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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 3 — Feb. 11, 2013
  • pp: 3125–3132
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Experimental and theoretical study of wide hysteresis cycles in 1550 nm VCSELs under optical injection

Peng Guo, Weijian Yang, Devang Parekh, Connie J. Chang-Hasnain, Anshi Xu, and Zhangyuan Chen  »View Author Affiliations


Optics Express, Vol. 21, Issue 3, pp. 3125-3132 (2013)
http://dx.doi.org/10.1364/OE.21.003125


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Abstract

We present experimental results of output power bistability in a vertical-cavity surface-emitting laser under optical injection induced by frequency detuning or power variation of the master laser. An ultra-wide hysteresis cycle of 3.7 nm (473.3 GHz) is achieved through frequency detuning, which is more than 11 times wider than that achieved in the state-of-the-art (37 GHz). Furthermore, the width of injection power induced hysteresis cycle we achieved is as large as 7.3 dB. We theoretically analyzed the hysteresis cycles based on standard optical injection locking rate equations including the interference effect of master laser reflection and found excellent agreement with experimental results.

© 2013 OSA

1. Introduction

Vertical-cavity surface-emitting lasers (VCSELs) have been proven to have a number of unique advantageous features over other types of semiconductor lasers. These advantages include cost efficiency, easiness for fiber coupling and intrinsically single longitudinal mode. Optical injection locking (OIL) of VCSELs has demonstrated significant performance improvement over directly modulated VCSELs in experiments [1

1. A. Ng'oma, D. Fortusini, D. Parekh, W. Yang, M. Sauer, S. Benjamin, W. Hofmann, M. C. Amann, and C. J. Chang-Hasnain, “Performance of a multi-Gb/s 60 GHz radio over fiber system employing a directly modulated optically injection-locked VCSEL,” J. Lightwave Technol. 28(16), 2436–2444 (2010). [CrossRef]

3

3. L. Chrostowski, X. Zhao, and C. J. Chang-Hasnain, “Microwave performance of optically injection-locked VCSELs,” IEEE Trans. Microw. Theory Tech. 54(2), 788–796 (2006). [CrossRef]

], which are well analyzed and explained from a theoretical point of view [4

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

6

6. W. Yang, P. Guo, D. Parekh, and C. J. Chang-Hasnain, “Reflection-mode optical injection locking,” Opt. Express 18(20), 20887–20893 (2010). [CrossRef] [PubMed]

]. Optical injection of VCSELs is also an attractive method to obtain polarization bistability [7

7. I. Gatare, K. Panajotov, and M. Sciamanna, “Frequency-induced polarization bistability in vertical-cavity surface-emitting lasers with orthogonal optical injection,” Phys. Rev. A 75(2), 023804 (2007). [CrossRef]

9

9. A. Hurtado, A. Quirce, A. Valle, L. Pesquera, and M. J. Adams, “Power and wavelength polarization bistability with very wide hysteresis cycles in a 1550 nm-VCSEL subject to orthogonal optical injection,” Opt. Express 17(26), 23637–23642 (2009). [CrossRef] [PubMed]

] which is promising for optical communication, optical switching, and optical data processing [10

10. S. H. Lee, H. W. Jung, K. H. Kim, M. H. Lee, B.-S. Yoo, J. Roh, and K. A. Shore, “1-GHz all-optical flip-flop operation of conventional cylindrical-shaped single-mode VCSELs under low power optical injection,” IEEE Photon. Technol. Lett. 22(23), 1759–1761 (2010). [CrossRef]

].

In this paper, we report ultra-wide hysteresis cycles of OIL-VCSEL power as a function of master laser frequency and power. Super wide hysteresis cycle of 473.3 GHz is achieved through high injection power (14 dBm), which is more than 11 times wider than that achieved in the state-of-the-art (37 GHz) [8

8. A. Quirce, A. Valle, and L. Pesquera, “Very wide hysteresis cycles in 1550 nm-VCSELs subject to orthogonal optical injection,” IEEE Photon. Technol. Lett. 21(17), 1193–1195 (2009). [CrossRef]

]. We provide theoretical analysis of the wide hysteresis cycles based on standard optical injection locking rate equation [5

