Abstract

We generalize earlier work on intrinsic and form birefringence for random distributions of aligned ellipsoids by taking the minimum separation of particle centers (the exclusion-correlation surface) as nonsimilar to the particle’s surface. For such cases, the bulk parameters involve a compound depolarization factor consisting of two distinct terms, one corresponding to particle shape (<i>S</i>) effects, and the other to configurational-correlation (<i>C</i>) effects. The associated bipolarization and birefraction expressions show form (<i>F</i>) effects in which <i>S</i> and <i>C</i> may either compete (and even cancel) or else reinforce. If they compete (e.g., for coaxial spheroidal particle and exclusion surfaces, both prolate or both oblate) then the <i>F</i> effects are less than the <i>S</i>; if they reinforce (coaxial spheroids, one prolate and one oblate) then the <i>F</i> effects are greater than the <i>S</i>. We show how the earlier explicit results for similar <i>C</i> and <i>S</i> can be generalized by inspection, and illustrate the procedure for key forms.

© 1979 Optical Society of America

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  1. V. Twersky, "Form and intrinsic birefringence," J. Opt. Soc. Am. 65, 239–245 (1975).
  2. J. C. Maxwell, A Treatise on Electricity and Magnetism, (Cambridge University, Cambridge, 1873); (Dover, New York, 1954).
  3. Lord Rayleigh, "On the influence of obstacles arranged in rectangular order upon the properties of a medium," Philos. Mag. 34,481–501 (1892).
  4. O. Weiner, "Die theorie des mischkörpers für das feld der stationären strömung," Sachsische Akad. Wiss. 32, 507–591 (1912).
  5. W. F. Brown, Jr., "Dielectrics," in Handbuch der Physik, Vol. 17, (Springer, Berlin, 1956), pp. 1–154.
  6. V. Twersky, "Coherent scalar field in pair-correlated random distributions of aligned scatterers," J. Math. Phys. 18, 2468–2486 (1977); "Coherent electromagnetic waves in pair-correlated distributions of aligned scatterers," J. Math. Phys. 19, 215–230 (1978).
  7. H. Reiss, H. L. Frisch, and J. L. Lebowitz, "Statistical mechanics of rigid spheres," J. Chem. Phys. 31, 369–380 (1959).
  8. V. Twersky, "Transparency of pair-correlated random distributions of small scatterers with applications to the cornea," J. Opt. Soc. Am. 65, 524–530 (1975).
  9. W. O. Smith, P. D. Foote, and P. F. Busang, "Packing of homogeneous spheres," Phys. Rev. 34, 1271–1298 (1929); G. D. Scott, "Packing of spheres," Nature 187, 908–909 (1960); J. D. Bernal and J. Mason, "Coordination of randomly packed spheres," Nature 187, 910–911 (1960); S. W. Hawley, T. H. Kays, and V. Twersky, "Comparison of distribution functions from scattering data on different sets of spheres," IEEE Trans. AP-15, 118–135 (1967).
  10. V. Twersky, "Constraint on the compound depolarization factor of aligned ellipsoids," J. Math. Phys. 19, 2576–2578 (1978).
  11. E. C. Stoner, "The demagnetizing factors for ellipsoids," Philos. Mag. 36, 803–821 (1945); J. A. Osborn, "Demagnetizing factors of the general ellipsoid," Phys. Rev. 67, 351–357 (1945).

1978

V. Twersky, "Constraint on the compound depolarization factor of aligned ellipsoids," J. Math. Phys. 19, 2576–2578 (1978).

1975

1959

H. Reiss, H. L. Frisch, and J. L. Lebowitz, "Statistical mechanics of rigid spheres," J. Chem. Phys. 31, 369–380 (1959).

1945

E. C. Stoner, "The demagnetizing factors for ellipsoids," Philos. Mag. 36, 803–821 (1945); J. A. Osborn, "Demagnetizing factors of the general ellipsoid," Phys. Rev. 67, 351–357 (1945).

1929

W. O. Smith, P. D. Foote, and P. F. Busang, "Packing of homogeneous spheres," Phys. Rev. 34, 1271–1298 (1929); G. D. Scott, "Packing of spheres," Nature 187, 908–909 (1960); J. D. Bernal and J. Mason, "Coordination of randomly packed spheres," Nature 187, 910–911 (1960); S. W. Hawley, T. H. Kays, and V. Twersky, "Comparison of distribution functions from scattering data on different sets of spheres," IEEE Trans. AP-15, 118–135 (1967).

1912

O. Weiner, "Die theorie des mischkörpers für das feld der stationären strömung," Sachsische Akad. Wiss. 32, 507–591 (1912).

1892

Lord Rayleigh, "On the influence of obstacles arranged in rectangular order upon the properties of a medium," Philos. Mag. 34,481–501 (1892).

Brown, Jr., W. F.

W. F. Brown, Jr., "Dielectrics," in Handbuch der Physik, Vol. 17, (Springer, Berlin, 1956), pp. 1–154.

Busang, P. F.

W. O. Smith, P. D. Foote, and P. F. Busang, "Packing of homogeneous spheres," Phys. Rev. 34, 1271–1298 (1929); G. D. Scott, "Packing of spheres," Nature 187, 908–909 (1960); J. D. Bernal and J. Mason, "Coordination of randomly packed spheres," Nature 187, 910–911 (1960); S. W. Hawley, T. H. Kays, and V. Twersky, "Comparison of distribution functions from scattering data on different sets of spheres," IEEE Trans. AP-15, 118–135 (1967).

