Abstract

We derive an exact equation for the transverse component of the electric field propagating along a given longitudinal z direction in the presence of an isotropic refractive-index distribution n(x,y).

© 2009 Optical Society of America

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References

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  1. S. Solimeno, B. Crosignani, and P. Di Porto, Guiding, Diffraction and Confinement of Optical Radiation (Academic, 1986).
  2. A. Yu. Savchencko and B. Ya. Zel'dovich, “Wave propagation in a guiding structure: one step beyond the paraxial approximation,” J. Opt. Soc. Am. B 13, 273-281 (1996).
    [CrossRef]
  3. A. Ciattoni, P. Di Porto, B. Crosignani, and A. Yariv, “Vectorial nonparaxial propagation equation in the presence of a tensorial refractive index perturbation,” J. Opt. Soc. Am. B 17, 809-819 (2000).
    [CrossRef]
  4. G. Brambilla, F. Xu, P. Horak, Y. Jung, F. Koizumi, N. Sessions, E. Koukharenko, X. Feng, G. Murugan, J. Wilkinson, and D. Richardson, “Optical fiber nanowires and microwires: fabrication and applications,” Adv. Opt. Photon 1, 107-161 (2009).
    [CrossRef]

2009 (1)

G. Brambilla, F. Xu, P. Horak, Y. Jung, F. Koizumi, N. Sessions, E. Koukharenko, X. Feng, G. Murugan, J. Wilkinson, and D. Richardson, “Optical fiber nanowires and microwires: fabrication and applications,” Adv. Opt. Photon 1, 107-161 (2009).
[CrossRef]

2000 (1)

1996 (1)

Brambilla, G.

G. Brambilla, F. Xu, P. Horak, Y. Jung, F. Koizumi, N. Sessions, E. Koukharenko, X. Feng, G. Murugan, J. Wilkinson, and D. Richardson, “Optical fiber nanowires and microwires: fabrication and applications,” Adv. Opt. Photon 1, 107-161 (2009).
[CrossRef]

Ciattoni, A.

Crosignani, B.

Di Porto, P.

Feng, X.

G. Brambilla, F. Xu, P. Horak, Y. Jung, F. Koizumi, N. Sessions, E. Koukharenko, X. Feng, G. Murugan, J. Wilkinson, and D. Richardson, “Optical fiber nanowires and microwires: fabrication and applications,” Adv. Opt. Photon 1, 107-161 (2009).
[CrossRef]

Horak, P.

G. Brambilla, F. Xu, P. Horak, Y. Jung, F. Koizumi, N. Sessions, E. Koukharenko, X. Feng, G. Murugan, J. Wilkinson, and D. Richardson, “Optical fiber nanowires and microwires: fabrication and applications,” Adv. Opt. Photon 1, 107-161 (2009).
[CrossRef]

Jung, Y.

G. Brambilla, F. Xu, P. Horak, Y. Jung, F. Koizumi, N. Sessions, E. Koukharenko, X. Feng, G. Murugan, J. Wilkinson, and D. Richardson, “Optical fiber nanowires and microwires: fabrication and applications,” Adv. Opt. Photon 1, 107-161 (2009).
[CrossRef]

Koizumi, F.

G. Brambilla, F. Xu, P. Horak, Y. Jung, F. Koizumi, N. Sessions, E. Koukharenko, X. Feng, G. Murugan, J. Wilkinson, and D. Richardson, “Optical fiber nanowires and microwires: fabrication and applications,” Adv. Opt. Photon 1, 107-161 (2009).
[CrossRef]

Koukharenko, E.

G. Brambilla, F. Xu, P. Horak, Y. Jung, F. Koizumi, N. Sessions, E. Koukharenko, X. Feng, G. Murugan, J. Wilkinson, and D. Richardson, “Optical fiber nanowires and microwires: fabrication and applications,” Adv. Opt. Photon 1, 107-161 (2009).
[CrossRef]

Murugan, G.

G. Brambilla, F. Xu, P. Horak, Y. Jung, F. Koizumi, N. Sessions, E. Koukharenko, X. Feng, G. Murugan, J. Wilkinson, and D. Richardson, “Optical fiber nanowires and microwires: fabrication and applications,” Adv. Opt. Photon 1, 107-161 (2009).
[CrossRef]

Richardson, D.

