Ursula Keller / Lukas Gallmann

ETH Zurich, Physics Department, Switzerlandwww.ulp.ethz.ch

Chapter 11: Frequency comb and carrier envelope offset phase

Ultrafast Laser Physics

Frontier: Ultrashort pulse generation

1960 1970 1980 1990 2000

First ML Laser Ti:Sapphire

KLMChirped Mirror

CEO control

FFWWHHMM

ppuull

ssee ww

iiddtthh

((sseecc

))

20001990198019701960 YYeeaarr

10 fs

100 fs

1 ps

1 fs

10 psTi:sapphire laser≈5.5 fs with ≈200 mW

dye laser27 fs with ≈10 mW

compressed

Science 286, 1507, 1999

CEOPhase

t

Controlled in Oscillator

H.R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, U. KellerAppl. Phys. B 69, 327 (1999)

Carrier-Envelope Offset (CEO) Phase

Mode-locked Pulse Train

Mode lockingby forcing all modes in a laser to operate phase-locked, noise is turned into

ideal ultrashort pulses

I (ω)

φ (ω)

0

I (t)

+π

-π

~

~φ ( t)

§ axial modes in laser not phase-locked

§ noise

I (ω) I (t)

φ (ω)

0

+π

-π

τ ≈ 1Δν

φ ( t)~

~

§ axial modes in laser phase-locked

§ ultrashort pulse§ inverse proportional to phase-locked spectrum

frep : pulse repetition rate frequency , fCEO : carrier envelope offset frequency

How can we stabilize the frequency comb ?

First proposed: H.R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, U. KellerAppl. Phys. B 69, 327 (1999)

f1 = fCEO + nfrep

frep

CEO phase Δϕ0

t

CEO phase controlled in laser oscillator

H.R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, U. KellerAppl. Phys. B 69, 327 (1999)

F. W. Helbing, G. Steinmeyer, U. KellerIEEE J. of Sel. Top. In Quantum Electron. 9, 1030, 2003

Carrier-Envelope Offset (CEO) Phase

Mode-locked pulse train

Pulse envelopeA(t)

Electric field: λ/c = 2.7 fs @800 nm

E t( ) = A t( )exp iω ct + iϕ0 (t)( )

fCEO =Δϕ0

2πTR

TR

frep : pulse repetition rate frequency , fCEO : carrier envelope offset frequency

How can we stabilize the frequency comb ?

First proposed: H.R. Telle, G. Steinmeyer, A. E. Dunlop, J. Stenger, D. H. Sutter, U. KellerAppl. Phys. B 69, 327 (1999)

Goal: Mode beating of fundamental and second harmonic frequency combf-to-2f interference technique: fCEO = 2f1 – f2

f1 = fCEO + nfrep

frep

f1

fCEO = 2f1 – f2

fCEOf2 = fCEO + 2nfrep

f2 2f1

2f1 = 2fCEO + 2nfrep

Ti:sapphire laser spectrum

detection limit required to avoid cycle slips

105

106

107

108

109

1010

1011

1012

mod

al fl

ux d

ensi

ty (1

/s)

500450400350300frequency (THz)

wavelength (nm)

1000900 800 700 600

direct SHG scheme

transfer osc.

Interval bisection

Schemes and feasibilty test to measure and stabilize carrier envelope offset (CEO)

H. R. Telle et al.Appl. Phys. B 69, 327, 1999

First demonstration using continuum generationD. J. Jones et al.,Science 288, 635, 2000 (April)A. Apolonski et al, Phys. Rev. Lett. 85, 740, 2000 (July)

Measurement set-up

Ti:sapphire

fCEO

25 µm

Ø 1.7 µm

micro structure fiber: J. Ranka et al.,OL 25, 25 (2000)

-60

-40

-20

0

Powe

r den

sity

[dBc

]

100500Frequency [MHz]

CEObeatsspurious

frep

First experimental demonstration:D.J. Jones et al., Science 288, 635 (2000)A. Apolonski et al., PRL 85, 740 (2000)

Ti:sapphire oscillator with stabilized CEO-frequency

(Implementation example from Yu et al., Opt. Express 15 (13), 8203 (2007))

• Group vs. phase velocity balance: fast fine control via pump power (AOM),slow coarse control via prism insertion

Feed-forward scheme for CEP = 0 locking

(Figures from Koke et al., Nat. Photon. 4, 465 (2010))

• f-to-2f interferometer measures CEO frequency

• Acousto-optical frequency shifter shifts frequency comb by measured frequency to zero offset

Carrier–Envelope Offset (CEO) Phase

Mode-locked Pulse Train*CEOPhase

t

Threshold

Controlled in OscillatorAmplifier

• Preserved by CPA, OPCPA, filament …• Disturbed by long beam paths

Individual Pulses* †

† M. Mehendale et al, Opt. Lett. 25 1672 (2000)

ω

Spec

trum

Interference

SHG

* H.R. Telle et al, Appl. Phys. B 69, 327 (1999)

CEO Phase Measurement

Phase-Stabilized

490 500 510 520 530Wavelength (nm)

Wavelength (nm)

CEO Phase Measurement

Phase-Stabilized

490 500 510 520 530

490 500 510 520 530Wavelength (nm)

Spec

tral D

ensi

ty (a

rb. u

nits

)

Free-Running

CEO stabilization is maintained!

