Microwave-envelope soliton threshold powers and soliton numbers

The peak power of 5.8-GHz backward-volume-wave pulses propagated in a 7.2-{μ}m-thick yttrium iron garnet film was measured as a function of input pulse width T₀ from 5.1 to 44 ns and input power from 0.05 to 3.5 W in a two-stripline microwave transducer structure. A threshold input power Pₜₕ for the onset of a nonlinear response was determined as a function of T₀. The dependence of Pₜₕ on T₀ followed a clear pattern consistent with theoretical considerations for soliton formation. Plots of Pₜₕ vs 1/T₀² showed two regions where Pₜₕ scaled linearly with respect to 1/T₀². The slopes of these two linear regions were in ratio 1:9, as expected from theory. A soliton-number parameter n calculated from the Pₜₕ data as a function of T₀ showed plateaus at n=1, 2, and 3. A one-to-one correlation was found between these calculated values of n and the number of peaks in output pulse profiles. These results demonstrate a simple connection between input pulse width, nonlinear power threshold, and soliton number.