Spatial and Temporal Dynamics of Dissipative Parametric Solitons in a ...

IEEE TRANSACTIONS ON MAGNETICS, VOL. 50, NO. 11, NOVEMBER 2014

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Spatial and Temporal Dynamics of Dissipative Parametric Solitons in a Ferromagnetic Film Active Ring Resonator Dmitrii V. Romanenko1, Sergey Grishin1 , Alexander Sadovnikov1, Yurii Sharaevskii1, and Sergey Nikitov1,2 1 Laboratory

2 Kotel’nikov

Metamaterials, Saratov State University, Saratov 410012, Russia Institute of Radio Engineering and Electronics, Russian Academy of Science, Moscow 125009, Russia

This paper reports the experimental results of spatial and temporal dynamics research of dissipative parametric solitons generated in a ferromagnetic film active ring resonator. Such dissipative structures are formed through three-wave parametric decay of a magnetostatic surface wave and frequency–time filtering. The spatio-temporal dynamics of dissipative parametric solitons has been investigated using the Brillouin light scattering technique. It is shown that quasi-stationary temporal structures are formed in a ring along a ferromagnetic film and are not observed in a ferromagnetic film, which is not incorporated into the ring. Index Terms— Ferrite films, solitons, spin waves (SWs).

I. I NTRODUCTION

I

T is known that envelope solitons of magnetostatic waves (MSWs) can exist in both ferromagnetusedic films [1]–[3] and active ring resonators based on them [4]–[7]. The MSW envelope solitons are formed in a ferromagnetic film when the balance between the spatial dispersion of MSW and cubic nonlinearity is present. This nonlinearity is a result of fourwave interaction of spin waves (SWs). The radio physics methods of envelope signal detection [1]–[7] and optical methods of measurement of scattered light intensity [8]–[11] can be used to identify MSW envelope solitons. The Brillouin light scattering (BLS) technique permits to research a spatiotemporal dynamics of wave beams that directly propagate in the investigated medium. In earlier experiments where the BLS technique was used, the spatio-temporal dynamics of 1-D and 2-D MSW envelope solitons propagating in narrow and wide ferromagnetic films has been researched [8]–[10]. Besides, the BLS technique is used to study the characteristics of 2-D solitons (bullets) in a ferromagnetic film active ring resonator [11]. As shown in [11], the compensation of dissipation in a ferromagnetic film by the inflow of energy (amplification) leads to the generation of quasi-stationary structures that are absent in a ferromagnetic film, which is not incorporated into the ring. In addition to four-wave SW interactions, there is a threewave parametric decay of MSW. Parametric processes are the reason of MSW nonlinear losses that can lead, for example, to the formation of short microwave (MW) pulses [12]. The spatio-temporal dynamics of such pulses was studied using the BLS technique [13]. As shown in [14]–[16], the threewave parametric decay of MSW can lead to the generation of dissipative structures in the form of soliton-like pulses when ferromagnetic films are used in active ring resonators. The durations of such structures are considerably greater than the time of a signal passing around a ring. The dissipative parametric solitons are self-generated through three-wave Manuscript received March 7, 2014; revised May 6, 2014; accepted May 16, 2014. Date of current version November 18, 2014. Corresponding author: D. V. Romanenko (e-mail: [email protected]). Digital Object Identifier 10.1109/TMAG.2014.2326598

parametric decay of a magnetostatic surface wave (MSSW) and frequency filtering that is realized using different resonant elements in a ring [14]–[16]. It should be noted that such structures are only observed in an active ring resonator and absent in a ferromagnetic film, which is not incorporated into the ring. In this regard, the study of spatio-temporal dynamics of dissipative parametric solitons directly generated in a ferromagnetic film is of great interest. This paper reports the results of the experimental study of spatio-temporal dynamics of dissipative parametric solitons. Such dissipative structures are formed in a ferromagnetic film both at frequencies MSSW and parametrically excited SW. Dissipative solitons are generated in the active ring resonator through the three-wave parametric decay of MSSW and time– frequency filtering [4]–[6], [11]. The spatio-temporal dynamics of such structures is investigated in a ferromagnetic film using the Brillouin spectroscopy. II. E XPERIMENTAL R ESULTS AND D ISCUSSION The investigated active ring resonator consists of a broadband amplifier, a volume resonator, and MSSW transmission line that are serially connected in a ring (Fig. 1). The amplifier works in the frequency range 2–4 GHz, and has a nonlinear response of a gain factor K that is used in the time filtering technique [17]. In the linear regime, the amplifier has K = 38 dB and it realizes the loss compensation in a ring [4]–[7], [11]. The volume resonator is used for the frequency filtering of both ring modes and SW self-modulation frequencies. The MSSW transmission line has standard configuration of a delay line and consists of an yttrium iron garnet (YIG) film as well as input and output microstrip transducers. The YIG film is grown on a gadolinium gallium garnet (GGG) substrate by the liquid-phase epitaxy technique. The YIG film has thickness d = 7.7 μm, width 3 mm, length 10 mm, and saturation magnetization 4π M0 = 1750 Gs; 50 μm microstrip transducers are used for excitation and detection of MSSW. The distance between them is L = 4 mm. The external static magnetic field H0 = 460 Oe is applied in such a way that Damon–Eshbach geometry is realized. The MSSW is excited in the frequency range where the three-wave parametric decay of MSSW is allowed [18].