Foote, P. D.

W. O. Smith, P. D. Foote, and P. F. Busang, "Packing of homogeneous spheres," Phys. Rev. 34, 1271–1298 (1929); G. D. Scott, "Packing of spheres," Nature 187, 908–909 (1960); J. D. Bernal and J. Mason, "Coordination of randomly packed spheres," Nature 187, 910–911 (1960); S. W. Hawley, T. H. Kays, and V. Twersky, "Comparison of distribution functions from scattering data on different sets of spheres," IEEE Trans. AP-15, 118–135 (1967).

Frisch, H. L.

H. Reiss, H. L. Frisch, and J. L. Lebowitz, "Statistical mechanics of rigid spheres," J. Chem. Phys. 31, 369–380 (1959).

Lebowitz, J. L.

H. Reiss, H. L. Frisch, and J. L. Lebowitz, "Statistical mechanics of rigid spheres," J. Chem. Phys. 31, 369–380 (1959).

Maxwell, J. C.

J. C. Maxwell, A Treatise on Electricity and Magnetism, (Cambridge University, Cambridge, 1873); (Dover, New York, 1954).

Rayleigh, Lord

Lord Rayleigh, "On the influence of obstacles arranged in rectangular order upon the properties of a medium," Philos. Mag. 34,481–501 (1892).

Reiss, H.

H. Reiss, H. L. Frisch, and J. L. Lebowitz, "Statistical mechanics of rigid spheres," J. Chem. Phys. 31, 369–380 (1959).

Smith, W. O.

W. O. Smith, P. D. Foote, and P. F. Busang, "Packing of homogeneous spheres," Phys. Rev. 34, 1271–1298 (1929); G. D. Scott, "Packing of spheres," Nature 187, 908–909 (1960); J. D. Bernal and J. Mason, "Coordination of randomly packed spheres," Nature 187, 910–911 (1960); S. W. Hawley, T. H. Kays, and V. Twersky, "Comparison of distribution functions from scattering data on different sets of spheres," IEEE Trans. AP-15, 118–135 (1967).

Stoner, E. C.

E. C. Stoner, "The demagnetizing factors for ellipsoids," Philos. Mag. 36, 803–821 (1945); J. A. Osborn, "Demagnetizing factors of the general ellipsoid," Phys. Rev. 67, 351–357 (1945).

Twersky, V.

V. Twersky, "Constraint on the compound depolarization factor of aligned ellipsoids," J. Math. Phys. 19, 2576–2578 (1978).

V. Twersky, "Form and intrinsic birefringence," J. Opt. Soc. Am. 65, 239–245 (1975).

V. Twersky, "Transparency of pair-correlated random distributions of small scatterers with applications to the cornea," J. Opt. Soc. Am. 65, 524–530 (1975).

V. Twersky, "Coherent scalar field in pair-correlated random distributions of aligned scatterers," J. Math. Phys. 18, 2468–2486 (1977); "Coherent electromagnetic waves in pair-correlated distributions of aligned scatterers," J. Math. Phys. 19, 215–230 (1978).

Weiner, O.

O. Weiner, "Die theorie des mischkörpers für das feld der stationären strömung," Sachsische Akad. Wiss. 32, 507–591 (1912).

J. Chem. Phys.

H. Reiss, H. L. Frisch, and J. L. Lebowitz, "Statistical mechanics of rigid spheres," J. Chem. Phys. 31, 369–380 (1959).

J. Math. Phys.

V. Twersky, "Constraint on the compound depolarization factor of aligned ellipsoids," J. Math. Phys. 19, 2576–2578 (1978).

J. Opt. Soc. Am.

Philos. Mag.

Lord Rayleigh, "On the influence of obstacles arranged in rectangular order upon the properties of a medium," Philos. Mag. 34,481–501 (1892).

E. C. Stoner, "The demagnetizing factors for ellipsoids," Philos. Mag. 36, 803–821 (1945); J. A. Osborn, "Demagnetizing factors of the general ellipsoid," Phys. Rev. 67, 351–357 (1945).

Phys. Rev.

W. O. Smith, P. D. Foote, and P. F. Busang, "Packing of homogeneous spheres," Phys. Rev. 34, 1271–1298 (1929); G. D. Scott, "Packing of spheres," Nature 187, 908–909 (1960); J. D. Bernal and J. Mason, "Coordination of randomly packed spheres," Nature 187, 910–911 (1960); S. W. Hawley, T. H. Kays, and V. Twersky, "Comparison of distribution functions from scattering data on different sets of spheres," IEEE Trans. AP-15, 118–135 (1967).

Sachsische Akad. Wiss.

O. Weiner, "Die theorie des mischkörpers für das feld der stationären strömung," Sachsische Akad. Wiss. 32, 507–591 (1912).

Other

W. F. Brown, Jr., "Dielectrics," in Handbuch der Physik, Vol. 17, (Springer, Berlin, 1956), pp. 1–154.

V. Twersky, "Coherent scalar field in pair-correlated random distributions of aligned scatterers," J. Math. Phys. 18, 2468–2486 (1977); "Coherent electromagnetic waves in pair-correlated distributions of aligned scatterers," J. Math. Phys. 19, 215–230 (1978).

J. C. Maxwell, A Treatise on Electricity and Magnetism, (Cambridge University, Cambridge, 1873); (Dover, New York, 1954).

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