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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Laser physics EAL 501 Lecture 3

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...

Laser physics EAL 501

Lecture 3

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)

Stimulated emission

E1 , N1

E2 , N2

)(2212 INBNdt

d

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

Inhomogeneous line broadening : due to Doppler effect Gaussian line shape

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