Vernier spectroscopy
A broad band cavity enhanced spectroscopy method with cw laser
resolution
Christoph Gohle, Albert Schliesser, Björn Stein, Akira Ozawa,
Jens Rauschenberger, Thomas Udem, Theodor W. Hänsch
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Broad band cavity enhanced Vernier spectroscopy
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Outline
•
•
•
•
•
Cavity enhanced spectroscopy
Broad band cavity enhanced methods
Adding phase sensitivity
The optical vernier
Conclusion
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Broad band cavity enhanced Vernier spectroscopy
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Fabry perot resonators
light source
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… enhance sensitivity
• Cavity enhanced
absorption
spectroscopy (CEAS)
– Increased interaction
length (
), i.e.
sensitivity
/

¡ r
• Cavity ring down
(CRD)
– Rejects source noise
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Broad band cavity enhanced Vernier spectroscopy
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Broad band CEAS
R
BB-Source (S)
T
• Broadband input source
– Low transm. (1 )
p
– Sens. gain ~ F
Spectrometer
S
R
• Frequency comb input*
– Sens. gain ~ F
– Ringdown method using
streak camera possible**
– Narrow probe frequencies
(if resolved)
T
S
R
T
*Gherman, T. & Romanini, D., Optics Express, 10, 1033-1042 (2002)
**Thorpe, M.J. et al., Science, 311, 1595-1599 , 2006
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Broad band cavity enhanced Vernier spectroscopy
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Comb matching
laser
frequency
comb
passive cavity
• In general r and ' will be complicated functions of !
… and the two combs can not be lined up
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Broad band cavity enhanced Vernier spectroscopy
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Adding phase sensitivity to
CEAS
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'
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Moiré pattern
Broad band cavity enhanced Vernier spectroscopy
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Scanning the comb
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With bad resolution
/

¡ r
!

 !
Á
 
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Broad band cavity enhanced Vernier spectroscopy
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Extract the information
es !
Á
E




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

r
!
Á
  !
Broad band cavity enhanced Vernier spectroscopy
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Some results
• Yields both loss and
dispersion
• Frequency comb is a
“dispersion free” reference
• Sensitivity ~ Finesse
• Demonstrated sens.: 10-6/cm,
1fs2@2THz resolution
• Resolution limited by
spectrometer
• May be useful for survey
trace gas detection
A. Schliesser et al., Optics Express, 14, 5975-5983 (2006)
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What about the comb?
The optical Vernier
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Idea
n = n r +CE
n n+1
c
m!
n r
Requirements:
• Finesse > m
• mr > spec. resolution
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Model
Close to a spot (k,l) the contributions
of all other frequencies can be
neglected:
…
3
2
1
k=0
l=0 1 2 3 …
Scanning length:
Sample absorbtion:
Y calibration:
Identified comb modes: k+m,l=k,l+1!2=(yk+m,l-yk,l+1)/c Assuming: n(k,l+1)=1
Steady state condition: one line width in more than one lifetime:
Scanspeed < ( FSR)2/Finesse2
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Broad band cavity enhanced Vernier spectroscopy
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Implementation
CCD
grating
lens
Air
Resonator Finesse ~ 3000
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Data
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•
Single scan
(10ms)
•
Blue box:
unique data
•
Red boxes:
identified
features
•
Gaussian PSF
much larger
than airy !
Brightness~Int
egral of airy
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Results*
Absorbtion:
•Noisefloor
O2 A-Band
< 10-5/cm (100 Hz)1/2=
< 10-6/cm Hz1/2
•> 4 THz bandwidth
1 GHz sampling (>4000 res.
Datapoints in 10 ms)
•Quantitative agreement in
Amplitude and Frequency
to HITRAN** database
Phase:
*looks good (dispersive features)
*not optimized for good phase sensitivity
* To be published in the near future
** Rothman, L. S. et al., J. Quant. Spect. Rad. Trans., 96, 139-204 (2005)
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Conclusions
• Pro’s
–
–
–
–
–
–
–
–
Comb resolution (i.e. Hz level if desired)
Fast (partly parallel acquisition)
Simple
Large bandwidth
Amplitude AND Phase sensitivity
Self calibrating
Reproducibility limited by primary frequency standard only
Subdoppler methods easily conceivable
• Con
Thank you for your attention!
– Transmitted power ~ 1/Finesse
– Sensitivity Gain ~ Finesse1/2 only (for shot noise limited
detection)
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Thanks
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Optical Resonators
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… enhance nonlinear conversion
• Pc=F/
– Output power grows
with finesse2 or
higher!
• Example:
– SHG 560nm->280nm
– 900mW driving power
– 20% conversion:
900mW->200mW
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Fs-Frequency Comb
Spectroscopy
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Basics
f=0
f=/2
f=
cosine-pulse
sine-pulse
+
-
cosine-pulse
E(t)=A(t)eict = S Am e-imrt-ict
m=-
!n = n!r + !CE
!CE=ÁCE/T
I()
c
1
• Optical clockwork, connects optical and radio
frequency
• 106 phaselocked cw-lasers for high accuracy
spectroscopy
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Spectroscopy with Combs
300 THz band width
and 100 MHz mode
spacing.
I(1)
300 THz
1
3,000,000 modes with 0.3 mW power
spectrosopy with a single mode hard but possible:
V.Gerginov et al. Optics Letters, 30, 1734 (2005)
1
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Two photon spectroscopy
all modes contribute.
I(1)
like a cw laser.
1
Pionieered by: Ye.V.Baklanov, V.P.Chebotayev, Appl. Phys 12, 97 (1977) and M.J.Snadden, A.S.Bell, E.Riis, A.I.Ferguson, Opt. Comm. 125, 70 (1996)
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… recent results
8s F= 4
1/2
8s F= 3
4.2 µm
1/2
7p
• Cs 6S-8S two photon
transition
ºs¡s
F    




