Development and application of plasma-waveguide based soft x-ray lasers

Institute of Atomic and Molecular Sciences Academia Sinica, Taiwan

National Central University, Taiwan

Core members of the experimental group

Prof. Jyhpyng Wang (汪治平) ), Academia Sinica (Taiwan)

Prof. Szu-yuan Chen (陳賜原), Academia Sinica (Taiwan)

Prof. Jiunn-Yuan Lin (林俊元), National Chung-Cheng Univ.

Prof. Hsu-Hsin Chu (朱旭新), National Central Univ.

Outline

• General concept of soft x-ray lasers
• Soft x-ray lasers pumped by optical-field ionization
• Fabrication of transient plasma waveguides
• Plasma waveguide based soft x-ray lasers
• Injection seeding with high-harmonic generation
• X-ray digital holographic microscopy
• 100-TW laser system at National Central Univ. (extra 10 min.)

General concept of soft x-ray lasers

X-ray lasers powered by nuclear bomb for “Star Wars”

1983

2p

3p

3s

Ne-like ions: Ar⁸⁺, Ti¹²⁺, Fe¹⁶⁺

collisional excitation (~200 eV)

fast relaxation

lasing

lifetime = ~3 ps

Energy levels of soft x-ray lasers

He-Ne laser

Transverse pumping scheme

solid target

line-focused high-power laser pulse

solid target

collisional excitation in hot plasma

solid target

x-ray lasing

solid target

reflected laser pulse

Pulse sequence for effective excitation

plasma generation

target

pump pulse

time delay to reduce plasma density

gradient by diffusion

plasma heating

Soft x-ray lasers pumped by optical-field ionization

multiphoton

ionization

tunneling

ionization

above-threshold

ionization

Optical-field ionization

appearance intensity for 1⁺ ion (λ=1 μm)

Xe: 8.7×10¹³ W/cm²

He: 1.5×10¹⁵ W/cm²

above-threshold

ionization heating

electrons gain

energy

electron-ion

collisional excitation

population inversion

and lasing

tunneling ionization

​

above-threshold-ionization heating

time

laser field

electron velocity

ionization to

specific ion stage

Pumping by optical-field ionization

Ionization of Xe as a function of intensity

When a laser pulse with appropriate laser intensity is incident into a gas jet, atoms in the jet can be ionized to specific ion species through optical-field-ionization.

Energy levels of soft x-ray lasers

pump pulse

nozzle

Longitudinally pumped optical-field-ionization x-ray lasers

λ

gas jet

defocusing quickly reduces intensity

pump pulse

lower refractive index

higher refractive index

advantages:

• high efficiency
• excellent beam profile
• no debris

problem:

• ionization defocusing

Simulation shows the pump beam diverges quickly due to ionization defocusing. As a result, the x-ray output is limited by the absorption from the weakly pumped medium at the tail.

Tomography of x-ray lasing

machining pulse: 30-mJ, 45-fs,

6-ns before pump pulse.

width of the line focus: 20 μm

6.6×10¹⁷ cm^-3

8.3×10¹⁷ cm^-3

1.1×10¹⁸ cm^-3

0

2

4

6

1

3

5

7

pump pulse: 240-mJ, 45-fs,

focused to 10-μm diameter.

Phys. Rev. A 74, 023804 (2006)

How to make an all optical plasma waveguide?

creating seed

electrons

heating up and

generating more

electrons

shock expansion &

collisional ionization

forming a plasma

waveguide

Plasma waveguide formation from a line focus

Phys. Plasmas 11, L21 (2004)

heater

ignitor

axicon

line focus

line focus

ignitor

heater

length > 1.2 cm

ignitor: 15 mJ, 55 fs

heater: 85 mJ, 80 ps (1.1 ns delay)

probe: 1.2 ns after heater

density variation < 20%

electron density profile

Phys. of Plasma 11, L21 (2004)

Laser drilled plasma waveguide

pump pulse: 45 fs, 235 mJ

ignitor: 45 fs, 45 mJ

heater: 80 ps, 225 mJ

ignitor-heater separation: 200 ps

hearer-pump delay: 2.5 ns

atom density: 1.6×10¹⁹ cm^-3

radial electron density profile

A uniform pure-Kr plasma waveguide of 9-mm length is produced with the axicon-ignitor-heater scheme. The guided beam size is smaller than 15 μm.

