Abstract

We study modulation properties of two-element phased-array semiconductor lasers that can be described by coupled mode theory. We consider four different waveguide structures and modulate the array either in phase or out of phase within the phase-locked regions, guided by stability diagrams obtained from direct numerical simulations. Specifically, we find that out-of-phase modulation allows for bandwidth enhancement if the waveguide structure is properly chosen; for example, for a combination of index antiguiding and gain-guiding, the achievable modulation bandwidth in the case of out-of-phase modulation could be much higher than the one when they are modulated in phase. Proper array design of the coupling, controllable in terms of the laser separation and the frequency offset between the two lasers, is shown to be beneficial to slightly improve the bandwidth but not the resonance frequency, while the inclusion of the frequency offset leads to the appearance of double peak response curves. For comparison, we explore the case of modulating only one element of the phased array and find that double peak response curves are found. To improve the resonance frequency and the modulation bandwidth, we introduce simultaneous external injection into the phased array and modulate the phased array or its master light within the injection locking region. We observe a significant improvement of the modulation properties, and in some cases, by modulating the amplitude of the master light before injection, the resulting 3 dB bandwidths could be enhanced up to 160 GHz. Such a record bandwidth for phased-array modulation could pave the way for various applications, notably optical communications that require high-speed integrated photonic devices.

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
  43. M. J. Adams, N. Q. Li, B. R. Cemlyn, H. Susanto, and I. D. Henning, “Effects of detuning, gain-guiding and index antiguiding on the dynamics of two laterally-coupled semiconductor lasers,” Phys. Rev. A 95, 053869 (2017).
    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]

2018 (4)

F. L. Wang, X. W. Ma, Y. Z. Huang, Y. D. Yang, J. Y. Han, and J. L. Xiao, “Relative intensity noise in high-speed hybrid square-rectangular lasers,” Photon. Res. 6, 193–197 (2018).
[Crossref]

N. Q. Li, H. Susanto, B. R. Cemlyn, I. D. Henning, and M. J. Adams, “Nonlinear dynamics of solitary and optically injected two-element laser arrays with four different waveguide structures: a numerical study,” Opt. Express 26, 4751–4765 (2018).
[Crossref]

N. Q. Li, H. Susanto, B. R. Cemlyn, I. D. Henning, and M. J. Adams, “Locking bandwidth of two laterally-coupled lasers subjected to optical injection,” Sci. Rep. 8, 109 (2018).
[Crossref]

N. Q. Li, H. Susanto, B. R. Cemlyn, I. D. Henning, and M. J. Adams, “Injection locking of two laterally-coupled semiconductor laser arrays,” Proc. SPIE 10682, 106820Z (2018).
[Crossref]

2017 (9)

N. Q. Li, H. Susanto, B. R. Cemlyn, I. D. Henning, and M. J. Adams, “Stability and bifurcation analysis of spin-polarized vertical-cavity surface-emitting lasers,” Phys. Rev. A 96, 013840 (2017).
[Crossref]

M. J. Adams, N. Q. Li, B. R. Cemlyn, H. Susanto, and I. D. Henning, “Effects of detuning, gain-guiding and index antiguiding on the dynamics of two laterally-coupled semiconductor lasers,” Phys. Rev. A 95, 053869 (2017).
[Crossref]

L. Fan, G. Q. Xia, X. Tang, T. Deng, J. J. Chen, X. D. Lin, Y. N. Li, and Z. M. Wu, “Tunable ultra-broadband microwave frequency combs generation based on a current modulated semiconductor laser under optical injection,” IEEE Access 5, 17764–17771 (2017).
[Crossref]

H. Han and K. A. Shore, “Zero crosstalk regime direct modulation of mutually coupled nanolasers,” IEEE Photon. J. 9, 1503412 (2017).
[Crossref]

J. M. Sarraute, K. Schires, S. LaRochelle, and F. Grillot, “Effects of gain nonlinearities in an optically injected gain lever semiconductor laser,” Photon. Res. 5, 315–319 (2017).
[Crossref]

S. T. M. Fryslie, Z. H. Gao, H. Dave, B. J. Thompson, K. Lakomy, S. Y. Lin, P. J. Decker, D. K. McElfresh, J. E. Schutt-Ainé, and K. D. Choquette, “Modulation of coherently coupled phased photonic crystal vertical cavity laser arrays,” IEEE J. Sel. Top. Quantum Electron. 23, 1700409 (2017).
[Crossref]

Z. X. Xiao, Y. Z. Huang, Y. D. Yang, M. Tang, and J. L. Xiao, “Modulation bandwidth enhancement for coupled twin-square microcavity lasers,” Opt. Lett. 42, 3173–3176 (2017).
[Crossref]

