Synchronization in Chaotic Vertical-Cavity Surface-Emitting Semiconductor Lasers Natsuki Fujiwara and Junji Ohtsubo Faculty of Engineering, Shizuoka University, 3-5-1 Johoku, Hamamatsu, 432-8561 Japan Abstract Chaos synchronization in polarization selected mutually injected Vertical-Cavity Surface-Emitting Semiconductor Lasers (VCSELs) is experimentally investigated at near lasing threshold. The two lasers synchronize in x- or y- polarization mode (x is the orthogonal mode to the y-polarization mode that is the direction along the optical axis of a laser material) depending on the injected polarization components. Keyword: VCSELs, chaos, injection locking, polarization 1. Introduction Vertical-cavity surface emitting lasers (VCSELs) have been studied extensively in the past few years because of several useful characteristics which make them very attractive for applications. Indeed, they show many advantages with respect to the standard semiconductor architectures, such as their small size and the possibility to connect them directly to optical fibers. They also present a very low threshold, high quantum efficiency, and can exhibit single longitudinal mode operation. Whereas, despite their high facet reflectivity (more than 99%), VCSELs are also sensitive to external optical feedback and optical injection like edge-emitting semiconductor lasers. 1,2 Chaos synchronization has been intensively investigated in various nonlinear dynamical systems for its potential applications in chaotic communications. 3-5 Up to now, we have examined various schemes of synchronization under mutually injected configuration of VCSELs at low-frequency fluctuation (LFF) regimes. 6 We observed chaotic synchronization of the laser outputs. In chaos synchronization, the polarization modes play the important role. We observed three typical cases of the synchronization in the mutual systems. One is the case of chaos synchronization under the x polarization modes (x-mode is the orthogonal to the y-mode which has the direction along the optical axis of the laser material). In this case, the y-modes also synchronize with each other due to anti-correlation oscillations, which are typical dynamic characteristics of VCSELs. The second case is synchronization of the y-modes under chaos synchronization and the x-modes synchronize by the anti-correlation oscillations. The third case is synchronization both for the x- and y-modes under chaos synchronization. In order to investigate in detail, we examined experiment that polarization selected mutually injection.
2. Experimental The experimental setup is shown in Fig. 1. The VCSELs (AXT VY-TI11-4FO1 VCSELs) used in the experiments were oscillated at a wavelength of 780 nm and a maximum optical power of 10 mw. The lasers oscillated at y-polarization mode just above the threshold (y is the direction along the optical axis of a laser material). The x- polarization mode is here defined as the counterpart oscillation of the y-polarization mode. With the increase of the injection current, the output power of the x-polarization mode increased and had a compatible power with that of the y- polarization mode in our experiments although the x-polarization mode had always lower than that of the y-polarization mode. The two lasers were mutually coupled through a neutral density filter NDF to control the injection ratios, thus VCSEL1 was injected by VCSEL2 and VCSEL2 was also injected by VCSEL1. The bias injection currents of the two lasers were controlled by stabilized current source drivers, and the laser temperature was stabilized by automatic temperature control circuits. The two lasers used in our experiments had similar values of the device parameters with each other. In spite of the similar device parameters, each VCSEL showed quite different characteristics of the oscillation for the threshold injection current and the L-I characteristics including x- and y-polarization outputs. The two lasers were mutually coupled through a polarization beam splitter PBS to select the injection polarization, thus VCSEL1 was injected by VCSEL2 was also injected by VCSEL1. Fig.1 Schematic diagram of mutually injected VCSELs. PBS: Polarization Beam Splitter, BS: Beam Splitter, OI: Optical Isolator, PL: Polarization Filter
The free-running threshold currents of VCSEL1 and VCSEL2 were 6.2 and 6.4 ma at that 25.8, respectively. The injection currents for VCSEL1 and VCSEL2 were biased slightly above threshold current. At the bias injection current, VCSEL1 showed a very low output power of the x-polarization mode and oscillated at almost only y- polarization mode. On the other hand, comparable output powers for the y- and x-polarization modes were observed in VCSEL2. Under these conditions, the lasers were oscillated at their lower order spatial modes (LP 01 and LP 11 mode). Each spatial mode was stable at solitary oscillation. The two lasers were separated 120 cm in space. Therefore, the coupling time of light between the two lasers was τ=4 ns. The outputs from the two lasers were detected by a high-speed photo-detector (NEW FOCUS 1537M-LF: bandwidth of 6.0 GHz). Chaotic waveforms were analyzed by a RF spectrum analyzer (HP 8595E: bandwidth of 6.5 GHz) and a fast digital oscilloscope (HP 54845A: bandwidth of 1.5 GHz). Also, the optical outputs were analyzed by an optical spectrum analyzer (ADVANTEST Q8344A, maximum resolution of 0.05 nm), a wavelength meter (ADVANTEST QT8325, maximum resolution of 0.001 nm), and a Fabry-Perot spectrometer (free spectral range of 10GHz). 3. Results and discussion We first show the result of mutually injection of the y-polarization components. The data were obtained for bias currents of 6.9 ma (1.11I th, where I th is the laser threshold current) for the VCSEL1 and 7.1 ma (1.15I th ) for the VCSEL2,wheres the substrate temperatures were 25.5 and 25.8. Figure 2 is time series of the y-polarization components for the two laser outputs. We can see LFFs in the waveforms, which have been recently observed in VCSELs with optical feedback; namely, sudden power dropouts and stepwise power recoveries after the dropouts. The time duration of each step in the power recovery process is coincident with the round-trip time 2τ of light in the mutual optical injection system. In this figure, VCSEL1 was a leader to VCSEL2 and the time lag between the waveforms was to be read 4 ns, which was equal to the coupling time τ of light between the two lasers. Figure 3 is correlation plot between the two waveforms. The correlation coefficient was 0.816. Since optical power of x-polarization components were too weak, time series waveforms were undetectable. But we can expect that the x-polarization mode of each VCSELs were oscillated at out-of-phase with the y-polarization component.