(1)

(2)

(1)

(2)

ignitor + heater pulses

pump pulse in waveguide

Unexpected immunity to ionization defocusing

Plasma waveguide based soft x-ray lasers

without waveguide

pump pulse: 45 fs, 235 mJ

focal position: 2.75 mm

pump polarization: circular

pure Kr waveguide

pump pulse: 45 fs, 235 mJ

pump polarization: circular

focal position: 500 μm

ignitor: 45 fs, 45 mJ

heater: 80 ps, 225 mJ

ignitor-heater separation: 200 ps

heater-pump delay: 2.5 ns

trade-off between larger gain coefficient

and more severe ionization defocusing

linear growth (reaching saturation)

exponential

growth

Phys. Rev. Lett. 99, 063904 (2007)

400-fold enhancement by waveguide

Atom density dependence for Ni-like Kr lasing at 32.8 nm

number of photon/pulse

pure Kr waveguide

pump pulse: 45 fs, 235 mJ

pump polarization: circular

focal position: 500 μm

ignitor: 45 fs, 45 mJ

heater: 80 ps, 225 mJ

ignitor-heater separation: 200 ps

heater-pump delay: 2.5 ns

Phys. Rev. Lett. 99, 063904 (2007)

linear growth (reaching saturation)

exponential growth

Pump power dependence for Ni-like Kr lasing at 32.8 nm

optimized lasing

without waveguide

pump energy (mJ)

number of photon/pulse

400 folds

Phys. Rev. Lett. 99, 063904 (2007)

Reduced divergence

without waveguide

with waveguide

energy diagram of Ne-like Ar

raw image recorded by x-ray spectrometer

46.9 nm

46.5 nm

45.1 nm

Phys. Rev. A 76, 053817 (2007)

Multi-line lasing for Ne-like Ar

intensity (arb. units)

Kr/Ar mixed-gas waveguide

pump pulse: 45 fs, 240 mJ

pump polarization: circular ignitor: 45 fs, 45 mJ

heater: 160 ps, 220 mJ Kr atom density: 9.1×10¹⁸ cm^-3

Ar atom density: 1.2×10¹⁹ cm^-3

ignitor-heater separation: 200 ps hearer-pump delay: 1.5 ns

raw image recorded by flat-field spectrometer

Phys. Rev. A 76, 053817 (2007)

gas mixture Kr : Ar = 0.9 : 1.2

Multi-species parallel x-ray lasing

Injection seeding with high-harmonic generation

Experimental set-up

x-ray mirror

parabolic

mirror

axicon

bored lens

parabolic

mirror

pump for high harmonic generation

high harmonic seed

x-ray laser pump

Ar jet

Kr jet

amplified x-ray

pulses for waveguide fabrication (ignitor + heater)

pulse timing diagram

time

Spectrum of the soft x-ray lasers

gas: argon

atom density: 7.1×10¹⁸ cm^-3

pump energy: 3.8 mJ

pump duration: 360 fs

focal position: 1250 μm

gas: krypton

atom density: 1.6×10¹⁹ cm^-3

pump pulse: 38 fs, 235 mJ

ignitor: 38 fs, 45 mJ

heater: 160 ps, 270 mJ

ignitor-heater separation: 200 ps

heater-pump delay: 2.5 ns

parameters of HHG seed:

parameters of x-ray amplifier:

seed-amplifier pump delay: 2 ps

Maximizing the 25th HHG output is achieved by adjusting the pump beam size, pump energy, focal position, and atom density.

The spectral overlap between HHG seed and amplifier is done by adjusting the chirp of HHG pump pulse.

high harmonic seed

unseeded laser

seeded laser

25th harmonic

Intensity (arb. units)

Angular distribution (with waveguide)

gas: argon

atom density: 7.1×10¹⁸ cm^-3

pump energy: 3.8 mJ

pump duration: 360 fs

focal position: 1250 μm

gas: krypton

atom density: 1.6×10¹⁹ cm^-3

pump pulse: 38 fs, 235 mJ

ignitor: 38 fs, 45 mJ

heater: 160 ps, 270 mJ

ignitor-heater separation: 200 ps

heater-pump delay: 2.5 ns

parameters of HHG seed:

parameters of x-ray amplifier:

seed-amplifier pump delay: 2 ps

fluctuations of beam pointing and

angular distribution ~0.13 mrad

With seeding the divergence of the x-ray laser is greatly reduced from 4.5 mrad to 1.1 mrad, which is about the same as that of the HHG seed.

With the waveguide-based soft-x-ray amplifier, the HHG seed is amplified by a factor of 10⁴.

unseeded laser

seeded laser

high harmonic seed

Controlled polarization

detector

polarization analyzer (I_s : I_p > 19)

x-ray laser

unseeded laser

seeded laser

high harmonic seed

The x-ray analyzer consists of two multilayer x-ray

mirrors which are strongly polarization dependent.

