small sphere, inversion symmetry is broken, allowing for SHG and other even order harmonics to occur. For a colloidal system of microparticles at relatively low concentrations, the total SH signal , is given by: where is the SH electric field generated by the jth particle, and n the density of particles. The SH light generated from each particle is coherent, but adds incoherently to the SH light generated by others (as long as density is low enough). Thus, SH light is only generated from the interfaces of the spheres and their environment and is independent of particle-particle interactions. It has also been shown that the second-harmonic electric field scales with the radius of the particle cubed, a3. Besides spheres, other small particles like rods have been studied similarly by SHG. Both immobilized and colloidal systems of small particles can be investigated. Recent experiments using second-harmonic generation of non-planar systems include transport kinetics across living cell membranes and demonstrations of SHG in complex nanomaterials. Radiation pattern The SHG radiation pattern generated by an exciting Gaussian beam also has a (homogeneous) 2D Gaussian profile if the nonlinear medium being excited is homogeneous (A). However, if the exciting beam is positioned at an interface between opposite polarities (± boundary, B) that is parallel to the beam propagation (see figure), the SHG will be split into two lobes whose amplitudes have opposite sign, i.e. are phase-shifted. These boundaries can be found in the sarcomeres of muscles (protein = myosin), for instance. Note that we have considered here only the forward generation. Moreover the SHG phase-matching can also result in : some SHG is also emitted in backward (epi direction). When the phase-matching is not fulfilled, as in biological tissues, the backward signal comes from a sufficiently high phase-mismatch which allow a small backward contribution to compensate for it. Unlike fluorescence, the spatial coherence of the process constrain it to emit only in those two directions, but the coherence length in backward is always way smaller than in forward, meaning there is always more forward than backward SHG signal. The forward (F) to backward (B) ratio is dependent on the arrangement of the different dipoles (green in figure) that are being excited. With only one dipole ((a) in the figure), F = B, but F becomes higher than B when more dipoles are stacked along the propagation direction (b and c). However, the Gouy phase-shift