Spontaneous Exact Spin-Wave Fractals in Magnonic Crystals

Exact fractals of nonlinear waves that rely on strong dispersion and nonlinearity and arise spontaneously out of magnetic media were observed for the first time. The experiments make use of a microwave to excite a spin wave in a quasi-one-dimensional magnonic crystal. When the power of the input microwave (P_{in}) is low, the output signal has a power-frequency spectrum that consists of a single peak. When P_{in} is increased to a certain level, new side modes are generated through modulational instability, resulting in a comblike frequency spectrum. With a further increase in P_{in}, each peak in the frequency comb can evolve into its own finer comb through the modulational instability. As P_{in} is increased further, one can observe yet another set of finer frequency combs. Such a frequency-domain fractal manifests itself as multiple layers of amplitude modulation in the time-domain signal.