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Letters International Journal of Bifurcation and Chaos, Vol. 11, No. 4 (2001) 1141–1147 c World Scientific Publishing Company
EXPERIMENTAL OBSERVATION OF SYNCHRONIZATION AND ANTI-SYNCHRONIZATION OF CHAOTIC LOW-FREQUENCY-FLUCTUATIONS IN EXTERNAL CAVITY SEMICONDUCTOR LASERS IMMO WEDEKIND and ULRICH PARLITZ∗ Drittes Physikalisches Institut, Universit¨ at G¨ ottingen, B¨ urgerstraße 42-44, D-37073 G¨ ottingen, Germany Received June 29, 2000; Revised July 25, 2000 Experimental investigations of synchronization and anti-synchronization of optically coupled semiconductor lasers with external cavities are presented. Both lasers show chaotic lowfrequency intensity fluctuations that are (anti-) synchronized due to optical coupling by light injection. For uni-directional coupling response lasers with and without external cavity are considered. In the case of bi-directional coupling synchronized fluctuations are observed even without external mirrors.
1. Introduction During the last decade synchronization of chaotic systems has been explored very intensively by many researchers in various fields ranging from physics, mathematics to engineering, where for the latter the main motivation has been potential practical applications in communication systems [Pecora & Carroll, 1990; Kocarev & Parlitz, 1995; Parlitz et al., 1996; Kennedy & Ogorzalek, 1997; Schuster, 1999]. Many modern communication devices are opto-electronic or all optical. Therefore, chaotic laser systems showing synchronization phenomena are of special interest and have been investigated theoretically as well as experimentally during the last years. Synchronization of chaotic lasers was first observed with Nd:YAG and CO2 lasers [Roy & Thornburg, 1994; Sugawara et al., 1994; Colet & Roy, 1994]. Recently, synchronization of chaotic erbium-doped fiber ring lasers [VanWiggeren & Roy, 1998a; Abarbanel et al., 1998; VanWiggeren & Roy, 1998b] and semiconductor ∗
lasers (SL) [Mirasso et al., 1996; Annovazzi-Lodi et al., 1997; Ahlers et al., 1999; Sivaprakasam & Shore, 1999; Takiguchi et al., 1999] has been demonstrated experimentally and numerically. Since they are compact and can easily be modulated [Agrawal & Dutta, 1993] chaotic semiconductor lasers are of particular importance for potential applications in communication systems. Chaos in semiconductor lasers arises in different ways: due to an external cavity (optical feedback) or due to electrooptical feedback where the pump current is modulated by the emitted light intensity. A communication scheme based on synchronization of chaotic laser diodes with electro-optical feedback was implemented experimentally by Goedgebuer et al. [1998]. Recently, Chen and Liu simulated successfully information transmission using optical feedback [Chen & Liu, 2000]. External cavity semiconductor lasers (ECSLs) have been a subject of extensive research during the last 15 years because of the importance of optical feedback phenomena in technical
E-mail: [email protected] 1141
1142 I. Wedekind & U. Parlitz
applications like optical data storage or optical fiber communications [Fischer et al., 1996]. In most of these cases, the effects of optical feedback are to be avoided. A typical effect due to feedback is low frequency fluctuations (LFF), which can be observed for moderate feedback and low pump current. This phenomenon has attracted considerable interest during the last few years. Numerical simulations based on a deterministic model [Ahlers et al., 1999] indicate that LFF dynamics is governed by a very high-dimensional chaotic attractor and are thus very difficult to distinguish from a stochastic signal, a feature that makes them an interesting candidate for an optical encryption system. Synchronization of ECSLs has previously been studied numerically using different coupling schemes [Mirasso et al., 1996; Annovazzi-Lodi et al., 1997; Ahlers et al., 1999]. Only recently, two groups succeeded in achieving synchronization of LFFs experimentally [Sivaprakasam & Shore, 1999; Takiguchi et al., 1999]. In this letter we show that not only synchronization but also antisynchronization can be achieved by means of a uni-directional optical coupling. Switching between both types of synchronization is possible, for example, by changing slightly the pump current of the drive system. In this way, such a configuration can in principle be used for chaos shift keying [Parlitz et al., 1992]. Furthermore, we demonstrate experimentally that with bi-directional coupling both lasers show synchronized LFFs without external mirrors.
