Conventional consideration of ultrasound propagation relates to running waves in an unbounded medium. In practice, an experimentalist investigates a specimen of definite dimensions and the wave generated by a transducer (e.g., piezoelectric one) is restricted in time. Typical investigated crystals are about 1 cm and harmonic (30÷300 MHz ) excitation of ultrasonic wave represents a radio-pulse of about 1 μs duration. In this case the pulse duration τ is less than the propagation time in the specimen and one can observe a series of echo-reflections. In fact, the receiver has a finite pass band Δf_r and changes the observed shape of the pulse. However, if the spectrum of the pulse Δf = 2τ^-1 < Δf_r the shape of the pulse does not vary much and the amplitude of the signal measured in the middle of the pulse can be assumed as one obtained with a harmonic running wave, infinite in time. In other words, one neglects transient is neglected and it is assumed that the transient is fast in comparison with pulse duration, even broadened by the finite pass-band. All the mentioned is correct if the elastic moduli do not manifest the frequency dispersion or, at least, it is too small. The opposite case represents frequency dependent elastic moduli and, therefore, the signal with finite spectrum Δf spreads while propagating in the specimen. It happens because the velocities of the waves with different frequencies vary. One of the reasons of strong frequency dispersion is resonant interaction of different subsystems characterizing the medium. For example, interaction of elastic and electromagnetic subsystems of a metal can manifests itself in resonant interaction of ultrasound with low damping electromagnetic waves (e.g., dopplerons) that can propagate in the presence of external magnetic field at low temperatures (T). Since dopploerons have circular polarization, interaction leads to rotation of the polarization for the initially linearly polarized wave and its ellipticity: the ultrasonic analogue of Faraday effect [1]. At very low temperatures, doppleron-phonon interaction becomes so strong that the ultrasonic radio-pulse broadens. Such broadening was observed in indium crystal at T=1.3 K [2].

In the present paper we show that the front and back areas of the radio-pulses (fore-runner and after-runner, respectively) have the structure close to a circularly polarized wave. Such transformation of the linear polarization can be considered as a new class of polarization phenomena, namely, the non-homogenous Faraday effect. Recently, resonant interaction of ultrasound with the Jahn-Teller complexes in magnetic field was found [3]. Possibility to observe such non-homogenous Faraday effect in the crystals doped with transition metal ions is discussed.

[2] V.V. Gudkov, V.D. Fil, Ultrasonic wave field transport by conduction electrons in indium. Physica Status Solidi (B), 1984, vol.121, No 1, p.433-440.

[3] V.V. Gudkov, I.B. Bersuker, S. Yasin, et al. Magnetoacoustic investigation of the Jahn-Teller effect in chromium doped ZnSe crystal. Solid State Phenomena, 2012, vol.1990, 707-710.