Observation of Self-Cavitating Envelope Dispersive Shock Waves in Yttrium Iron Garnet Thin Films

The formation and properties of envelope dispersive shock wave (DSW) excitations from repulsive nonlinear waves in a magnetic film are studied. Experiments involve the excitation of a spin wave step pulse in a low-loss magnetic ${\mathrm{Y}}_3{\mathrm{Fe}}_5{\mathrm{O}}_{12}$ thin film strip, in which the spin wave amplitude increases rapidly, realizing the canonical Riemann problem of shock theory. Under certain conditions, the envelope of the spin wave pulse evolves into a DSW that consists of an expanding train of nonlinear oscillations with amplitudes increasing from front to back, terminated by a black soliton. The onset of DSW self-cavitation, indicated by a point of zero power and a concomitant 180° phase jump, is observed for sufficiently large steps, indicative of the bidirectional dispersive hydrodynamic nature of the DSW. The experimental observations are interpreted with theory and simulations of the nonlinear Schrödinger equation.

Figure 1

Experimental configuration and spin-wave characteristics. (a) Schematic of the experimental setup. (b) Transmission response of the YIG film strip measured at an input power of $P=20\mu \mathrm{W}$. (c) Experimental (blue) and theoretical (red) dispersion curves of spin waves in the YIG film strip. (d) Output power of the YIG film strip device measured as a function of $P$ at 6.045 GHz.

Figure 2

Demonstration of a cavitating envelope DSW. (a) Input signal: top—amplitude; bottom—phase. (b) Output signal: top—amplitude; bottom—phase. (c) Zoom-in display of the output signal shown in (b): top—power (amplitude square); bottom—phase; insert—phase derivative ($\mathrm{degree}/\mathrm{ns}$). The red curve in (c) shows a numerical fit to a black soliton profile.

Figure 3

Dependence of DSW formation on $P_2/P_1$. In each diagram, the signal is shown in blue while the phase is shown in red; $P_2/P_1$ is indicated on the top. For all the measurements, $P_2$ was fixed at 3.47 mW.

Figure 4

Dependence of DSW formation on $P_1$ and $P_2$. In each diagram, the signal is shown in blue while the phase is shown in red; the input power levels are indicated on the top. For all the measurements, $P_2/P_1$ was kept constant at 24.

Figure 5

Spatial development of DSW. Each diagram shows the spin wave signal measured by an inductive probe at a distance of $x$ away from the excitation transducer. The measurements were conducted at $P_1=0.14\mathrm{mW}$ and $P_2=3.47\mathrm{mW}$.

Figure 6

Simulation results. (a) Signals measured at different positions. (b) Amplitude (blue, left axis) and phase (red, right axis) profiles of the signal measured at $x=20.8\mathrm{mm}$. (c) The same data as in (b) in a narrower time window.