Z. Gao, S. T. M. Fryslie, B. J. Thompson, P. Scott Carney, and K. D. Choquette, “Parity-time symmetry in coherently coupled vertical cavity laser arrays,” Optica 4, 323–329 (2017).
[Crossref]

Y. Kominis, V. Kovanis, and T. Bountis, “Controllable asymmetric phase-locked states of the fundamental active photonic dimer,” Phys. Rev. A 96, 043836 (2017).
[Crossref]

2016 (1)

J. Shena, J. Hizanidis, V. Kovanis, and G. P. Tsironis, “Turbulent chimeras in large semiconductor laser arrays,” Sci. Rep. 7, 42116 (2016).
[Crossref]

2015 (6)

C. Wang, M. E. Chaibi, H. M. Huang, D. Erasme, P. Poole, J. Even, and F. Grillot, “Frequency-dependent linewidth enhancement factor of optical injection-locked quantum dot/dash lasers,” Opt. Express 23, 21761–21770 (2015).
[Crossref]

C. Z. Sun, D. Liu, B. Xiong, Y. Luo, J. Wang, Z. B. Hao, Y. J. Han, L. Wang, and H. T. Li, “Modulation characteristics enhancement of monolithically integrated laser diodes under mutual injection locking,” IEEE J. Sel. Top. Quantum Electron. 21, 1802008 (2015).
[Crossref]

S. T. M. Fryslie, M. P. Tan, D. F. Siriani, M. T. Johnson, and K. D. Choquette, “37-GHz modulation via resonance tuning in single-mode coherent vertical-cavity laser arrays,” IEEE Photon. Technol. Lett. 27, 415–418 (2015).
[Crossref]

J. M. Sarraute, K. Schires, S. LaRochelle, and F. Grillot, “Enhancement of the modulation dynamics of an optically injection-locked semiconductor laser using gain lever,” IEEE J. Sel. Top. Quantum Electron. 21, 1801408 (2015).
[Crossref]

Z. A. Sattar and K. A. Shore, “Analysis of the direct modulation response of nanowire lasers,” J. Lightwave Technol. 33, 3028–3033 (2015).
[Crossref]

K. Ding, J. O. Diaz, D. Bimberg, and C. Z. Ning, “Modulation bandwidth and energy efficiency of metallic cavity semiconductor nanolasers with inclusion of noise effects,” Laser Photon. Rev. 9, 488–497 (2015).
[Crossref]

2014 (1)

2013 (3)

H. Dalir and F. Koyama, “29  GHz directly modulated 980  nm vertical-cavity surface emitting lasers with bow-tie shape transverse coupled cavity,” Appl. Phys. Lett. 103, 091109 (2013).
[Crossref]

X. M. Lv, Y. Z. Huang, L. X. Zou, H. Long, and Y. Du, “Optimization of direct modulation rate for circular microlasers by adjusting mode Q factor,” Laser Photon. Rev. 7, 818–829 (2013).
[Crossref]

C. Wang, F. Grillot, V. I. Kovanis, J. D. Bodyfelt, and J. Even, “Modulation properties of optically injection-locked quantum cascade lasers,” Opt. Lett. 38, 1975–1977 (2013).
[Crossref]

2011 (1)

N. Blackbeard, H. Erzgräber, and S. Wieczorek, “Shear-induced bifurcations and chaos in models of three coupled lasers,” SIAM J. Appl. Dyn. Syst. 10, 469–509 (2011).
[Crossref]

2009 (1)

R. Santos and H. Lamela, “Experimental observation of chaotic dynamics in two coupled diode lasers through lateral model locking,” IEEE J. Quantum Electron. 45, 1490–1494 (2009).
[Crossref]

2008 (6)

H. Erzgräber, S. Wieczorek, and B. Krauskopf, “Dynamics of two laterally coupled semiconductor lasers: strong- and weak-coupling theory,” Phys. Rev. E 78, 066201 (2008).
[Crossref]

N. H. Zhu, W. Li, J. M. Wen, W. Han, W. Chen, and L. Xie, “Enhanced modulation bandwidth of a Fabry–Perot semiconductor laser subject to light injection from another Fabry–Perot laser,” IEEE J. Quantum Electron. 44, 528–535 (2008).
[Crossref]

E. K. Lau, H. K. Sung, and M. C. Wu, “Frequency response enhancement of optical injection-locked lasers,” IEEE J. Quantum Electron. 44, 90–99 (2008).
[Crossref]

