The formation and evolution of spin wave band gaps in the transmission spectrum of a magnonic crystal have been studied. A time and space resolved magneto inductive probing system has been used to map the spin wave propagation and evolution in a geometrically structured yttrium iron garnet film. Experiments have been carried out using (1) a chemically etched magnonic crystal supporting the propagation of magnetostatic surface spin waves, (2) a short microwave pulsed excitation of the spin waves, and (3) direct spin wave detection using a movable magneto inductive probe connected to a synchronized fast oscilloscope. The results show that the periodic structure not only modifies the spectra of the transmitted spin waves but also influences the distribution of the spin wave energy inside the magnonic crystal as a function of the position and the transmitted frequency. These results comprise an experimental confirmation of Bloch 0 s theorem in a spin wave system and demonstrate good agreement with theoretical observations in analogue phononic and photonic systems. Theoretical prediction of the structured transmission spectra is achieved using a simple model based on microwave transmission lines theory. Here, a spin wave system illustrates in detail the evolution of a much more general physical concept: the band gap.
We report the theoretical calculations and the experimental demonstration of acoustic Bloch oscillations and Wannier-Stark ladders in linear tilted multilayer structures based on porous silicon. The considered structures consist of layers with constant porosity alternated by layers with a linear gradient in the parameter g ¼ 1=v 2L along the growth direction in order to tilt the acoustic band gap. The purpose of this gradient is to mimic the tilted electronic miniband structure of a superlattice semiconductor under an external electric field. In this way, acoustic Wannier-Stark ladders of equidistant modes are formed and they were experimentally confirmed in the transmission spectrum around 1.2 GHz. Their frequency separation defines the period of the acoustic Bloch oscillations. We fabricated three different structures with the same thicknesses but different values in the g parameter to observe the effect on the period of the Bloch oscillations. We measured the acoustic transmission spectra in the frequency domain, and by using the Fourier transform, we obtained the transmission in the time domain. The transmission spectra of the fabricated samples show acoustic Bloch oscillations with periods of 27, 24, and 19 ns. The experimental results are in good agreement with the transfer matrix calculations. The observed phenomenon is the acoustic counterpart of the well known electronic Bloch oscillations. V C 2014 AIP Publishing LLC.
The propagation of longitudinal acoustic waves in multilayer structures based on porous silicon and the experimental measurement of acoustic transmission for the structures in the gigahertz range are reported and studied theoretically. The considered structures exhibit band gaps in the transmission spectrum and these are localized modes inside the band gap, coming from defect layers introduced in periodic systems. The frequency at which the acoustic resonances appear can be tuned by changing the porosity and/or thickness of the defect layer.
The longwave phenomenological model is used to make simple and precise calculations of various physical quantities such as the vibrational energy density, the vibrational energy, the relative mechanical displacement, and the one-dimensional stress tensor of a porous silicon distributed Bragg reflector. From general principles such as invariance under time reversal, invariance under space reflection, and conservation of energy density flux, the equivalence of the tunneling times for both transmission and reflection is demonstrated. Here, we study the tunneling times of acoustic phonon packets through a distributed Bragg reflector in porous silicon multilayer structures, and we report the possibility that a phenomenon called Hartman effect appears in these structures.
A straightforward scattering matrix method derived from the Hybrid matrix method is proposed to study band gaps of elastic waves propagating along an arbitrary direction in one-dimensional ordered and disordered phononic crystals. We show that this is a suitable alternative methodology to overcome the numerical degradation manifested by the standard transfer matrix method even in calculations where nonlossy elastic medium and/or relatively low angles of incidence are involved. Using the wave equation in the matrix Sturm-Liouville form, we show analytically that we can use the value of the determinant of the associated transfer matrix T, to check the numerical accuracy of our calculations. The localization factor concept and transmittance spectra are used to describe the band gaps. In contrast to the matrix T, the numerical stability of the proposed scattering matrix allows to obtain true transmittance spectra whose band gaps correspond to those predicted by the localization factor values for both ordered and disordered phononic crystals. Furthermore, for the numerical examples provided, the proposed method requires fewer iterations to obtain the same value of the Lyapunov exponent compared with the standard transfer matrix method.
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