  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.