E. K. Lau, L. J. Wong, X. X. Zhao, Y. K. Chen, C. J. Chang-Hasnain, and M. C. Wu, “Bandwidth enhancement by master modulation of optical injection-locked lasers,” J. Lightwave Technol. 26, 2584–2593 (2008).
[Crossref]

D. Parekh, X. X. Zhao, W. Hofmann, M. C. Amann, L. A. Zenteno, and C. J. Chang-Hasnain, “Greatly enhanced modulation response of injection-locked multimode VCSELs,” Opt. Express 16, 21582–21586 (2008).
[Crossref]

L. Chrostowski and W. Shi, “Monolithic injection-locked high-speed semiconductor ring lasers,” J. Lightwave Technol. 26, 3355–3362 (2008).
[Crossref]

2007 (2)

L. Chrostowski, B. Faraji, W. Hofmann, M. C. Amann, S. Wieczorek, and W. W. Chow, “40  GHz bandwidth and 64  GHz resonance frequency in injection-locked 1.55  μm VCSELs,” IEEE J. Sel. Top. Quantum Electron. 13, 1200–1208 (2007).
[Crossref]

M. Radziunas, A. Glitzky, U. Bandelow, M. Wolfrum, U. Troppenz, J. Kreissl, and W. Rehbein, “Improving the modulation bandwidth in semiconductor lasers by passive feedback,” IEEE J. Sel. Top. Quantum Electron. 13, 136–142 (2007).
[Crossref]

2005 (1)

2003 (1)

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, 1196–1204 (2003).
[Crossref]

2001 (1)

H. Lamela, M. Leones, G. Carpintero, C. Simmendinger, and O. Hess, “Analysis of the dynamics behavior and short-pulse modulation scheme for laterally coupled diode lasers,” IEEE J. Sel. Top. Quantum Electron. 7, 192–200 (2001).
[Crossref]

2000 (1)

G. Morthier, R. Schatz, and O. Kjebon, “Extended modulation bandwidth of DBR and external cavity lasers by utilizing a cavity resonance for equalization,” IEEE J. Quantum Electron. 36, 1468–1475 (2000).
[Crossref]

1997 (1)

J. Mercier and M. McCall, “Stability and dynamics of an injection-locked semiconductor laser array,” Opt. Commun. 138, 200–210 (1997).
[Crossref]

1996 (1)

T. B. Simpson and J. M. Liu, “Small-signal analysis of modulation characteristics in a semiconductor laser subject to strong optical injection,” IEEE J. Quantum Electron. 32, 1456–1468 (1996).
[Crossref]

1994 (1)

O. Hess and E. Scholl, “Spatio-temporal dynamics in twin-stripe semiconductor lasers,” Physica D 70, 165–177 (1994).
[Crossref]

1993 (1)

1991 (1)

G. A. Wilson, R. K. DeFreez, and H. G. Winful, “Modulation of phased-array semiconductor lasers at K-band frequencies,” IEEE J. Quantum Electron. 27, 1696–1704 (1991).
[Crossref]

1990 (1)

H. G. Winful and L. Rahman, “Synchronized chaos and spatiotemporal chaos in arrays of coupled lasers,” Phys. Rev. Lett. 65, 1575–1578 (1990).
[Crossref]

1988 (2)

H. G. Winful and S. S. Wang, “Stability of phase-locking in coupled semiconductor laser arrays,” Appl. Phys. Lett. 53, 1894–1896 (1988).
[Crossref]

S. S. Wang and H. G. Winful, “Dynamics of phase-locked semiconductor laser arrays,” Appl. Phys. Lett. 52, 1774–1776 (1988).
[Crossref]

1985 (2)

R. S. Tucker, “High-speed modulation of semiconductor lasers,” J. Lightwave Technol. 3, 1180–1192 (1985).
[Crossref]

L. Goldberg, H. F. Taylor, J. F. Weller, and D. R. Scifres, “Injection locking of coupledstripe diode laser arrays,” Appl. Phys. Lett. 46, 236–238 (1985).
[Crossref]

1984 (1)

Adams, M. J.

