Abstract

We experimentally investigate the dynamical characteristics of semiconductor lasers subject to both the optical injection (OI) and the optical feedback (OF). By coupling the OI and the OF lights into the same fiber before injecting into the slave laser (SL), the ratio between the two perturbations can be accurately determined and controlled. The frequency shifts in the cavity resonance frequency of the SL (νSL) induced by the OI and the OF lights are compared quantitatively. To study the competition between the OI and the OF in the SL, the mapping of the dynamical scenarios and states are plotted in the parameter space. This mapping serves as the guideline for choosing the appropriate operation conditions in various applications employing both the OI and the OF at the same time. In this paper, the suitable feedback strengths to narrow the linewidths of photonic microwave signals generated by the OI are studied. The limitation of using OI in enhancing the bandwidths of the chaos states generated by the OF is discussed. Moreover, to suppress the unwanted dynamics due to the feedback, the optimal injection parameters of the OI are shown.

© 2013 Optical Society of America

1. Introduction

Nonlinear dynamics of semiconductor lasers subject to optical injection (OI) and optical feedback (OF) have been studied extensively in recent years [14]. With the OI, dynamical states including period-1 oscillation (P1), period-2 oscillation (P2), chaos oscillation (CO), and stable locking (L) have been observed and applications in photonic microwave signals generation [57], laser stabilization [8], and bandwidth enhancements [912] have been explored. With the OF, dynamical states including P1, quasi-periodic oscillation (QP), and CO have been found and applications in chaos generation [3, 13, 14] and linewidth narrowing [15] have been investigated. To utilize the advantages from both schemes, semiconductor lasers employing both the OI and the OF have also been considered in many applications.

For example, to reduce the linewidths of the microwave photonic signals generated with the OI scheme, delay feedback loops are added for laser stabilization [1618]. In applications requiring chaos signals with broad bandwidths, OI is used to broaden the bandwidths of the chaos generated with the OF scheme [19,20]. To suppress the unwanted dynamics induced by the optical feedback, the laser is injected with a strong OI light to lock the laser into the stable-locking state [8]. While mixing the effects from multiple perturbations could make the dynamics of the laser become very complicated, the dynamical characteristics of semiconductor lasers subject to both the OI and the OF have not been investigated in detail. More particularly, to have the best performance in the above-mentioned applications, the requirements and limitations on the operation conditions and the relative strengths between the OI and the OF lights have not been quantitatively studied.

In this paper, we experimentally investigate the dynamical scenarios and states of semiconductor lasers subject to both the OI and the OF. By coupling the OI and the OF lights into the same fiber before injecting into a slave laser (SL), the ratio between the two perturbations can be accurately determined and controlled. The frequency-pushing effect in the cavity resonance frequency of the SL induced by the OI and the OF are compared quantitatively. To study the competition between the OI and the OF in the SL, the mapping of the dynamical scenarios and states are plotted and overlapped in the parameter space. Using the mapping as the guideline, the optimal operation conditions in applications employing both the OI and the OF are discussed.

2. Experimental setup

Figure 1 shows the experimental setup of a semiconductor laser subject to both the OI and the OF. A tunable laser (Yenista, Tunics-T100S, O-band) is used as the master laser (ML) while a single-mode distributed-feedback (DFB) semiconductor laser (MITSUBISHI, ML725B11F) is used as the SL. By varying the temperature, the wavelength of the SL is tuned to about λSL = 1308.78 nm. The bias current of the SL is set at 8 mA (1.7Ith). The detuning frequency f (f is the difference of the cavity resonance frequencies between the ML and the SL under the free running condition) is controlled by tuning the wavelength of the injection light from the ML. The normalized injection strength ξi and feedback strength ξfb (ξ is the ratio of the optical field of the injection/feedback light to the optical field of the SL output) are adjusted by the optical variable attenuators. To assure the relative values between the ξi and ξfb that are injected and fed back to the SL, the OI and OF lights are first coupled into a single-mode fiber through a 50/50 polarization-maintaining coupler and then injected into the SL through exactly the same optical path. The feedback loop has a length of L = 16 m, which is long enough so that the dynamics from the OF is insensitive to the feedback phase but mainly determined by the ξfb. The output of the SL is analyzed with an optical spectrum analyzer (Advantest, Q8384) and a microwave spectrum analyzer (R&S FSV30), where a 40-GHz photodetector (Discovery semiconductor, DSC-R409) is used.

 figure: Fig. 1

Fig. 1 Experimental setup of the semiconductor laser subject to both the OI and the OF.

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3. Results and discussions

Figures 2(a) and 2(b) show the transitions of the optical spectra when the SL is subject to solely the OI and the OF individually under different ξi and ξfb, respectively. The cavity resonance frequencies of the SL (νSL) under different conditions are marked with the red dots. As can be seen in Fig. 2(a), when ξi increases, νSL decreases and shifts toward the negative offset frequency (relative to the oscillation frequency of the free-running SL) due to the frequency-pushing effect associated with the OI light [21]. As shown in Fig. 2(b), we found a similar frequency-pushing effect in the SL subject to the OF when ξfb increases. To quantitatively compare the responses of the SL to the OI and the OF lights, the shifts in the cavity resonance frequency (Δf) for different ξi and ξfb are shown in Fig. 3.

 figure: Fig. 2

Fig. 2 Transitions of the optical spectra for the SL subject to (a) OI with f = 5.6 GHz and (b) OF with different ξi and ξfb, respectively. The red dots mark the νSL.

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 figure: Fig. 3

Fig. 3 Δf of the SL under different ξi and ξfb. The solid squares, triangles, and circles are obtained with the OI scheme for detuning frequencies of f = 5.6, 9.3, and 13.7 GHz, and open circles are obtained with the OF scheme, respectively.

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The Δf of the SL subject to the OI under different ξi are plotted in Fig. 3, where the solid squares, triangles, and circles are obtained with detuning frequencies of f = 5.6, 9.3, and 13.7 GHz, respectively. As can be seen, the Δf decreases as the ξi increases, where the frequency-pushing effect is stronger when the detuning frequency is smaller. In another word, the pushing is more effectively if the frequency of the injection light is closer to the νSL. The open circles shown in Fig. 3 are the Δf under different ξfb when the SL is subject to the OF. Compared to the OI scheme, we found that the Δf shifts more significantly in the OF scheme when the SL is under the same injection and feedback strengths. The difference in the responses of the Δf to the injection and feedback lights is because of that, the main oscillation frequency of the feedback light constantly shifts together with the frequency-pushed νSL while the frequency of the injection light from the ML is fixed and detuned away from the νSL as it is pushed away. Moreover, although reducing the detuning frequency might increase the Δf in the OI scheme, the SL can easily get locked by the ML if the detuning frequency is too small where the νSL will be depleted by the OI light completely. As the result, the SL is expected to be more sensitive to the perturbation from the OF light than the OI light when adding both to the laser simultaneously.

