Abstract

Since 2001 the intrinsic birefringence of fluorine has been accessible to experiment. It is known that its intrinsic anisotropy is entirely due to spatial dispersion, and that the index surface of fluorine and crystals with the same symmetry has seven optical axes, four of them intersecting this surface at pairs of conical points. I point out the fact that there is no internal conical refraction, but only simple refraction (and without walk-off), with these conical points. I also explain why the rays are not a priori normal to the index surface in the case of fluorine because of its spatial dispersion; and I discuss two particular cases of spatial dispersion where the Poynting vector remains orthogonal to the index surface.

© 2006 Optical Society of America

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References

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  1. J. D. Jackson, Classical Electrodynamics, 2nd edition (Wiley, New York, 1975): pp. 14–16.
  2. V. L. Ginzburg, “On crystal optics with spatial dispersion,” Physics reports 194, 245–251 (1990).
    [Crossref]
  3. H. A. Lorentz, Collected papers, Vol. II (Martinus Nijohff, The Hague, 1936): p. 79.
  4. V. M. Agranovich and V. L. Ginzburg, Crystal Optics with Spatial Dispersion, and Excitons, 2nd edition, Solid-State Science vol. 42 (Springer, Berlin, 1984).
  5. J. H. Burnett, Z. H. Levine, and E. L. Shirley, “Intrinsic birefringence in calcium fluoride and barium fluoride,” Phys. Rev. B 64, 241102(R) (2001).
    [Crossref]
  6. L. Dettwiller, “Observation récente d’une forme de biréfringence dans certains cristaux à symétrie cubique: théorie et conséquences pratiques,” Bull. Un. Prof. Phys. Chim. 99 (2), 77–103 (2005).
  7. J. H. Burnett, Z. H. Levine, E. L. Shirley, and J. H. Bruning, “Symmetry of spatial-dispersion-induced birefringence and its implications for CaF2 ultraviolet optics,” J. Microlith., Microfab., Microsyst. 1, 213–224 (2002).
    [Crossref]
  8. M. Born and E. Wolf, Principles of optics - Electromagnetic theory of propagation interference and diffraction of light (Pergamon, Oxford, 1980): p. 668.
  9. G. Bruhat, Cours de physique générale - Optique (Masson, Paris, 1992): pp. 462–463.
  10. see for example L. Landau and E. Lifchitz, Physique théorique - tome 8 - Électrodynamique des milieux continus (Mir, Moscou, 1969).
  11. L. Dettwiller, “Propagation de la lumière, dispersion et absorption”, in EGEM, Optique géométrique et propagation, J.-L. MEYZONNETTE ed. (Hermès Lavoisier, Paris, 2003): pp. 63–64.
  12. L. Dettwiller, “Propriétés inédites de la biréfringence des cristaux à symétrie cubique du type de la fluorine,” presented at Horizons de l’Optique 2005, Chambéry, France, 8-10 Nov. 2005

2005 (1)

L. Dettwiller, “Observation récente d’une forme de biréfringence dans certains cristaux à symétrie cubique: théorie et conséquences pratiques,” Bull. Un. Prof. Phys. Chim. 99 (2), 77–103 (2005).

2002 (1)

J. H. Burnett, Z. H. Levine, E. L. Shirley, and J. H. Bruning, “Symmetry of spatial-dispersion-induced birefringence and its implications for CaF2 ultraviolet optics,” J. Microlith., Microfab., Microsyst. 1, 213–224 (2002).
[Crossref]

2001 (1)

J. H. Burnett, Z. H. Levine, and E. L. Shirley, “Intrinsic birefringence in calcium fluoride and barium fluoride,” Phys. Rev. B 64, 241102(R) (2001).
[Crossref]

1990 (1)

V. L. Ginzburg, “On crystal optics with spatial dispersion,” Physics reports 194, 245–251 (1990).
[Crossref]

Agranovich, V. M.

V. M. Agranovich and V. L. Ginzburg, Crystal Optics with Spatial Dispersion, and Excitons, 2nd edition, Solid-State Science vol. 42 (Springer, Berlin, 1984).

Born, M.

M. Born and E. Wolf, Principles of optics - Electromagnetic theory of propagation interference and diffraction of light (Pergamon, Oxford, 1980): p. 668.

Bruhat, G.

G. Bruhat, Cours de physique générale - Optique (Masson, Paris, 1992): pp. 462–463.

Bruning, J. H.

J. H. Burnett, Z. H. Levine, E. L. Shirley, and J. H. Bruning, “Symmetry of spatial-dispersion-induced birefringence and its implications for CaF2 ultraviolet optics,” J. Microlith., Microfab., Microsyst. 1, 213–224 (2002).
[Crossref]

Burnett, J. H.

