Terahertz microscopy using laser feedback interferometry based on a generalised phase-stepping algorithm.

In this paper we report an improved method of coherent sensing through the use of a generalized phase-stepping algorithm to extract magnitude and phase information from interferometric fringes acquired by laser feedback interferometry (LFI). Our approach allows for significantly reduced optical sampling and acquisition times whilst also avoiding the need for fitting to complex models of lasers under optical feedback in post-processing. We investigate theoretically the applicability of this method under different levels of optical feedback, different laser parameters, and for different sampling conditions. We furthermore validate its use experimentally for LFI-based sensing using a terahertz (THz)-frequency laser in both far-field and near-field sensing configurations. Finally we demonstrate our approach for two-dimensional nanoscale imaging of the out-of-plane field supported by individual micro-resonators at THz frequencies. Our results show that fully coherent sensing can be achieved reliably with as little as 4 sampling points per imaging pixel, opening up opportunities for fast coherent sensing not only at THz frequencies but across the visible and infra-red spectrum.

Compact terahertz harmonic generation in the Reststrahlenband using a graphene-embedded metallic split ring resonator array.

Harmonic generation is a result of a strong non-linear interaction between light and matter. It is a key technology for optics, as it allows the conversion of optical signals to higher frequencies. Owing to its intrinsically large and electrically tunable non-linear optical response, graphene has been used for high harmonic generation but, until now, only at frequencies < 2 THz, and with high-power ultrafast table-top lasers or accelerator-based structures. Here, we demonstrate third harmonic generation at 9.63 THz by optically pumping single-layer graphene, coupled to a circular split ring resonator (CSRR) array, with a 3.21 THz frequency quantum cascade laser (QCL). Combined with the high graphene nonlinearity, the mode confinement provided by the optically-pumped CSRR enhances the pump power density as well as that at the third harmonic, permitting harmonic generation. This approach enables potential access to a frequency range (6-12 THz) where compact sources remain difficult to obtain, owing to the Reststrahlenband of typical III-V semiconductors.

Terahertz near-field microscopy of metallic circular split ring resonators with graphene in the gap.

Optical resonators are fundamental building blocks of photonic systems, enabling meta-surfaces, sensors, and transmission filters to be developed for a range of applications. Sub-wavelength size (< λ/10) resonators, including planar split-ring resonators, are at the forefront of research owing to their potential for light manipulation, sensing applications and for exploring fundamental light-matter coupling phenomena. Near-field microscopy has emerged as a valuable tool for mode imaging in sub-wavelength size terahertz (THz) frequency resonators, essential for emerging THz devices (e.g. negative index materials, magnetic mirrors, filters) and enhanced light-matter interaction phenomena. Here, we probe coherently the localized field supported by circular split ring resonators with single layer graphene (SLG) embedded in the resonator gap, by means of scattering-type scanning near-field optical microscopy (s-SNOM), using either a single-mode or a frequency comb THz quantum cascade laser (QCL), in a detectorless configuration, via self-mixing interferometry. We demonstrate deep sub-wavelength mapping of the field distribution associated with in-plane resonator modes resolving both amplitude and phase of the supported modes, and unveiling resonant electric field enhancement in SLG, key for high harmonic generation.