optical frequency combs and frequency comb spectroscopywimu/educ/tulip-2.pdf · optical frequency...
TRANSCRIPT
![Page 1: Optical frequency combs and frequency comb spectroscopywimu/EDUC/TULIP-2.pdf · Optical frequency combs and frequency comb spectroscopy J. Hall T.W. Hänsch “for their contributions](https://reader033.vdocuments.mx/reader033/viewer/2022042005/5e6facfed8fdfb7fff6118a1/html5/thumbnails/1.jpg)
TULIP Summer School IV 2009TULIP Summer School IV 2009NoordwijkNoordwijk, April 15, April 15--1818
WimWim UbachsUbachs
Optical frequency combs and frequency comb spectroscopy
J. Hall T.W. Hänsch
“for their contributions to the development of laser-basedprecision spectroscopy including theoptical frequency comb technique”
Frequency Combs: A revolution in measuring
Nobel 2005
![Page 2: Optical frequency combs and frequency comb spectroscopywimu/EDUC/TULIP-2.pdf · Optical frequency combs and frequency comb spectroscopy J. Hall T.W. Hänsch “for their contributions](https://reader033.vdocuments.mx/reader033/viewer/2022042005/5e6facfed8fdfb7fff6118a1/html5/thumbnails/2.jpg)
On Pulsed and Continuous wave lasers
A laser consists mainly of a gain medium and an optical cavity:
Consider from time and frequency domain perspectives
![Page 3: Optical frequency combs and frequency comb spectroscopywimu/EDUC/TULIP-2.pdf · Optical frequency combs and frequency comb spectroscopy J. Hall T.W. Hänsch “for their contributions](https://reader033.vdocuments.mx/reader033/viewer/2022042005/5e6facfed8fdfb7fff6118a1/html5/thumbnails/3.jpg)
ModelockingModelocking a lasera laser
Basic idea:Basic idea:build a laser cavity that is lowbuild a laser cavity that is low--loss for intense pulses, loss for intense pulses, but highbut high--loss for lowloss for low--intensity continuous beamintensity continuous beamSolutions:Solutions:IntracavityIntracavity saturablesaturable absorber, or Kerrabsorber, or Kerr--lensinglensing::
• Intensity-dependent refractive index: n = n0 + nKerr I• Gaussian transverse intensity profile leads to a refractive index
gradient, resembling a lens!
![Page 4: Optical frequency combs and frequency comb spectroscopywimu/EDUC/TULIP-2.pdf · Optical frequency combs and frequency comb spectroscopy J. Hall T.W. Hänsch “for their contributions](https://reader033.vdocuments.mx/reader033/viewer/2022042005/5e6facfed8fdfb7fff6118a1/html5/thumbnails/4.jpg)
A laser running on multiple modes: a pulsed laser
SUM
aff =
fff a Δ+=
fff a Δ+= 4
fff a Δ+= 3
fff a Δ+= 2
And so forth: add 30 waves:
fΔ
lasers with “mode-locking”
![Page 5: Optical frequency combs and frequency comb spectroscopywimu/EDUC/TULIP-2.pdf · Optical frequency combs and frequency comb spectroscopy J. Hall T.W. Hänsch “for their contributions](https://reader033.vdocuments.mx/reader033/viewer/2022042005/5e6facfed8fdfb7fff6118a1/html5/thumbnails/5.jpg)
Ultrafast lasers
Pulsing back and forth inside the cavity
![Page 6: Optical frequency combs and frequency comb spectroscopywimu/EDUC/TULIP-2.pdf · Optical frequency combs and frequency comb spectroscopy J. Hall T.W. Hänsch “for their contributions](https://reader033.vdocuments.mx/reader033/viewer/2022042005/5e6facfed8fdfb7fff6118a1/html5/thumbnails/6.jpg)
Ultrafast lasers
Phase
Time
