Abstract

The propagation characteristics of a scalar Gaussian beam in a homogeneous anisotropic medium are considered. The medium is described by a generic wave-number profile wherein the field is formulated by a Gaussian plane-wave distribution and the propagation is obtained by saddle-point asymptotics to extract the Gaussian beam phenomenology in the anisotropic environment. The resultant field is parameterized in terms of e.g., the spatial evolution of the Gaussian beam’s curvature, beam width, which are mapped to local geometrical properties of the generic wave-number profile.

© 2003 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |

  1. Y.-J. Cai, Q. Lin, and D. Ge, J. Opt. Soc. Am. A 19, 2036 (2002).
    [CrossRef]
  2. Y. J. Li, V. Gurevich, M. Krichever, J. Katz, and E. Marom, Appl. Opt. 40, 2709 (2001).
    [CrossRef]
  3. A. V. Vershubskii, V. N. Parygin, and Yu. G. Rezvov, Acoust. Phys. 47, 22 (2001).
    [CrossRef]
  4. L. I. Perez M. T. Garea, Optik (Stuttgart) 111, 297 (2000).
  5. L. I. Perez, J. Mod. Opt. 47, 1645 (2000).
    [CrossRef]
  6. E. Poli, G. V. Pereverzev, and A. G. Peeters, Phys. Plasmas 6, 5 (1999).
    [CrossRef]
  7. R. Simon N. Mukunda, J. Opt. Soc. Am. A 15, 1361 (1998).
    [CrossRef]
  8. A. V. Vershubskii and V. N. Parygin, Acoust. Phys. 44, 23 (1998).
  9. C. W. Tam, Opt. Eng. 37, 229 (1998).
    [CrossRef]
  10. V. N. Parygi and A. V. Vershoubskiy, Photon. Optoelectron. 4, 55 (1997).
  11. G. D. Landry and T. A. Maldonado, Appl. Opt. 35, 5870 (1996).
    [CrossRef] [PubMed]
  12. X.-B. and Wu R. Wei, Radio Sci. 30, 403 (1995).
    [CrossRef]
  13. S. Nowak and A. Orefice, Phys. Fluids B 5, 1945 (1993).
    [CrossRef]
  14. B. Lu, B. Zhang, X. Xu, and B. Cai, Optik (Stuttgart) 94, 39 (1993).
  15. T. Sonoda and S. Kozaki, Trans. Inst. Electron. Inf. Commun. Eng. B-II J72B-II, 468 (1989).
  16. A. Hanyga, Geophys. J. R. Astron. Soc. 85, 473 (1986).
    [CrossRef]
  17. R. Simon, J. Opt. 14, 92 (1985).
  18. R. Simon, Opt. Commun. 55, 381 (1985).
    [CrossRef]
  19. T. Melamed, J. Electromagn. Waves Appl. 11, 739 (1997).
    [CrossRef]
  20. K. Sundar, N. Mukunda, R. Simon, J. Opt. Soc. Am. A 12, 560 (1995).
    [CrossRef]
  21. M. Spies, NDT & E Int. 33, 155 (2000).
    [CrossRef]
  22. S. Y. Shin and L. B. Felsen, Applied Phys. 5, 239 (1974).

Other (22)

Y.-J. Cai, Q. Lin, and D. Ge, J. Opt. Soc. Am. A 19, 2036 (2002).
[CrossRef]

Y. J. Li, V. Gurevich, M. Krichever, J. Katz, and E. Marom, Appl. Opt. 40, 2709 (2001).
[CrossRef]

A. V. Vershubskii, V. N. Parygin, and Yu. G. Rezvov, Acoust. Phys. 47, 22 (2001).
[CrossRef]

L. I. Perez M. T. Garea, Optik (Stuttgart) 111, 297 (2000).

L. I. Perez, J. Mod. Opt. 47, 1645 (2000).
[CrossRef]

E. Poli, G. V. Pereverzev, and A. G. Peeters, Phys. Plasmas 6, 5 (1999).
[CrossRef]

R. Simon N. Mukunda, J. Opt. Soc. Am. A 15, 1361 (1998).
[CrossRef]

A. V. Vershubskii and V. N. Parygin, Acoust. Phys. 44, 23 (1998).

C. W. Tam, Opt. Eng. 37, 229 (1998).
[CrossRef]

V. N. Parygi and A. V. Vershoubskiy, Photon. Optoelectron. 4, 55 (1997).

G. D. Landry and T. A. Maldonado, Appl. Opt. 35, 5870 (1996).
[CrossRef] [PubMed]

X.-B. and Wu R. Wei, Radio Sci. 30, 403 (1995).
[CrossRef]