2. Uni-Directional Coupling The experimental set-up is shown in Fig. 1 where the optical diode (Faraday Isolator, Optics For Research IO-635-HP) is used only for unidirectional coupling. The fluctuating intensities of the semiconductor lasers (Mitsubishi ML 1412R) are measured with photo detectors, amplified (and inverted) and sampled with 1 Giga Sample per second using a digital oscilloscope (LeCroy LC 574AM) that is also used for display and further processing of the data. As pointed out in [Ahlers et al., 1999] at the response laser the light reflected from the mirror of the external cavity can be “replaced” by the light injected from the drive laser, i.e. the response laser can also synchronize without possessing an external cavity. In the following we shall consider both cases.
2.1. Response laser with external cavity Intensity fluctuations of drive and response laser without coupling are shown in Fig. 2. If the coupling is switched on one may either observe synchronization (Fig. 3) or anti-synchronization (Fig. 4) depending on the pump currents and temperatures of both lasers. To compensate the phase shift between the signals from both photo detectors due to the propagation of light from drive to response the detectors have been connected with the digital oscilloscope by cables of suitable length.
photo detector
beamsplitter laser diode 1 mirror optical diode (Faraday−Isolator)
35 cm photo detector
laser diode 2 beamsplitter 51.8 cm 34 cm Fig. 1.
mirror
Experimental setup of two uni-directionally coupled external cavity semiconductor lasers.
Experimental Observation in External Cavity Semiconductor Lasers 1143
Fig. 2. Low frequency fluctuations of the light intensities of drive (1, red) and response (2, blue) laser without coupling. Both signals are inverted. Horizontal scale: 0.2 µs/unit; Vertical scales: 20 mV/unit.
(a)
(b)
Fig. 3. Synchronization of uni-directionally coupled external cavity lasers (compare Fig. 2). (a) Inverted intensities of drive (1, red) and response (2, blue) versus time. Horizontal scale: 0.1 µs/unit; Vertical scales: 20 mV/unit (red) and 50 mV/unit (blue). (b) Inverted intensity of drive versus inverted intensity of response.
2.2. Response laser without external cavity If the mirror of the external cavity of the response system is removed and only the light intensity of
the drive is injected into the response laser, both lasers may still synchronize [Ahlers et al., 1999] as shown in Fig. 5. Again anti-synchronization may be observed by detuning the temperature (i.e. the wavelength) or the pump current (Fig. 6). For
1144 I. Wedekind & U. Parlitz
(a)
(b)
Fig. 4. Anti-synchronization of uni-directionally coupled external cavity lasers (compare with Fig. 3). (a) Inverted intensities of drive (1, red) and response (2, blue) versus time. Horizontal scale: 0.1 µs/unit; Vertical scales: 20 mV/unit (red) and 50 mV/unit (blue). (b) Inverted intensity of drive versus inverted intensity of response.
(a)
(b)
Fig. 5. Synchronization of uni-directionally coupled semiconductor lasers where only the drive laser possesses an external cavity. (a) Inverted intensities of drive (1, red) and response (2, blue) versus time. Horizontal scale: 0.1 µs/unit; Vertical scales: 20 mV/unit (red) and 50 mV/unit (blue). (b) Inverted intensity of drive versus inverted intensity of response.
transmitting a binary message one may want to switch between synchronization and antisynchronization of the response laser. The efficiency of such a method would be limited by the length of the synchronization transient. Therefore we have used a periodic rectangular modulation of the
drive current with 200 KHz in order to simulate a binary message. Figure 7 shows the intensities of drive and response and a transition from synchronization to anti-synchronization. The current modulation changes slightly the intensity of the driving laser which is clearly visible in the figure due to
Experimental Observation in External Cavity Semiconductor Lasers 1145
(a)
(b)
Fig. 6. Anti-synchronization of uni-directionally coupled semiconductor lasers where only the drive laser possesses an external cavity (compare with Fig. 5). (a) Inverted intensities of drive (1, red) and response (2, blue) versus time. Horizontal scale: 0.1 µs/unit; Vertical scales: 20 mV/unit (red) and 50 mV/unit (blue). (b) Inverted intensity of drive versus inverted intensity of response.
Fig. 7. Switching between synchronization and anti-synchronization by changing the pump current of the drive (drive (1, red) and response (2, blue)). Horizontal scale: 0.2 µs/unit; Vertical scales: 36 mV/unit (red) and 100 mV/unit (blue).
