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Polarisation-resolved chaos and instabilities in a vertical cavity surface emitting laser subject to optical injection
Optics Communications 216 (2003) 185–189 www.elsevier.com/locate/optcom
Polarisation-resolved chaos and instabilities in a vertical cavity surface emitting laser subject to optical injection Y. Hong *, P.S. Spencer, S. Bandyopadhyay, P. Rees, K.A. Shore University of Wales, Bangor, School of Informatics, Bangor LL57 1UT, Wales, UK Received 14 June 2002; received in revised form 28 November 2002; accepted 28 November 2002
Abstract Instabilities in the polarisation-resolved output of a vertical cavity surface emitting laser (VCSEL) subject to optical injection have been investigated experimentally. It is found that regions of chaotic behaviour exist for both positive and negative detuning from the stable injection locking regime. Outside the chaos regimes, several nonlinear dynamical phenomena including frequency pushing, nearly degenerate four-wave mixing (NDFWM), injection locking, limit cycle and period doubling, were also observed. Ó 2002 Elsevier Science B.V. All rights reserved.
1. Introduction Vertical cavity surface emitting lasers (VCSELs) are characterised by a very short optical cavity, high facet reflectivities, cylindrical symmetry structure and light emission from the top or bottom surface. These characteristics mean that VCSELs have many advantages compared to edge-emitting lasers, such as a low threshold current, single longitudinal mode operation, a circular output-beam profile and wafer scale integrability. In addition to examining the properties of standalone VCSELs, effort has been given to understanding the response of VCSELs subject to optical feedback and optical injection [1–9]. Specific
*
Corresponding author. Fax: +44-1248-361-429. E-mail address: [email protected] (Y. Hong).
interest arises in regard to the effects of optical injection on VCSELs emission. Work has shown that nearly degenerate four-wave mixing in VCSELs [2] is similar to that in edge-emitting laser diodes. It has been demonstrated that the linear polarisation state of single-mode VCSELs can be switched by optical injection [1] and also that external optical injection could be used to convert a two-mode VCSEL into a single-mode device [10]. Recently we have demonstrated experimentally how the properties of VCSELs can be influenced by optical injection [11–14]. However, all of this previous work has been concerned with effects arising due to optical injection over relatively small frequency detuning ranges. The aim of this letter is to report our experimental investigations of the effect that external optical injection has on the dynamical behaviour of a single transverse mode VCSEL, over a large range of frequency detuning and optical injection
0030-4018/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. doi:10.1016/S0030-4018(02)02296-4
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Y. Hong et al. / Optics Communications 216 (2003) 185–189
power. These studies have been motivated not only by technological application but also from the viewpoint of increased understanding of the operating characteristics of VCSELs. In this process we make what we believe to be the first report of the observation of regions of polarisation-resolved chaos either side of the stable locking regime in a VCSEL subject to optical injection. The observations reported here contrast with the behaviour of edge-emitting lasers in two ways. Firstly, the present phenomena relate to polarisation-resolved output whereas in edge-emitting lasers chaos is seen in the total output power. Secondly we observe two chaos regimes for one at positive and one at negative detuning from the stable locking regime. A very detailed experimental study of the optical injection response of edge-emitting Fabry– Perot lasers was reported by Kovanis et al. [15]. In that work regimes of chaos were identified only for positive detunings from the stable locking regime. Theoretical work by Wieczorek et al. [16] and Hwang and Liu [17] has analysed the dynamical characteristics of an optically injected edge-emitting laser diodes. Those papers cite experimental work [18] which reveals the presence of two chaotic regimes on the same detuning side of the stable locking regime. In recent experimental work reported by Wieczored et al. [19] it was found that there are three chaos regimes in a distributed feedback (DFB) semiconductor laser subject to the optical injection. Two chaos regimes are found at the positive detunings from the stable-locking regime and one chaos regime at negative detunings. That behaviour is clearly distinct from the phenomena observed in the experiments reported here.
