Shengwang Du

2015, the Year of Light

! 3.3 Energy & Momentum

uE =ε02E 2 uB =

12µ0

B2

For plane wave: E =CBu = uE +uB = ε0E

2 = B2 /µ0 Energy density

Energy flow density S = uc = cε0E2 = cε0EcB = c

2ε0EB =1µ0EB

Poynting vector !S = c2ε0

!E ×!B = 1

µ0

!E ×!B

!S =!E ×!H

Vacuum

Medium u = 1

2(!E ⋅!D+!H ⋅!B)

!

Average Energy and Power of EM Wave

u = ε0E2 = ε0E0

2 cos2(!k ⋅ !r −ωt) = 1

2ε0E0

2 1+ cos2(!k ⋅ !r −ωt)#

$%&

!E =!E0 cos(

!k ⋅ !r −ωt) = Re{ei(

!k ⋅!r−ωt )}

=12ε0E0

2 +12ε0E0

2 cos2(!k ⋅ !r −ωt)

Time-averaged 〈u〉T =12ε0E0

2 +12ε0E0

2 〈cos2(!k ⋅ !r −ωt)〉T =

12ε0E0

2

Optical frequency ~1015 Hz

I = 〈S〉T = c〈u〉T =12cε0E0

2Intensity average energy per unit area and per unit time (W/m2)

P = IA = 12cε0E0

2APower average energy through the area A per unit time (W)

! "  Photon: particle (quantization) of EM field – chargeless and massless

3.3.3 Photons

Energy of a photon in the plane wave:

Photon of a plane wave (!k,ω)

!ω = hν

Momentum of a photon in the plane wave: !k = hλ

Mean photon flux Φ =P!ω

!

!

Photon Counts of a coherent light

!

! EM Wave VS Photon !E =!E0 (!r, t)cos(

!k ⋅ !r −ωt) = Re{

!E0 (!r, t)ei(

!k ⋅!r−ωt )}

〈u〉T =12ε0E0

2 (!r, t) = N(!r, t)!ω

N(!r, t) = ε0E02 (!r, t)2!ω

Photon # density ~ E02 (!r, t)

! " Accelerating charge # Radiation

3.4 Radiation: Classical EM Read texbook

! Synchrotron Radiation

! Synchrotron Light Source

https://en.wikipedia.org/wiki/Synchrotron_light_source

! Electric Dipole Radiation

More on: https://en.wikipedia.org/wiki/Dipole_antenna

!

Quantum Physics of Radiation

! Laser Cooling and Trapping

1997 Nobel Prize in Physics

!

2D 85Rb MOT @ HKUST

Number of atoms: ~108 Temperature: ~10 uK

!

Light in Bulk (Dielectric) Matter

!D = ε0

!E +!P = ε

!E

!H =

!Bµ0

−!M =

!Bµ

∇×!E = −∂

!B∂t

∇×!H =!J f +

∂!D∂t

∇⋅!D = ρ f

∇⋅!B = 0ε0 ⇒ ε = ε(ω)

µ0 ⇒ µ = µ(ω)

For most material (nonmagnetic) µ = µ(ω) ≅ µ0

Dispersion

!

Dispersion (Dielectric)

v(ω) = 1ε(ω)µ(ω)

=c

n(ω)

n(ω) = ε(ω)µ(ω)ε0µ0

= KE (ω)KM (ω)

KE (ω) =ε(ω)ε0 Dielectric constant

KM (ω) =µ(ω)µ0

≅1

! 3.6 EM-Photon Spectrum

! EM Spectrum

! " QFT: wave-particle duality

! Wave is the field of its particle ! Particle of the particle of its field.

" QED (Quantum Electrodynamics): Quantum theory of EM field and light-matter interaction.

3.7 Quantum Field Theory