Abstract

The main purpose of this study is to find the wave path of a beam wave in an inhomogeneous medium in which the permittivity is assumed to decrease linearly in one direction. A two-dimensional Gaussian beam is considered which can be described as a superposition of a number of plane waves. Variations of amplitude of the beam are illustrated. There are some differences between the path of the beam and the ray path obtained by Fermat’s principle.

© 1976 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. L. M. Brekhovskikh, Waves in Layered Media (Academic, New York, 1960), pp. 168–232.
  2. S. Nemoto and T. Makimoto, J. Inst. Electron. Commun. Engrs. (Jpn.) 53-B, 217 (1971).
  3. B. R. Horowitz and T. Tamir, J. Opt. Soc. Am. 61, 586 (1971).
    [Crossref]
  4. H. K. V. Lotsch, Optik 32, 116, 189, 299, and 553 (1970/71).
  5. B. R. Horowitz and T. Tamir, Appl. Phys. 1, 31 (1973).
    [Crossref]

1973 (1)

B. R. Horowitz and T. Tamir, Appl. Phys. 1, 31 (1973).
[Crossref]

1971 (2)

S. Nemoto and T. Makimoto, J. Inst. Electron. Commun. Engrs. (Jpn.) 53-B, 217 (1971).

B. R. Horowitz and T. Tamir, J. Opt. Soc. Am. 61, 586 (1971).
[Crossref]

Brekhovskikh, L. M.

L. M. Brekhovskikh, Waves in Layered Media (Academic, New York, 1960), pp. 168–232.

Horowitz, B. R.

B. R. Horowitz and T. Tamir, Appl. Phys. 1, 31 (1973).
[Crossref]

B. R. Horowitz and T. Tamir, J. Opt. Soc. Am. 61, 586 (1971).
[Crossref]

Lotsch, H. K. V.

H. K. V. Lotsch, Optik 32, 116, 189, 299, and 553 (1970/71).

Makimoto, T.

S. Nemoto and T. Makimoto, J. Inst. Electron. Commun. Engrs. (Jpn.) 53-B, 217 (1971).

Nemoto, S.

S. Nemoto and T. Makimoto, J. Inst. Electron. Commun. Engrs. (Jpn.) 53-B, 217 (1971).

Tamir, T.

B. R. Horowitz and T. Tamir, Appl. Phys. 1, 31 (1973).
[Crossref]

B. R. Horowitz and T. Tamir, J. Opt. Soc. Am. 61, 586 (1971).
[Crossref]

Appl. Phys. (1)

B. R. Horowitz and T. Tamir, Appl. Phys. 1, 31 (1973).
[Crossref]

J. Inst. Electron. Commun. Engrs. (Jpn.) (1)

S. Nemoto and T. Makimoto, J. Inst. Electron. Commun. Engrs. (Jpn.) 53-B, 217 (1971).

J. Opt. Soc. Am. (1)

Optik (1)

H. K. V. Lotsch, Optik 32, 116, 189, 299, and 553 (1970/71).

Other (1)

L. M. Brekhovskikh, Waves in Layered Media (Academic, New York, 1960), pp. 168–232.

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 (3)

FIG. 1
FIG. 1

Geometry for a limited beam wave in an inhomogeneous medium.

FIG. 2
FIG. 2

Amplitudes of the beam wave. aλ = 0.1, ϕ = 60°, bλ = 0.007, z0/λ = 50.

FIG. 3
FIG. 3

Comparison between wave theory and ray theory denoted by dotted and solid lines, respectively. aλ = 0.1, ϕ = 60°, bλ = 0.007, z0/λ = 50.

Equations (11)

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

2 E x y 2 + 2 E x z 2 + ω 2 μ 0 0 ( z ) E x = 0 ,
E i x i ( y i , x i ) = 1 2 π - + A ( α ) exp [ - j z i ( k 0 2 - α 2 ) 1 / 2 - j y i α ] d α ,
A ( α ) = - E i x i ( y i , 0 ) exp ( j α y i ) d y i .
E i x ( y , z ) = 1 2 π - A ( α ) exp [ - j ( z + z 0 ) ( k 0 2 - p 2 ) 1 / 2 - j y p ] d α ,
( z ) = 0 ( 1 - b z ) ,
E x ( y , z ) = 1 π - A ( α ) A i ( w ) exp [ - j z 0 ( k 0 2 - p 2 ) 1 / 2 - j y p ] d α { A i ( w ) } z = 0 + j 1 / ( k 0 2 - p 2 ) 1 / 2 { A i ( w ) } z = 0 ,
E x i ( y i , 0 ) = exp ( - ( a y i ) 2 ) ,
A ( α ) = ( π / a ) exp ( - ( α 2 / 4 a 2 ) ) .
[ x y - y p I z - z ] = [ 1 0 0 0 cos ϕ p sin ϕ p 0 - sin ϕ p cos ϕ p ] [ X I Y I Z I ]
ϕ p = sin - 1 ( sin ϕ / 1 - b z p ) ,
y p I = z 0 tan ϕ + ( 2 / b ) sin ϕ ( cos ϕ - cos 2 ϕ - b z p ) .