Microwave Magnetic Envelope Solitons Research Articles

Spatial evolution of multipeaked microwave magnetic envelope solitons in yttrium iron garnet thin films

The spatial evolution of multi-peaked microwave magnetic envelope solitons in a thin yttrium iron garnet (YIG) film has been measured and analyzed. The experiments were done on a long and narrow $5\text{\ensuremath{-}}\ensuremath{\mu}\mathrm{m}$-thick single-crystal YIG film strip. Double-peaked and triple-peaked magnetostatic backward volume wave soliton pulses were excited at a nominal carrier frequency of $7.0\phantom{\rule{0.3em}{0ex}}\mathrm{GHz}$. The measurements utilized a movable inductive magnetodynamic probe detection system. The formation of these multi-peaked soliton (MPS) pulses is a two step process. First, an initial single large amplitude pulse gradually separates into two or more nonsolitonic peaks. After a certain propagation time, these nonsolitonic peaks evolve, in sequence, into solitonic peaks with constant phase (CP) and an overall stair-like profile. Typically, the larger amplitude peaks lead in time and become solitonic first. As the MPS signals propagate and decay, the peaks lose their CP character in reverse sequence. The region of existence for the ``fully formed'' MPS pulses for which all the individual peaks have CP character is extremely narrow, typically on the order of a few tenths of a millimeter. The velocities of the individual peaks scale linearly with the peak powers. A nonlinear response analysis of the peak velocity based on the method of envelopes gives a reasonable match to the data.

Self-generation of bright microwave magnetic envelope soliton trains in ferrite films through frequency filtering

Resonant ring feedback with frequency filtering has been used for the self-generation of bright soliton trains. The solitons were produced from magnetostatic backward volume spin waves propagated in an in-plane magnetized magnetic film delay line as part of the resonant ring structure. The amplitude and phase time profiles, together with the power spectra of the self-generated pulses, confirm their bright soliton nature.

Suppression of microwave magnetic envelope solitons by continuous wave magnetostatic wave signals

The influence of continuous wave (cw) magnetostatic wave signals on microwave magnetic envelope soliton pulse formation and propagation in magnetic films has been examined. Pulsed and cw microwave signals were applied to the input of a single crystal yttrium–iron–garnet film magnetostatic wave delay line. The nominal operating frequency was 4.8 GHz. The pulse signals served to form solitons with no cw power present. Under suitable conditions, the cw signal served to inhibit or eliminate the soliton formation and propagation. The suppression effect was measured as a function of the cw signal frequency and power. The suppression is maximized when the cw signal frequency coincides with the pulse carrier frequency. At this frequency, an input cw power of 80 mW is sufficient to suppress completely a soliton pulse formed from a 10 ns wide, 500 mW peak power input pulse.

Brillouin light-scattering observation of the nonlinear spin-wave decay in yttrium iron garnet thin films

The direct observation of nonlinear spin-wave decay in thin yttrium iron garnet (YIG) films is reported. The second-order parametric spin waves were excited by a series of nonlinear magnetostatic backward volume wave (MSBVW) pulses propagated in a microstrip structure at 5 GHz. Brillouin light-scattering techniques were used to detect spin waves in the YIG at a point along the propagation path. Data were obtained as a function of the input pulse duty cycle and peak power level. These data yielded the decay rate ${\ensuremath{\eta}}_{\mathrm{eff}}$ for the parametric spin waves vs input power ${P}_{\mathrm{in}}.$ This ${\ensuremath{\eta}}_{\mathrm{eff}}$ was equal to the usual spin-wave relaxation rate at low power, but decreased rapidly with increasing ${P}_{\mathrm{in}}.$ As ${P}_{\mathrm{in}}$ approached the threshold power for complete MSBVW soliton formation at the observation point, ${\ensuremath{\eta}}_{\mathrm{eff}}$ leveled off to a relatively constant value that was about a factor of 5--10 smaller than the low power value. The initial decrease in ${\ensuremath{\eta}}_{\mathrm{eff}}$ with power is due to the compensation of the usual spin-wave decay by the simultaneous parametric pumping of the spin waves by Suhl processes. The leveling off in ${\ensuremath{\eta}}_{\mathrm{eff}}$ at the soliton threshold is due to the spin-wave shedding that is needed to maintain order one eigenmode soliton propagation at high input power levels. These experiments demonstrate the reduction in the spin-wave decay rate with power below the threshold for spin-wave instability. This reduction is a key element in spin-wave instability theory that has never been observed directly. The data also demonstrate the enhanced production of parametric spin waves that accompanies microwave magnetic envelope soliton formation.

