Example Xe Cl
Emitting species is the Xe Cl molecule.
Level 1, Xe atom+Cl atom ( HCl molecule)
Pulsed Electrical discharge: Ne 98.68%, Xe 1.27%, HCl 0.05%: 5 kV
Xe à Xe* (probably via Xe+)
Xe* + HCl à Xe Cl* (v ≠ 0) level 4
XeCl* (v ≠ 0) à XeCl* (v = 0) (via collisions)
XeCl* (v = 0) à XeCl (‘up’ ground state potential) level 2, laser emission
XeCl à Xe + Cl (dissociation and collisions)
Not very monochromatic. Why? Therefore beam rather divergent.
Pulse ~ 10 nsec . Cavity ~ 1 metre in length, therefore very few amplifying transits (~3) of the cavity are involved.
Laser transition is an allowed transition (B32 large) therefore do not need to build up ρ(n) as much as some other lasers do.
The Dye Laser
A tunable laser – the laser wavelength can be selected.
Organic dye molecule – M in solution
M (ground state), level 1 à M*, level 4
pumping by excimer, YAG or flash lamp
M* à M* (S1, v = 0), level 3
– internal conversion
M* (S1, v = 0) à M* (S0, v ≠ 0), level 2
M* (S0, v ≠ 0) à M (ground state)
There is a broad band of
M* (S1, v = 0) à M* (S0, v ≠ 0)
transitions that can be selected – any λ from the fluorescence spectrum of M.
1(S0, v = 0) à 4 (Sn, v) à 3(S1, v = 0)
Very fast. Absorption followed by vibrational relaxation, psec timescale.
3(S1, v = 0) à 2 (S0, v) laser. Level 2 unoccupied, nsecs.
2 à1 vibrational relaxation, psecs.
Wide range of levels 2 available. Output is tunable. Use grating to select laser wavelength.
Hansch set up of a dye laser.
Can cover the UV/visible/near-IR region with available dyes.
Pumped with XeCl excimer laser, typically 0.5 – 5 mJ pulse-1, 3 ns pulse width.
Pass laser beam through another cell containing laser medium pumped in the same way. Stimulated emission amplifies laser beam.
Pass laser beam through ‘doubling crystal’, some fraction of the incoming energy appears as photons of twice the frequency:
Does frequency doubling double the complete range of wavelengths covered by dye lasers?
Molecular Spectroscopic lines
Lasers provide light with a very narrow band width. (Dye laser typically 20 000.0 ± 0.3 cm-1, 20 000.000 ± 0.003 cm-1 not difficult). Need to prepare sample in a manner to use this accuracy.
Energy levels have a width due to the Heisenberg Uncertainty Principle:
E ± ΔE
where the width is related to the life-time of the state
ΔE Δt ≥ h/4Π
Therefore spectroscopic transitions, E1 à E2 have a definite width (E2 - E1) ± (ΔE1+ ΔE2)
This is realised in the line shape of the transition.
Ideally the laser should be narrower than the line width. In practice often the line are very close together and overlap.
G - full width at half maximum and the line shape is described mathematically be the Lorentz function:
(I(E)/Io) = (G/2)2 / [ (E – Ej)2 + (G/2)2 ]
The line shape with no external influences is the homogeneous line shape. 2 external influences need to be considered.
Collisions shorten the lifetime of a state. The shorter the lifetime, the larger the energy width and the larger is G of a spectroscopic transition.
Can be shown that broadening (increased frequency width): Dn = (2p tcol)-1 (tcol – time between collisions).
Molecules are in motion as high speed
(What is the average speed of He atom, an O2 molecule at room temperature?)
Doppler effect shifts the frequency of the radiation:
The observed line shape is the sum of the line shapes of the absorptions of the individual molecules. Much broader.
The frequency, n, experienced by the molecule moving with velocity vx:
n = n0 [1 – (vx / c)]-1 (n0 – stationary freq.)
The Maxwell-Boltzmann distribution of velocities:
n(vx) / N = (2p/kT)-1/2 exp (-mvx2/2kT)
(fraction of molecules with velocity vx per unit volume)
the number molecules that can absorb at frequency n
n(n) = (const.) exp( -m(n-n0)2c2/ 2kTn2 )
This is a Gaussian distribution and as Intensity of Absorption is proportional to the number of molecules:
I/I0 = exp( -m(n-n0)2c2/ 2kTn2 )
fwhm, Dn = (2n/c)(2 ln2 kT / m)1/2
The combined effect of pressure broadening and Doppler effect is to make the observed lineshape considerably greater than the bandwidth of a laser.
Can remove these effects with a molecular jet system.
Molecular sample doped in rare gas. Typically 25 mbar sample in 3 bar He (Ar).
Pinhole usually pulsed, open ~ msecs.
Vacuum chamber ~ 10-7 mbar
Expansion into vacuum results in dramatic cooling of sample.
Collisions between sample molecules and rare gas converts molecular rotational and vibrational energy to translational energy..
Have to specify temperatures for each molecular motion – translation, rotation, vibration.
Typically: T(trans) < T(rot) < T(vib)
5K 10K 50K
Greatly reduces the number of occupied energy levels, reduces the number of transitions.
No collisions in jet, no pressure broadening.
For laser beam perpendicular to jet, no Doppler broadening.
The observed line width is the homogeneous linewidth or the laser bandwidth.