Abstract

With reference to the analysis contained in J. Opt. Soc. Am. 73, 920 (1983), certain comments on and clarifications of the paraxial wave equation pertaining to the extraordinary-mode beam propagating obliquely to the optic axis in a uniform uniaxial crystal are presented.

© 2001 Optical Society of America

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References

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  1. S. Y. Shin, L. B. Felsen, “Gaussian beams in anisotropic media,” Appl. Phys. 5, 239–250 (1974).
    [CrossRef]
  2. J. A. Fleck, M. D. Feit, “Beam propagation in uniaxial anisotropic media,” J. Opt. Soc. Am. 73, 920–926 (1983).
    [CrossRef]

1983

1974

S. Y. Shin, L. B. Felsen, “Gaussian beams in anisotropic media,” Appl. Phys. 5, 239–250 (1974).
[CrossRef]

Feit, M. D.

Felsen, L. B.

S. Y. Shin, L. B. Felsen, “Gaussian beams in anisotropic media,” Appl. Phys. 5, 239–250 (1974).
[CrossRef]

Fleck, J. A.

Shin, S. Y.

S. Y. Shin, L. B. Felsen, “Gaussian beams in anisotropic media,” Appl. Phys. 5, 239–250 (1974).
[CrossRef]

Appl. Phys.

S. Y. Shin, L. B. Felsen, “Gaussian beams in anisotropic media,” Appl. Phys. 5, 239–250 (1974).
[CrossRef]

J. Opt. Soc. Am.

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Equations (21)

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ayy=sin2 θ+γ2 cos2 θ,
ayz=(γ2-1)sin 2θ,
azz=cos2 θ+γ2 sin2 θ,
γ2=ne2no2
tan θ=ayz2ayy,
z˜=z-y tan θ,
y˜=y.
y=y˜-tan θ z˜,
z=z˜.
2Ezx2+(ayy tan2θ-ayz tan θ+azz) 2Ezz˜2+ayy 2Ezy˜2+k02ne2Ez=0,
2Ez0y2,2Ez0yz,2Ez0z2
Ez0y+tan θ Ez0z=0.
2Ezx2+γ2ayy 2Ezz˜2+ayy 2Ezy˜2+k02ne2Ez=0.
exp(-ikyy˜),ky=k0ne(ayy)1/2.
Ez=Ez0(x, y˜, z˜)exp(-ikyy˜),
2Ez0x2+γ2ayy 2Ez0z˜2-2ik0ne(ayy)1/2 Ez0y˜=0.
2Ez0x2+γ2ayy 2Ez0z2-2ik0ne(ayy)1/2×y+tan θ zEz0=0.
Ez0(x, y=0, z)=exp-(x2+z2)2σ2,
Ez0(x, y, z)=1-i ybx-1/21-i ybz-1/2×exp-x22σ2(1-iy/bx)-(z-y tan θ)22σ2(1-iy/bz),
bx=k0σ2ne(ayy)1/2,
bz=k0σ2 no2ne(ayy)3/2.

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