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Frequency combs in the extreme UV. Johann G. Danzl, 2005/11/09. Frequency combs – What for?. Measurement/synthesis of optical frequencies Measure frequencies rather than wavelengths Optical atomic clocks Subcycle physics High resolution spectroscopy Test fundamental theories

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Frequency combs in the extreme uv

Frequency combs in the extreme UV

Johann G. Danzl, 2005/11/09


Frequency combs what for
Frequency combs – What for?

  • Measurement/synthesis of optical frequencies

  • Measure frequencies rather than wavelengths

  • Optical atomic clocks

  • Subcycle physics

  • High resolution spectroscopy

  • Test fundamental theories

  • Fundamental constants

  • Technological applications of metrology


Harmonic frequency chains
Harmonic Frequency Chains

Complex, delicate and expensive

Designed to measure just one single optical frequency

Very few put in operation


Frequency combs

time

Fourier transform

(sin(1.5*t)+sin(1.6*t))^2

Mode separation = fr=

(sin(1.5*t)+sin(1.6*t)+sin(1.7*t))^2

Spectral width of the comb Δω↑

Shorter pulses

(sin(1.5*t)+sin(1.6*t)+sin(1.7*t)+sin(1.8*t))^2

Frequency combs

10 ns

10 fs


t

fc optical carrier frequency

A(t) … periodic envelope function (amplitude and phase modulation)

A(t)strictly periodic with periodicity => Fourier series in fr

fc= nc fr + f0


Cundiff & Ye, Rev Mod Phys, 75, 325-342 (2003)

vg≠vφ

Phaseshift determines position of the comb


Determining the frequencies in the comb

Udem et al., Nature, Vol 416, 14 March 2002, p 233-237

Determining the frequencies in the comb

used in feedback to stabilize

the position of the comb


Femtosecond mode locked lasers
Femtosecond mode locked lasers

Working horse:

Ti-Sapphire Kerr-lens mode locked laser

Gain bandwidth ~ 128 THz (300nm)

Repetition rate ~ 100 MHz – 1 GHz

Central λ ~ 800 nm

Octave spanning combs

Pulse durations down to 5 fs

Pumped with green cw diode laser

www.wikipedia.org


Mode locking

U. Keller, Nature 424, 831-838 (2003)

Kerr lens + effective aperture

→ Gain for pulsed mode

n, I

n, I

effective aperture: overlap with pump laser

C.w.

Pulse

High peak intensity

Kerr effect

Mode locking

C.w. operation:

No fixed phase relation between the modes

Phase locking or Mode locking:Fixed phase relationship between the modes of the laser resonator cavity →interference → pulses


Tisa mode locked fs laser

measured via beat as described

before, stabilized with feedback loop

to pump-laser intensity nTiSa = n(T)

movable mirror

2 n fr + f0

n fr + f0

beat f0

2 x

2 n fr + 2 f0

TiSa mode locked fs laser

Compensating the dispersion of the crystal: prisms or chirped mirrors


Photonic crystal fiber

Jones et al., Science, 288, Issue 5466, 635-639, (2000)

Photonic crystal fiber

Dispersion and Nonlinearity can be designed

Increases comb bandwidth

4-wave mixing process

Band structure (crystal)


Gohle et al., Nature, 436, 234-237 (2005)

20 fs @ 112 MHz

chirped mirrors

Sapphire windows

Brewster angled

Full repetition rate of the laser!

  • Time domain: coherent pulse addition

  • Round trip time of pulse = period of laser

  • Pulse envelope does not change shape during one round trip

  • Carrier envelope phase shift is the same for laser and resonator

XUV

HHG

Xenon jet


Spectrum inside the resonator

Gohle et al., Nature, 436, 234-237 (2005)

Interferometric Autocorrelation: used to estimate pulse duration:

Intensity of 2ω light scales with square of incident intensity

filter to block the fundamental wavelength

www.wikipedia.org

Spectrum inside the resonator

TiSa laser

Resonator

Chirp free pulse of 28 fs duration

Average power in resonator: 38 W

Peak power: 12 MW

Intensity in the focus: 5*1013 W/cm2


Jones et al., PRL, 94, 193201 (2005)

effective cavity finesse: 2500

Repetition rate 100 MHz

frequency resolved optical gating (FROG):

pulse duration 48 fs (incident), 60 fs (transmitted)

pulse energy 4.8 µJ

enhancement factor 600 vs. incident pulse

peak intracavity intensity: > 3 x 1013 W/cm2


High harmonic generation in rare gases

Lindner et al., PRA 68, 013814 (2003)

High harmonic generation in rare gases


Distance from nucleus

E(t)

time

Corkum, PRL, 71, 1994-1997 (1993)

very high intensities

> 1013 W/cm2

ponderomotive energy

Ip atomic ionization potential

Lewenstein et al., PRA, 49, 2117-2132 (1994)

Baltuska et al., Nature, 421, 611-615 (2003)


Xuv output

Gohle et al., Nature, 436, 234-237 (2005)

Coherence?

XUV comb structure of the k-th laser harmonic:

Widely spaced comb (112 MHz)

Link to Cs atomic clock

Jones et al., PRL, 94, 193201 (2005)

XUV output

23 eV

Comb of odd laser harmonics that stem from the periodicity of carrier wave

Nested comb with frequency spacing given by laser repetition rate


Coherence

Jones et al., PRL, 94, 193201 (2005)

Coherence

High frequency roll-off:photomultiplier amplifier

BBO: beta barium-borate optical crystal


Coherence1

Gohle et al., Nature, 436, 234-237 (2005)

Coherence

3rd harmonic of Nd:YVO4 laser repetition rate phase locked to 2nd harmonic of TiSa repetition rate


Spacial coherence

Gohle et al., Nature, 436, 234-237 (2005)

Power of the spectral features

Feature at 103 nm:

Rydberg levels of the atom

Stark shifted into 8 or 9 photon

Resonance during pulse?

Presently: > 1 nW in the range 120 nm – 60 nm → 10-8 of laser power (Gohle)

10 µW in the 3rd harmonic → 10-8 conversion efficiency (Jones)

Spacial coherence

Divergence angles 14, 11, 10 mrad for 7th, 9th, 11th harmonic, resp.

Approximately diffraction limit: tight focusing


Future
Future

precision dispersion characterization: enhancement factors of 1000

high energy oscillators (extended cavity Ti:sapphire, Yb:YAG) - 1µJ pulses

intracavity pulses: 100 µJ (but nonlinear effects)

XUV output in the mW range

High resolution spectroscopy in the XUV

New tests of fundamental physical theories

XUV interferometry

holography

nanolithography

microscopy

X-ray atomic clocks


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