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. 6 The Comb as a Ruler in Frequency Space 2. Basic Features: Frequency Combs 8 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 9 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 10 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 12 3. Frequency Metrology Self Referencing the Frequency Comb 14 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: 30 1s-2s two-photon transition in hydrogen