5. E. K. Lau, L. Wong, and M. C. Wu, “Enhanced modulation characteristics of optical injection-locked lasers: A tutorial,” IEEE J. Sel. Top. Quantum Electron. 15(3), 618–633 (2009). [CrossRef]

] including the interference effect of master laser reflection [6

6. W. Yang, P. Guo, D. Parekh, and C. J. Chang-Hasnain, “Reflection-mode optical injection locking,” Opt. Express 18(20), 20887–20893 (2010). [CrossRef] [PubMed]

] for the first time. The changed trend of output power and the shape of hysteresis cycles are calculated. The simulation results show excellent agreement with our experimental results.

2. Experimental setup

The experimental setup is shown in Fig. 1(a)
Fig. 1 (a) Schematic of experimental setup. (VCSEL: vertical-cavity surface-emitting laser; TUL: tunable laser; OC: optical circulator; PC: polarization controller; OSA: optical spectrum analyzer; PM: Power Meter). (b) Spectrum of the 1550 nm-VCSEL. The two modes (λ = 1531.30 nm, λ = 1531.02 nm) correspond to the two polarizations of the fundamental transverse mode of the VCSEL.
. A commercial high power tunable laser is used as the master laser. The slave laser is a single-mode 1.55 μm VCSEL designed with buried tunnel junction (BTJ) structure to confine both current and light [11

11. W. Hofmann, N. H. Zhu, M. Ortsiefer, G. Bohm, Y. Liu, and M.-C. Amann, “High speed (>11 GHz) modulation of BCB-passivated 1.55 µm InGaAlAs-InP VCSELs,” Electron. Lett. 42(17), 976–977 (2006). [CrossRef]

]. The master laser injection-locks the slave laser through an optical circulator (OC). Polarization controller (PC) is used to match the master polarization with the VCSEL’s preferred polarization. An optical spectrum analyzer (OSA) is used to monitor the locking condition and an optical power meter is used to monitor the total optical power.

The VCSEL is biased at 7.0 mA to yield −5.0 dBm free-running output power at room temperature 294.0 K. Figure 1(b) shows the optical spectrum of this VCSEL. Two polarization modes are 0.28 nm apart from each other (λ = 1531.30 nm, λ = 1531.02 nm) with 30 dB side mode suppression ratio. The polarization of master laser is controlled by PC to match the strong polarization mode (λ) of VCSEL.

3. Experimental results

3.1 Hysteresis cycles achieved by sweeping wavelength detuning

We investigate the locking range and output power of an OIL-VCSEL as a function of the direction of sweep of the master laser wavelength. The master laser sweeping from a wavelength shorter than that of the slave laser, the locking range is significantly larger than the other way around. Figures 2(a)
Fig. 2 (a) Total optical output power on the locking map with increased wavelength detuning. (b) Total optical output power on the locking map with decreased wavelength detuning.
and 2(b) show the locking maps of VCSEL as a function of wavelength detuning and injection power ratio. Figure 2(a) shows the master wavelength increasing from a value shorter than VCSEL wavelength, and the other way around in (b). The total VCSEL output power is shown as color contours. In this experiment, the injection power of master laser is changed from 10.0 dBm to 15.0 dBm, so injection ratio (Rinj = PMaster/PSlave) changes from 15.0 dB to 20.0 dB correspondingly. Wavelength detuning (Δλ = λMaster–λSlave∥) changes from −1.2 nm to 5.4 nm. The locking cut-off wavelengths on the blue side (short) are nearly the same. However, the red edges of the locking ranges are significantly different due to the slave laser cavity resonance shift with strong light injection [4

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

,12

12. P. Guo, W. Yang, D. Parekh, A. Xu, Z. Chen, and C. J. Chang-Hasnain, “An ellipse model for cavity mode behavior of optically injection-locked VCSELs,” Opt. Express 20(7), 6980–6988 (2012). [CrossRef] [PubMed]

].

