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A nonlinear phase shift of low-power spin waves (SWs) induced by a high-power pumping SW excited both inside and outside the magnonic band-gaps of a magnonic crystal has been studied. The magnonic crystal with spatially periodic thickness is fabricated from an yttrium iron garnet film by chemical etching. The results show that the phase shift of the low-power SWs can be effectively controlled by variation of power level of the pumping SW. This induced nonlinear phase shift is weakened if the pump frequency lies in the magnonic bandgap. The data obtained are well explained by contradirectional coupling of the high-power forward and reflected spin waves. A theoretical model for this effect is presented. Our findings are important for the further progress in SW computing.

An induced nonlinear phase shift of spin waves excited in an yttrium iron garnet film waveguide has been studied. Experiments were performed with two microwave magnonic signals, being operating and pumping waves, co-propagated at different frequencies. The results show that a nonlinear phase shift up to 180° for the low-power operating wave is induced when increasing the pump-wave power. A theory describing the induced nonlinear phase shift is developed taking into account four-wave parametric coupling and nonlinear damping of two waves. The observed phenomenon paves the way to elaborate different types of nonlinear magnonic logic circuits.

Introduction. Optical backscatter reflectometry is one of the most promising methods used to examine characteristic parameters relevant to the design of microring resonators. This method paves the way for experimental determination of the coupling coefficient and propagation loss. However, experimental verification of this technique by comparing the transmission characteristics obtained by reflectometry and those directly measured by an optical vector analyzer has not been carried out.Aim. To determine the parameters of microring resonators by optical reflectometry and to calculate on their basis the transmission characteristics of microring resonators. To compare the calculated transmission characteristics with those obtained experimentally using a high-resolution vector analyzer.Materials and methods. The characteristic parameters of silicon-on-insulator microring resonators were investigated using an ultra-high resolution reflectometer. An original algorithm was employed to derive the characteristic parameters of microring resonators from reflectograms. An optical vector analyzer was used to study the transmission characteristics of microring resonators. Numerical modeling of transmission characteristics considering the obtained parameters was carried out according an analytical approach based on partial wave analysis.Results. The obtained values of the power coupling coefficient κ = 0.167 and propagation losses α = 3.25 dB/cm were used for numerical simulation of the transmission characteristics of a microring resonator. These characteristics were found to agree well with those obtained experimentally. The free spectral range of 88.8 GHz and Q-factor of 45 000 were determined.Conclusion. An experimental study of the characteristic parameters of silicon-on-insulator microring resonators was conducted using an optical backscatter reflectometer. The performed comparison of the experimental and theoretical transmission characteristics showed good agreement, which indicates the high accuracy of the determined resonator parameters and, as a result, the relevance of the described method.

A bistability phenomenon in a ring resonator consisting of a delay line on surface spin waves and a microwave amplifier has been experimentally investigated. It is shown that an enhancement of the gain coefficient above a specified value provides an appearance of a hysteresis at the resonator transmission characteristic. A frequency range of the bistability broadens due to an increase of the gain coefficient as well as the external magnetic field. While the value of the gain is limited from above by a transition of the ring into a self-oscillating regime, an increase in the magnetic field from 1150 Oe up to 3150 Oe provides an expansion of the frequency range of the hysteresis from 77 kHz to 185 kHz.