N. Q. Li, H. Susanto, B. R. Cemlyn, I. D. Henning, and M. J. Adams, “Locking bandwidth of two laterally-coupled lasers subjected to optical injection,” Sci. Rep. 8, 109 (2018).
[Crossref]

N. Q. Li, H. Susanto, B. R. Cemlyn, I. D. Henning, and M. J. Adams, “Injection locking of two laterally-coupled semiconductor laser arrays,” Proc. SPIE 10682, 106820Z (2018).
[Crossref]

N. Q. Li, H. Susanto, B. R. Cemlyn, I. D. Henning, and M. J. Adams, “Nonlinear dynamics of solitary and optically injected two-element laser arrays with four different waveguide structures: a numerical study,” Opt. Express 26, 4751–4765 (2018).
[Crossref]

N. Q. Li, H. Susanto, B. R. Cemlyn, I. D. Henning, and M. J. Adams, “Stability and bifurcation analysis of spin-polarized vertical-cavity surface-emitting lasers,” Phys. Rev. A 96, 013840 (2017).
[Crossref]

M. J. Adams, N. Q. Li, B. R. Cemlyn, H. Susanto, and I. D. Henning, “Effects of detuning, gain-guiding and index antiguiding on the dynamics of two laterally-coupled semiconductor lasers,” Phys. Rev. A 95, 053869 (2017).
[Crossref]

Altug, H.

Amann, M. C.

D. Parekh, X. X. Zhao, W. Hofmann, M. C. Amann, L. A. Zenteno, and C. J. Chang-Hasnain, “Greatly enhanced modulation response of injection-locked multimode VCSELs,” Opt. Express 16, 21582–21586 (2008).
[Crossref]

L. Chrostowski, B. Faraji, W. Hofmann, M. C. Amann, S. Wieczorek, and W. W. Chow, “40  GHz bandwidth and 64  GHz resonance frequency in injection-locked 1.55  μm VCSELs,” IEEE J. Sel. Top. Quantum Electron. 13, 1200–1208 (2007).
[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. Quantum Electron. 39, 1196–1204 (2003).
[Crossref]

Bandelow, U.

M. Radziunas, A. Glitzky, U. Bandelow, M. Wolfrum, U. Troppenz, J. Kreissl, and W. Rehbein, “Improving the modulation bandwidth in semiconductor lasers by passive feedback,” IEEE J. Sel. Top. Quantum Electron. 13, 136–142 (2007).
[Crossref]

Bimberg, D.

K. Ding, J. O. Diaz, D. Bimberg, and C. Z. Ning, “Modulation bandwidth and energy efficiency of metallic cavity semiconductor nanolasers with inclusion of noise effects,” Laser Photon. Rev. 9, 488–497 (2015).
[Crossref]

Blackbeard, N.

N. Blackbeard, H. Erzgräber, and S. Wieczorek, “Shear-induced bifurcations and chaos in models of three coupled lasers,” SIAM J. Appl. Dyn. Syst. 10, 469–509 (2011).
[Crossref]

Bodyfelt, J. D.

Botez, D.

D. Botez and D. R. Scifres, Diode Laser Arrays (Cambridge University, 1994).

Bountis, T.

Y. Kominis, V. Kovanis, and T. Bountis, “Controllable asymmetric phase-locked states of the fundamental active photonic dimer,” Phys. Rev. A 96, 043836 (2017).
[Crossref]

Caliman, A.

Carpintero, G.

H. Lamela, M. Leones, G. Carpintero, C. Simmendinger, and O. Hess, “Analysis of the dynamics behavior and short-pulse modulation scheme for laterally coupled diode lasers,” IEEE J. Sel. Top. Quantum Electron. 7, 192–200 (2001).
[Crossref]

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N. Q. Li, H. Susanto, B. R. Cemlyn, I. D. Henning, and M. J. Adams, “Injection locking of two laterally-coupled semiconductor laser arrays,” Proc. SPIE 10682, 106820Z (2018).
[Crossref]

N. Q. Li, H. Susanto, B. R. Cemlyn, I. D. Henning, and M. J. Adams, “Locking bandwidth of two laterally-coupled lasers subjected to optical injection,” Sci. Rep. 8, 109 (2018).
[Crossref]

N. Q. Li, H. Susanto, B. R. Cemlyn, I. D. Henning, and M. J. Adams, “Nonlinear dynamics of solitary and optically injected two-element laser arrays with four different waveguide structures: a numerical study,” Opt. Express 26, 4751–4765 (2018).
[Crossref]

N. Q. Li, H. Susanto, B. R. Cemlyn, I. D. Henning, and M. J. Adams, “Stability and bifurcation analysis of spin-polarized vertical-cavity surface-emitting lasers,” Phys. Rev. A 96, 013840 (2017).
[Crossref]