Figure 4 shows the mapping of the dynamical scenarios under different ξi and ξfb when the SL is subject to both the OI and the OF simultaneously. The detuning frequency of the injection light is fixed at f = 5.6 GHz. Different dynamical scenarios (separated with the black curves) are defined and differentiated by whether the dynamics and the characteristics frequencies originated from the OI or the OF alone are being preserved (P), shifted (S), or suppressed (S′) after both the OI and the OF lights are simultaneously injected. The letter L is used when the SL is stably locked by the OI light. In the two-letter symbols, the first and the second letters are each corresponding to the effects from the OI and the OF respectively [22]. To show the dynamical states of the SL subject to both the OI and the OF in the same parameter space, the regions of dynamical states including the period-one (P1), period-two (P2), quasi-periodic (QP), chaos oscillation (CO), and stable locking (L) are also colored in red, cyan, green, gray, and yellow, respectively.

 figure: Fig. 4

Fig. 4 Mapping of dynamical scenarios and states under different ξi and ξfb when the SL is subject to both the OI and the OF simultaneously. The detuning frequency is fixed at f = 5.6 GHz. Different dynamical scenarios (separated with the black curves) are defined and differentiated by whether the dynamics and the characteristics frequencies originated from the OI or the OF alone are being preserved (P), shifted (S), or suppressed (S′) after both the OI and the OF lights are simultaneously injected. The letter L is used when the SL is stably locked by the OI light. In the two-letter symbols, the first and the second letters are each corresponding to the effects from the OI and the OF respectively. Regions of dynamical states including the period-one (P1), period-two (P2), quasi-periodic (QP), chaos oscillation (CO), and stable locking (L) are colored in red, cyan, green, gray, and yellow, respectively.

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As can be seen, the scenario PP occurs at the corner where both ξi and ξfb are very small. In this scenario, the SL is weakly disturbed by the OI and the OF, where the P1 state with a oscillation frequency close to the relaxation oscillation frequency of the SL is observed. Scenario SP is located at the region next to the left vertical axis. In this scenario, the dynamics of the SL is mainly determined by the OF light where the CO states induced by the OF occupy the region. The scenario PS is located near the region on the bottom above the horizontal axis. In this scenario, the dynamics of the SL is mainly determined by the OI while the weak OF light mainly contributes in narrowing the linewidth of the oscillation frequency [17]. Period-doubling and reverse period-doubling bifurcation routes with the P1, P2, and CO states induced by the OI are clearly seen. Note that, the range of the horizontal axis is an order greater than that of the vertical axis, this is to accommodate the fact that the SL is much sensitive to the perturbation from the OF light than the OI light as previously discussed in Fig. 3. As the result, when compared with the OI, only a relatively weak OF light is needed to drive the SL into instabilities.

With moderate OI and OF lights, the scenario SS is observed around the center of the mapping. In this scenario, the dynamics of the SL are determined by the contribution from both the OI and the OF. Various dynamical states including the P1, P2, QP, and CO are found in this region. In the region where ξi is much larger than ξfb near the vertical axis on the right, the scenario LS′ is found. In this scenario, the SL is stably locked by the strong OI light and the perturbation from the OF is completely suppressed. As the result, the L state occupies this region. Unlike the dual-beam OI scheme discussed in [22] where the SL is injected with two independent optical beams, scenarios S′L, S′S′ and LL do not exist in the SL subject to both the OI and the OF since the νSL is never depleted by the OF light even with a very strong ξfb (i.e. the dynamics is not locked (L) or suppressed (S′) by the OF light). Using the mapping as the guideline, the optimal operation conditions in applications employing both the OI and the OF are then studied.

Adding feedback loops to stabilize the microwave signals generated by the optically injected semiconductor lasers have been demonstrated in many applications [1618]. With the mapping of the dynamical scenarios and states shown in Fig. 4, the ranges of ξfb for best laser stabilization under different ξi can be determined. Figures 5(a) and 5(d) show the power spectra of the P2 and P1 states when the SL is subject to only the OI with ξi = 0.21 and 0.31, respectively. Their relative locations in the parameter space are also marked in Fig. 4. When ξfb is increased to 0.008 before crossing the boundary between the PS and the SS scenarios, the power spectra of the P2 and P1 states with their oscillation frequencies remain unchanged are shown in Figs. 5(b) and 5(e), respectively. Compared with Figs. 5(a) and 5(d), the 3-dB linewidths of the main oscillation frequencies are narrowed from about 50 MHz to less than 1 MHz. However, if the ξfb is increased to 0.03 (about one-tenth of the ξi) crossing the boundary into the SS scenario, as shown in Figs. 5(c) and 5(f), the oscillation frequencies of the P2 and P1 states are shifted and the linewidths of the main oscillation frequencies are broadened to larger than 100 MHz. As the result, to have the optimal linewidth narrowing by the OF, the ξfb has to be controlled so that the SL remains in the preferred PS scenario without crossing into the SS scenario.

 figure: Fig. 5

Fig. 5 Power spectra of the (a)–(c) P2 and (d)–(f) P1 states obtained with ξi = 0.21 and ξi = 0.31 when ξfb is increased from 0, 0.008, to 0.03, respectively. The relative locations of these states in the parameter space are also marked in Fig. 4.

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In applications of broadband chaos generation, additional OI light is often used to enhance the bandwidth of the chaos generated by the semiconductor laser subject to OF [20]. The region suitable for the broadband chaos generation is also outlined by the mapping shown in Fig. 4. Figures 6(a)–6(c) show the power spectra of the chaos generated with ξfb = 0.06 while the ξi is increased from 0 (no injection), 0.15, to 0.21 to enhance the bandwidths, respectively. As can be seen in Figs. 6(a) and 6(b), the oscillation frequency increases from about 3 GHz to 9 GHz after the SL is injected with the OI light. According to the convention of 80% total power containment [23], the bandwidths of these chaos states increase from 4.80 GHz to 9.02 GHz, respectively. When further increasing ξi to 0.21, as shown in Fig. 6(c), the bandwidth is broadened to 9.88 GHz due to the further increased oscillation frequency. (Note that, from another convention that measures only those spectral segments accounting for 80% of the total power in the chaos power spectrum [24], the effective bandwidth of the chaos states shown in Figs. 6(a)–6(c) increases from 3.50 GHz to 6.08 GHz and then decreases back to 5.56 GHz.) Here the limit of the ξi that can apply on the SL to increase the bandwidths of the chaos states generated can be determined from the mapping shown in Fig. 4. As can be seen, for certain ξfb, adding an OI light too strong drives the SL from the chaos states into other narrowband oscillation states such as the P1, P2, or QP. In general, for the SL to remain in the CO state, the ξfb has to be stronger if a stronger ξi is intended to apply.

 figure: Fig. 6

Fig. 6 Power spectra of the (a)–(c) CO and (d) L states obtained with ξfb = 0.06 when ξi is increased from 0, 0.15, 0.21, to 0.85, respectively. The relative locations of these states in the parameter space are also marked in Fig. 4.