Excitation of bright and dark microwave magnetic envelope solitons in a resonant ring

The excitation of both bright and dark microwave magnetic envelope solitons has been realized for one and the same resonant ring containing a yttrium–iron–garnet film magnetostatic wave (MSW) delay line. The resonant ring modifies the MSW character to produce a series of frequency intervals with alternating regions of positive and negative dispersion. These alternating regions support bright and dark soliton production, respectively.

Modeling of the power-dependent velocity of microwave magnetic envelope solitons in thin films

Recently obtained single soliton solutions to the nonlinear Schrödinger equation with additional higher order nonlinear and dispersion terms have been used to model the properties of microwave magnetic envelope solitons in thin films and, in particular, the recently observed power-dependent soliton velocity in these films. The modeling is based on an empirical scaling between the dimensionless amplitude parameters in the higher order nonlinear Schrödinger (HONLS) equation and the pulse power levels in the experiment. Based on this scaling, the amplitude-dependent soliton velocity from the HONLS equation solution is shown to match the velocity versus power response from the experiment.

Modeling of microwave magnetic envelope solitons in thin ferrite films through the nonlinear Schrödinger equation

A theoretical analysis of microwave magnetic envelope soliton profiles and the soliton peak power response for high power magnetostatic wave (MSW) excitations in yttrium iron garnet (YIG) thin films has been made. This analysis was based on the standard nonlinear Schrödinger equation with all key parameters based on experiment. The measurements were done for magnetostatic backward volume waves in a 10.2 μm YIG film, with a band edge at 5.06–5.07 GHz and operating point frequencies from 4.80 to 5.00 GHz. The use of accurate dispersion and group velocity parameters and the transmitted power versus frequency response of the MSW signal was critical. It was possible to accurately model both the shapes of the soliton pulses and the peak output versus peak input power response over a wide range of power levels.

Calculation of the formation time for microwave magnetic envelope solitons

The theoretical formation and propagation properties of microwave magnetic envelope solitons were modeled from the nonlinear Schrodinger equation without damping. Based on soliton threshold input amplitude criteria from inverse scattering theory, input amplitudes were set midpoint between the one- and two-soliton threshold values. The soliton formation time T/sub s/ was defined as the time required for the pulse amplitude to stabilize after launch. This T/sub s/ was found to be independent of the nonlinear response coefficient N and to vary as the inverse of the dispersion coefficient D. One possible way to model these T/sub s/ dependencies is through the relation T/sub s//spl ap/[T/sub d/ T/sub nl/]/sup 1/2/, where T/sub d/ and T/sub nl/ are characteristic dispersion and nonlinear response times, respectively. This result suggests a simple geometric mean relation between these characteristic times.

Self-Generation of Microwave Magnetic Envelope Soliton Trains in Yttrium Iron Garnet Thin Films

The self-generation of microwave magnetic envelope solitons in magnetic films has been realized for the first time. Solitons with a width of 20 ns and a carrier frequency of 5.1555 GHz were generated for the magnetostatic backward volume wave (MSBVW) configuration in a $5.2\ensuremath{\mu}\mathrm{m}$ thick yttrium iron garnet film. The film and MSBVW propagation structure were part of a ring with an overall gain of $+4\mathrm{dB}$. Pulse modulation at 10 MHz provided the interrupted feedback and the active mode locking which was needed to produce a stable and continuous stream of self-generated soliton pulses. Pulse width and phase measurements confirmed the soliton nature of the self-generated pulses.

Amplification of Microwave Magnetic Envelope Solitons in Thin Yttrium Iron Garnet Films by Parallel Pumping

The parametric amplification of 4.01 GHz, 22 ns wide microwave magnetic envelope (MME) backward volume wave pulses by parallel pumping has been realized in yttrium iron garnet (YIG) films. The parametric parallel pumping was achieved with 15--23 ns wide pulses applied to a strip line resonator at a frequency ${\ensuremath{\omega}}_{p}$ approximately twice the signal frequency ${\ensuremath{\omega}}_{s}$. Low power linear MME pulse signals were pumped to form solitons with a gain of 20 dB, and soliton signals could be boosted by 8 dB. These large gain factors occur only when ${\ensuremath{\omega}}_{p}$ is upshifted from $2{\ensuremath{\omega}}_{s}$ by 30 MHz. This upshift is critical and is related to the nonlinear nature of the soliton signal.

Phase profiles of microwave magnetic envelope solitons

A new method for the analysis of microwave magnetic envelope (MME) solitons has been developed. This method is based on the determination and analysis of output microwave pulse phase profiles. Simple analytical results based on the nonlinear Schrödinger equation show that MME soliton phase profiles contain the necessary and sufficient information needed to define a particular pulse as a linear dispersive pulse or a fully formed soliton. The effects are demonstrated both theoretically and experimentally for magnetostatic backward volume wave and magnetostatic surface wave pulse signals. Theoretical phase profiles are considered for Gaussian, hyperbolic secant, and rectangular pulse shapes. Experimental profiles are obtained for rectangular input pulses. The measured phase profiles compare favorably with the numerical results. Both the data and the theory show that a constant phase profile across the pulse provides a consistent and quantitative criterion for an MME soliton.

