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IEEE TRANSACTIONS ON MAGNETICS, VOL. 47, NO. 10, OCTOBER 2011
Self-Generation of Chaotic Dissipative Soliton Trains in Active Ring Resonator With 1-D Magnonic Crystal Sergey V. Grishin , Yurii P. Sharaevskii , Sergey A. Nikitov , Evgenii N. Beginin , and Svetlana E. Sheshukova Department of Electronics, Oscillations and Waves, Saratov State University, Saratov 410012, Russia Nonlinear Physics Department, Saratov State University, Saratov 410012, Russia Kotel’nikov Institute of Radio Engineering and Electronics of Russian Academy of Science, Moscow 125009, Russia Self-generation of chaotic dissipative soliton trains was observed in an active ring resonator based on 1-D periodical ferromagnetic structure (1-D magnonic crystal) in a groove’s grating form. The grooves were cut off on the surface of yttrium iron garnet film with the help of a scribing technique and placed perpendicularly to the magnetostatic surface wave (MSSW) propagation. The presence of three magnon decay processes of MSSW, a frequency filtration, and a passive synchronization of the spin-wave self-modulation frequencies caused the self-generation of chaotic dissipative soliton trains. Passive synchronization was realized at frequencies of the first band gap because of the presence of a saturable absorption of a microwave signal. Index Terms—Chaos, ferrite films, magnetostatic waves (MSW), solitons.
I. INTRODUCTION
N
OWADAYS, structures localized in space or time, formed in the nonlinear systems with an amplification and loss, are being intensively investigated. These structures are known as the dissipative solitons [1]. Research on dissipative solitons is significant both for the fundamental science and applied applications, such as the telecommunication systems, especially, the optical communication lines [2], [3]. In microwave (MW) frequency range, the dissipative soliton trains can be formed in the active ring resonators based on the nonlinear transmission lines with the ferromagnetic films [4]–[8]. As shown in [6]–[8], such systems, self-generation of the repetition MW pulse trains occurs: an envelope produces a soliton-like response with a quasi-periodic change and an envelope phase has a chaotic change from soliton to soliton. Such structures are named as the chaotic dissipative solitons. They are formed, when the following three conditions are met: 1) existence of three-magnon (3M) decay processes of the magnetostatic waves (MSW), which leads to chaotization of the MW signal [9]; 2) presence of a frequency-selective element; and 3) synchronization of the spin-wave self-modulation frequencies of a chaotic MW signal. In [6] and [7], a self-synchronization of the spin-wave selfmodulation frequencies caused self-generation of the chaotic dissipative soliton trains. In [8], a passive synchronization of the spin-wave self-modulation frequencies in the active ring was carried out with the help of additional nonlinear transmission line with a saturable absorption known as a signal-to-noise enhancer [10]. In the case of passive synchronization, the certain phase relationship between the spin-wave self-modulation frequencies was established because of automatic selection of the frequency components with the certain amplitudes by the use of nonlinear element with the saturable absorption. In recent years, researches on ferromagnetic film structures with periodic inhomogeneities of micrometer and submicromManuscript received February 18, 2011; revised May 08, 2011; accepted May 24, 2011. Date of current version September 23, 2011. Corresponding author: S. V. Grishin (e-mail:
[email protected]). Digital Object Identifier 10.1109/TMAG.2011.2158293
eter sizes (magnonic crystals) are attracting significant interest [11]–[14]. Magnonic crystals as well as optical photonic crystals [15] must demonstrate a wider spectrum of the nonlinear phenomena than those in the homogeneous ferromagnetic films. However, currently, investigations of the nonlinear processes in such structures are limited, and only a few studies could be found in this area, in which the authors have examined the formation of the envelope solitons in the frequency range, where 3M decay processes of MSW were disabled [16]–[19]. The study demonstrates the self-generation of the chaotic dissipative soliton trains in the active ring resonator with 1-D magnonic crystal. The self-generation of such soliton trains is observed in the frequency band, where 3M decay processes of MSW are allowed. In contrast to [8], the passive synchronization of the spin-wave self-modulation frequencies is carried out at frequencies of the first band gap of 1-D magnonic crystal, and the additional nonlinear element with the saturable absorption is not required in the ring. II. EXPERIMENTAL RESULTS AND DISCUSSIONS 1-D periodical structure in a groove’s grating form was cut off on the surface of yttrium iron garnet (YIG) film with the help of a scribing technique. The film had the width of 3.5 mm, length of m, and saturation magnetization 10 mm, thickness of of 1680 Gs. The groove’s length was 3.5 mm, width was 2.8 m, and depth was 0.2 m (see the inset in Fig. 1). In cross section, the grooves had a triangular profile with an angle . m and the length of The period of the structure was the periodic structure was 6.2 mm. Experiments with 1-D magnonic crystal were carried out on a delay line, which consisted of two (input and output) shortened microstrip transducers with a width of 30 m. The distance between them was 4 mm. The YIG film was put over the transducers and the magnetostatic surface waves (MSSW) were excited in the film at the external magnetic field of Oe. In this case, 3M decay processes of MSSW were allowed. From the amplitude–frequency characteristic of MSSW delay line (see Fig. 1), it can be observed that the central frequency of the first band gap of 1-D magnonic crystal is MHz, the attenuation on this frequency is dB,
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GRISHIN et al.: SELF-GENERATION OF CHAOTIC DISSIPATIVE SOLITON TRAINS IN ACTIVE RING RESONATOR WITH 1-D MAGNONIC CRYSTAL
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Fig. 3. Scheme of the active ring resonator. Fig. 1. MW transmission response of the MSSW delay line measured at the dBm. Inset shows the scheme of the YIG film with the input power grating of grooves.
