Abstract

We define the accumulated Gouy phase shift as the on-axis phase accumulated by a Gaussian beam in passing through an optical system, in excess of the phase accumulated by a plane wave. We give an expression for the accumulated Gouy phase shift in terms of the parameters of the system through which the beam propagates. This quantity complements the beam diameter and the wave-front radius of curvature to constitute three parameters that uniquely characterize the beam with respect to a reference point in the system. Measurement of these parameters allows one to uniquely recover the parameters characterizing the first-order system through which the beam propagates.

© 1997 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).
  2. M. J. Bastiaans, “Wigner distribution function and its application to first-order optics,” J. Opt. Soc. Am. 69, 1710–1716 (1979).
    [Crossref]
  3. H. M. Ozaktas, D. Mendlovic, “Fractional Fourier optics,” J. Opt. Soc. Am. A 12, 743–751 (1995).
    [Crossref]
  4. K. B. Wolf, Integral Transforms in Science and Engineering (Plenum, New York, 1979).
  5. M. Nazarathy, J. Shamir, “First-order optics—a canonical operator representation: lossless systems,” J. Opt. Soc. Am. 72, 356–364 (1982).
    [Crossref]
  6. S. Abe, J. T. Sheridan, “Optical operations on wave functions as the Abelian subgroups of the special affine Fourier transformation,” Opt. Lett. 19, 1801–1803 (1994).
    [Crossref] [PubMed]
  7. A. E. Siegman, Lasers (University Science Books, Mill Valley, Calif., 1986).
  8. M. Nazarathy, A. Hardy, J. Shamir, “Generalized mode propagation in first-order optical systems with loss or gain,” J. Opt. Soc. Am. 72, 1409–1420 (1982).
    [Crossref]
  9. H. M. Ozaktas, B. Barshan, D. Mendlovic, L. Onural, “Convolution, filtering, and multiplexing in fractional Fourier domains and their relation to chirp and wavelet transforms,” J. Opt. Soc. Am. A 11, 547–559 (1994).
    [Crossref]
  10. A. W. Lohmann, “Image rotation, Wigner rotation, and the fractional Fourier transform,” J. Opt. Soc. Am. A 10, 2181–2186 (1993).
    [Crossref]
  11. H. M. Ozaktas, D. Mendlovic, “Fractional Fourier transform as a tool for analyzing beam propagation and spherical mirror resonators,” Opt. Lett. 19, 1678–1680 (1994).
    [Crossref] [PubMed]

1995 (1)

1994 (3)

1993 (1)

1982 (2)

1979 (1)

Abe, S.

Barshan, B.

Bastiaans, M. J.

Hardy, A.

Lohmann, A. W.

Mendlovic, D.

Nazarathy, M.

Onural, L.

Ozaktas, H. M.

Saleh, B. E. A.

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).

Shamir, J.

Sheridan, J. T.

Siegman, A. E.

A. E. Siegman, Lasers (University Science Books, Mill Valley, Calif., 1986).

Teich, M. C.

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).

Wolf, K. B.

K. B. Wolf, Integral Transforms in Science and Engineering (Plenum, New York, 1979).

J. Opt. Soc. Am. (3)

J. Opt. Soc. Am. A (3)

Opt. Lett. (2)

Other (3)

A. E. Siegman, Lasers (University Science Books, Mill Valley, Calif., 1986).

K. B. Wolf, Integral Transforms in Science and Engineering (Plenum, New York, 1979).

B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics (Wiley, New York, 1991).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Equations (41)

Equations on this page are rendered with MathJax. Learn more.

U(x, y, z)=A(x, y, z)exp(ikz),
A(x, y, z)=A1q(z) exp[ik(x2+y2)/2q(z)],
q(z)=z-iz0,
1q(z)=1r(z)+i λπw2(z),
A(x, y, z)=A0 w0w(z) exp-x2+y2w2(z)expiπ x2+y2λr(z)×exp[-iζ(z)],
w(z)=w01+z2/z02,r(z)=z(1+z02/z2),
ζ(z)=tan-1 z/z0,w0=λz0/π.
pout(x)=-h(x, x)pin(x)dx,
h(x, x)=K exp[iπ(αx2-2βxx+γx2)],
TABCDγ/β1/β-β+αγ/βα/β,
pout(x)=exp(ikL0)-h˜(x, x)pin(x)dx,
h˜(x, x)=1iB expiπB (Dx2-2xx+Ax2).
pout(x, y)=exp(ikL0)--h˜(x, x)h˜(y, y)×pin(x, y)dxdy.
ζ(z)=tan-1 πw2(z)λr(z).
-ζ˜=arg{pout(0, 0)}-arg{ pin(0, 0)}-kL0,
λqout=Aλqin+BCλqin+D.
wout2=win2A+Bλrin2+B2π2win2,
1rout=λC+Drin A+Bλrin+BDλπ2win4A+Bλrin2+B2π2win4.
tan ζ˜=BA+Bλrinπwin2.
A=woutwin cosζ˜-πwinwout sin ζ˜λrin,
B=πwinwout sin ζ˜,
C=Aλrout-Bπ2win4+1λrin A+BλrinA+Bλrin2+B2π2win4,
D=1+BCA.
pout(x, y)=exp(ikL0)--h˜(x, x)h˜(y, y)×pin(x, y)dxdy,
pin(x, y)=Ain w0win exp-x2+y2win2expiπ x2+y2λrin.
- exp(-x2r2-qx)dx=πr expq24r2.
pout(x, y)=Ain w0wout exp(ikL0)exp-x2+y2wout2×expiπ x2+y2λroutexp(-iζ˜),
wout2=win2A+Bλrin2+B2π2win2,
1rout=λC+Drin A+Bλrin+BDλπ2win4A+Bλrin2+B2π2win4,
tan ζ˜=BA+Bλrinπwin2.
tan ζ˜1=B1A1+B1λrin1πwin12,
tan ζ˜2=B2A2+B2λrout1πwout12.
ABCD=A2B2C2D2 A1B1C1D1.
ζ˜1+ζ˜2=ζ˜r=tan-1 BA+Bλrin1πwin12,
T1λd01.
Ain(x, y)=A0 w0win exp-x2+y2win2expiπ x2+y2λrin.
Aout(x, y)=A0 w0wout exp-x2+y2wout2expiπ x2+y2λrout×exp(-iζ˜),
tan ζ˜=λd1+drinπwin2.
T=10-1λf1,
Aout(x, y)=A0 w0win exp-x2+y2win2expiπ x2+y2λrin×exp-iπ x2λf.
TABCD1(A-1)/C01 10C1 1(D-1)/C01.

Metrics