Inhomogeneous broadening and luminescence (Ch. 13) Nov. 27, 2017 |
• Inhomogeneous broadening: Atoms can be
discriminated by physical parameters (e.g. Doppler effect,
different mass owing to different isotopes, nuclear spin,
Zeeman splitting) that result in shifts in their spectra.
: Atoms can be
Consequences --
Line shape functions are the sum
of `g(nu)` for individual group.
Saturation can be group selective.
• Doppler effect: When atoms are moving, energy or
freq. absorbed depends on their velocity
(`vec v`) -- `omega_o = omega - vec k cdot vec v`
Lineshape function for each
group
`g(v_z , nu ) = {Delta nu_h}/{ 2pi} 1/ {(nu -nu_o -nu_o v_z/c)^2+((Delta nu_h}/2)^2}`
Probability density function of atom with certain velocity
in `z`
direction, `v_z`, is given by Maxwell-Boltzmann
distribution
`{dN}/N = sqrt{M/{2 pi k T}} e^{-{Mv_z^2}/{2kT}} dv_z`
Now `g_{"total"} (nu) = int g(v_z,nu) {dN}/N`
which will give a total lineshape function known as Voight
distribution.
Consider 2 extreme cases --
Doppler width `Delta nu_D`
(Maxwell distribution width >> Lorentzian
width `Delta nu_h`
Normal (Gaussian) lineshape, i.e.
and
`Delta nu_D (FWHM) = nu_o sqrt{{8kT ln 2}/{M c^2}}`
In terms
of `Delta nu_D`,
`g(nu) = sqrt{{4ln2}/{Delta nu_D^2 pi}} e^{-4 ln2 ({nu - nu_o}/{Delta nu_D})^2)`
Opposite
case, `Delta nu_D` << `Delta nu_h ->`
Lorentzian lineshape function.
• Stark effect: Another effect for inhomogeneous
broadening where local electric field in crystals causes
level splitting. The local field of each splitting is
determined by lattice vibration differently.
Luminescence and scattering: During luminescence, the system
absorbs and subsequently emits photon. Light can be
scattered by atomic or molecular system (lattice).
Cathodoluminescence, Sonoluminescence, Chemiluminescence,
Bioluminescence, Electrouminescence.
• Photoluminescence -- high energy photons exchanged for low
energy photons.
From spin-allowed transition
(singlet `->`
singlet), generate fluorescence which has short lifetime and
useful for laser.
For spin-forbidden transition
(singlet `->`
triplet), generate phosphorescence (long lifetime).
2 classes of photoluminescence -- single photon and
>multiphoton
Multiphoton photoluminescence allows absorption of many
photons to generate fewer high energy photons.
Applications -- two photon laser scanning fluorescence
microscopy, multiphoton laser scanning fluorescence
microscopy and 3D multiphoton microlithography.
Upconversion fluorescence is used in infrared sensor card.
Rayleigh scattering is proportional
to `lambda_o^{-4}`
for refractive index variation or particle
size `< lambda_o / {10}`
For opposite case, we need to consider Mie scattering.
Raman scattering (RS) and Brillouin scattering (BS) are
caused by phonon and acoustic vibration. They can generate
low freq (Stokes scattering) and high freq (anti-Stokes
scattering which is rare).
In Stimulated RS and BS, there are input photons to provoke
the excited atoms that are excited by a high photon energy
pump to release more photons. They have applications in
lasers and optical amplifiers.