Digital holography is an imaging technique that enables a 3-dimensional reconstruction of the electromagnetic field scattered by an object in both amplitude and phase. We demonstrated its use in microscopy in linear regime for the full 3-D mapping of the field scattered by single nanostructures such as nano-antennas and near-field probes. Holography is a technique based on interferences, which can be obtained at the laser illumination wavelength, but also with Second Harmonic Generation (SHG), since the latter is produced in a coherent process. Here, we describe the development of a harmonic holographic microscope for single-shot mapping of the second harmonic 3D radiation pattern near samples with nonzero second harmonic susceptibilities. The knowledge of the scattered field (amplitude and phase) in a given plane (that of the camera) allows its reconstruction in any other plane using e.g. the angular spectrum representation of the optical fields, and assuming propagation in homogeneous media, a process called 3D numerical back-propagation [6]. In addition to providing 3D reconstruction, thus enhancing the imaging capabilities beyond those of back focal-plane imaging, the harmonic holography microscope also benefits from an amplification effect since the signal from the sample is multiplied by an intense reference in the interference term, making the method particularly well suited to measure the weak SHG signals. After a first validation on dielectric samples made of nonlinear micro-crystals and cornea collagen, we are implementing the technique to obtain SHG fields radiated by plasmonic nano-antennas.
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