Abstract

We consider a plane wave as it approaches a dielectric medium that is split along a plane parallel to the wave motion. As the wave penetrates into the two-layered medium, its phase velocity is different in the two regions of index n1 and n2. The deformation of the plane wave is studied. Plots of the field irradiance and phase are obtained by numerical evaluation of an integral. The analysis is based on the expansion of the field in terms of normal modes. Backscattering of the wave incident on the layered medium is ignored. The results presented here are closely related to interference microscopy, because the distortion of the plane wave caused by diffraction may show up as a fringe shift.

© 1974 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. A. Hale, The Interference Microscope in Biological Research (Livingston, Edinburgh, 1958).
  2. V. V. Shevchenko, Continuous Transitions in Open Waveguides (Golem, Boulder, Colo., 1971).
  3. D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1972).
  4. D. Marcuse, Bell Syst. Tech. J. 63, 63 (1973).
    [Crossref]
  5. D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974).

1973 (1)

D. Marcuse, Bell Syst. Tech. J. 63, 63 (1973).
[Crossref]

Hale, J. A.

J. A. Hale, The Interference Microscope in Biological Research (Livingston, Edinburgh, 1958).

Marcuse, D.

D. Marcuse, Bell Syst. Tech. J. 63, 63 (1973).
[Crossref]

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974).

D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1972).

Shevchenko, V. V.

V. V. Shevchenko, Continuous Transitions in Open Waveguides (Golem, Boulder, Colo., 1971).

Bell Syst. Tech. J. (1)

D. Marcuse, Bell Syst. Tech. J. 63, 63 (1973).
[Crossref]

Other (4)

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, New York, 1974).

J. A. Hale, The Interference Microscope in Biological Research (Livingston, Edinburgh, 1958).

V. V. Shevchenko, Continuous Transitions in Open Waveguides (Golem, Boulder, Colo., 1971).

D. Marcuse, Light Transmission Optics (Van Nostrand Reinhold, New York, 1972).

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 (4)

Fig. 1
Fig. 1

Schematic diagram of the problem. A plane wave approaches a two-layer medium. The media and wave front extend to infinity perpendicular to the plane of the drawing.

Fig. 2
Fig. 2

Irradiance |Eg|2 and phase ϕ of the field as a function of distance x/λ from the dielectric interface at z/λ = 10.

Fig. 3
Fig. 3

Same as Fig. 2, z/λ = 25.

Fig. 4
Fig. 4

Same as Fig. 2, z/λ = 46.

Equations (30)

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

n 1 > n 3 > n 2 .
n 2 k < β < n 1 k ,
y ( 1 ) = A e - γ x e - i β z ,             x > 0
y ( 1 ) = A ( cos σ x - γ σ sin σ x ) e - i β z ,             x < 0
A = { 4 ω μ 0 σ 2 P π β ( σ 2 + γ 2 ) } 1 2 ,
γ 2 = ( n 1 2 - n 2 2 ) k 2 - σ 2
β 2 = n 1 2 k 2 - σ 2 .
0 < β < n 2 k
0 < β < ,
y ( 2 ) = B cos ( ρ x ) e - i β z ,             x > 0
y ( 2 ) = B cos ( σ x ) e - i β z ,             x < 0
B = { 4 ω μ 0 P π β ( 1 + ρ / σ ) } 1 2
ρ 2 = σ 2 - ( n 1 2 - n 2 2 ) k 2 .
y ( 3 ) = C σ ρ sin ( ρ x ) e - i β z ,             x > 0
y ( 3 ) = C sin ( σ x ) e - i β z ,             x < 0
C = { 4 ω μ 0 P π β ( 1 + σ / ρ ) } 1 2 .
x = - i ω μ 0 y z ,
z = i ω μ 0 y x .
- 1 2 - y σ ( i ) x σ ( j ) * d x = P δ ( σ - σ ) δ i j .
E y = 0 V a ( σ ) y σ ( 1 ) d σ + V [ b ( σ ) y σ ( 2 ) + c ( σ ) y σ ( 3 ) ] d σ ,
V = ( n 1 2 - n 2 2 ) 1 2 k .
E y = A i e - i n 3 k z             for             z < 0.
a ( σ ) = β A i 2 ω μ 0 P - y σ ( 1 ) d x = A i σ γ { β π ω μ 0 P ( σ 2 + γ 2 ) } 1 2 ,
b ( σ ) = 0 ,
c ( σ ) = A i σ ρ 2 { β ρ π ω μ 0 P ( ρ + σ ) } 1 2 ( σ 2 - ρ 2 ) .
n 1 n 2 .
E y = 2 π A i { 0 V 1 γ e - γ x e - i β z d σ + V σ - ρ ρ 2 sin ( ρ x ) e - i β z d σ } for x > 0 ,
E y = 2 π A i { 0 V 1 γ [ cos σ x - γ σ sin σ x ] e - i β z d σ + V σ - ρ ρ 2 sin ( σ x ) e - i β z d σ } for             x < 0.
n 1 = 1.542 , n 2 = 1.518.
Δ ϕ = ( n 1 - n 2 ) k z ,