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c fields and the resonant frequency, respectively. The subscript ‘0’ represents the unperturbed fields. Source: David M. Pozar, Microwave Engineering, Page 340342, John Willy amp。 Sons, INC. 1998 Relate the resonant frequency shift of the cavity to the change in the permittivity or permeability. ?Nonmagic samples, so Δμ=0. ?The numerator is the actual perturbed energy from the sample. ?Two Femlab structure, E and E0, are exported to a matlab script for calculating this integral. ?The denominator is the total energy from the cavity. ?It is difficult to calculate the total energy numerically. CAVITY PERTURBATION THEORY (continued) perturbed energy total energy The Total energy determination of bulk TiO2 ? Blue curve is the experiment data. ? Red dots are the calculated perturbed energy. Scaling ~1012 between two curves gives the total energy Thin Film Samples Ratio of energy integrals ?The perturbed energies are ca