Recently we proposed a paradigm shift in light confinement strategy showing how relaxed total internal reflection and photonic skin-depth engineering can lead to sub-diffraction waveguides without metal (S. Jahani and Z. Jacob, Transparent sub-diffraction optics: nanoscale light confinement without metal, Optica 1, 96-100 (2014)). Here, we show that such extreme-skin-depth (e-skid) waveguides can counter-intuitively confine light better than the best-case all-dielectric design of high index silicon waveguides surrounded by vacuum. We also analytically establish that figures of merit related to light confinement in dielectric waveguides are fundamentally tied to the skin depth of waves in the cladding, a quantity surprisingly overlooked in dielectric photonics. We contrast the propagation characteristics of the fundamental mode of e-skid waveguides and conventional waveguides to show that the decay constant in the cladding is dramatically larger in e-skid waveguides, which is the origin of sub-diffraction confinement. We also propose an approach to verify the reduced photonic skin depth in experiment using the decrease in the Goos-Hanschen phase shift. Finally, we provide a generalization of our work using concepts of transformation optics where the photonic-skin depth engineering can be interpreted as a transformation on the momentum of evanescent waves.
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