Lecture 7Light - Matter Interactions

HG Wells, War of the Worlds, Pearson’s Magazine, 1897

"In some way they (the Martians) are able to generate an intense heat in a chamber of practically absolute nonconductivity... This intense heat they project in a parallel beam against any object they choose, by means of a polished parabolic mirror of unknown composition... However it is done, it is certain that a beam of heat is the essense of the matter.  What is combustible flashes into flame at its touch, lead runs like water, it softens iron, crack and melts glass, and when it falls upon water, that explodes into steam."

4kW laser cutting 1.5mm mild steel

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A metallic cavity with dilute gas

Lz

Ly

Lx

x

y

z

Excited atom

Ground state atom

e-E/kT

E1

E2

n1

n2

NN

Light-Atom Interaction

E1

E2

n1

n2

hν = E2-E1Absorption

SpontaneousEmission

Available Processes

E1

E2

B12 n1 uRate it happens is:

This is equal to: -dn1/dt

as well as: dn2/dt

A21 n2

dn1/dt

-dn2/dt

In thermal equilibrium ….

Thermal Equilibrium Rate Equations

dn1/dt = -B12 n1 u + A21 n2 = 0

A21 / B12 = n1 / n2 u

A21 / B12 = exp(ΔE/(k T)) 8 π h ν3/c3 x 1/(exp(ΔE/(k T)-1)]

How can this be?????????

All Processes

E1

E2

B12 n1 uRate it happens is:

This is equal to: -dn1/dt

as well as: dn2/dt

A21 n2

dn1/dt

-dn2/dt

In thermal equilibrium ….

dn1/dt

-dn2/dt

B21 n2 u

Thermal Equilibrium Rate Equations

dn1/dt = -B12 n1 u + A21 n2 + B21 n2 u = 0

A21 / B12 = 8 π h ν3/c3 ***** SECOND LAW

A21 / B12 =( exp(ΔE/(k T)) -1) 8 π h ν3/c3 x 1/(exp(ΔE/(k T)-1)]

As T → ∞,

-B12 N/2 u + B21 N/2 u = 0

B12 = B21 ***** FIRST LAWResubstituting:

Java Demos

http://www.colorado.edu/physics/2000/lasers/lasers2.html

http://www.colorado.edu/physics/2000/lasers/lasers3.html

Stimulated Light

Outgoing generated photon shares every property withthe incoming (generating photon):

FrequencyPhasePolarizationDirection

Is the light we see around us generated by stimulated or spontaneous processes?

A21 / B21 = 8 π h ν3/c3 Hard to build X-raylasers

B21 n2 u / (A21 n2 ) = u c3/ (8 π h ν3) = u/(h νΝν

How many photons per mode for a thermal source?i.e. T ~ 1000K, and visible photons ~ 3 x 1014Hz

Equ = 1/( exp (hν/kT) -1 ) ~ 10-6

So almost all photons are generated by thermal processesin normal circumstances. Once get more than unityoccupation number then situation completely changes