Detailed material-invariant analysis on spatial resonances of power absorption for microwave-assisted material processing with distributed sources

This paper presents a comprehensive, closed-form-based material-invariant analysis on the occurrence and characterization of spatial resonances in microwave-induced absorbed-power distribution within a material. We have shown that occurrence of resonance depends on competitive interactions between sinusoidal and exponential position dependencies characterized by wave number (N-w) and penetration number (N-p) confining the resonating regime of absorbed power within thick- (N-p > 1) and thin-sample (N-w < 0.5) asymptotic limits, where it has been shown for the first time that the thick-sample limit depends on distribution of microwave source (phi(0)) while the thin-sample limit is invariant of phi(0). Within the resonating regime, distribution of microwave source (phi(0)) and wave number of surrounding free space (N-w,N-0) have shown to play an important role in deciding resonating features of absorbed power in addition to N-w and N-p, which in the literature have been considered to be the only governing factors for resonance. For example, absorbed power for the case of one-side incidence (phi(0) = 0 or 1) shows resonance only if N-w,N-0 not approximate to root N-w(2) + N-p(2) +/4 pi(2), where locations of resonating peaks are strong function of N-w,N-0 in addition to N-w and N-p. On the other hand, for both-side incidence with equal power input from left and right sides (phi(0) = (1)/(2)), occurrence of resonance as well as locations of resonating peaks are independent of N-w,N-0. For intermediate phi(0), the absorbed power shows resonance if N-w, N-p, N-w,N-0, and phi(0) satisfy the condition C-n,C-3 not equal 0 as given in this work. We have performed a detail analysis for all the cases in order to quantify various resonating features of absorbed power and derived correlations for predicting the locations of resonating peaks, which are shown to be in good accordance with actual positions.