Visible supercontinuum generation in solid-state materials excited with

=A˜1(ω) 2+A˜3(ω) 2+2A˜1(ω) A˜3(ω) cos 2φcep+ωτd−π 2 , (5.11)

where ˜A3(ω) is a spectral amplitude of a TH. We derived the CEP effect on the phase of the

interference pattern obtained by the nonlinear interferometry. The phase shift of an interference fringe is affected by the CEP of the laser pulses two times more for the f -to-3 f interferometry than for the f -to-2 f interferometry. From these dependence, we could distinguish the order of an optical nonlinear effect from the analysis of the amount of the phase shift in the interference pattern induced by a arbitrary CEP change. Therefore we could examine an origin of a unknown nonlinear effect by this method. Later this technique will be used to determine the physical origin of the visible supercontinuum.

5.1.3

Visible supercontinuum generation in solid-state materials excited

with infrared pulses

As seen above, to obtain the information about the CEP of an ultrashort pulse, an octave-spanning spectrum is necessary to utilize a nonlinear interferometry. For our case, because the few-cycle infrared pulses obtained from the infrared OPCPA system do not have an octave-spanning spec- trum, we have to resort to any spectral broadening to achieve it. We have tried broadening by two ways, spectral broadening in a gas-filled hollow fiber [33] and supercontinuum generation in solid-state materials [72]. The use of supercontinuum generation in solid-state materials turned out to be the only choice for this purpose. The gas-filled hollow fiber did not produce any broad- ening of the infrared pulses. The generated supercontinuum, shown in Fig. 5.1 (A) and (B),

has its broadened spectrum mainly in the visible and not in the infrared. Several-µJ compressed

pulses were focused by a concave mirror (f=100 mm) into transparent materials (fused silica, sapphire, and undoped YAG). Fig. 5.1 (A) shows visible supercontinuum spectra obtained with 1.5-mm-thick fused silica (blue line), 2.0-mm-thick sapphire (green line), and 2.0-mm-thick un- doped YAG (red line), compared to the fundamental spectrum without any sample (black line). Fig. 5.1 (B) shows the fundamental infrared pulse spectrum without any sample (black line) and the broadened spectrum with sapphire (red line). From this figure, in the infrared range around

2.1 µm, while a red wing of the fundamental spectrum was not extended so much, its blue

part was slightly broadened in sapphire. However the fundamental spectrum is still not enough broadened for CEP detection. Despite the unexpected spectral range of the obtained supercon- tinuum, several features such as its conical emission [278, 279], its large beam divergence more than that of the fundamental [280], and its polarization identical to the fundamental pulses were convincing, to some extent, to be identified as the supercontinuum.

500 1000 1500 0.00 0.05 0.10 700 600 500 400 300 200 1.6 1.8 2.0 2.2 2.4 2.6 2.8 0.0 0.5 1.0 Frequency (THz) 750 400 No r m a lize d in te n sity ( a r b . u n its) W avelength (nm) No sample 2 mm pure YAG 2 mm sapphire 1.5 mm FS (B) (A) Fundamental spectra Fundamental without broadening

Fundamental with broadening in sapphire plate

In te n sity ( a r b . u n its) W avelength ( m)

Figure 5.1: Spectral broadening of the few-cycle infrared pulse in solids: generation of supercon- tinuum in the visible. (A): supercontinua in the visible obtained with 1.5-mm-thick fused silica (blue line), 2.0-mm-thick sapphire (green line), and 2.0-mm-thick undoped YAG (red line) and the fundamental spectrum without any sample (black line). (B): Fundamental spectra without broadening (black line) and with broadening in sapphire (red line).

In the early days, spectral broadening of the nanosecond-picosecond pulses has been ob- served in liquid [281] and solid [282, 283] and main contribution to spectral broadening has been attributed to the SPM effect. Because of the availability of ultrashort laser pulses with the duration of hundred femtoseconds from 1980s, supercontinuum generation has been observed by use of femtosecond laser pulses [87]. In the case of the femtosecond pump pulse, self-steepening of the exciting pulse as well as SPM plays an important role in the spectral broadening [284]. Al- though the wider broadening should be expected for a sample with the higher Kerr-nonlinearity in this scenario this is not the case in the real experiment [285] and even supercontinuum in a less nonlinear medium proves to be broader [286]. A currently accepted scenario is that self-focusing and self-steepening of the ultrashort laser pulse contribute to the asymmetric broadening [287] and self-focusing is halted before the catastrophic pulse collapse due to the negative contribution to the refractive index from the plasmas created by the multiphoton ionization in the medium. Therefore the cut-off of spectral broadening becomes dependent on the band gap of a medium and the cut-off becomes more extended for a medium with the higher band gap [286, 288, 289, 280]. This tendency is clearly observed in Fig. 5.1. The supercontinuum obtained in the fused silica, which has the highest band gap among the three samples has the bluest cut-off of the supercon- tinuum and the undoped YAG resulted in the spectral broadening in the infrared region. So far

the longest wavelength of pump pulses, which can generate a visible supercontinuum, is 1.5µm

[290]. To confirm the origin of the visible emission, where CEP detection and stabilization will be achieved by use of nonlinear interferometry, the spectral phase relation between the funda- mental and supercontinuum could be derived using the above formulation of CEP dependence from the spectral phase of the interference pattern. In the next subsection, nonlinear interfer-

5.1 Visible supercontinuum generation in solid-state materials and CEP detection of

infrared pulses by use of an f -to-3 f interferometry 89

ometry will be achieved by spectrally overlapping the TH of the fundamental and the obtained visible supercontinuum possibly around 700 nm (an f -to-3 f nonlinear interferometry) and we will study its phase dependence on the CEP.