Ray-Theory Analysis of Magnetoelastic Delay Lines

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Abstract
Magnetoelastic wave propagation at microwave frequencies in single‐crystal yttrium iron garnet, of various nonellipsoidal geometries, has been intensively investigated experimentally in recent years in connection with delay‐line applications. However, two important features, namely the detailed nature of the energy paths and the magnetic excitation mechanisms, have received scant attention. This paper examines these features from the viewpoint of geometrical ray theory. Attention is first directed to two basic phenomena: magnetoelastic wave anisotropy, which gives rise to deflection of the group velocity from the phase velocity vector, and refraction, which arises from the inhomogeneous internal magnetic field. Consideration is then given to justifiable approximations for the wave behavior and magnetic field, and guidelines which enable a specification of the launching surface to be made. Ray plots are presented for the axially magnetized rod, which is found to be strongly focusing, and for the complementary geometry where the demagnetizing field everywhere is reversed in sign, which is found to be strongly defocusing. The field shape for minimum refraction is determined and certain delay‐frequency characteristics of practical importance are investigated to assess their lens character. Finally, consideration is given to the excitation probem. It is concluded that in the axially magnetized rod magnetostatic waves are excited at the end face, transforming to spin waves and ultimately to elastic waves. This mechanism is consistent with experimental observations.