J. H. Burnett, Z. H. Levine, E. L. Shirley, and J. H. Bruning, “Symmetry of spatial-dispersion-induced birefringence and its implications for CaF2 ultraviolet optics,” J. Microlith., Microfab., Microsyst. 1, 213–224 (2002).
[Crossref]

J. H. Burnett, Z. H. Levine, and E. L. Shirley, “Intrinsic birefringence in calcium fluoride and barium fluoride,” Phys. Rev. B 64, 241102(R) (2001).
[Crossref]

Dettwiller, L.

L. Dettwiller, “Observation récente d’une forme de biréfringence dans certains cristaux à symétrie cubique: théorie et conséquences pratiques,” Bull. Un. Prof. Phys. Chim. 99 (2), 77–103 (2005).

L. Dettwiller, “Propagation de la lumière, dispersion et absorption”, in EGEM, Optique géométrique et propagation, J.-L. MEYZONNETTE ed. (Hermès Lavoisier, Paris, 2003): pp. 63–64.

L. Dettwiller, “Propriétés inédites de la biréfringence des cristaux à symétrie cubique du type de la fluorine,” presented at Horizons de l’Optique 2005, Chambéry, France, 8-10 Nov. 2005

Ginzburg, V. L.

V. L. Ginzburg, “On crystal optics with spatial dispersion,” Physics reports 194, 245–251 (1990).
[Crossref]

V. M. Agranovich and V. L. Ginzburg, Crystal Optics with Spatial Dispersion, and Excitons, 2nd edition, Solid-State Science vol. 42 (Springer, Berlin, 1984).

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 2nd edition (Wiley, New York, 1975): pp. 14–16.

Landau, L.

see for example L. Landau and E. Lifchitz, Physique théorique - tome 8 - Électrodynamique des milieux continus (Mir, Moscou, 1969).

Levine, Z. H.

J. H. Burnett, Z. H. Levine, E. L. Shirley, and J. H. Bruning, “Symmetry of spatial-dispersion-induced birefringence and its implications for CaF2 ultraviolet optics,” J. Microlith., Microfab., Microsyst. 1, 213–224 (2002).
[Crossref]

J. H. Burnett, Z. H. Levine, and E. L. Shirley, “Intrinsic birefringence in calcium fluoride and barium fluoride,” Phys. Rev. B 64, 241102(R) (2001).
[Crossref]

Lifchitz, E.

see for example L. Landau and E. Lifchitz, Physique théorique - tome 8 - Électrodynamique des milieux continus (Mir, Moscou, 1969).

Lorentz, H. A.

H. A. Lorentz, Collected papers, Vol. II (Martinus Nijohff, The Hague, 1936): p. 79.

Shirley, E. L.

J. H. Burnett, Z. H. Levine, E. L. Shirley, and J. H. Bruning, “Symmetry of spatial-dispersion-induced birefringence and its implications for CaF2 ultraviolet optics,” J. Microlith., Microfab., Microsyst. 1, 213–224 (2002).
[Crossref]

J. H. Burnett, Z. H. Levine, and E. L. Shirley, “Intrinsic birefringence in calcium fluoride and barium fluoride,” Phys. Rev. B 64, 241102(R) (2001).
[Crossref]

Wolf, E.

M. Born and E. Wolf, Principles of optics - Electromagnetic theory of propagation interference and diffraction of light (Pergamon, Oxford, 1980): p. 668.

Bull. Un. Prof. Phys. Chim. (1)

L. Dettwiller, “Observation récente d’une forme de biréfringence dans certains cristaux à symétrie cubique: théorie et conséquences pratiques,” Bull. Un. Prof. Phys. Chim. 99 (2), 77–103 (2005).

J. Microlith., Microfab., Microsyst. (1)

J. H. Burnett, Z. H. Levine, E. L. Shirley, and J. H. Bruning, “Symmetry of spatial-dispersion-induced birefringence and its implications for CaF2 ultraviolet optics,” J. Microlith., Microfab., Microsyst. 1, 213–224 (2002).
[Crossref]

Phys. Rev. B (1)

J. H. Burnett, Z. H. Levine, and E. L. Shirley, “Intrinsic birefringence in calcium fluoride and barium fluoride,” Phys. Rev. B 64, 241102(R) (2001).
[Crossref]

Physics reports (1)

V. L. Ginzburg, “On crystal optics with spatial dispersion,” Physics reports 194, 245–251 (1990).
[Crossref]

Other (8)

H. A. Lorentz, Collected papers, Vol. II (Martinus Nijohff, The Hague, 1936): p. 79.

V. M. Agranovich and V. L. Ginzburg, Crystal Optics with Spatial Dispersion, and Excitons, 2nd edition, Solid-State Science vol. 42 (Springer, Berlin, 1984).

