Real-time characterization of temporal behaviors of ultrafast lasers is an important and challenging task. Existing methods are typically limited to a few spatial modes or a two-dimensional (2D) space, which is insufficient for adequately portraying the propagation of ultrafast lasers in a medium when superluminal motion is involved. To accurately characterize the propagation of ultrafast lasers in the presence of superluminal motion, it is necessary to record the complete four-dimensional (4D) space-time (x, y, z, t) in which the laser pulse exists. However, most ultrafast cameras are incapable of three-dimensional (3D) imaging. Additionally, when 2D imaging is performed, the tradeoff between the light throughput and imaging depth of field can be a hindrance for capturing superluminal motions, which typically occurs when the light is propagating at a large angle with respect to the camera plane. The objectives of this study were to develop efficient 3D ultrafast imaging methods that can capture the complete 4D space-time with an extended depth of field and to record and analyze superluminal motions with a high spatiotemporal resolution.
Light field tomography (LIFT), which leverages intelligent algorithms and novel optics, is a new method capable of 3D imaging of ultrafast phenomena with a picosecond-scale temporal resolution. The core idea of LIFT is to reformulate image formation as a computed-tomography problem. In LIFT, the spherical lens is replaced with a cylindrical lens, allowing each pixel to record a line integral of the scene along the direction of the invariant axis of the lens (one without optical power). With a one-dimensional (1D) sensor placed at the focal plane of the cylindrical lens, a parallel beam projection of the scene can be obtained, similar to that in X-ray computed tomography. By using a linear array of such cylindrical lenses, each oriented at a distinct angle with respect to the 1D sensor, projection data along different angles can be simultaneously recorded for computationally reconstructing the scene. Meanwhile, the light field information of the scene is obtained by the cylindrical lens array, which allows 3D depth extraction at each time instant; thus, complete 4D imaging is achieved. With an intelligent optimization algorithm, we improved the 3D imaging quality and achieved a light field image resolution of 128×128×7 with a time sequence of 1016 points, allowing the imaging depth of field to be increased approximately sevenfold.
Using LIFT, we captured the reflection of a picosecond laser pulse upon incidence on a mirror in 3D space. As the laser pulse propagates away from the camera, the measured propagation speed of the laser pulse is lower than the actual speed of light, and the speed is further reduced after the laser is reflected by the mirror, which modifies the propagation angle of the laser pulse. Such superluminal motion is made even more evident by coupling the laser into a multimode light-diffusing-fiber and then winding the fiber in a round-trip fashion. In this case, the forward propagation of the laser has a speed of only approximately 36% of the actual speed of light in the fiber, whereas the reverse propagation appears to be significantly faster: the apparent velocity is 135% of the actual speed, which is far faster than the forward propagation. Interestingly, the light field capability of LIFT is found to be critical for clearly resolving the fiber structure, as conventional imaging of the entire fiber structure with a single focal plane induces significant defocus blur. Moreover, we examined the laser pulse broadening inside the multimode fiber. While pulse broadening is common in multimode fibers, doping the light-diffusing fiber core with nanostructures for scattering light accelerates the broadening: within a propagation time of 720 ps, the picosecond laser pulse width increases from 10 ps to 50, 72, and 88 ps at three different points on the fiber. This is similar to laser pulse broadening after propagation through a thin scattering medium.
Using the novel LIFT method, we demonstrated in this study that it is important to consider the 3D nature of light propagation when characterizing the spatiotemporal behaviors of ultrafast lasers. Without accurate 3D information of the laser pulses, the observed speed of light propagation depends heavily on the imaging geometry and the propagation angle of the light. The resultant superluminal motion will distort the spatiotemporal profile of the ultrafast laser pulse, leading to inaccurate interpretations of the dynamics of the laser inside the medium. With accurate 3D information, LIFT can correctly identify the superluminal motions of the ultrafast laser and clarify the temporal variations of the laser pulse at each spatial position, owing to its high spatial resolution (128×128), large depth of field, and deep time sequence (up to 1016 points) acquired with a single snapshot. This paves the way for fully correcting the spatiotemporal distortion of ultrafast lasers caused by superluminal motions, which we aim to achieve in future research.