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?

6 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.

The Comb as a Ruler in Frequency Space

8 2. Basic Features: Frequency Combs

9 Carrier Envelope Offset Frequency E(t) = A(t) e -i ω c t m = - ∞ = Σ +∞ A m e -im1 r t - i ω c t ω n = m ω r + ω C = n ω r + ω CE ω CE < ω r I(ω) 1 ωcωc 7=0 7=p cosine-pulsesine-pulse - cosine-pulse 7=p/2 D7=p/2

10 I(ω) 1 Carrier Envelope Phase of the Pulses group velocity ≠phase velocity group velocity = phase velocity I(ω) 1 ω n = n ω r repetition rate: ω r = 2π/T T ω n = n ω r + ω CE

Self Referencing the Comb In general comparing the k th and the l th harmonics of the frequencycomb will do the job Requires that the frequency comb is octave spanning i.e. n th and 2n th mode of the comb have enough power ω n1 r + 1 CE x2 2( n1 r + 1 CE ) 2n1 r + 1 CE I(ω) n2n n1 r + 1 CE x2 2( n1 r + 1 CE ) 2n1 r + 1 CE n2n n ω r + ω CE x2 2( n ω r + ω CE ) 2n ω r + ω CE = ω CE n2n Phys. Rev. Lett. 84, 5102 (2000) & Phys. Rev. Lett. 84, 3232 (2000)

12 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

3. Frequency Metrology

14 Self Referencing the Frequency Comb

f to 2f interferometer

Offset Frequency and Repetition Rate Repetition rate Carrier envelope offset frequency

Optical Frequency Synthesizer ω n = n ω r + ω CE locked to a Cs atomic clock 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

2 Compilation of the results for the measurements of the 2 G 7/2 - 2 F 5/2 transition (statistical error)

Line broadening contributions

30 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: accuracy: achieved: predicted: quantum limited stabilty: achieved:

1s-2s two-photon transition in hydrogen