Abstract

The spreading of a three-dimensional quasi-monochromatic progressive directional wave packet (such as a laser pulse) propagating freely in a linear and transparent birefringent medium is described geometrically by means of the ellipsoid representative of the pulse’s second-order moments. The medium is characterized by a second-order expansion of its dispersion relation ω(K) about the mean wave vector Km of the pulse, i.e., by its Hessian matrix (HKmω), which plays two important roles. Then, for some elements of (HKmω), practical expressions are provided that are related to the curvature and dispersion properties of the normal surface of the medium. Then cases in which these properties determine completely the asymptotic transverse or axial spreadings of the wave packet are specified, and the results of an experiment are discussed.

© 2004 Optical Society of America

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References

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  1. J. E. Rothenberg, E. Joshua, “Complete all-optical switching of visible picosecond pulses in birefringent fiber,” Opt. Lett. 18, 796–798 (1993).
    [CrossRef] [PubMed]
  2. M. Trippenbach, Y. B. Band, “Propagation of light pulses in nonisotropic media,” J. Opt. Soc. Am. B 13, 1403–1411 (1996).
    [CrossRef]
  3. R. Petit, Ondes électromagnétiques en radioélectricité et en optique (Masson, Paris, 1988).
  4. C. Radzewicz, J. S. Krasinsky, M. J. la Grone, M. Trippenbach, Y. B. Band, “Interferometric measurement of femtosecond wavepacket tilting in rutile crystals,” J. Opt. Soc. Am. B 14, 420–424 (1997).
    [CrossRef]
  5. L. Dettwiller, “Asymptotic evolution of a three-dimensional wave packet propagating in a linear dispersive medium,” Eur. J. Phys. 23, 35–44 (2002).
    [CrossRef]
  6. L. Dettwiller, “Propagation de la lumière, dispersion, et absorption,” in EGEM—Optique géométrique et propagation, J.-L. Meyzonnette, ed. (Hermès Lavoisier, Paris, 2003), Chap. 1.
  7. M. Born, E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 6th ed. (Pergamon, Oxford, 1980).
  8. A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), pp. 79–82.
  9. M. Miyagi, S. Nishida, “Pulse spreading in a single-mode fiber due to third-order dispersion,” Appl. Opt. 18, 678–682 (1979).
    [CrossRef] [PubMed]
  10. M. Miyagi, S. Nishida, “Pulse spreading in a single-mode optical fiber due to third-order dispersion: effect of optical source bandwidth,” Appl. Opt. 18, 2237–2240 (1979).
    [CrossRef] [PubMed]
  11. S. A. Akhmanov, A. P. Sukhorukov, S. A. Chirkin, “Stationary phenomena and space-time analogy in non-linear optics,” Sov. Phys. JETP 28, 748–757 (1969).
  12. E. B. Treacy, “Optical pulse compression with diffraction gratings,” IEEE J. Quantum Electron. QE-5, 454–458 (1969).
    [CrossRef]
  13. G. Bruhat, Cours de physique générale Optique (Masson, Paris, 1992).
  14. A. Gray, Modern Differential Geometry of Curves and Surfaces (CRC, Boca Raton, Fla., 1993).
  15. A. J. Schell, N. Bloembergen, “Laser studies of internal conical diffraction. I. Quantitative comparison of experimental and theoretical intensity distribution in aragonite,” J. Opt. Soc. Am. 68, 1093–1098 (1978).
    [CrossRef]
  16. A. J. Schell, N. Bloembergen, “Laser studies of internal conical diffraction. II. Intensity patterns in an optically active crystal, α-iodic acid,” J. Opt. Soc. Am. 68, 1098–1106 (1978).
    [CrossRef]
  17. W. J. Tropf, M. E. Thomas, T. J. Harris, “Properties of crystals and glasses,” in Handbook of Optics, Vol. 2, M. Bass, ed. (McGraw-Hill, New York, 1995). Gives (pp. 33.61–33. 67) dispersion formulas for a hundred crystals at room temperature (and for rutile the Sellmeier relations no2≅5.913+0.2441 μm2λ02-0.0803 μm2,ne2≅7.197+0.3322 μm2λ02-0.0843 μm2 from 0.43 to 1.5 µm); it gives again the refractive indices of calcite from 0.198 to 3.324 µm, p. 33.70.
  18. See, for example, C. Doss-Bachelet, J.-P. Françoise, C. Piquet, Géométrie différentielle (Ellipses, Paris, 2000), p. 37.
  19. See, for example, E. W. Weisstein, CRC Concise Encyclopedia of Mathematics, 2nd ed. (Chapman & Hall/CRC, Boca Raton, Fla., 2003), p. 869.
  20. J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, Physik Daten (Fachinformationszentrum, Karlsruhe, Germany, 1981).
  21. E. D. Palik, Handbook of Optical Constants of Solids (Academic, Boston, Mass., 1985), Vol. 1, and 1991 Vol. 2.
  22. Landolt-Börnstein Numerical Data and Functional Relationships in Science and Technology (Springer, Berlin, 1985), Vol. 15b.
  23. J. M. Bennett, “Polarizers,” in Handbook of Optics, Vol. 2, M. Bass, ed. (McGraw-Hill, New York, 1995). Gives (pp. 3.5–3.6) the refractive indices and the absorption coefficients of calcite from 0.1318 to 3.4 µm.
  24. F. J. Micheli, “Ueber den Einfluss der Temperatur auf die Dispersion ultravioletter Strahlen in Flussspat, Steinsalz, Quarz und Kalkspat,” Ann. Phys. 7, 772–789 (1902). Gives the temperature coefficients of the ordinary and extraordinary indices of quartz and calcite at approximately 20 wavelengths from 211 to 643 nm.
    [CrossRef]
  25. K. Kato, E. Takaoka, “Sellmeier and thermo-optic dispersion formulas for KTP,” Appl. Opt. 41, 5040–5044 (2002).
    [CrossRef] [PubMed]
  26. J. A. Ratcliffe, Magneto-Ionic Theory and Its Applications (Cambridge U. Press, Cambridge, UK, 1959).
  27. K. G. Budden, Radio Waves in The Ionosphere (Cambridge U. Press, Cambridge, UK, 1961).