J. D. Jackson, Classical Electrodynamics, 2nd edition (Wiley, New York, 1975): pp. 14–16.

M. Born and E. Wolf, Principles of optics - Electromagnetic theory of propagation interference and diffraction of light (Pergamon, Oxford, 1980): p. 668.

G. Bruhat, Cours de physique générale - Optique (Masson, Paris, 1992): pp. 462–463.

see for example L. Landau and E. Lifchitz, Physique théorique - tome 8 - Électrodynamique des milieux continus (Mir, Moscou, 1969).

L. Dettwiller, “Propagation de la lumière, dispersion et absorption”, in EGEM, Optique géométrique et propagation, J.-L. MEYZONNETTE ed. (Hermès Lavoisier, Paris, 2003): pp. 63–64.

L. Dettwiller, “Propriétés inédites de la biréfringence des cristaux à symétrie cubique du type de la fluorine,” presented at Horizons de l’Optique 2005, Chambéry, France, 8-10 Nov. 2005

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Equations (22)

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ε j l ( ω , q ) ε 0 = n 0 2 ( ω ) δ j l − α ( ω ) q j q l − [ β ( ω ) q 2 + γ ( ω ) q j q l ] δ j l
n i ≡ n 0 ( 1 + β q 0 2 ) − 1 2
q × ( q × E ) = q 0 2 ( ε r ) E
ε j l ( ω , q ) ε 0 = [ n 0 2 − ( β + γ 3 ) q 2 ] δ j l − α q j q l .
n [ 1 1 ¯ 0 ] = n [ 11 2 ¯ ] = n 0 [ 1 + ( β + γ 3 ) q 0 2 ] − 1 2
ω μ H ¯ = q × E ¯
− ω ( ε ) E ¯ = q × H ¯
ω μ d H ¯ = d q × E ¯ + q × d E ¯
− ω [ ( d ε ) E ¯ + ( ε ) d E ¯ ] = d q × H ¯ + q × d H ¯ ;
ω [ H ¯ * . μ d H ¯ + E ¯ * . ( d ε ) E ¯ + E ¯ * . ( ε ) d E ¯ ] = ( d q × E ¯ ) . H ¯ * + ( q × d E ¯ ) . H ¯ * − ( d q × H ¯ ) . E ¯ * − ( q × d H ¯ ) . E ¯ *
( d q × E ¯ ) . H ¯ * − ( d q × H ¯ ) . E ¯ * = d q . ( E ¯ × H ¯ * + E ¯ * × H ¯ ) = d q . 4 〈 R 〉
d H ¯ . ( ω μ H ¯ ) * = d H ¯ . ( q × E ¯ * ) = − ( q × d H ¯ ) . E ¯ *
ω [ E ¯ * . ( d ε ) E ¯ + E ¯ * . ( ε ) d E ¯ ] = − ( q × H ¯ * ) d E ¯ + d q . 4 〈 R 〉 .
ω E ¯ * . ( d ε ) E ¯ − d q . 4 〈 R 〉 = ω [ d E ¯ . ( ε ) * E ¯ * − E ¯ * . ( ε ) d E ¯ ]
= ω [ E ¯ * . ( ε ) + d E ¯ − E ¯ * . ( ε ) d E ¯ ]
= − 2 ω E ¯ * . ( ε ) ah d E ¯
4 〈 R 〉 . d q = ω E ¯ * . ( d ε ) E ¯ .
ε j l ( ω , q ) ε 0 = n 0 2 ( ω ) δ j l + ∑ m = 1 3 p ( ω ) ε j lm i q m
E ¯ * . ( d ε ) E ¯ = E ¯ * . ( − i p d q × E ¯ ) = − i p ( E ¯ × E ¯ * ) . d q
4 〈 R 〉 . d q = ω E ¯ * . ( d ε ) E ¯ = 0
( d ε j l ) ε 0 = − α ( q j d q l + q l d q j ) − 2 β q . d q δ j l
4 〈 R 〉 . d q = − ω ε 0 { α [ ( E ¯ * . q ) ( E ¯ . d q ) + ( E ¯ * . d q ) ( E ¯ . q ) ] + 2 β ( q . d q ) ( E ¯ * . E ¯ ) } = 0

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