Abstract

A simple electric multipole of finite size in the form of a spherical current sheet with a surface current density in the θ direction varying as sin2θ is considered. The electromagnetic fields outside the spherical surface are of the same form as that of the corresponding point electric multipole situated at the origin and oriented in the z direction. The power is separated into the radiative and the reactive parts and compared with the separation made on the basis of propagating and evanescent waves. The evanescent waves contribute only to the reactive power, and the propagating waves contribute to both the radiative and the reactive powers. The power flux density is also separated into the real and the reactive parts, and the characteristics of the two parts of the power flux density are discussed.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. T. Padhi and S. R. Seshadri, “Radiated and reactive powers in a magnetoionic medium,” Proc. IEEE 55, 1123-1125 (1967).
  2. S. R. Seshadri, Fundamentals of Transmission Lines and Electromagnetic Fields (Addison-Wesley, 1971), pp. 67-71.
  3. S. R. Seshadri, “Constituents of power of an electric dipole of finite size,” J. Opt. Soc. Am. A 25, 805-810 (2008).
    [CrossRef]
  4. S. R. Seshadri, Fundamentals of Transmission Lines and Electromagnetic Fields (Addison-Wesley, 1971), pp. 223-227.
  5. E. Wolf and J. T. Foley, “Do evanescent waves contribute to the far field?” Opt. Lett. 23, 16-18 (1998).
    [CrossRef]

2008 (1)

1998 (1)

1967 (1)

T. Padhi and S. R. Seshadri, “Radiated and reactive powers in a magnetoionic medium,” Proc. IEEE 55, 1123-1125 (1967).

Foley, J. T.

Padhi, T.

T. Padhi and S. R. Seshadri, “Radiated and reactive powers in a magnetoionic medium,” Proc. IEEE 55, 1123-1125 (1967).

Seshadri, S. R.

S. R. Seshadri, “Constituents of power of an electric dipole of finite size,” J. Opt. Soc. Am. A 25, 805-810 (2008).
[CrossRef]

T. Padhi and S. R. Seshadri, “Radiated and reactive powers in a magnetoionic medium,” Proc. IEEE 55, 1123-1125 (1967).

S. R. Seshadri, Fundamentals of Transmission Lines and Electromagnetic Fields (Addison-Wesley, 1971), pp. 223-227.

S. R. Seshadri, Fundamentals of Transmission Lines and Electromagnetic Fields (Addison-Wesley, 1971), pp. 67-71.

Wolf, E.

J. Opt. Soc. Am. A (1)

Opt. Lett. (1)

Proc. IEEE (1)

T. Padhi and S. R. Seshadri, “Radiated and reactive powers in a magnetoionic medium,” Proc. IEEE 55, 1123-1125 (1967).

Other (2)

S. R. Seshadri, Fundamentals of Transmission Lines and Electromagnetic Fields (Addison-Wesley, 1971), pp. 67-71.

S. R. Seshadri, Fundamentals of Transmission Lines and Electromagnetic Fields (Addison-Wesley, 1971), pp. 223-227.

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 (62)

