The Frequency Comb (R)evolution Thomas Udem Max-Planck Institut fr - - PowerPoint PPT Presentation

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The Frequency Comb (R)evolution

Thomas Udem

Max-Planck Institut für Quantenoptik Garching/Germany

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• The History of the Comb
• Derivation of the Comb
• Self-Referencing

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Mode Locked Laser as a Comb Generator Mode Locked Laser as a Comb Generator

• N = 105 … 106 modes phase synchronized
• spectral width = 1/ = 100 THz
• pulse repetition rate T -1 = 100 MHz … 1 GHz

Typical Ti:sapphire Kerr-lens mode locked laser:

• pulse duration = 10 fs

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The History of the Comb The History of the Comb

The First Continuous Wave Laser The First Continuous Wave Laser

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William Bennett and Ali Javan with the first continuous wave laser 1961

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Coherent Waves with Frequencies? Coherent Waves with Frequencies?

Scully, Zubairy - Quantum Optics

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Laser Beat Notes Laser Beat Notes

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Laser Beat Notes Laser Beat Notes

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Increasing the Measureable Frequency Difference 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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Stanford Mode Locked Laser 1978 Stanford Mode Locked Laser 1978

J.Eckstein E.Weber A.Ferguson T.W.Hänsch J.Goldsmith

Carrier envelope offset phase and frequency described in detail in Jim Eckstein‘s Thesis Stanford 1978

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Frequency Differences and „Absolute“ Frequencies Frequency Differences and „Absolute“ Frequencies

890 GHz

Harmonic Frequency Chains Harmonic Frequency Chains

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Boulder Novosibirsk

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Harmonic Frequency Chains Harmonic Frequency Chains

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How to Improve the Optical Counter How to Improve the Optical Counter

Kourogi Type Frequency Comb Generator Kourogi Type Frequency Comb Generator

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Kourogi‘s Comb Generator in our Lab Kourogi‘s Comb Generator in our Lab

• Opt. Lett. 23, 1387 (1998)

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Optical Interval Dividers Optical Interval Dividers

Optical Interval Divider (Differential Gear)

f 1 f 3 f 2 f 1 f 3 f 2

T.W.Hänsch in “The Hydrogen Atom” G.F.Bassani, M.Inguscio, T.W.Hänsch eds, Springer 1989

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Optical Counter Optical Counter

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Phase Noise Phase Noise

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Phase Noise: Why the Comb shouldn‘t work Phase Noise: Why the Comb shouldn‘t work

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Phase Noise: Why the Comb shouldn‘t work Phase Noise: Why the Comb shouldn‘t work

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Phase Noise Phase Noise

• Th. Udem, lab book 1994

Phase Locked Loop Phase Locked Loop

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Testing the Mode Spacing Constancy Testing the Mode Spacing Constancy

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Testing the Mode Spacing Constancy Testing the Mode Spacing Constancy

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Derivation of the Comb Derivation of the Comb

(from the pulse train)

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Mode Locked Laser Mode Locked Laser 1m = m1r 1n = n1r + 1CE with 1CE < 1r

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Mode Locked Laser Mode Locked Laser

E(t) = A(t) ei1ct

1m = m1r + 1C

I (1)

1 1c

= Am eim1rti1ct

m

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Spectrum of N+1 Pulses Spectrum of N+1 Pulses

(shift theorem)

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Spectrum of N+1 Pulses Spectrum of N+1 Pulses

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Fourier limited Line Width of the Modes Fourier limited Line Width of the Modes

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Line Width of real Lasers Line Width of real Lasers

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Resolving the Modes of the Comb Resolving the Modes of the Comb

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Self-Referencing Self-Referencing

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How to Measure the Comb Offset How to Measure the Comb Offset Measure any frequency difference between different harmonics of the same laser (or comb).

Carrier-Envelope Phase Carrier-Envelope Phase

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The first self-referenced Frequency Comb

3.5f -4f self-referencing (N=7, M=8)

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Generating an Octave Spanning Comb 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 1n= n1r+ 1CE

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A much more compact Device

f -2f self-referencing (N=1, M=2)

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Compact Ringlaser Compact Ringlaser

• wedge and EOM for slow and fast 1CE control.
• translation stage and PZT for slow and fast 1r control.

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Simplest way of Self Referencing: M=2 N=1 Simplest way of Self Referencing: M=2 N=1

It is simple to detect 1CE of an octave wide frequency comb:

1CE = 2(n1r + 1CE ) – (2n1r + 1CE )

• J. Reichert et al., PRL 84, 3232 (2000)

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Fiberlaser Fiberlaser

• pump power controls 1CE
• fiber stretcher for 1r control

Fixpoint Concept I Fixpoint Concept I

• Cavity length L „elastic tape“ : (n1r + 1CE) (1 + L/ L)

fixpoint at 1= 0

Fixpoint Concept II Fixpoint Concept II

• Pump power „accordion“ : m1r (1+) + 1C

fixpoint at m = 0 (1= 1C) Fixpoint important for locking and noise compensation! Better to enumerate mode number m from fixpoint.

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Controlling the Frequency Comb Controlling the Frequency Comb 1n = n1r + 1CE

depends on the pump power depends on the cavity length

we can measure an and control

1r = 2/ T an

and 1CE = 7/ T

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Optical Frequency Counter Optical Frequency Counter 1n = n1r + 1CE

locked to a Cs atomic clock every mode can be used for

• ptical frequency measurement

a million stabilized lasers in a single beam!

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Frequency Conversions with the Comb Frequency Conversions with the Comb

radio frequency

• r
• ptical frequency

radio frequency

• r
• ptical frequency
• ptical frequencies

locked to a Cs clock

radio frequency optical frequency

Science 293, 825 (2001)

countable clock output locked to a stable laser locked to

• ptical frequency radio frequency
• ptical frequency optical frequency

measure another laser locked to a stable laser locked to

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Thank you for your Attention Thank you for your Attention