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Fig. 3. (a) Power spectrum and (b) time profiles (middle and bottom diagrams) of dissipative solitons are generated in the nonautonomous regime. In (b), the upper time diagram corresponds to the amplitude profile of external pulses, and middle and bottom diagrams correspond to the amplitude and phase profiles of dissipative solitons, respectively.

Fig. 1. Scheme diagram of the ferromagnetic film active ring resonator, the BLS setup, and MW equipment.

Fig. 2. (a) Power spectrum and (b) time profiles of amplitude (upper diagram) and phase (bottom diagram) of a chaotic signal that is self-generated in the autonomous regime.

Fig. 2 shows spectral and temporal characteristics of a self-generated signal measured by a spectrum analyzer and a real-time oscilloscope with the bandwidth of 10 GHz. As shown in Fig. 1, these MW devices are connected with an active ring resonator through directional couplers DC-2 and DC-3, respectively. It should be noted that the mathematical processing is applied to the measured time realizations. The digital filtration is used for the minimization of the quantization noise, and the Hilbert transform is used to calculate the envelope phase profiles. In the last case, the rapid phase change at the central frequency of a signal power spectrum f 0 = 3114 MHz is excepted. The self-generation of chaotic sequence of dissipative solitons at f 0 is observed when a signal power level in a ring is P = −9.9 dBm that exceeds three-wave parametric threshold by 16 dB (Fig. 2). The amplitude and repetition interval of such structures have chaotically variations all over time realization. The pulsewidth measured by 0.7 level from peak power has the value Td ∼160 ns. In this case, the value Td is greater than the time of a signal passing around a ring τr = 120 ns. The power spectrum of a self-generated MW signal is continuous, and has the width of about 25 MHz measured at the pedestal base. Fig. 2 also shows phase profiles. As follows from Fig. 2, dissipative solitons have a linear phase transformation inside each pulse, and the phase incursion from

pulse to pulse has chaotically variation. It is known that the time filtering technique is used to generate the periodic pulse sequences in ferromagnetic film active ring resonators [4], [11], [17]. It can be realized by either switches [4], [11] or external MW pulses [17]. In the last case, an external MW signal controls a ring gain. In time intervals when an external signal has a large amplitude, a ring gain is small and the own dynamics of self-oscillating system is suppressed. Vice versa, in time intervals when an external signal is absent or has a small amplitude, a ring gain is large and an MW signal self-generation is observed. These time filtering features are attractive to control a signal power level in a ring that leads to the active synchronization of selfmodulation frequencies and generation of periodic sequences of MSW envelope solitons [4], [11]. In the investigated active ring resonator, both the frequency and time filtering techniques are realized. For time filtering, an external pulse-modulated MW signal is used [17]. The external MW pulses are formed by the MW pulse generator that is connected to a ring through a directional coupler DC-1 (Fig. 1). Besides, the external pulses are used to control the BLS setup and synchronize the process of measurements. So, for example, in time intervals where external pulses are absent, the photon counter is ON. Vice versa, the photon counter is OFF when external pulses are present. Fig. 3 shows the spectral and time characteristics of a signal that is generated in the nonautonomous regime. These characteristics were measured at the output of the volume resonator by the spectrum analyzer and oscilloscope. The carrier frequency of an external pulsemodulated MW signal f c = 2060 MHz is outside the MSSW frequency band, but inside the amplifier frequency band. The duration and repetition interval of external MW pulses are selected in such a way that the quasi-periodic sequence of solitary pulses are generated in a ring. In Fig. 3, the dissipative solitons have the pulsewidth Td ∼ 120 ns (Td = τr ) and repetition interval Tr = 2 μs. These structures are formed in time intervals where external pulses are absent. From phase profiles of Fig. 3(b), it is followed that the generated dissipative solitons are not analogues of the bright solitons because the phase profile inside pulses is not constant [19]. In this case, the signal power level exceeds the bright soliton threshold and the phase profile has rapid changes [15], [16]. The spatio-temporal dynamics of dissipative solitons in a ferromagnetic film is studied using the BLS setup. Fig. 4

ROMANENKO et al.: SPATIAL AND TEMPORAL DYNAMICS OF DISSIPATIVE PARAMETRIC SOLITONS

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Fig. 4. Spatial distributions of the square amplitude of magnetization measured at frequencies f MSSW (gray scale) and f SW (isolines). The measured amplitudes are time averaged.

