Time reversed optical waves by arbitrary vector spatiotemporal field generation

[M. Mounaix et al., Nat. Commun., 11 (2020)]

Time-reversal allows precisely tailoring the spatio-temporal field and was originally demonstrated in acoustics. Time-reversal requires to temporally modulate the optical field independently over a large number of pixels, which is challenging in optical experiments. In the present paper, the authors developed a system allowing the modulation of the optical field spectrally and spatially over a 2d array. Harnessing this new tool, they perform a time-reversal experiment to focus and shape the optical field temporally and spatially through a multimode fiber.



The idea of time-reversal is the following; when a short pulse excites locally a complex medium, the signal is broadened temporally and spatially in a seemingly random fashion after propagation. By recording the temporal signal at a given set of positions, and sending the signals reversed in time, the time-reversal symmetry of the wave equation guarantees that the light focuses back to its original position into a short pulse. In essence, time-reversal allows pre-distorting the wavefront to compensate for the spatio-temporal distortion induces by the inhomogeneity of a linear medium, regardless of its complexity.

Wavefront shaping experiments done in the monochromatic regime usually allows modulating the complex field on 2 spatial dimensions transverse to the optical axis using a spatial light modulator. Over the past decade, demonstration of optical time reversal has been made using 2 dimensions, either two spatial dimensions or one temporal or spectral dimension and one spatial dimension. In the first case,  light focusing through a complex media is obtained by only modulating the optical field spatially using a short excitation pulse. The temporal degrees of freedom are not controlled independently on the different pixels of the modulator, limiting the efficiency of the approach compared to optimal theoretical results. In the latter case, one spatial dimension is sacrificed to allows for the temporal or the spectral control, this time reducing the spatial degrees of freedom controlled. These limitations are imposed by the 2d nature of the SLM array.


3D spatio-temporal shaper

In this paper, M. Mounaix et al. present a device capable of measuring and generating arbitrary spatiotemporal optical beams. It allows modulating independently the temporal degrees of freedom of the optical beam on a 2d array. The key component is a multiplane light convert that allows mapping one dimension of the SLM into a 2d array of spots. While one dimension of the SLM is used to control the spectral component of the optical field, it allows achieving a full 3d modulation (2 spatial dimensions plus one temporal/spectral dimension).

A simplified schematic of the device is presented in Fig.1. The input light beam propagates towards a multi-port (45 inputs per polarization) polarization-resolved spectral pulse shaper. The output ports of the pulse shaper are aligned on a linear 1D array of 45 Gaussian spots. The amplitude and phase of each spot can be controlled by programming the spatial light modulator (SLM) inside the pulse shaper. The SLM is split into two parts, one for each orthogonal polarization state. The vertical axis of the SLM enables spatial steering along the 1D array, while the horizontal axis corresponds to the spectral control. The 1D array of Gaussian spots is mapped to a 2D set of Hermite-Gaussian (HG) modes through a multi-plane light conversion device.

Figure 1: Simplified schematic of the device capable of generating any arbitrary vector spatiotemporal output field.


Optical time-reversal

The goal is then to use this 3D wavefront shaper to compensate for the spatio-temporal distortion introduced by a complex medium. In this work, the authors choose to use a multimode fiber. A schematic of the full setup is presented in Fig.2. To demonstrate full optical time reversal, the device must be able to compensate for any scattering path light can take along propagation through the medium. The output of the device is coupled to a 5-meter-long graded-index (OM3) multimode fiber, that supports 45 propagating modes per polarization state. The first step of the time-reversal experiment consists in measuring the full polarization-resolved multi-spectral transmission matrix which is equivalent to measuring the impulse response of the system as it is done in typical acoustic experiments. To do so, the authors measure the output spatial fields for each polarization component as a function of frequency for each of the 90 input modes between 1535 nm and 1570 nm, with a spectral resolution of 0.12 nm.


 Figure 2: Schematic of spatiotemporal field generation and characterisation apparatus.

Time-reversal allows generating any arbitrary complex vector fields at the output of the fiber. This is done by convoluting the time-reversed impulse response of the system by a target signal. In the matrix formalism, it amounts to multiplying the desired output spatiotemporal or spatiospectral states by the conjugate transpose of the measured transmission matrix at each wavelength. The input field is generated by programming a phase mask onto the SLM. Once the hologram is displayed on the spatial light modulator, the output field is characterized.



Fig.3 illustrates various examples of full spatio-spectral and full spatio-temporal control at the output of the fiber, where arbitrary fields can be created in arbitrary polarizations at arbitrary delays with a spectral resolution of ~0.12 nm and a temporal resolution ~230 fs. For spatiotemporal patterns, the desired output is specified in the time domain rather than in the spectral domain. The output field is characterized in the spectral domain using swept wavelength digital holography, and its Fourier transform yields the corresponding temporal response. Extensive technical details are discussed in the Supplementary Information.

This new ability to fully control a light beam can open interesting perspectives for optical imaging, nonlinear optics, and optical manipulation.