Abstract

The scattered fields from a black half plane which absorbs all the incoming electromagnetic energy are evaluated by defining a new modified theory of physical optics surface current. This current eliminates the reflected fields, coming from the first stationary point of the reflection integral and only creates a reflected diffracted field. The incident scattered fields are found from the same integral, written for the perfectly conducting half plane. The scattered fields are evaluated by using the stationary phase method and edge point technique. The evaluated fields are plotted numerically.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |

  1. F. Kottler, �??Diffraction at a black screen. I. Kirchhof�??s theory,�?? Prog. Opt. 4, 281-314 (1965).
    [CrossRef]
  2. A. Sommerfeld, Optics (Academic Press, New York, 1954).
  3. J. F. Nye, J. H. Hannay and W. Liang, �??Diffraction by a black half-plane: theory and observation,�?? Proc. Royal Soc. London A 449, 515-535 (1995).
    [CrossRef]
  4. J. F. Nye and W. Liang, �??Near-field diffraction by two slits in a black screen,�?? Proc. Royal Soc. London A 454, 1635-1658 (1998).
    [CrossRef]
  5. Y. Z. Umul, �??Modified theory of physical optics,�?? Opt. Express 12, 4959-4972 (2004), <a href="http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-20-4959.">http://www.opticsexpress.org/abstract.cfm?URI=OPEX-12-20-4959</a>.
    [CrossRef] [PubMed]
  6. L. B. Felsen and N. Marcuwitz, Radiation and scattering of waves (IEEE Press, New York, 1994).
    [CrossRef]
  7. M. Berry, �??Geometry of phase and polarization singularities, illustrated by edge diffraction and the tides,�??in Singular Optics (optical Vertices): Fundamentals and Applications II, Proc. SPIE 4403, 1-12 (2001).
    [CrossRef]

Opt. Express

Proc. Royal Soc. London A

J. F. Nye, J. H. Hannay and W. Liang, �??Diffraction by a black half-plane: theory and observation,�?? Proc. Royal Soc. London A 449, 515-535 (1995).
[CrossRef]

J. F. Nye and W. Liang, �??Near-field diffraction by two slits in a black screen,�?? Proc. Royal Soc. London A 454, 1635-1658 (1998).
[CrossRef]

Proc. SPIE

M. Berry, �??Geometry of phase and polarization singularities, illustrated by edge diffraction and the tides,�??in Singular Optics (optical Vertices): Fundamentals and Applications II, Proc. SPIE 4403, 1-12 (2001).
[CrossRef]

Prog. Opt.

F. Kottler, �??Diffraction at a black screen. I. Kirchhof�??s theory,�?? Prog. Opt. 4, 281-314 (1965).
[CrossRef]

Other

A. Sommerfeld, Optics (Academic Press, New York, 1954).

L. B. Felsen and N. Marcuwitz, Radiation and scattering of waves (IEEE Press, New York, 1994).
[CrossRef]

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 (7)

Fig. 1.
Fig. 1.

Reflection geometry from a PEC half plane

Fig. 2.
Fig. 2.

Comparison of the PO and MTPO integrals for the places of the stationary points

Fig. 3.
Fig. 3.

Comparison of MTPO and incident diffracted fields

Fig. 4.
Fig. 4.

Comparison of MTPO and incident total fields

Fig. 5.
Fig. 5.

MTPO and incident total diffracted fields

Fig. 6.
Fig. 6.

MTPO and incident total fields

Fig. 7
Fig. 7

MTPO total diffracted fields

Equations (56)