AC-coupling of the signal from the photo detectors. The synchronization transient takes about 0.6 µs. The clear visibility of the modulation in the transmitter light intensity and the relatively long synchronization transient suggest that further improvements are necessary before this coupled system may be considered as a
useful building block of an optical communication system.
3. Bi-Directional Coupling When removing the optical diode in Fig. 1 we obtain a bi-directionally coupled system of
1146 I. Wedekind & U. Parlitz
LFF) but also short pulses of high intensity. The bi-directional optical coupling offers new ways for generating chaotic (LFF) intensity oscillations that may also be useful as building blocks in chaos-based optical communication systems or (e.g. in combination with chaos control) for generating pulses of special shapes.
Acknowledgments
Fig. 8. Synchronization of bi-directionally coupled semiconductor lasers without external mirrors. Horizontal scale: 0.2 µs/unit; Vertical scales: 27.5 mV/unit (red) and 62 mV/unit (blue).
semiconductor lasers. Again synchronization and anti-synchronization may be observed with one or both lasers possessing an external cavity. However, even without any external mirrors such a pair of semiconductor lasers may generate nontrivial dynamics. Figure 8 shows as an example chaotic intensity oscillations which are quite similar to the synchronized low-frequency-fluctuations presented in the previous section. In contrast to the signal from a single (driving) laser with external cavity the signal-to-noise ratio is much better with the bidirectionally coupled pair. The possibility of generating (hyper-?) chaotic dynamics using optical coupling and without external mirrors also warrants further investigations.
4. Conclusion In this letter we presented experimental observations of (anti-)synchronization of uni-directionally and bi-directionally coupled semiconductor lasers with and without external cavities. In the unidirectional case it was shown that binary messages can in principle be transmitted by switching between synchronization and anti-synchronization. However, to apply this mode of communication practically shorter transient times are necessary and for cryptographic purposes the switching should not affect physical variables (e.g. amplitudes or (light) frequencies) whose changes could be detected quite easily. Using anti-synchronization one may generate not only drop-outs of the intensity (as with ordinary
The authors thank L. Junge, L. Kocarev, W. Lauterborn and H. D. I. Abarbanel, for stimulating discussions on chaos synchronization and our technical staff for practical support with the preparation of the electronic and optical devices. This work was supported by the Deutsche Forschungsgemeinschaft (grant PA-643/1-2).
References Abarbanel, H. D. I. & Kennel, M. B. [1998] “Synchronizing high-dimensional chaotic optical ring dynamics,” Phys. Rev. Lett. 80(10), 3153–3156. Agrawal, G. P. & Dutta, N. K. [1993] Semiconductor Lasers, 2nd edition (Van Nostrand Reinhold, NY). Ahlers, V., Parlitz, U. & Lauterborn, W. [1999] “Hyperchaotic dynamics and synchronization of external cavity semiconductor lasers,” Phys. Rev. E58(6), 7208–7213. Annovazzi-Lodi, V., Donati, S. & Scir`e, A. [1997] “Synchronization of chaotic lasers by optical feedback for cryptographic applications,” IEEE J. Quant. Electron. 33(9), 1449–1454. Chen, H. F. & Liu, J. M. [2000] “Open-loop chaotics synchronization of injection-locked semiconductor lasers with Gigahertz range modulation,” IEEE J. Quant. Electron. 36(1), 27–34. Colet, P. & Roy, R. [1994] “Digital communication with synchronized chaotic lasers,” Opt. Lett. 19(24), 2056–2058. Fischer, I., van Tartwijk, G. H. M., Levine, A. M., Els¨ aßer, W., G¨ obel, E. & Lenstra, D. [1996] “Fast pulsing and chaotic itinerancy with a drift in the coherence collapse of semiconductor lasers,” Phys. Rev. Lett. 76(2), 220–223. Goedgebuer, J.-P., Larger, L. & Porte, H. [1998] “Optical cryptosystem based on synchronization of hyperchaos generated by a delayed feedback tunable laser diode,” Phys. Rev. Lett. 80(10), 2249–2252. Kennedy, M. P. & Ogorzalek, M. J. (eds.) [1997] “Special issue on chaos synchronization and control: Theory and applications,” IEEE Trans. Circuits Syst. 44(10). Kocarev, L. & Parlitz, U. [1995] “General approach for chaotic synchronization with applications to communcation,” Phys. Rev. Lett. 74, 5028–5031.
