Evanescent field-induced breakdown of quasi-static nonlinear effective medium theory at deep-subwavelength scales

Deep-subwavelength, dilute, weakly nonlinear dielectric composites are widely assumed to obey the nonlinear Maxwell-Garnett effective medium theory (NMGT). Here, we demonstrate that evanescent fields can cause NMGT breakdown at deep-subwavelength scales. We show that strong evanescent fields near linear dielectric components, even at λ₀/100 scale, create local optical hotspots and zero-field regions. When nonlinear components are positioned within these regions, the composite's nonlinear response becomes highly sensitive to component placement, a behavior that conventional NMGT fails to capture due to its averaging approximation. We overcome this limitation by developing a semi-analytic corrected NMGT that incorporates evanescent-field effects in dilute, weakly nonlinear composites. By harnessing these evanescent fields, we further demonstrate a nonlinear quenching effect and design a metamaterial with extreme nonlinear anisotropy. Our findings unveil the mechanisms underlying NMGT breakdown at deep-subwavelength scales and enable new strategies for nonlinear optical engineering.