Abstract

The equivalent source theorem, which is an important technique in the study of radiation and scattering by apertures, is improved by using the two axioms of the modified theory of physical optics. The method is applied to the problem of radiation of electromagnetic waves by a parallel plate waveguide. The results are investigated numerically.

© 2009 Optical Society of America

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References

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  1. R. F. Harrington, Time-Harmonic Electromagnetic Fields (IEEE-Wiley, 2001).
    [CrossRef]
  2. C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, 1989).
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  4. Y. Z. Umul, “Modified theory of physical optics,” Opt. Express 12, 4959-4972 (2004).
    [CrossRef] [PubMed]
  5. Y. Z. Umul, “Edge dislocation waves in the diffraction process by an impedance half-plane,” J. Opt. Soc. Am. A 24, 507-511 (2007).
    [CrossRef]
  6. Y. Z. Umul, “Young-Kirchhoff-Rubinowicz theory of diffraction in the light of Sommerfeld's solution,” J. Opt. Soc. Am. A 25, 2734-2742 (2008).
    [CrossRef]
  7. Y. Z. Umul, “Modified diffraction theory of Kirchhoff,” J. Opt. Soc. Am. A 25, 1850-1860 (2008).
    [CrossRef]
  8. Y. Z. Umul, “The relation between the boundary diffraction wave theory and physical optics,” Opt. Commun. 281, 4844-4848 (2008).
    [CrossRef]
  9. A. S. Marathay and J. F. McCalmont, “Vector diffraction theory for electromagnetic waves,” J. Opt. Soc. Am. A 18, 2585-2593 (2001).
    [CrossRef]
  10. J. A. Romero and L. Hernandez, “Vectorial approach to Huygens's principle for plane waves: circular aperture and zone plates,” J. Opt. Soc. Am. A 23, 1141-1145 (2006).
    [CrossRef]
  11. J. A. Romero and L. Hernandez, “Diffraction by a circular aperture: an application of the vectorial theory of Huygens's principle in the near field,” J. Opt. Soc. Am. A 25, 2040-2043 (2008).
    [CrossRef]
  12. R. P. Feynman, “Space-time approach to quantum electrodynamics,” Phys. Rev. 76, 769-789 (1949).
    [CrossRef]
  13. J. Gribbin, Schrödinger's Kittens and the Search for Reality (Orion/Dent, 1995).

2008

2007

2006

2004

2001

1949

R. P. Feynman, “Space-time approach to quantum electrodynamics,” Phys. Rev. 76, 769-789 (1949).
[CrossRef]

Balanis, C. A.

C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, 1989).

Feynman, R. P.

R. P. Feynman, “Space-time approach to quantum electrodynamics,” Phys. Rev. 76, 769-789 (1949).
[CrossRef]

Gribbin, J.

J. Gribbin, Schrödinger's Kittens and the Search for Reality (Orion/Dent, 1995).

Harrington, R. F.

R. F. Harrington, Time-Harmonic Electromagnetic Fields (IEEE-Wiley, 2001).
[CrossRef]

Hernandez, L.

Marathay, A. S.

McCalmont, J. F.

Romero, J. A.

Stutzman, W. L.

W. L. Stutzman and G. A. Thiele, Antenna Theory and Design (Wiley, 1988).

Thiele, G. A.

W. L. Stutzman and G. A. Thiele, Antenna Theory and Design (Wiley, 1988).

Umul, Y. Z.

J. Opt. Soc. Am. A

Opt. Commun.

Y. Z. Umul, “The relation between the boundary diffraction wave theory and physical optics,” Opt. Commun. 281, 4844-4848 (2008).
[CrossRef]

Opt. Express

Phys. Rev.

R. P. Feynman, “Space-time approach to quantum electrodynamics,” Phys. Rev. 76, 769-789 (1949).
[CrossRef]

Other

J. Gribbin, Schrödinger's Kittens and the Search for Reality (Orion/Dent, 1995).

R. F. Harrington, Time-Harmonic Electromagnetic Fields (IEEE-Wiley, 2001).
[CrossRef]

C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, 1989).

W. L. Stutzman and G. A. Thiele, Antenna Theory and Design (Wiley, 1988).

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Figures (12)

Fig. 1
Fig. 1

Equivalent source theorem for a volume source distribution.

Fig. 2
Fig. 2

Geometry of a discontinuous surface.

Fig. 3
Fig. 3

Application of the equivalent source theorem.

Fig. 4
Fig. 4

Variable unit vector of the edge.

Fig. 5
Fig. 5

Scattered rays in PO.

Fig. 6
Fig. 6

Definition of the variable unit normal vector on the aperture.

Fig. 7
Fig. 7

Geometry of the waveguide.

Fig. 8
Fig. 8

Variable unit normal vectors of the aperture.

Fig. 9
Fig. 9

Comparison of the theories for n = 1 .

Fig. 10
Fig. 10

Zoomed version of Fig. 9.

Fig. 11
Fig. 11

Comparison of the electric fields for n = 2 .

Fig. 12
Fig. 12

Comparison of the electric fields for n = 3 .