2002 (2)

L. Dettwiller, “Asymptotic evolution of a three-dimensional wave packet propagating in a linear dispersive medium,” Eur. J. Phys. 23, 35–44 (2002).
[CrossRef]

K. Kato, E. Takaoka, “Sellmeier and thermo-optic dispersion formulas for KTP,” Appl. Opt. 41, 5040–5044 (2002).
[CrossRef] [PubMed]

1997 (1)

1996 (1)

1993 (1)

1979 (2)

1978 (2)

1969 (2)

S. A. Akhmanov, A. P. Sukhorukov, S. A. Chirkin, “Stationary phenomena and space-time analogy in non-linear optics,” Sov. Phys. JETP 28, 748–757 (1969).

E. B. Treacy, “Optical pulse compression with diffraction gratings,” IEEE J. Quantum Electron. QE-5, 454–458 (1969).
[CrossRef]

1902 (1)

F. J. Micheli, “Ueber den Einfluss der Temperatur auf die Dispersion ultravioletter Strahlen in Flussspat, Steinsalz, Quarz und Kalkspat,” Ann. Phys. 7, 772–789 (1902). Gives the temperature coefficients of the ordinary and extraordinary indices of quartz and calcite at approximately 20 wavelengths from 211 to 643 nm.
[CrossRef]

Akhmanov, S. A.

S. A. Akhmanov, A. P. Sukhorukov, S. A. Chirkin, “Stationary phenomena and space-time analogy in non-linear optics,” Sov. Phys. JETP 28, 748–757 (1969).

Band, Y. B.

Bennett, J. M.

J. M. Bennett, “Polarizers,” in Handbook of Optics, Vol. 2, M. Bass, ed. (McGraw-Hill, New York, 1995). Gives (pp. 3.5–3.6) the refractive indices and the absorption coefficients of calcite from 0.1318 to 3.4 µm.

Bloembergen, N.

Born, M.

M. Born, E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 6th ed. (Pergamon, Oxford, 1980).

Bruhat, G.

