Deterministic light focusing in space and time through multiple scattering media with a time-resolved transmission matrix approach

We report a method to characterize the propagation of an ultrashort pulse of light through a multiple scattering medium by measuring its time-resolved transmission matrix. This method is based on the use of a spatial light modulator together with a coherent time-gated detection of the transmitted speckle field. Using this matrix, we demonstrate the focusing of the scattered pulse at any arbitrary position in space and time after the medium. Our approach opens different perspectives for both fundamental studies and applications in imaging and coherent control in disordered media.

Figure 1

Apparatus for measuring a time-resolved transmission matrix (TRTM) of a scattering medium. An ultrashort pulse of light generated by a Ti:sapphire laser [central frequency: 800 nm; ${\tau }_0\approx 110$ fs full width at half maximum (FWHM)] is split between a reference and a control path using a combination of a half-wave plate (HWP) and a polarizing beam splitter (PBS). In the control arm, the pulse is reflected by a SLM and injected into a sample of ZnO nanoparticles with a thickness of approximately 100 $\mu \text{m}$ using a microscope objective. The scattered light is collected in transmission by another objective and interferes with the reference pulse onto a beam splitter (BS). The microscope objective together with the lens (L) image of the output surface of the scattering medium onto a charge-coupled device (CCD) camera. A polarizer (P) is used to select only one output polarization. The delay line (DL) inserted in the reference path controls the relative optical path delay between the reference and the scattered pulse. Ph: Pinhole.

Figure 2

Results of spatiotemporal focusing at a given output position and a given time by phase conjugating the time-resolved transmission matrix $H\left(t_a\right)$ measured at the arrival time $t_a=1.6$ ps (denoted by the top arrows). (a) Temporal profiles recorded at the targeted spatial output position in cases of spatiotemporal focusing (red) and spatial-only focusing (blue line) processes. The spatial-only focusing process is performed by applying the phase-conjugation technique to a monochromatic transmission matrix measured at the central wavelength of the incoming pulse. The target position is visible on the CCD image in the inset. An average output temporal profile of the pulse (black line) is obtained by averaging temporal profiles over 100 different speckle grains at the output. The dwell time of the medium is evaluated from this averaged profile to be about ${\tau }_m\simeq 2$ ps. (b) and (c) show temporal profiles and the corresponding CCD camera images for spatiotemporal focusing processes performed at two different spatial positions using the same transmission matrix $H\left(t_a\right)$. The averaged temporal profiles are drawn in black. The scale bars on the CCD images in the inset correspond to 2 $\mu \text{m}$.

Figure 3

Spatiotemporal control of light with a set of transmission matrices ${\left\{H\left(t_a\right)\right\}}_{t_a}$ measured at different arrival times. (a) Temporal profiles acquired using spatiotemporal focusing processes at the same output position and different arrival times (colored arrows). The spatially averaged speckle is used as a reference temporal profile (black curve). Phase components of the TRTM measured are drawn in the inset. (b) Signal-to-background ratio (SBR) measured on the CCD camera for different targeted arrival times and different numbers of modes controlled at the input. The SBR is the ratio of the intensity at the targeted pixel of the CCD camera over the mean intensity value of the full speckle image. The scale bar is 2 $\mu \text{m}$.

Figure 4

Complex spatiotemporal shaping of the output pulse by exploiting the full TRTM. (a) Temporal profiles recorded using a spatiotemporal focusing process at one spatial position and two different arrival times $t_1=1$ ps and $t_2=2.2$ ps. The CCD image in the inset shows the position of the spatial target. (b) Temporal profiles recorded using a spatiotemporal focusing process at the same two different arrival times and at two different spatial positions, visible on the CCD image in the inset. The scale bar is 5 $\mu \text{m}$.