The hysteresis of output power under three specific conditions (Rinj = 16.0 dB, 17.5 dB, 19.0 dB) are plotted in Fig. 3
Fig. 3 Total output power curves when wavelength detuning increases (solid lines) and decreases (dashed lines), for an injection ratio of (a) 16.0 dB, (b) 17.5 dB, and (c) 19.0 dB.
, which correspond to straight lines at fixed x-axis in Figs. 2(a) and 2(b). In Fig. 3(a), injection ratio is fixed at 16.0 dB. The output power is 4.4 dBm when the slave laser is unlocked. When detuning is increased to −0.62 nm, VCSEL is injection locked. The total output power decreases with a further detuning. The minimum output power goes to −2.2 dBm when the VCSEL is locked. As red detuning of master laser wavelength continues, VCSEL is suddenly unlocked and the output power returns to 4.4 dBm. The black dashed curve exhibits the output power when wavelength detuning direction is reversed. Under this condition, locking range shrinks from 2.2 nm to 0.8 nm, so the width of this hysteresis cycle is 1.4 nm (= 2.2 nm - 0.8 nm).

When injection ratio is increased, the width of the hysteresis cycle increases. The widths are 2.3 nm and 3.7 nm respectively in Figs. 3(b) and 3(c), corresponding to Rinj = 17.5 dB and 19.0 dB. They all display anticlockwise optical bistability under these three conditions.

In our experiment, the polarization of master laser matches the strong polarization mode (λ) of VCSEL. It should be pointed out that similar results can be obtained with optical injection to match the weak polarization mode (λ) of VCSEL.

3.2 Hysteresis cycles achieved by sweeping injection ratio

When wavelength detuning is fixed, hysteresis cycles can be obtained by sweeping injection ratio. This corresponds to lines at fixed y-values in Figs. 2(a) and 2(b). In Fig. 4(a)
Fig. 4 Total output power curves when injection ratio increases (solid lines) and decreases (dashed lines), for a wavelength detuning of (a) 0.25 nm, (b) 0.32 nm, and (c) 0.44 nm.
, when injection ratio increases to 15.7 dB, VCSEL is switched from free running condition to injection locked condition. The output power changes from 4.0 dBm to 2.4 dBm. When injection ratio decreases, the switch point of injection ratio from locking to free running is at 11.6 dB. At this point, output power suddenly increases from −7.3 dBm to 0.7 dBm. The width of the hysteresis cycle is 4.1 dB (= 15.7 dB - 11.6 dB).

Figure 4 compares the wavelength detuning dependence of the hysteresis cycles. When the detuning increases from 0.25 nm to 0.44 nm, the width of the cycles increases from 4.1 dB to 7.3 dB. They are all clockwise optical bistability cycles under these three conditions.

4. Theory and simulation results

4.1 Simulate hysteresis phenomenon based on standard OIL rate equations

Hysteresis cycles can be easily explained by frequency pulling effect in a very intuitive way. However, this hysteresis phenomenon has never been analyzed by standard OIL rate equations. We present the hysteresis cycle simulated based on these equations for the first time. The standard OIL rate equations are used for numerical simulation as follows [5

5. E. K. Lau, L. Wong, and M. C. Wu, “Enhanced modulation characteristics of optical injection-locked lasers: A tutorial,” IEEE J. Sel. Top. Quantum Electron. 15(3), 618–633 (2009). [CrossRef]

]:

dSdt=[Γvggn(NNtr)Va(1+εS)1τp]S+βBVaN2+2κSinjScosϕ
(1)
dϕdt=α2[Γvggn(NNtr)Va(1+εS)1τp]2πΔfκSinjSsinϕ
(2)
dNdt=IbiasqNτNΓvggn(NNtr)Va(1+εS)S
(3)

The locking state of black point in Fig. 5 is stable in our calculation, so the black point’s stable values of S0, ϕ0 and N0 are achieved and act as red point’s initial values. For the red point’s calculation, Figs. 6(a)
Fig. 6 (a)-(c) The details of red point’s S (photon number), ϕ (relative phase difference) and N (carrier number) in time domain within the 0.1 ns time series are plotted. (d) The trace of N~As (optical field vector) is plotted in 3D space.
to 6(c) show the evolution of S, ϕ and N in time domain based on standard OIL rate Eqs. (1) to (3). These three values are converged after 0.05 ns as is depicted in Figs. 6(a) to 6(c), which means the locking condition is stable at this red point. In order to clearly and distinctly see how these three values become stable, Fig. 6(d) is plotted. Horizontal dimension of Fig. 6(d) is corresponding to light field complex plane which can be calculated by S and ϕ in Figs. 6(a) and 6(b). Vertical dimension of Fig. 6(d) is corresponding to the carrier number which is the same as Fig. 6(c). Thus the convergence trajectory is easily verified, and the coordinate point converges to a stable red point in Fig. 6(d).

