Wavelength – Frequency Measurements
Frequency:
- unit to be measured most accurately in physics
- frequency counters + frequency combs (gear wheels)
- clocks for time-frequency
Wavelength:
- no longer fashionable
- unit [m] no longer directly defined
- always problem of the medium- index of refraction
Units: exercise convert
- Ångstrom -> nm
- eV, J, cm-1, Hz
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Notes
Laser Spectroscopy, Vol 1
W. Demtröder
Chapter 4 Spectroscopic instrumentation (4.1 – 4.4)
Spectrographs, Monochromators, Prisms and Gratings
Interferometers
Fabry-Perot (etalon), Michelson, Mach-Zehnder
Wave meters
Michelson, Sigma, Fizeau, Fabry-Perot
Chapter 9 Frequency measurement/Frequency comb (9.7)
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(Wave)Length standard
Krypton (Kr):
International Standard of Length
Until 1960
Now, since 1983
L  c t
m
s
c  299792458
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The picture shows a device holding a tube of krypton gas.
The isotope Kr-86 contained in the tube can be excited so
that it emits light. The international standard of length is one
meter, which is 1,650,763.73 wavelengths of radiation
emitted by Kr-86.
A practical realisation of the metre is usually delineated
(not defined) today in labs as 1,579,800.298728(39)
wavelengths of helium-neon laser light in a vacuum.
Time standard (and realization)
the duration of 9,192,631,770 periods
of the radiation corresponding to the
transition between the two hyperfine levels
of the ground state of the cesium 133 atom
10-13 accuracy
Cs fountain clock
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Classical Spectrometers
Spectral resolution
limited by the diffraction determined by total aperture
(size of prism or grating)
 study this
Prisms:
how does the dispersion (resolution) depend on
geometry/material of prism
Grating:
study the avantages of the “Echelle grating”
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Spectroscopy and Calibration
Absolute measurements (wavelength or frequency)
Relative measurements (line separations)
Spectral referencing (use of atlases)
I2, Te2, Hollow-cathode lamps, Th-Ar
Scanning vs Multiplex spectroscopy
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Example: The Ultraviolet-Visibile Echelle grating spectrometer at VLT
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8 m mirror at VLT
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Detection of all orders on the CCD
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Instant calibration of all orders by illuminating with ThAr lamp
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Science CCD’s
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Calibration CCD’s
Calibration with an Echelle-grating spectrometer
m  Dsin   sin  
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Neon lamp +
Laser input
Spectral referencing in laser spectroscopy
H2O
absorption
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Frequency conversion and calibration
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Referencing against tellurium 130Te2
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Precision Doppler Free Spectroscopy
1.
2.
3.
4.
Saturation spectroscopy – Lamb dips
Polarization spectroscopy
Two-photon spectroscopy
Molecular beam spectroscopy
Bennet peak
Bennet hole
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Burn a fraction out of
the velocity distribution
Lamb Dips
Saturation holes
Lamb dip in scanning
Willis E Lamb
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Nobel Prize in Physics 1955
Lamb Dips
Saturation in
Homogeneous broadening
Saturation in
Heterogeneous broadening
Standing wave field
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Saturation in
Heterogeneous case
Weak field
probing
Lamb dip spectroscopy unraveling overlapping lines
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Saturated absorption for referencing
+ Phase sensitive detection
lock-in principle
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Doppler-free two-photon absorption (excitation)
Doppler shift:
 
'    k  v
Resonance condition:

  
E f  Ei /   1 '2 '  1  2  v  k1  k2

All molecules, independent of their velocities, absorb at the sum frequency
1  2  2
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Sub-Doppler spectroscopy in a beam
 
'  0  k  v  0  kvx
Reduction of the Doppler width:
D '  D sin 
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D  20
vp
c
ln 2
Molecular beam spectroscopy;
Two-fold advantage: resolution + cooling
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Laser-based calibration techniques
“Harmonics” + “saturation”
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Calibration of H2 spectral lines (in XUV)
P(3)
C-X
(1,0)
R(0) B-X
(9,0) line
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Frequency measurements in the optical domain
with a frequency comb laser
• Principle:
fn=f0 + n frep
I
frep=1/T
f0=frep /2
• Pulses in time generated by mode-locked laser
• Frequency spectrum of discrete, regularly spaced sharp lines
Is it a pulsed or a CW laser ?
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f
Broadening the spectrum to “octave spanning”
1.7 mm
2f
10 fs, 2 nJ in a 1.7 mm
fused silica core holey fiber
- self phase modulation
- shockwave formation
- Raman scattering, FWM ...
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f
Frequency measurements in the optical domain
fn=f0 + n frep
Measure rep
Feedback
f:2f interferometer
Extend the spectrum to octave spanning
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Measure ce
Feedback to stabilize the laser on RF signals
PID
15 MHz
Rb atomic
clock
GPS
correction
1:1012
f - 2f
CE-detection
10 GHz
temp.
control
PID
holey
fiber
piezo
pump
laser
AOM
Kerr-lens 11 fs
Ti:Sapphire laser
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11 fs, 75 MHz
Using the FC-laser as an optical reference standard
f0
atomic
clock
fr
VIS-NIR comb
Int.
0
frequency
CW ultrastable laser
precision
spectroscopy
f
RF beat-note:
result
f result   f  nf rep  f 0
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