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 Typical Ti:sapphire Kerr-lens mode locked laser: -pulse repetition ratet -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 5
The First Continuous Wave Laser William Bennett and Ali Javan with the first continuous wave laser 1961 6
Coherent Waves with Frequencies? Scully, Zubairy - Quantum Optics 7
Laser Beat Notes 8
Laser Beat Notes 9
Increasing the Measureable Frequency Difference direct measurement of optical beat frequencies is limited by the detector bandwidth to a few 100 GHz wit h some tricks to a few THz. 10
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Stanford Mode Locked Laser 1978 A.Ferguson J.Eckstein T.W.Hänsch J.Goldsmith E.Weber Carrier envelope offset phase and frequency described in detail in Jim Eckstein s Thesis Stanford 1978 12
Frequency Differences and Absolute Frequencies 890 GHz 13
Harmonic Frequency Chains Boulder Novosibirsk 14
Harmonic Frequency Chains 15
How to Improve the Optical Counter 16
Kourogi Type Frequency Comb Generator 17
Kourogi s Comb Generator in our Lab Opt. Lett. 23, 1387 (1998) 18
Optical Interval Dividers f 1 f 3 f 2 f 1 f 3 f 2 Optical Interval Divider (Differential Gear) T.W.Hänsch in The Hydrogen Atom G.F.Bassani, M.Inguscio, T.W.Hänsch eds, Springer 1989 19
Optical Counter 20
Phase Noise 21
Phase Noise: Why the Comb shouldn t work 22
Phase Noise: Why the Comb shouldn t work 23
Phase Noise Th. Udem, lab book 1994 24
Phase Locked Loop 25
Testing the Mode Spacing Constancy 26
Testing the Mode Spacing Constancy 27
Derivation of the Comb (from the pulse train) 28
Mode Locked Laser 1 n = n1 r + 1 m 1 CE = m1 with r 1 CE < 1 r 29
Mode Locked Laser E(t) = A(t) e i1 ct = A m e im1 rt i1 c t m I (1) 1 c 1 1 m = m1 r + 1 C 30
Spectrum of N+1 Pulses (shift theorem) 31
Spectrum of N+1 Pulses 32
Fourier limited Line Width of the Modes 33
Line Width of real Lasers 34
Resolving the Modes of the Comb 35
Self-Referencing 36
How to Measure the Comb Offset Measure any frequency difference between different harmonics of the same laser (or comb). 37
Carrier-Envelope Phase
The first self-referenced Frequency Comb 3.5f -4f self-referencing (N=7, M =8) 39
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 1 n = n1 r + 1 CE 40
A much more compact Device f -2f self-referencing (N=1, M =2) 41
Compact Ringlaser -wedge and EOM for slow and fast 1 CE cont rol. -translation stage and PZT for slow and fast1 r cont rol. 42
Simplest way of Self Referencing: M =2 N=1 It is simple to detect 1 CE of an oct ave wide frequency comb: 1 CE = 2(n1 r + 1 CE ) (2n1 r + 1 CE ) J. Reichert et al., PRL 84, 3232 (2000) 43
Fiberlaser -pump power controls1 CE -fiberstretcherfor1 r cont rol 44
Fixpoint Concept I fixpoint at 1=0 Cavity length L elast ic t ape : (n1 r + 1 CE ) (1 + L/L)
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 depends on the cavity length 1 n = n1 r + 1 CE depends on the pump power we can measure and cont rol 1 r = 2 /Tand 1 CE = 7/T 47
Optical Frequency Counter locked to a Cs atomic clock 1 n = n1 r + 1 CE every mode can be used for opt ical frequency measurement a million st abilized lasers in a single beam! 48
Frequency Conversions with the Comb radio frequency or optical frequency radio frequency optical frequency locked to a Cs clock optical frequencies optical frequency locked to a stable laser radio frequency locked to countable clock output radio frequency or optical frequency optical frequency locked to a stable laser measure another laser optical frequency locked to Science 293, 825 (2001) 49
Thank you for your Attention 50