Scattering of Electromagnetic Waves
S.P. Yushanov, J.S. Crompton, and K.C.
Koppenhoefer
1
Overview
• Motivation
• Theory
– Cross Section Calculations
– Optical Theorem
– Radiation Force
• Use of COMSOL Multiphysics
• Results
• Summary
2
Motivation
• Comparison with analytical solution for EM
scattering
– Dielectric, metal and magnetic materials
• Provide methodology for other users
• Extend solutions to sizing applications
– Atmospheric
– Droplets in fluids
– Cell nuclei
3
Theory
• Scattering - charge excitation and re-radiation of
electromagnetic energy
• Elastic scattering - frequency of scattered wave
equals incident wave
• Total wave:
E  Einc  E sca
H  H inc  H sca
4
Extinction Cross-Section
 ext   abs   sca ,
m 
2
Optical theorem:
4
 ext 
Im f 0/ Einc
k
In COMSOL:
E far  lim rE sca
r 
Direct calculation:
 ext 
 m 2 
4
Im E far 0 ,
kE inc

5
Radiation Force
From radiation cross section:
1
F   pr Pinc ,
c
N 
Integrating Maxwell’s stress tensor over particle
surface:


1  
1 


ˆ
T  ReE D  H B  E  D  H   B Iˆ ,
2 
2

Electric flux density:
D  E
Pa
Magnetic flux density,
B  H
6
Use of COMSOL
• Far-field calculations are done on the inner
boundary of the PML domain
• S is used to calculate total scattered energy
• Incident plane wave travels in positive x-direction
• Electric field polarized along the z-axis
7
Use of COMSOL Multiphysics
Quantity
Expression in Comsol
emw.Qh
Unit
Wabs , Eq. 12
intop1_Vp(emw.Qh)
W / m3
W
Wsca , Eq. 13
intop2_S(-(emw.relPoavx*nx+emw.relPoavy*ny+ emw.relPoavz*nz))
W
 ext , Eq. 14
b ,
-4*pi/emw.k0*imag(emw.Efarz*1[m])/E0, evaluated at point F
m2
4*pi*(emw.normEfar*1[m]/E0)^2, evaluated at point B
intop2_S(-(emw.relPoavx*nx+emw.relPoavy*ny+emw.relPoavz*nz)*(-nx))/P0/sig_sca
m2
1
intop3_Sp(emw.dnTx+ emw.dnTy+ emw.dnTz)
N
Qloss , Eq. 11
cos  , Eq. 18
F , Eq. 21
The following integration coupling operators are used in the table:
intop1_Vp( ) : domain integration operator over particle volume
intop2_S( ) : boundary integration operator over imaginary surface S
intop3_Sp( ) : boundary integration operator over particle surface S P
The following Electromagnetic Waves (emw) interface predefined variables are used in the table:
emw.Qh: total power dissipation density, W / m
3
emw.relPoavx, emw.relPoavy, emw.relPoavz: time average Poynting vector components of the scattered field, W / m
emw.Efarz: far-field variable, z-component, V / m
emw.dnTx, emw.dnTy, emw.dnTz: Maxwell upward stress tensor components, Pa
8
3
Results - Magnetic Particle
9
Results – Magnetic Particle
10
Summary
• Scattering solution for EM waves calculated for
three particle types – metal, dielectric and
magnetic
• Paper fully describes method for others to use
• Results compared with Mie solution
• Excellent agreement for cross sections and
radiation force
11