Decay properties of microwave-magnetic-envelope solitons in yttrium iron garnet films

Microwave magnetic envelope (MME) wave-packet propagation in a nominal 7.2-\ensuremath{\mu}m-thick yttrium iron garnet film has been investigated to determine the decay properties of linear and nonlinear MME pulses. The data were obtained in the magnetostatic backward volume wave configuration with an in-plane static field of 1088 Oe and an operating frequency of 5 GHz. Output pulse profiles, peak powers, and integrated pulse energies were measured for 13 ns wide input pulses and propagation distances from 3 to 10 mm. The pulse energy decay rate \ensuremath{\mathrm{B}} is found to be 10.6\ifmmode\times\else\texttimes\fi{}${10}^{6}$nrad/s and independent of the input power level up to 400 mW, even though the nonlinear response begins at 80 mW. This \ensuremath{\mathrm{B}} value is twice the relaxation rate \ensuremath{\eta} from ferromagnetic resonance. In the linear regime below 80 mW, the amplitude decay rate \ensuremath{\alpha} of the dynamic microwave magnetization peak amplitude is nearly constant at a value ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{low}}$\ensuremath{\approx}7.8\ifmmode\times\else\texttimes\fi{}${10}^{6}$nrad/s, which is somewhat greater than \ensuremath{\mathrm{B}}/2 and significantly less than \ensuremath{\mathrm{B}}. This ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{low}}$ is greater than the decay rate due to damping, \ensuremath{\eta}=\ensuremath{\mathrm{B}}/2, because of dispersion. With the onset of the nonlinear soliton response above 80 mW, \ensuremath{\alpha} gradually increases and saturates for input powers greater than 200 mW at a value ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{high}}$ which is equal to the energy decay rate \ensuremath{\mathrm{B}}. This result indicates that the amplitude decay rate for MME solitons is very close to twice the relaxation rate. This result is predicted in the limit of a vanishingly small damping. Experimentally, it appears to be valid even when the relaxation is significant. The transition region from ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{low}}$ to ${\mathrm{\ensuremath{\alpha}}}_{\mathrm{high}}$ has been quantitatively modeled through the nonlinear Schr\"odinger equation, and demonstrates an explicit change in the critical propagation length for soliton formation from 8 mm at the low power end of the transition to 3 mm at the high power end.

Propagation properties of microwave magnetic envelope solitons in thin yttrium–iron–garnet films at 5 GHz (abstract)

Microwave magnetic wave packets propagating in thin yttrium–iron–garnet (YIG) films show potential for novel devices as well as improved understanding of the basic properties of linear and nonlinear waves. The propagation characteristics of these excitations that have been studied up to now, however, do not provide a clear separation between linear and soliton regimes or a clear separation of the different contributions to the decay during propagation. The objective of this work was to study such characteristics for 5 GHz, 13–40 ns wide backward volume wave (BVW) magnetostatic wave square pulses in both the low-power linear and in the high-power soliton regimes and address these issues. The measurements were made with a delay time structure with a long and narrow 7.2 μm thick YIG film and 50 μm wide transducers, and input powers from 5 mW to 2 W. The output peak power Pout versus input pulse power Pin exhibits the same nonlinear response reported previously,1 with a linear response region A followed by a region B response with a more rapid increase in Pout and a high power region C in which Pout goes through a maximum and decreases. However, the integrated output pulse power, or pulse energy, is a strictly linear function of input pulse power over both the A and the B regions. At the same time, one finds a small but measurable increase in the average propagation velocity for the pulses as power is increased. The measured decay in the total pulse energy with propagation time leads to an unambiguous separation of the decay contributions due to dispersion and loss. This allows, in turn, a clear separation between the linear pulse and soliton regimes. The results were modeled from the nonlinear Schrödinger (NLS) equation with propagation and damping terms included. Agreement is good for regions A and B but the NLS model fails completely for region C.

