EM Scattering
Homework assignment 4
Problem 1:
Use the Rayleigh approximation (small particle approximation) and calculate the scattering cross
section of a small dielectric sphere with the dielectric constant d and radius a ( a is much
smaller than the w
EM Scattering
Homework assignment 3
Problem 1:
Ei
Consider the problem of normal scattering from an
y
infinitely long, perfectly conducting cylinder of radius
a whose axis is along the z-axis. Assume the
ki
electric field of the incident wave to be polari
EM Scattering
Homework assignment 4
Problem 1:
Use the Rayleigh approximation (small particle approximation) and calculate the scattering cross
section of a small dielectric sphere with the dielectric constant d and radius a ( a is much
smaller than the w
EM Scattering
Homework assignment 3
Problem 1:
Consider the problem of normal scattering from an
Ei
y
infinitely long, perfectly conducting cylinder of radius
a whose axis is along the z-axis. Assume the
electric field of the incident wave to be polarized
EM Scattering
Homework assignment 3
Problem 1:
y
z
A uniform TM plane wave (electric field along the
z-direction) is normally incident on a perfectly
conducting wedge with the angle 300 at an
ki
angle 0 60 deg . The amplitude of the incident
0
wave is E0
EM Scattering
Homework assignment 3
Problem 1:
y
z
A uniform TM plane wave (electric field along the zdirection) is normally incident on a perfectly
conducting wedge with 30deg at an angle 0 .
ki
The amplitude of the incident wave is E0 . Calculate
0
the
EM Scattering
Homework assignment 3
Problem 1:
y
z
A uniform TM plane wave (electric field along the
z-direction) is normally incident on a perfectly
conducting wedge with the angle 240 at an
ki
angle 0 120 deg . The amplitude of the incident
0
wave is E0
EM Scattering
Homework assignment 3
Problem 1:
y
z
A uniform TM plane wave (electric field along the zdirection) is normally incident on a perfectly
conducting wedge with 30deg at an angle 0 .
ki
The amplitude of the incident wave is E0 . Calculate
0
the
EM Scattering
Homework assignment 2
Problem 1:
A plane wave traveling in the x direction in vacuum is scattered by a perfectly conducting, infinite
cylinder with the radius of 1cm whose axis coincides with the z-axis. The frequency of the incident
wave is
EM Scattering
Homework assignment 2
Problem 1:
A plane wave traveling in the x direction in vacuum is scattered by a perfectly conducting, infinite
cylinder with the radius of 1cm whose axis coincides with the z-axis. The frequency of the incident
wave is
EM Scattering
Homework assignment 2
Problem 1:
A plane wave traveling in the x direction in vacuum is scattered by a perfectly conducting, infinite
cylinder with the radius of 1cm whose axis coincides with the z-axis. The frequency of the incident
wave is
EM Scattering
Homework assignment 2
Problem 1:
A plane wave traveling in the x direction in vacuum is scattered by a perfectly conducting, infinite
cylinder with the radius of 1cm whose axis coincides with the z-axis. The frequency of the incident
wave is
EM Scattering
Homework assignment 1
Problem 1:
For a dielectric object with a volume V and space-dependent dielectric constant p ( r ) , the
scattered field in the far field zone is given by
k 2 exp jkr
Es (r )
k s k s exp jks r p (r ) 0 E (r )dV
4 0 r
EM Scattering
Homework assignment 1
Problem 1:
An incident wave travels in free space (dielectric
constant
0 , permeability
z
0 , wave number
k 0 0 ) and impinges upon a dielectric
cylinder with the radius a , height h , and the
relative dielectric const
EM Scattering
Homework assignment 1
Problem 1:
An incident wave travels in free space (dielectric constant 0 , permeability 0 , wave number
k 0 0 ) and impinges upon a dielectric cylinder with the radius a , height h , and the
relative dielectric constant
EM Scattering
Homework assignment 1
Problem 1:
For a dielectric object with a volume V and space-dependent dielectric constant p ( r ) , the
scattered field in the far field zone is given by
k 2 exp jkr
Es (r )
k s k s exp jks r p (r ) 0 E (r )dV
4 0 r
Geometrical optics
Consider the wave equation for the electric field propagating in a
source-free, homogeneous medium
2 E k 2 E 0
k 2 2
E 0
Luneberg-Kline high frequency approximation:
E r ; exp jk r
m 0
Em r
j
m
r : real function of position
Geomet
Electromagnetic scattering
Graduate Course
Electrical Engineering (Communications)
1st Semester, 1388-1389
Sharif University of Technology
Contents of lecture 9
High frequency approximations:
Physical optics
Geometrical optics
Maxwell equations at high fr
Electromagnetic scattering
Graduate Course
Electrical Engineering (Communications)
1st Semester, 1388-1389
Sharif University of Technology
Contents of lecture 8
Contents of lecture 8:
Scattering from small dielectric objects (Rayleigh scattering)
Volume i
Equations for a finite wire
We would now like to consider the case of a finite, but thin
conductive cylindrical wire (along the z-axis)
Note: the case of an infinite cylindrical wire was solved before
by using the exact cylindrical vector function
y
L
x
z
Surface integral equations for conductors
Let us return to our surface integral
0 , 0
equations, but now assume that the
scattering object is a perfect conductor.
The immediate result is the surface
Vc
V0
integral equation
S
n
n Ei ( r ) j 0 n G0 ( r , r
Surface integral equations for dielectrics
We can now derive a set of coupled surface integral equations
for the tangential components of the electric and magnetic fields
(they are continuous across interface)
0 Ei ( r ) j 0 G0 ( r , r ) n H ( r ) dS
S
r
Electromagnetic scattering
Graduate Course
Electrical Engineering (Communications)
1st Semester, 1388-1389
Sharif University of Technology
Contents of lecture 7
Contents of lecture 7:
Scattering from complex objects
General formulation
Volume integral equ
Electromagnetic scattering
Graduate Course
Electrical Engineering (Communications)
1st Semester, 1388-1389
Sharif University of Technology
Contents of lecture 5
Contents of lecture 5:
Scattering from a conductive wedge
The scalar wave equation
The vector
Scattering matrix of the interface
Let us consider a generalized version of the problem: when
waves are incident on the interface from both media
TE scattering:
z 0 E y A exp jk 0, z z B exp jk 0, z z
z 0 E y C exp jk1, z z D exp jk1, z z
D exp jk1, z z
Electromagnetic scattering
Graduate Course
Electrical Engineering (Communications)
1st Semester, 1388-1389
Sharif University of Technology
Contents of lecture 3
Lecture 3: Scattering from layered media
Introduction
Field equations
Scattering from the inte
Electromagnetic scattering
Graduate Course
Electrical Engineering (Communications)
1st Semester, 1390-1391
Sharif University of Technology
General information
Information about the instructor:
Instructor: Behzad Rejaei
Affiliation: Sharif University of Te