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On the other hand, if the chaos and instability induced by the OF are considered as the unwanted dynamics and are meant to be eliminated, injecting a strong OI light can suppress them and stabilize the laser. This will occur when the SL is in the LS′ region shown in Fig. 4, where the SL is stabilized and injection-locked by the OI light. Figure 6(d) shows the power spectrum of the SL when the ξi is increased to 0.85 (an order greater than the ξfb), where the instability (chaos) induced by the OF shown in Figs. 6(a)–6(c) is completely suppressed. From the boundary between the SS and the LS′ scenarios, the minimum ξi needed for different ξfb to suppress the unwanted dynamics can also be determined.

Figure 7 shows the locking boundaries of the SL for different feedback strengths of ξfb = 0 (black curve), 0.08 (red curve), and 0.18 (blue curve), respectively. As can be seen, with a stronger feedback, stronger injection is needed for the SL to enter into the locking region (scenario LS′) and suppress the instability induced by the OF. The stars marked at the apexes of each locking regions indicate the optimal operation points where minimum ξi are required to stabilize the SL. As can be seen, when increasing the ξfb, the optimal detuning frequency fopt to have the minimum ξi shifts toward the negative detuning. We found that the shift in fopt is directly corresponding to the frequency shift Δf of the νSL caused by the OF previously shown in Figs. 2 and 3.

 figure: Fig. 7

Fig. 7 The boundaries of injection locking for different ξfb. The dashed lines are the fitting curves of the Hopf and saddle-node bifurcations. The stars marked at the apexes of each locking regions indicate the optimal operation points where minimum ξi are required to stabilize the SL.

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Figure 8(a) shows the fopt (solid black curve labeled on the left) and the frequency shift Δf of the νSL (dashed gray curve labeled on the right) for different ξfb. As can be seen, they match well with each other and decrease from −7.5 GHz to −16.54 GHz as the ξfb increases from 0 to 0.18. As the results, the optimal detuning frequency fopt to have the minimum ξi is when the OI light has exactly the same frequency as the frequency-pushed νSL, where the suppression due to the gain depletion is most effective. Figure 8(b) shows the threshold (minimum) injection strength ξi,th needed to stabilize the laser under different ξfb. The black curve is obtained when the detuning frequency f is optimized under different ξfb according to the fopt shown in Fig. 8(a). The red and blue curves are obtained with fixed f at −7.5 GHz and 5.6 GHz, respectively. As can be seen, when the detuning frequency f of the OI light is optimized to fopt, the ξi,th is substantially lower compared to the cases when the detuning frequencies are fixed at certain values. As the result, by simply measuring the Δf under different ξfb as that is shown in Fig. 3, the optimal detuning frequency fopt of the OI light to effectively stabilize the laser under different ξfb can be determined. Hence, finding the boundaries of the locking regions under different ξfb as shown in Fig. 7 is therefore no longer necessary.

 figure: Fig. 8

Fig. 8 (a) fopt (solid black curve labeled on the left) and Δf (dashed gray curve labeled on the right) for different ξfb. (b) The threshold (minimum) injection strength ξi,th needed to stabilize the laser under different ξfb. The black curve is obtained when the detuning frequency f is optimized under different ξfb according to the fopt shown in Fig. 8(a). The red and blue curves are obtained with fixed f at −7.5 GHz and 5.6 GHz, respectively.

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4. Conclusions

In conclusion, we experimentally investigate the dynamical characteristics of the semiconductor laser subject to the OI and the OF simultaneously. By coupling the OI and the OF lights into the same fiber to have a common path before injecting into the SL, the relative ratio of the ξi and the ξfb can be determined and controlled. Since the main oscillation frequency of the feedback light shifts together with the frequency-pushed νSL, the frequency-pushing effect induced by the OF light is found to be more significant than that by the OI light. As the result, when affecting by both perturbations simultaneously, the SL is found to be more sensitive to the influences from the OF than the OI light. To study the competition between the OI and the OF, the mapping of the dynamical scenarios and states are plotted and overlapped for different ξi and ξfb. Dynamical scenarios of PP, PS, SP, SS, and LS′ and dynamical states of P1, P2, QP, CO, and L are observed. The mapping is shown to be useful in determining the appropriate operation conditions in applications such as the linewidth narrowing and broadband chaos generation where the SL employing both the OI and the OF at the same time. Moreover, we also show that without really plotting the locking regions, the optimal detuning frequency fopt of the OI light to effectively stabilize the laser can be determined by simply measuring the Δf under different ξfb.

Acknowledgments

This study was funded by the National Science Council of Taiwan under contract NSC 100-2112-M-007-012-MY3 and by the National Tsing Hua University under grant 102N2081E1.

References and links

1. T. B. Simpson, J. M. Liu, K. F. Huang, and K. Tai, “Nonlinear dynamics induced by external optical injection in semiconductor lasers,” Quantum Semiclass. Opt. 9, 765–784 (1997). [CrossRef]  

2. S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, “The dynamical complexity of optically injected semiconductor lasers,” Phys. Rep. 416, 1–128 (2005). [CrossRef]  

3. J. Ohtsubo, “Feedback induced instability and chaos in semiconductor lasers and their applications,” Opt. Rev. 6, 1–15 (1999). [CrossRef]  

4. T. Heil, I. Fischer, W. Elsäβer, B. Krauskopf, K. Green, and A. Gavrielides, “Delay dynamics of semiconductor lasers with short external cavities: Bifurcation scenarios and mechanisms,” Phys. Rev. E 67, 066214 (2003). [CrossRef]  

5. S. C. Chen, S. K. Hwang, and J. M. Liu, “Period-one oscillation for photonic microwave transmission using an optically injected semiconductor laser,” Opt. Express 15, 14921–14935 (2007). [CrossRef]  

6. Y. S. Juan and F. Y. Lin, “Ultra broadband microwave frequency combs generated by an optical pulse-injected semiconductor laser,” Opt. Express 17, 18596–18605 (2009). [CrossRef]  

7. Y. S. Juan and F. Y. Lin, “Photonic generation of broadly tunable microwave signals utilizing a dual-beam optically injected semiconductor lasers,” IEEE Photonics J. 3, 644–650 (2011). [CrossRef]  

8. J. S. Lawrence and D. M. Kane, “Injection locking suppression of coherence collapse in a diode laser with optical feedback,” Opt. Commun. 167, 273–282 (1999). [CrossRef]  

9. T. B. Simpson and J. M. Liu, “Enhanced modulation bandwidth in injection-locked semiconductor lasers,” IEEE Photon. Technol. Lett. 9, 1322–1324 (1997). [CrossRef]  

10. A. Murakami, K. Kawashima, and K. Atsuki, “Cavity resonance shift and bandwidth enhancement in semiconductor lasers with strong light injection,” IEEE J. of Quantum Electron. 39, 1196–1204 (2003). [CrossRef]  

11. Y. Takiguchi, K. Ohyagi, and J. Ohtsubo, “Bandwidth-enhanced chaos synchronization in strongly injection-locked semiconductor lasers with optical feedback,” Opt. Lett. 28, 319–321 (2003). [CrossRef]   [PubMed]  

12. E. K. Lau, X. Zhao, H. K. Sung, D. Parekh, C. C. Hasnain, and M. C. Wu, “Strong optical injection-locked semiconductor lasers demonstrating > 100-GHz resonance frequencies and 80-GHz intrinsic bandwidths,” Opt. Express 16, 6609–6618 (2008). [CrossRef]   [PubMed]  