ºs¡s
F    




822 nm
456 nm
80
(a)
photon count rat$ (kHz)
fr$p / 2
6s F= 3
1/2
6s F= 3
1/2
65
50
0
20
40
fr$qu$ncy shift at 820 nm (MHz)
(b)
9000
7000
data-fit (%)
Similar method: A. Marian et al, PRL, 95, 023001 (2005)
photon count rat$ (Hz)
11000
Peter Fendel et al., (… almost submitted)
5
0
-5
-4
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60
-2
0
2
fr$qu$ncy shift at 820 nm (MHz)
Broad band cavity enhanced Vernier spectroscopy
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Comb Spectroscopy?
• Fs-frequency combs combine
– High peak power of a fs-laser
– High spectral quality of cw-laser
• Good for applications where there are
no continous lasers available
–
First impressive steps: S. Witte et al., Science, 307, 400 (2005)
• Highly nonlinear spectroscopy?
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High Accuracy at high Energy?
• Planck Scale
• Frequency measurements
– Optical atomic clocks
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Hydrogen like
He+
• He+ is an ion
– Can be trapped and
cooled
– Long interaction times
– Reduced (eliminated)
Doppler broadening &
shift
– Control over other
systematics
– Reduced (no) recoil
Hydrogen
Z - Scaling
Helium
Energy levels
1S-2S: 10eV
Z2
40 eV ~ 60 nm
Lamb shift
1S: 8GHz
Z4
128 GHz
Z6
64 times stronger
Unverified QED correc.
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Optical Resonators for
Frequency combs
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Fs-Buildup resonator
• Enhance entire frequency comb
• Produce XUV frequency comb
– Via high order harmonic generation
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Real resonator
seed laser:
Pavg =
t
=
Ppeak =
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700 mW
20 fs
300 kW
F=¼  
x55
x40
intracavity:
Pavg =
t
=
Ppeak =
38 W
28 fs
12 MW
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XUV Output
C. Gohle et al., Nature, 436, 234 (2005)
R. J. Jones et al., PRL, 94, 193201 (2005)
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High Harmonics Hierarchy
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Coherence (of the 3rd harm.)
C. Gohle et al., Nature, 436, 234 (2005)
R. J. Jones et al., PRL, 94, 193201 (2005)
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Real resonator
seed laser:
Pavg =
t
=
Ppeak =
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700 mW
20 fs
300 kW
F=¼  
x55
x40
intracavity:
Pavg =
t
=
Ppeak =
38 W
28 fs
12 MW
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Complete resonator
characterization
With high sensitivity
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Experimental Setup
f-to-2f interferometer photodiode+counter
2x piezo-actuated mirrors
silica wedges in laser
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Data from an “empty” cavity
A. Schliesser et al., Optics Express, 14, 5975-5983 (2006)
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Result
•to cover entire spectrum, perform multiple measurements with different lock points
(here 780.5 and 801.0 nm)
•wide bandwidth: 150nm
•„wiggles“ at 760 and 825 nm?