Δ

SHG

H. R. Telle et al., Appl. Phys. B 69, 327 (1999)

Lock-in loop OFF

Lock-in loop ON

M. Kakehata et al., Optics Lett. 26, 1436 (2001)

ON: Phase-StabilizedOFF: Free-Running

10-15

1s/1'000'000 yr

Atom clock (ON, PTB,..)

10-12

GPS

10-9

1s/10yr

Quartz clock

10-6

1 min/d

Best mech.clocks

10-3

Hour glass

0.001 Hz 1 Hz 10 MHz 9 GHz

Oscillation (e.g., pendulum) frequency:

• the higher the oscillation frequency, the more accurate the clock can be

• optical clocks oscillate 10'000x faster than present atomic (Cs+) clocks

Accuracy of clocks

Magnification:100'000 x

u Spectrum of a femtosecond laser pulse consists of millions of sharp lines

Magnification:100'000 x

u These lines are aequidistant across the entire spectrum

u A femtosecond laser is a „ruler“ for frequencies !

The frequency ruler is extremely accurateT. Udem, R. Holzwarth, T. W. Hänsch, Nature 416, 233 (2002)

Femtosecond lasers as clockworks

Frequency comb

unknownfrequency

Detector

Detector

How to measure time with femtosecond laser

• measuring time means counting the tick-tocks of the pendulum

• optical frequencies are too fast to be counted directly

• thus, detector measures beating between two nearby frequencies

• measure distance between comb lines

• measure distance between unknownfrequency and neighboring comb line

• read frequency ruler (count number of comb lines)

• optical gear box or clockwork

• optical frequency becomes countable

Conventional Fourier-transform spectroscopy

Conventional FT spectroscopy

• Michelson type interferometer

• Scan with moving mirror

• Collect interferogram

• Fourier transform to frequency domain

Conventional FT spectroscopy

• Michelson type interferometer

• Scan with moving mirror

• Collect interferogram

• Fourier transform to frequency domain

Conventional Fourier-transform spectroscopy

Frequency

Dual-comb spectroscopy

Dual-comb spectroscopy• Two pulse trains with different

repetition rates• One pulse scans the other

• Collect interferogram

• Fourier Transform

[1] S. Schiller, Opt. Lett. 27, 766 (2002).[2] I. Coddington, N. R. Newbury, and W. Swann, Optica 3, 414 (2016).

optical frequency [THz]

comb 1frep,1

optical frequency [THz]

comb 2frep,2

Dual-comb spectroscopy

optical frequency [THz]

comb 1frep,1

comb 2frep,2 = frep,1+∆

microwave frequency [MHz]

Δ

Δ 2Δ 3Δ NΔ

• Combine two optical frequency combs

• Intensity beat on photodetector

• Down-conversion to radio frequencies (RF)

[1] S. Schiller, Opt. Lett. 27, 766 (2002).[2] I. Coddington, N. R. Newbury, and W. Swann, Optica 3, 414 (2016).

Dual-comb spectroscopy

+ very fast acquisition+ high precision- two frequency combs:

complex & expensive

Dual-comb SDLs• Versatile• Cost efficient• Compact

optical frequency [THz]

comb 1frep,1

comb 2frep,2 = frep,1+∆

microwave frequency [MHz]

Δ

Δ 2Δ 3Δ NΔ

[1] S. Schiller, Opt. Lett. 27, 766 (2002).[2] I. Coddington, N. R. Newbury, and W. Swann, Optica 3, 414 (2016).

• Combine two optical frequency combs

• Intensity beat on photodetector

• Down-conversion to radio frequencies (RF)

• Absorption mapped to RF-domain

Dual-comb MIXSEL (semiconductor disk laser)

optical frequency [THz]

frep,1 frep,2 = frep,1+∆

Intracavity birefringent crystal (BC)• Two spatially separated beams

• Orthogonal polarizations

• Different optical path length

[1] S. M. Link, A. Klenner, M. Mangold, C. A. Zaugg, M. Golling, B. W. Tilma, and U. Keller, Opt. Express 23, 5521 (2015).

[2] S. M. Link, D. J. H. C. Maas, D. Waldburger, and U. Keller, Science 356, 1164 (2017).

time

1

2

CEO phase effects in time domain

Attosecond pulse generation

Strong-field ionization

Ionization “upward” Ionization “downward”Symmetric ionization

One as pulse One as pulseTwo as pulses

ϕCEO = 0 ϕCEO = π 2 ϕCEO = π

Stereo-ATI phase meter for CEP measurement

• Measures absolute carrier-envelope offset phase (CEP)• Uses short (few-cycle) visible/infrared pulse and above-

threshold ionization (ATI) in an atomic gas• Electron yield in ATI depends exponentially on field strength

(tunnel rate in tunnel ionization)• Phase is obtained directly from left-right-asymmetry

(Pictures taken from Hui Li, “Ultrafast Dynamics from Quantum to Classical Regime”, PhD thesis, LMU Munich, 2016; Figures 2.8, 2.9 and 2.10)

For details, see D. B. Miloševic et al., J. Phys. B: At. Mol. Opt. Phys. 39, R203 (2006)