Multi-spectral PSF engineering through a complex medium with a transmission matrix approach (Conference Presentation)

Propagation of coherent light through a disordered medium generates a speckle pattern at the output, due to light scrambling by multiple scattering events. Over the last decade, wavefront shaping techniques have opened a new way to perform imaging through disordered systems, using spatial light modulators (SLM). In particular, the optical transmission matrix (TM) links the input field, modulated by the SLM, to the output field. It enables arbitrary diffraction limited spatial focusing of light after propagation in the medium. We recently extended this technique to arbitrary focus shape, by numerically computing a mask (amplitude and/or phase) onto a virtual pupil accessible via a Fourier transform operation. This TM method has also recently been extended to the spectral domain using the Multi-Spectral Transmission Matrix (MSTM). MSTM is a stack of monochromatic TMs for different wavelengths of a broadband pulse. In conjunction with a SLM, this operator makes a scattering medium behave like a arbitrary dispersive element or pulse shaper. Here, we generalize our PSF-control ability to the spectral domain, we experimentally demonstrate focusing a broadband pulse with a different PSF for two different wavelengths domains. Controlling these spectrally dependent k-spaces opens also interesting perspectives to achieve Temporal Focusing (improved depth sectioning for multiphoton excitation), at the output of thick scattering medium. We present numerical simulations of such temporal focusing, and study the advantages of our technique compared with conventional temporal focusing methods.