Fig. 2. Output power versus input power response of the MSSW delay line measured at frequency .
and the bandwidth of the first band gap on 3 dB level is MHz. As shown in Fig. 2, four ranges can be determined on the experimental response of the output power versus the input power . Range I is observed at dBm and corresponds to the linear regime of MSSW delay line. Power corresponds to the threshold value of the input power at which the attenuation level is changed to 1 dB comparatively with the linear regime. At (Range II), additional nonlinear losses appear in the delay line and achieve a maximum value at dBm. The decay processes of MSSW causes the presence of nonlinear losses. In this case, the output power level is limited. In Range III, the signal attenuation value is decreased with the increase in the input power value. It corresponds to a saturable absorption of the MW signal. At dBm (Range IV), the attenuation is constant, but its value is larger than that in the linear regime.
The experimental setup of the investigated active ring resonator (see Fig. 3) comprises two MW power amplifiers based on GaAs Schottky-gate FETs, a volume resonator, a variable attenuator, and an MSSW delay line based on the 1-D magnonic dB in the crystal. The power amplifiers have the gain of bandwidth 2–4 GHz. The usage of two power amplifiers in the ring is necessary to obtain a total gain of more than 40 dB on the central frequency of the first band gap. The volume resonator MHz, the attenuation has the resonant frequency of value on the resonant frequency is dB, and the loaded value is . The MW signal from the output of the second power amplifier is fed to the input of the spectrum analyzer ESA-E E4402B and the real-time oscilloscope Infiniium DSO81004B, via directional couplers DC-1 and DC-2, respectively. The signal power level is changed by the variable attenuator and measured by the power meter N1912A that is coupled to the ring via a directional coupler DC-3. From experimental research, it was determined that at a ring , the monochromatic signal self-generation apgain of pears on a frequency of one of the ring modes. The typical scenario of transition to the chaos, coupled with the stochastization of spin-wave self-modulation frequencies [9], could be observed in the system with the increase in the value of ( 2–3 dB). The spectrum of an MW signal is continuous over the bandwidth of 10–15 MHz and a waveform envelope chaotically changes in time. In this case, the integral power level of a chaotic MW signal at the input of the MSSW delay line is more than , but less than . The power spectra and time series of the chaotic MW signal, which are measured at various values of , are shown in Fig. 4. These results are obtained when a signal integral power at the . At dB [ input of the delay line is dBm, see Fig. 4(a)], the spectrum of the chaotic MW signal becomes wider and has the frequency band of MHz. In this case, the next high-frequency ring mode is excited and the spectral power level on the frequency of this mode is maximal. Each of these two modes is “noisy” due to the aforementioned mechanism. In this case, a signal power spectrum is a comb of frequencies located on a noise background; in the time domain, a quasi-periodic train of dissipative solitons with a repetition
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Fig. 4. Power spectra (left) and time series (right) of the chaotic MW signal at dB, (b) dB, (c) dB, and various values of : (a) dB. The spectra are measured at a receiver bandwidth of 10 kHz. (d)
period s is observed. It corresponds to the spin-wave self-modulation frequencies 650–700 kHz, which define the interval between the frequencies of the comb. measured at half-level from the maximum A pulse duration value of an MW signal is s, and a pulse ratio . At , the saturable absorption is is present and the spectral components of a low-power level ( dBm dBm) are attenuated more than those of a dBm). Thus, the spectral compohigh-power level ( nents of the low-power level of a multifrequency signal will be effectively attenuated near the central frequency in which the spectral power level is higher. This effect leads to the passive synchronization of the spin-wave self-modulation frequencies of two modes with the overlap spectra. The duration of dissipative solitons and their repetition period s and s) with the increase increase ( in the value of [ dBm, see Fig. 4(b)]. In this case, the spin-wave self-modulation frequencies and pulse ratio 167–182 kHz and , respectively. The decrease to
IEEE TRANSACTIONS ON MAGNETICS, VOL. 47, NO. 10, OCTOBER 2011