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

E rz = e j π 4 kE i 2 π 0 e jkx ' cos ϕ 0 e jkR kR sin ( β + ϕ 0 2 ) dx '
I ( k , r ) = 0 f ( r , x ' ) e jkg ( r , x ' ) dx '
f ( r , x ' ) = e j π 4 kE i 2 π sin ( β + ϕ 0 2 ) kR
g ( r , x ' ) = R x ' cos ϕ 0 = ρ cos γ + x ' ( cos β cos ϕ 0 )
cos ϕ 0 cos β = 0
β s 1 = ϕ 0 , β s 2 = 2 π ϕ 0
I f ( x s ) e j [ kg ( x s ) + π 4 ] 2 π kg ' ' ( x s )
I E i e jkρ cos ( ϕ + ϕ 0 )
E rz = e j π 4 kE i 2 π 0 e jkx ' cos ϕ 0 e jkR kR sin ( β ϕ 0 2 ) dx '
I f ( x e ) jkg ' ( x e ) e jkg ( x e )
E rds = E i 2 π cos ϕ ϕ 0 2 cos ϕ + cos ϕ 0 e jkρ
J MTPO = e z 2 E i Z 0 sin β + ϕ 0 2 e jkx ' cos ϕ 0
J MTPO = 2 H i ( e x cos β ϕ 0 2 e y sin β ϕ 0 2 ) e jkx ' cos ϕ 0
u A = u i + u di
u S = u r + u dr .
u S + u S = u i
( u S + u i + u di ) S + ( u S + u di ) S = u i
( u S + u di ) S + = ( u S + u di ) S
u S S = u di S
J es = n × H T S = 0
J ms = n × E T S = 0
J es = n 1 × H T S 0
J ms = n 1 × E T S 0
J es = e z E i Z 0 sin β + ϕ 0 2 sin β + ϕ 0 2 e jkx ' cos ϕ 0
J ms = E i ( e x cos β ϕ 0 2 e y sin β ϕ 0 2 ) sin β ϕ 0 2 e jkx ' cos ϕ 0
J es = n × H T S = 0
n × E T S = 0
J es = n 1 × H T S 0
n 1 × E T S = 0
J es = e z 2 E i Z 0 sin β + ϕ 0 2 sin β ϕ 0 2 e jkx ' cos ϕ 0
E sz = kE i 2 π e j π 4 0 e jkx ' cos ϕ 0 sin β ϕ 0 2 sin β + ϕ 0 2 e jkR kR dx '
n × H T S = 0
J ms = n × E T S = 0
n × H T S = 0
J ms = n × E T S 0
J ms = 2 E i ( e x cos β ϕ 0 2 e y sin β ϕ 0 2 ) sin β ϕ 0 2 e jkx ' cos ϕ 0
F = ε 0 4 π ∫∫ s J ms e jkR R dS ' .
E s = e j π 4 2 2 π 0 × ( J ms e jkR kR ) dx '
jk e jkR kR ( R x sin β ϕ 0 2 + R y cos β ϕ 0 2 ) = jk e jkR kR sin β + ϕ 0 2
E sz = kE i 2 π e j π 4 0 e jkx ' cos ϕ 0 sin β ϕ 0 2 sin β + ϕ 0 2 e jkR kR dx '
E tz = kE i 2 π e j π 4 ( e jkx ' cos ϕ 0 sin β + ϕ 0 2 e jkR kR dx ' 0 e jkx ' cos ϕ 0 sin β ϕ 0 2 sin β + ϕ 0 2 e jkR kR dx ' )
E is = e jkρ cos ( ϕ ϕ 0 ) u ( ξ i ) e j π 4 2 2 π cos ϕ ϕ 0 2 e jkρ
E dr = e j π 4 2 2 π e jkρ
E dr = e j π 4 2 2 π ( 1 1 cos ϕ ϕ 0 2 ) e jkρ
E dtc = e j π 4 2 2 π ( sgn ( ξ i ) cos ϕ 0 2 1 cos ϕ ϕ 0 2 ) e jkρ
E di = e j π 4 2 2 π e j 2 cos 2 ϕ ϕ 0 2 2 cos ϕ ϕ 0 2 e jkρ cos ( ϕ ϕ 0 )
E di = F ̂ ( 2 cos ϕ ϕ 0 2 ) e jkρ cos ( ϕ ϕ 0 )
E diu = F ( ξ i ) sgn ( ξ i ) e jkρ cos ( ϕ ϕ 0 )
F ( x ) = e j π 4 π x e jt 2 dt .
E Su = E i e jkρ cos ( ϕ ϕ 0 ) F ( ξ i ) + E i e j π 4 2 2 π cos ( ϕ 0 2 ) e jkρ sgn ( ξ i )
J es = e z 2 E i Z 0 sin β + ϕ 0 2 sin β ϕ 0 2 cos ϕ 0 2 e jkx ' cos ϕ 0 sgn ( ξ i )
E sz = e jkρ cos ( ϕ ϕ 0 ) F ( 2 cos ϕ ϕ 0 2 )
E Sz = e jkρ cos ( ϕ ϕ 0 ) F ( 2 cos ϕ ϕ 0 2 ) sgn ( 2 cos ϕ ϕ 0 2 ) .
E dr = e j π 4 2 2 π e j 2 cos 2 ϕ 0 2 2 cos ϕ 0 2 e jkρ cos ϕ 0 sgn ( ξ i )
E dr = F ̂ ( 2 cos ϕ 0 2 ) e jkρ cos ϕ 0 sgn ( ξ i )
E dr = F ( 2 cos ϕ 0 2 ) sgn ( 2 cos ϕ 0 2 ) sgn ( ξ i ) e jkρ cos ϕ 0

Metrics