![Page 7: Optical frequency combs and frequency comb spectroscopywimu/EDUC/TULIP-2.pdf · Optical frequency combs and frequency comb spectroscopy J. Hall T.W. Hänsch “for their contributions](https://reader033.vdocuments.mx/reader033/viewer/2022042005/5e6facfed8fdfb7fff6118a1/html5/thumbnails/7.jpg)
Fourier principle for short pulses
Time Domain:Short pulse
Frequency
Spectral Domain:Wide spectrum
![Page 8: Optical frequency combs and frequency comb spectroscopywimu/EDUC/TULIP-2.pdf · Optical frequency combs and frequency comb spectroscopy J. Hall T.W. Hänsch “for their contributions](https://reader033.vdocuments.mx/reader033/viewer/2022042005/5e6facfed8fdfb7fff6118a1/html5/thumbnails/8.jpg)
Frequency comb principle
Frequency
Time Domain:Pulse train
Spectral domain:
‘Comb-like’ spectrumMany narrow-band,Well-defined frequencies
![Page 9: Optical frequency combs and frequency comb spectroscopywimu/EDUC/TULIP-2.pdf · Optical frequency combs and frequency comb spectroscopy J. Hall T.W. Hänsch “for their contributions](https://reader033.vdocuments.mx/reader033/viewer/2022042005/5e6facfed8fdfb7fff6118a1/html5/thumbnails/9.jpg)
Some math: Propagation of a single pulse (described as a wave packet)
ωω ωω deeEztE tizik −∞
∞−∫= )()(),(
Insert an inverse Fourier transform E(τ) for E(ω)
ωττπ
ωωωτ deedeEztE tiziki −∞
∞−
∞
∞−∫ ∫= )()(
21),(
Propagator ωπ
τ ωτω detG zkti∫∞
∞−
−−=− ))()((21)(
τττ dztGEztE ∫∞
∞−−= ),()(),(
Propagation of the field
This can be used with
)(])11(exp[),(gg
l vztEz
vviztE −−=
φω
)()()( 20 kO
ddkkk l
l
+−+= ωωω
ωω
Difference between group and phase velocitycauses an extra phase
When traveling through dispersive mediumThe carrier/envelop phase continuously changes
![Page 10: Optical frequency combs and frequency comb spectroscopywimu/EDUC/TULIP-2.pdf · Optical frequency combs and frequency comb spectroscopy J. Hall T.W. Hänsch “for their contributions](https://reader033.vdocuments.mx/reader033/viewer/2022042005/5e6facfed8fdfb7fff6118a1/html5/thumbnails/10.jpg)
Some math: Propagation of a multiple pulses in a train
)()(1
0single nTtEtE
N
n−= ∑
−
=
T is time delay between pulses
( ) ( ) Ti
TiNN
n
Tin
eeEeEE ω
ωω ωωω −
−−
=
−
−−
== ∑11)( single
1
0singletrain
( ) ( )( )2/sin
2/sin)( 2
2
singletrain TTNII
ωωωω = ( ) ( )∑
∞
=∞ −=
0singletrain, 2)(
nnTII πωδωωIn the limit
With dispersion ( ) ( )∑∞
=∞ −−=
0singletrain, 2)(
nCEnTII φπωδωω
Phase shift
![Page 11: Optical frequency combs and frequency comb spectroscopywimu/EDUC/TULIP-2.pdf · Optical frequency combs and frequency comb spectroscopy J. Hall T.W. Hänsch “for their contributions](https://reader033.vdocuments.mx/reader033/viewer/2022042005/5e6facfed8fdfb7fff6118a1/html5/thumbnails/11.jpg)
Frequency comb principle
frep= 1/Tfceo=(Δϕceo/2π) frep
Frequency
T
ϕceo= π/2 ϕceo= 0ϕceo= π
2 RF frequenciesdetermine the entire optical spectrum!
f = n frep + fceo
tested to <10-19 level
![Page 12: Optical frequency combs and frequency comb spectroscopywimu/EDUC/TULIP-2.pdf · Optical frequency combs and frequency comb spectroscopy J. Hall T.W. Hänsch “for their contributions](https://reader033.vdocuments.mx/reader033/viewer/2022042005/5e6facfed8fdfb7fff6118a1/html5/thumbnails/12.jpg)
Both frep and fceo are in the radio-frequency domaincan be detected using RF electronics.