13. J. Ohtsubo, “Chaos synchronization and chaotic signal masking in semiconductor lasers with optical feedback,” IEEE J. of Quantum Electron. 38, 1141–1154 (2002). [CrossRef]  

14. R. Vicente, J. Daudén, P. Colet, and R. Toral, “Analysis and characterization of the hyperchaos generated by a semiconductor laser subject to a delayed feedback loop,” IEEE J. of Quantum Electron. 41, 541–548 (2005). [CrossRef]  

15. R. W. Tkach and A. R. Chraplyvy, “Regions of feedback effects in 1.5-um distributed feedback laser,” J. Light-wave Technol. LT-4, 1655–1661 (1986). [CrossRef]  

16. S. C. Chan and J. M. Liu, “Tunable narrow-linewidth photonic microwave generation using semiconductor laser dynamics,” IEEE J. of Sel. Top. Quantum Electron. 10, 1025–1032 (2004). [CrossRef]  

17. J. P. Zhuang and S. C. Chan, “Tunable photonics microwave generation using optically injected semiconductor laser dynamics with optical feedback stabilization,” Opt. Lett. 38, 344–346 (2013). [CrossRef]   [PubMed]  

18. T. B. Simpson, J. M. Liu, M. AlMulla, N. G. Usechak, and V. Kovanis, “Linewidth sharpening via polarization-rotated feedback in optically injected semiconductor oscillators,” IEEE J. of Sel. Top. Quantum Electron. 19, 1500807 (2013). [CrossRef]  

19. A. B. Wang, Y. C. Wang, and H. C. He, “Enhancing the bandwidth of the optical chaotic signal generated by a semiconductor laser with optical feedback,” IEEE Photonic Technol. Lett. 20, 1633–1635 (2008). [CrossRef]  

20. A. B. Wang, Y. C. Wang, and J. F. Wang, “Route to broadband chaos in a chaotic laser diode subject to optical injection,” Opt. Lett. 34, 1144–1146 (2009). [CrossRef]   [PubMed]  

21. S. C. Chan, “Analysis of an optically injected semiconductor laser for microwave generation,” IEEE J. Quantum Electron. 46, 421–428 (2010). [CrossRef]  

22. Y. H. Liao, J. M. Liu, and F. Y. Lin, “Dynamical characteristics of a dual-beam optically injected semiconductor laser,” IEEE J. of Sel. Top. Quantum Electron. 19, 1500606 (2013). [CrossRef]  

23. F. Y. Lin and J. M. Liu, “Nonlinear dynamical characteristics of an optically injected semiconductor laser subject to optoelectronic feedback,” Opt. Commun. 221, 173–180 (2003). [CrossRef]  

24. F. Y. Lin, Y. K. Chao, and T. C. Wu, “Effective bandwidths of broadband chaotic signals,” IEEE J. of Quantum Electron. 48, 1010–1014 (2011). [CrossRef]  

References

  • View by:

  1. T. B. Simpson, J. M. Liu, K. F. Huang, and K. Tai, “Nonlinear dynamics induced by external optical injection in semiconductor lasers,” Quantum Semiclass. Opt. 9, 765–784 (1997).
    [Crossref]
  2. S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, “The dynamical complexity of optically injected semiconductor lasers,” Phys. Rep. 416, 1–128 (2005).
    [Crossref]
  3. J. Ohtsubo, “Feedback induced instability and chaos in semiconductor lasers and their applications,” Opt. Rev. 6, 1–15 (1999).
    [Crossref]
  4. T. Heil, I. Fischer, W. Elsäβer, B. Krauskopf, K. Green, and A. Gavrielides, “Delay dynamics of semiconductor lasers with short external cavities: Bifurcation scenarios and mechanisms,” Phys. Rev. E 67, 066214 (2003).
    [Crossref]
  5. S. C. Chen, S. K. Hwang, and J. M. Liu, “Period-one oscillation for photonic microwave transmission using an optically injected semiconductor laser,” Opt. Express 15, 14921–14935 (2007).
    [Crossref]
  6. Y. S. Juan and F. Y. Lin, “Ultra broadband microwave frequency combs generated by an optical pulse-injected semiconductor laser,” Opt. Express 17, 18596–18605 (2009).
    [Crossref]
  7. Y. S. Juan and F. Y. Lin, “Photonic generation of broadly tunable microwave signals utilizing a dual-beam optically injected semiconductor lasers,” IEEE Photonics J. 3, 644–650 (2011).
    [Crossref]
  8. J. S. Lawrence and D. M. Kane, “Injection locking suppression of coherence collapse in a diode laser with optical feedback,” Opt. Commun. 167, 273–282 (1999).
    [Crossref]
  9. T. B. Simpson and J. M. Liu, “Enhanced modulation bandwidth in injection-locked semiconductor lasers,” IEEE Photon. Technol. Lett. 9, 1322–1324 (1997).
    [Crossref]
  10. A. Murakami, K. Kawashima, and K. Atsuki, “Cavity resonance shift and bandwidth enhancement in semiconductor lasers with strong light injection,” IEEE J. of Quantum Electron. 39, 1196–1204 (2003).
    [Crossref]
  11. Y. Takiguchi, K. Ohyagi, and J. Ohtsubo, “Bandwidth-enhanced chaos synchronization in strongly injection-locked semiconductor lasers with optical feedback,” Opt. Lett. 28, 319–321 (2003).
    [Crossref] [PubMed]
  12. E. K. Lau, X. Zhao, H. K. Sung, D. Parekh, C. C. Hasnain, and M. C. Wu, “Strong optical injection-locked semiconductor lasers demonstrating > 100-GHz resonance frequencies and 80-GHz intrinsic bandwidths,” Opt. Express 16, 6609–6618 (2008).
    [Crossref] [PubMed]
  13. J. Ohtsubo, “Chaos synchronization and chaotic signal masking in semiconductor lasers with optical feedback,” IEEE J. of Quantum Electron. 38, 1141–1154 (2002).
    [Crossref]
  14. R. Vicente, J. Daudén, P. Colet, and R. Toral, “Analysis and characterization of the hyperchaos generated by a semiconductor laser subject to a delayed feedback loop,” IEEE J. of Quantum Electron. 41, 541–548 (2005).
    [Crossref]
  15. R. W. Tkach and A. R. Chraplyvy, “Regions of feedback effects in 1.5-um distributed feedback laser,” J. Light-wave Technol. LT-4, 1655–1661 (1986).
    [Crossref]
  16. S. C. Chan and J. M. Liu, “Tunable narrow-linewidth photonic microwave generation using semiconductor laser dynamics,” IEEE J. of Sel. Top. Quantum Electron. 10, 1025–1032 (2004).
    [Crossref]
  17. J. P. Zhuang and S. C. Chan, “Tunable photonics microwave generation using optically injected semiconductor laser dynamics with optical feedback stabilization,” Opt. Lett. 38, 344–346 (2013).
    [Crossref] [PubMed]
  18. T. B. Simpson, J. M. Liu, M. AlMulla, N. G. Usechak, and V. Kovanis, “Linewidth sharpening via polarization-rotated feedback in optically injected semiconductor oscillators,” IEEE J. of Sel. Top. Quantum Electron. 19, 1500807 (2013).
    [Crossref]
  19. A. B. Wang, Y. C. Wang, and H. C. He, “Enhancing the bandwidth of the optical chaotic signal generated by a semiconductor laser with optical feedback,” IEEE Photonic Technol. Lett. 20, 1633–1635 (2008).
    [Crossref]
  20. A. B. Wang, Y. C. Wang, and J. F. Wang, “Route to broadband chaos in a chaotic laser diode subject to optical injection,” Opt. Lett. 34, 1144–1146 (2009).
    [Crossref] [PubMed]
  21. S. C. Chan, “Analysis of an optically injected semiconductor laser for microwave generation,” IEEE J. Quantum Electron. 46, 421–428 (2010).
    [Crossref]
  22. Y. H. Liao, J. M. Liu, and F. Y. Lin, “Dynamical characteristics of a dual-beam optically injected semiconductor laser,” IEEE J. of Sel. Top. Quantum Electron. 19, 1500606 (2013).
    [Crossref]
  23. F. Y. Lin and J. M. Liu, “Nonlinear dynamical characteristics of an optically injected semiconductor laser subject to optoelectronic feedback,” Opt. Commun. 221, 173–180 (2003).
    [Crossref]
  24. F. Y. Lin, Y. K. Chao, and T. C. Wu, “Effective bandwidths of broadband chaotic signals,” IEEE J. of Quantum Electron. 48, 1010–1014 (2011).
    [Crossref]

