P
P..Jójárt Jójárt 1,4 1,4 , , Á.Börzsönyi Á.Börzsönyi 1,4 1,4 , M.Merı , M.Merı 2 2 , B.Borchers , B.Borchers 3 3 , G.Steinmeyer , G.Steinmeyer 3 3 , , K K..Osvay Osvay 1 1
1.
1. Dept Dept. of Optics & Quantum Electronics, University of Szeged, Szeged, . of Optics & Quantum Electronics, University of Szeged, Szeged, Hungary Hungary 2.
2. Research Group on Laser Physics, HAS, Szeged, Research Group on Laser Physics, HAS, Szeged, Hungary Hungary 3. Max Born Institute, Berlin, Germany
3. Max Born Institute, Berlin, Germany 4.
4. CE Optics Kft., Szeged, Hungary CE Optics Kft., Szeged, Hungary
The definition of CEP and its drift The definition of CEP and its drift
Phase difference between the carrier wave and the peak of the envelope
Symbol: ϕCE
The CEP is drifting from pulse to pulse, unless we stabilize it [1]
In the simplest case the phase increases always by the same amount: ∆ϕCE
On the figure below: ∆ϕCE= π/2
ϕCE,1=0 ϕCE,2=π/2 ϕCE,3=π ϕCE,4=3π/2 t E(t)
Pulse- envelope
(vgroup)
Carrier- wave (vphase) E(t)
t
ϕCE
Use of CEP stabilized pulses
High precision optical frequency-measurements (by stable ”frequency-comb”, ”frequency-ruler” [1])
Attosecond physics
High precision refractive index measurement
Calibration of astronomical mirrors
Usual methods of CEP drift detection
[2]octave-spanning spectral bandwidth is essential;
a nonlinear conversion step is required.
Motivation Motivation Aim
Aim
To develop a new method, which is:
Linear
Bandwidth independent
Applicable to a wide range of lasers:
(sub-)picosecond lasers
Lasers with GHz repetition rates
UV and far infrared lasers
Theory Theory
( ) ( )
20 2 1 2
1 cosmod ,2
)
(
⋅ ⋅ − ⋅∆
⋅
⋅
⋅
⋅
=
∑
= N
a
CE a
a c L R a
R T T
Tω ω ϕ π
where: L is the total optical length of the resonant ring atω; T1,T2 transmission of the beamsplitters, R1,R2
reflection of beamsplitters, N is the number of round trips, when the pulse intensity goes below 1% of the initial.
Transmission at a frequency ω ω ω ω
Dispersion of optical elements can be measured by a Fabry-Perot Interferometer (FPI) [5], from the spectral phase shift of ultrashort laser pulses. → Could be the initial phase, that is, CEP also determined?
Why the spectral transmission of the ring depends on CEP?
BS2
BS1
R1 R2
R≈100%
∆L
Spectrograph
BS2
BS1
R1 R2
R≈100%
∆L
Spectrograph
Max-Born-Institut
Cross calibration with f Cross calibration with f--to to--2f 2f
Pump f-to-2f AOM
interferometer
W0 W0 Ti:S
OC CM CM
Imaging spectrograph
BS1 BS2
Stabilized He-Ne CCD
Multiple Beam Interferometer
Active stabilization of the interferometer (calculated to phase noise at 800 nm) Light source: A commercial Ti:S oscillator ( 10 fs, rep.rate 84.7 MHz, λ=803 nm, ∆λ = 70 nm) with CEP stabilization. Cep shift measured by f-to-2f, tuned by an intracavity FS wedge pair
0 2 4 6 8
Time [hours]
-0.3 -0.2 -0.1 0 0.1 0.2 0.3
Phase [rad] @ 800 nm
Active length stabilization details -A very long resonant ring instead of FPI.
-Length almost equal to the oscillator cavity -Spectral interference at the output
This work was jointly supported by the Hungarian Scientific Research Found (OTKA) under grant No K75149, and by National Office for Research and Technology (NKTH) under grant no. Baross TECH-
07-2008-0050. Financial support from the EU and co-funded by the European Social Fund through the grants no. ”TÁMOP-4.2.1/B-09/1/KONV- 2010- 0005” and ”TÁMOP 4.2.2/B-10/1-2010-0012” are also acknowledged.