The polarization of seeded soft-x-ray laser

follows that of the HHG seed.

spectral brightness (photon/sec/mm²/mrad²) for

NSRRC (Taiwan)

x-ray laser (HHG seeding)

​

6.6×10¹⁴

9.8×10¹²

3.3×10²⁶

7.9×10¹⁴

average spectral brightness at 32.8 nm

peak spectral brightness at 32.8 nm

repetition rate

10⁶ Hz

10 Hz

wavelength

tunable

discrete set

pulse duration

100 ps

200 fs*

Comparing our x-ray laser with synchrotron radiation

* assuming the pulse duration is limited by bandwidth

X-ray digital holographic microscopy

Working principle

focused x-ray laser

object

focusing mirror

CCD camera

constructed images

Experimental set-up

Opt. Lett. 34, 623 (2009)

resolution: 0.5 μm

SEM image

working distance: 20 cm

10 μm

Image of an AFM tip

Opt. Lett. 34, 623 (2009)

100-TW laser at National Central Univ.

Block diagram of the system

100-TW laser system

preamplifier

2nd-stage amplifier

3rd-stage amplifier

power amplifier

compressor chambers

beam switching chambers

experimental stations

experimental stations

full view of the laboratory

100-TW laser at National Central University

energy/duration

peak

power

15-TW beamline

(807 nm)

450 mJ/27 fs

16.7 TW

5-TW beamline

(900 nm)

200 mJ/32 fs

6 TW

100-TW beamline

(808 nm)

3.3 J/33 fs

100 TW

contrast

at

-100 ps

> 10⁸

rep. rate: 10 Hz

2%

2%

3.4%

energy

fluctuation

enclosed

energy*

*energy enclosed in the Gaussian focal spot

66%

75%

78%

> 10⁷

>10⁷

beam-

pointing

fluctuation

18 μrad

3.9 μrad

24 μrad

1.1-1.2 times Fourier transform limit

focal

spot dia.

(×diffraction

limit)

8.0 μm (1.3)

6.0 μm (1.1)

10 μm (1.1)

Focal spot image

Energy stability

standard deviation = 2%

Beam pointing stability

Pulse contrast

Spectra of the three beamlines

• 800-nm, 100-TW beamline� central wavelength = 808 nm� bandwidth = 36 nm (FWHM)
• 800-nm, 15-TW beamline� central wavelength = 808 nm� bandwidth = 36 nm (FWHM)
• 900-nm, 100-TW beamline� central wavelength = 880 nm� bandwidth = 35 nm (FWHM)

Single-shot autocorrelation

• 800-nm, 100-TW beamline

• corresponding pulse duration ~33 fs
• 1.2× Fourier transform limit

100-TW laser test-run data

(750 mJ, 38 fs)

Challenges

• How to increase the acceleration distance to reach the GeV level under sustainable conditions?
• How to control the injection (instead of letting it happen by instability) and inject a large electron bunch?

Ion channel x-ray free-electron laser

Laser-wakefield

electron accelerator

transient ion channel induced

by ponderomotive force

radiation at turning

x-ray output

driving pulse

transverse shifter

for driving pulse

With 500-MeV, 1nC input electron beam, 1-μW,10 KeV x-ray can be produced.

Theoretical estimation:

Ref: Phys. Rev. Lett. 93, 135004 (2004)

Laser-driven proton accelerator

Proton acceleration by target-normal sheath

deflected proton beam

by magnetic field

zero point

proton energy (MeV)

energy spectrum

proton image

proton number (10⁹/MeV)

100-TW laser test-run data

Pulsed spallation neutron source

Proton beam

lead

neutron beam

energy > 10 MeV

conversion efficiency

Ref: New Journal of Physics 7, 253 (2005)

Challenges

• How to beat the scaling laws of current theories and simulations? (10~30 MeV for 100-TW laser)
• How to make the acceleration mono-energetic?

High-harmonic generation

Quasi-phase matching by selective zoning

pump pulse

counter-propagating pulse

beat wave

small phase modulation if

However, for harmonic of order n, the phase modulation is multiplied by n,

which is enough to ruin the phase coherence of harmonic generation.

Ref: Optics Express 1, 125 (1997)

Quasi-phase matching by selective zoning

pump pulse

counter-propagating pulses

harmonic generation

reverse process suppressed

making a long pulse train with only 8-μm period by beating a 6-ps 810-nm

pulse with a co-propagating 6-ps 900-nm pulse

short period to phase match high harmonics

plasma jets in astrophysics

e⁺e^- plasma in astrophysics

proton accelerator

probing high-density plasma

isotope conversion

studying nuclear physics

probing magnetic materials

probing material composition

probing material structure

x-ray laser and high harmonics

nanometer fabrication

flash bio-imaging

electron accelerator

Integrated applications of new techniques

resolving chemical reaction

terahertz-infrared

radiation

100-TW laser

spallation neutron source

free-electron laser

pulsed laser deposition

Thanks for your attention.