2013 (3)

J. P. Zhuang and S. C. Chan, “Tunable photonics microwave generation using optically injected semiconductor laser dynamics with optical feedback stabilization,” Opt. Lett. 38, 344–346 (2013).
[Crossref] [PubMed]

T. B. Simpson, J. M. Liu, M. AlMulla, N. G. Usechak, and V. Kovanis, “Linewidth sharpening via polarization-rotated feedback in optically injected semiconductor oscillators,” IEEE J. of Sel. Top. Quantum Electron. 19, 1500807 (2013).
[Crossref]

Y. H. Liao, J. M. Liu, and F. Y. Lin, “Dynamical characteristics of a dual-beam optically injected semiconductor laser,” IEEE J. of Sel. Top. Quantum Electron. 19, 1500606 (2013).
[Crossref]

2011 (2)

F. Y. Lin, Y. K. Chao, and T. C. Wu, “Effective bandwidths of broadband chaotic signals,” IEEE J. of Quantum Electron. 48, 1010–1014 (2011).
[Crossref]

Y. S. Juan and F. Y. Lin, “Photonic generation of broadly tunable microwave signals utilizing a dual-beam optically injected semiconductor lasers,” IEEE Photonics J. 3, 644–650 (2011).
[Crossref]

2010 (1)

S. C. Chan, “Analysis of an optically injected semiconductor laser for microwave generation,” IEEE J. Quantum Electron. 46, 421–428 (2010).
[Crossref]

2009 (2)

2008 (2)

A. B. Wang, Y. C. Wang, and H. C. He, “Enhancing the bandwidth of the optical chaotic signal generated by a semiconductor laser with optical feedback,” IEEE Photonic Technol. Lett. 20, 1633–1635 (2008).
[Crossref]

E. K. Lau, X. Zhao, H. K. Sung, D. Parekh, C. C. Hasnain, and M. C. Wu, “Strong optical injection-locked semiconductor lasers demonstrating > 100-GHz resonance frequencies and 80-GHz intrinsic bandwidths,” Opt. Express 16, 6609–6618 (2008).
[Crossref] [PubMed]

2007 (1)

2005 (2)

S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, “The dynamical complexity of optically injected semiconductor lasers,” Phys. Rep. 416, 1–128 (2005).
[Crossref]

R. Vicente, J. Daudén, P. Colet, and R. Toral, “Analysis and characterization of the hyperchaos generated by a semiconductor laser subject to a delayed feedback loop,” IEEE J. of Quantum Electron. 41, 541–548 (2005).
[Crossref]

2004 (1)

S. C. Chan and J. M. Liu, “Tunable narrow-linewidth photonic microwave generation using semiconductor laser dynamics,” IEEE J. of Sel. Top. Quantum Electron. 10, 1025–1032 (2004).
[Crossref]

2003 (4)

F. Y. Lin and J. M. Liu, “Nonlinear dynamical characteristics of an optically injected semiconductor laser subject to optoelectronic feedback,” Opt. Commun. 221, 173–180 (2003).
[Crossref]

A. Murakami, K. Kawashima, and K. Atsuki, “Cavity resonance shift and bandwidth enhancement in semiconductor lasers with strong light injection,” IEEE J. of Quantum Electron. 39, 1196–1204 (2003).
[Crossref]

Y. Takiguchi, K. Ohyagi, and J. Ohtsubo, “Bandwidth-enhanced chaos synchronization in strongly injection-locked semiconductor lasers with optical feedback,” Opt. Lett. 28, 319–321 (2003).
[Crossref] [PubMed]

T. Heil, I. Fischer, W. Elsäβer, B. Krauskopf, K. Green, and A. Gavrielides, “Delay dynamics of semiconductor lasers with short external cavities: Bifurcation scenarios and mechanisms,” Phys. Rev. E 67, 066214 (2003).
[Crossref]

2002 (1)

J. Ohtsubo, “Chaos synchronization and chaotic signal masking in semiconductor lasers with optical feedback,” IEEE J. of Quantum Electron. 38, 1141–1154 (2002).
[Crossref]

1999 (2)

J. Ohtsubo, “Feedback induced instability and chaos in semiconductor lasers and their applications,” Opt. Rev. 6, 1–15 (1999).
[Crossref]

J. S. Lawrence and D. M. Kane, “Injection locking suppression of coherence collapse in a diode laser with optical feedback,” Opt. Commun. 167, 273–282 (1999).
[Crossref]

1997 (2)

T. B. Simpson and J. M. Liu, “Enhanced modulation bandwidth in injection-locked semiconductor lasers,” IEEE Photon. Technol. Lett. 9, 1322–1324 (1997).
[Crossref]

T. B. Simpson, J. M. Liu, K. F. Huang, and K. Tai, “Nonlinear dynamics induced by external optical injection in semiconductor lasers,” Quantum Semiclass. Opt. 9, 765–784 (1997).
[Crossref]

1986 (1)

R. W. Tkach and A. R. Chraplyvy, “Regions of feedback effects in 1.5-um distributed feedback laser,” J. Light-wave Technol. LT-4, 1655–1661 (1986).
[Crossref]

AlMulla, M.

T. B. Simpson, J. M. Liu, M. AlMulla, N. G. Usechak, and V. Kovanis, “Linewidth sharpening via polarization-rotated feedback in optically injected semiconductor oscillators,” IEEE J. of Sel. Top. Quantum Electron. 19, 1500807 (2013).
[Crossref]

Atsuki, K.

