EPJ Web of Conferences 205, 02023 (2019)
UP 2018

https://doi.org/10.1051/epjconf /201920502023

High harmonic generation in solids driven by sub-cycle
mid-infrared pulses from laser filamentation
Fumitoshi Kumaki1,2 , Hideto Shirai1 , Yutaka Nomura1 , and Takao Fuji1,∗
1
2Institute for Molecular Science, 38 Nishigonaka, Myodaiji, Okazaki 444-8585, JapanThe Graduate University for Advanced Studies (SOKENDAI), Myodaiji, Okazaki 444-8585, Japan
Abstract. Carrier-envelope phase (CEP) controlled subcycle mid-infrared

pulses from two-color laser filamentation have been applied for high harmonic(HH) generation in a crystalline silicon membrane. The HH spectrum reaches
the ultraviolet region (<300 nm), beyond the direct band gap of the silicon.
The shape of the HH spectrum shows the strong dependency on the CEP of theinput pulse. The complete waveform characterization of the sub-cycle driverpulse with frequency-resolved optical gating capable of CEP determination isthe effective method for the studies of the sub-cycle dynamics.

1 Introduction
In the last few years, high harmonic generation (HHG) in solids has been actively researchedin the field of ultrafast science and solid-state physics. HHG in solids would be more efficientsince the atomic density is much higher than in gases. Therefore, HHG in solids is expected
to become a key technology to realize compact solid-state attosecond pulse generator andPHz electronics.
One of the most straightforward approaches to investigate the single-cycle ultrafast phenomena like HHG is the experimental study with well-characterized single-cycle or sub-cycle
pulses [1]. It enables us to observe the phenomena driven by single-cycle fields. In the MIR
experiment, the waveform dependence, namely carrier-envelope-phase (CEP) dependence, ofthe high-harmonic (HH) spectra has not been studied. In this contribution, we report the HHG
in the silicon membrane driven by CEP-controlled sub-cycle MIR pulses generated throughfilamentation.

2 Experiment
The light source was based on a Ti:sapphire multipass amplifier (800 nm, 30 fs, 0.85 mJ
at 1 kHz, Femtopower compactPro, FEMTOLASERS). CEP stable sub-cycle MIR pulses(4 μm, 8.5 fs, 360 nJ) were generated from two-color filamentation [2]. The intensity andelectric field strength of the MIR pulse was estimated as about 0.5×1012 W/cm2 and 0.18 V/Å.
The waveform of the MIR pulse was characterized with frequency-resolved optical gating capable of the CEP determination (FROG-CEP) [3]. The characterized MIR pulse was focused
onto a crystalline (100) silicon membrane (Si, t =200 nm, Norcada). The spectrum of the HH
generated from the back surface of the membrane was introduced into a spectrograph with anelectron-multiplying CCD camera (SP-2358 and ProEM1600, Princeton Instruments).
∗ e-mail: fuji@ims.ac.jp© The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the Creative
Commons Attribution License 4.0 (http://creativecommons.org/licenses/by/4.0/).

EPJ Web of Conferences 205, 02023 (2019)
UP 2018

https://doi.org/10.1051/epjconf /201920502023

3 ResultField (arb.units)

Phase (rad/π)Power (arb.units)

Wavelength (µm)
Figure 1(a) shows a power1(b)10 532
spectrum and spectral phase of2the MIR pulse measured with(a)1FROG-CEP. The power spec01.5
trum is broader than three oc0.8-0.10π
taves. The spectral phase has
1some nonlinear term, which
-10.6
10.5
means that the MIR pulses
are slightly chirped.
Fig−0.10π
0.40ure 1(b) shows the character0ized waveforms of the sub0.2-0.5−0.77π-0.77πcycle MIR pulses for thephases of −0.10π, and −0.77π
0-1-1
00.2
0.40.60.8
at 4 μm. Figure 2 shows-40-2002040
Photon energy (eV)the HH spectra driven by theTime (fs)MIR pulses shown in Fig. 1(b).
The HH spectrum reaches theFigure 1. (a) Power spectrum and absolute spectral phases.
ultraviolet region (<300 nm).
(b) Retrieved waveforms of the MIR pulses.
The shape of the HH spectrum
is very complex. There is no clear structure such as plateau or cutoff in the spectrum, eventhe orders of the harmonics is unclear.

