In recent decades matamaterials and their two-dimensional form, metasurfaces, have generated a great deal of scientific and industrial interest due to the novel optical responses that they enable.  Importantly, it has been shown that metasurfaces provide a low weight, small footprint device for nonlinear optical generation.  At the same time there has been recent interest in Bound States in the Continuum (BICs) for their ability to create ultra-high quality factor resonances, or quasi-BICs, with recent work demonstrating that harmonic generation can be enhanced by orders of magnitude using such BIC derived resonances.  The enhancement of wave-mixing in the classical process of Sum Frequency Generation (SFG) and the quantum process of photon-pair generation, however require resonances simultaneously at multiple frequencies.  In this talk I will present my work in designing metasurfaces supporting multiple quasi-BICs for tailoring and enhancing multi-wavelength nonlinear wave interactions and especially entangled photon-pair generation.

I will first demonstrate the ability to tune quasi-BICs dynamically by using liquid crystals to vary the refractive index of the medium surrounding the meta-atoms of a metasurface.  I will also discuss the creation of quasi-BICs in a one-dimensional metamaterial of LiNbO gratings.

I will then present a novel design for metasurfaces that contain multiple reconfigurable BICs, which I have dubbed Ghost Oligomer metasurfaces.  The platform allows for a great degree of control over the eigenspace of the modes of the metasurface as well as over the frequency of the BICs that form within it.  It thus allows us to tailor nonlinear conversion at the engineered frequencies that are determined by the design parameters of the metasurface.  

I will further demonstrate that second harmonic generation and SFG can be enhanced by many orders of magnitude by placing quasi-BICs at both the signal and idler wavelengths, with a linewidth in the picometer range and wavelengths that are reconfigurable over a broadband range.  These design principles can also facilitate the generation of photon-pairs with picometer linewidths and increased spectral brightness.  I show that the symmetry of the metasurface has a profound effect on the distribution of photon-pairs in k-space via a novel form of the transverse phase matching requirement of spontaneous parametric down conversion in metasurfaces.  I will also illustrate how the polarisation entanglement of the photon-pairs can be tuned to any value via the polarisation of the pump beam.

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