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Unit 2 Interaction between Light and Matter,Interaction between Light and Matter
Einstein coefficients
Lifetime of excited states
Lineshapes and linewidths of optical transitions
Linewidth broadening
Natural linewidth
Homogeneous linewidths
Inhomogeneous linewidths
Doppler broadening #,Based on Planck’s theory of the blackbody radiation
1905, 1921; 1916, Einstein
developed the quantum description
of absorption and emission of radiation.
introduced the notion of spontaneous and stimulated emission
opened the way for the concept of light amplification.
#,Interaction between Light and Matter,Interaction between Light and Matter,Spontaneous emission
Stimulated emission
Absorption
#,Einstein coefficients,Spontaneous emission : A21
Stimulated emission : W21=B21
Absorption: W12=B12
n2 /n1 : Boltzmann statistics
rate equation
#,Einstein coefficients,The ratios of the coefficients
The A coefficient for a given system -- measure or calculate
the B coefficients --Use the formulas to calculate
the coefficients for stimulated emission and absorption are equal.
---Stimulated emission and absorption are the same processes going in the opposite direction.
#,Einstein coefficients,Spontaneous emission / Stimulated emission
(1) A21/W21 -- T
(2) A21/W21 -- hv
R～ν, hv
(1) R～1
(2) R >> 1 , hv>> kT
Spontaneous emission is far more probable than stimulated emission
e.g -- a light bulb (blackbody)
(a) T=2000K ; visible wavelengths-- (ν ～5x1014Hz).
R >> 1 (R ～ 105)
(b) visible wavelengths, R <1; then T=30,000K
(3) R <<1 #,Einstein coefficients,Spontaneous emission / Stimulated emission
(3) R <<1 hv << kT
W21～ν
Stimulated emission can become significant if the frequency is low enough.
e.g. -- Microwave amplifiers
Frequency -- 1010Hz
Room temperature, T=300K.
R -- 0.015
#,Lifetime of excited states,spontaneous lifetime.
metastable states.
non-radiative transitions
1/teff = 1/trad + 1/tnonrad #,Lineshapes and linewidths of optical transitions,linewidth -- the range of frequencies--FWHM
-- the full width at half maximum of the spectrum.
Lineshape-- the profile of the frequency spread
lineshape function g().
The linewidth and lineshape are two concepts
that play an important role in the physics of
lasers.,lineshape function g(),.
Linewidth
＃,,,Linewidth broadening,Natural linewidth
Other processes can increase the linewidth, but the linewidth cannot be smaller than the natural linewidth
homogeneous broadening
all the atoms emit or absorb radiation in the same way.
inhomogeneous broadening
Inhomogeneous broadening occurs when the atoms in a system interact with the radiation differently. ＃,Linewidth broadening,Natural linewidth
the linewidth cannot be smaller than the natural linewidth
the uncertainty principle
The shorter the uncertainty of this time, the larger the uncertainty of the energy
ΔE : the uncertainty in the energy ＃,Homogeneous broadening,Collisions broadening.
homogeneous broadening—— all the atoms of the given system interact in an identical way with the EM radiation.
homogeneous broadening—— all the atoms emit or absorb radiation in the same way.
homogeneous broadening—— no distinction between the atoms.
e.g. the finite lifetime of the transitions
homogeneous broadening—— Lorentzian lineshape #,Homogeneous broadening,homogeneous broadening—— Lorentzian lineshape
Lorentzian lineshape function of a
homogeneously broadened transition
#,Inhomogeneous broadening,Doppler broadening -- Inhomogeneous broadening
Inhomogeneous broadening occurs when the atoms in a system (gas, liquid, solid) interact with the radiation differently.
Inhomogeneous broadening is the envelope of the many-many homogeneous broadenings coming from each individual atom.
Theoretically, all transitions are homogeneously broadened
and also inhomogeneously broadened. #,Inhomogeneous broadening,Doppler broadening --The Gaussian lineshape #,Transition probability,1. = 0
Spontaneous emission : A21 (1-1)
Stimulated emission : W21=B21 (1-2)
Stimulated absorption : W12=B12
2. ≠ 0
A21() =A21g() ； A21
；
Laser field
Continuum light
field #,Unit 2 Interaction between Light and Matter,Learning outcomes
discuss spontaneous and stimulated emission, and absorption of radiation by atomic systems
calculate the ratio of spontaneous to stimulated
emission rates in blackbodies
discuss natural linewidth and homogeneous and
inhomogeneous linewidths
discuss Doppler broadening , broadenings due to
nonradiative decay, dephasing collisions and so on.
##,
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