keV Harmonics from Solid Targets -

The Relatvisitic Limit and Attosecond pulses

Matt Zepf

Queens University Belfast

B.Dromey et al. Queen’s University BelfastK. Krushelnick et al, Imperial CollegeP. Norreys et al, RAL

Outline

High Harmonic Generation from Solid Targets

Harmonics from solid targets – Background

Experimental resultsThe relativistic limit – high conversion efficiencieskeV harmonics – coherent fs radiationAngular distribution- beamed keV radiation

Potential for very bright attosecond pulse generation

Ultra High Harmonic Generation - the principle

• High power pulse tightly focused onto a solid target

• Critical surface oscillates with v approaching cRelativistically oscillating mirror = (1+(a0)2/2)1/2

• Reflected waveform is modified from sine to ~sawtooth

Incident Pulse

Reflected Pulse

Process intrinsically phased locked for all harmonics!

Zeptosecond pulses possible at keV

Harmonic efficiency is FT of reflected waveformTrain of as pulses (analogous to mode-locking)

Typical spectra – Conversion efficiency follows power law scaling

Conversion efficiency scales

q~n-p

With p=5.5…3.3 forI=5 1017…1019Wcm-2

(a0=0.6 .. 3)

Very high orders become rapidly more efficient at high intensitiese.g. 100th harmonic~I3

From Norreys, Zepf et al., PRL, 1832 (1996)

PIC predicts q~n-2.5 >1020Wcm-2. (a0>10) and 1000s of orders

0.01

0.1

1

10

100

1000

10 100 1000 10000

Pu

lse

du

rati

on

(as

)

nF

Duration of attosecond pulses

n=(21/p-1)nF

Few as pulsespossible <1keV

Zeptosecond@>1keV

nFExtremely short pulses are possible by filtering the phase locked HHG(G. D. Tsakiris et al.,New J. Phys. 8, 19(2006)

Harmonic efficiency slope as n-p

Atto pulse efficiency:~n-p+1~n-1.5

Realistic experimental configuration

Filters (~0.1µm thick) have negligible dispersion

(G. D. Tsakiris et al.,New J. Phys. 8, 19(2006)

Consequences from the oscillating mirror model

Oscillating Mirror

Flat, sharply defined critical density surface

• Flatness results in specular

reflection of the harmonics

• Well defined mirror surfacegives high conversion efficiency Phase locked harmonics – as pulses possible

Surface denting/bowing in response to laser can change collimation.Surface roughness important for Ångstrom radiation.

Harmonic efficiency depends strongly on plasma scale length, L

L/ 0.1-0.2

Short, high contrast pulses appear ideal.

Single cycle pulses to generate atto pulses

Experimental Setup:

CCD or image plate detectors

Grating spectrometer or von Hamos crystal spectrometer

Target position

Double plasma Mirror Setup

Incident laser pulse: f3 cone

Pulse Energy: up to 500JPulse energy with PM:up to 150 JPulse duration: 500-600fsContrast (no PM) >107:1Contrast with PMs: >1011:1Peak intensity (with PM) 2.5 1020Wcm-2

Experimental data from Vulcan PW shows p=2.5.2 for a=10

HIGH EFFICIENCY10-4@60 eV (17nm)10-6@250eV (4nm)

Extremely high photon numbersand brightness:

10131 photons10231ph s-1mrad-2 (0.1%BW)

Relativistic scaling pREL=2.5

Published: B. Dromey et al, Nature Physics, 2006

10

1

10-1

10-2

Inte

nsit

y/

/arb

. unit

sN

orm

alis

ed

at

1200

th

ord

er

Order, n1200 3200

2.5 .5x1020 Wcm-2

1.5.5x1020 Wcm-2

Harmonic efficiency n-

2.55

Relativistic limit

~n-2.55 ±.2

Photon Energy1414KeV 3767KeV

Intensity dependent roll-over

keV harmonics + the efficiency roll-over

First coherent, femtosecond, sub-nm source

I

t

FWHM 1’ ~ 500fs

1

10

100

1000

10000

1 10 100

a0

Ro

ll-o

ver

po

siti

on

(o

rder

n)

Roll over scaling confirmed as ~3

83

4

22

Roll-over measurements

Vulcan 1996highest observed

(6 1020Wcm-2m2)

Roll over ~3 10 keV pulse @ a0~30 (1021Wcm-2m2)

1

0.8

0.6

0.4

0.2 7x1019Wcm-2

2.5x1020Wcm-2

Inte

nsit

y/

arb

. unit

s

Wavelength /Å2 3 4 5 6 7 8

kT~1.5keV

kT~3keV

Standard contrast (~10-7) – Bright thermal emitters.

Planckian Spectrum observed for standard contrastSignal brightness ~2x HHG signalPlasma mirrors are essentialAbsorption much higher for low contrast pulses.