M. J. Adams, N. Q. Li, B. R. Cemlyn, H. Susanto, and I. D. Henning, “Effects of detuning, gain-guiding and index antiguiding on the dynamics of two laterally-coupled semiconductor lasers,” Phys. Rev. A 95, 053869 (2017).
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S. T. M. Fryslie, M. P. Tan, D. F. Siriani, M. T. Johnson, and K. D. Choquette, “37-GHz modulation via resonance tuning in single-mode coherent vertical-cavity laser arrays,” IEEE Photon. Technol. Lett. 27, 415–418 (2015).
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L. Chrostowski, B. Faraji, W. Hofmann, M. C. Amann, S. Wieczorek, and W. W. Chow, “40  GHz bandwidth and 64  GHz resonance frequency in injection-locked 1.55  μm VCSELs,” IEEE J. Sel. Top. Quantum Electron. 13, 1200–1208 (2007).
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[Crossref]

Z. Gao, S. T. M. Fryslie, B. J. Thompson, P. Scott Carney, and K. D. Choquette, “Parity-time symmetry in coherently coupled vertical cavity laser arrays,” Optica 4, 323–329 (2017).
[Crossref]

S. T. M. Fryslie, M. P. Tan, D. F. Siriani, M. T. Johnson, and K. D. Choquette, “37-GHz modulation via resonance tuning in single-mode coherent vertical-cavity laser arrays,” IEEE Photon. Technol. Lett. 27, 415–418 (2015).
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S. T. M. Fryslie, Z. H. Gao, H. Dave, B. J. Thompson, K. Lakomy, S. Y. Lin, P. J. Decker, D. K. McElfresh, J. E. Schutt-Ainé, and K. D. Choquette, “Modulation of coherently coupled phased photonic crystal vertical cavity laser arrays,” IEEE J. Sel. Top. Quantum Electron. 23, 1700409 (2017).
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C. Z. Sun, D. Liu, B. Xiong, Y. Luo, J. Wang, Z. B. Hao, Y. J. Han, L. Wang, and H. T. Li, “Modulation characteristics enhancement of monolithically integrated laser diodes under mutual injection locking,” IEEE J. Sel. Top. Quantum Electron. 21, 1802008 (2015).
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N. Q. Li, H. Susanto, B. R. Cemlyn, I. D. Henning, and M. J. Adams, “Locking bandwidth of two laterally-coupled lasers subjected to optical injection,” Sci. Rep. 8, 109 (2018).
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[Crossref]

N. Q. Li, H. Susanto, B. R. Cemlyn, I. D. Henning, and M. J. Adams, “Nonlinear dynamics of solitary and optically injected two-element laser arrays with four different waveguide structures: a numerical study,” Opt. Express 26, 4751–4765 (2018).
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[Crossref]

M. J. Adams, N. Q. Li, B. R. Cemlyn, H. Susanto, and I. D. Henning, “Effects of detuning, gain-guiding and index antiguiding on the dynamics of two laterally-coupled semiconductor lasers,” Phys. Rev. A 95, 053869 (2017).
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Katz, J.

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J. Shena, J. Hizanidis, V. Kovanis, and G. P. Tsironis, “Turbulent chimeras in large semiconductor laser arrays,” Sci. Rep. 7, 42116 (2016).
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Koyama, F.

H. Dalir and F. Koyama, “29  GHz directly modulated 980  nm vertical-cavity surface emitting lasers with bow-tie shape transverse coupled cavity,” Appl. Phys. Lett. 103, 091109 (2013).
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H. Erzgräber, S. Wieczorek, and B. Krauskopf, “Dynamics of two laterally coupled semiconductor lasers: strong- and weak-coupling theory,” Phys. Rev. E 78, 066201 (2008).
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M. Radziunas, A. Glitzky, U. Bandelow, M. Wolfrum, U. Troppenz, J. Kreissl, and W. Rehbein, “Improving the modulation bandwidth in semiconductor lasers by passive feedback,” IEEE J. Sel. Top. Quantum Electron. 13, 136–142 (2007).
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R. Santos and H. Lamela, “Experimental observation of chaotic dynamics in two coupled diode lasers through lateral model locking,” IEEE J. Quantum Electron. 45, 1490–1494 (2009).
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J. M. Sarraute, K. Schires, S. LaRochelle, and F. Grillot, “Enhancement of the modulation dynamics of an optically injection-locked semiconductor laser using gain lever,” IEEE J. Sel. Top. Quantum Electron. 21, 1801408 (2015).
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C. Z. Sun, D. Liu, B. Xiong, Y. Luo, J. Wang, Z. B. Hao, Y. J. Han, L. Wang, and H. T. Li, “Modulation characteristics enhancement of monolithically integrated laser diodes under mutual injection locking,” IEEE J. Sel. Top. Quantum Electron. 21, 1802008 (2015).
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N. Q. Li, H. Susanto, B. R. Cemlyn, I. D. Henning, and M. J. Adams, “Locking bandwidth of two laterally-coupled lasers subjected to optical injection,” Sci. Rep. 8, 109 (2018).
[Crossref]

