Post on 01-Feb-2021
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P. Piot, PHYS 630 – Fall 2008
Absorption
• A medium with absorption can be characterized by a complexsusceptibility
• Which implies a complex permittivity
• For a monochromatic wave we have
which we write as
• Considering a wave
the intensity is
Absorption (or attenuation) coefficient
P. Piot, PHYS 630 – Fall 2008
Weakly absorbing medium
• taking refractive index to be related to β via
we have
• Case of weakly absorbing media
expand
• So that
• And finally
/
/
/
/
P. Piot, PHYS 630 – Fall 2008
Strongly absorbing medium
• Case when
• So
• Remembering that
• We get
• Only “+” solution is selected to insure α>0
P. Piot, PHYS 630 – Fall 2008
Resonant medium: Lorentz model
• Consider the differential equation
• Take and then
• Take we get
P. Piot, PHYS 630 – Fall 2008
Resonant medium II
• Real and imaginary part of the susceptibility
• Limiting cases
For
!
"0
#0
$
P. Piot, PHYS 630 – Fall 2008
Resonant medium III
-χ’’χ’
ΔωΔω
χ0
χ0Q
Q=ω0/Δω
P. Piot, PHYS 630 – Fall 2008
Resonant medium IV
• Around the resonance
• For media with multiple resonance the index of refraction is written
(Sellmeier equation)
=Δω
P. Piot, PHYS 630 – Fall 2008
Dispersion
• Dispersion arises from
• Example Snell-Descartes’ law
P. Piot, PHYS 630 – Fall 2008
Phase and Group Velocity
• Group velocity is the velocity of the “envelope” A(t) of a signal. Takethe Fourier transform
• Expand the wavevector
• Gives
• So
the envelope propagates at velocity v
P. Piot, PHYS 630 – Fall 2008
Group Velocity Dispersion (GVD)
• GVD is defined as
• Introducing the group index
• The GVD takes the form
• Or alternatively
P. Piot, PHYS 630 – Fall 2008
Higher Order Dispersion
• Generally can Taylor-expand the wave vector as
• Group velocity
• Group velocity (or delay) dispersion (GVD or GDD)
• Third order dispersion (TOD)
Very important to generate veryshort (
P. Piot, PHYS 630 – Fall 2008
Dispersion effects
• Two cases– Dω>0: normal dispersion– Dω
P. Piot, PHYS 630 – Fall 2008
Dispersion application: chirp pulse amplification
• Produce a pulse• Propagate it in, e.g., a normal dispersion
medium• Amplify it• Compress it using, e.g., an anomalous
dispersion medium
t
ω
amplifier
Chirp mirror
P. Piot, PHYS 630 – Fall 2008
Meta-material: an old idea
• Topic of Friday Colloquium on Nov 11, 2008 (talk by S. Antipov fromANL)
• “Doubly-negative medium”: both the electric permittivity and themagnetic permeability are negative
P. Piot, PHYS 630 – Fall 2008
Meta-material: basics & applications
• In standard materials
• In left-hander materials
• Poynting vector has oppositedirection compared to k vectorconsequence: n
P. Piot, PHYS 630 – Fall 2008
Meta-material: experimental verification I
• Experimental evidence in the microwave regime (~10 GHz)
P. Piot, PHYS 630 – Fall 2008
Meta-material: experimental verification I cnt’d
P. Piot, PHYS 630 – Fall 2008
Meta-material: experimental verification II
• Experimental evidencein the optical regimereported last year…