2. Experimental set-up The experimental set-up used for this work is shown in Fig. 1. An external cavity laser diode with more than 20 nm tuning range (Model SDLTC 10-1385) was employed as the master laser. The master laser emits linearly polarised light in a single frequency with a linewidth of about 2 MHz. A commercial VCSEL (HFE-4085-321) with a threshold current of 3.1 mA was used as the slave
Fig. 1. The experimental set-up. TL, tunable laser; SL, slave laser; L, lens; ISO, optical isolator; BS, beamsplitter; ATTN, variable optical attenuator; ND, neutral density filter; k=2, halfwave plate; PS, polarising beamsplitter; B, removable beam block; M, mirror; PM, power meter, PD, photo detector; OSA, optical spectrum analyser; F-P, Fabry–Perot interferometer; D, detector; PC, computer.
laser. In the experiment, the VCSEL was biased just above threshold at 3.58 mA so that it supported only the fundamental transverse mode of one polarisation (X-polarisation) and operated at wavelength of 848.6 nm with an output power of 73:7 lW. The linewidth of the VCSEL is about 250 MHz. Both master and slave lasers were mounted on heat sinks and were temperature controlled to within 6 0:01 °C. The VCSEL was driven by an ultra-low-noise current source (ILXLightwave Model LDX-3620). An isolator of >40 dB attenuation was inserted between the master laser and the slave laser to prevent optical feedback into the master laser. A variable optical attenuator and a neutral density filter were used to change the injection power. A power meter was employed to monitor the injection power. The injection power was measured just before the light entered the laser diode objective (in front of the slave laser). Two other isolators of >40 dB attenuation were used to eliminate the feedback from the optical spectrum analyser and the Fabry–Perot interferometer. These were used to obtain the spectral characteristics of the slave laser. The free spectral range of the Fabry–Perot interferometer is 15 GHz. A half-wave plate inserted between the master laser and the slave laser was used to adjust the polarisation of the master laser so that it was
Y. Hong et al. / Optics Communications 216 (2003) 185–189
parallel to that of the free-running VCSEL. When we recorded the spectrum of the slave laser, a beam block was used to block the reflective beam from mirror M. The position of the master laser frequency can be checked by removing the beam block. The time trace of the light emitting from the VCSEL was recorded by replacing the optical spectrum analyser (in the dash frame of Fig. 1) by a high bandwidth (6 GHz) fast photo detector and high bandwidth (1 GHz) oscilloscope. The time trace of the total output power was measured by removing the polarisation beamsplitter.
3. Results Fig. 2 shows the optical spectra of the VCSEL at X-polarisation subject to optical injection with about 19 lW injection power. The optical spec-
Fig. 2. Optical spectra of the VCSEL subject to optical injection with about 19 lW injection power. The arrows mark the master laser frequency position. The frequency detuning is (a) 2.72 GHz, (b) 0.77 GHz, (c) )0.17 GHz, (d) )1.26 GHz, (e) )2.66 GHz, (f) )2.71 GHz.
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trum in the Y-polarisation (perpendicular to the Xpolarisation) is negligible in all cases. The arrows mark the master laser (ML) frequency position. The zero of X-axis coincides with the slave laser free running frequency. The frequency detuning is Dx ¼ xinj x0 , where xinj is the frequency of the master laser and x0 is the VCSEL free-running frequency. In Fig. 2(a), Dx ¼ 2:72 GHz, the spectrum consists of narrow, weak sidebands at the same frequency offset either side of the main peak. These narrow side peaks correspond to the amplified signal and conjugate beam xc from four-waving between the injection signal beam and the slave laser main peak. In Fig. 2(b), with a frequency detuning of Dx ¼ 0:77 GHz, the spectrum is dominated by a broad pedestal; such a spectrum is indicative of chaotic dynamics. Decreasing the frequency detuning to )0.17 GHz, as shown in Fig. 2(c), the spectrum is dominated by three sharp peaks separated by the relaxation oscillation frequency, between the sharp peaks, smaller features were observed, which indicates period doubling dynamics. For Fig. 2(d), the detuning was )1.26 GHz, and in this case the slave laser frequency locks to the injected frequency, two side peaks also appeared in the spectrum, which indicates limit cycle behaviour. For a further decrease of the detuning to )2.66 GHz, Fig. 2(e), a single sharp peak at the injected frequency and a small feature residing at approximately 3 GHz were observed in the spectrum. The small feature is a part of the spectrum of the free-running VCSEL and corresponds to another transverse mode. As described