G. Bruhat, Cours de physique générale Optique (Masson, Paris, 1992).

Budden, K. G.

K. G. Budden, Radio Waves in The Ionosphere (Cambridge U. Press, Cambridge, UK, 1961).

Chirkin, S. A.

S. A. Akhmanov, A. P. Sukhorukov, S. A. Chirkin, “Stationary phenomena and space-time analogy in non-linear optics,” Sov. Phys. JETP 28, 748–757 (1969).

Dettwiller, L.

L. Dettwiller, “Asymptotic evolution of a three-dimensional wave packet propagating in a linear dispersive medium,” Eur. J. Phys. 23, 35–44 (2002).
[CrossRef]

L. Dettwiller, “Propagation de la lumière, dispersion, et absorption,” in EGEM—Optique géométrique et propagation, J.-L. Meyzonnette, ed. (Hermès Lavoisier, Paris, 2003), Chap. 1.

Doss-Bachelet, C.

See, for example, C. Doss-Bachelet, J.-P. Françoise, C. Piquet, Géométrie différentielle (Ellipses, Paris, 2000), p. 37.

Françoise, J.-P.

See, for example, C. Doss-Bachelet, J.-P. Françoise, C. Piquet, Géométrie différentielle (Ellipses, Paris, 2000), p. 37.

Gray, A.

A. Gray, Modern Differential Geometry of Curves and Surfaces (CRC, Boca Raton, Fla., 1993).

Harris, T. J.

W. J. Tropf, M. E. Thomas, T. J. Harris, “Properties of crystals and glasses,” in Handbook of Optics, Vol. 2, M. Bass, ed. (McGraw-Hill, New York, 1995). Gives (pp. 33.61–33. 67) dispersion formulas for a hundred crystals at room temperature (and for rutile the Sellmeier relations no2≅5.913+0.2441 μm2λ02-0.0803 μm2,ne2≅7.197+0.3322 μm2λ02-0.0843 μm2 from 0.43 to 1.5 µm); it gives again the refractive indices of calcite from 0.198 to 3.324 µm, p. 33.70.

Joshua, E.

Kato, K.

Koch, E. E.

J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, Physik Daten (Fachinformationszentrum, Karlsruhe, Germany, 1981).

Krafka, C.

J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, Physik Daten (Fachinformationszentrum, Karlsruhe, Germany, 1981).

Krasinsky, J. S.

la Grone, M. J.

Lynch, D. W.

J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, Physik Daten (Fachinformationszentrum, Karlsruhe, Germany, 1981).

Micheli, F. J.

F. J. Micheli, “Ueber den Einfluss der Temperatur auf die Dispersion ultravioletter Strahlen in Flussspat, Steinsalz, Quarz und Kalkspat,” Ann. Phys. 7, 772–789 (1902). Gives the temperature coefficients of the ordinary and extraordinary indices of quartz and calcite at approximately 20 wavelengths from 211 to 643 nm.
[CrossRef]

Miyagi, M.

Nishida, S.

Palik, E. D.

E. D. Palik, Handbook of Optical Constants of Solids (Academic, Boston, Mass., 1985), Vol. 1, and 1991 Vol. 2.

Petit, R.

R. Petit, Ondes électromagnétiques en radioélectricité et en optique (Masson, Paris, 1988).

Piquet, C.

See, for example, C. Doss-Bachelet, J.-P. Françoise, C. Piquet, Géométrie différentielle (Ellipses, Paris, 2000), p. 37.

Radzewicz, C.

Ratcliffe, J. A.

J. A. Ratcliffe, Magneto-Ionic Theory and Its Applications (Cambridge U. Press, Cambridge, UK, 1959).

Rothenberg, J. E.

Schell, A. J.

Sukhorukov, A. P.

S. A. Akhmanov, A. P. Sukhorukov, S. A. Chirkin, “Stationary phenomena and space-time analogy in non-linear optics,” Sov. Phys. JETP 28, 748–757 (1969).

Takaoka, E.

Thomas, M. E.