Measuring frep is straightforward: Counting
Stabilization of Stabilization of ffreprep
![Page 13: Optical frequency combs and frequency comb spectroscopywimu/EDUC/TULIP-2.pdf · Optical frequency combs and frequency comb spectroscopy J. Hall T.W. Hänsch “for their contributions](https://reader033.vdocuments.mx/reader033/viewer/2022042005/5e6facfed8fdfb7fff6118a1/html5/thumbnails/13.jpg)
Measuring fceo is more difficult, requires production of a beat signal between a high-f comb mode and the SHG of a low-f comb mode.
f:2f interferometer
Detection of Detection of ffceoceo
![Page 14: Optical frequency combs and frequency comb spectroscopywimu/EDUC/TULIP-2.pdf · Optical frequency combs and frequency comb spectroscopy J. Hall T.W. Hänsch “for their contributions](https://reader033.vdocuments.mx/reader033/viewer/2022042005/5e6facfed8fdfb7fff6118a1/html5/thumbnails/14.jpg)
SupercontinuumSupercontinuum generationgeneration
This fThis f--toto--2f detection scheme requires an octave2f detection scheme requires an octave--wide spectrum wide spectrum
spectral broadening in nonlinear mediumspectral broadening in nonlinear medium
Photonic crystal fiber:Photonic crystal fiber:
![Page 15: Optical frequency combs and frequency comb spectroscopywimu/EDUC/TULIP-2.pdf · Optical frequency combs and frequency comb spectroscopy J. Hall T.W. Hänsch “for their contributions](https://reader033.vdocuments.mx/reader033/viewer/2022042005/5e6facfed8fdfb7fff6118a1/html5/thumbnails/15.jpg)
Detection of Detection of ffceoceo
f : 2f
Beat-note measurement(frequency counter)
![Page 16: Optical frequency combs and frequency comb spectroscopywimu/EDUC/TULIP-2.pdf · Optical frequency combs and frequency comb spectroscopy J. Hall T.W. Hänsch “for their contributions](https://reader033.vdocuments.mx/reader033/viewer/2022042005/5e6facfed8fdfb7fff6118a1/html5/thumbnails/16.jpg)
Stabilization of Stabilization of ffceoceo
The fThe f--toto--2f interferometer output is used in a feedback loop.2f interferometer output is used in a feedback loop.An AOM controls the pump power to stabilize An AOM controls the pump power to stabilize ffceoceo
![Page 17: Optical frequency combs and frequency comb spectroscopywimu/EDUC/TULIP-2.pdf · Optical frequency combs and frequency comb spectroscopy J. Hall T.W. Hänsch “for their contributions](https://reader033.vdocuments.mx/reader033/viewer/2022042005/5e6facfed8fdfb7fff6118a1/html5/thumbnails/17.jpg)
Scanning of Scanning of ffreprep
Linear cavity required for longLinear cavity required for long--range scanningrange scanning
Multiple reflections on single mirror to increase scan rangeMultiple reflections on single mirror to increase scan range
Scan range determined by:– Cavity stability range– Alignment sensitivity
![Page 18: Optical frequency combs and frequency comb spectroscopywimu/EDUC/TULIP-2.pdf · Optical frequency combs and frequency comb spectroscopy J. Hall T.W. Hänsch “for their contributions](https://reader033.vdocuments.mx/reader033/viewer/2022042005/5e6facfed8fdfb7fff6118a1/html5/thumbnails/18.jpg)
A frequency comb as a calibration toolfor “spectroscopy laser”
The frequency of a laser can directly be determined The frequency of a laser can directly be determined by beating it with the nearest frequency comb mode:by beating it with the nearest frequency comb mode:
frep
fbeat
flaser = n frep + fceo + fbeat
Cf: Hänsch and co-workers: atomic hydrogen
![Page 19: Optical frequency combs and frequency comb spectroscopywimu/EDUC/TULIP-2.pdf · Optical frequency combs and frequency comb spectroscopy J. Hall T.W. Hänsch “for their contributions](https://reader033.vdocuments.mx/reader033/viewer/2022042005/5e6facfed8fdfb7fff6118a1/html5/thumbnails/19.jpg)
Direct frequency comb spectroscopy
Time-domain Ramsey spectroscopcy
Full control over pulse timing required
Cf :Ramsey spectroscopyAtomic fountain clocks
