Abstract

There are two parameters in the one-term Sellmeier formula for refractive index. Two different ways are proposed to express them in terms of the number of electrons, the dielectric constant, and the first excitation energy of the molecule. In the normal-dispersion region, one construction will make the formula an upper bound and the other, a lower bound. Furthermore, if a measured value at a particular frequency is used for the determination of the parameters, then the Sellmeier formula is an upper bound for frequencies below that reference frequency and a lower bound for frequencies above it. The various bounding properties are illustrated for the case of atomic hydrogen.

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  1. H. A. Lorentz, Theory of Electrons, 2nd ed. (Dover, New York, 1952), pp. 137 and 305.
  2. H. A. Kramers and W. Heisenberg, Physik 31, 681 (1925). See also, J. C. Slater, Quantum Theory of Atomic Structure, Vol. I, (McGraw-Hill, New York, 1960), p. 154.
  3. W. Sellmeier, Pogg. Ann. Physik 143, 271 (1871); 145, 399, 520 (1872); 147, 386, 525 (1872).
  4. See, for example, S. A. Korff and G. Breit, Rev. Mod. Phys. 4, 471 (1932).
  5. C. R. Mansfield and E. R. Peck, J. Opt. Soc. Am. 59, 199 (1969).
  6. See, for example, J. M. Stone, Radiation and Optics (McGraw-Hill, New York, 1963), p. 377.
  7. A. Maryott and F. Burkley, Tables of Dielectric and Electric Dipole Moments of Substances in the Gaseous State, Natl. Bur. Std. (U. S.) Circ. 537 (U. S. Government Printing Office, Washington, D. C., 1953).
  8. K. T. Tang, Phys. Rev. Letters 23, 1271 (1969).
  9. W. Kuhn, Z. Physik 33, 408 (1925); W. Thomas, Naturwiss. 13, 627 (1925); F. Reiche and W. Thomas, Z. Physik 34, 510 (1925).
  10. K. T. Tang, Phys. Rev. 177, 108 (1969).
  11. M. Karplus and H. J. Kolker, J. Chem. Phys. 39, 1493 (1963).

1969 (3)

C. R. Mansfield and E. R. Peck, J. Opt. Soc. Am. 59, 199 (1969).

K. T. Tang, Phys. Rev. Letters 23, 1271 (1969).

K. T. Tang, Phys. Rev. 177, 108 (1969).

1963 (1)

M. Karplus and H. J. Kolker, J. Chem. Phys. 39, 1493 (1963).

1932 (1)

See, for example, S. A. Korff and G. Breit, Rev. Mod. Phys. 4, 471 (1932).

1925 (2)

W. Kuhn, Z. Physik 33, 408 (1925); W. Thomas, Naturwiss. 13, 627 (1925); F. Reiche and W. Thomas, Z. Physik 34, 510 (1925).

H. A. Kramers and W. Heisenberg, Physik 31, 681 (1925). See also, J. C. Slater, Quantum Theory of Atomic Structure, Vol. I, (McGraw-Hill, New York, 1960), p. 154.

1871 (1)

W. Sellmeier, Pogg. Ann. Physik 143, 271 (1871); 145, 399, 520 (1872); 147, 386, 525 (1872).

Breit, G.

See, for example, S. A. Korff and G. Breit, Rev. Mod. Phys. 4, 471 (1932).

Burkley, F.

A. Maryott and F. Burkley, Tables of Dielectric and Electric Dipole Moments of Substances in the Gaseous State, Natl. Bur. Std. (U. S.) Circ. 537 (U. S. Government Printing Office, Washington, D. C., 1953).

Heisenberg, W.

H. A. Kramers and W. Heisenberg, Physik 31, 681 (1925). See also, J. C. Slater, Quantum Theory of Atomic Structure, Vol. I, (McGraw-Hill, New York, 1960), p. 154.

Karplus, M.

M. Karplus and H. J. Kolker, J. Chem. Phys. 39, 1493 (1963).

Kolker, H. J.

M. Karplus and H. J. Kolker, J. Chem. Phys. 39, 1493 (1963).

Korff, S. A.

See, for example, S. A. Korff and G. Breit, Rev. Mod. Phys. 4, 471 (1932).

Kramers, H. A.

H. A. Kramers and W. Heisenberg, Physik 31, 681 (1925). See also, J. C. Slater, Quantum Theory of Atomic Structure, Vol. I, (McGraw-Hill, New York, 1960), p. 154.

Kuhn, W.

W. Kuhn, Z. Physik 33, 408 (1925); W. Thomas, Naturwiss. 13, 627 (1925); F. Reiche and W. Thomas, Z. Physik 34, 510 (1925).

Lorentz, H. A.

H. A. Lorentz, Theory of Electrons, 2nd ed. (Dover, New York, 1952), pp. 137 and 305.

Mansfield, C. R.

C. R. Mansfield and E. R. Peck, J. Opt. Soc. Am. 59, 199 (1969).

Maryott, A.

A. Maryott and F. Burkley, Tables of Dielectric and Electric Dipole Moments of Substances in the Gaseous State, Natl. Bur. Std. (U. S.) Circ. 537 (U. S. Government Printing Office, Washington, D. C., 1953).

Peck, E. R.

C. R. Mansfield and E. R. Peck, J. Opt. Soc. Am. 59, 199 (1969).

Sellmeier, W.

W. Sellmeier, Pogg. Ann. Physik 143, 271 (1871); 145, 399, 520 (1872); 147, 386, 525 (1872).

Stone, J. M.

See, for example, J. M. Stone, Radiation and Optics (McGraw-Hill, New York, 1963), p. 377.

Tang, K. T.

K. T. Tang, Phys. Rev. Letters 23, 1271 (1969).

K. T. Tang, Phys. Rev. 177, 108 (1969).

Other (11)

H. A. Lorentz, Theory of Electrons, 2nd ed. (Dover, New York, 1952), pp. 137 and 305.

H. A. Kramers and W. Heisenberg, Physik 31, 681 (1925). See also, J. C. Slater, Quantum Theory of Atomic Structure, Vol. I, (McGraw-Hill, New York, 1960), p. 154.

W. Sellmeier, Pogg. Ann. Physik 143, 271 (1871); 145, 399, 520 (1872); 147, 386, 525 (1872).

See, for example, S. A. Korff and G. Breit, Rev. Mod. Phys. 4, 471 (1932).

C. R. Mansfield and E. R. Peck, J. Opt. Soc. Am. 59, 199 (1969).

See, for example, J. M. Stone, Radiation and Optics (McGraw-Hill, New York, 1963), p. 377.

A. Maryott and F. Burkley, Tables of Dielectric and Electric Dipole Moments of Substances in the Gaseous State, Natl. Bur. Std. (U. S.) Circ. 537 (U. S. Government Printing Office, Washington, D. C., 1953).

K. T. Tang, Phys. Rev. Letters 23, 1271 (1969).

W. Kuhn, Z. Physik 33, 408 (1925); W. Thomas, Naturwiss. 13, 627 (1925); F. Reiche and W. Thomas, Z. Physik 34, 510 (1925).

K. T. Tang, Phys. Rev. 177, 108 (1969).

M. Karplus and H. J. Kolker, J. Chem. Phys. 39, 1493 (1963).

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