Equations (60)

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E i = 1 j w ϵ 0 μ 0 × × A ,
H i = 1 μ 0 × A ,
A = μ 0 4 π V 1 J ν exp ( j k R ) R d V ,
J s = n 1 × H i S ,
M s = n 1 × E i S ,
E i = 1 j w μ 0 ϵ 0 × × A 1 ϵ 0 × F ,
H i = 1 j w μ 0 ϵ 0 × × F + 1 μ 0 × A ,
A = μ 0 4 π S n 1 × H i S exp ( j k R ) R d S ,
F = ϵ 0 4 π S n 1 × E i S exp ( j k R ) R d S ,
M s = 2 n 1 × E i S .
E i = 1 ϵ 0 × F ,
H i = 1 j w μ 0 ϵ 0 × × F
F = ϵ 0 2 π S n 1 × E i S exp ( j k R ) R d S
J s = 2 n 1 × H i S ,
E i = 1 j w μ 0 ϵ 0 × × A ,
H i = 1 μ 0 × A
A = μ 0 2 π S n 1 × H i S exp ( j k R ) R d S ,
e i . ν u + e r . ν u = 0 ,
e i . ν u + e d . ν u = 0 ,
2 ν + α β = π
ν = π 2 + β α 2 .
n 1 = sin β + α 2 t cos β + α 2 n
H x = H n cos ( n π a y ) exp ( j k x x ) ,
H y = j k x a n π H n sin ( n π a y ) exp ( j k x x ) ,
E z = j k Z 0 a n π H n sin ( n π a y ) exp ( j k x x )
k x = k 2 ( n π a ) 2 ,
H x = H n 2 [ exp ( j n π a y ) + exp ( j n π a y ) ] exp ( j k x x ) ,
H y = k x a 2 n π H n [ exp ( j n π a y ) exp ( j n π a y ) ] exp ( j k x x ) ,
E z = k Z 0 a 2 n π H n [ exp ( j n π a y ) exp ( j n π a y ) ] exp ( j k x x ) ,
H x = H n 2 { exp [ j k ρ cos ( ϕ + α n ) ] + exp [ j k ρ cos ( ϕ α n ) ] } ,
H y = k x a 2 n π H n { exp [ j k ρ cos ( ϕ + α n ) ] exp [ j k ρ cos ( ϕ α n ) ] } ,
E z = k Z 0 a 2 n π H n { exp [ j k ρ cos ( ϕ + α n ) ] exp [ j k ρ cos ( ϕ α n ) ] } ,
n 1 = cos β + η n 2 e x + sin β + η n 2 e y ,
n 2 = cos β + η n 2 e x sin β + η n 2 e y
H = H 1 + H 2 ,
H 1 = H n 2 ( e x sin η n cos η n e y ) exp [ j k ρ cos ( ϕ α n ) ] ,
H 2 = H n 2 ( e x + sin η n cos η n e y ) exp [ j k ρ cos ( ϕ + α n ) ] .
J s = J 1 + J 2 ,
J 1 = 2 n 1 × H 1 x = 0 ,
J 2 = 2 n 2 × H 2 x = 0
J 1 = H n cos η n sin β η n 2 exp ( j k y cos η n ) e z ,
J 2 = H n cos η n sin β η n 2 exp ( j k y cos η n ) e z .
A = A 1 + A 2
A 1 = e z μ 0 H n 4 π cos η n y = 0 a z = sin β η n 2 exp ( j k y cos η n ) exp ( j k R 1 ) R 1 d z d y ,
A 2 = e z μ 0 H n 4 π cos η n y = 0 a z = sin β η n 2 exp ( j k y cos η n ) exp ( j k R 1 ) R 1 d z d y .
A 1 = e z μ 0 H n exp ( j π 4 ) 2 2 π cos η n y = 0 a sin β η n 2 exp ( j k y cos η n ) exp ( j k R ) k R d y ,
A 2 = e z μ 0 H n exp ( j π 4 ) 2 2 π cos η n y = 0 a sin β η n 2 exp ( j k y cos η n ) exp ( j k R ) k R d y
E j w A
E 1 j w A 1 ,
E 2 j w A 2 ,
E 1 e z k Z 0 H n exp ( j π 4 ) 2 2 π cos η n y = 0 a sin β η n 2 exp ( j k y cos η n ) exp ( j k R ) k R d y ,
E 2 e z k Z 0 H n exp ( j π 4 ) 2 2 π cos η n y = 0 a sin β η n 2 exp ( j k y cos η n ) exp ( j k R ) k R d y .
J s = 2 n × H i S .
J s = e z 2 j k x a n π H n sin ( n π a y )
A = e z μ 0 k x a H n n π 2 π exp ( j π 4 ) 0 a sin ( n π a y ) exp ( j k R ) k R d y ,
E = e z k Z 0 k x a H n n π 2 π exp ( j π 4 ) 0 a sin ( n π a y ) exp ( j k R ) k R d y
E e z k Z 0 H n exp ( j π 4 ) 2 π cos η n y = 0 a sin β η n 2 sin ( n π a y ) exp ( j k R ) k R d y
E e z j k Z 0 H n 2 cos η n y = 0 a sin β η n 2 sin ( n π a y ) H 0 ( 2 ) ( k R ) d y
E = e z j k Z 0 k x a H n 2 n π 0 a sin ( n π a y ) H 0 ( 2 ) ( k R ) d y
E = e z j Z 0 k sin η n H n 2 cos η n 0 a sin ( n π a y ) H 0 ( 2 ) ( k R ) d y

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