A. Murakami, K. Kawashima, and K. Atsuki, “Cavity resonance shift and bandwidth enhancement in semiconductor lasers with strong light injection,” IEEE J. of Quantum Electron. 39, 1196–1204 (2003).
[Crossref]

Chan, S. C.

J. P. Zhuang and S. C. Chan, “Tunable photonics microwave generation using optically injected semiconductor laser dynamics with optical feedback stabilization,” Opt. Lett. 38, 344–346 (2013).
[Crossref] [PubMed]

S. C. Chan, “Analysis of an optically injected semiconductor laser for microwave generation,” IEEE J. Quantum Electron. 46, 421–428 (2010).
[Crossref]

S. C. Chan and J. M. Liu, “Tunable narrow-linewidth photonic microwave generation using semiconductor laser dynamics,” IEEE J. of Sel. Top. Quantum Electron. 10, 1025–1032 (2004).
[Crossref]

Chao, Y. K.

F. Y. Lin, Y. K. Chao, and T. C. Wu, “Effective bandwidths of broadband chaotic signals,” IEEE J. of Quantum Electron. 48, 1010–1014 (2011).
[Crossref]

Chen, S. C.

Chraplyvy, A. R.

R. W. Tkach and A. R. Chraplyvy, “Regions of feedback effects in 1.5-um distributed feedback laser,” J. Light-wave Technol. LT-4, 1655–1661 (1986).
[Crossref]

Colet, P.

R. Vicente, J. Daudén, P. Colet, and R. Toral, “Analysis and characterization of the hyperchaos generated by a semiconductor laser subject to a delayed feedback loop,” IEEE J. of Quantum Electron. 41, 541–548 (2005).
[Crossref]

Daudén, J.

R. Vicente, J. Daudén, P. Colet, and R. Toral, “Analysis and characterization of the hyperchaos generated by a semiconductor laser subject to a delayed feedback loop,” IEEE J. of Quantum Electron. 41, 541–548 (2005).
[Crossref]

Elsäßer, W.

T. Heil, I. Fischer, W. Elsäβer, B. Krauskopf, K. Green, and A. Gavrielides, “Delay dynamics of semiconductor lasers with short external cavities: Bifurcation scenarios and mechanisms,” Phys. Rev. E 67, 066214 (2003).
[Crossref]

Fischer, I.

T. Heil, I. Fischer, W. Elsäβer, B. Krauskopf, K. Green, and A. Gavrielides, “Delay dynamics of semiconductor lasers with short external cavities: Bifurcation scenarios and mechanisms,” Phys. Rev. E 67, 066214 (2003).
[Crossref]

Gavrielides, A.

T. Heil, I. Fischer, W. Elsäβer, B. Krauskopf, K. Green, and A. Gavrielides, “Delay dynamics of semiconductor lasers with short external cavities: Bifurcation scenarios and mechanisms,” Phys. Rev. E 67, 066214 (2003).
[Crossref]

Green, K.

T. Heil, I. Fischer, W. Elsäβer, B. Krauskopf, K. Green, and A. Gavrielides, “Delay dynamics of semiconductor lasers with short external cavities: Bifurcation scenarios and mechanisms,” Phys. Rev. E 67, 066214 (2003).
[Crossref]

Hasnain, C. C.

He, H. C.

A. B. Wang, Y. C. Wang, and H. C. He, “Enhancing the bandwidth of the optical chaotic signal generated by a semiconductor laser with optical feedback,” IEEE Photonic Technol. Lett. 20, 1633–1635 (2008).
[Crossref]

Heil, T.

T. Heil, I. Fischer, W. Elsäβer, B. Krauskopf, K. Green, and A. Gavrielides, “Delay dynamics of semiconductor lasers with short external cavities: Bifurcation scenarios and mechanisms,” Phys. Rev. E 67, 066214 (2003).
[Crossref]

Huang, K. F.

T. B. Simpson, J. M. Liu, K. F. Huang, and K. Tai, “Nonlinear dynamics induced by external optical injection in semiconductor lasers,” Quantum Semiclass. Opt. 9, 765–784 (1997).
[Crossref]

Hwang, S. K.

Juan, Y. S.

Y. S. Juan and F. Y. Lin, “Photonic generation of broadly tunable microwave signals utilizing a dual-beam optically injected semiconductor lasers,” IEEE Photonics J. 3, 644–650 (2011).
[Crossref]

Y. S. Juan and F. Y. Lin, “Ultra broadband microwave frequency combs generated by an optical pulse-injected semiconductor laser,” Opt. Express 17, 18596–18605 (2009).
[Crossref]

Kane, D. M.

J. S. Lawrence and D. M. Kane, “Injection locking suppression of coherence collapse in a diode laser with optical feedback,” Opt. Commun. 167, 273–282 (1999).
[Crossref]

Kawashima, K.

A. Murakami, K. Kawashima, and K. Atsuki, “Cavity resonance shift and bandwidth enhancement in semiconductor lasers with strong light injection,” IEEE J. of Quantum Electron. 39, 1196–1204 (2003).
[Crossref]

Kovanis, V.

T. B. Simpson, J. M. Liu, M. AlMulla, N. G. Usechak, and V. Kovanis, “Linewidth sharpening via polarization-rotated feedback in optically injected semiconductor oscillators,” IEEE J. of Sel. Top. Quantum Electron. 19, 1500807 (2013).
[Crossref]

Krauskopf, B.

S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, “The dynamical complexity of optically injected semiconductor lasers,” Phys. Rep. 416, 1–128 (2005).
[Crossref]

T. Heil, I. Fischer, W. Elsäβer, B. Krauskopf, K. Green, and A. Gavrielides, “Delay dynamics of semiconductor lasers with short external cavities: Bifurcation scenarios and mechanisms,” Phys. Rev. E 67, 066214 (2003).
[Crossref]

Lau, E. K.

Lawrence, J. S.

J. S. Lawrence and D. M. Kane, “Injection locking suppression of coherence collapse in a diode laser with optical feedback,” Opt. Commun. 167, 273–282 (1999).
[Crossref]

Lenstra, D.

S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, “The dynamical complexity of optically injected semiconductor lasers,” Phys. Rep. 416, 1–128 (2005).
[Crossref]

Liao, Y. H.

Y. H. Liao, J. M. Liu, and F. Y. Lin, “Dynamical characteristics of a dual-beam optically injected semiconductor laser,” IEEE J. of Sel. Top. Quantum Electron. 19, 1500606 (2013).
[Crossref]

Lin, F. Y.

Y. H. Liao, J. M. Liu, and F. Y. Lin, “Dynamical characteristics of a dual-beam optically injected semiconductor laser,” IEEE J. of Sel. Top. Quantum Electron. 19, 1500606 (2013).
[Crossref]

F. Y. Lin, Y. K. Chao, and T. C. Wu, “Effective bandwidths of broadband chaotic signals,” IEEE J. of Quantum Electron. 48, 1010–1014 (2011).
[Crossref]

Y. S. Juan and F. Y. Lin, “Photonic generation of broadly tunable microwave signals utilizing a dual-beam optically injected semiconductor lasers,” IEEE Photonics J. 3, 644–650 (2011).
[Crossref]

Y. S. Juan and F. Y. Lin, “Ultra broadband microwave frequency combs generated by an optical pulse-injected semiconductor laser,” Opt. Express 17, 18596–18605 (2009).
[Crossref]

F. Y. Lin and J. M. Liu, “Nonlinear dynamical characteristics of an optically injected semiconductor laser subject to optoelectronic feedback,” Opt. Commun. 221, 173–180 (2003).
[Crossref]

Liu, J. M.