4 CEP dependence of the HH spectrum

Power (arb.units)

Wavelength (µm)
Figure 3(a) shows the CEP dependence of0.7
0.60.50.40.3
the HH spectrum recorded continuously
105−0.10πwhile CEP scanning from −π to π. Three−0.77π
104features can be seen in this figure. First isthat the HH spectrum shifts to higher pho103
ton energy region as the CEP of the MIR
102
pulse increases. Second is that the samespectrum appears at every π phase shift.
101
Third is that the CEP dependence of the100
22.5
33.5
4
HH spectrum discontinuously changes at
Photon energy (eV)around 3.1 eV, which corresponds to thedirect band gap energy of Si. We believe
Figure 2. The HH spectra generated by the subthat this change is due to the increase incycle MIR pulses shown in Fig. 1(b)the imaginary part of the refractive index
at around the direct band gap.
To investigate the complex structure and CEP dependence of the HH spectrum, we numerically simulated the CEP dependence of the HH spectrum based on the optical Blochequations generalized to the case of a two-band semiconductor [4]. In this numerical simulation, we used the waveform of the sub-cycle MIR pulse measured with FROG-CEP as adriving field.
Figure 3(b) shows the HH spectrum CEP dependence obtained by the simulation. As isthe case with experimental results in Fig. 3(a), the structure of the HH spectrum shifts tohigher photon energy region by increasing of the CEP of the driving pulses and, the samespectrum appears at every π phase shift. There is also the discontinuous change of the CEP2

EPJ Web of Conferences 205, 02023 (2019)
UP 2018

https://doi.org/10.1051/epjconf /201920502023

Phase (rad/π)Phase (rad/π)Phase (rad/π)dependence of the HH spectrum at around 3.1 eV. In this simulation, the main features of theexperimental result have been reproduced qualitatively.
Next, to clarify the effect of subWavelength (μm)
cycle driving pulse, we simulated the0.7 0.6
0.5
0.4
0.3
CEP dependence of the HH spectrum
1105(a)with the transform-limited pulses, ob104
0.5
tained by assuming a flat phase with the103
same spectrum measured with FROG0102
CEP. Figure 3(c) is the CEP dependence−0.5101of the HH spectrum simulated by using−1100
the transform-limited pulse. In contrast
1105
to the simulation result obtained by us(b)1040.5ing the waveform measured in the ex103
periment, the spectrum does not shift to0102
higher photon energy region by chang−0.5
101
ing the CEP. This result indicates that theCEP dependence of the HH spectrum is−11001105
very sensitive to the chirp of the driver
(c)
104
0.5
pulse.

5 Conclusion

103
0−0.5

102101The sub-cycle MIR pulse generated
−1100
22.5
33.5
4
through filamentation has enough intenPhoton energy (eV)sity to induce nonlinear effects in solids.
The HH spectrum in a silicon membrane
Figure 3. CEP dependence of the HH spectrum.
driven by the sub-cycle pulse spread to(a) Experimental result. (b) Numerical simulathe ultraviolet region (<300 nm). Sincetion result obtained from optical Bloch equations.
the spectrum of the sub-cycle pulse is(c) Simulation result with the transform-limited
broader than three octaves, many orpulses.
ders of the harmonics interfere with eachother. The interference signal of the HH
spectrum is very sensitive to the CEP ofthe input pulse. Therefore, FROG-CEP measurement which can determine the waveform of
the pulse including the absolute CEP value is very useful to investigate field sensitive nonlinear phenomena in solid state [5].

References[1] T. T. Luu, M. Garg, Y. Kruchinin, A. Moulet, M. T. Hassan, and E. Goulielmakis,Nature 521, 498 (2015).
[2] T. Fuji, Y. Nomura, and H. Shirai, IEEE J. Sel. Quantum Electron. 21, 8700612 (2015).
[3] Y. Nomura, H. Shirai, and T. Fuji, Nat. Commun. 4, 2820 (2013).
[4] C. F. Klingshirn, Semiconductor Optics (Graduate Texts in Physics, Springer, 2012) 813.
[5] H. Shirai, F. Kumaki, Y. Nomura, and T. Fuji, Opt. Lett. 43, 2094 (2018).

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