Abstract

The full-wave generalization of the scalar Gaussian paraxial beam is determined by an analytical continuation of the field of a point source for the Helmholtz equation. The regions of validity of the analytically continued fields are investigated for the outgoing and the incoming waves. The two independent wave functions valid for the two half-spaces separating the secondary source plane are deduced.

© 2007 Optical Society of America

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References

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  1. G. A. Deschamps, Electron. Lett. 7, 684 (1971).
    [CrossRef]
  2. L. B. Felsen, J. Opt. Soc. Am. 66, 751 (1976).
    [CrossRef]
  3. C. J. R. Sheppard and S. Saghafi, Phys. Rev. A 57, 2971 (1998).
    [CrossRef]
  4. C. J. R. Sheppard and S. Saghafi, J. Opt. Soc. Am. A 16, 1381 (1999).
    [CrossRef]
  5. C. J. R. Sheppard and S. Saghafi, Opt. Lett. 24, 1543 (1999).
    [CrossRef]
  6. C. J. R. Sheppard and S. Saghafi, Optik (Stuttgart) 110, 487 (1999).
  7. S. R. Seshadri, J. Opt. Soc. Am. A 23, 3238 (2006).
    [CrossRef]
  8. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995), pp. 287-290.

2006 (1)

1999 (3)

1998 (1)

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

1995 (1)

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995), pp. 287-290.

1976 (1)

1971 (1)

G. A. Deschamps, Electron. Lett. 7, 684 (1971).
[CrossRef]

Deschamps, G. A.

G. A. Deschamps, Electron. Lett. 7, 684 (1971).
[CrossRef]

Felsen, L. B.

Mandel, L.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995), pp. 287-290.

Saghafi, S.

C. J. R. Sheppard and S. Saghafi, J. Opt. Soc. Am. A 16, 1381 (1999).
[CrossRef]

C. J. R. Sheppard and S. Saghafi, Opt. Lett. 24, 1543 (1999).
[CrossRef]

C. J. R. Sheppard and S. Saghafi, Optik (Stuttgart) 110, 487 (1999).

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

Seshadri, S. R.

Sheppard, C. J. R.

C. J. R. Sheppard and S. Saghafi, J. Opt. Soc. Am. A 16, 1381 (1999).
[CrossRef]

C. J. R. Sheppard and S. Saghafi, Opt. Lett. 24, 1543 (1999).
[CrossRef]

C. J. R. Sheppard and S. Saghafi, Optik (Stuttgart) 110, 487 (1999).

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

Wolf, E.

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995), pp. 287-290.

Electron. Lett. (1)

G. A. Deschamps, Electron. Lett. 7, 684 (1971).
[CrossRef]

J. Opt. Soc. Am. (1)

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

Opt. Lett. (1)

Optik (Stuttgart) (1)

C. J. R. Sheppard and S. Saghafi, Optik (Stuttgart) 110, 487 (1999).

Phys. Rev. A (1)

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

Other (1)

L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge U. Press, 1995), pp. 287-290.

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Equations (19)

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( 2 ρ 2 + 1 ρ ρ + 2 z 2 + k 2 ) F ( ρ , z ) = 0 ,
G out ( ρ , z ) = exp ( i k r ) 4 π r ,
G in ( ρ , z ) = exp ( i k r ) 4 π r = G out * ( ρ , z )
F out + ( ρ , z ) = i b exp ( k b ) exp ( i k s ) s ,
s ( z ) = [ ρ 2 + ( z i b ) 2 ] 1 2 .
F out + 0 ( ρ , z ) = exp ( i k z ) ( i b z i b ) exp [ i k ρ 2 2 ( z i b ) ] .
F ̃ out + ( ρ , z ; t ) = C d ω exp ( i ω t ) F out + ( ρ , z ; ω ) .
F out + ( ρ , z ; ω ) = exp ( ρ 2 w 0 2 ) exp [ ( i ω r ω i ) z c ] .
ω 0 = 2 c w 0 2 ( i z ρ ) .
F in + ( ρ , z ) = i b exp ( k b ) exp ( i k s * ) s * .
F in + 0 ( ρ , z ) = exp ( i k z ) ( i b z + i b ) exp [ i k ρ 2 2 ( z + i b ) ] .
F ̃ in + ( ρ , z ; t ) = C d ω exp ( i ω t ) F in + ( ρ , z ; ω ) .
F + ( ρ , z ) = N out F out + ( ρ , z ) + N in F in + ( ρ , z ) ,
S z ( ρ , z ) = 1 2 Re [ i ω F + * ( ρ , z ) z F + ( ρ , z ) ] ,
S z ( ρ , z ) = 1 2 Re { i ω [ N out 2 F out + * ( ρ , z ) z F out + ( ρ , z ) + N in 2 F in + * ( ρ , z ) z F in + ( ρ , z ) ] } .
P = 0 d ρ 2 π ρ S z ( ρ , z ) .
P = ( π ω b 2 ) ( N out 2 N in 2 ) [ 1 exp ( k 2 w 0 2 ) ] .
F out ( ρ , z ) = F out + ( ρ , z ) = i b exp ( k b ) exp ( i k s * ) s * ,
F in ( ρ , z ) = F in + ( ρ , z ) = i b exp ( k b ) exp ( i k s ) s .

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