Y. H. Liao, J. M. Liu, and F. Y. Lin, “Dynamical characteristics of a dual-beam optically injected semiconductor laser,” IEEE J. of Sel. Top. Quantum Electron. 19, 1500606 (2013).
[Crossref]

T. B. Simpson, J. M. Liu, M. AlMulla, N. G. Usechak, and V. Kovanis, “Linewidth sharpening via polarization-rotated feedback in optically injected semiconductor oscillators,” IEEE J. of Sel. Top. Quantum Electron. 19, 1500807 (2013).
[Crossref]

S. C. Chen, S. K. Hwang, and J. M. Liu, “Period-one oscillation for photonic microwave transmission using an optically injected semiconductor laser,” Opt. Express 15, 14921–14935 (2007).
[Crossref]

S. C. Chan and J. M. Liu, “Tunable narrow-linewidth photonic microwave generation using semiconductor laser dynamics,” IEEE J. of Sel. Top. Quantum Electron. 10, 1025–1032 (2004).
[Crossref]

F. Y. Lin and J. M. Liu, “Nonlinear dynamical characteristics of an optically injected semiconductor laser subject to optoelectronic feedback,” Opt. Commun. 221, 173–180 (2003).
[Crossref]

T. B. Simpson, J. M. Liu, K. F. Huang, and K. Tai, “Nonlinear dynamics induced by external optical injection in semiconductor lasers,” Quantum Semiclass. Opt. 9, 765–784 (1997).
[Crossref]

T. B. Simpson and J. M. Liu, “Enhanced modulation bandwidth in injection-locked semiconductor lasers,” IEEE Photon. Technol. Lett. 9, 1322–1324 (1997).
[Crossref]

Murakami, A.

A. Murakami, K. Kawashima, and K. Atsuki, “Cavity resonance shift and bandwidth enhancement in semiconductor lasers with strong light injection,” IEEE J. of Quantum Electron. 39, 1196–1204 (2003).
[Crossref]

Ohtsubo, J.

Y. Takiguchi, K. Ohyagi, and J. Ohtsubo, “Bandwidth-enhanced chaos synchronization in strongly injection-locked semiconductor lasers with optical feedback,” Opt. Lett. 28, 319–321 (2003).
[Crossref] [PubMed]

J. Ohtsubo, “Chaos synchronization and chaotic signal masking in semiconductor lasers with optical feedback,” IEEE J. of Quantum Electron. 38, 1141–1154 (2002).
[Crossref]

J. Ohtsubo, “Feedback induced instability and chaos in semiconductor lasers and their applications,” Opt. Rev. 6, 1–15 (1999).
[Crossref]

Ohyagi, K.

Parekh, D.

Simpson, T. B.

T. B. Simpson, J. M. Liu, M. AlMulla, N. G. Usechak, and V. Kovanis, “Linewidth sharpening via polarization-rotated feedback in optically injected semiconductor oscillators,” IEEE J. of Sel. Top. Quantum Electron. 19, 1500807 (2013).
[Crossref]

S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, “The dynamical complexity of optically injected semiconductor lasers,” Phys. Rep. 416, 1–128 (2005).
[Crossref]

T. B. Simpson, J. M. Liu, K. F. Huang, and K. Tai, “Nonlinear dynamics induced by external optical injection in semiconductor lasers,” Quantum Semiclass. Opt. 9, 765–784 (1997).
[Crossref]

T. B. Simpson and J. M. Liu, “Enhanced modulation bandwidth in injection-locked semiconductor lasers,” IEEE Photon. Technol. Lett. 9, 1322–1324 (1997).
[Crossref]

Sung, H. K.

Tai, K.

T. B. Simpson, J. M. Liu, K. F. Huang, and K. Tai, “Nonlinear dynamics induced by external optical injection in semiconductor lasers,” Quantum Semiclass. Opt. 9, 765–784 (1997).
[Crossref]

Takiguchi, Y.

Tkach, R. W.

R. W. Tkach and A. R. Chraplyvy, “Regions of feedback effects in 1.5-um distributed feedback laser,” J. Light-wave Technol. LT-4, 1655–1661 (1986).
[Crossref]

Toral, R.

R. Vicente, J. Daudén, P. Colet, and R. Toral, “Analysis and characterization of the hyperchaos generated by a semiconductor laser subject to a delayed feedback loop,” IEEE J. of Quantum Electron. 41, 541–548 (2005).
[Crossref]

Usechak, N. G.

T. B. Simpson, J. M. Liu, M. AlMulla, N. G. Usechak, and V. Kovanis, “Linewidth sharpening via polarization-rotated feedback in optically injected semiconductor oscillators,” IEEE J. of Sel. Top. Quantum Electron. 19, 1500807 (2013).
[Crossref]

Vicente, R.

R. Vicente, J. Daudén, P. Colet, and R. Toral, “Analysis and characterization of the hyperchaos generated by a semiconductor laser subject to a delayed feedback loop,” IEEE J. of Quantum Electron. 41, 541–548 (2005).
[Crossref]

Wang, A. B.

A. B. Wang, Y. C. Wang, and J. F. Wang, “Route to broadband chaos in a chaotic laser diode subject to optical injection,” Opt. Lett. 34, 1144–1146 (2009).
[Crossref] [PubMed]

A. B. Wang, Y. C. Wang, and H. C. He, “Enhancing the bandwidth of the optical chaotic signal generated by a semiconductor laser with optical feedback,” IEEE Photonic Technol. Lett. 20, 1633–1635 (2008).
[Crossref]

Wang, J. F.

Wang, Y. C.

A. B. Wang, Y. C. Wang, and J. F. Wang, “Route to broadband chaos in a chaotic laser diode subject to optical injection,” Opt. Lett. 34, 1144–1146 (2009).
[Crossref] [PubMed]

A. B. Wang, Y. C. Wang, and H. C. He, “Enhancing the bandwidth of the optical chaotic signal generated by a semiconductor laser with optical feedback,” IEEE Photonic Technol. Lett. 20, 1633–1635 (2008).
[Crossref]

Wieczorek, S.

S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, “The dynamical complexity of optically injected semiconductor lasers,” Phys. Rep. 416, 1–128 (2005).
[Crossref]

Wu, M. C.

Wu, T. C.

F. Y. Lin, Y. K. Chao, and T. C. Wu, “Effective bandwidths of broadband chaotic signals,” IEEE J. of Quantum Electron. 48, 1010–1014 (2011).
[Crossref]

Zhao, X.

Zhuang, J. P.