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

J ( r ) = z ̂ d I m δ ( r ) z .
( 2 + k 2 ) Λ z ( r ) = μ d I m δ ( r ) z ,
A z ( r ) = μ d I m z exp ( i k r ) 4 π r = μ d I m k 2 exp ( i k r ) 4 π ( 1 i k r + 1 k 2 r 2 ) cos θ .
A r ( r , θ ) = μ d I m k 2 exp ( i k r ) 4 π ( 1 i k r + 1 k 2 r 2 ) cos 2 θ ,
A θ ( r , θ ) = μ d I m k 2 exp ( i k r ) 4 π ( 1 i k r + 1 k 2 r 2 ) cos θ sin θ ,
A ϕ ( r , θ ) = 0 .
H r ( r , θ ) = H θ ( r , θ ) = 0 ,
H ϕ ( r , θ ) = i d I m k 3 sin 2 θ exp ( i k r ) 8 π ( 1 i k r + 3 k 2 r 2 3 i k 3 r 3 ) .
E r ( r , θ ) = i d I m k 3 η 0 ( 3 cos 2 θ + 1 ) exp ( i k r ) 8 π ( 1 k 2 r 2 3 i k 3 r 3 3 k 4 r 4 ) ,
E θ ( r , θ ) = i d I m k 3 η 0 sin 2 θ exp ( i k r ) 8 π ( 1 i k r + 3 k 2 r 2 6 i k 3 r 3 6 k 4 r 4 ) ,
E ϕ ( r , θ ) = 0 .
J ( r , θ ) = θ ̂ J θ sin 2 θ δ ( r a ) = J * ( r , θ ) ,
A z ( r ) = μ d M z sin k r 4 π r = μ d M k 2 4 π ( cos k r k r sin k r k 2 r 2 ) cos θ .
A r ( r , θ ) = μ d M k 2 4 π ( cos k r k r sin k r k 2 r 2 ) cos 2 θ ,
A θ ( r , θ ) = μ d M k 2 4 π ( cos k r k r sin k r k 2 r 2 ) cos θ sin θ ,
A ϕ ( r , θ ) = 0 .
H r ( r , θ ) = H θ ( r , θ ) = 0 ,
H ϕ ( r , θ ) = d M k 3 8 π sin 2 θ ( sin k r k r + 3 cos k r k 2 r 2 3 sin k r k 3 r 3 ) ,
E r ( r , θ ) = i η 0 d M k 3 8 π ( 1 + 3 cos 2 θ ) ( sin k r k 2 r 2 + 3 cos k r k 3 r 3 3 sin k r k 4 r 4 ) ,
E θ ( r , θ ) = i η 0 d M k 3 8 π sin 2 θ ( cos k r k r 3 sin k r k 2 r 2 6 cos k r k 3 r 3 + 6 sin k r k 4 r 4 ) ,
E ϕ ( r , θ ) = 0 .
M = M N I m M D ,
M N = exp ( i k a ) ( 1 i k a + 3 k 2 a 2 6 i k 3 a 3 6 k 4 a 4 ) ,
M D = cos k a k a 3 sin k a k 2 a 2 6 cos k a k 3 a 3 + 6 sin k a k 4 a 4 ,
J θ sin 2 θ = H ϕ ( r = a , θ ) H ϕ ( r = a + , θ ) .
J θ = d k I m 8 π a 2 M D .
P C = P R + i P I = 1 2 E ( r ) J * ( r ) d r ,
P C = J θ π a 2 0 π d θ sin θ sin 2 θ E θ ( a , θ ) .
P C = 2 15 J θ I m k 3 a 2 d η 0 exp ( i k a ) ( 1 k a + i 3 k 2 a 2 6 k 3 a 3 i 6 k 4 a 4 ) .
P C = η 0 d 2 I m 2 k 4 60 π S ( k a ) ,
S ( k a ) = exp ( i k a ) M D ( 1 k a + i 3 k 2 a 2 6 k 3 a 3 i 6 k 4 a 4 ) .
S ( r , θ ) = r ̂ η 0 d 2 I m 2 k 4 128 π 2 sin 2 2 θ r 2 .
P 0 = 0 2 π d ϕ 0 π d θ sin θ r 2 η 0 d 2 I m 2 k 4 sin 2 2 θ 128 π 2 r 2 = η 0 d 2 I m 2 k 4 60 π .
Re S ( k a ) = 1 ,
Im S ( k a ) = S N M D ,
S N = sin k a k a + 3 cos k a k 2 a 2 6 sin k a k 3 a 3 6 cos k a k 4 a 4 .
Im S ( k a ) = 30 k 5 a 5 for k a 1 .
S ( r , θ ) = S R ( r , θ ) + i S I ( r , θ ) ,
S R ( r , θ ) = r ̂ S R r ( r , θ ) = r ̂ η 0 d 2 I m 2 k 6 128 π 2 sin 2 2 θ k 2 r 2 ,
S I ( r , θ ) = r ̂ S I r ( r , θ ) + θ ̂ S I θ ( r , θ ) ,
S I r ( r , θ ) = η 0 d 2 I m 2 k 6 128 π 2 sin 2 2 θ ( 3 k 5 r 5 + 18 k 7 r 7 ) ,
S I θ ( r , θ ) = η 0 d 2 I m 2 k 6 128 π 2 ( 3 cos 2 θ + 1 ) sin 2 θ ( 1 k 3 r 3 + 3 k 5 r 5 + 9 k 7 r 7 ) .
( 2 ρ 2 + 1 ρ ρ + 2 z 2 + k 2 ) A z ( ρ , z ) = μ d I m δ ( ρ ) 2 π ρ z δ ( z ) .
A z ( ρ , z ) = 0 d η η J 0 ( η ρ ) A ¯ z ( η , z ) ,
δ ( z ) = 0 d η η J 0 ( η ρ ) ,
( 2 z 2 + ζ 2 ) A ¯ z ( η , z ) = μ d I m 2 π z δ ( z ) ,
ζ = ( k 2 η 2 ) 1 2 .
A ¯ z ( η , z ) = ± μ d I m 4 π exp ( i ζ z ) ,
A z ( ρ , z ) = ± μ d I m 4 π 0 d η η J 0 ( η ρ ) exp ( i ζ z ) .
E z ( ρ , z ) = 1 i ω μ ε ( 2 ρ 2 + 1 ρ ρ ) A z ( ρ , z ) .
E z ( ρ , z ) z = η 0 d I m 4 π k 0 d η η 3 ζ J 0 ( η ρ ) exp ( i ζ z ) .
P C = 1 2 d I m [ E z ( ρ , z ) z ] z = 0 , ρ = 0 .
P C = η 0 d 2 I m 2 8 π k 0 d η η 3 ζ .
P C = η 0 d 2 I m 2 8 π k 0 k d η η 3 ζ = η 0 d 2 I m 2 k 4 60 π ,
A z ( ρ , z ) = 1 2 π A ¯ z ( ρ , ζ ) exp ( i ζ z ) d ζ ,
δ ( z ) = 1 2 π exp ( i ζ z ) d ζ .
( 2 ρ 2 + 1 ρ ρ + η 2 ) A ¯ z ( ρ , ζ ) = μ d I m δ ( ρ ) 2 π ρ i ζ ,
η = ( k 2 ζ 2 ) 1 2 .
A z ( ρ , z ) = μ d I m 8 π d ζ ζ H 0 ( 1 ) ( η ρ ) exp ( i ζ z ) ,
E z ( ρ , z ) z = η 0 d I m 8 π k d ζ ζ 2 ( k 2 ζ 2 ) H 0 ( 1 ) ( η ρ ) exp ( i ζ z ) .
P C = η 0 d 2 I m 2 16 π k d ζ ζ 2 ( k 2 ζ 2 ) [ H 0 ( 1 ) ( η ρ ) ] ρ = 0 .
P R = η 0 d 2 I m 2 16 π k k k d ζ ζ 2 ( k 2 ζ 2 ) = η 0 d 2 I m 2 k 4 60 π ,

Metrics