in [20], for the VCSEL with the two parallel transverse mode, the two mode are shown independent. So the dominant mode of the VCSEL was injecting locked to the master laser. When the detuning was decreased to )2.71 GHz, as shown in Fig. 2(f), the VCSEL again showed chaos. Further decreases of the detuning the spectrum of the VCSEL shows a period doubling features. We can see that the VCSEL shows chaos characteristics at two different detuning frequencies for a fixed injection power. The polarisation-resolved spectra shown in Fig. 2 were all measured with an injection power of 19 lW. The lower (negatively frequency detuned from the stable injection locking regime) chaotic region only exists for a narrow band of frequencies
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for this injection power, and in fact the spectrum shown in Fig. 2(f) is on the boundary between the regimes. Consequently the spectrum is not as broad as that of Fig. 2(b), however, similar spectra to that of Fig. 2(b) have been measured in the lower chaotic region but at higher injection powers. The output temporal dynamics of both polarisation directions of the VCSEL were measured and negligible emission in the Y-polarisation was detected in all cases except for the two chaotic regimes. It appears that when chaotic light emission occurs in the X-polarisation a sufficiently large perturbation is induced in the VCSEL to allow emission in the fundamental mode of the other polarisation (Y-polarisation). The dynamics of both polarisations were found to be in antiphase and their amplitudes were such that the total intensity was constant, Fig. 3(a). Hence, only polarisation-resolved chaotic dynamics were observed, Fig. 3(b). This contrast strongly with the edge-emission laser diode case were chaotic dynamics are seen in the total output power. In Fig. 4, we plot the regions of chaos and stable injection locking. It is clear that the two chaotic regions are located on the positive and negative detuning sides of the injection locking region. This is in contrast to the case of edgeemitting semiconductor lasers – where two chaotic regimes are located on the same detuning side of the injection locking region in Fabry–Perot lasers [15] and three chaos regimes in a DFB laser [19]. We note that the chaos on the positive detuning side exists over a wider range of injection powers than the chaos on the negative detuning side. It is noted that the spectrum shown in Fig. 2(f) is on the boundary between two regimes, and hence the spectrum is not as broad as that of Fig. 2(b). When
Fig. 4. Stable injection locking and chaos regions as a function of injection power. (S) Stable injection locking.
the frequency detuning and injection power were set outside the stable injection locking, a frequency pushing effect was observed [4]. For large injection power, there was no clear transition between limit cycle oscillations and multiwave mixing with positive detuning from injection locking region, which is similar to the case of edge-emitting semiconductor lasers [15]. 4. Conclusion In conclusion, we have undertaken a systematic experimental investigation of the dynamics of VCSELs subjection to optical injection. Chaotic regions were observed for both positive and negative detuning from the stable injection locking regime. For positive detuning there is wider range of chaos than that on the negative detuning side. From the time traces, we confirm that polarisation-resolved chaos has been observed in the VCSEL. Outside the chaos regions, we also observed rich dynamical behaviours in the VCSEL; namely, nearly degenerate four-wave mixing (NDFWM), injection locking, limit cycle and period doubling. Acknowledgements
Fig. 3. Time traces for the emitted power of the VCSEL. (a) The total output power, (b) X-polarised output power.
This work was supported by the UK EPSRC under grant GR/N03181 and School of Informatics, University of Wales, Bangor, UK.
Y. Hong et al. / Optics Communications 216 (2003) 185–189
References [1] Z.G. Pan, S. Jiang, M. Dagenais, R.A. Morgan, K. Kojima, M.T. Asom, R.E. Leibenguth, G.D. Guth, M.W. Focht, Appl. Phys. Lett. 63 (1993) 2999. [2] S. Jiang, M. Dagenais, R.A. Morgan, Appl. Phys. Lett. 65 (1994) 1334. [3] H. Kawaguchi, I.S. Hidayat, Electron. Lett. 31 (1995) 1150. [4] H. Li, T.L. Lucas, J.G. McInerney, M.W. Wright, R.A. Morgan, IEEE J. Quantum Electron. 32 (1996) 227. [5] S.F. Yu, J. Lightwave Technol. 15 (1997) 1032. [6] A. Valle, L. Pesquera, K.A. Shore, IEEE Photon. Technol. Lett. 10 (1998) 639. [7] P. Besnard, M.L. Chares, G. Stephan, J. Opt. Soc. Am. B 16 (1999) 1059. [8] K. Panajotov, F. Berghmans, M. Peeters, G. Verschaffelt, J. Danckaert, I. Veretennicoff, H. Thienpont, IEEE Photon. Technol. Lett. 11 (1999) 985. [9] D.L. Boiko, G.M. Stephan, P. Besnard, J. Appl. Phys. 86 (1999) 4096.
