Deviation of the plane-wave approximation for optical fields in thin metallic films at various frequencies and temperatures

The frequency and temperature dependence of the size effect on the profile distribution of electromagnetic fields inside thin metallic films within the anomalous skin-effect region is theoretically studied. The relaxation time of conduction electrons is stated as tau approximate to (aT + b omega(2))(-1) in accord with Matthiessen's rule for current conduction. The errors of using the plane wave solution e(-uWz) turns out to be as large as 5.5% compared to the total field including the higher-order terms for silver films with a thickness of 30 nm. However, the imaginary parts of the electric field for thinner metal films at lower temperatures are less affected by higher-order terms.