Laser physics EAL 501 Lecture 3. Energy units 1 eV= 1.6x10 -19 (C) x 1 V= 1.6x10 -19 J E =hc/ λ...
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Transcript of Laser physics EAL 501 Lecture 3. Energy units 1 eV= 1.6x10 -19 (C) x 1 V= 1.6x10 -19 J E =hc/ λ...
Energy units
• 1 eV= 1.6x10-19 (C) x 1 V= 1.6x10-19 J• E =hc/λ• 1/λ=E/hc=1J/(6.6x10-34x108x100) 1 cm-1 =1.5 x10-23 J =.00012 eV
Absorption, Emission, and Dispersion of Light • Electron Oscillator Model• Spontaneous Emission• Absorption• Thermal Radiation• Emission and Absorption of Narrowband Light• Collision Broadening• Doppler Broadening• The Voigt Profile• Radiative Broadening• Absorption and Gain Coefficients
Absorption of gases• White light propagating through a gas is absorbed at
the resonance frequencies of the atoms or molecules. Sodium, for instance, has strong absorption lines in the yellow region at 589.0 and 589.6 nm
The absorbed energy is dissipated in • Heat (translational kinetic energy of the atoms) • Collision• Resonance fluorescence :Re-emission in all directions (• Radiation quenching :When the pressure of the gas is
increased, collisions may rapidly convert the absorbed radiation into heat before it can be reradiated.
Lorentz model• This hypothesis states that an electron in an atom
responds to light as if it were bound to its atom or molecule by a simple spring. As a consequence the electron can be imagined to oscillate about the nucleus.
),( txeEFe kxFx
vFv .
)cos(.
.
.
2
2
2
2
2
2
tEexm
k
dt
dx
mdt
xd
dt
xdm
dt
dxkxEe
dt
xdmF
Electron Natural oscillation: Solution if no external field and no friction
This corresponds to the spontaneous emissionIn the presence of External field , the electron can absorb energy only if ω= ωo
The friction correspond to radiation losses in the material.
m
ktAxx
m
k
dt
xdoo )cos(
2
2
Semi classical viewspontaneous emission
E1 , N1
E2 , N2
22121 NANdt
dN
dt
d
A21 is the rate of spontaneous emission = 1/ τ21 the level 2 life timeOr Decay time of level 2 to level 1
21)0()( 22t
eNtN
m
nmn AAFor multi level decay
Tk
EE
BeNN12
12 /
Boltzman Law
Some forms of spontaneous emission• Electroluminescence : If excitation occurs in an
electric discharge such as a spark. • Chemiluminescence : If excitation produced as a by-
product of a chemical reaction.• Bioluminescence : If excitation occurs in a living
organism (such as a firefly),.• Fluorescence refers to spontaneous emission from
an excited state produced by the absorption of light. • Phosphorescence describes the situation in which
the emission persists long after the exciting light is turned off and is associated with a metastable
Absorption
E1 , N1
E2 , N2
)()(1121 SINBNdt
d
S is the line shapeThe simplest is the Lorentzian line shape L
22)(
/)(
oo
o
vL
Spectral energy density of radiation
It is convenient to define a spectral energy density ρ(ν), such that ρ(ν) d ν is the electromagnetic energy per unit volume in the frequency band ν , ν+dν
The intensity, or energy flux, is the velocity of light times the energy density. Therefore
I(ν)dν = cρ(ν)
Thermal Radiation
• A black body is a body that absorbs all the energy incident
1
/8)(
33
e Tk
h
B
ch
][2898
max mT
Einstein relations
2132
3
21
211122
8A
hg
cB
BgBg
So for a two level system in the presence of radiation we can write
12122
1112
12122111212
))(()(
)()()()(
NANg
gNSB
NANSBNSBNdt
dN
dt
d
Line shapes
Natural line brodening : due to spontaneous emission Lorentzian line shape
Homogeneous line broadening : due to atomic collisions broadening increase with pressure
4/ nmrad A
2/atecollisionro
Propagation of light through a 2 level medium
Suppose a light of intensity Iv(0) is incident on the material.The intensity In is equal to the energy density per unit volume times the wave propagation velocity.The rate at which electromagnetic energy passes through a plane cross-sectional area A at z is Iv(z)A, and at an adjacent plane at z+dz this rate is Iv(z+dz)A; the difference is
dzAzIz
AzIzzI v
))(())()((
The rate at which energy is accumulated or depleted in the volume Δz is
zAzIz
zAut
))(())((
The change in radiation in the medium could be due to absorption and emission. If we neglect the spontaneous emission for the time being
The rate of increase of N2 equals the rate of decrease of the field so
.)()1(
.)()(
)1(
))(()()1(
11
22
21
11
2221
IgIztc
INg
gN
c
SBhI
ztc
Ng
gNSuBhI
ztc
))((8
)( 11
22
212
Ng
gNS
Ag
The gain coefficient has dimension m-1 . If g >0 it is amplification. If g<0 it is absorption
Remember that the wave length here λ is the wave length inside the material which equals the wavelength in vacuum divided by the index of refraction of the material (the frequency doesn’t change inside the material
))((8
)( 11
222
212
Ng
gNS
n
Ag