Extremely local electric field enhancement and light confinement in dielectric waveguide

The extremely local electric field enhancement and light confinement is demonstrated in dielectric waveguide with corner and gap geometry. The numerical results reveal the local electric field enhancement in the vicinity of the apex of fan-shaped waveguide. Classical electromagnetic theory predicts that the field enhancement and confinement abilities increase with decreasing radius of rounded corner ($r$) and gap ($g$), and show singularity for infinitesimal $r$ and $g$. For practical parameters with $r=g=10\,\mathrm{nm}$, the mode area of opposing apex-to-apex fan-shaped waveguides can be as small as $4\times10^{-3}A_{0}$ ($A_{0}=\lambda^{2}/4$), far beyond the diffraction limit. This way of breaking diffraction limit with no loss outperforms plasmonic waveguides, where light confinement is realized at the cost of huge intrinsic loss in the metal. Furthermore, we propose a structure with dielectric bow-tie antenna on a silicon-on-insulator waveguide, whose field enhancement increases by one order. The lossless dielectric corner and gap structures offer an alternative method to enhance the light-matter interaction without metal nano-structure, and will find applications in quantum electrodynamics, sensors and nano-particle trapping.