New closed form analysis of resonances in microwave power for material processing

A new closed form material invariant analysis on resonances of microwave induced power absorption is presented. It is shown that resonances in average power is confined within two asymptotic limits of thin and thick samples, and the resonances occur if λm ⩽ 1.5Dp,m for λm ≈ λ0 and λm ⩽ 3Dp,m for λm ≉ λ0. Here λm and Dp,m denote the wavelength and penetration depth within the sample, respectively, and λ0 is the wavelength within the free space. It has been shown that average absorbed power does not exhibit resonance for one side incidence if λm ≈ λ0, while the occurrence of resonance is independent of ϕl for λm ≉ λ0. Here, ϕl is the fractional power input from the left side. The amplitudes of subsequent resonating peaks are also shown to decay monotonically with sample length for λm ≈ λ0, while they vary nonmonotonically for λm ≉ λ0 and ϕl ≉ 0, 1 or 1/2 due to suppressions of odd (for λm < λ0), or even (for λm > λ0) resonating peaks, which increase as ϕl approaches 1/2 from either 0 or 1. Finally, at ϕl ≈ 1/2 with λm ≉ λ0 odd (for λm < λ0), or even (for λm > λ0) resonating peaks of average absorbed power vanish reducing the number of resonating points by a factor of two from one side incidence (ϕl ap; &0 or 1), to both side incidence with equal power input from left and right sides (ϕl ≈ 1/2). This work provides correlations (corresponding to λm ≈ λ0 and λm ≉ λ0) for predicting the locations of resonating peaks as function of λm/λ0, λm/Dp,m, and ϕl. The theoretical prediction on average power characteristics have been shown to be useful in forecasting the heating patterns for efficient material processing.