ISSN 10637850, Technical Physics Letters, 2011, Vol. 37, No. 11, pp. 1065–1069. © Pleiades Publishing, Ltd., 2011. Original Russian Text © E.N. Beginin, S.V. Grishin, S.A. Nikitov, Yu.P. Sharaevskii, S.E. Sheshukova, 2011, published in Pis’ma v Zhurnal Tekhnicheskoi Fiziki, 2011, Vol. 37, No. 22, pp. 50–60.
Generation of Chaotic Dissipative Solitons in Active Ring Resonator with OneDimensional Periodic Ferromagnetic Miscrostructure E. N. Beginin, S. V. Grishin*, S. A. Nikitov, Yu. P. Sharaevskii, and S. E. Sheshukova Saratov State University, Saratov, 410012 Russia Kotelnikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences, Moscow, 125009 Russia *email:
[email protected] Received June 9, 2011
Abstract—Generation of chaotic dissipative solitons has been observed in an active ring resonator with one dimensional periodic ferromagnetic microstructure comprising a singlecrystalline film of yttrium iron garnet (YIG) with a lattice of grooves oriented perpendicular to the direction of propagation of a magnetostatic sur face wave (MSSW). A quasiperiodic train of chaotic dissipative solitons was generated in this system under the conditions of threemagnon processes of MSSW decay due to the passive synchronization (PS) of spin wave selfmodulation in a frequency band corresponding to the first bandgap. The PS onset was caused by the saturable absorption of microwave signals within the bandgap of the MSSW transmission line. DOI: 10.1134/S1063785011110204
Currently, intensive investigations are being carried out into the formation of spatially or temporally local ized wave structures called dissipative solitons or dissi pative solitons in nonlinear systems with gain and losses [1]. These investigations are of interest both from the standpoint of basic science and for practical applications, since these wave structures can be used for data processing and transmission in telecommuni cation systems—in particular, optical communication lines [2, 3].
weak nonlinearity. More recently, the PS of MSW self modulation frequencies was achieved [8, 9] in a ring system with an additional nonlinear transmission line with saturable absorption (known as “signaltonoise enhancer”) [11]. The PS consists in (i) the establish ment of certain phase relations between the MSW self modulation frequencies and (ii) the automatic separa tion of frequency components with definite intensities due to the presence of an element with saturable absorption in the ring [1].
In the microwave range, dissipative solitons can be generated in active ring resonators based on nonlinear transmission lines with ferromagnetic films [4–9]. It has been demonstrated [6–9] that these systems can ensure the autonomous generation of quasiperiodic trains of solitonlike pulses with chaotic variation of the phase difference from pulse to pulse, which may also be called chaotic dissipative solitons [8]. The cha otic dissipative solitons can form provided that three necessary conditions are met: (i) the existence of threemagnon (3M) processes of magnetostatic wave (MSW) decay in the ferromagnetic film, which lead to chaotization of the generated microwave signal [10]; (ii) the presence of a frequencyselective element pro ducing the frequency filtration of spectral components of the generated chaotic microwave signal; and (iii) the synchronization of selfmodulation frequencies of the chaotic microwave signal.
In recent years, increased attention has been devoted to studying structures based on ferromagnetic films with periodic inhomogeneities on the micron or submicron scale, which have been called magnonic crystals [12–14]. The magnonic crystals, by analogy with the optical photonic crystals [15], are expected to exhibit a broader spectrum of nonlinear phenomena than that of homogeneous ferromagnetic films. How ever, nonlinear processes in these structures have been insufficiently studied to date. Only separate investiga tions in this field have been reported, which were devoted to the thresholds of 3M processes of MSW decay (see, e.g., [16]) and features of the formation of envelope solitons at frequencies where the 3M pro cesses of MSW decay are forbidden [17–20].
Previously, chaotic dissipative solitons were gener ated [7] due to the selfsynchronization of MSW self modulation frequencies in a klystron amplifier with
This Letter presents data on the generation of cha otic dissipative solitons in an active ring resonator with onedimensional periodic ferromagnetic microstruc ture at frequencies where the 3M processes of MSW decay are allowed. In contrast to previous studies [8, 9], the PS of MSW selfmodulation frequencies in this
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The onedimensional periodic ferromagnetic microstructure represent a singlecrystalline YIG film stripe with a width of 3.5 mm, a length of 10 mm, and a thickness of d = 22 μm that possessed a saturation magnetization of 4πM0 = 1680 G. The film surface was scribed by a diamond cutter so as to form a lattice of 3.5mmlong, 2.8μmwide and ~0.2 μm deep grooves (see inset to Fig. 1a) of triangular cross section with a vertex angle of α = 130°. The structure had a period of T = 200 μm and a total length of 6.2 mm.
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The experimental setup of the transmission line comprised input and output 30μmwide microstrip transducers (shorted at one end and spaced by 4 mm from each other) and a onedimensional periodic fer romagnetic microstructure based on the YIG film that was placed onto the microstrip transducers. A constant external magnetic field H0 was oriented along the Z axis parallel to the YIG film surface in order to excite magnetostatic surface waves (MSSWs) propagating in the film along the X axis. The field mag nitude H0 was selected so as to make 3M decay of MSSWs possible.