W. J. Tropf, M. E. Thomas, T. J. Harris, “Properties of crystals and glasses,” in Handbook of Optics, Vol. 2, M. Bass, ed. (McGraw-Hill, New York, 1995). Gives (pp. 33.61–33. 67) dispersion formulas for a hundred crystals at room temperature (and for rutile the Sellmeier relations no2≅5.913+0.2441 μm2λ02-0.0803 μm2,ne2≅7.197+0.3322 μm2λ02-0.0843 μm2 from 0.43 to 1.5 µm); it gives again the refractive indices of calcite from 0.198 to 3.324 µm, p. 33.70.

Treacy, E. B.

E. B. Treacy, “Optical pulse compression with diffraction gratings,” IEEE J. Quantum Electron. QE-5, 454–458 (1969).
[CrossRef]

Trippenbach, M.

Tropf, W. J.

W. J. Tropf, M. E. Thomas, T. J. Harris, “Properties of crystals and glasses,” in Handbook of Optics, Vol. 2, M. Bass, ed. (McGraw-Hill, New York, 1995). Gives (pp. 33.61–33. 67) dispersion formulas for a hundred crystals at room temperature (and for rutile the Sellmeier relations no2≅5.913+0.2441 μm2λ02-0.0803 μm2,ne2≅7.197+0.3322 μm2λ02-0.0843 μm2 from 0.43 to 1.5 µm); it gives again the refractive indices of calcite from 0.198 to 3.324 µm, p. 33.70.

Weaver, J. H.

J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, Physik Daten (Fachinformationszentrum, Karlsruhe, Germany, 1981).

Weisstein, E. W.

See, for example, E. W. Weisstein, CRC Concise Encyclopedia of Mathematics, 2nd ed. (Chapman & Hall/CRC, Boca Raton, Fla., 2003), p. 869.

Wolf, E.

M. Born, E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 6th ed. (Pergamon, Oxford, 1980).

Yariv, A.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), pp. 79–82.

Yeh, P.

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), pp. 79–82.

Ann. Phys. (1)

F. J. Micheli, “Ueber den Einfluss der Temperatur auf die Dispersion ultravioletter Strahlen in Flussspat, Steinsalz, Quarz und Kalkspat,” Ann. Phys. 7, 772–789 (1902). Gives the temperature coefficients of the ordinary and extraordinary indices of quartz and calcite at approximately 20 wavelengths from 211 to 643 nm.
[CrossRef]

Appl. Opt. (3)

Eur. J. Phys. (1)

L. Dettwiller, “Asymptotic evolution of a three-dimensional wave packet propagating in a linear dispersive medium,” Eur. J. Phys. 23, 35–44 (2002).
[CrossRef]

IEEE J. Quantum Electron. (1)

E. B. Treacy, “Optical pulse compression with diffraction gratings,” IEEE J. Quantum Electron. QE-5, 454–458 (1969).
[CrossRef]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. B (2)

Opt. Lett. (1)

Sov. Phys. JETP (1)

S. A. Akhmanov, A. P. Sukhorukov, S. A. Chirkin, “Stationary phenomena and space-time analogy in non-linear optics,” Sov. Phys. JETP 28, 748–757 (1969).

Other (15)

G. Bruhat, Cours de physique générale Optique (Masson, Paris, 1992).

A. Gray, Modern Differential Geometry of Curves and Surfaces (CRC, Boca Raton, Fla., 1993).

J. A. Ratcliffe, Magneto-Ionic Theory and Its Applications (Cambridge U. Press, Cambridge, UK, 1959).

K. G. Budden, Radio Waves in The Ionosphere (Cambridge U. Press, Cambridge, UK, 1961).

R. Petit, Ondes électromagnétiques en radioélectricité et en optique (Masson, Paris, 1988).

L. Dettwiller, “Propagation de la lumière, dispersion, et absorption,” in EGEM—Optique géométrique et propagation, J.-L. Meyzonnette, ed. (Hermès Lavoisier, Paris, 2003), Chap. 1.

M. Born, E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 6th ed. (Pergamon, Oxford, 1980).

A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984), pp. 79–82.