For decreasing wavelength detuning condition, the locking state of gray point is unstable in our calculation, so the free running stable values should be used as blue point’s initial values. For the blue point’s calculation, Figs. 7(a)
Fig. 7 (a)-(c) The details of blue point’s S, ϕ and N in time domain within the 0.1 ns time series are plotted. (d) The trace of N~As is plotted in 3D space.
to 7(c) show the evolution of S, ϕ and N in initial 0.1 ns. Phase value of Fig. 7(b) is limited between 0 and 2π. These three values are not converged in 10.0 ns based on our calculation which means the locking condition is unstable at this blue point. The divergent trajectory is easily verified in Fig. 7(d), and the coordinate point doesn’t converge to a stable point during a reasonable long period of time. The frequency of this oscillation is corresponding to the frequency difference between the master and the slave laser (beating frequency: f = Δλ = 200 GHz). The average output power in time domain is fixed after a reasonable long period of time (2 ns in the blue point calculation), and the average output power is used to plot the hysteresis cycle in Fig. 5.

Based on above analysis, the red and the blue points’ locking states are different, even though they are under the same locking condition (Rinj = 15.0 dB, Δλ = 1.6 nm). This leads to the hysteresis of OIL-VCSEL output power.

4.2 Calculate the hysteresis cycle including the interference effect

5. Discussion: an intuitive explanation of hysteresis cycles based on ellipse model

After simulating hysteresis cycles based on standard OIL rate equations, an intuitive visualization and simple explanation can be provided based on the ellipse model [12

12. P. Guo, W. Yang, D. Parekh, A. Xu, Z. Chen, and C. J. Chang-Hasnain, “An ellipse model for cavity mode behavior of optically injection-locked VCSELs,” Opt. Express 20(7), 6980–6988 (2012). [CrossRef] [PubMed]

]. We previously reported a new graphical tool to analyze OIL-VCSELs. It predicts the cavity mode behavior for VCSELs under injection locking. Figure 9(a)
Fig. 9 The ellipse model provides an intuitive visualization of the OIL bistability process and spectra. The origin is set to be λslave0 and the x-axis and y-axis is λcavity and λmaster. For each detuning value, a horizontal line y = λmaster intersects y = x and the solid blue curve. The x-coordinates of the two intersecting points represent the optical spectrum of λmaster and λcavity. (a) Increased wavelength detuning. (b) Decreased wavelength detuning.
shows the positions of master laser’s wavelength and slave laser’s cavity mode under different locking conditions with increased wavelength detuning. When λmaster = λi, the slave laser is not locked and stays at the origin which is set to be λslave0. The locking starts when λmaster increases further to y = λii, which intercepts with the ellipse at point a. This continues until the master wavelength increases beyond point b. Before point b, master laser’s wavelength pushes the slave laser’s cavity mode to red shift which is called frequency pulling effect [4

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

]. Figure 9(b) shows the other condition with decreasing wavelength detuning. When λmaster = λiv, the slave laser is not locked and stays at the origin λslave0. The locking starts when λmaster decreases further to y = λiii, which intercepts with the ellipse at points b’ and c’. In the beginning of this locking, the slave laser’s cavity mode is located at point c’. The ϕ of this point on the ellipse is π/2. However, only when ϕ falls in the range from -π/2-π/2 to cot−1α (α: linewidth enhancement factor) can the slaved laser reach a steady locking state [4

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

, 5

5. E. K. Lau, L. Wong, and M. C. Wu, “Enhanced modulation characteristics of optical injection-locked lasers: A tutorial,” IEEE J. Sel. Top. Quantum Electron. 15(3), 618–633 (2009). [CrossRef]

]. So the cavity mode of slave laser will red shift from point c’ to point b’, and reach a steady locking state on the ellipse. This continues until the master wavelength decreases below point a’.