189
[10] J.Y. Law, G.H.M. van Tartwijk, G.P. Agrawal, Quantum Semiclass. Opt. 9 (1997) 737. [11] Y. Hong, K.A. Shore, A. Larsson, M. Ghisoni, J. Halonen, Electron. Lett. 36 (2000) 2019. [12] Y. Hong, K.A. Shore, A. Larsson, M. Ghisoni, J. Halonen, IEE Proc-Optoelectron. 148 (2001) 31. [13] Y. Hong, P.S. Spencer, K.A. Shore, Electron. Lett. 37 (2001) 569. [14] S. Bandyopadhyay, Y. Hong, P.S. Spencer, K.A. Shore, Opt. Commun. 202 (2002) 145. [15] V. Kovanis, A. Gavrielides, T.B. Simpson, J.M. Liu, Appl. Phys. Lett. 67 (1995) 2780. [16] S. Wieczorek, B. Krauskopf, D. Lenstra, Opt. Commun. 172 (1999) 279. [17] S.K. Hwang, J.M. Liu, Opt. Commun. 183 (2000) 195. [18] T.B. Simpson, J.M. Liu, K.F. Huang, K. Tai, Quantum Semiclass. Opt. 9 (1997) 765. [19] S. Wieczored, T.B. Simpson, B. Krauskopf, D. Lenstra, Phys. Rev. E 65 (2002) 045207(R). [20] Y. Hong, P.S. Spencer, P. Rees, K.A. Shore, IEEE J. Quantum Electron. 38 (2002) 274.
Polarisation-resolved chaos and instabilities in a vertical cavity surface emitting laser subject to optical injection Y. Hong *, P.S. Spencer, S. Bandyopadhyay, P. Rees, K.A. Shore University of Wales, Bangor, School of Informatics, Bangor LL57 1UT, Wales, UK Received 14 June 2002; received in revised form 28 November 2002; accepted 28 November 2002
Abstract Instabilities in the polarisation-resolved output of a vertical cavity surface emitting laser (VCSEL) subject to optical injection have been investigated experimentally. It is found that regions of chaotic behaviour exist for both positive and negative detuning from the stable injection locking regime. Outside the chaos regimes, several nonlinear dynamical phenomena including frequency pushing, nearly degenerate four-wave mixing (NDFWM), injection locking, limit cycle and period doubling, were also observed. Ó 2002 Elsevier Science B.V. All rights reserved.
1. Introduction Vertical cavity surface emitting lasers (VCSELs) are characterised by a very short optical cavity, high facet reflectivities, cylindrical symmetry structure and light emission from the top or bottom surface. These characteristics mean that VCSELs have many advantages compared to edge-emitting lasers, such as a low threshold current, single longitudinal mode operation, a circular output-beam profile and wafer scale integrability. In addition to examining the properties of standalone VCSELs, effort has been given to understanding the response of VCSELs subject to optical feedback and optical injection [1–9]. Specific
*
Corresponding author. Fax: +44-1248-361-429. E-mail address: [email protected] (Y. Hong).
