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Synchronization of chaos in unidirectionally coupled vertical-cavity surface-emitting semiconductor lasers Yanhua Hong, Min Won Lee, Paul S. Spencer, and K. Alan Shore School of Informatics, University of Wales, Bangor, Bangor LL57 1UT, Wales, UK Received December 22, 2003 Synchronization of chaos is achieved experimentally in unidirectionally coupled external-cavity vertical-cavity surface-emitting semiconductor lasers operating in an open-loop regime. Synchronization is observed when the polarization of the transmitter is perpendicular to the polarization (x polarization) of the free-running receiver. The ratio of transmitter output to y-polarized receiver output power shows normal (positive-slope) synchronization. However, inverse (negative-slope) synchronization is found to arise between the transmitter output and the x-polarized receiver output power. © 2004 Optical Society of America OCIS codes: 140.1540, 250.7260, 260.5430, 060.4510.
The use of chaos in secure communication has attracted considerable attention in recent years. The idea is to encode a message into the noiselike chaotic transmitter and then decode the message by using a receiver that is chaos-synchronized to the transmitter. Synchronization of chaotic systems has been demonstrated in Nd:YAG,1 CO2 ,2 and f iber lasers3 and in distributed Bragg ref lection laser diodes.4 Much effort has been devoted to the study of chaos synchronization and message encoding and decoding in edge-emitting semiconductor lasers.5 – 8 Verticalcavity surface-emitting lasers (VCSELs) have many desirable characteristics, such as low threshold current, single-longitudinal operation, circular outputbeam prof iles, and wafer-scale integrability. It can be anticipated that, owing to the relatively low output powers of VCSELs, chaos synchronization may require operation of the lasers well above threshold. A salient feature of VCSELs is their tendency to exhibit changes in emission polarization that are due to changes, e.g., in bias current and operating temperature. Polarization effects may therefore be expected to be of some importance in VCSEL synchronization. Interest in implementing chaotic communications by using VCSELs is demonstrated by previous theoretical and experimental work performed on chaotic synchronization in VCSELs.9,10 Recently Fujiwara et al.10 reported experimental observation of chaotic synchronization in mutually coupled stand-alone VCSELs. In this Letter we experimentally demonstrate chaos synchronization in unidirectionally coupled VCSELs. The transmitter was rendered chaotic by optical feedback, whereas the receiver was a stand-alone VCSEL. One polarization component of the transmitter was coupled into the receiver. Synchronization was observed when the polarization of the transmitter was perpendicular to the polarization (x polarization) of the free-running receiver. The experimental arrangement is shown schematically in Fig. 1. Two commercial VCSELs (Avalon Photonics, V-850-GMP) were used, one in the transmitter and one in the receiver. Both VCSELs were driven by a low-noise current source (Prof ile LDC 202), and their temperatures were controlled to within 0.01 ±C. 0146-9592/04/111215-03$15.00/0
VCSEL1 was used as the transmitter. VCSEL2 was used as a receiver. The free-running threshold current (Ith ) of VCSEL1 and VCSEL2 was 3.2 and 2.5 mA, respectively. Near threshold, VCSEL1 lased in one polarization direction (x polarization). When the current was increased to 7.25 mA, the polarization abruptly switched to orthogonal polarization ( y polarization), whereas with decreasing current the polarization switched back to the x direction at 6.66 mA. This result indicates that there is a bistability regime in VCSEL1. VCSEL2 lased along one polarization direction (x polarization) near threshold and remained lasing in this direction up to a bias current of 8.7 mA. When the bias current was higher than 8.7 mA, the y-polarization component started to lase and the x-polarization component saturated. VCSEL1 was collimated by an antiref lection-coated laser diode objective (Newport F-LA11). A nonpolarizing beam splitter (BS1) directed ⬃50% of VCSEL1’s output power to a mirror (M1), which formed an external cavity. The cavity length was approximately 39 cm. The optical feedback ratio was adjusted by a variable attenuator (NDF1) such that the transmitter was rendered chaotic. A half-wave plate (HWP1) was used to adjust the polarization of the transmitter beam to ensure that only the x-polarized component
Fig. 1.
Experimental setup.