Decay Free Microwave Magnetic Envelope Soliton Pulse Trains in Yttrium Iron Garnet Thin Films

Microwave magnetic envelope soliton pulse trains with no decay in amplitude have been obtained in magnetic films for the first time. The solitons were formed from magnetostatic spin waves with negative dispersion, or backward volume waves, propagated in a long and narrow $5.2\ensuremath{\mu}\mathrm{m}$ thick yttrium iron garnet film strip biased at 1096 Oe. An interrupted feedback technique was used to produce the soliton pulse trains from an initial 25 ns wide input pulse at a carrier frequency of 5.0 GHz. The train extended for over $40\ensuremath{\mu}\mathrm{s}$, 2 orders of magnitude longer than the single soliton lifetime. Measurements of the soliton width and phase profiles confirmed the soliton nature of the pulses over the entire train.

Formation, propagation, reflection, and collision of microwave envelope solitons in yttrium iron garnet films.

The end edge reflection and collision of backward volume wave bright microwave magnetic envelope solitons in long and narrow yttrium iron garnet single-crystal films has been studied experimentally. The experiments were done on 5.1-\ensuremath{\mu}m-thick, 1-mm-wide films. The bright solitons were excited by single or double 8-36-ns-wide microwave pulses with a nominal carrier frequency of 5.8 GHz. The experiments utilized a movable transducer structure to make measurements for a range of transducer separations from 2 to 15 mm and for pulses before and after reflection. The soliton character was established from single-pulse decay versus time and distance measurements. Three decay regions were observed, a slow decay region before soliton formation, a fast decay region characteristic of solitons, and a second slow decay for linear pulses. The soliton region included both incident and reflected pulses. The exponential decay rate for the soliton regime was greater than for the linear. The soliton pulses retained the same shape and speed after edge reflection. An observed drop in pulse amplitude after passing under the pickup transducer provided a way to measure the actual power and amplitude of the soliton signal. The measured amplitudes and widths were in fair agreement with predictions for a simple sech-type order one soliton pulse. For properly timed double-pulse experiments in which a reflected lead pulse collides with the follow-on pulse before detection, the effects of soliton collisions could be examined. In the single soliton power regime, the pulses were found to retain their shape and speed after collision. At higher powers, shapes were not retained. In addition, a wake effect was observed in which the lead pulse causes a change in the detected signal for the follow-on pulse, even without collision.

Phase properties of microwave magnetic envelope dark solitons in yttrium iron garnet thin films (abstract)

Although microwave magnetic envelope (MME) solitons in thin yttrium iron garnet (YIG) films have been studied extensively, only recently have dark MME solitons been observed. For a single dark soliton, one has a carrier phase change of 180°. Reference 1 indicated such a change. However, the overall phase change for a given dark pulse experiment should be 0°. The objective of this work was to examine phase profiles in detail for the dark soliton experiment. The results show that both of the above expectations are, in fact, satisfied. The 5 GHz measurements were done with a magnetostatic wave delay line structure with a long and narrow 7.2 μm thick single crystal YIG film oriented in the surface wave configuration. A GaAs microwave switch produced 300 ns long bright pulses separated by a dark pulse with a width in the 15 ns range. The input power was 0.002–1.0 W. The output signal showed two main dark pulse features, independent of power level. At low powers, the changes in phase across both features were small. With increasing power, the phase change across the first feature showed a rapid increase while the phase change for the second feature remained small. The phase change for the first feature saturated at a large value, on the order of 200°, relative to the phase change at low power. The phase change over the entire profile was always 0°. These results show: (1) There are significant phase changes at both low and high powers in the dark pulse experiment. (2) The phase change for a dark soliton must take into account the background phase change at lower powers. (3) Only the main dark pulse feature in the output profile exhibits single dark soliton characteristics through a clearly resolved phase saturation at 180°. (4) These thresholds are on the order of 10 mW for typical strip line transducer structures, compared to 100 mW or so for bright solitons.

Forward volume wave microwave envelope solitons in yttrium iron garnet films: Propagation, decay, and collision

Magnetostatic forward volume wave (FVW) microwave magnetic envelope solitons in 7.2 μm thick, single-crystal yttrium iron garnet films have been studied at 5.6–6.0 GHz. Rectangular input pulses with peak powers up to 3 W and pulse widths 5–50 ns were used. Single soliton output pulses with a characteristic increase in amplitude and pulse narrowing are observed when the power or width of the rectangular input microwave pulse exceeds threshold levels. Above these levels, output pulse peak power versus input power or pulse width exhibits a nonlinear increase and shows saturation effects. Multiple peak output profiles are observed for pulse powers and widths well above threshold. Solitons could be formed for all frequencies within the usable, low transmission loss portion of the magnetostatic FVW band. The use of reflected pulses from the film edge made it possible to study soliton decay and soliton collisions. The soliton decay rate was found to be approximately twice the linear rate, as expected from theory. The collision of solitons was found to occur with no significant change in shape and velocity. The various characteristic times from theory for pulse decay, pulse dispersion, nonlinear response, and propagation are found to be consistent with the experimental results.