Experimental Observation in External Cavity Semiconductor Lasers 1147
Mirasso, C. R., Colet, P. & Garc´ıa-Fern´andez, P. [1996] “Synchronization of chaotic semiconductor lasers: Application to encoded comunnications,” IEEE Phot. Technol. Lett. 8, 299–301. Parlitz, U., Chua, L. O., Kocarev, Lj., Halle, K. S. & Shang, A. [1992] “Transmission of digital signals by chaotic synchronization,” Int. J. Bifurcation and Chaos 2(4), 973–977; [1993] Chua’s Circuit: A Paradigm for Chaos, ed. Madan, R. N., World Scientific Series on Nonlinear Science, Series B, Vol. 1 (World Scientific, Singapore). Parlitz, U., Kocarev, L., Stojanovski, T. & Preckel, H. [1996] “Encoding messages using chaotic synchronization,” Phys. Rev. E53, 4351–4361. Pecora, L. M. & Carroll, T. L. [1990] “Synchronization in chaotic systems,” Phys. Rev. Lett. 64, 821–824. Roy, R. & Thornburg, K. S. [1994] “Experimental synchronization of chaotic lasers,” Phys. Rev. Lett. 72(13), 2009–2012.
Schuster, H. G. (ed.) [1999] Handbook of Chaos Control (Wiley-VCH, Weinheim). Sivaprakasam, S. & Shore, K. A. [1999] “Demonstration of optical synchronization of chaotic external-cavity laser diodes,” Opt. Lett. 24(7), 466–468. Sugawara, T., Tachikawa, M., Tsukamoto, T. & Shimizu, T. [1994] “Observation of synchronization in laser chaos,” Phys. Rev. Lett. 72(22), 3502–3505. Takiguchi, Y., Fujino, H. & Ohtsubo, J. [1999] “Experimental synchronization of chaotic oscillations in externally injected semiconductor lasers in a low-frequency fluctuation regime,” Opt. Lett. 24(22), 1570–1572. VanWiggeren, G. D. & Roy, R. [1998a] “Communication with chaotic lasers,” Science 279, 1198–1200. VanWiggeren, G. D. & Roy, R. [1998b] “Optical communication with chaotic waveforms,” Phys. Rev. Lett. 81(16), 3547–3550.
EXPERIMENTAL OBSERVATION OF SYNCHRONIZATION AND ANTI-SYNCHRONIZATION OF CHAOTIC LOW-FREQUENCY-FLUCTUATIONS IN EXTERNAL CAVITY SEMICONDUCTOR LASERS IMMO WEDEKIND and ULRICH PARLITZ∗ Drittes Physikalisches Institut, Universit¨ at G¨ ottingen, B¨ urgerstraße 42-44, D-37073 G¨ ottingen, Germany Received June 29, 2000; Revised July 25, 2000 Experimental investigations of synchronization and anti-synchronization of optically coupled semiconductor lasers with external cavities are presented. Both lasers show chaotic lowfrequency intensity fluctuations that are (anti-) synchronized due to optical coupling by light injection. For uni-directional coupling response lasers with and without external cavity are considered. In the case of bi-directional coupling synchronized fluctuations are observed even without external mirrors.