W. J. Tropf, M. E. Thomas, T. J. Harris, “Properties of crystals and glasses,” in Handbook of Optics, Vol. 2, M. Bass, ed. (McGraw-Hill, New York, 1995). Gives (pp. 33.61–33. 67) dispersion formulas for a hundred crystals at room temperature (and for rutile the Sellmeier relations no2≅5.913+0.2441 μm2λ02-0.0803 μm2,ne2≅7.197+0.3322 μm2λ02-0.0843 μm2 from 0.43 to 1.5 µm); it gives again the refractive indices of calcite from 0.198 to 3.324 µm, p. 33.70.

See, for example, C. Doss-Bachelet, J.-P. Françoise, C. Piquet, Géométrie différentielle (Ellipses, Paris, 2000), p. 37.

See, for example, E. W. Weisstein, CRC Concise Encyclopedia of Mathematics, 2nd ed. (Chapman & Hall/CRC, Boca Raton, Fla., 2003), p. 869.

J. H. Weaver, C. Krafka, D. W. Lynch, E. E. Koch, Physik Daten (Fachinformationszentrum, Karlsruhe, Germany, 1981).

E. D. Palik, Handbook of Optical Constants of Solids (Academic, Boston, Mass., 1985), Vol. 1, and 1991 Vol. 2.

Landolt-Börnstein Numerical Data and Functional Relationships in Science and Technology (Springer, Berlin, 1985), Vol. 15b.

J. M. Bennett, “Polarizers,” in Handbook of Optics, Vol. 2, M. Bass, ed. (McGraw-Hill, New York, 1995). Gives (pp. 3.5–3.6) the refractive indices and the absorption coefficients of calcite from 0.1318 to 3.4 µm.

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Equations (73)

