Chem. Phys. 30, 648–660 (1959).

Penn, D. R.

D. R. Penn, "Wave-number-dependent dielectric function of semiconductors," Phys. Rev. 128, 2093–2097 (1962).

Roy, S. K.

K. S. Krishnan and S. K. Roy, "The dispersion formulae and the polarization fields," Philos. Mag. 43, 1000 (1952).

Vedam, K.

Vysin, V.

V. Vysin, "Note on the theory of the rotatory dispersion of crystals," Proc. Phys. Soc. 87, 55–60 (1966).

Zitter, R. N.

G. G. Douglas and R. N. Zitter, "Transport processes of photoinduced carriers in bismuth germanium oxide (Bi12GeO20)," J. Appl. Phys. 39, 2133–2135 (1968).

J. Appl. Phys.

G. G. Douglas and R. N. Zitter, "Transport processes of photoinduced carriers in bismuth germanium oxide (Bi12GeO20)," J. Appl. Phys. 39, 2133–2135 (1968).

R. F. Aldrich, S. L. Hou, and M. L. Harvill, "Electrical and optical properties of Bi12GeO20," J. Appl. Phys. 42, 493–494 (1971).

J. Chem. Phys.

C. W. Deutsche, "Theory of optical activity of crystalline benzil," J. Chem. Phys. 53, 1134 (1970).

E. U. Condon, W. Altar, and H. Eyring, "One electron rotatory power," J. Chem. Phys. 5, 753 (1937).

M. Moffitt and A. Moscovitz, "Optical activity in absorbing media," J. Chem. Phys. 30, 648–660 (1959).

S. C. Abrahams, P. B. Jamieson, and J. L. Bernstein, "Crystal structure of piezoelectric bismuth germanium oxide Bi12GeO20," J. Chem. Phys. 47, 4034–4041 (1967).

J. Opt. Soc. Am.

Opt. Spectrosc.

V. A. Kizel, Y. I. Krasilov, V. I. Burkov, V. A. Madii, and 2. M. Alikanova, "The gyrotropy of cubic crystals of uranyl compounds," Opt. Spectrosc. 27, 344–347 (1969).

Philos. Mag.

K. S. Krishnan and S. K. Roy, "The dispersion formulae and the polarization fields," Philos. Mag. 43, 1000 (1952).

Phys. Rev.

D. R. Penn, "Wave-number-dependent dielectric function of semiconductors," Phys. Rev. 128, 2093–2097 (1962).

Proc. Phys. Soc.

V. Vysin, "Note on the theory of the rotatory dispersion of crystals," Proc. Phys. Soc. 87, 55–60 (1966).

Z. Phys. Chem.

W. Kuhn, "Quantitative Verhaltnisse und Beziehungen bei der natürlichen optischen Aktivität," Z. Phys. Chem. B4, 14–36 (1929).

W. Kuhn and K. Bein, "Beschaffenheit und raumliche Ausdehnung des Streumomentes bei optisch activen Molekülen," Z. Phys. Chem. B22, 406–422 (1933).

Other

S. Chandrasekhar, "Theoretical interpretation of the optical activity of quartz," Proc. Ind. Acad. Sci. 37A, 468–484 (1953); "Optical rotatory dispersion of crystals," Proc. R. Soc. 259A, 531–533 (1961).

V. M. Agranovich, "Theory of the inherent optical activity of molecular crystals, I. Classical theory," Opt. Spectrosc. 1, 338–347 (1956); "Theory of the inherent optical activity of molecular crystals, II. Quantum theory," Opt. Spectrosc. 2, 738–746 (1957).

P. Hennessey, "Piezo- and Thermooptical Properties of Bismuth Germanium Oxide," Ph.D. Thesis, The Pennsylvania State University, 1972 (University Microfilms, Ann Arbor, Michigan, Order No. 72–33, 172).

P. Drude, Lehrbuch der Optik (Leipzig, 1900) (English translation, Dover, New York, 1959), Chap. VI.

M. Born, "Uber die naturliche optische Aktivitat von Flussigkeiten und Gasen," Phys. Zeit. 16, 251 (1915); "Elecktronentheorie das naturlichen optischen Drehungsvermogens isotroper und anisotroper Flussigkeiten," Ann. Phys. 55, 177–240 (1918); Optik (Springer, Berlin, 1933), Sec. 84.

P. Hennessey, "Piezo- and thermo-optical properties of bismuth germanium oxide IV. The absorptive properties," J. Opt. Soc. Am. (to be published).

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