6. Conclusion

Acknowledgments

The authors wish to acknowledge the support of the National Basic Research Program of China (973 Program 2012CB315606 and 2010CB328201), the State Key Laboratory of Advanced Optical Communication Systems and Networks, China. CCH acknowledges support by the US Department of Defense National Security Science and Engineering Faculty Fellowship N00244-09-1-0013, and Chang Jiang Scholar Endowed Chair Professorship. The authors thank Ms. Rongrong Gu for correcting the English manuscript.

References and links

1.

A. Ng'oma, D. Fortusini, D. Parekh, W. Yang, M. Sauer, S. Benjamin, W. Hofmann, M. C. Amann, and C. J. Chang-Hasnain, “Performance of a multi-Gb/s 60 GHz radio over fiber system employing a directly modulated optically injection-locked VCSEL,” J. Lightwave Technol. 28(16), 2436–2444 (2010). [CrossRef]

2.

D. Parekh, B. Zhang, X. Zhao, Y. Yue, W. Hofmann, M. C. Amann, A. Willner, and C. J. Chang-Hasnain, “Long distance single-mode fiber transmission of multimode VCSELs by injection locking,” Opt. Express 18(20), 20552–20557 (2010). [CrossRef] [PubMed]

3.

L. Chrostowski, X. Zhao, and C. J. Chang-Hasnain, “Microwave performance of optically injection-locked VCSELs,” IEEE Trans. Microw. Theory Tech. 54(2), 788–796 (2006). [CrossRef]

4.

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

5.

E. K. Lau, L. Wong, and M. C. Wu, “Enhanced modulation characteristics of optical injection-locked lasers: A tutorial,” IEEE J. Sel. Top. Quantum Electron. 15(3), 618–633 (2009). [CrossRef]

6.

W. Yang, P. Guo, D. Parekh, and C. J. Chang-Hasnain, “Reflection-mode optical injection locking,” Opt. Express 18(20), 20887–20893 (2010). [CrossRef] [PubMed]

7.

I. Gatare, K. Panajotov, and M. Sciamanna, “Frequency-induced polarization bistability in vertical-cavity surface-emitting lasers with orthogonal optical injection,” Phys. Rev. A 75(2), 023804 (2007). [CrossRef]

8.

A. Quirce, A. Valle, and L. Pesquera, “Very wide hysteresis cycles in 1550 nm-VCSELs subject to orthogonal optical injection,” IEEE Photon. Technol. Lett. 21(17), 1193–1195 (2009). [CrossRef]

9.

A. Hurtado, A. Quirce, A. Valle, L. Pesquera, and M. J. Adams, “Power and wavelength polarization bistability with very wide hysteresis cycles in a 1550 nm-VCSEL subject to orthogonal optical injection,” Opt. Express 17(26), 23637–23642 (2009). [CrossRef] [PubMed]

10.

S. H. Lee, H. W. Jung, K. H. Kim, M. H. Lee, B.-S. Yoo, J. Roh, and K. A. Shore, “1-GHz all-optical flip-flop operation of conventional cylindrical-shaped single-mode VCSELs under low power optical injection,” IEEE Photon. Technol. Lett. 22(23), 1759–1761 (2010). [CrossRef]

11.

W. Hofmann, N. H. Zhu, M. Ortsiefer, G. Bohm, Y. Liu, and M.-C. Amann, “High speed (>11 GHz) modulation of BCB-passivated 1.55 µm InGaAlAs-InP VCSELs,” Electron. Lett. 42(17), 976–977 (2006). [CrossRef]

12.

