Dynamical Franz-Keldysh Effect in Diamond in the Deep Ultraviolet Probed by Transient Absorption and Dispersion Spectroscopy Using a Miniature Beamline

Here, we introduce a miniature beamline for transient absorption and dispersion spectroscopy, using a tailored deep ultraviolet field immediately after the noncollinear generation without subsequent optical elements. We explore the near-band-gap region in diamond in the presence of a few-femtosecond pump pulse where the delayed dynamical Franz-Keldysh effect and the almost instantaneous optical Kerr effect coexist.

Figure 1

Miniature beamline for DUV transient absorption and dispersion. (a) The VIS-IR pulses $A$ and $B$ are used to generate the DUV pulses $U$ and $V$ in the generation sample (${\mathrm{MgF}}_2$). The TADS sample (diamond) is placed a few centimeters behind the generation sample where it is overlapped with the pump pulse $R$. The polarization of all fields is in $y$ direction. The normalized electric fields of the pulse sequence locally at the TADS sample is shown in (b). The transverse beam profiles of $U$, $V$, and $R$ at the location of the TADS sample are shown in (c). (d) The spatial resolution in the $y$ dimension of a DUV spectrometer is used to discriminate the signal (originating from the spatial overlap of the DUV pulses with $R$ in (c) and the reference [originating from a location outside the beam profile of $R$ in (c)].

Figure 2

The sketches provide a visual interpretation of transient absorption (a) and transient dispersion (b). The experimental data of a 250 nm-thick diamond membrane are shown in (c) and (e). The magnitude $|\mathrm{\Delta }T|$ is displayed in (c) and the phase ${\phi }_{\mathrm{\Delta }T}$ in (d). The average in the interval $[5.3,5,5]\mathrm{eV}$ is shown in (e) for comparison with the calculations using two bands (f) and three bands (g).

Figure 3

The calculation of TADS in a 5 nm-thick diamond membrane using two bands [(a) and (b)] and three bands [(c) and (d)]. The magnitude $|\mathrm{\Delta }T|$ is displayed in (a) and (c) and the phase ${\phi }_{\mathrm{\Delta }T}$ in (b) and (d).

Figure 4

(a) The three characteristic regions of the DFKE. (b) The magnitude $|\mathrm{\Delta }T|$ calculated using two bands with $t_U^{\mathrm{FWHM}}=1\mathrm{fs}$ and ${\omega }_U^{\mathrm{center}}=6.5\mathrm{eV}$. (c) the band energies (see Supplemental Material) for the calculations with two bands (${\omega }_1$ and ${\omega }_2$) and 3 bands (additionally ${\omega }_3$); $a$ is the lattice constant. (d) The electric field of $U$ ($E_U$, blue solid) and the linear polarization response ($P$, blue dotted) in spectral domain. The extinction coefficient (the imaginary part of the refractive index of the band model) is shown in red. The time-domain representations of $E_U$ and $P$ are shown in (e) and (f).