Temporal recompression through a scattering medium via a broadband transmission matrix

Abstract

The transmission matrix is a unique tool to control light through a scattering medium. A monochromatic transmission matrix does not allow temporal control of broadband light. Conversely, measuring multiple transmission matrices with spectral resolution allows fine temporal control when a pulse is temporally broadened upon multiple scattering, but requires very long measurement time. Here, we show that a single linear operator, measured for a broadband pulse with a co-propagating reference, naturally allows for spatial focusing, and interestingly generates a two-fold temporal recompression at the focus, compared with the natural temporal broadening. This is particularly relevant for non-linear imaging techniques in biological tissues.When monochromatic coherent light propagates in a medium with high refractive index inhomogeneities, it quickly develops into a speckle. Despite the complex structure of speckle patterns, each speckle grain has a deterministic relation to the input fields [1]. Over the last decade, wavefront shaping has turned to be an efficient tool to control monochromatic light through highly scattering systems [2], notably by exploiting the transmission matrix [3].Under illumination with a source of large bandwidth, each spectral component can generate a different speckle pattern [4]. Therefore one needs to adjust these additional spectral/temporal degrees of freedom to temporally control the output pulse [5]. This can be achieved using methods such as nonlinear optical processes [6,7], time-gating [8,9], and frequency-resolved measurements [10,11]. However, these methods underly either low signal-to-noise measurements (non-linear processes), or stability issues as they require lengthy acquisition procedures [12] and the need of external reference.An alternative approach is to use self-referencing signals, at the expense of lacking control on spectral degrees of freedom. Recently, "broadband wavefront shaping" experiments reported outcomes disparate from what is expected from monochromatic wavefront shaping, such as a decrease in the independent spectral degrees of freedom [13,14], and recovery of pure polarization states [15]. Notably, these results could have an impact on biomedical imaging [16]. Nonetheless, the exact temporal properties of the obtained output pulse via broadband wavefront shaping remain elusive. In this letter, we report the first characterization of the so-called broadband transmission matrix of a scattering medium. We exploit it for focusing purposes, and we analyze and interpret its temporal behavior. Unexpectedly, the characterized average pulse length is shorter than the pulse propagating without shaping. Figure 1a illustrates and summarizes propagation of broadband light (ultrashort pulse of duration δt, spectral width ∆λ) through an optically thick scattering medium. Transmitted light results in a speckle intensity pattern with low contrast C 0 < 1. This low contrast results from the incoherent summation of various uncorrelated speckles corresponding to different spect...

Focusing large spectral bandwidths through scattering media

“…5b) and reaches ∆ 3 values of 260 nm, about a factor 3 above the bandwidth obtained in the ps (close to monochromatic) regime. This increase is attributed to the coherent gating effect produced by the measurement of the broadband TM transmission matrix [38], which intrinsically enlarges spectral capabilities as recently demonstrated by time gating [41]. When tuning the 2 distance ( 1 is fixed at 2 mm from the diffuser) ( Fig.…”

“…The measured 'broadband TM' has to be distinguished from the 'multispectral TM' reconstructed from a collection of individual monochromatic TM's. The broadband TM has been shown in particular to preserve the short pulse nature of the refocus, due to an intrinsic coherent time gating effect produced by self-reference interferometry [38], provided that the medium bandwidth is comparable with the laser bandwidth. As a consequence a broadband refocus exploits favourably short propagation paths in a scattering medium [40] [38].…”

“…The broadband TM has been shown in particular to preserve the short pulse nature of the refocus, due to an intrinsic coherent time gating effect produced by self-reference interferometry [38], provided that the medium bandwidth is comparable with the laser bandwidth. As a consequence a broadband refocus exploits favourably short propagation paths in a scattering medium [40] [38]. This effect, which has been exploited for nonlinear imaging [9] and polarization-preserved imaging [40], should also have consequences on the spectral bandwidth of the refocus.…”

Manipulating the transmission matrix of scattering media for nonlinear imaging beyond the memory effect

“…External references deliver flat wavefronts, but suffer from instability and make the setup more complex and less compact. The use of an internal reference circumvents this and furthermore benefits from an inherent coherence gating that preserves short pulses [6]. However, there are two drawbacks when using an internal reference encoded onto a spatial light modulator (SLM).…”

Enhanced stability of the focus obtained by wavefront optimization in dynamical scattering media

“…One last perspective could be to extend this study to the broadband regime. Mounaix et al demonstrated a selection of short scattering sequences by exploiting the short coherence length of a pulsed laser through a homogeneous scattering media [24]. By exploiting this effect, one could obtain a further increase in the stability of the focus.…”