Complete $S$ matrix in a microwave cavity at room temperature

We experimentally study the widths of resonances in a two-dimensional microwave cavity at room temperature. By developing a model for the coupling antennas, we are able to discriminate their contribution from those of Ohmic losses to the broadening of resonances. Concerning Ohmic losses, we experimentally put to evidence two mechanisms: damping along propagation and absorption at the contour, the latter being responsible for variations of widths from mode to mode due to its dependence on the spatial distribution of the field at the contour. A theory, based on an $S$-matrix formalism, is given for these variations. It is successfully validated through measurements of several hundreds of resonances in a rectangular cavity.

Figure 1

Schematic view of the microwave cavity with locations of antennas.

Figure 2

Schematic cut view of a coupling antenna. Physical regions introduced in our model are displayed along with the associated characteristic lengths.

Figure 3

Experimentally based estimation of $T^2\left({\omega }_n\right)$ as given by Eq. (56) (crosses). The gray region corresponds to its theoretical expression (51) for values of $l_{eff}$ between 1.7 mm and 2.3 mm $(l*=1.65\mathrm{cm})$.

Figure 4

Comparison of Eq. (59) with $2T^2\left({\omega }_n\right){\mid {\psi }_{l,m}^{\left(0\right)}(x_a,y_a)\mid }^2$ at the ten antennas (indices are introduced in Fig. 1) for resonances $n=78$ and $n=238$.

Figure 5

Comparison between the experimental quantity ${⟨\frac{1}{36}{\sum }_{b<c\ne a}\mid A_n^{ab}\mid \mid A_n^{ac}\mid ∕\mid A_n^{bc}\mid ⟩}_a$ (crosses) with the prediction $2T^2\left({\omega }_n\right){⟨{\mid {\psi }_{l,m}^{\left(0\right)}(x_a,y_a)\mid }^2⟩}_a$ (line). Inset: enlarged view within the range 2–3 GHz.

Figure 6

Values of $({\xi }_{\mathrm{l},m}-1)$ after Eq. (61) for all resonances up to 5.5 GHz.

Figure 7

Behavior of the Ohmic widths up to 3 GHz. Comparison is shown between theoretical Ohmic widths (crosses) and experimental Ohmic widths (continuous curve). The dashed curve indicates the smooth contribution ${\mathrm{\Gamma }}^{\mathrm{prop}}\left(\omega \right)$.