Proposal for sub-femtosecond pulse generation with controlled carrier-envelope phase

Proposal for

Proposal for sub sub - - femtosecond femtosecond pulse generation with pulse generation with controlled carrier

controlled carrier - - envelope phase envelope phase

Zoltán Tibai *

¹

, György Tóth

¹

, Mátyás I. Mechler

²

, József A. Fülöp

²

, Gábor Almási

^1,2

, János Hebling

^1,2

1. Institute of Physics, University of Pécs, Ifjúság ú. 6, 7624 Pécs, Hungary

2. HAS-PTE High Field Terahertz Research Group, Ifjúság ú. 6, 7624 Pécs, Hungary

* tibai@fizika.ttk.pte.hu

References

[1] F. Reiter et al., Phys. Rev. Lett. 105, 243902 (2010) [2] http://www.pulsar.nl/gpt/

[3] W.D. Kimura et al., Phys. Rev. Lett. 92, 054801 (2004)

[4] J. D. Jackson: Classical Electrodynamics 3rd ed., Wiley, ISBN 0-471-30932-X

Acknowledgement

This work was carried out with the financial support of the Hungarian Scientific Research Fund (OTKA) grant numbers 101846, the SROP-4.2.2/B-10/2/2010- 0029, the SROP-4.2.1.B-10/2/KONV-2010-0002 and hELIos ELI_09-01-2010- 0013 projects.

Institute of Physics

Deptartment of Experimental Phyisics http://physics.ttk.pte.hu

Conclusion

• A robust method for producing CEP-controlled half-cycle –few-cycle pulses in the EUV–VUV spectral range was proposed

• Shorter than 10 nm microbunch length can be achieved by using a single period undulator with an undulator period shorter than resonant one, and small undulator parameter

• Since up to a few nJ pulse energy can be achieved, these CEP stable pulse can be used as pump in pump – probe measurements

• Generation of attosecond pulses as short as 35 as pulse is possible by the proposed method

• These pulses can be used as seed in SESA FEL

Introduction

• Generation of waveform-controlled single- or few-cycle electromagnetic pulses down to the extreme ultraviolet (EUV) wavelengths is of

considerable interest [1].

• Generation of carrier-envelope phase (CEP) stabilized fs pulses in the VIS- NIR wavelength range is well established, however there are no reliable techniques available for CEP control of attosecond pulses.

• We propose a robust method for producing CEP-controlled half-cycle – few-cycle pulses in the EUV–VUV spectral range.

The proposed setup

• The scheme of the proposed setup is shown in the figure below.

• Method based on

- ultrathin electron layer generation, - coherent undulator radiation.

• We used the General Particle Tracer (GPT) [2] numerical code for

simulation of microbunching by inverse free electron laser (modulator or nanobuncher undulator).

• We calculated the temporal shape of the electric field of the radiation generated in a second undulator (radiator undulator).

Production of ultrathin electron layers

The shortest microbunch length parameters

• Thus far the shortest microbunch length was about 800 nm [3].

• This was obtained with the following parameters:

- undulator parameter: K=3, - undulator period number: 10,

- the undulator period length satisfies the resonant condition:

Simulation results of microbunching

• In order to produce shorter microbunch length we used - smaller undulator parameter: K=0.25,

- High modulator laser power, - only 1 undulator period,

- shorter than resonant undulator period (see the figure on the right).

• During the radiation process the acceleration, velocity and position of the macroparticles were followed numerically by taking into account the Lorentz-force equation:

• We are interested in the temporal shape of the ultrashort pulses emitted by the extremely short electron microbunches in the radiator undulator. We calculated it in a plane 8 m behind the middle of the radiator undulator according to [4]:

( )

( )

ret R

R

v R

R R

t q r E

 

 

 





 

 

 





⋅

−

 





 



 − ×

×

=

⁰ ₃

.

) 4 ,

( β

β π

µ

r r

r r

r r

r r

( ) ^{( )}

)

( q v B z t

dt v m

d r

r r

×

γ =

Scheme of the proposed setup

Our starting parameters

THz Thomson-scattering

• Advantages:

- lower needed electron energy - easier carrier waveform control

• Disadvantages:

- lower attosecond pulse energy - high THz pulse energy needed

Results for resonant (9.7 mm) and optimal (6.7 mm) undulator period

Dependence of the pulse fluence on for 30 nm (blue triangles) 60 nm (green squares) and 1 µm (orange dots).

Examples for pulses generated by undulator radiation (brown) and THz Thomson-scattering (green)

Generated attosecond pulse shapes with different CEP

Single-cycle attosecond pulse generation 0.75 nJ

120 as 42 mT

60 nm 13 cm

1100

0.5 nJ

35 as

100 mT 20 nm

8.7 cm 1960

0.1 nJ 120 as

14 MV/cm 80 nm

3 mm 100

1 µm 60 nm 22 nm 18 nm

λ₀

2 nJ 2.5 fs

4.7 mT 0.9 m

700

0.72 nJ 120 as

62 mT 8.6 cm

900

0.25 nJ 50 as

0.35 T 2.5 cm

900

35 as

∆t

0.1 nJ 465 mT

1.8 cm 900

E_as E_THz,B_u

λ_l , λ_u γ

Calculation method of the electric field and results

0.7 mm Laser beam size inside buncher u.

3.9 TW Laser power

1.3 µm Laser wavelength

9.7 mm Undulator period length

140 µm E-beam radius

3.2 mm mrad E-beam normalized emittance

≈ 1.8 ps E-beam pulse length (1σ)

1.2 nC E-beam charge (total pulse)

0.04 % E-beam intrinsic energy spread (1σ)

32 MeV E-beam energy

Value Parameter

2 / K 1

2

2 l 2

u

+

λ

= γ

λ

^{Resonant Optimal}