1. Introduction During the last decade synchronization of chaotic systems has been explored very intensively by many researchers in various fields ranging from physics, mathematics to engineering, where for the latter the main motivation has been potential practical applications in communication systems [Pecora & Carroll, 1990; Kocarev & Parlitz, 1995; Parlitz et al., 1996; Kennedy & Ogorzalek, 1997; Schuster, 1999]. Many modern communication devices are opto-electronic or all optical. Therefore, chaotic laser systems showing synchronization phenomena are of special interest and have been investigated theoretically as well as experimentally during the last years. Synchronization of chaotic lasers was first observed with Nd:YAG and CO2 lasers [Roy & Thornburg, 1994; Sugawara et al., 1994; Colet & Roy, 1994]. Recently, synchronization of chaotic erbium-doped fiber ring lasers [VanWiggeren & Roy, 1998a; Abarbanel et al., 1998; VanWiggeren & Roy, 1998b] and semiconductor ∗
lasers (SL) [Mirasso et al., 1996; Annovazzi-Lodi et al., 1997; Ahlers et al., 1999; Sivaprakasam & Shore, 1999; Takiguchi et al., 1999] has been demonstrated experimentally and numerically. Since they are compact and can easily be modulated [Agrawal & Dutta, 1993] chaotic semiconductor lasers are of particular importance for potential applications in communication systems. Chaos in semiconductor lasers arises in different ways: due to an external cavity (optical feedback) or due to electrooptical feedback where the pump current is modulated by the emitted light intensity. A communication scheme based on synchronization of chaotic laser diodes with electro-optical feedback was implemented experimentally by Goedgebuer et al. [1998]. Recently, Chen and Liu simulated successfully information transmission using optical feedback [Chen & Liu, 2000]. External cavity semiconductor lasers (ECSLs) have been a subject of extensive research during the last 15 years because of the importance of optical feedback phenomena in technical
E-mail: [email protected] 1141
1142 I. Wedekind & U. Parlitz
applications like optical data storage or optical fiber communications [Fischer et al., 1996]. In most of these cases, the effects of optical feedback are to be avoided. A typical effect due to feedback is low frequency fluctuations (LFF), which can be observed for moderate feedback and low pump current. This phenomenon has attracted considerable interest during the last few years. Numerical simulations based on a deterministic model [Ahlers et al., 1999] indicate that LFF dynamics is governed by a very high-dimensional chaotic attractor and are thus very difficult to distinguish from a stochastic signal, a feature that makes them an interesting candidate for an optical encryption system. Synchronization of ECSLs has previously been studied numerically using different coupling schemes [Mirasso et al., 1996; Annovazzi-Lodi et al., 1997; Ahlers et al., 1999]. Only recently, two groups succeeded in achieving synchronization of LFFs experimentally [Sivaprakasam & Shore, 1999; Takiguchi et al., 1999]. In this letter we show that not only synchronization but also antisynchronization can be achieved by means of a uni-directional optical coupling. Switching between both types of synchronization is possible, for example, by changing slightly the pump current of the drive system. In this way, such a configuration can in principle be used for chaos shift keying [Parlitz et al., 1992]. Furthermore, we demonstrate experimentally that with bi-directional coupling both lasers show synchronized LFFs without external mirrors.
2. Uni-Directional Coupling The experimental set-up is shown in Fig. 1 where the optical diode (Faraday Isolator, Optics For Research IO-635-HP) is used only for unidirectional coupling. The fluctuating intensities of the semiconductor lasers (Mitsubishi ML 1412R) are measured with photo detectors, amplified (and inverted) and sampled with 1 Giga Sample per second using a digital oscilloscope (LeCroy LC 574AM) that is also used for display and further processing of the data. As pointed out in [Ahlers et al., 1999] at the response laser the light reflected from the mirror of the external cavity can be “replaced” by the light injected from the drive laser, i.e. the response laser can also synchronize without possessing an external cavity. In the following we shall consider both cases.
2.1. Response laser with external cavity Intensity fluctuations of drive and response laser without coupling are shown in Fig. 2. If the coupling is switched on one may either observe synchronization (Fig. 3) or anti-synchronization (Fig. 4) depending on the pump currents and temperatures of both lasers. To compensate the phase shift between the signals from both photo detectors due to the propagation of light from drive to response the detectors have been connected with the digital oscilloscope by cables of suitable length.
photo detector
beamsplitter laser diode 1 mirror optical diode (Faraday−Isolator)
35 cm photo detector
laser diode 2 beamsplitter 51.8 cm 34 cm Fig. 1.
mirror
Experimental setup of two uni-directionally coupled external cavity semiconductor lasers.
Experimental Observation in External Cavity Semiconductor Lasers 1143
Fig. 2. Low frequency fluctuations of the light intensities of drive (1, red) and response (2, blue) laser without coupling. Both signals are inverted. Horizontal scale: 0.2 µs/unit; Vertical scales: 20 mV/unit.
(a)
(b)
Fig. 3. Synchronization of uni-directionally coupled external cavity lasers (compare Fig. 2). (a) Inverted intensities of drive (1, red) and response (2, blue) versus time. Horizontal scale: 0.1 µs/unit; Vertical scales: 20 mV/unit (red) and 50 mV/unit (blue). (b) Inverted intensity of drive versus inverted intensity of response.