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[Crossref]

N. Q. Li, H. Susanto, B. R. Cemlyn, I. D. Henning, and M. J. Adams, “Nonlinear dynamics of solitary and optically injected two-element laser arrays with four different waveguide structures: a numerical study,” Opt. Express 26, 4751–4765 (2018).
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M. J. Adams, N. Q. Li, B. R. Cemlyn, H. Susanto, and I. D. Henning, “Effects of detuning, gain-guiding and index antiguiding on the dynamics of two laterally-coupled semiconductor lasers,” Phys. Rev. A 95, 053869 (2017).
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N. H. Zhu, W. Li, J. M. Wen, W. Han, W. Chen, and L. Xie, “Enhanced modulation bandwidth of a Fabry–Perot semiconductor laser subject to light injection from another Fabry–Perot laser,” IEEE J. Quantum Electron. 44, 528–535 (2008).
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L. Fan, G. Q. Xia, X. Tang, T. Deng, J. J. Chen, X. D. Lin, Y. N. Li, and Z. M. Wu, “Tunable ultra-broadband microwave frequency combs generation based on a current modulated semiconductor laser under optical injection,” IEEE Access 5, 17764–17771 (2017).
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Ning, C. Z.

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H. Lamela, M. Leones, G. Carpintero, C. Simmendinger, and O. Hess, “Analysis of the dynamics behavior and short-pulse modulation scheme for laterally coupled diode lasers,” IEEE J. Sel. Top. Quantum Electron. 7, 192–200 (2001).
[Crossref]

Simpson, T. B.

T. B. Simpson and J. M. Liu, “Small-signal analysis of modulation characteristics in a semiconductor laser subject to strong optical injection,” IEEE J. Quantum Electron. 32, 1456–1468 (1996).
[Crossref]

Sirbu, A.

Siriani, D. F.

S. T. M. Fryslie, M. P. Tan, D. F. Siriani, M. T. Johnson, and K. D. Choquette, “37-GHz modulation via resonance tuning in single-mode coherent vertical-cavity laser arrays,” IEEE Photon. Technol. Lett. 27, 415–418 (2015).
[Crossref]

Sun, C. Z.

C. Z. Sun, D. Liu, B. Xiong, Y. Luo, J. Wang, Z. B. Hao, Y. J. Han, L. Wang, and H. T. Li, “Modulation characteristics enhancement of monolithically integrated laser diodes under mutual injection locking,” IEEE J. Sel. Top. Quantum Electron. 21, 1802008 (2015).
[Crossref]

Sung, H. K.

E. K. Lau, H. K. Sung, and M. C. Wu, “Frequency response enhancement of optical injection-locked lasers,” IEEE J. Quantum Electron. 44, 90–99 (2008).
[Crossref]

Susanto, H.

N. Q. Li, H. Susanto, B. R. Cemlyn, I. D. Henning, and M. J. Adams, “Locking bandwidth of two laterally-coupled lasers subjected to optical injection,” Sci. Rep. 8, 109 (2018).
[Crossref]

N. Q. Li, H. Susanto, B. R. Cemlyn, I. D. Henning, and M. J. Adams, “Injection locking of two laterally-coupled semiconductor laser arrays,” Proc. SPIE 10682, 106820Z (2018).
[Crossref]

N. Q. Li, H. Susanto, B. R. Cemlyn, I. D. Henning, and M. J. Adams, “Nonlinear dynamics of solitary and optically injected two-element laser arrays with four different waveguide structures: a numerical study,” Opt. Express 26, 4751–4765 (2018).
[Crossref]

N. Q. Li, H. Susanto, B. R. Cemlyn, I. D. Henning, and M. J. Adams, “Stability and bifurcation analysis of spin-polarized vertical-cavity surface-emitting lasers,” Phys. Rev. A 96, 013840 (2017).
[Crossref]

M. J. Adams, N. Q. Li, B. R. Cemlyn, H. Susanto, and I. D. Henning, “Effects of detuning, gain-guiding and index antiguiding on the dynamics of two laterally-coupled semiconductor lasers,” Phys. Rev. A 95, 053869 (2017).
[Crossref]

Tan, M. P.

S. T. M. Fryslie, M. P. Tan, D. F. Siriani, M. T. Johnson, and K. D. Choquette, “37-GHz modulation via resonance tuning in single-mode coherent vertical-cavity laser arrays,” IEEE Photon. Technol. Lett. 27, 415–418 (2015).
[Crossref]

Tang, M.

