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In this work we present a simple transfer-matrix based modeling tool for arbitrarily layered stacks of resonant plasmonic metasurfaces interspersed with dielectric and metallic multilayers. We present the application of this model by analyzing three seminal problems in nanophotonics. These are the scenario of perfect absorption in plasmonic Salisbury screens, strong coupling of microcavity resonances with the resonance of plasmon nano-antenna metasurfaces, and the hybridization of cavities, excitons and metasurface resonances.

We exploit recently developed topology-optimization techniques to design complex, wavelength-scale resonators for enhancing various nonlinear \\(\\chi^{(2)}\\) and \\(\\chi^{(3)}\\) frequency conversion processes. In particular, we demonstrate aperiodic, multi-track ring resonators and 2D slab microcavities exhibiting long lifetimes \\(Q \\gtrsim 10^4\\), small modal volumes \\(V \\gtrsim (\\lambda/2n)^3\\), and among the largest nonlinear overlaps (a generalization of phase matching in large-etalon waveguides) possible, paving the way for efficient, compact, and wide-bandwdith integrated nonlinear devices.