2.2. Response laser without external cavity If the mirror of the external cavity of the response system is removed and only the light intensity of
the drive is injected into the response laser, both lasers may still synchronize [Ahlers et al., 1999] as shown in Fig. 5. Again anti-synchronization may be observed by detuning the temperature (i.e. the wavelength) or the pump current (Fig. 6). For
1144 I. Wedekind & U. Parlitz
(a)
(b)
Fig. 4. Anti-synchronization of uni-directionally coupled external cavity lasers (compare with Fig. 3). (a) Inverted intensities of drive (1, red) and response (2, blue) versus time. Horizontal scale: 0.1 µs/unit; Vertical scales: 20 mV/unit (red) and 50 mV/unit (blue). (b) Inverted intensity of drive versus inverted intensity of response.
(a)
(b)
Fig. 5. Synchronization of uni-directionally coupled semiconductor lasers where only the drive laser possesses an external cavity. (a) Inverted intensities of drive (1, red) and response (2, blue) versus time. Horizontal scale: 0.1 µs/unit; Vertical scales: 20 mV/unit (red) and 50 mV/unit (blue). (b) Inverted intensity of drive versus inverted intensity of response.
transmitting a binary message one may want to switch between synchronization and antisynchronization of the response laser. The efficiency of such a method would be limited by the length of the synchronization transient. Therefore we have used a periodic rectangular modulation of the
drive current with 200 KHz in order to simulate a binary message. Figure 7 shows the intensities of drive and response and a transition from synchronization to anti-synchronization. The current modulation changes slightly the intensity of the driving laser which is clearly visible in the figure due to
Experimental Observation in External Cavity Semiconductor Lasers 1145
(a)
(b)
Fig. 6. Anti-synchronization of uni-directionally coupled semiconductor lasers where only the drive laser possesses an external cavity (compare with Fig. 5). (a) Inverted intensities of drive (1, red) and response (2, blue) versus time. Horizontal scale: 0.1 µs/unit; Vertical scales: 20 mV/unit (red) and 50 mV/unit (blue). (b) Inverted intensity of drive versus inverted intensity of response.
Fig. 7. Switching between synchronization and anti-synchronization by changing the pump current of the drive (drive (1, red) and response (2, blue)). Horizontal scale: 0.2 µs/unit; Vertical scales: 36 mV/unit (red) and 100 mV/unit (blue).
AC-coupling of the signal from the photo detectors. The synchronization transient takes about 0.6 µs. The clear visibility of the modulation in the transmitter light intensity and the relatively long synchronization transient suggest that further improvements are necessary before this coupled system may be considered as a
useful building block of an optical communication system.
3. Bi-Directional Coupling When removing the optical diode in Fig. 1 we obtain a bi-directionally coupled system of
1146 I. Wedekind & U. Parlitz
LFF) but also short pulses of high intensity. The bi-directional optical coupling offers new ways for generating chaotic (LFF) intensity oscillations that may also be useful as building blocks in chaos-based optical communication systems or (e.g. in combination with chaos control) for generating pulses of special shapes.
Acknowledgments
Fig. 8. Synchronization of bi-directionally coupled semiconductor lasers without external mirrors. Horizontal scale: 0.2 µs/unit; Vertical scales: 27.5 mV/unit (red) and 62 mV/unit (blue).
semiconductor lasers. Again synchronization and anti-synchronization may be observed with one or both lasers possessing an external cavity. However, even without any external mirrors such a pair of semiconductor lasers may generate nontrivial dynamics. Figure 8 shows as an example chaotic intensity oscillations which are quite similar to the synchronized low-frequency-fluctuations presented in the previous section. In contrast to the signal from a single (driving) laser with external cavity the signal-to-noise ratio is much better with the bidirectionally coupled pair. The possibility of generating (hyper-?) chaotic dynamics using optical coupling and without external mirrors also warrants further investigations.
4. Conclusion In this letter we presented experimental observations of (anti-)synchronization of uni-directionally and bi-directionally coupled semiconductor lasers with and without external cavities. In the unidirectional case it was shown that binary messages can in principle be transmitted by switching between synchronization and anti-synchronization. However, to apply this mode of communication practically shorter transient times are necessary and for cryptographic purposes the switching should not affect physical variables (e.g. amplitudes or (light) frequencies) whose changes could be detected quite easily. Using anti-synchronization one may generate not only drop-outs of the intensity (as with ordinary
The authors thank L. Junge, L. Kocarev, W. Lauterborn and H. D. I. Abarbanel, for stimulating discussions on chaos synchronization and our technical staff for practical support with the preparation of the electronic and optical devices. This work was supported by the Deutsche Forschungsgemeinschaft (grant PA-643/1-2).