S. Nowak and A. Orefice, Phys. Fluids B 5, 1945 (1993).
[CrossRef]

B. Lu, B. Zhang, X. Xu, and B. Cai, Optik (Stuttgart) 94, 39 (1993).

T. Sonoda and S. Kozaki, Trans. Inst. Electron. Inf. Commun. Eng. B-II J72B-II, 468 (1989).

A. Hanyga, Geophys. J. R. Astron. Soc. 85, 473 (1986).
[CrossRef]

R. Simon, J. Opt. 14, 92 (1985).

R. Simon, Opt. Commun. 55, 381 (1985).
[CrossRef]

T. Melamed, J. Electromagn. Waves Appl. 11, 739 (1997).
[CrossRef]

K. Sundar, N. Mukunda, R. Simon, J. Opt. Soc. Am. A 12, 560 (1995).
[CrossRef]

M. Spies, NDT & E Int. 33, 155 (2000).
[CrossRef]

S. Y. Shin and L. B. Felsen, Applied Phys. 5, 239 (1974).

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.


Figures (1)

Fig. 1
Fig. 1

Local beam coordinate frame for a Gaussian beam propagating in an anisotropic medium. The beam axis is directed along unit vector κˆ. The local transverse coordinates xb are given by the transformation in Eq. (13). The transverse local coordinates are located over the x1,x2 plane, which is in general nonorthogonal to the beam axis. The rotation transformation of x1,x2 into xb1,xb2 by α is carried out such that the resultant field in Eq. (16) exhibits Gaussian decay in the local coordinates.

Equations (24)

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

u˜0ξ=-d2xu0xexp-ikξ·x,
u0x=k/2π2d2ξu˜0ξexpikξ·x,
u0x=exp-½kx2/β,
u˜0ξ=2πβ/kexp-½kβξ2.
ur=βk2πd2ξ expikΦξ,r, Φξ,r=ξ·x+ζξz+i2βξ2.
ξΦ=x+ξζξ|ξsz+iβξs=0.
x+zξζ0=0,
κˆ=cos ϑ1,cos ϑ2,cos ϑ3,
cos ϑ1,2=-cos ϑ3ξ1,2ζ0, cos ϑ3=1ξ1ζ02+ξ2ζ02+11/2.
ΦΦ0+Φ1·ξ+½ξΦ2ξ,
Φ0=Φξ=0=ζ0z,    Φ1=Φξ=0=ξζ0z+x,
Φ2=iβ+ξ12ζ0zξ1ξ22ζ0zξ1ξ22ζ0ziβ+ξ22ζ0z,
ur=β-det Φ2expikSr, Sr=Φ0-½Φ1Φ2-1Φ1.
rb=Tr,    T=cos αsin α-cos ϑ2 sin α-cos ϑ1 cos α/cos ϑ3-sin αcos α-cos ϑ2 cos α+cos ϑ1 sin α/cos ϑ3001/cos ϑ3,
tan 2α=-2ξ1ξ22ζ0/ξ22ζ0-ξ12ζ0.
T-1=cos α-sin αcos ϑ1sin αcos αcos ϑ200cos ϑ3.
ur=β-Γ1Γ2×expikζ0zb cos ϑ3+12xb12Γ1+xb22Γ2,
Γ1,2=-ξ12ζ0z+ξ22ζ0z+2iβξ12ζ0z-ξ22ζ0z2+4ξ1ξ22ζ0z21/22.
Γ1,2=zba1,2-iβ, a1,2=cos ϑ3cos2αξ12ζ0-cos2 αsin2 α+ξ22ζ0sin2 α-cos2 α.
1Γ1,2=1R1,2+ikD1,22,
D1,2=F1,2/k1+a1,22zb-Z1,22/F1,221/2,
R1,2=a1,2zb-Z1,2+F1,22/a1,2zb-Z1,2,
Z1,2=-βi/a1,2,    F1,2=βr.
ur=-iβz-iβexpikz+½x2/z-iβ.

Metrics