IEEE J. of Quantum Electron. (4)

A. Murakami, K. Kawashima, and K. Atsuki, “Cavity resonance shift and bandwidth enhancement in semiconductor lasers with strong light injection,” IEEE J. of Quantum Electron. 39, 1196–1204 (2003).
[Crossref]

J. Ohtsubo, “Chaos synchronization and chaotic signal masking in semiconductor lasers with optical feedback,” IEEE J. of Quantum Electron. 38, 1141–1154 (2002).
[Crossref]

R. Vicente, J. Daudén, P. Colet, and R. Toral, “Analysis and characterization of the hyperchaos generated by a semiconductor laser subject to a delayed feedback loop,” IEEE J. of Quantum Electron. 41, 541–548 (2005).
[Crossref]

F. Y. Lin, Y. K. Chao, and T. C. Wu, “Effective bandwidths of broadband chaotic signals,” IEEE J. of Quantum Electron. 48, 1010–1014 (2011).
[Crossref]

IEEE J. of Sel. Top. Quantum Electron. (3)

T. B. Simpson, J. M. Liu, M. AlMulla, N. G. Usechak, and V. Kovanis, “Linewidth sharpening via polarization-rotated feedback in optically injected semiconductor oscillators,” IEEE J. of Sel. Top. Quantum Electron. 19, 1500807 (2013).
[Crossref]

Y. H. Liao, J. M. Liu, and F. Y. Lin, “Dynamical characteristics of a dual-beam optically injected semiconductor laser,” IEEE J. of Sel. Top. Quantum Electron. 19, 1500606 (2013).
[Crossref]

S. C. Chan and J. M. Liu, “Tunable narrow-linewidth photonic microwave generation using semiconductor laser dynamics,” IEEE J. of Sel. Top. Quantum Electron. 10, 1025–1032 (2004).
[Crossref]

IEEE J. Quantum Electron. (1)

S. C. Chan, “Analysis of an optically injected semiconductor laser for microwave generation,” IEEE J. Quantum Electron. 46, 421–428 (2010).
[Crossref]

IEEE Photon. Technol. Lett. (1)

T. B. Simpson and J. M. Liu, “Enhanced modulation bandwidth in injection-locked semiconductor lasers,” IEEE Photon. Technol. Lett. 9, 1322–1324 (1997).
[Crossref]

IEEE Photonic Technol. Lett. (1)

A. B. Wang, Y. C. Wang, and H. C. He, “Enhancing the bandwidth of the optical chaotic signal generated by a semiconductor laser with optical feedback,” IEEE Photonic Technol. Lett. 20, 1633–1635 (2008).
[Crossref]

IEEE Photonics J. (1)

Y. S. Juan and F. Y. Lin, “Photonic generation of broadly tunable microwave signals utilizing a dual-beam optically injected semiconductor lasers,” IEEE Photonics J. 3, 644–650 (2011).
[Crossref]

J. Light-wave Technol. (1)

R. W. Tkach and A. R. Chraplyvy, “Regions of feedback effects in 1.5-um distributed feedback laser,” J. Light-wave Technol. LT-4, 1655–1661 (1986).
[Crossref]

Opt. Commun. (2)

J. S. Lawrence and D. M. Kane, “Injection locking suppression of coherence collapse in a diode laser with optical feedback,” Opt. Commun. 167, 273–282 (1999).
[Crossref]

F. Y. Lin and J. M. Liu, “Nonlinear dynamical characteristics of an optically injected semiconductor laser subject to optoelectronic feedback,” Opt. Commun. 221, 173–180 (2003).
[Crossref]

Opt. Express (3)

Opt. Lett. (3)

Opt. Rev. (1)

J. Ohtsubo, “Feedback induced instability and chaos in semiconductor lasers and their applications,” Opt. Rev. 6, 1–15 (1999).
[Crossref]

Phys. Rep. (1)

S. Wieczorek, B. Krauskopf, T. B. Simpson, and D. Lenstra, “The dynamical complexity of optically injected semiconductor lasers,” Phys. Rep. 416, 1–128 (2005).
[Crossref]

Phys. Rev. E (1)

T. Heil, I. Fischer, W. Elsäβer, B. Krauskopf, K. Green, and A. Gavrielides, “Delay dynamics of semiconductor lasers with short external cavities: Bifurcation scenarios and mechanisms,” Phys. Rev. E 67, 066214 (2003).
[Crossref]

Quantum Semiclass. Opt. (1)

T. B. Simpson, J. M. Liu, K. F. Huang, and K. Tai, “Nonlinear dynamics induced by external optical injection in semiconductor lasers,” Quantum Semiclass. Opt. 9, 765–784 (1997).
[Crossref]

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Figures (8)

Fig. 1
Fig. 1 Experimental setup of the semiconductor laser subject to both the OI and the OF.
Fig. 2
Fig. 2 Transitions of the optical spectra for the SL subject to (a) OI with f = 5.6 GHz and (b) OF with different ξi and ξfb, respectively. The red dots mark the νSL.
Fig. 3
Fig. 3 Δf of the SL under different ξi and ξfb. The solid squares, triangles, and circles are obtained with the OI scheme for detuning frequencies of f = 5.6, 9.3, and 13.7 GHz, and open circles are obtained with the OF scheme, respectively.
Fig. 4
Fig. 4 Mapping of dynamical scenarios and states under different ξi and ξfb when the SL is subject to both the OI and the OF simultaneously. The detuning frequency is fixed at f = 5.6 GHz. Different dynamical scenarios (separated with the black curves) are defined and differentiated by whether the dynamics and the characteristics frequencies originated from the OI or the OF alone are being preserved (P), shifted (S), or suppressed (S′) after both the OI and the OF lights are simultaneously injected. The letter L is used when the SL is stably locked by the OI light. In the two-letter symbols, the first and the second letters are each corresponding to the effects from the OI and the OF respectively. Regions of dynamical states including the period-one (P1), period-two (P2), quasi-periodic (QP), chaos oscillation (CO), and stable locking (L) are colored in red, cyan, green, gray, and yellow, respectively.
Fig. 5
Fig. 5 Power spectra of the (a)–(c) P2 and (d)–(f) P1 states obtained with ξi = 0.21 and ξi = 0.31 when ξfb is increased from 0, 0.008, to 0.03, respectively. The relative locations of these states in the parameter space are also marked in Fig. 4.
Fig. 6
Fig. 6 Power spectra of the (a)–(c) CO and (d) L states obtained with ξfb = 0.06 when ξi is increased from 0, 0.15, 0.21, to 0.85, respectively. The relative locations of these states in the parameter space are also marked in Fig. 4.
Fig. 7
Fig. 7 The boundaries of injection locking for different ξfb. The dashed lines are the fitting curves of the Hopf and saddle-node bifurcations. The stars marked at the apexes of each locking regions indicate the optimal operation points where minimum ξi are required to stabilize the SL.
Fig. 8
Fig. 8 (a) fopt (solid black curve labeled on the left) and Δf (dashed gray curve labeled on the right) for different ξfb. (b) The threshold (minimum) injection strength ξi,th needed to stabilize the laser under different ξfb. The black curve is obtained when the detuning frequency f is optimized under different ξfb according to the fopt shown in Fig. 8(a). The red and blue curves are obtained with fixed f at −7.5 GHz and 5.6 GHz, respectively.

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