interest arises in regard to the effects of optical injection on VCSELs emission. Work has shown that nearly degenerate four-wave mixing in VCSELs [2] is similar to that in edge-emitting laser diodes. It has been demonstrated that the linear polarisation state of single-mode VCSELs can be switched by optical injection [1] and also that external optical injection could be used to convert a two-mode VCSEL into a single-mode device [10]. Recently we have demonstrated experimentally how the properties of VCSELs can be influenced by optical injection [11–14]. However, all of this previous work has been concerned with effects arising due to optical injection over relatively small frequency detuning ranges. The aim of this letter is to report our experimental investigations of the effect that external optical injection has on the dynamical behaviour of a single transverse mode VCSEL, over a large range of frequency detuning and optical injection
0030-4018/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. doi:10.1016/S0030-4018(02)02296-4
186
Y. Hong et al. / Optics Communications 216 (2003) 185–189
power. These studies have been motivated not only by technological application but also from the viewpoint of increased understanding of the operating characteristics of VCSELs. In this process we make what we believe to be the first report of the observation of regions of polarisation-resolved chaos either side of the stable locking regime in a VCSEL subject to optical injection. The observations reported here contrast with the behaviour of edge-emitting lasers in two ways. Firstly, the present phenomena relate to polarisation-resolved output whereas in edge-emitting lasers chaos is seen in the total output power. Secondly we observe two chaos regimes for one at positive and one at negative detuning from the stable locking regime. A very detailed experimental study of the optical injection response of edge-emitting Fabry– Perot lasers was reported by Kovanis et al. [15]. In that work regimes of chaos were identified only for positive detunings from the stable locking regime. Theoretical work by Wieczorek et al. [16] and Hwang and Liu [17] has analysed the dynamical characteristics of an optically injected edge-emitting laser diodes. Those papers cite experimental work [18] which reveals the presence of two chaotic regimes on the same detuning side of the stable locking regime. In recent experimental work reported by Wieczored et al. [19] it was found that there are three chaos regimes in a distributed feedback (DFB) semiconductor laser subject to the optical injection. Two chaos regimes are found at the positive detunings from the stable-locking regime and one chaos regime at negative detunings. That behaviour is clearly distinct from the phenomena observed in the experiments reported here.
2. Experimental set-up The experimental set-up used for this work is shown in Fig. 1. An external cavity laser diode with more than 20 nm tuning range (Model SDLTC 10-1385) was employed as the master laser. The master laser emits linearly polarised light in a single frequency with a linewidth of about 2 MHz. A commercial VCSEL (HFE-4085-321) with a threshold current of 3.1 mA was used as the slave
Fig. 1. The experimental set-up. TL, tunable laser; SL, slave laser; L, lens; ISO, optical isolator; BS, beamsplitter; ATTN, variable optical attenuator; ND, neutral density filter; k=2, halfwave plate; PS, polarising beamsplitter; B, removable beam block; M, mirror; PM, power meter, PD, photo detector; OSA, optical spectrum analyser; F-P, Fabry–Perot interferometer; D, detector; PC, computer.
laser. In the experiment, the VCSEL was biased just above threshold at 3.58 mA so that it supported only the fundamental transverse mode of one polarisation (X-polarisation) and operated at wavelength of 848.6 nm with an output power of 73:7 lW. The linewidth of the VCSEL is about 250 MHz. Both master and slave lasers were mounted on heat sinks and were temperature controlled to within 6 0:01 °C. The VCSEL was driven by an ultra-low-noise current source (ILXLightwave Model LDX-3620). An isolator of >40 dB attenuation was inserted between the master laser and the slave laser to prevent optical feedback into the master laser. A variable optical attenuator and a neutral density filter were used to change the injection power. A power meter was employed to monitor the injection power. The injection power was measured just before the light entered the laser diode objective (in front of the slave laser). Two other isolators of >40 dB attenuation were used to eliminate the feedback from the optical spectrum analyser and the Fabry–Perot interferometer. These were used to obtain the spectral characteristics of the slave laser. The free spectral range of the Fabry–Perot interferometer is 15 GHz. A half-wave plate inserted between the master laser and the slave laser was used to adjust the polarisation of the master laser so that it was
Y. Hong et al. / Optics Communications 216 (2003) 185–189
parallel to that of the free-running VCSEL. When we recorded the spectrum of the slave laser, a beam block was used to block the reflective beam from mirror M. The position of the master laser frequency can be checked by removing the beam block. The time trace of the light emitting from the VCSEL was recorded by replacing the optical spectrum analyser (in the dash frame of Fig. 1) by a high bandwidth (6 GHz) fast photo detector and high bandwidth (1 GHz) oscilloscope. The time trace of the total output power was measured by removing the polarisation beamsplitter.
