Omnidirectional field enhancements drive giant nonlinearities in epsilon-near-zero waveguides

Bulk materials with a relative electric permittivity ε close to zero exhibit giant Kerr nonlinearities. However, harnessing this response in guided-wave geometries is not straightforward, due to the extreme and counterintuitive properties of such epsilon-near-zero materials. Here we investigate, through rigorous calculations of the nonlinear coefficient, how the remarkable nonlinear properties of such materials can be exploited in several structures, including bulk films, plasmonic nanowires, and metal nanoapertures. We find the largest nonlinear response when the modal area and group velocity are simultaneously minimized, leading to omnidirectional field enhancement. This insight will be key for understanding nonlinear nanophotonic systems with extreme nonlinearities and points to new design paradigms.