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was coupled into the receiver. HWP2 was used to rotate polarization of the injected beam to make the entire beam transmit through a polarizing beam splitter (PBS2). PBS2 and an isolator (ISO1) together ensured that the output from the receiver was not injected back into the transmitter; the typical isolation was 240 dB. NDF2 and HWP3 were used to change the injected power and polarization, respectively. HWP4 and HWP5 were used to direct the orthogonal polarization to a detector (PD2). ISO2 and ISO3 were used to prevent feedback of light into the VCSELs. PD1 and PD2 are two identical photodetectors (Newport Model AD-70xr) with a 6-GHz bandwidth. M2 directed the transmitter output power to BS2, which then coupled transmitter output power into both the receiver and PD1. The output power of the receiver was measured by PD2. The outputs from the photodetectors were stored in a digital oscilloscope (Tektronix TDS 7404, 4 GHz) and then acquired by a PC. In the experiment, VCSEL1 was biased at 7.58 mA (2.4Ith ). At this bias current, almost all the output power was in the y-polarized lasing mode. The lasing wavelength was 853.2 nm. We def ine the optical feedback ratio as the ratio of the feedback power to the free-running output power. The feedback power was measured just before the light returned to the laser diode objective (in front of the laser). When the feedback ratio was 20%, VCSEL1 exhibited large irregular f luctuations in the output power. VCSELs have feedback regimes similar to that of an edge-emitting laser,11 and chaotic behavior is seen in the output power over a wide range of operating currents for longer external cavities.12 So the large irregular f luctuation is associated with chaotic dynamics. The x-polarized component was excited and showed antiphase dynamics with the y-polarized component. Because VCSEL1 was biased at relatively higher currents,13 within the experimentally available feedback level VCSEL1 exhibited fully developed chaos; the low-frequency f luctuation regime was not observed. VCSEL2 was biased at 8.27 mA (3.3Ith ). Most of the output power was contained in the x-polarized mode. The lasing wavelength was 853.2 nm. The x-polarized component of the transmitter was selected and rotated to y polarization and injected into receiver VCSEL2. The spectrum, output power, and dynamics of the transmitter remained unchanged when the transmitter was coupled into the receiver. The setup is thus clearly unidirectionally coupled. The ratio of the injection power to the output power of the receiver is termed the injection ratio. The injection power is measured just before the light is injected into the laser diode objective (in front of the receiver). Figure 2 shows the time evolution of chaos synchronization when the injection ratio was ⬃3.3%. Figure 2(a) shows a time trace of the injected beam and a time trace of VCSEL2 in y polarization. The time trace of the injected beam has been shifted up for clarity. These time traces show evidence of synchronization between the injected beam and the y-polarization component of VCSEL2. Figure 2(b) shows a time trace of the injected beam and a time
trace of VCSEL2 in x polarization taken at a slightly different time from those in Fig. 2(a). For clarity, the time trace of the injected beam was also shifted up. The f luctuations in the time trace of the injected beam and the VCSEL2 time trace in x polarization can be seen to be in antiphase, consistent with previous observations of antiphase dynamics of orthogonal polarizations in unstable VCSELs.14,15 One can readily demonstrate synchronization by plotting the instantaneous injected power against the receiver output power at the same time. As described in many papers,8,10 one measures the quality of the synchronization by calculating the cross correlation between the time series of the transmitter and the receiver. Because the detector noise level was ⬃25 dB lower than the chaos signal, the detector noise level was neglected in the measurement. Figure 3(a) shows the injected power versus the y-polarization component of the receiver. It demonstrates that good synchronization was obtained between the injected beam and the y-polarization component of the receiver. The correlation coeff icient was 0.844. Figure 3(b) shows the injected power as a function of the x-polarization component of the receiver. The injected power and the x-polarization component of the receiver also show reasonable synchronization; however, the gradient of the synchronization is negative. Such synchronization has been termed “inverse synchronization.”16 The absolute correlation coefficient is 0.768, which is lower than that of chaotic synchronization between the injected beam and the y-polarization component of the receiver. The reason for the better correlation between the y-polarization output power of the receiver and the injected beam is that the y-polarization mode of the receiver was locked to the transmitter’s frequency.17,18 x- and y-polarization components of the receiver laser show
Fig. 2. Time series plots of (a) the injected beam (top trace) and the receiver output (bottom trace) in y polarization and (b) the injected beam (top trace) and the receiver output (bottom trace) in x polarization.
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receiver exhibit inverse synchronization because of the antiphase dynamics between the two orthogonal polarizations in the unstable operation regime of a VCSEL. The results presented here show the possibility of chaos communication in VCSELs, and future effort will examine the feasibility of encoding and decoding messages by use of this conf iguration. This study was supported by the UK Engineering and Physical Sciences Research Council under grant GR/S22936/01 and by the European Union Optical Chaos Communication Using Laser Transmitters (OCCULT) project (grant IST-2000-29683). K. A. Shore’s e-mail address is
[email protected]. ac.uk. References
Fig. 3. Synchronization plots: (a) injected beam versus the y-polarization component of the receiver, (b) injected beam versus the x-polarization component of the receiver.
antiphase correlation with optical feedback (without optical injection from the transmitter) at 8.27-mA bias current, and antiphase dynamics of orthogonal polarizations in unstable VCSELs were previously reported.14,15 It is clear that the x-polarization component of the receiver and the injected beam shows inverse (negative-slope) chaos synchronization because the x-polarization component is in antiphase to the y-polarization component. We achieved the chaos synchronization described above by adjusting the optical injection power, bias current, and VCSEL temperature. It was not necessary to adjust the position of the injected beam carefully; hence the approach is quite robust. It would, of course, be interesting to undertake detailed studies of the effects of the spatial modes on the chaos synchronization. In conclusion, we have experimentally demonstrated, for the f irst time to our knowledge, synchronization of chaos in unidirectionally coupled VCSELs. In the experiment, one polarization component of the transmitter was coupled to the receiver. The polarization of the injected beam was perpendicular to that of the free-running receiver (x polarization). The injected beam and the y-polarized component of the receiver show good synchronization. The injected beam and the x-polarized component of the
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