Abstract

An exact closed-form representation is derived of a vector elegant Laguerre–Gaussian wave packet. Its space–time representation consists of three mutually orthogonal field components—of a common azimuthal index and different radial indices—uniquely distinguished by first three powers of the paraxial parameter. The transverse components are of tm-radial and te-azimuthal polarization and appear, under their normal incidence, to be eigenmodes of any horizontally planar, homogeneous and isotropic structure, with eigenvalues given by the reflection and transmission coefficients. In this context, the interrelations between the cross-polarization symmetries of wave packets in free space and at medium planar interfaces are discussed.

© 2013 Optical Society of America

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References

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2011 (1)

W. Szabelak and W. Nasalski, J. Phys. B 44, 215403(2011).
[CrossRef]

2008 (1)

2006 (2)

W. Nasalski, Phys. Rev. E 74, 056613 (2006).
[CrossRef]

I. Białynicki-Birula and Z. Białynicka-Birula, Opt. Commun. 264, 342 (2006).
[CrossRef]

2004 (3)

2002 (1)

1999 (1)

L. Allen, M. J. Padgett, and M. Babiker, Prog. Opt. 39, 291 (1999).
[CrossRef]

1998 (1)

C. J. R. Sheppard and S. Saghafi, Phys. Rev A 57, 2971 (1998).
[CrossRef]

1996 (1)

1994 (1)

S. M. Barnett and L. Allen, Opt. Commun. 110, 670 (1994).
[CrossRef]

1986 (2)

E. Zauderer, J. Opt. Soc. Am. A 3, 465 (1986).
[CrossRef]

P. Hillion, J. Appl. Phys. 60, 2981 (1986).
[CrossRef]

1985 (3)

A. Sezginer, J. Appl. Phys. 57, 678 (1985).
[CrossRef]

R. W. Ziolkowski, J. Math. Phys. 26, 861 (1985).

T. Takenaka, M. Yokota, and O. Fukumitsu, J. Opt. Soc. Am. A 2, 826 (1985).
[CrossRef]

1984 (1)

1983 (1)

J. N. Brittingham, J. Appl. Phys. 54, 1179 (1983).
[CrossRef]

1973 (1)

Allen, L.

L. Allen, M. J. Padgett, and M. Babiker, Prog. Opt. 39, 291 (1999).
[CrossRef]

S. M. Barnett and L. Allen, Opt. Commun. 110, 670 (1994).
[CrossRef]

April, A.

Babiker, M.

L. Allen, M. J. Padgett, and M. Babiker, Prog. Opt. 39, 291 (1999).
[CrossRef]

Bandres, M. A.

Barnett, S. M.

S. M. Barnett and L. Allen, Opt. Commun. 110, 670 (1994).
[CrossRef]

Bateman, H.

H. Bateman, The Mathematical Analysis of Electrical and Optical Wave-motion on the Basis of Maxwell’s Equations (Cambridge University, 1915).

Belanger, P. A.

Bialynicka-Birula, Z.

I. Białynicki-Birula and Z. Białynicka-Birula, Opt. Commun. 264, 342 (2006).
[CrossRef]

Bialynicki-Birula, I.

I. Białynicki-Birula and Z. Białynicka-Birula, Opt. Commun. 264, 342 (2006).
[CrossRef]

Brittingham, J. N.

J. N. Brittingham, J. Appl. Phys. 54, 1179 (1983).
[CrossRef]

Chavez-Cerda, S.

Enderlein, J.

Fukumitsu, O.

Gutierrez-Vega, J. C.

Hall, D. G.

Hillion, P.

P. Hillion, J. Appl. Phys. 60, 2981 (1986).
[CrossRef]

Nasalski, W.

W. Szabelak and W. Nasalski, J. Phys. B 44, 215403(2011).
[CrossRef]

W. Nasalski, Phys. Rev. E 74, 056613 (2006).
[CrossRef]

Padgett, M. J.

L. Allen, M. J. Padgett, and M. Babiker, Prog. Opt. 39, 291 (1999).
[CrossRef]

Pampaloni, F.

Rodriguez-Morales, G.

Saghafi, S.

C. J. R. Sheppard and S. Saghafi, Phys. Rev A 57, 2971 (1998).
[CrossRef]

Seshadri, S. R.

Sezginer, A.

A. Sezginer, J. Appl. Phys. 57, 678 (1985).
[CrossRef]

Sheppard, C. J. R.

C. J. R. Sheppard and S. Saghafi, Phys. Rev A 57, 2971 (1998).
[CrossRef]

Siegman, A. E.