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investigation takes place in a frequency band corre sponding to the first bandgap and does not require using an additional nonlinear element with saturable absorption. It should be noted that ultrashort optical pulses in ring resonators are frequently generated using the PS of modes ensured by an element with sat urable absorption [1]. In contrast to these optical schemes, we employed the PS of selfmodulation fre quencies for chaotic microwave signals.
Figure 1a shows the amplitude–frequency charac teristic of the transmission line measured at H0 = 149 Oe, which shows that the central frequency of the first bandgap is f1 = 2078 MHz, the attenuation coef ficient at this frequency is K1 = –38.9 dB, and the first bandgap width on a level of –35.9 dB is Δf = 11 MHz. Figure 1b presents a response of the output power (Pout) versus input power (Pin) for the same transmis sion line measured at f = f1. This curve reveals four characteristic regions depending on the Pin level. Region I (where Pin < Pth1 = –19.5 dBm) corresponds to a linear regime of the transmission line, in which the signal attenuation level corresponds to K1. For Pin ⭓ Pth1 (region II), the transmission line introduces addi tional nonlinear losses caused by the 3M processes of MSSW decay, which reach a maximum level at Pin = Pth2 = –2.5 dBm. These losses lead to a limitation of the output power and the appearance of a curve por tion with negative slope. Region III (Pin > Pth2) has a positive slope that corresponds to a decrease in the level of microwave signal attenuation with increasing input power (saturable microwave absorption). Finally, at Pin > Pth3 = 9.1 dBm (region IV), the atten uation becomes constant but still greater than that in the linear regime. The inset to Fig. 1b show a block scheme of the experimental setup of the selfoscillatory ring system, which comprises two microwave power amplifiers (1 and 2) on GaAsbased fieldeffect transistors (FETs), volume resonator 5, tunable attenuator 6, and nonlin ear MSSW transmission line 8 based on the periodic ferromagnetic microstructure. The FET power ampli fiers ensured a gain of K ~ 34 dB in the linear regime
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Fig. 2. Chaotic microwave signal generated in the active ring resonator with YIGbased onedimensional periodic ferromagnetic microstructure at a gain of G = 14.2 dB: (a) power spectrum; (b) amplitude time series.
within a frequency band of 2–4 GHz. The use of two amplifiers in the ring selfoscillatory system was nec essary in order to provide for a total gain above 40 dB at the central frequency of the first bandgap. The res onator had a resonance frequency of f0 = 2080 MHz, attenuation value on the resonant frequency of K0 = ⎯2.87 dB, and a loadedQ value of QL = 520. The fre quency band of the volume resonator fell completely within the first bandgap. The microwave signal from the output of ampli fier 2 was fed via directional couplers 3 and 4 to the input of realtime oscilloscope 9 and spectrum ana lyzer 10. The power level in the ring was controlled by variable attenuator 6 and measured by power TECHNICAL PHYSICS LETTERS
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meter 11 that was connected to the system via direc tional coupler 7. The experiments showed that, at a ring gain of G = 0, the system generates a monochromatic microwave sig nal at a frequency of one of the ring modes, namely, that occurring within the band of the volume resona tor. As the gain is increased (G ~ 2–3 dB), the system features the typical scenario of a transition from sin glefrequency generation to a narrowband chaotic microwave generation, which is caused by the mecha nism of stochastization of the MSW selfmodulation process [10]. The spectrum of generated microwaves becomes continuous in a 10–15 MHz band, while the signal envelope exhibits chaotic variations with the time. In this case, the integral power of the generated chaotic microwave signal at the delay line input is below Pth2. Figure 2 shows the power spectrum and time series of chaotic microwave signals measured in the active ring at Pin > Pth2. At Pin = +4.9 dBm, the spectrum of the chaotic microwave signal expands to occupy a frequency band of ~40 MHz and the next highfre quency ring oscillation mode appears in a jumplike manner, for which the spectral power level becomes maximum. The frequency interval between these modes is about 10 MHz, which corresponds to a sig nal delay time of τ ~ 100 ns, and each mode is “noisy” due to the aforementioned mechanism. In this case, the power spectrum reveals a comb of fre quencies located on a noise background, while the time series displays a quasiperiodic train of dissipative solitons with a repetition period of Tr = 1.4–1.5 μs that corresponds to an MSW selfmodulation frequency of 2011
