Probing the $\pi -{\pi }^{*}$ transitions in conjugated compounds with an infrared femtosecond laser

We show that the processes of $\pi -{\pi }^{*}$ transitions imprint themselves on the high-harmonic spectra when conjugated molecules interact with intense femtosecond laser pulses. It is found that a noninteger order peak appears in the harmonic spectrum with the photon energy equaling the excitation energy of the $\pi -{\pi }^{*}$ excitation. Further studies prove that this radiation is caused by the $\pi -{\pi }^{*}$ transition. The transition signals are prominent and can be easily measured as the corresponding radiation intensities are comparable to those of integer order harmonics. Our results pave the way for the study of excited-state electron-ion dynamics using high-harmonic spectroscopy. In comparison to the traditional absorption spectroscopy method relying on the synchrotron radiation source, the present approach is easily accessible for the use of a tabletop laser-based source. Furthermore, our study also provides a potential tool to probe the $\pi -{\pi }^{*}$ transition processes in femtosecond resolution.

Figure 1

(a) The optical absorption spectra of the benzene for the $x$ and $z$ directions. (b) The schematic illustration of the $\pi -{\pi }^{*}$ transition between the HOMOs (${\pi }_1$ and ${\pi }_2$) and LUMOs (${\pi }_3^{*}$ and ${\pi }_4^{*}$) of the benzene in the optical absorption response. The geometrical configuration of the benzene molecule and the coordinate system are presented at the top. (c) and (d) The high-harmonic spectra of the benzene driven by laser pulses polarized in the $x$ axis and $z$ axis, respectively. The wavelength of the laser pulse is 800 nm and the laser intensity is $8\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$.

Figure 2

(a) The optical absorption spectra of the trans-1,3-butadiene for the $x$ and $z$ directions. (b) The schematic illustration of the $\pi -{\pi }^{*}$ transition between HOMO (${\pi }_1$) and LUMO (${\pi }_2^{*}$) of the trans-1,3-butadiene molecule in the optical absorption response. The geometrical configuration of the trans-1,3-butadiene and the coordinate system are presented at the top. (c) and (d) The high-harmonic spectra of the trans-1,3-butadiene driven by laser pulses polarized in the $x$ axis and $z$ axis, respectively. The wavelength of the laser pulse is 800 nm and the laser intensity is $8\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$.

Figure 3

High-harmonic spectra of the (a)–(d) benzene and (e)–(h) trans-1,3-butadiene by varying the laser wavelength ranging from 740 to 920 nm. The laser pulse is polarized along the $x$ axis, and the laser intensity is $8\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$. The pink dashed vertical lines indicate the excitation energies of $\pi -{\pi }^{*}$ transitions. The gray dashed diagonal lines indicate the fifth harmonic.

Figure 4

(a) and (b) The schematic illustrations of geometrical configuration and elevation angle $\varphi$ for the benzene and trans-1,3-butadiene, respectively. (c) and (d) The normalized intensities of the parallel component for the H3, H5, H11, and the $\pi -{\pi }^{*}$ transition radiation for the benzene and trans-1,3-butadiene, respectively. $|{\mathbf{d}}_{\pi -{\pi }^{*}}^{\varphi }{|}^2$ presents the modulus square of the transition dipole component parallel to the driving laser. $\varphi$ varies from $0^{\circ }$ to ${90}^{\circ }$. The wavelength of the laser pulse is 800 nm and the laser intensity is $8\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$.

Figure 5

The time-frequency spectra calculated by SST for (a) benzene and (b) trans-1,3-butadiene. The laser pulse is polarized along the $x$ axis. The wavelength of the laser pulse is 800 nm and the laser intensity is $8\times {10}^{13}\mathrm{W}/{\mathrm{cm}}^2$. The dashed horizontal lines indicate the excitation energies $\mathrm{\Delta }E$ of $\pi -{\pi }^{*}$ transitions.