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

The Frequency Comb (R)evolution Thomas Udem Max-Planck Institut für Quantenoptik Garching/Germany 1

• The History of the Comb • Derivation of the Comb • Self-Referencing 2

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Mode Locked Laser as a Comb Generator Mode Locked Laser as a Comb Generator Typical Ti:sapphire Kerr-lens mode locked laser: - pulse repetition rate T -1 = 100 MHz … 1 GHz - pulse duration � = 10 fs - spectral width = 1/ �� = 100 THz - N = 10 5 … 10 6 modes phase synchronized 4

The History of the Comb The History of the Comb 5

The First Continuous Wave Laser The First Continuous Wave Laser William Bennett and Ali Javan with the first continuous wave laser 1961 6

Coherent Waves with Frequencies? Coherent Waves with Frequencies? 7 Scully, Zubairy - Quantum Optics

Laser Beat Notes Laser Beat Notes 8

Laser Beat Notes Laser Beat Notes 9

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. 10

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Stanford Mode Locked Laser 1978 Stanford Mode Locked Laser 1978 T.W.Hänsch A.Ferguson J.Eckstein E.Weber J.Goldsmith 12 Carrier envelope offset phase and frequency described in detail in Jim Eckstein‘s Thesis Stanford 1978

Frequency Differences and „Absolute“ Frequencies Frequency Differences and „Absolute“ Frequencies 890 GHz 13

Harmonic Frequency Chains Harmonic Frequency Chains Boulder Novosibirsk 14

Harmonic Frequency Chains Harmonic Frequency Chains 15

How to Improve the Optical Counter How to Improve the Optical Counter 16

Kourogi Type Frequency Comb Generator Kourogi Type Frequency Comb Generator 17

Kourogi‘s Comb Generator in our Lab Kourogi‘s Comb Generator in our Lab 18 Opt. Lett. 23, 1387 (1998)

Optical Interval Dividers Optical Interval Dividers f 1 f 2 f 3 f 1 f 2 f 3 Optical Interval Divider (Differential Gear) 19 T.W.Hänsch in “The Hydrogen Atom” G.F.Bassani, M.Inguscio, T.W.Hänsch eds, Springer 1989

Optical Counter Optical Counter 20

Phase Noise Phase Noise 21

Phase Noise: Why the Comb shouldn‘t work Phase Noise: Why the Comb shouldn‘t work 22

Phase Noise: Why the Comb shouldn‘t work Phase Noise: Why the Comb shouldn‘t work 23

Phase Noise Phase Noise 24 Th. Udem, lab book 1994

Phase Locked Loop Phase Locked Loop 25

Testing the Mode Spacing Constancy Testing the Mode Spacing Constancy 26

Testing the Mode Spacing Constancy Testing the Mode Spacing Constancy 27

Derivation of the Comb Derivation of the Comb (from the pulse train) 28

Mode Locked Laser Mode Locked Laser 1 n = n1 r + 1 CE with 1 CE < 1 r 1 m = m1 r 29

Mode Locked Laser Mode Locked Laser �� � E ( t ) = A ( t ) e � i1 c t A m e � im1 r t � i1 c t = m � �� I ( 1 ) 1 m = m1 r + 1 C 1 c 1 30

Spectrum of N +1 Pulses Spectrum of N +1 Pulses (shift theorem) 31

Spectrum of N +1 Pulses Spectrum of N +1 Pulses 32

Fourier limited Line Width of the Modes Fourier limited Line Width of the Modes 33

Line Width of real Lasers Line Width of real Lasers 34

Resolving the Modes of the Comb Resolving the Modes of the Comb 35

Self-Referencing Self-Referencing 36

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). 37

Carrier-Envelope Phase Carrier-Envelope Phase

The first self-referenced Frequency Comb 3.5 f -4 f self-referencing ( N =7, M =8) 39

Generating an Octave Spanning Comb Generating an Octave Spanning Comb Photonic crystal fiber: William Wadsworth note: if the action of the fiber is the same Jonathan Knight Tim Birks for all the pulses the field stays stricly Phillip Russell periodic. This property is the only one U. of Bath England necessary to derive 1 n = n1 r + 1 CE 40

A much more compact Device f -2 f self-referencing ( N =1, M =2) 41

Compact Ringlaser Compact Ringlaser - wedge and EOM for slow and fast 1 CE control. - translation stage and PZT for slow and fast 1 r control. 42

Simplest way of Self Referencing: M =2 N =1 Simplest way of Self Referencing: M =2 N =1 It is simple to detect 1 CE of an octave wide frequency comb: 1 CE = 2( n1 r + 1 CE ) – (2 n1 r + 1 CE ) 43 J. Reichert et al ., PRL 84, 3232 (2000)

Fiberlaser Fiberlaser - pump power controls 1 CE - fiber stretcher for 1 r control 44

Fixpoint Concept I Fixpoint Concept I fixpoint at 1 = 0 • Cavity length L „ elastic tape“ : ( n1 r + 1 CE ) ( 1 + � L/ L )

Fixpoint Concept II Fixpoint Concept II fixpoint at m = 0 ( 1 = 1 C ) • Pump power „ accordion“ : m1 r (1+ � ) + 1 C Fixpoint important for locking and noise compensation! Better to enumerate mode number m from fixpoint.

Controlling the Frequency Comb Controlling the Frequency Comb depends on the cavity length 1 n = n1 r + 1 CE depends on the pump power we can measure an and control 1 r = 2 � / T an and 1 CE = � 7/ T 47

Optical Frequency Counter Optical Frequency Counter locked to a Cs atomic clock 1 n = n1 r + 1 CE every mode can be used for optical frequency measurement a million stabilized lasers in a single beam! 48

Frequency Conversions with the Comb Frequency Conversions with the Comb radio frequency optical frequency locked to a Cs clock radio frequency or optical frequency optical frequencies optical frequency radio frequency locked to a stable laser locked to countable clock output optical frequency optical frequency locked to a stable laser locked to radio frequency or optical frequency measure another laser 49 Science 293, 825 (2001)

Thank you for your Attention Thank you for your Attention 50