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s(r, t)=Re s_(r, t)=2 Re (S)s˜(K)exp-i[ω(K)t-K·r]d3 K/(2π)3,
s_(r, t)=s_0(r, t)exp-i(ωmt-Km·r),
ω(Km+k)ωm+vgm·k+12k·(HKmω)k,
s_(r, t)[s_0(r, 0)*Fg-1](r-vgmt)×exp[-i(ωmt-Km·r)],
Fg-1(r)=1|det(HKmωt)|exp i-σπ4+12r·(HKmωt)-1r,
MjlCr(t)R3|s_(r, t)|2(xj-x¯j(t))(xl-x¯l(t))d3rR3|s_(r, t)|2d3r(xj-x¯j(t))(xl-x¯l(t))¯=xjxl¯(t)-x¯j(t)x¯l(t),
(MCr)(t)(MCvg)t2 ast,
MjlCvg(S)|s˜(K)|2ωKj-ω¯Kj(K)ωKl-ω¯Kl(K)d3K(S)|s˜(K)|2d3K(vgj-vgj¯)(vgl-vgl¯)¯=vgjvgl¯-vgj¯ vgl¯.
MjlCK(Kj-Kj¯)(Kl-Kl¯)¯=kjkl¯.
(MCvg)(HKmω)(MCK)(HKmω);
(HKmω)=vgm/Km000vgm/Km000dvg/dK.
ΔX(t)|vgm|ΔKXKmt,ΔY(t)|vgm|ΔKYKmt,
ΔZ(t)dvgdKΔKZt.
vgm/Km=(vgm/K0)(1/R),
ω2=c2n2(ω, uj)K2,
HjlvglKj=2ωKjKl=vgjKlHlj
2ωKx2Ky,Kz=fxωωKxKy,Kz+fxxxKxKy,Kz+fxyyKxKy,Kz.
x=cKxωandy=cKyω;
xKxKy,Kz=cω-cKxω2ωKxKy,Kz
=cω=1K0,
yKxKy,Kz=-cKyω2ωKxKy,Kz=0,
2ωKx2Ky,Kz=1K0fxx=λ02πfxx.
vg=vr1-λ0nnλ0ujN,
fxx=(vgNx)x=vgxNx+vgNxx,
Hxx2ωKx2Ky,Kz=vgmK0NxxM=vgmK01Rxx.
Hyy2ωKy2Kx,Kz=vgmK0NyyM=vgmK01Ryy,
Hxy2ωKxKyKz=vgmK0NyxM=vgmK01Rxy=vgmK0NxyM=2ωKyKxKzHyx;
1Rxx+1Ryy=2m=1Rxx+1Ryy,
1Rxx1Ryy=g=1Rxx1Ryy-1Rxy2,
Hxz2ωKxKzKy=2ωKzKxKyHzx,
Hxz=1K0vgxω,y=Hzx.
R·(MCr)-1R=1.
(MCvg)Hxx2kx2¯000Hyy2ky2¯+Hyz2kz2¯Hzy(Hyyky2¯+Hzzkz2¯)0Hyz(Hyyky2¯+Hzzkz2¯)Hzz2kz2¯+Hzy2ky2¯.
vgZ=(ω/KZ)KX,KY=cn-λ0(n/λ0)uj;
2ωKZ2KX,KY=vgZKZKX,KY=vgZλ0KX,KYKZλ0KX,KY,
KZλ0KX,KY=KZλ0uj
vgZλ0KX,KY=vgZλ0uj=-vgZ2DZ=vgZ2λ0c2nλ02uj.
KZ=n(λ0, uj)2πλ0uZ,
KZλ0uj=-2πλ02n-λ0nλ0uj=-2πλ02cvgZ.
HZZ2ωKZ2KX,KY=-vgZ3λ032πc22nλ02uj=vgZ3λ022πcDZ.
vgZ3λ032πc22nλ02ujΔKzt.
dvl/dλ0=Ω×vl.
dudλ0=ddλ0i=13ulvl=l=13(u˙lvl+ulΩ×vl)=l=13u˙lvl+Ω×u=0,
u˙l=-j,k=13ljkΩjuk,
ljk=+1forl=1,j=2,k=3,andanyevenpermutation-1foranyoddpermutation0ifanytwoindicesareequal.
n˙l=13nl2ul2(n2-nl2)2=nl=13nln˙lul2(n2-nl2)2+1nl=13nl2ulu˙ln2-nl2.
Dl=0nl2El=0(u·E)n2nl2uln2-nl2,
l=13nl2ulu˙ln2-nl2=-l,j,k=13ljknl2ulΩjukn2-nl2=-10(u·E)n2l,j,k=13ljkDlΩjuk=-D·(Ω×u)0n2 sin αE,
l=13nl2ul2(n2-nl2)2=cot2 αn2,
D=0n2 cos αE.
ξ˙ln˙l/nl,
Ll=13ξ˙luln2-nl2vl=l=13ξ˙lEln2(u·E)vl;
n˙=n2 tan αnL+u×Ωn·DD.
Iξ˙mEn2(u·E)andξ˙m13l=13ξ˙l
n˙n=n2cot αI+C+u×Ωn2·DD=ξ˙m+tan α(n2C+u×Ω)·DD.
αm=arcsin|ne2-no2|2(no4+ne4)5.84°,
cnmc2.6731.121.108 m s-1,
vr=c2no2+ne2c2.659.
Km=2πλ0nm0sin αmcos αm
(G)=[Δx(0)]2000[Δy(0)]2000[Δz(0)]2,
τΔz(0)(Hzz2kz2¯+Hzy2ky2¯)1/2.
τΔz(0)|HZZ|ΔKZ,τ2[Δz(0)]2|HZZ|10-11 s
El=(u·E)n2uln2-nl2;
(u·E)2=E2 sin2 α=sin2 αl=13El2
1n2 sin2 α=l=13n2ul2(n2-nl2)2=l=131n2-nl2+nl2(n2-nl2)2ul2.
l=13ul2n2-nl2=1n2l=13ul2+l=13nl2ul2n2-nl2=1n2,
1n2 sin2 α=1n2+l=13nl2ul2(n2-nl2)2=1n2(1+cot2 α),
l=13nl2ul2(n2-nl2)2=cot2 αn2.
D2n2=l=13Dl2nl2,
D2n2=[0(u·E)n2]2l=13nluln2-nl22=[0En2 sin α]2l=13nl2ul2(n2-nl2)2,
D=0n2 cos αE.
no25.913+0.2441μm2λ02-0.0803μm2,
ne27.197+0.3322μm2λ02-0.0843μm2

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