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Electromagnetic Waves for EE Students

1) Maxwell's equations describe electromagnetic waves and predict their wavelike behavior, such as propagation and reflection. 2) Electromagnetic waves can be characterized by their frequency, wavelength, wave velocity, and polarization. Plane waves have a wave vector k that conveys wavelength and direction of propagation. 3) The polarization of electromagnetic waves describes the orientation of the electric field and can take many forms, including linear, circular, and elliptical polarization. Polarization is important for properties like impedance and absorption.

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Bill White
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114 views1 page

Electromagnetic Waves for EE Students

1) Maxwell's equations describe electromagnetic waves and predict their wavelike behavior, such as propagation and reflection. 2) Electromagnetic waves can be characterized by their frequency, wavelength, wave velocity, and polarization. Plane waves have a wave vector k that conveys wavelength and direction of propagation. 3) The polarization of electromagnetic waves describes the orientation of the electric field and can take many forms, including linear, circular, and elliptical polarization. Polarization is important for properties like impedance and absorption.

Uploaded by

Bill White
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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ELECTROMAGNETIC WAVES Pioneering 21st Century

Electromagnetics and Photonics

EE 3321 Electromagnetic Field Theory http://emlab.utep.edu

Maxwell’s Equations Solution to Wave Equation Waves can only do 2.5 things:
Pure Oscillation Pure Decay
•D = 0 D, E ⊥ k  Ex + k Ex = 02 2

 E + k E = 0 →  E y + k E y = 0 → Ei ( z ) = Ae + Be
− jkz + jkz
B, H ⊥ k
2 2 2 2
•B = 0 Both
Forward Backward
  E = − j H  Ez + k Ez = 0
2 2
Wave Wave
Predicts waves
  H = j E Plane Waves Time-Domain Relation Between
E&H
Wave Equation
â1
P = E1aˆ1 + E2 aˆ2 (
E ( t ) = P cos t − k • r ) Directionality: E ⊥ k ⊥ H
Frequency-Domain Magnetic Field
Helmholtz Wave Equation k P
 
2 u  disturbance
â2 k (
E ( ) = P exp − jk • r ) H ( ) =

(
exp − jk • r )
 u +  u = 0
2
  frequency Impedance
v v  velocity
Wave Vector Also conveys E0  
Inhomogeneous Media Conveys In vacuum. refractive index n = =
k = 2  wavelength  k = k0 = 2 0 k = k0 n when frequency H0 1 +  j
Used
1  inside medium is known.
     E  =  2 E mostly in
numerical  
  analysis. Polarization Properties  =
2 14
1 + (  ) 
Homogeneous Media ˆ ( j
P = E1a1 + E2 e a2 e
ˆ j
) Expanded
Polarization Vector Loss Tangent  
Used mostly in Linear Polarization (LP) tan  =     P ( z ) = P0 e − k z  = 0.5 tan (  )
 E +   E = 0
2 2
closed-form LP 90°
Test:  = 0°
analysis. Propagation Constant Poincaré Sphere
 
2
LP 0° LP 45°  =  + j  E ( z ) = E0e − z
k  wave
k =   =  
2 2
RCP
All polarizations
map to a point
number v Attenuation Coefficient on the Poincaré
  sphere.
Circular Polarization (CP)  = 1 + (  ) − 1
2
EM Wave Velocity 2  
Test:  = +90° and E1 = E2 LCP
v =1  c0 = 1  0 0 Right-Hand CP (RCP):  = +90° Phase Constant
Left-Hand CP (LCP):  = -90°  
 = 1 + (  ) + 1
2

v = c0 n 2  
c0 = 299,792,458 m s Elliptical Polarization (EP) EP Opposite sides
n  refractive index
Absorption Coefficient
n = r  r
Test: not LP or CP indicate orthogonal
LP and CP are just special cases of EP.  abs = k = 2 P ( z ) = P0e − abs z
polarization.

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