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A four-wave-mixing, frequency-comb-based, hyperspectral imaging technique that is spectrally precise, potentially rapid, and can in principle be applied to any material, is demonstrated in a near-diffraction-limited microscopy application.

The magnetic force is retained in the Lorentz Oscillator Model and a perturbation solution is derived beyond the dipole approximation. Perturbation series for the electric dipole, magnetic dipole, and electric quadrupole moments in addition to their macroscopic, spatially-averaged counterparts are also obtained. These expressions are shown to describe many optical phenomena: the normal, linear Zeeman, Faraday, and magneto-optic Kerr effects, the linear Stark, Pockels, and Kerr effects (when the restoring force is anharmonic), the momentum and angular momentum of a photon in matter (contributing to the Abraham-Minkowski debate), the photon drag and inverse Faraday effects, and sum-frequency and second-harmonic generation in centrosymmetric media. The qualitative and quantitative accuracy is assessed by comparison to both experiment and more fundamental theory (e.g. quantum mechanics). New insights into the relationship between the Stark and Pockels/Kerr effects also emerge.

Multi-dimensional coherent spectroscopy (MDCS)1,2 is a powerful method for optical spectroscopy that has become an important tool for studying ultrafast dynamics in a wide range of systems. It is an optical analog of multidimensional nuclear magnetic resonance spectroscopy that enables the measurement of homogeneous linewidths in inhomogeneously broadened systems, many-body interactions, and coupling between excited resonances, all of which are not simultaneously accessible by any other linear or non-linear method. Current implementations of MDCS require a bulky apparatus and suffer from resolution and acquisition speed limitations that constrain their applications outside the laboratory3-5. Here we propose and demonstrate an approach to nonlinear coherent spectroscopy that utilizes three frequency combs with slightly different repetition rates. Unlike traditional nonlinear methods, tri-comb spectroscopy uses only a single photodetector and no mechanical moving elements to enable faster acquisition times, while also providing comb resolution. As a proof of concept, a multidimensional coherent spectrum with comb cross-diagonal resolution is generated using only 365 ms of data. These improvements make multidimensional coherent spectroscopy relevant for systems with narrow resonances (especially cold atomic and molecular systems). In addition the method has the potential to be field deployable for chemical sensing applications.