Abstract

We examine the value ni/neffθt, the ratio of the indices of refraction for waves transmitted from an isotropic medium to an anisotropic medium. It is found that total reflection can occur in the case of propagation from a rarer medium to a denser medium.

© 1998 Optical Society of America

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References

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  1. G. R. Fowles, Introduction to Modern Optics, 2nd ed. (Holt, Rinehart & Winston, New York, 1975).
  2. E. Hecht, Optics, 2nd ed. (Addison-Wesley, Reading, Mass., 1987).
  3. K. D. Moller, Optics (University Science, Mill Valley, Calif., 1988).
  4. M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980).
  5. J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975).

Born, M.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980).

Fowles, G. R.

G. R. Fowles, Introduction to Modern Optics, 2nd ed. (Holt, Rinehart & Winston, New York, 1975).

Hecht, E.

E. Hecht, Optics, 2nd ed. (Addison-Wesley, Reading, Mass., 1987).

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975).

Moller, K. D.

K. D. Moller, Optics (University Science, Mill Valley, Calif., 1988).

Wolf, E.

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980).

Other (5)

G. R. Fowles, Introduction to Modern Optics, 2nd ed. (Holt, Rinehart & Winston, New York, 1975).

E. Hecht, Optics, 2nd ed. (Addison-Wesley, Reading, Mass., 1987).

K. D. Moller, Optics (University Science, Mill Valley, Calif., 1988).

M. Born and E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980).

J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975).

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Figures (4)

Fig. 1
Fig. 1

Incident plane and the elliptical surface of nt with minor axis ne and major axis no.

Fig. 2
Fig. 2

neffθt and ni in the range 0θiθc, with no=1.8, ne=1.2, β=0.7, and ni=1.49056.

Fig. 3
Fig. 3

Reflection coefficient r in the range 0θiπ/2.

Fig. 4
Fig. 4

lnr in the range 0θiπ/2.

Equations (17)

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ntx2ne2+nty2no2=1.
neffθt=noneno2 sin2 γ+ne2 cos2 γ1/2,
ki·yˆ=kt·yˆ
ni sin θi=neffθtsin θt.
nt·yˆymax,
ymax=noneneff0=no2 sin2 β+ne2 cos2 β1/2.
θc=sin-1nonenineff0.
θtc=β+tan-1ne2 cos βno2 sin β+δ,
neffθtc=no4 sin2 β+ne4 cos2 βno2 sin2 β+ne2 cos2 β1/2.
ymax<ni<neffθtc.
sin2 θt=C2-2AB+signC2C2-4AA+B1/22B2+C2,
A=ni2 sin2 θino2 sin2 β+ne2 cos2 β, B=ni2 sin2 θino2-ne2cos2β-no2ne2, C=ni2 sin2 θino2-ne2sin2β,
C2-4AA+B=4ni2 sin2 θino2ne2×noneneff2-ni2 sin2 θi.
r=q-pq+p,
p=no2 sin γ sin β+ne2 cos γ cos βNγ cos θi,
q=no2ne2Nγnineffθt,
Nγ=no4 sin2 γ+ne4 cos2 γ1/2.

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