References Abarbanel, H. D. I. & Kennel, M. B. [1998] “Synchronizing high-dimensional chaotic optical ring dynamics,” Phys. Rev. Lett. 80(10), 3153–3156. Agrawal, G. P. & Dutta, N. K. [1993] Semiconductor Lasers, 2nd edition (Van Nostrand Reinhold, NY). Ahlers, V., Parlitz, U. & Lauterborn, W. [1999] “Hyperchaotic dynamics and synchronization of external cavity semiconductor lasers,” Phys. Rev. E58(6), 7208–7213. Annovazzi-Lodi, V., Donati, S. & Scir`e, A. [1997] “Synchronization of chaotic lasers by optical feedback for cryptographic applications,” IEEE J. Quant. Electron. 33(9), 1449–1454. Chen, H. F. & Liu, J. M. [2000] “Open-loop chaotics synchronization of injection-locked semiconductor lasers with Gigahertz range modulation,” IEEE J. Quant. Electron. 36(1), 27–34. Colet, P. & Roy, R. [1994] “Digital communication with synchronized chaotic lasers,” Opt. Lett. 19(24), 2056–2058. Fischer, I., van Tartwijk, G. H. M., Levine, A. M., Els¨ aßer, W., G¨ obel, E. & Lenstra, D. [1996] “Fast pulsing and chaotic itinerancy with a drift in the coherence collapse of semiconductor lasers,” Phys. Rev. Lett. 76(2), 220–223. Goedgebuer, J.-P., Larger, L. & Porte, H. [1998] “Optical cryptosystem based on synchronization of hyperchaos generated by a delayed feedback tunable laser diode,” Phys. Rev. Lett. 80(10), 2249–2252. Kennedy, M. P. & Ogorzalek, M. J. (eds.) [1997] “Special issue on chaos synchronization and control: Theory and applications,” IEEE Trans. Circuits Syst. 44(10). Kocarev, L. & Parlitz, U. [1995] “General approach for chaotic synchronization with applications to communcation,” Phys. Rev. Lett. 74, 5028–5031.
Experimental Observation in External Cavity Semiconductor Lasers 1147
Mirasso, C. R., Colet, P. & Garc´ıa-Fern´andez, P. [1996] “Synchronization of chaotic semiconductor lasers: Application to encoded comunnications,” IEEE Phot. Technol. Lett. 8, 299–301. Parlitz, U., Chua, L. O., Kocarev, Lj., Halle, K. S. & Shang, A. [1992] “Transmission of digital signals by chaotic synchronization,” Int. J. Bifurcation and Chaos 2(4), 973–977; [1993] Chua’s Circuit: A Paradigm for Chaos, ed. Madan, R. N., World Scientific Series on Nonlinear Science, Series B, Vol. 1 (World Scientific, Singapore). Parlitz, U., Kocarev, L., Stojanovski, T. & Preckel, H. [1996] “Encoding messages using chaotic synchronization,” Phys. Rev. E53, 4351–4361. Pecora, L. M. & Carroll, T. L. [1990] “Synchronization in chaotic systems,” Phys. Rev. Lett. 64, 821–824. Roy, R. & Thornburg, K. S. [1994] “Experimental synchronization of chaotic lasers,” Phys. Rev. Lett. 72(13), 2009–2012.
Schuster, H. G. (ed.) [1999] Handbook of Chaos Control (Wiley-VCH, Weinheim). Sivaprakasam, S. & Shore, K. A. [1999] “Demonstration of optical synchronization of chaotic external-cavity laser diodes,” Opt. Lett. 24(7), 466–468. Sugawara, T., Tachikawa, M., Tsukamoto, T. & Shimizu, T. [1994] “Observation of synchronization in laser chaos,” Phys. Rev. Lett. 72(22), 3502–3505. Takiguchi, Y., Fujino, H. & Ohtsubo, J. [1999] “Experimental synchronization of chaotic oscillations in externally injected semiconductor lasers in a low-frequency fluctuation regime,” Opt. Lett. 24(22), 1570–1572. VanWiggeren, G. D. & Roy, R. [1998a] “Communication with chaotic lasers,” Science 279, 1198–1200. VanWiggeren, G. D. & Roy, R. [1998b] “Optical communication with chaotic waveforms,” Phys. Rev. Lett. 81(16), 3547–3550.