Tang, X.

L. Fan, G. Q. Xia, X. Tang, T. Deng, J. J. Chen, X. D. Lin, Y. N. Li, and Z. M. Wu, “Tunable ultra-broadband microwave frequency combs generation based on a current modulated semiconductor laser under optical injection,” IEEE Access 5, 17764–17771 (2017).
[Crossref]

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[Crossref]

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[Crossref]

Wang, L.

C. Z. Sun, D. Liu, B. Xiong, Y. Luo, J. Wang, Z. B. Hao, Y. J. Han, L. Wang, and H. T. Li, “Modulation characteristics enhancement of monolithically integrated laser diodes under mutual injection locking,” IEEE J. Sel. Top. Quantum Electron. 21, 1802008 (2015).
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S. S. Wang and H. G. Winful, “Dynamics of phase-locked semiconductor laser arrays,” Appl. Phys. Lett. 52, 1774–1776 (1988).
[Crossref]

H. G. Winful and S. S. Wang, “Stability of phase-locking in coupled semiconductor laser arrays,” Appl. Phys. Lett. 53, 1894–1896 (1988).
[Crossref]

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L. Goldberg, H. F. Taylor, J. F. Weller, and D. R. Scifres, “Injection locking of coupledstripe diode laser arrays,” Appl. Phys. Lett. 46, 236–238 (1985).
[Crossref]

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N. H. Zhu, W. Li, J. M. Wen, W. Han, W. Chen, and L. Xie, “Enhanced modulation bandwidth of a Fabry–Perot semiconductor laser subject to light injection from another Fabry–Perot laser,” IEEE J. Quantum Electron. 44, 528–535 (2008).
[Crossref]

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N. Blackbeard, H. Erzgräber, and S. Wieczorek, “Shear-induced bifurcations and chaos in models of three coupled lasers,” SIAM J. Appl. Dyn. Syst. 10, 469–509 (2011).
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H. Erzgräber, S. Wieczorek, and B. Krauskopf, “Dynamics of two laterally coupled semiconductor lasers: strong- and weak-coupling theory,” Phys. Rev. E 78, 066201 (2008).
[Crossref]

L. Chrostowski, B. Faraji, W. Hofmann, M. C. Amann, S. Wieczorek, and W. W. Chow, “40  GHz bandwidth and 64  GHz resonance frequency in injection-locked 1.55  μm VCSELs,” IEEE J. Sel. Top. Quantum Electron. 13, 1200–1208 (2007).
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G. A. Wilson, R. K. DeFreez, and H. G. Winful, “Modulation of phased-array semiconductor lasers at K-band frequencies,” IEEE J. Quantum Electron. 27, 1696–1704 (1991).
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Winful, H. G.

G. A. Wilson, R. K. DeFreez, and H. G. Winful, “Modulation of phased-array semiconductor lasers at K-band frequencies,” IEEE J. Quantum Electron. 27, 1696–1704 (1991).
[Crossref]

H. G. Winful and L. Rahman, “Synchronized chaos and spatiotemporal chaos in arrays of coupled lasers,” Phys. Rev. Lett. 65, 1575–1578 (1990).
[Crossref]

S. S. Wang and H. G. Winful, “Dynamics of phase-locked semiconductor laser arrays,” Appl. Phys. Lett. 52, 1774–1776 (1988).
[Crossref]

H. G. Winful and S. S. Wang, “Stability of phase-locking in coupled semiconductor laser arrays,” Appl. Phys. Lett. 53, 1894–1896 (1988).
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Wolfrum, M.

M. Radziunas, A. Glitzky, U. Bandelow, M. Wolfrum, U. Troppenz, J. Kreissl, and W. Rehbein, “Improving the modulation bandwidth in semiconductor lasers by passive feedback,” IEEE J. Sel. Top. Quantum Electron. 13, 136–142 (2007).
[Crossref]

Wong, L. J.

Wu, M. C.

E. K. Lau, L. J. Wong, X. X. Zhao, Y. K. Chen, C. J. Chang-Hasnain, and M. C. Wu, “Bandwidth enhancement by master modulation of optical injection-locked lasers,” J. Lightwave Technol. 26, 2584–2593 (2008).
[Crossref]

E. K. Lau, H. K. Sung, and M. C. Wu, “Frequency response enhancement of optical injection-locked lasers,” IEEE J. Quantum Electron. 44, 90–99 (2008).
[Crossref]

Wu, Z. M.

