No abstract

Self-imaging of waves is an intriguing and spectacular effect. The phenomenon was first observed for light in 1836 by Henry Fox Talbot and to this day is the subject of research in many areas of physics, for various types of waves and in terms of different applications. This paper is a Talbot-effect study for spin waves in systems composed of a thin, ferromagnetic waveguide with a series of single-mode sources of spin waves flowing into it. The proposed systems are studied with the use of micromagnetic simulations, and the spin wave self-imaging dependencies on many parameters are examined. We formulated conditions required for the formation of self-images and suitable for experimental realization. The results of the research form the basis for the further development of self-imaging-based magnonic devices.

oscillations propagating without charge transfer in magnetic materials. [2][3][4][5] This property, combined with a wider range of available frequencies than in electronics and the ability to encode information both in amplitude and phase, makes SWs an important candidate for an information carrier in a new generation of computing devices, where Joule-Lenz heat and other obstacles may be significantly reduced. [6][7][8][9] Magnonic circuits (systems utilizing SWs) [10,11] may consist of waveguides through which SWs propagate, [12][13][14][15] and interference areas at crossings, for example, for creating majority gates. [16][17][18][19][20] The waveguides may also couple with other waveguides [21,22] to implement a logical operation. In this manner, it has been possible to demonstrate a 32-bit magnonic full adder [21] and SWbased approximate 4:2 compressor. [23] Another strategy is to use wide ferromagnetic film areas for SW operation and narrow waveguides as SW inputs. This approach was used to redirect [24][25][26] and process SWs. [27][28][29][30][31][32] Operation of these systems is based on the interference of incoming SWs. Therefore, a local modification of the medium (the magnonic equivalent of the refractive index) in which SWs propagate is crucial to design and optimize its functionality. It was recently shown that it could be achieved by an introduction of defects in so-called inverse design approach, [32] placement of programmable magnetic elements on top of that region, [30] or utilization of noncolinear magnetization textures. [33][34][35] This interference based strategy appears promising also for the realization of physical neural networks operating on SWs. [30,33] Thereby, interference effects open a promising avenue for the development of SWbased beyond-CMOS solutions.A plane wave passing through a system of periodically spaced obstacles (diffraction gratings or holes) interferes, creating a characteristic diffraction pattern in the near field, reproducing the grating image at specific distances from the input apertures. This phenomenon is known as the Talbot or the selfimaging effect, and was observed for light already in the 19th century. [36] The resulting interference pattern is called a Talbot carpet, and we have recently theoretically demonstrated that this effect can also occur for SWs. [37] The properties of Talbot carpets created by SWs strongly depend on material parameters, geometry, type, thickness of a magnetic material, and on dynamic parameters such as wavelength, orientation, and the value of an external magnetic field.Here, we exploit the self-imaging phenomenon occurring in a thin ferromagnetic multimode waveguide with SWs introduced by periodically spaced single-mode input waveguides. SWs entering the multimode waveguide have a controllable phase. In particular, we present a new class of reprogrammable magnonic blocks implementing array indexing operations.Inclusion of spin waves into the computing paradigm, where complementary metal-oxide-semiconductor devices are still at th...