![Page 20: Optical frequency combs and frequency comb spectroscopywimu/EDUC/TULIP-2.pdf · Optical frequency combs and frequency comb spectroscopy J. Hall T.W. Hänsch “for their contributions](https://reader033.vdocuments.mx/reader033/viewer/2022042005/5e6facfed8fdfb7fff6118a1/html5/thumbnails/20.jpg)
QM analysis of pulse sequences
Wave function of two-level atom:
From Schrödinger equation, and some approximations (dipole, rotating wave) the upper statedensity can be calculated for two-pulse sequence:
T is time between pulsesφ is difference in fceo between pulses
For N pulses:
Excited state population
N=4
N=3
N=2“the comb superimposedonto the atom”
![Page 21: Optical frequency combs and frequency comb spectroscopywimu/EDUC/TULIP-2.pdf · Optical frequency combs and frequency comb spectroscopy J. Hall T.W. Hänsch “for their contributions](https://reader033.vdocuments.mx/reader033/viewer/2022042005/5e6facfed8fdfb7fff6118a1/html5/thumbnails/21.jpg)
Feasibility experiment in deepFeasibility experiment in deep--UV (Kr atom)UV (Kr atom)
With amplification in With amplification in Titanium:SapphireTitanium:Sapphire((Amplification == Phase controlAmplification == Phase control))
532 nm
2 x 212 nm
ionization limit
4p5 5p [1/2]0
4p6
τ=23 ns
212 nm 532 nmionization
pulse
time13.3 ns 60 ns
![Page 22: Optical frequency combs and frequency comb spectroscopywimu/EDUC/TULIP-2.pdf · Optical frequency combs and frequency comb spectroscopy J. Hall T.W. Hänsch “for their contributions](https://reader033.vdocuments.mx/reader033/viewer/2022042005/5e6facfed8fdfb7fff6118a1/html5/thumbnails/22.jpg)
Problem with frequency comb calibration:mode ambiguity
3.5 MHz accuracy withTHz bandwidth laser pulses
84Kr: 4p6 – 4p5 5p [1/2]0
Cavitylength
![Page 23: Optical frequency combs and frequency comb spectroscopywimu/EDUC/TULIP-2.pdf · Optical frequency combs and frequency comb spectroscopy J. Hall T.W. Hänsch “for their contributions](https://reader033.vdocuments.mx/reader033/viewer/2022042005/5e6facfed8fdfb7fff6118a1/html5/thumbnails/23.jpg)
Combs in the VUV and beyond
IR UV
frequency
DUV VUV XUVharmonicconversion
frequency comb = high power pulses = 'easy' harmonic generation
combination of high peak power and accuracy
Harmonic conversion
![Page 24: Optical frequency combs and frequency comb spectroscopywimu/EDUC/TULIP-2.pdf · Optical frequency combs and frequency comb spectroscopy J. Hall T.W. Hänsch “for their contributions](https://reader033.vdocuments.mx/reader033/viewer/2022042005/5e6facfed8fdfb7fff6118a1/html5/thumbnails/24.jpg)
Combs in the VUV and beyondComb is retained in harmonics due to pulse structurePhase control/measurement is the crucial issue
![Page 25: Optical frequency combs and frequency comb spectroscopywimu/EDUC/TULIP-2.pdf · Optical frequency combs and frequency comb spectroscopy J. Hall T.W. Hänsch “for their contributions](https://reader033.vdocuments.mx/reader033/viewer/2022042005/5e6facfed8fdfb7fff6118a1/html5/thumbnails/25.jpg)
Measurements at the 7th harmonic (of Ti:Sa)
Probing Xe (5p6 5p55d) at 125 nm (Vacuum ultraviolet frequency comb)
![Page 26: Optical frequency combs and frequency comb spectroscopywimu/EDUC/TULIP-2.pdf · Optical frequency combs and frequency comb spectroscopy J. Hall T.W. Hänsch “for their contributions](https://reader033.vdocuments.mx/reader033/viewer/2022042005/5e6facfed8fdfb7fff6118a1/html5/thumbnails/26.jpg)
Phase stability (between pulses) in the VUV(effect on relative phase)
O2 pressure dependence:-0.12 (0.29) mrad/mbar=-1.5(3.4) kHz/mbar
UV dependence:-8.7(5.8) mrad/μJ = -104(70) kHz/μJ
![Page 27: Optical frequency combs and frequency comb spectroscopywimu/EDUC/TULIP-2.pdf · Optical frequency combs and frequency comb spectroscopy J. Hall T.W. Hänsch “for their contributions](https://reader033.vdocuments.mx/reader033/viewer/2022042005/5e6facfed8fdfb7fff6118a1/html5/thumbnails/27.jpg)
Novel development: Miniaturisation of frequency comb lasers
I -VNeedle probes
~1 cm
Mode-locked diode lasersInP quantum dot material
Result from hybrid modelocking