G. Brambilla, F. Xu, P. Horak, Y. Jung, F. Koizumi, N. Sessions, E. Koukharenko, X. Feng, G. Murugan, J. Wilkinson, and D. Richardson, “Optical fiber nanowires and microwires: fabrication and applications,” Adv. Opt. Photon 1, 107-161 (2009).
[CrossRef]

Savchencko, A. Yu.

Sessions, N.

G. Brambilla, F. Xu, P. Horak, Y. Jung, F. Koizumi, N. Sessions, E. Koukharenko, X. Feng, G. Murugan, J. Wilkinson, and D. Richardson, “Optical fiber nanowires and microwires: fabrication and applications,” Adv. Opt. Photon 1, 107-161 (2009).
[CrossRef]

Solimeno, S.

S. Solimeno, B. Crosignani, and P. Di Porto, Guiding, Diffraction and Confinement of Optical Radiation (Academic, 1986).

Wilkinson, J.

G. Brambilla, F. Xu, P. Horak, Y. Jung, F. Koizumi, N. Sessions, E. Koukharenko, X. Feng, G. Murugan, J. Wilkinson, and D. Richardson, “Optical fiber nanowires and microwires: fabrication and applications,” Adv. Opt. Photon 1, 107-161 (2009).
[CrossRef]

Xu, F.

G. Brambilla, F. Xu, P. Horak, Y. Jung, F. Koizumi, N. Sessions, E. Koukharenko, X. Feng, G. Murugan, J. Wilkinson, and D. Richardson, “Optical fiber nanowires and microwires: fabrication and applications,” Adv. Opt. Photon 1, 107-161 (2009).
[CrossRef]

Yariv, A.

Zel'dovich, B. Ya.

Adv. Opt. Photon (1)

G. Brambilla, F. Xu, P. Horak, Y. Jung, F. Koizumi, N. Sessions, E. Koukharenko, X. Feng, G. Murugan, J. Wilkinson, and D. Richardson, “Optical fiber nanowires and microwires: fabrication and applications,” Adv. Opt. Photon 1, 107-161 (2009).
[CrossRef]

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

Other (1)

S. Solimeno, B. Crosignani, and P. Di Porto, Guiding, Diffraction and Confinement of Optical Radiation (Academic, 1986).

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Equations (14)

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2 E E + ω 2 c 2 n 2 ( r ) E = 0 ,
E = 0 ,
2 E + ω 2 c 2 n 2 ( r ) E = 0 .
E ( r ) = A ( r ) exp ( ikz ) .
2 ik z A + 2 A + 2 k 2 Δ n A = 0 ,
E ( r , z ) = E + E = d k exp ( i k r ) ε ( k , z ) exp [ ih ( k ) z ] + ε ( k , z ) exp [ ih ( k ) z ] ,
( i z + L ̂ ) E = k 2 L ̂ ( Δ n E ) + [ Δ n 1 L ̂ ( E E ) ] 1 L ̂ [ ( Δ n E ) ] ,
( i z L ̂ ) E = k 2 L ̂ ( Δ n E ) + [ Δ n 1 L ̂ ( E E ) ] + 1 L ̂ [ ( Δ n E ) ] .
i z E + L ̂ ( E E ) = 2 [ Δ n 1 L ̂ ( E E ) ] ,
i z ( E E ) + L ̂ E = 2 k 2 L ̂ ( Δ n E ) 2 L ̂ [ ( Δ n E ) ] .
2 z 2 E + 2 E + k 2 E + 2 k 2 ( Δ n E ) + 2 ( E Δ n ) = 4 { Δ n [ k 2 + ] [ 1 L ̂ 2 ( Δ n E ) ] } = 4 [ Δ n ( Δ n E ) ] ,
2 E + k 2 ( n n 0 ) 2 E + 2 { E [ Δ n + ( Δ n ) 2 ] } = 4 [ ( Δ n ) 2 E ] .
2 E + k 2 ( n 2 / n 0 2 ) E + 2 ( E Δ n ) = 0 .
2 ik z A + 2 A + 2 k 2 Δ n A + 2 { A [ Δ n + ( Δ n ) 2 ] } = 4 [ ( Δ n ) 2 A ] ,

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