Acknowledgement References
1. L.Xu et. al., Opt.Lett. 21, 2008 (1996) 2. H.R. Telle et al., Appl.Phys.B 69, 327 (1999) 3. T. Udem et al. Nature 416, 233 (2002) 4. S. Koke et al. Nature Photonics 4, 462 (2010) 5. T. Fuji et al., Opt. Lett. 29, 632 (2004)
6. K. Osvay et al., Opt. Lett. 32, 3095 (2007) 7. K. Osvay et al., Opt. Lett. 20(1995) 2339-2341 8. K. Osvay et al., App. Phys. B 87, 457 (2007) 9. L. Lepetit et al., J. Opt. Soc. Am. B. 12, 2467 (1995) 10. C. Grebing et al., Appl. Phys. B. 95, 81 (2009) 11. T. Wittmann et al., Nature Physics 5, 357 (2009)
Why the spectral transmission of the ring depends on CEP?
(This figure is for demonstration only, in reality one output spectral fringe is more than 10000 comb lines!)
Cross calibration
Cross calibration results results
Conclusion Conclusionss::
1. The results of the two methods are correlated.
1. The results of the two methods are correlated.
2. Our method can detect CEP shift CHANGES only, that’s why the additive constant . 2. Our method can detect CEP shift CHANGES only, that’s why the additive constant . 3. The previous limitation is not a problem for stabilization.
3. The previous limitation is not a problem for stabilization.
0 400 800 1200
Time [s]
2 2.4 2.8 3.2 3.6 4
CEO phase of MBI [rad]
-40 0 40 80 120
FS wedge position [µm]
1.2 1.6 2 2.4 2.8
CEO phase of f-to-2f [rad]
80 120 160
Time [s]
4 4.4 4.8 5.2 5.6 6
CEO phase of MBI [rad]
-40 0 40 80 120
FS wedge position [µm]
1.2 1.6 2 2.4 2.8
CEO phase of f-to-2f [rad]
1.2 1.6 2 2.4 2.8
CEO phase of f-to-2f [rad]
2 2.4 2.8 3.2 3.6 4
CEO phase of MBI [rad]
Feedback loop to piezo
Stability of 8.65 nm over 3.54 m Stability of 8.65 nm over 3.54 m ( 68 mrad of phase noise at 800 nm) ( 68 mrad of phase noise at 800 nm) Our interferometer
• very long resonant ring
• active length stabilization
• output: spectral interference pattern
• fringe density ~ ∆L
• fringe position ~ ∆L and CEP shift
• evaluation by FFT
Active length stabilization details
• frequency stabilized He-Ne laser, 2D interference
• firewire CCD camera, 500 frame/second
• acoustic vibration of interferometer analyzed
• thermal expancion compensation by a piezo stage
• limits: ±1°C (sufficient in air conditioned laboratory)
FS wedge moved sinusoidally
Conclusion Conclusion::
Good 1 to 1 correlation between the two methods Good 1 to 1 correlation between the two methods
Cross calibration result
To challenge the interferometric method further, and remove all thermal effects, we made a measurement using random wedge positions. Then plotted the CEO phase changes of the two results against each other.
Conclusion Conclusion::
Succesful CEP shift stabilization of ~ 140 mrad.
The method works, but still needs minor revisions.
0 200 400 600
Time [s]
-2 0 2 4 6 8
CEP drift [rad]
Free running Stabilized
Intracavity stabilization of CEP shift Intracavity stabilization of CEP shift
Stabilized He-Ne
Piezo translator CCD
Photodiode + freq. counter
Multiple Beam Interferometer
Evaluation of spectral interferograms:
fringe density ~ opt. length difference fringe position ~ CEP drift and rep.rate CEP shift calculation,
wedge pair motor control Ti:S osc. + isochronic wedge pair
Pump 532 nm
Spectro- graph
Isochronic wedge pair into a Ti:S oscillator’s cavity ( rep.rate 70.165 MHz, λ=790 nm, ∆λ = 50 nm) CEP shift tuning: 3.83 rad/mm, unwanted rep.rate tuning 0.68 Hz/mm (negligible)
Experimental setup, block diagram Experimental results
-1 0 1
CEO phase change of f-to-2f [rad]
-1 0 1
CEO phase change of MBI [rad]
0 1000 2000 3000
Frequency difference from central frequency [MHz]
0 0.2 0.4 0.6 0.8 1
Transmission
Transmission of ring Frequency comb of laser What a spectrograph can see The spectral lines
overlap, maximal transmitted intensity
The spectral lines don’t overlap, minimal transmitted
intensity
The principle of operation:
Oscillator's frequency comb and the resonant ring transmission spectra consists of narrow spectral lines
An aliasing effect occurs. (the oscillator spectrum is "sampled" at the transmission lines of the ring)
Using a spectrograph with finite resolution we get a smooth spectral interference pattern
If CEP shift changes, oscillator's spectral lines move, the spectral pattern moves together
If repetition rate changes, the spectral pattern density and position changes, but can be compensated
