Imaging through nonlinear media using digital holography

It is well known that one cannot image directly through a nonlinear medium, as intensity-dependent phase changes distort signals as they propagate. Indirect methods can be used, but none has allowed for the measurement of internal wave mixing and dynamics. Recently, the reconstruction of nonlinear pulse propagation in fibres was demonstrated by generalizing the techniques of digital holography to the nonlinear domain. The method involves two steps: (1) recording the total field (both amplitude and phase) exiting a nonlinear medium and (2) numerically back-propagating the wavefunction. Here, we extend this process to two-dimensional spatial beams and experimentally demonstrate it in a self-defocusing photorefractive crystal, giving examples in soliton formation, dispersive radiation and imaging. For known nonlinearity, the technique enables reconstruction of wave dynamics within the medium and suggests new methods of super-resolved imaging, including subwavelength microscopy and lithography. For unknown nonlinearity, the method facilitates modelling and characterization of the optical response.