In traditional imaging, one tries to create a perfect image directly. In computational imaging, a distortion is added to the optical path, so that the recorded picture no longer resembles the object. Since the distortion is known, however, an image can be reconstructed numerically. This a priori information can be used to obtain "extra" information about the object, such as increased resolution and depth. We have generalized computational imaging to include nonlinear dynamics and are applying it to super-resolution microscopy, phase retrieval, and biomedical imaging.
Intuitively, the propagation of light can be considered as the flow of a “fluid” from high-intensity to low-intensity, e.g. light illuminating the shadows of a room. In my group, we are developing an “optical hydrodynamics” that formalizes this intuition. Light intensity acts as fluid density, the gradient of the phase determines the flow velocity, and nonlinearity gives an effecting pressure. New features arise, however, as wave diffraction (rather than viscosity or surface tension) serves to moderate the dynamics.
When the light is partially incoherent, then its propagation can be treated as a statistical fluid, i.e. as a plasma. In this photonic plasma, nonlinearity creates an effective plasma frequency, while the finite correlation length creates an effective Debye length. This formalism not only provides a unified treatment of previous nonlinear statistical optics, it predicts fundamentally new dynamics for nonlinear light propagation. It also allows observation of phenomena that are difficult, if not impossible, to observe in material plasma.
Photonic lattices, such as waveguide arrays, facilitate the guiding and control of light. Typically periodic structures, they are difficult to fabricate, especially in a nonlinear medium. In our group, we bypass these difficulties by holographically inducing photonic structures in a photosensitive material (e.g. a photorefractive crystal). The waveguides then acquire the nonlinearity of the medium, allowing studies of wave mixing constrained by geometry. Applications include all-optical material modeling, nonlinear spectroscopy, and spectral filtering.