effect of decrease in the value of with the increase in the value of in such ring systems has been observed for the first time. In our opinion, this effect is coupled with the narrowing of the spectrum of multifrequency MW signal because of saturable absorption. The narrowing of the spectrum leads to the increase in the duration of dissipative solitons and, consequently, to the increase in their repetition period. In this case, the pulse form is similar to the form of pulse propagated through a delay line at the frequencies, where 3M decay processes of MSSW are allowed [20]. dBm; The subsequent increase in the value of [ see Fig. 4(c)] leads to the increase in the dissipative soliton dus and their repetition period of ration of up to up to s. This is the reason for the decrease in the spin-wave self-modulation frequency and the pulse ratio of up kHz and , respectively. At to dB [see Fig. 4(d)], an MW signal similar to the monochromatic one is generated. Thus, with the increase in the ring gain, a new scenario of transition from chaos to the single-frequency regime through a repetition of a very long MW pulse train could be observed. The mechanism of transition from chaos to single-frequency regime is coupled with the presence of two power channels in the MSSW delay line. The first channel is the YIG film, in which a power transition is carried out by the slow MSSW. The second one is a free space channel, in which a power transition is carried out by the fast electromagnetic wave. In a linear regime, the main part of the power is transmitted through the first channel. , a power transition through the first With the increase of channel is deteriorated because of MSSW nonlinear losses. At , the loss levels are comparable in both the channels. At , the main part of the power is transmitted through the second channel. Histograms represented in Fig. 5 confirm this assumption. They were determined on the basis of experimental time series, and in the case of large amount of MW signal instantaneous , the histograms correspond to the distrivalues butions of probability density. In Fig. 5(a), the random process with distribution different from the normal distribution is observed. The presence of a pulse train [see Fig. 4(a)] is the cause that the greatest values of probability density correspond to the zero instantaneous values of the MW signal. With the power , periodical and random processes occur signal tending to simultaneously [see Fig. 5(b)] because of the turn-on of the second (linear) channel. Two additional maximums of the distribution confirm the presence of the periodical process in the active ring. The values of probability density at zero instantaneous values of the MW signal are decreased because the repetition period and pulse duration are increased [see Fig. 4(b)]. With the further increase in the signal power, the values of probability density at zero instantaneous values of the MW signal are not maximal [see Fig. 5(c)]. When the signal power is greater , the pulse train is not observed and only the periodical than process is presented [see Figs. 4(d) and 5(d)]. In this case, the main part of the power is transmitted through the second channel that causes the formation of harmonic signal of a large power level. As shown in [21], the influence of an external harmonic
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REFERENCES
Fig. 5. Distribution of the probability density of MW signal instantaneous dB, (b) dB, (c) values at various values of : (a) dB, and (d) dB.
signal of a large power level on the wideband chaotic MW signal generated by an active ring resonator can be a cause of the determined chaos suppression and single-signal generation. The continuous spectrum of an MW signal and its instantaneous phase randomly drifted from pulse to pulse determine the chaotic nature of these dissipative solitons [6]. III. CONCLUSION In conclusion, it should be pointed out that the usage of the 1-D magnonic crystal delay line in the active ring resonator makes possible a generation of chaotic MW signal as well as passive synchronization of its frequency components. In this case, the chaotic dissipative soliton trains formed in such device get new features: the pulse duration and repetition period are increased at the increase of a ring gain. The obtained results give the opportunity to expand the possible usage of magnonic crystals and to create the sources of chaotic MW pulses for communication systems [22]. ACKNOWLEDGMENT This work was supported by the Grant from the President of Russian Federation for Support of Leading Scientific Schools under Project 3407.2010.2 and by the Government of Russian Federation for Support of Scientific Research in the Russian Universities Under the Guidance of Leading Scientists under Project 11.G34.31.0030.
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