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fam = 650–700 kHz determining the interval between frequencies of the comb. The pulse duration Td mea sured at halfmaximum level of the microwave amplitude amounts to Td ~ 0.7 μs and the pulse ratio is about q = Tr/Td ~2. Since Pth2 < Pin < Pth3 , which corresponds to the region with saturable absorption (see Fig. 1b), this regime leads to a stronger attenua tion of the spectral components with lower power level (–5.6 dBm < Pin < +4.9 dBm) relative to those with higher power level (Pin ≅ +4.9 dBm). Thus, the spectral components of a multifrequency signal will be more effectively attenuated near a certain fre quency where the spectral power corresponds to the aforementioned interval of low powers. This effect leads to the PS of the MSW selfmodulation fre quencies of the two neighboring modes with over lapping spectra. The chaotic nature of dissipative solitons is con firmed by the continuous spectrum of microwave signals and the random variation of the phase differ ence from one to another peak of the envelope. The envelope phase was calculated by applying the Hil bert transform to the measured time series of the microwave signal. Figure 3 shows the temporal vari ation of the phase difference between the neighbor ing envelope peaks relative to the average phase dif ference calculated for one of the time series at a given G value. These results show that the phase dif ference between the neighboring envelope peaks randomly varies from peak to peak rather than remains constant. However, these fluctuations of the phase difference are observed in a certain region where the interval of phase differences amounts to ~100°. It should be noted that, in contrast to the system studied in [8, 9], the PS of the MSW self modulation frequencies is observed in a wider fre quency band and the increase in G leads to an increase (rather than a decrease) in Tr and the gen eration of dissipative solitons of greater duration (Td ~ 50 μs). Analysis of these features is beyond the scope of this short communication and will be pre sented in a future publication. In conclusion, it should be noted that a transmis sion line based on the given onedimensional periodic ferromagnetic microstructure is characterized by a decrease in nonlinear losses in the frequency band corresponding to the first bandgap (where the 3M pro cesses of MSW decay are allowed) at a certain level of the input signal power, which leads to saturable absorption of microwave signals. The system with a transmission line based on this microstructure in the ring resonator makes possible simultaneous genera tion of a chaotic microwave signal and the PS of its spectral components. The chaotic dissipative solitons generated in the proposed device exhibit new proper ties related to an increase in their duration and repeti
tion period with increasing gain of the ring. Based on the obtained results, it is possible to expand the field of application of the periodic ferromagnetic structures and to create sources of chaotic microwave pulses for data transmission and telecommunication systems [21]. Acknowledgments. This study was supported by the Government of the Russian Federation (Program for Support of Scientific Research in Higher Technical School under Supervision of Leading Scientists, project no. 11.G34.31.0030) and the Ministry of Sci ence and Education of the Russian Federation (project no. RNP 2.1.1/9525). REFERENCES 1. Dissipative Solitons, Ed. by N. A. Akhmediev and A. A. Ankevich (Fizmatlit, Moscow, 2008) [in Rus sian]. 2. G. P. Agraval, Lightwave Technology: Telecommunica tion Systems (Wiley–Interscience, Hoboken, NJ, 2005). 3. N. N. Akhmediev and A. Ankevich, Solitons, Nonlinear Pulses and Beams (Chapman & Hall, 1997). 4. B. A. Kalinikos, M. M. Scott, and C. E. Patton, Phys. Rev. Lett. 84, 4697 (2000). 5. M. M. Scott, B. A. Kalinikos, and C. E. Patton, Appl. Phys. Lett. 78, 970 (2001). 6. E. N. Beginin, S. V. Grishin, and Yu. P. Sharaevskii, Pis’ma Zh. Eksp. Teor. Fiz. 88, 743 (2008) [JETP Lett. 88, 647 (2008)]. 7. S. V. Grishin, B. S. Dmitriev, Yu. D. Zharkov, et al., Pis’ma Zh. Tekh. Fiz. 36 (2), 62 (2010) [Tech. Phys. Lett. 36, 76 (2010)]. 8. S. V. Grishin and Yu. P. Sharaevskii, Proceedings of the 18th IEEE Workshop on Nonlinear Dynamics of Elec tronic Systems (Dresden, Germany, 2010), p. 218. 9. E. N. Beginin, S. V. Grishin, and Yu. P. Sharaevskii, Pis’ma Zh. Tekh. Fiz. 36 (22), 37 (2010) [Tech. Phys. Lett. 36, 1042 (2010)]. 10. V. E. Demidov and N. G. Kovshikov, Zh. Tekh. Fiz. 69 (8), 100 (1999) [Tech. Phys. 44, 960 (1999)]. 11. J. D. Adam and S. N. Stitzer, Appl. Phys. Lett. 36, 485 (1980). 12. Yu. V. Gulyaev and S. A. Nikitov, Dokl. Akad. Nauk 380, 469 (2001) [Dokl. Phys. 46, 687 (2001)]. 13. Yu. V. Gulyaev, S. A. Nikitov, L. V. Zhivotovskii, et al., Pis’ma Zh. Eksp. Teor. Fiz. 77, 670 (2003) [JETP Lett. 77, 567 (2003)]. 14. S. L. Vysotskii, S. A. Nikitov, and Yu. A. Filimonov, Zh. Eksp. Teor. Fiz. 128, 636 (2006) [JETP 101, 547 (2005)].
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Translated by P. Pozdeev
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