P. Guo, W. Yang, D. Parekh, A. Xu, Z. Chen, and C. J. Chang-Hasnain, “An ellipse model for cavity mode behavior of optically injection-locked VCSELs,” Opt. Express 20(7), 6980–6988 (2012). [CrossRef] [PubMed]

OCIS Codes
(140.3520) Lasers and laser optics : Lasers, injection-locked
(190.1450) Nonlinear optics : Bistability
(250.7260) Optoelectronics : Vertical cavity surface emitting lasers

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: December 5, 2012
Revised Manuscript: January 11, 2013
Manuscript Accepted: January 23, 2013
Published: February 1, 2013

Citation
Peng Guo, Weijian Yang, Devang Parekh, Connie J. Chang-Hasnain, Anshi Xu, and Zhangyuan Chen, "Experimental and theoretical study of wide hysteresis cycles in 1550 nm VCSELs under optical injection," Opt. Express 21, 3125-3132 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-3-3125


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References

  1. A. Ng'oma, D. Fortusini, D. Parekh, W. Yang, M. Sauer, S. Benjamin, W. Hofmann, M. C. Amann, and C. J. Chang-Hasnain, “Performance of a multi-Gb/s 60 GHz radio over fiber system employing a directly modulated optically injection-locked VCSEL,” J. Lightwave Technol.28(16), 2436–2444 (2010). [CrossRef]
  2. D. Parekh, B. Zhang, X. Zhao, Y. Yue, W. Hofmann, M. C. Amann, A. Willner, and C. J. Chang-Hasnain, “Long distance single-mode fiber transmission of multimode VCSELs by injection locking,” Opt. Express18(20), 20552–20557 (2010). [CrossRef] [PubMed]
  3. L. Chrostowski, X. Zhao, and C. J. Chang-Hasnain, “Microwave performance of optically injection-locked VCSELs,” IEEE Trans. Microw. Theory Tech.54(2), 788–796 (2006). [CrossRef]
  4. A. Murakami, K. Kawashima, and K. Atsuki, “Cavity resonance shift and bandwidth enhancement in semiconductor lasers with strong light injection,” IEEE J. Quantum Electron.39(10), 1196–1204 (2003). [CrossRef]
  5. E. K. Lau, L. Wong, and M. C. Wu, “Enhanced modulation characteristics of optical injection-locked lasers: A tutorial,” IEEE J. Sel. Top. Quantum Electron.15(3), 618–633 (2009). [CrossRef]
  6. W. Yang, P. Guo, D. Parekh, and C. J. Chang-Hasnain, “Reflection-mode optical injection locking,” Opt. Express18(20), 20887–20893 (2010). [CrossRef] [PubMed]
  7. I. Gatare, K. Panajotov, and M. Sciamanna, “Frequency-induced polarization bistability in vertical-cavity surface-emitting lasers with orthogonal optical injection,” Phys. Rev. A75(2), 023804 (2007). [CrossRef]
  8. A. Quirce, A. Valle, and L. Pesquera, “Very wide hysteresis cycles in 1550 nm-VCSELs subject to orthogonal optical injection,” IEEE Photon. Technol. Lett.21(17), 1193–1195 (2009). [CrossRef]
  9. A. Hurtado, A. Quirce, A. Valle, L. Pesquera, and M. J. Adams, “Power and wavelength polarization bistability with very wide hysteresis cycles in a 1550 nm-VCSEL subject to orthogonal optical injection,” Opt. Express17(26), 23637–23642 (2009). [CrossRef] [PubMed]
  10. S. H. Lee, H. W. Jung, K. H. Kim, M. H. Lee, B.-S. Yoo, J. Roh, and K. A. Shore, “1-GHz all-optical flip-flop operation of conventional cylindrical-shaped single-mode VCSELs under low power optical injection,” IEEE Photon. Technol. Lett.22(23), 1759–1761 (2010). [CrossRef]
  11. W. Hofmann, N. H. Zhu, M. Ortsiefer, G. Bohm, Y. Liu, and M.-C. Amann, “High speed (>11 GHz) modulation of BCB-passivated 1.55 µm InGaAlAs-InP VCSELs,” Electron. Lett.42(17), 976–977 (2006). [CrossRef]
  12. P. Guo, W. Yang, D. Parekh, A. Xu, Z. Chen, and C. J. Chang-Hasnain, “An ellipse model for cavity mode behavior of optically injection-locked VCSELs,” Opt. Express20(7), 6980–6988 (2012). [CrossRef] [PubMed]

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