Fiber optic communication TE-504

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Fiber optic communication TE-504

• Lecture 03

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Light Interaction with Matter
Maxwells Equations
Divergence equations
Curl equations
D Electric flux density
B Magnetic flux density
E Electric field vector
H Magnetic field vector
J current density
? charge density
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Constitutive Relations
Constitutive relations relate flux density to
polarization of a medium
When P is proportional to E
Electric
-

-

-

-

Electric polarization vector Material
dependent!!
?0 Dielectric constant of vacuum 8.85 ? 10-12
C2N-1m-2 F/m
? Material dependent dielectric constant
Total electric flux density Flux from external
E-field flux due to material polarization
Magnetic
Magnetic flux density
Magnetic polarization vector
Magnetic field vector
µ0 permeability of free space 4px10-7 H/m
Note For now, we will focus on materials for
which
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Divergence Equations
How did this relation come
?
Coulomb
? Charges of same sign repel each other ( and
or and -)
? Charges of opposite sign attract each other (
and -)
? He explained this using the concept of an
electric field F qE
Every charge has some field lines associated with
it

-
? He found Larger charges give rise to stronger
forces between charges
? Coulomb explained this with a stronger field
(more field lines)
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Gauss' Law for Electricity

• The electric flux out of any closed surface is
  proportional to the total charge enclosed within
  the surface.
• .
• While the area integral of the electric field
  gives a measure of the net charge enclosed, the
  divergence of the electric field gives a measure
  of the density of sources. It also has
  implications for the conservation of charge.

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Gauss' Law for Magnetism

• The net magnetic flux out of any closed surface
  is zero.
• This amounts to a statement about the sources of
  magnetic field.
• For a magnetic dipole, any closed surface the
  magnetic flux directed inward toward the south
  pole will equal the flux outward from the north
  pole.
• The net flux will always be zero for dipole
  sources. If there were a magnetic monopole
  source, this would give a non-zero area integral.

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Faraday's Law of Induction

• The line integral of the electric field around a
  closed loop is equal to the negative of the rate
  of change of the magnetic flux through the area
  enclosed by the loop.
• This line integral is equal to the generated
  voltage or emf in the loop,

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Ampere's Law

• In the case of static electric field, the line
  integral of the magnetic field around a closed
  loop is proportional to the electric current
  flowing through the loop.
• This is useful for the
• calculation of magnetic field for simple
  geometries.

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Summary Maxwells Equations
Divergence equations
Curl equations
Flux lines start and end on charges or poles
Changes in fluxes give rise to fields
Currents give rise to H-fields
Note No constants such as µ0 ?0, µ ?, c, ?,.
appear when Eqs are written this way.
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The Wave Equation
Plausibility argument for existence of EM waves
H
H
E
E
E
.
Curl equations Changing E-field results in
changing H-field results in changing E- field.
The real thing
Goal Derive a wave equation
for E and H
Solution Waves propagating with a (phase)
velocity v
Position
Time
Starting point The curl equations
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The Wave Equation for the E-field
Goal
Curl Eqs
(Materials with M 0 only)
a)
b)
Step 1 Try and obtain partial differential
equation that just depends on E
Apply curl on both side of a)
Step 2 Substitute b) into a)
Cool!....looks like a wave equation already
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The Wave Equation for the E-field
Compare
With
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Dielectric Media
Linear, Homogeneous, and Isotropic Media
P linearly proportional to E
? is a scalar constant called the electric
susceptibility
All the materials properties
Define relative dielectric constant as
Results from P
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Properties of EM Waves in Bulk Materials
We have derived a wave equation for EM waves!
Euh.
Now what ?
Lets look at some of their properties
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Speed of an EM Wave in Matter
Speed of the EM wave
Compare
and
Where c02 1/(?0 µ0) 1/((8.85x10-12 C2/m3kg)
(4? x 10-7 m kg/C2)) ( 3.0 x 108 m/s)2
Optical refractive index
Refractive index is defined by
Note Including polarization results in same wave
equation with a different ?r c becomes v
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Summary
Maxwells Equations
Curl Equations lead to
(under certain conditions)
Linear, Homogeneous, and Isotropic Media
Wave Equation with v c/n