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Optical resonance imaging: An optical analog to MRI with sub-diffraction-limited capabilities.

We propose here optical resonance imaging (ORI), a direct optical analog to magnetic resonance imaging (MRI). The proposed pulse sequence for ORI maps space to time and recovers an image from a heterodyne-detected third-order nonlinear photon echo measurement. As opposed to traditional photon echo measurements, the third pulse in the ORI pulse sequence has significant pulse-front tilt that acts as a temporal gradient. This gradient couples space to time by stimulating the emission of a photon echo signal from different lateral spatial locations of a sample at different times, providing a widefield ultrafast microscopy. We circumvent the diffraction limit of the optics by mapping the lateral spatial coordinate of the sample with the emission time of the signal, which can be measured to high precision using interferometric heterodyne detection. This technique is thus an optical analog of MRI, where magnetic-field gradients are used to localize the spin-echo emission to a point below the diffraction limit of the radio-frequency wave used. We calculate the expected ORI signal using 15 fs pulses and 87° of pulse-front tilt, collected using f/2 optics and find a two-point resolution 275 nm using 800 nm light that satisfies the Rayleigh criterion. We also derive a general equation for resolution in optical resonance imaging that indicates that there is a possibility of superresolution imaging using this technique. The photon echo sequence also enables spectroscopic determination of the input and output energy. The technique thus correlates the input energy with the final position and energy of the exciton.