Transcript Document

Frequency combs – evolutionary tree
Overview
• Frequency Metrology
• Measuring Frequency Gaps
• Frequency Combs as Optical Synthesizers
• Time Domain Applicatons
• Stabilizing the Carrier Envelope Phase
• Old and new Precision Spectroscopies
• Towards new Frequency Domains
Spectrum of the pulse train
1. Optical Frequency Combs, what for?
Increasing the measureable Frequency Difference
direct measurement of optical beat frequencies
is limited by the detector bandwidth to a few
100 GHz with some tricks to a few THz.
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The Comb as a Ruler in Frequency Space
2. Basic Features: Frequency Combs
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Carrier Envelope Offset Frequency
7=p/2
7=0
7=p
D7=p/2
D7=p/2
cosine-pulse
- cosine-pulse
sine-pulse
-i ω ct
E(t) = A(t) e
+∞
Am e
Σ
m -∞
=
-im1rt - i ω ct
=
ω n = m ω r + ω C = n ω r + ω CE
ω CE < ω r
I(ω)
ω
c
1
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Carrier Envelope Phase of the Pulses
group velocity = phase velocity
I(ω)
1
T
repetition rate: ωr = 2π/T
group velocity ≠phase velocity
ωn=nωr
I(ω)
1
ω n = n ω r + ω CE
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Self Referencing the Comb
I(ω)
n nn
2n2n2n
ω
x2x2
x2
n1nn1
+
ω
1
+
ω
+
1
2(n1
+1
2(2(
n1
1CE
2n1
1CE
ωCE
2n
ωCE
r r CE
r CE CE
rn
r+1
r+
r+
r)+ )ω CE ) 2n1
r+ ω CE = ω CE
Requires that the frequency comb is octave spanning
i.e. nth and 2nth mode of the comb have enough power
In general comparing the kth and the lth
harmonics of the
frequencycomb will do the job
Phys. Rev. Lett. 84, 5102 (2000) & Phys. Rev. Lett. 84, 3232 (2000)
Generating an Octave Spanning Comb
Photonic crystal fiber:
William Wadsworth
Jonathan Knight
Tim Birks
Phillip Russell
U. of Bath England
note: if the action of the fiber is the same for
all the pulses the field stays stricly periodic.
This property is the only one necessary to
derive ω n=n ω r+ ω CE
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3. Frequency Metrology
Self Referencing the Frequency Comb
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f to 2f interferometer
Offset Frequency and Repetition Rate
Carrier
envelope
offset
frequency
Repetition
rate
Optical Frequency Synthesizer
locked to a Cs atomic clock
ω n = n ω r + ω CE
every mode can be used for
optical frequency measurement
a million stabilized lasers in a single beam!
Collinear fast ion laser spectroscopy
Relevant Arll energy level diagram
Block diagram of the experimental setup
Velocity bunching in collinear fast beam
spectroscopy (diagram)
Figure: Schematic representation of a velocity spread reduction
Relativistic Formalism
Exact formula for obtaining the absolute
frequency of an atomic transition
Calibration to determine the absolute wavelength
Simultaneous recording of two beat frequencies
LIF spectra of
+ with simultaneously measured
collinear and anticollinear laser radiation
Compilation of the results for the measurements of
the2G7/2-2F5/2 transition (statistical error)
Line broadening contributions
Measurement of Optical Frequencies
- fs frequency combs provide a simple tool for measuring optical frequencies
of 100‘s or even 1000‘s of THz.
- they provide a phase corenent link between the optical and the rf region.
- they can be used as a clockwork mechanism in an all optical clock:
quantum limited stabilty:
accuracy:
predicted:
achieved:
achieved:
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1s-2s two-photon transition in hydrogen