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The reflection coefficients of extensional guided modes from notches of different axial, circumferential and through-thickness extent in pipes of different diameters have been studied using finite element analysis. A selection of the predictions has also been validated by experiments. For part-thickness notches of a given circumferential extent and minimal axial extent, the reflection coefficient increases monotonically with depth at all frequencies, and increases with frequency at a given depth. When the wavelength is long compared to the pipe wall thickness, the reflection coefficient from part-thickness notches of a given circumferential extent is a strong function of the defect axial extent, the reflection being a maximum at an axial extent of about 25 per cent of the wavelength and a minimum at 0 and 50 per cent. The reflection coefficient is a linear function of the defect circumferential extent at higher frequencies (with frequency-diameter products greater than about 3000 kHz mm) where a ray theory analysis explains the behaviour, while at low frequencies the reflection coefficient at a given circumferential extent is reduced. In the high-frequency regime, the axial extent of a through-thickness defect has little influence on the reflection coefficient, while it is important at lower frequencies. Three-dimensional, finite element predictions in the high-frequency regime have shown that the reflection coefficient from a part-thickness, part-circumferential defect can be predicted by multiplying the reflection coefficient for an axisymmetric defect of the same depth and axial extent by that for a through-thickness defect of the same circumferential extent.

Electro-optic polymer thin-films were characterized at microwave frequencies, for possible applications in GHz modulators. Single layers of the polymers were spin coated on low loss magnesium oxide substrates for characterizing the polymers at microwave frequencies. Coplanar waveguide test structures were designed for evaluation of the relative dielectric permittivity as well as the loss-tangent of the polymers at microwave frequencies. A conformal mapping technique was used for the extraction of relative dielectric constant of the polymer films based on the microwave scattering parameter measurements. As an example, a DR1-PMMA polymer had a relative dielectric permittivity of 3.01 and a loss-tangent of 0.075 at 8 GHz. The design of the test structures, the procedure for the accurate determination of the dielectric permittivity and the loss-tangent of the polymer films are discussed in this paper.

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