deletions | additions       diff --git a/When_a_laser_beam_of__1.tex b/When_a_laser_beam_of__1.tex  index cd0d248..609c025 100644  --- a/When_a_laser_beam_of__1.tex  +++ b/When_a_laser_beam_of__1.tex 
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When a laser beam of sufficient energy is incident on a medium, the absorption of the electromagnetic radiation leads to an increase of the local temperature. Due to thermal effects, displacements occur in the medium which can propagate as elastic waves. Elastic waves can be separated in two components in a bulk: compression waves, corresponding to a curl-free propagation; and shear waves, corresponding to a divergence-free propagation \cite{aki2002quantitative}. This phenomenon has been notably observed in metals. Measures of the compression and shear waves is notably used as a method of inspection to reveal potential cracks in the solid.  In a medical context, induction of compression waves by laser has been studied for the last ten years, with the development of photoacoustic imaging \cite{Xu_2006}. In this technique, a laser beam is absorbed by the tissue, which induces by thermal expansion compression waves, which are themselves acquired by acoustic transducers. Time of flight measurements allows then to find the source of the waves and thus, to map optical absorption of the tissues \cite{22442475}. As the optical absorption coefficient of the tissue depends on the optical wavelength, different structures can be observed by tuning properly the laser wavelength. For example, oxygenated and de-oxygenated haemoglobin can be discriminated in this way way.  Noninvasive imaging of hemoglobin concentration and oxygenation in the rat brain using high-resolution photoacoustic tomography\cite{16674205}. The frequency of the elastic waves used in photoacoustic imaging are typically of a few megahertz. At this frequency, shear waves are quickly attenuated, typically over a few microns in soft tissues, so only compression waves can propagate over a few centimeters. We hypothesized in this study that a laser beam in a soft tissue can nevertheless induce shear waves in addition to compression waves. Shear waves have drawn an increasing interest in medical imaging, with the development for the last two decades of shear wave elastography methods \cite{muthupillai1995magnetic}, \cite{10385964}, \cite{sandrin2002shear}. As its names indicates, this term covers the techniques used to measure or map the elastic properties of biological tissues using shear wave propagation. The shear modulus, directly proportional to Young's modulus in soft tissues, varies indeed of several orders of magnitude in human body and potentially offers an excellent contrast. As a shear wave propagates in an organ at a speed proportional to the square root of the shear modulus, measuring its speed throughout the organ allows to compute the shear modulus of the tissue \cite{10385964}. Shear wave elastography techniques have been successfully applied for the detection of various pathologies in organs such as the liver \cite{sandrin2003transient}, the breast \cite{goddi2012breast}, \cite{sinkus2005viscoelastic}, the prostate \cite{cochlin2002elastography}, \cite{souchon2003visualisation}, the bladder \cite{25574440} and the eye cornea \cite{tanter2009high}, \cite{22627517}. 
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