3. Results Fig. 2 shows the optical spectra of the VCSEL at X-polarisation subject to optical injection with about 19 lW injection power. The optical spec-
Fig. 2. Optical spectra of the VCSEL subject to optical injection with about 19 lW injection power. The arrows mark the master laser frequency position. The frequency detuning is (a) 2.72 GHz, (b) 0.77 GHz, (c) )0.17 GHz, (d) )1.26 GHz, (e) )2.66 GHz, (f) )2.71 GHz.
187
trum in the Y-polarisation (perpendicular to the Xpolarisation) is negligible in all cases. The arrows mark the master laser (ML) frequency position. The zero of X-axis coincides with the slave laser free running frequency. The frequency detuning is Dx ¼ xinj x0 , where xinj is the frequency of the master laser and x0 is the VCSEL free-running frequency. In Fig. 2(a), Dx ¼ 2:72 GHz, the spectrum consists of narrow, weak sidebands at the same frequency offset either side of the main peak. These narrow side peaks correspond to the amplified signal and conjugate beam xc from four-waving between the injection signal beam and the slave laser main peak. In Fig. 2(b), with a frequency detuning of Dx ¼ 0:77 GHz, the spectrum is dominated by a broad pedestal; such a spectrum is indicative of chaotic dynamics. Decreasing the frequency detuning to )0.17 GHz, as shown in Fig. 2(c), the spectrum is dominated by three sharp peaks separated by the relaxation oscillation frequency, between the sharp peaks, smaller features were observed, which indicates period doubling dynamics. For Fig. 2(d), the detuning was )1.26 GHz, and in this case the slave laser frequency locks to the injected frequency, two side peaks also appeared in the spectrum, which indicates limit cycle behaviour. For a further decrease of the detuning to )2.66 GHz, Fig. 2(e), a single sharp peak at the injected frequency and a small feature residing at approximately 3 GHz were observed in the spectrum. The small feature is a part of the spectrum of the free-running VCSEL and corresponds to another transverse mode. As described in [20], for the VCSEL with the two parallel transverse mode, the two mode are shown independent. So the dominant mode of the VCSEL was injecting locked to the master laser. When the detuning was decreased to )2.71 GHz, as shown in Fig. 2(f), the VCSEL again showed chaos. Further decreases of the detuning the spectrum of the VCSEL shows a period doubling features. We can see that the VCSEL shows chaos characteristics at two different detuning frequencies for a fixed injection power. The polarisation-resolved spectra shown in Fig. 2 were all measured with an injection power of 19 lW. The lower (negatively frequency detuned from the stable injection locking regime) chaotic region only exists for a narrow band of frequencies
188
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for this injection power, and in fact the spectrum shown in Fig. 2(f) is on the boundary between the regimes. Consequently the spectrum is not as broad as that of Fig. 2(b), however, similar spectra to that of Fig. 2(b) have been measured in the lower chaotic region but at higher injection powers. The output temporal dynamics of both polarisation directions of the VCSEL were measured and negligible emission in the Y-polarisation was detected in all cases except for the two chaotic regimes. It appears that when chaotic light emission occurs in the X-polarisation a sufficiently large perturbation is induced in the VCSEL to allow emission in the fundamental mode of the other polarisation (Y-polarisation). The dynamics of both polarisations were found to be in antiphase and their amplitudes were such that the total intensity was constant, Fig. 3(a). Hence, only polarisation-resolved chaotic dynamics were observed, Fig. 3(b). This contrast strongly with the edge-emission laser diode case were chaotic dynamics are seen in the total output power. In Fig. 4, we plot the regions of chaos and stable injection locking. It is clear that the two chaotic regions are located on the positive and negative detuning sides of the injection locking region. This is in contrast to the case of edgeemitting semiconductor lasers – where two chaotic regimes are located on the same detuning side of the injection locking region in Fabry–Perot lasers [15] and three chaos regimes in a DFB laser [19]. We note that the chaos on the positive detuning side exists over a wider range of injection powers than the chaos on the negative detuning side. It is noted that the spectrum shown in Fig. 2(f) is on the boundary between two regimes, and hence the spectrum is not as broad as that of Fig. 2(b). When
Fig. 4. Stable injection locking and chaos regions as a function of injection power. (S) Stable injection locking.
