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keV Harmonics from Solid Targets - The Relatvisitic Limit and Attosecond pulses. Matt Zepf Queens University Belfast. B.Dromey et al. Queen’s University Belfast K. Krushelnick et al, Imperial College P. Norreys et al, RAL. Outline. High Harmonic Generation from Solid Targets

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slide1

keV Harmonics from Solid Targets -

The Relatvisitic Limit and Attosecond pulses

Matt Zepf

Queens University Belfast

B.Dromey et al. Queen’s University Belfast

K. Krushelnick et al, Imperial College

P. Norreys et al, RAL

slide2

Outline

High Harmonic Generation from Solid Targets

Harmonics from solid targets – Background

Experimental resultsThe relativistic limit – high conversion efficiencies

keV harmonics – coherent fs radiation

Angular distribution- beamed keV radiation

Potential for very bright attosecond pulse generation

slide3

Ultra High Harmonic Generation - the principle

  • High power pulse tightly focused onto a solid target
    • Critical surface oscillates with v approaching c

Relativistically oscillating mirror  = (1+(a0)2/2)1/2

Process intrinsically phased locked for all harmonics!

Zeptosecond pulses possible at keV

Incident Pulse

Reflected Pulse

  • Reflected waveform is modified from sine to ~sawtooth

Harmonic efficiency is FT of reflected waveform

Train of as pulses (analogous to mode-locking)

slide4

Typical spectra –

Conversion efficiency follows power law scaling

Conversion efficiency scales

q~n-p

With p=5.5…3.3 for

I=5 1017…1019Wcm-2

(a0=0.6 .. 3)

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

Very high orders become rapidly more efficient at high intensities

e.g. 100th harmonic~I3

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

slide5

Duration of attosecond pulses

Few as pulses

possible <1keV

Zeptosecond@>1keV

nF

Extremely short pulses are possible

by filtering the phase locked HHG

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

nF

Dn=(21/p-1)nF

Harmonic efficiency slope as n-p

Atto pulse efficiency:

h~n-p+1~n-1.5

slide6

Realistic experimental configuration

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

Filters (~0.1µm thick) have negligible dispersion

slide7

Consequences from the oscillating mirror model

  • Flatness results in specular
  • Well defined mirror surface

gives high conversion efficiency Phase locked harmonics – as pulses possible

reflection of the harmonics

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, highcontrast pulses appear ideal.

Single cycle pulses to generate atto pulses

Oscillating Mirror

Flat, sharply defined critical density surface

slide8

Experimental Setup:

Double plasma Mirror Setup

Incident laser pulse: f3 cone

Target position

Pulse Energy: up to 500J

Pulse energy with PM:up to 150 J

Pulse duration: 500-600fs

Contrast (no PM) >107:1

Contrast with PMs: >1011:1

Peak intensity (with PM) 2.5 1020Wcm-2

Grating spectrometer or von Hamos crystal spectrometer

CCD or image plate detectors

slide9

Relativistic scaling pREL=2.5

Experimental data from

Vulcan PW shows

p=2.5.2 for a=10

HIGH EFFICIENCY

10-4@60 eV (17nm)

10-6@250eV (4nm)

Extremely high photon numbers

and brightness:

10131 photons

10231ph s-1mrad-2 (0.1%BW)

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

kev harmonics the efficiency roll over

Intensity dependent roll-over

I

FWHM 1’ ~ 500fs

t

keV harmonics + the efficiency roll-over

10

1.5.5x1020 Wcm-2

2.5 .5x1020 Wcm-2

h~n-2.55±.2

1

Intensity/ /arb. units

Normalised at 1200th order

10-1

Harmonic efficiencyn-2.55Relativistic limit

10-2

1200

3200

Order, n

3767KeV

1414KeV

Photon Energy

First coherent, femtosecond,

sub-nm source

roll over scaling confirmed as g 3
Roll over scaling confirmed as ~g3

Roll-over measurements

8g3

4g2

Vulcan 1996

highest observed

22

(6 1020Wcm-2m2)

Roll over ~g3 10 keV pulse @ a0~30 (1021Wcm-2m2)

slide12

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

1

0.8

kT~3keV

0.6

Intensity/ arb. units

2.5x1020Wcm-2

0.4

kT~1.5keV

0.2

7x1019Wcm-2

2 3 4 5 6 7 8

Wavelength /Å

Planckian Spectrum observed for standard contrast

Signal brightness ~2x HHG signal

Plasma mirrors are essential

Absorption much higher for low contrast pulses.

slide13

Beamed keV harmonic radiation - coherent keV radiation

1

0.8

0.6

X-ray Signal > 1 keV

4º FWHM Gaussian fit to beamed HHG signal

0.4

0.2

-100 50 0 50 100 150

specular

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

X-ray emission above 1keV and 3w 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

slide14

Surface denting

Laser

Ponderomotive pressure can deform surface.

(under the current conditions some deformation is unavoidable

Denting required to explain our results:~ 0.1m

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

 Solution: use shorter pulses to prevent surface deformation

slide15

Summary

  • 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
slide16

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
slide17

Imprinted phase aberration

  • Phase errors in fundamental beam are passed on to harmonics

Dfn~n DfLaser

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

slide18

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 waveform
  • no cut-off infinitely fast risetime components (unphysical)
  • Recently: Rollover for n> 4g2

(Gordienko et al (PRL,93, 115002, 2004)

  • Revised theory predicts rollover for n>81/2g3

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

Very different predictions for reaching 10,000 harmonics:

4g2: a0=50 81/2g3: a0=22

slide20

What determines the angular distribution?

1) What determines the angular distribution?

Diffraction limited peformance would suggest qharmonic~qLaser/n

 qharmonic~10-4 rad for keV harmonics.

  • 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 g)
slide21

High Efficiency

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

Extremely powerful attosecond source

Ultrahigh brightness may be possible with DL performance

slide22

Experimental paramters

Pulse Energy (No Plasma Mirror):up to 500J

Pulse energy with PM: up to 150 J

Pulse duration: 500-600fs

Contrast (no PM) >107:1

Contrast with PMs: >1011:1

Spot size: ~7m

Peak intensity (with PM) 2.5 1020Wcm-2

slide23

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)

slide24

PIC predicts asymptotic limit of pREL~2.5-3

Exact value of p is pulseshape dependent

Orders > 1000,

keV harmonics!

Gordienko et al. PRL 93, 115001, 2004

slide25

Conversion efficiency into attosecond pulses

~n-3/2

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

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

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

slide26

Laser contrast is the key to high efficiency.

1.3x104

1.2x104

1.1x104

1x104

9x103

Reference Spectrum (arb.)

Harmonic Spectrum (arb.)

Signal (arb)

8x103

~

~

~

~

No plasma mirrorContrast ~10-8

1200

b)

C-line @3.4nm

1000

800

C-line @4.01nm

600

Source Broadening increases

linewidth in no PM case

400

200

0

360 380 400 420 440 460 480 500

Pixel number

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