VCSEL2 VCSEL1 Fig. 2 Time series of y-polarization mode at synchronization. Fig. 3 Correlation plot of y-polarization. Figure 4 shows the optical spectra at solitary and mutually coupled oscillations observed by the optical spectrum analyzer. Table1 is a summary of the data analyzed by wavelength meter and power meter. These data correspond to the laser oscillations in Fig. 2. The upper and lower traces in Fig. 4 are the spectra at solitary and optically coupled oscillations, respectively. Each peak optical power of the observed spectrum was normalized to the total oscillation intensity. After the optical coupling, the power of y-components were amplified, x-polarization components were reduced. The wavelengths of the both lasers were shifted by the mutual optical injection. After optical coupling, the main oscillation wavelengths of the y-polarization components coincided with each other at 778.911 nm. The wavelengths of the y-polarization modes were locked with each other at 778.911 nm under mutual optical injection, while the x-components had different wavelengths. It was considered that the y-polarization mode of VCSEL2 was locked to that of VCSEL1 and the two lasers synchronized at that wavelength. We also studied mutually injection of the x-polarization components. The chaotic synchronization was obtained for bias currents of 7.9 ma (1.26Ith) for the VCSEL1 and 7.6 ma (1.14Ith) for the VCSEL2,wheres the substrate temperatures were 25.5 and 25.8. Figure 5 is time series of the y-polarization components for the two laser outputs. We can see chaotic waveforms. In this case, VCSEL2 was a leader to VCSEL1 and the time lag between the waveforms was to be read 4 ns. The correlation coefficient was 0.677 (Fig. 6). Although the optical powers of the x-polarization components were amplified by optical injection, the optical powers were insufficiency to detect time series waveforms.
Fig. 4 Optical spectra of laser oscillation for (a) x-and (b) y-polarization modes. Solid lines show the spectra for VCSEL1 and the broken lines for VCSEL2. Table 1 Summary of wavelength and power. Figure 7 shows the optical spectra at solitary and mutually coupled oscillations observed by the optical spectrum analyzer. Table2 is a summary of the data analyzed by wavelength meter and power meter. These data correspond to the laser oscillations in Fig. 3. Each peak optical power of the observed spectrum was normalized to the total oscillation intensity. Before optical coupling, x-polarization had a very low power but it showed significant power after optical injection. On the other hand, y-polarization power is reduced. The wavelengths of the both lasers were
shifted by the mutual optical injection. The wavelength difference between the x-components of two lasers at optical coupling was 0.006nm. On the other hand, the wavelength difference of the y-components was 0.035 nm. It was considered that the x-polarization mode of VCSEL2 was locked to that of VCSEL1. VCSEL2 VCSEL1 Fig. 5 Time series of y-polarization mode at synchronization. Fig. 6 Fig. 7 Optical spectra of laser oscillation for (a) x-and (b) y-polarization modes. Solid lines show the spectra for VCSEL1 and the broken lines for VCSEL2. Correlation plot of y-polarization.
Table 2 Summary of wavelength and power. 4. Conclusion We have experimentally demonstrated synchronization of chaotic oscillations in polarization selected mutually injected VCSELs. In chaos synchronization in VCSELs, the polarization modes play an important role. If y-polarization components are injected, synchronization will occur in y-polarization components. At this time, the optical outputs of y- polarization mode of both VCSELs are amplified, on the other hands, the outputs of x-polarization mode decreases. When x-polarization components inject, there is same tendency: the x-polarization mode are injection-locked, x- polarization mode are amplified and y-polarization mode are decreased. Scheme of synchronization depends on the parameter conditions, such as bias injection current, and the experimental configurations. They also determine a leading (master) or lagging (slave) laser in the synchronization system. Although we have focused on the low-order mode, the qualitative nature of the results is expected to remain unaffected under multi-mode operation. Chaos synchronization is desirable in many applications such as high bit-rate secure telecommunications.
References [1] S. Jhiang, Z. Pan, M. Dagenais, R. A. Morgan, and K. Kojima, IEEE Photon. Technol. Lett. 6, 34 (1994). [2] N. Fujiwara, Y. Takiguchi, and J. Ohtsubo, Opt. Lett. 28, 896 (2003). [3] M. Sondermann, H. Bohnet, and T. Ackemann, Phys. Rev. E. 67, 021802(R) (2003). [4] J. Ohtsubo, Progress in Optics 44, Ch. 1, Ed. E. Wolf (Elsevier Science B. V., Amsterdam, 2002). [5] J. Ohtsubo, IEEE J. Quantum. Electron. 38, 1141 (2002). [6] N. Fujiwara, Y. Takiguchi, and J. Ohtsubo, Opt. Lett. 28, 1677 (2003). J. Ohtsubo s e-mail address is tajohts@ipc.shizuoka.ac.jp.