the frequency detuning and injection power were set outside the stable injection locking, a frequency pushing effect was observed [4]. For large injection power, there was no clear transition between limit cycle oscillations and multiwave mixing with positive detuning from injection locking region, which is similar to the case of edge-emitting semiconductor lasers [15]. 4. Conclusion In conclusion, we have undertaken a systematic experimental investigation of the dynamics of VCSELs subjection to optical injection. Chaotic regions were observed for both positive and negative detuning from the stable injection locking regime. For positive detuning there is wider range of chaos than that on the negative detuning side. From the time traces, we confirm that polarisation-resolved chaos has been observed in the VCSEL. Outside the chaos regions, we also observed rich dynamical behaviours in the VCSEL; namely, nearly degenerate four-wave mixing (NDFWM), injection locking, limit cycle and period doubling. Acknowledgements
Fig. 3. Time traces for the emitted power of the VCSEL. (a) The total output power, (b) X-polarised output power.
This work was supported by the UK EPSRC under grant GR/N03181 and School of Informatics, University of Wales, Bangor, UK.
Y. Hong et al. / Optics Communications 216 (2003) 185–189
References [1] Z.G. Pan, S. Jiang, M. Dagenais, R.A. Morgan, K. Kojima, M.T. Asom, R.E. Leibenguth, G.D. Guth, M.W. Focht, Appl. Phys. Lett. 63 (1993) 2999. [2] S. Jiang, M. Dagenais, R.A. Morgan, Appl. Phys. Lett. 65 (1994) 1334. [3] H. Kawaguchi, I.S. Hidayat, Electron. Lett. 31 (1995) 1150. [4] H. Li, T.L. Lucas, J.G. McInerney, M.W. Wright, R.A. Morgan, IEEE J. Quantum Electron. 32 (1996) 227. [5] S.F. Yu, J. Lightwave Technol. 15 (1997) 1032. [6] A. Valle, L. Pesquera, K.A. Shore, IEEE Photon. Technol. Lett. 10 (1998) 639. [7] P. Besnard, M.L. Chares, G. Stephan, J. Opt. Soc. Am. B 16 (1999) 1059. [8] K. Panajotov, F. Berghmans, M. Peeters, G. Verschaffelt, J. Danckaert, I. Veretennicoff, H. Thienpont, IEEE Photon. Technol. Lett. 11 (1999) 985. [9] D.L. Boiko, G.M. Stephan, P. Besnard, J. Appl. Phys. 86 (1999) 4096.
189
[10] J.Y. Law, G.H.M. van Tartwijk, G.P. Agrawal, Quantum Semiclass. Opt. 9 (1997) 737. [11] Y. Hong, K.A. Shore, A. Larsson, M. Ghisoni, J. Halonen, Electron. Lett. 36 (2000) 2019. [12] Y. Hong, K.A. Shore, A. Larsson, M. Ghisoni, J. Halonen, IEE Proc-Optoelectron. 148 (2001) 31. [13] Y. Hong, P.S. Spencer, K.A. Shore, Electron. Lett. 37 (2001) 569. [14] S. Bandyopadhyay, Y. Hong, P.S. Spencer, K.A. Shore, Opt. Commun. 202 (2002) 145. [15] V. Kovanis, A. Gavrielides, T.B. Simpson, J.M. Liu, Appl. Phys. Lett. 67 (1995) 2780. [16] S. Wieczorek, B. Krauskopf, D. Lenstra, Opt. Commun. 172 (1999) 279. [17] S.K. Hwang, J.M. Liu, Opt. Commun. 183 (2000) 195. [18] T.B. Simpson, J.M. Liu, K.F. Huang, K. Tai, Quantum Semiclass. Opt. 9 (1997) 765. [19] S. Wieczored, T.B. Simpson, B. Krauskopf, D. Lenstra, Phys. Rev. E 65 (2002) 045207(R). [20] Y. Hong, P.S. Spencer, P. Rees, K.A. Shore, IEEE J. Quantum Electron. 38 (2002) 274.