Tomographic imaging with harmonic holography in tissues of known refractive index distribution

High-resolution imaging in thick biological tissues beyond a few transport mean free path of photons remains a formidable challenge to modern science and technology. Recent advancements in optical tomography have enabled the reconstruction of the three-dimensional (3D) refractive index distribution in biological samples, which is crucial in the prediction of light propagation in that sample. Here we propose a new technique for imaging second harmonic radiating imaging probes (SHRIMPs) through a tissue using harmonic holography based on the extracted refractive index map. We analyze the spatiotemporal intensity distribution of light pulses using a new model that separate scattering by orders (times of deflections) and show that wide-field excitation and detection of the SHG in tissues beyond one cm thickness is possible with resonant nonlinear plasmonic nanocavities as the SHRIMP. We demonstrate with numerical simulations that the 3D image of SHRIMPs can be extracted by matching the measured second harmonic speckle pattern with that predicted for each point in the sample given the refractive index. We analyze the impact of measurement error in the refractive index on the SNR of the recovered image. We further discuss the influence of the frequency-domain memory effect.