shows the spatial distribution of the square amplitude of magnetization measured in the YIG film at both MSSW frequency f MSSW = 3110 MHz and parametrically excited SW frequency f SW = 1556 MHz. The spatial distribution of magnetization at f MSSW corresponds to the superposition of odd (first and third) width modes [20]. The SW excitation is mainly observed in both the spatial area that is located near the input microstrip transducer and areas where MSSW amplitude has local maxima. Far away from the input microstrip transducer, the MSSW amplitude is decreased that is a reason of less efficient excitation of SW. Fig. 5(a) and (d) shows the spatial distribution of dissipative soliton durations. As follows from the obtained results, the duration of dissipative solitons generated at frequencies MSSW and SW has different values both along and across the YIG film. In Fig. 5(a), MSSW dissipative solitons have maximal duration in the spatial area where the width mode propagation is observed (Fig. 4). In this area, the dissipative soliton duration remains quasi-stationary along the YIG film. As shown in Fig. 3, the MSSW dissipative soliton has the duration Td ∼120 ns when it goes to the input microstip transducer. From the BLS experimental results shown in Fig. 5(b), it is shown that the MSSW dissipative soliton with the integrated amplitude profile has the same duration and shape in the YIG film at L 1 = 0 mm only. When the soliton-like pulse propagates along the YIG film (L 2 = 2 mm and L 3 = 4 mm), the peak amplitude and shape of this pulse are changed stronger than the pulse duration. So, the soliton duration is increased 1.4 times and the peak amplitude is decreased 10 times at the output transducer in comparison with the input one. Thus, the soliton-like pulse shape is changed from one element to another element of the ring, but it is stationary in time at each ring element. It should be noted that the dissipative soliton duration is nonstationary across the YIG film because the width mode propagation is inhomogeneous across the film. Thus, the duration of MSSW dissipative solitons (with integrated and nonintegrated amplitude profiles) is quasistationary along the YIG film and nonstationary across it. Fig. 5 also shows the behavior of dissipative soliton duration at the frequency f SW . In contrast to the MSSW dissipative soliton duration map [Fig. 5(a)], the soliton durations measured at the frequency f SW are nonstationary both along and across the YIG film [Fig. 5(d)]. This fact can be explained by the local

Fig. 5. Spatial distributions of dissipative soliton duration measured in the YIG film, which is incorporated in the active ring resonator. The measurements are done at frequencies (a) f MSSW and (d) f SW . In (b) and (c), time profiles of magnetization integrated across the YIG film are shown at fixed spatial points along the film: L 1 = 0 mm, L 2 = 2 mm, and L 3 = 4 mm. The measurements are done at frequencies (b) f MSSW and (c) f SW .

excitation of SW in the spatial points where MSSWs have amplitude maxima and nonpropagation of SW along the YIG film. The SW fast dissipates across the film because they have losses greater than the ones of MSSW [18]. From the results of Fig. 5(b) and (c), it follows that the peak amplitude of the MSSW dissipative soliton at the point L 2 is four times less than the one at the point L 1 . In this case, the peak amplitude of the SW dissipative soliton is decreased 40 times. Thus, the peak amplitude of SW soliton fast dissipates along the YIG film more than the peak amplitude of MSSW soliton. It should be noted that the duration of SW dissipative solitons with integrated profiles has a small change (from 200 to 180 ns) and is quasi-stationary. For comparison, the spatial distributions of duration of MW pulses propagating through the MSSW transmission line are shown in Fig. 6. The duration (measured at the pulse base), repetition interval, and peak power of MW pulses at the input of this line correspond to the same characteristics of MSSW dissipative solitons in the ring. In contrast to the spatial distribution of the MSSW dissipative soliton duration [Fig. 5(a)], the spatial distribution of the duration of MSSW pulses passing through the YIG film is nonstationary both along and across it [Fig. 6(a)]. The duration of MSSW pulses (measured at the half-amplitude value) with integrated profiles

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Fig. 6. Spatial distributions of pulsewidth measured in the YIG film, which is not incorporated in the active ring resonator. The measurements are done at frequencies (a) f MSSW and (d) f SW . In (b) and (c), time profiles of magnetization integrated across the YIG film are shown at fixed spatial points along the film: L 1 = 0 mm, L 2 = 2 mm, and L 3 = 4 mm. The measurements are done at frequencies (b) f MSSW and (c) f SW .

[Fig. 6(b)] is changed from 500 ns at L 1 to 90 ns at L 3 , and is also nonstationary. The analog situation is observed for the SW pulses [Fig. 6(c)]. In this case, the SW pulsewidth is changed from 270 ns at L 1 to 500 ns at L 2 . These facts indicate that these pulses are not dissipative parametric solitons, because in the YIG film, there is no energy inflow and the balance between the amplification and loss is not observed here. III. C ONCLUSION In conclusion, the results of the experimental research of MSSW and SW dissipative solitons that are formed due to the three-wave parametric decay of MSSW in the ferromagnetic film active ring resonator are present. It is shown that the duration of MSSW dissipative structures is quasi-stationary along the film that is not observed in the ferromagnetic film, which is not incorporated into the ring. The obtained results are of great interest to develop dissipative soliton generators for communication systems. ACKNOWLEDGMENT This work was supported in part by the Russian Foundation for Basic Research under Project 14-07-00273 and in part by

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