Finding efficient and reliable methods for the extraction of the phase in optical measurements is challenging and has been widely investigated. Although sophisticated optical settings, e.g. holography, measure directly the phase, the use of algorithmic methods has gained attention due to its efficiency, fast calculation and easy setup requirements. We investigated three phase retrieval methods: the maximum entropy technique (MEM), the Kramers-Kronig relation (KK), and for the first time deep learning using the Long Short-Term Memory network (LSTM). LSTM shows superior results for the phase retrieval problem of coherent anti-Stokes Raman spectra in comparison to MEM and KK.

Plasmonic gratings are simple and effective platforms for nonlinear signal generation since they provide a well-defined momentum for photon–plasmon coupling and local hot spots for frequency conversion. Here, a plasmonic azimuthally chirped grating (ACG), which provides spatially resolved broadband momentum for photon–plasmon coupling, was exploited to investigate the plasmonic enhancement effect in two nonlinear optical processes, namely two-photon photoluminescence (TPPL) and second harmonic generation (SHG). The spatial distributions of the nonlinear signals were determined experimentally by hyperspectral mapping with ultrashort pulsed excitation. The experimental spatial distributions of nonlinear signals agree very well with the analytical prediction based on photon–plasmon coupling with the momentum of the ACG, revealing the “antenna” function of the grating in plasmonic nonlinear signal generation. This work highlights the importance of the antenna effect of the gratings for nonlinear signal generation and provides insight into the enhancement mechanism of plasmonic gratings in addition to local hot spot engineering.

Plasmonic enhancement of nonlinear light-matter interaction can be achieved via dedicated optimization of resonant plasmonic modes that are spectrally matched to the different wavelengths involved in the particular nonlinear optical process. Here, the generation and enhancement of broadband four-wave mixing (FWM) are investigated in a plasmonic azimuthally chirped grating (ACG). The azimuthally varying grating periodicity in an ACG offers a well-defined channel to mediate the near field and the far field over a broad range of wavelengths. However, the particular mechanism responsible for field enhancement in such a platform depends on the interplay between the effects manifested by both the groove geometry and the grating's periodicity. This work delineates the collective contribution of groove geometry-dependent localized surface plasmon resonance and periodicity-dependent plasmonic surface lattice resonance over a broad range of wavelengths to bring into effect the enhancement of broadband FWM in an ACG.