Abstract

We theoretically investigate light beam propagation in (1+1)D homogeneous anisotropic uniaxials where ordinary and extraordinary waves are decoupled, accounting for the vectorial character of the electromagnetic field and addressing the nonparaxial limit.

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References

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2010 (1)

2009 (1)

A. Yang, S. Moore, B. Schmidt, M. Klug, M. Lipson, and D. Erickson, Nature 457, 71 (2009).
[PubMed]

2008 (2)

2007 (1)

2006 (1)

2004 (1)

2003 (2)

A. Ciattoni and C. Palma, J. Opt. Soc. Am. A 20, 2163 (2003).

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[PubMed]

2002 (2)

1986 (1)

1983 (1)

1979 (1)

1975 (1)

M. Lax, W. Louisell, and W. McKnight, Phys. Rev. A 11, 1365 (1975).

1972 (1)

1967 (1)

D. Bhawalkar, A. Goncharenko, and R. Smith, Br. J. Appl. Phys. 18, 1431 (1967).

Agrawal, G.

April, A.

Bandres, M.

Bhawalkar, D.

D. Bhawalkar, A. Goncharenko, and R. Smith, Br. J. Appl. Phys. 18, 1431 (1967).

Carter, W. H.

Chen, C.

Chen, L.

Ciattoni, A.

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[PubMed]

Erickson, D.

A. Yang, S. Moore, B. Schmidt, M. Klug, M. Lipson, and D. Erickson, Nature 457, 71 (2009).
[PubMed]

Feit, M.

Ferrera, J.

Fleck, J.

Goncharenko, A.

D. Bhawalkar, A. Goncharenko, and R. Smith, Br. J. Appl. Phys. 18, 1431 (1967).

Goodman, J.

Heilmann, R.

Ishihara, T.

Klug, M.

A. Yang, S. Moore, B. Schmidt, M. Klug, M. Lipson, and D. Erickson, Nature 457, 71 (2009).
[PubMed]

Konkola, P.

Lax, M.

M. Lax, W. Louisell, and W. McKnight, Phys. Rev. A 11, 1365 (1975).

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[PubMed]

Lipson, M.

A. Yang, S. Moore, B. Schmidt, M. Klug, M. Lipson, and D. Erickson, Nature 457, 71 (2009).
[PubMed]

L. Chen, J. Shakya, and M. Lipson, Opt. Lett. 31, 2133(2006).
[PubMed]

Louisell, W.

M. Lax, W. Louisell, and W. McKnight, Phys. Rev. A 11, 1365 (1975).

Luo, X.

McKnight, W.

M. Lax, W. Louisell, and W. McKnight, Phys. Rev. A 11, 1365 (1975).

Moore, S.

A. Yang, S. Moore, B. Schmidt, M. Klug, M. Lipson, and D. Erickson, Nature 457, 71 (2009).
[PubMed]

Nazarathy, M.

Palange, E.

Palma, C.

Pattanayak, D.

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[PubMed]

Rizza, C.

Schattenburg, M.

Schmidt, B.

A. Yang, S. Moore, B. Schmidt, M. Klug, M. Lipson, and D. Erickson, Nature 457, 71 (2009).
[PubMed]

Seshadri, S.

Shakya, J.

Smith, R.

D. Bhawalkar, A. Goncharenko, and R. Smith, Br. J. Appl. Phys. 18, 1431 (1967).

Vega, J. G.

Yang, A.

A. Yang, S. Moore, B. Schmidt, M. Klug, M. Lipson, and D. Erickson, Nature 457, 71 (2009).
[PubMed]

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Figures (2)

Fig. 1
Fig. 1

(a), (d) Beam waist versus z; blue solid curves and red symbols refer to paraxial Gaussian beams and numerical solutions of Eq. (8), respectively. (b), (e) | H e x | 2 versus y / λ , normalized to its peak and computed for (from left to right) z / λ = 0 , 53, 105, and 158; solid and dashed curves are HG profiles and numerical solutions, respectively, of Eq. (8). (c), (f) Relative error between the profiles in (b) and (e). Top and bottom graphs are computed for w 0 / λ = 0.5 and w 0 / λ = 2 , respectively. Here ϵ = 2.89 , ϵ = 2.25 , and γ = π / 4 . Inset, unit vectors s ^ and t ^ .

Fig. 2
Fig. 2

(a) Computed transverse profile of Re ( S ) along s ^ and (b) relative error with respect to the paraxial expression [Eq. (7)] for w 0 / λ = 0.5 ; Re ( S ) is normalized to its peak for fixed z, and each curve corresponds to the same z / λ of Fig. 1. (c) Ratio between maxima (subscript m) of | E t e | and | E s e | for fixed z and (d) ratio between maxima of odd and even parts of Eq. (7) versus w 0 / λ .

Equations (12)

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( ζ 2 + σ 2 ξ 2 + k 0 2 n e 2 ) H x e = 0 ,
( z 2 + y 2 + k 0 2 ϵ x x ) E x o = 0 ,
S = 1 2 s ^ [ j ω n e 2 ϵ 0 cos δ ( H x e ) * ζ H x e + j sin δ ω ϵ 0 ϵ z z ( H x e ) * ξ H x e ] + 1 2 t ^ [ j cos δ ω ϵ 0 ϵ z z ( H x e ) * ξ H x e ] ,
· S = j Z 0 2 k 0 n e 2 { | z H x e | 2 + D | y H x e | 2 + 2 tan ( δ ) Re [ y H x e z ( H x e ) * ] k 0 2 n e 2 | H x e | 2 } .
Re ( S ) = 1 2 s ^ ρ 2 [ Z 0 n e cos δ sin ( δ ) ξ Φ ω ϵ 0 ϵ z z ζ Φ ω n e 2 cos δ ] + t ^ cos δ 2 ω ϵ 0 ϵ z z ρ 2 ξ Φ .
S 1 2 [ s ^ Z 0 n e cos δ | A | 2 + y ^ j ω ϵ 0 ϵ z z A * ξ A ] ,
· S j Z 0 n e { Im [ A * ( z A + tan δ y A ) ] + D | y A | 2 2 k 0 n e } .
A = A 0 e j ( n + 1 ) Φ ( ζ ) w ( ζ ) c n H n ( ξ 2 w ( ζ ) ) e [ 1 w 2 ( ζ ) j k 0 n e 2 σ 2 R ( ζ ) ] ξ 2 ,
A * ξ A = 2 | A 0 | 2 w c n H n [ 2 n w H n 1 ξ ( j k 0 n e 2 R σ 2 + 1 w 2 ) H n ] e 2 ξ 2 / w 2 ,
Re ( S ) = Z 0 | A 0 | 2 2 n e w c n ( s ^ cos δ + ξ y ^ R ) H n 2 e 2 ξ 2 / w 2 .
H x e = 1 2 π H ( k y ) e j ( k y y + k 0 2 n l 2 ( k y ) k y 2 z ) d k y ,
E t / s e = Z 0 2 π c t / s ( k y ) H ( k y ) n l ( k y ) cos [ δ l ( k y ) ] e j ( k y y + k 0 2 n l 2 ( k y ) k y 2 z ) d k y ,

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