Radiation of Caustic Beams from a Collapsing Bullet

We show both theoretically and experimentally that a collapsing ($2+1$)-dimensional wave packet in a medium with cubic nonlinearity and a two-dimensional dispersion of an order higher than parabolic irradiates untrapped dispersive waves. The studies are performed for a spin-wave bullet propagating in an in-plane magnetized ferrimagnetic film. An induced uniaxial anisotropy in such a medium leads to the formation of narrow spin-wave caustic beams whose angles to the bullet’s propagation direction are modified by the motion of the source.

Figure 1

Snapshots of spin-wave packets measured at different input powers and at 50 ns time intervals. Arrows show the bullet propagation direction. It coincides with the direction of the bias magnetic field $\mathbf{H}$ and the coordinate axis $\mathbf{z}$.

Figure 2

Irradiation of caustic beams from the collapsing bullet. Left panel: Experiment. Right panel: Simulation.

Figure 3

Spectrum of the guided modes for the longitudinally magnetized film waveguide. The calculation assumes pinned spins at the stripe edges. The family of symmetric modes $n=1,3,\dots ,65$ is shown. The mode which is the lowest in frequency is the fundamental width mode for the waveguide $n=1$. Inset: A section of the spectrum close to the frequency ${\omega }_B/2\pi$. The horizontal blue dashed lines in the main field of the figure and in the inset show the carrier frequency ${\omega }_0/2\pi$ of the input microwave pulse. The oblique red lines show the Doppler-shifted frequencies of an excitation source which moves in the positive direction. The bold sections of these lines show the modes responsible for formation of the respective caustics.

Figure 4

Slowness curves for the immobile and the mobile excitation sources (a) and the respective angles (b). In (a) bold solid lines are the slowness curves for the frequency given by the horizontal dashed line in Fig. 3. Thin solid lines are the slowness curves for the Doppler-shifted frequencies. The red bold dashed line connects zero-curvature points of the thin solid lines. Dark blue arrows are normal to the thick solid line and show the caustic directions for excitation by an immobile source. Gray arrows are normal to the family of the thin solid lines and show the DEF for the moving source. In (b) the arrow indicates the direction of source motion. Thin blue solid lines: Caustic directions for the immobile source. Red dotted lines: Two DEF for the moving source. Green dashed lines: Directions along the observed caustic beams.