A. E. Siegman, J. Opt. Soc. Am. 63, 1093 (1973).
[CrossRef]

A. E. Siegman, Lasers (University Science, 1986).

Stratton, J. A.

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).

Szabelak, W.

W. Szabelak and W. Nasalski, J. Phys. B 44, 215403(2011).
[CrossRef]

Takenaka, T.

Yokota, M.

Zauderer, E.

Ziolkowski, R. W.

R. W. Ziolkowski, J. Math. Phys. 26, 861 (1985).

J. Appl. Phys. (3)

J. N. Brittingham, J. Appl. Phys. 54, 1179 (1983).
[CrossRef]

A. Sezginer, J. Appl. Phys. 57, 678 (1985).
[CrossRef]

P. Hillion, J. Appl. Phys. 60, 2981 (1986).
[CrossRef]

J. Math. Phys. (1)

R. W. Ziolkowski, J. Math. Phys. 26, 861 (1985).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (4)

J. Phys. B (1)

W. Szabelak and W. Nasalski, J. Phys. B 44, 215403(2011).
[CrossRef]

Opt. Commun. (2)

S. M. Barnett and L. Allen, Opt. Commun. 110, 670 (1994).
[CrossRef]

I. Białynicki-Birula and Z. Białynicka-Birula, Opt. Commun. 264, 342 (2006).
[CrossRef]

Opt. Lett. (5)

Phys. Rev A (1)

C. J. R. Sheppard and S. Saghafi, Phys. Rev A 57, 2971 (1998).
[CrossRef]

Phys. Rev. E (1)

W. Nasalski, Phys. Rev. E 74, 056613 (2006).
[CrossRef]

Prog. Opt. (1)

L. Allen, M. J. Padgett, and M. Babiker, Prog. Opt. 39, 291 (1999).
[CrossRef]

Other (3)

H. Bateman, The Mathematical Analysis of Electrical and Optical Wave-motion on the Basis of Maxwell’s Equations (Cambridge University, 1915).

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).

A. E. Siegman, Lasers (University Science, 1986).

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Equations (19)

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E̲(tm)=21/2f(e^̲Rzς++e^̲Lzς)Mz2e^̲zς+ςMz,
H̲(tm)=i21/2f(e^̲Rctς+e^̲Lctς)Mz.
(2iz++ς+ς)Gp,±l=0;Gp,±l=ς±pςp+lg,
Gp,±l=(1)p+lv2(p+l+1)ς±lp!Lpl(u2)exp(u2),
G˜p,±l=i2p+lκpκ±p+lexp(κ+κv2),
E̲(tm)=i21/2e^̲{R,L}(f1Gp+1,±(l1)+f+1Gp+2,±(l1))+i21/2e^̲{L,R}(f1Gp,±(l+1)+f+1Gp+1,±(l+1))2e^̲zGp+1,±l,
H̲(tm)=±21/2e^̲{R,L}(f1Gp+1,±(l1)f+1Gp+2,±(l1))21/2e^̲{L,R}(f1Gp,±(l+1)f+1Gp+1,±(l+1)),
Gp,l1exp(±2iϕ)=Gp1,l±1;Gp,l1exp(±iϕ)=Gp1/2,l.
E̲(tm)=ie^̲ρ(f1Gp+1/2,l+f+1Gp+3/2,l)2e^̲zGp+1,l,
H̲(tm)=ie^̲ϕ(f1Gp+1/2,lf+1Gp+3/2,l),
E̲=if1(αe^̲ρβe^̲ϕ)Gp+1/2,l2αe^̲zGp+1,l+if+1(αe^̲ρ+βe^̲ϕ)Gp+3/2,l,
H̲=if1(βe^̲ρ+αe^̲ϕ)Gp+1/2,l2βe^̲zGp+1,l+if+1(βe^̲ραe^̲ϕ)Gp+3/2,l.
E̲if1(αe^̲ρβe^̲ϕ)G{p+1/2,p+3/2},l,
H̲if1(βe^̲ρ±αe^̲ϕ)G{p+1/2,p+3/2},l.
{E̲,H̲}(z+,ωt)=α,βp,l{E̲,H̲}(z+)exp(iωz/c),
{̲,̲}(z+,t)=π1{E̲,H̲}(z+,wt)ψ(ω)dω.
r̲̲=[r+e+2iφrrr+e2iφ];t̲̲=[t+te2iφte+2iφt+].
r̲̲E˜̲(tm)=rpE˜̲(tm);t̲̲E˜̲(tm)=ηtpE˜̲(tm),
r̲̲E˜̲(te)=rsE˜̲(te);t̲̲E˜̲(te)=tsE˜̲(te),

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