1

0.8

0.6

0.4

0.2

-100 50 0 50 100 150

Angle from target normal/deg (Specular reflection 45º, incident -45º)

X-r

ay S

ign

al >

1 k

eV

4º FWHM Gaussian fit to beamed HHG signal

specular

Beamed keV harmonic radiation - coherent keV radiation

X-ray emission above 1keV and 3 is beamed into ~f/3 cone (laser also f/3) for nm rms roughness targets.No beaming observed for

-shots with micron rms targets-shots without plasma mirrors

Surface denting

Ponderomotive pressure can deform surface. (under the current conditions some deformation is unavoidableDenting required to explain our results:~ 0.1m

This would lead to the same divergence for all harmonics in agreement with results.

Solution: use shorter pulses to prevent surface deformation

Laser

• Harmonics from solids are efficient way of producing as pulses up to keV photon energies.

•Ideal for converting ultra high power pulses (100’s of TW)

•HHG in the relativistic limit has been demonstrated.

• Simple geometry for as-pulse production (surface harmonics, phase locked with flat phase, dispersion free system)

•Two possible schemes: polarisation switching or single cycle pulses

•Angular divergence limit remains a question mark: have we reached DL performance?

•Contrast requirements (>1010) are a challenge for fs lasers

Summary

Surface roughness

Laser

Surface roughness would impact on the highest orders only-Unlikely to be a major factor in this experiment

Solution: highly polished targets

Imprinted phase aberration

Phase errors in fundamental beam are passed on to harmonics

n~n Laser

Divergence of harmonics can be strongly affected (cf doubling of high power laser beams)

The cut-off question.

Until recently no firm theoretical basis for a cut-off

Should one expect a cut-off?Harmonic spectrum is simply FT of reflected waveformno cut-off infinitely fast risetime components (unphysical)

Recently: Rollover for n> 42 (Gordienko et al (PRL,93, 115002, 2004)

Revised theory predicts rollover for n>81/23

(T. Baeva et al, PRE and talk after break)

Very different predictions for reaching 10,000 harmonics:

42: a0=50 81/23: a0=22

What determines the angular distribution?

2) Why do keV harmonics beam at all?Surface roughness should prevent beaming(Wavelength<< initial surface roughness for keV harmonics)what reduces the surface roughness

a) smoothing in the expansion phase?b) Relativistic length contraction (highest harmonics are only generatedat max. surface )

1) What determines the angular distribution?Diffraction limited peformance would suggest harmonic~Laser/n harmonic~10-4 rad for keV harmonics.

High Efficiency

Spectral range

Number of photons

Pulse duration

20-70 eV(Al filter)

~7 *1015 84 as

80-200 eV(Zr filter)

~2*1014 38 as

400-1000 eV(Cu filter)

~2*1012 5 as

Assuming 1J,5fs(projected ELI front end)

Extremely powerful attosecond sourceUltrahigh brightness may be possible with DL performance

Experimental paramters

Pulse Energy (No Plasma Mirror):up to 500JPulse energy with PM: up to 150 JPulse duration: 500-600fsContrast (no PM) >107:1Contrast with PMs: >1011:1Spot size: ~7mPeak intensity (with PM) 2.5 1020Wcm-2

Attosecond pulses by spectral filtering

Removing optical harmonics + fundamental changes wave from from saw-tooth to individual as-pulses and sub-as pulsesfrom (G. D. Tsakiris et al.,New J. Phys. 8, 19(2006)

PIC predicts asymptotic limit of pREL~2.5-3

Orders > 1000,keV harmonics!

Exact value of p is pulseshape dependent

Gordienko et al. PRL 93, 115001, 2004

Conversion efficiency into attosecond pulses

Conv eff at filter peak: f|~(nf)-p

Bandwidth: n~(21/p-1)nF

Pulse efficiency: pulse~(21/p-1)nF-(p-1)~n-3/2

1.00E-07

1.00E-06

1.00E-05

1.00E-04

1.00E-03

1.00E-02

1.00E-01

1.00E+00

1 10 100 1000 10000

Centre frequency (n)

Co

nv

ers

ion

eff

icie

nc

y

~n-3/2

Laser contrast is the key to high efficiency.

360 380 400 420 440 460 480 500

Harmonic Spectrum (arb.) Reference Spectrum (arb.)

Pixel number

C-line @3.4nm 

C-line @4.01nm

9x103

1x104

1.1x104

1.3x104

0

1.2x104

~

200

~No plasma mirrorContrast ~10-8

Source Broadening increaseslinewidth in no PM case

Sig

nal

(ar

b)

b)

~~

8x103

400

600

800

1000

1200

Shot 1:Contrast 1011

(2 plasma mirrors)

Strong harmonic signal.

Shot 2:Contrast 107

(No plasma mirrors)

Weak C-line emission

Harmonics >100x brighter than thermal source in water window