•empirical reproducibility: 1fs² in GDD (1.6 THz BW) and 4*10-4 in r
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Verification
Sapphire plate @
Brewster‘s angle
2 identical highreflectivity
dielectric stack
mirrors
Measurement of cavity before and after insertion of additional components
yields individual contributions.
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Empty cavity?
•to cover entire spectrum, perform multiple measurements with different lock points
(here 780.5 and 801.0 nm)
•wide bandwidth: 150nm
•„wiggles“ at 760 and 825 nm?
•empirical reproducibility: 1fs² in GDD (1.6 THz BW) and 4*10-4 in r
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Comparison with simulation
HITRAN data,
convoluted with
spectrometer
ILS and
multiplied with
0.98
HITRAN data
(RT, 1atm, 21%)
Phase excursion
~10-3 rad
(on top of a simple
quadratic phasedep.)
 n ~ 5 £ 10-11
L. S. Rothman et al., The HITRAN 2004 molecular spectroscopic database," J. Quant. Spect. Rad. Trans. 96, 139204, (2005)
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Air filled resonator!
O2
H2O
•to cover entire spectrum, perform multiple measurements with different lock points
(here 780.5 and 801.0 nm)
•wide bandwidth: 150nm
•„wiggles“ at 760 and 825 nm?
•empirical reproducibility: 1fs² in GDD (1.6 THz BW) and 4*10-4 in r
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Outlook
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High power XUV comb
seed laser: 10 MHz CPO (120 nJ; 30 fs)
Reflected Power (AC-Coupled)
enhancement cavity:
vacuum setup (3.5 m length)
Powerspectrum [au]
16
14
12
Laser
Resonator
10
8
6
4
2
750
775
800
Wavelength [nm]
825
0.20
11ms decay -> Finesse 300
0.15
0.10
0.05
0.00
-0.05
-0.10
-0.15
-0.20
-10
0
10
20
30
40
50
Time [µs]
Input: 120nJ, 30fs, 4MW peak
x 100
12µJ, 30fs, 400MW peak
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Cooling laser system
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Helium Spectroscopy
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… provide stable references
• Narrow Markers in
Frequency space
=F
– If high finesse
• High stability
– ~10-14 @ 1 s
– Few Hz linewidth @ 1
PHz
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Experimental Setup
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Laser Lock
Mutual fluctuations of laser/high-F cavity length make a lock at one
frequency necessary. Active feedback keeps both on resonance at
!
lock: Ã
!


 Á  7! 
¡
Á 
!
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Analysis when locked




Ã


r
!
Á
  !
!
@
!


¡  
¡
Á
!    
!
 
@!
!
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O2?
Air: 21% Oxygen
Molecular oxygen „A“ band ~760 nm
M. J. Thorpe et al.: Precise measurements of optical cavity
dispersion and mirror coating properties via
femtosecond combs. Opt. Exp. 13, 882 (2005)
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J. Zhang et al.: Precision measurement of the refractive
index of air with frequency combs. Opt. Lett. 30, 3314
(2005)
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