Single-shot compressed optical field topography

Abstract

Femtosecond lasers are powerful in studying matter's ultrafast dynamics within femtosecond to attosecond time scales. Drawing a three-dimensional (3D) topological map of the optical field of a femtosecond laser pulse including its spatiotemporal amplitude and phase distributions, allows one to predict and understand the underlying physics of light interaction with matter, whose spatially resolved transient dielectric function experiences ultrafast evolution. However, such a task is technically challenging for two reasons: first, one has to capture in single-shot and squeeze the 3D information of an optical field profile into a two-dimensional (2D) detector; second, typical detectors are only sensitive to intensity or amplitude information rather than phase. Here we have demonstrated compressed optical field topography (COFT) drawing a 3D map for an ultrafast optical field in single-shot, by combining the coded aperture snapshot spectral imaging (CASSI) technique with a global 3D phase retrieval procedure. COFT can, in single-shot, fully characterize the spatiotemporal coupling of a femtosecond laser pulse, and live stream the light-speed propagation of an air plasma ionization front, unveiling its potential applications in ultrafast sciences.

Fig. 1. Principle of COFT based on wavefront recovery and non-collinear FROG.

a The experimental setup. An arbitrary optical field at CP, the checking point, is split by beam splitters (BS1, BS2) into three copies: the first copy goes to the Non-Collinear FROG for spectral phase ${\phi }_{\mathrm{Spectral}}^{\left(x_0,y_0\right)}\left(\omega \right)$ measurement; the second one is imaged by a lens L1 to the coded aperture; and the third one is focused by L2 to a far-field which is imaged to the coded aperture by L3. The last two copies are spatially off-set and captured by a CASSI system including the coded aperture, a lens L4, a prism, and a camera. Raw data is shown in the inset. b CASSI reconstruction results for the second copy corresponding to the near field intensity distribution ${∣E_{\omega }\left(x,y\right)∣}^2$ (the top row) and the third one corresponding to the far-field intensity distribution ${∣E_{\omega }\left(k_x,k_y\right)∣}^2$ (the bottom row), for three wavelengths at 780 nm (left), 800 nm (middle), 820 nm (right). c Wavefronts [2D spatial phase distributions ${\phi }_{\mathrm{Spatial}}^{\left(\omega \right)}\left(x,y\right)$] for three spectral components with the wavelength of 780 nm (left), 800 nm (middle), 820 nm (right), which are retrieved based on corresponding near- and far-field intensity profiles shown in b. d Spectral phase ${\phi }_{\mathrm{Spectral}}^{\left(x_0,y_0\right)}\left(\omega \right)$ reconstructed from the non-collinear FROG trace, with the assistance of 2D optical field information of each spectral component. The inset schematically shows the principle of non-collinear FROG: two copies of the incident pulse cross each other at a thin nonlinear BBO crystal, and they have a linearly varying temporal delay along the transverse direction, generating transversely distributed sum frequency signal or the FROG trace

Fig. 2. 3D topographic maps of femtosecond laser pulses measured by COFT based on wavefront retrieval and non-collinear FROG.

a Spatiotemporal distribution of the electric field of a femtosecond laser pulse from a kilohertz, millijoule femtosecond laser amplifier. b Temporal profile of the electric field (blue lines) at the central point $\left(x,y\right)=\left(0,0\right)$ of the laser pulse in a, and the red dashed line shows the amplitude envelope. c Similar to a, but for spatiotemporal electric field distribution of a femtosecond laser pulse with spatiotemporal coupling, which is induced by propagating the laser pulse in a glass prism at CP. To avoid too fast oscillations of the field and get a clear visualization, the carrier wave frequency in c has been numerically reduced by 10 times. d Similar to b, but for the temporal profile of the electric field at the central point in c. To clearly show the peaks and valleys of the optical fields in a and c, only regions where the absolute amplitude is higher than 0.4 times the peak absolute amplitude are shown

Fig. 3. Visualization of light-speed propagation of an air plasma ionization front by COFT measurement of the probe pulse.

a Schematic diagram of the pump-probe experiment visualizing the light-speed propagation of the air plasma ionization front in air. The pump pulse (1 mJ, 40 fs) propagating along the x-direction is focused and ionizes the air. The probe pulse detects the pump-induced refractive index shift transversely and enters a COFT system based on wavefront retrieval and non-collinear FROG, with the interacting region as CP. The inset cartoon shows the process of the probe picking up the pump-induced phase shift. At time t₁, the pump and the plasma channel overlap with the leading edge of the probe; at time t₂, with the probe central part; at time t₃, with the trailing edge. b Representative frames of the probe pulse transverse phase shift profiles in the x-y plane at $t=0,285,579$ fs. The yellow dashed line shows the position of the ionization front at different time. c Linear fitting of the ionization front positions at different time, and the slope is consistent with light speed. d Free electron density profile along the black dashed line in b, reconstructed via a standard Abel inversion scheme

Fig. 4. Principle of COFT based on 3D spectral holography.

a The experimental setup. The incident optical field at CP, the checking point, is pre-chirped by an SF11 glass rod (GR1) and split by beam splitter BS1. The transmitted gating pulse is focused by the lens L1 to a thin glass plate as the Kerr medium. The reflected pulse is further chirped by an SF11 glass rod (GR2) and manipulated by a Mach-Zehnder interferometer (MZI) to generate a time-delayed reference-signal pulse pair. The reference-signal pulses are imaged by lens L2 to the Kerr medium, and the signal pulse picks up phase shift induced by the gating in the Kerr medium. After the cross-polarized gating pulse is filtered out by a polarization beam splitter (PBS), the remaining reference and signal pulses interfere and generate a 3D spectral hologram, which is imaged by lens L3 to the coded aperture of a CASSI system. Raw data is shown in the inset. b CASSI reconstruction of the 3D spectral hologram $S\left(x,y,\omega \right)$ due to interference between the reference and the modulated signal probe. c The ${∣E\left(k_x,k_y,t\right)∣}^2$ and ${∣E\left(x,y,\omega \right)∣}^2$ 3D intensity profiles of the incident optical field. The former is predominantly obtained from the phase shift $\theta \left(x,y,\omega \right)$ coded in the 3D spectral hologram. ${∣E\left(x,y,\omega \right)∣}^2$ and $\theta \left(x,y,\omega \right)$ are reconstructed from the 3D spectral hologram $S\left(x,y,\omega \right)$ through the standard interference fringe analysis procedure

Fig. 5. 3D topographic maps of femtosecond laser pulses measured by COFT based on 3D spectral holography.

a Spatiotemporal distribution of the electric field of a femtosecond laser pulse from the same laser system as Fig. 2. To clearly show the peaks and valleys of the optical fields, only regions where the absolute amplitude is higher than 0.4 times the peak absolute amplitude are shown. b Temporal profile of the electric field (blue lines) at the central point $\left(x,y\right)=\left(0,0\right)$ of the laser pulse in a, and the red dashed line shows the amplitude envelope