Adequacy of the linearized local electric field determination in a cubically nonlinear composite

The adequacy of the linearised approximation of the local electric field in certain dilute nonlinear optical composites was investigated. The permittivity of the host medium was taken to be cubically nonlinear while that of the spherical inclusions was linear. After eliminating inter-dimensional coupling because it was linear, the essential nonlinearity in the local field determination was captured in a cubic equation. The real-valued roots of this cubic equation were numerically investigated. A clear upper bound on the adequate use of the linearized approximation was established from numerical studies.