Abstract

The relationship between the mode content and the fractional Fourier and fractional Hankel transforms of a function is established. It is shown that the Laguerre–Gauss spectrum of a rotationally symmetric wave front can be determined from the wave front’s fractional Hankel transforms taken at the optical axis.

© 1999 Optical Society of America

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References

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  1. D. Mendlovic and H. M. Ozaktas, J. Opt. Soc. Am. A 10, 1875 (1993).
    [CrossRef]
  2. L. Yu, Y. Ku, X. Zheng, M. C. Huang, M. Chen, W. Huang, and Z. Zhu, Opt. Lett. 23, 1158 (1998).
    [CrossRef]
  3. A. W. Lohmann, J. Opt. Soc. Am. A 10, 2181 (1993).
    [CrossRef]
  4. A. Sahin, H. M. Ozaktas, and D. Mendlovic, Appl. Opt. 37, 2130 (1998).
    [CrossRef]
  5. M. G. Raymer, M. Beck, and D. F. McAlister, Phys. Rev. Lett. 72, 1137 (1994).
    [CrossRef] [PubMed]

1998

1994

M. G. Raymer, M. Beck, and D. F. McAlister, Phys. Rev. Lett. 72, 1137 (1994).
[CrossRef] [PubMed]

1993

Beck, M.

M. G. Raymer, M. Beck, and D. F. McAlister, Phys. Rev. Lett. 72, 1137 (1994).
[CrossRef] [PubMed]

Chen, M.

Huang, M. C.

Huang, W.

Ku, Y.

Lohmann, A. W.

McAlister, D. F.

M. G. Raymer, M. Beck, and D. F. McAlister, Phys. Rev. Lett. 72, 1137 (1994).
[CrossRef] [PubMed]

Mendlovic, D.

Ozaktas, H. M.

Raymer, M. G.

M. G. Raymer, M. Beck, and D. F. McAlister, Phys. Rev. Lett. 72, 1137 (1994).
[CrossRef] [PubMed]

Sahin, A.

Yu, L.

Zheng, X.

Zhu, Z.

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Equations (27)

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Fu1,u2,α1,α2=Rα1,α2fxu=-fxKα1x1,u1×Kα2x2,u2dx,
Kαjxj,uj=1-i cotαj2π1/2×expicos αjxj2+uj2-2xjuj2 sin αj.
Ψnx=π2nn!-1/2 exp-x2/2Hnx,
RαΨnxu=exp-iαnΨnu,
-ΨnxΨmxdx=0nm1n=m,
fx=n=0m=0fn,mΨnx1Ψmx2,
fn,m=--Ψnx1Ψmx2fx1,x2dx1dx2.
Fu1,u2,α1,α2=Rα1,α2fxu=n=0m=0fn,m exp-iα1n+α2m×Ψnu1Ψmu2.
Zu,p=02π02πRα1,α2fxu×expiα1p1+α2p2dα1dα2,
Zu,p=n=0m=0fn,mΨnu1Ψmu2×δp1-nδp2-m,
Zu0,n,m=fn,mΨnu1,0Ψmu2,0.
Z0,2n,2m=f2n,2mΨ2n0Ψ2m0.
Ψ2n0=-1n2n!2nπ1/4n!n.
Fu,α=Rαfxu=0fxHαx,uxdx,
Hαx,u=1-i cot αJ0xu/sin α×expi cot αx2+u2/2
Φnx=2Lnx2exp-x2/2,
RαΦnxu=exp-2iαnΦnu,
0ΦnxΦmxxdx=0nm1n=m,
fx=n=0fnΦnx,
fn=0Φnxfxxdx.
Fu,α=n=0fn exp-2iαnΦnu.
Su,p=0πFu,αexpi2αpdα,
Su,p=n=0fnΦnuδp-n,
Su0,n=fnΦnu0.
S0,n=fn.
Fu,α=0ρFu,αdu,
fn=Su,n/Fu,α.

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