L. Fan, G. Q. Xia, X. Tang, T. Deng, J. J. Chen, X. D. Lin, Y. N. Li, and Z. M. Wu, “Tunable ultra-broadband microwave frequency combs generation based on a current modulated semiconductor laser under optical injection,” IEEE Access 5, 17764–17771 (2017).
[Crossref]

Xia, G. Q.

L. Fan, G. Q. Xia, X. Tang, T. Deng, J. J. Chen, X. D. Lin, Y. N. Li, and Z. M. Wu, “Tunable ultra-broadband microwave frequency combs generation based on a current modulated semiconductor laser under optical injection,” IEEE Access 5, 17764–17771 (2017).
[Crossref]

Xiao, J. L.

Xiao, Z. X.

Xie, L.

N. H. Zhu, W. Li, J. M. Wen, W. Han, W. Chen, and L. Xie, “Enhanced modulation bandwidth of a Fabry–Perot semiconductor laser subject to light injection from another Fabry–Perot laser,” IEEE J. Quantum Electron. 44, 528–535 (2008).
[Crossref]

Xiong, B.

C. Z. Sun, D. Liu, B. Xiong, Y. Luo, J. Wang, Z. B. Hao, Y. J. Han, L. Wang, and H. T. Li, “Modulation characteristics enhancement of monolithically integrated laser diodes under mutual injection locking,” IEEE J. Sel. Top. Quantum Electron. 21, 1802008 (2015).
[Crossref]

Yang, Y. D.

Yariv, A.

Zenteno, L. A.

Zhao, X. X.

Zhu, N. H.

N. H. Zhu, W. Li, J. M. Wen, W. Han, W. Chen, and L. Xie, “Enhanced modulation bandwidth of a Fabry–Perot semiconductor laser subject to light injection from another Fabry–Perot laser,” IEEE J. Quantum Electron. 44, 528–535 (2008).
[Crossref]

Zou, L. X.

X. M. Lv, Y. Z. Huang, L. X. Zou, H. Long, and Y. Du, “Optimization of direct modulation rate for circular microlasers by adjusting mode Q factor,” Laser Photon. Rev. 7, 818–829 (2013).
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H. Dalir and F. Koyama, “29  GHz directly modulated 980  nm vertical-cavity surface emitting lasers with bow-tie shape transverse coupled cavity,” Appl. Phys. Lett. 103, 091109 (2013).
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H. G. Winful and S. S. Wang, “Stability of phase-locking in coupled semiconductor laser arrays,” Appl. Phys. Lett. 53, 1894–1896 (1988).
[Crossref]

S. S. Wang and H. G. Winful, “Dynamics of phase-locked semiconductor laser arrays,” Appl. Phys. Lett. 52, 1774–1776 (1988).
[Crossref]

L. Goldberg, H. F. Taylor, J. F. Weller, and D. R. Scifres, “Injection locking of coupledstripe diode laser arrays,” Appl. Phys. Lett. 46, 236–238 (1985).
[Crossref]

IEEE Access (1)

L. Fan, G. Q. Xia, X. Tang, T. Deng, J. J. Chen, X. D. Lin, Y. N. Li, and Z. M. Wu, “Tunable ultra-broadband microwave frequency combs generation based on a current modulated semiconductor laser under optical injection,” IEEE Access 5, 17764–17771 (2017).
[Crossref]

IEEE J. Quantum Electron. (7)

G. Morthier, R. Schatz, and O. Kjebon, “Extended modulation bandwidth of DBR and external cavity lasers by utilizing a cavity resonance for equalization,” IEEE J. Quantum Electron. 36, 1468–1475 (2000).
[Crossref]

T. B. Simpson and J. M. Liu, “Small-signal analysis of modulation characteristics in a semiconductor laser subject to strong optical injection,” IEEE J. Quantum Electron. 32, 1456–1468 (1996).
[Crossref]

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, 1196–1204 (2003).
[Crossref]

N. H. Zhu, W. Li, J. M. Wen, W. Han, W. Chen, and L. Xie, “Enhanced modulation bandwidth of a Fabry–Perot semiconductor laser subject to light injection from another Fabry–Perot laser,” IEEE J. Quantum Electron. 44, 528–535 (2008).
[Crossref]

E. K. Lau, H. K. Sung, and M. C. Wu, “Frequency response enhancement of optical injection-locked lasers,” IEEE J. Quantum Electron. 44, 90–99 (2008).
[Crossref]

G. A. Wilson, R. K. DeFreez, and H. G. Winful, “Modulation of phased-array semiconductor lasers at K-band frequencies,” IEEE J. Quantum Electron. 27, 1696–1704 (1991).
[Crossref]

R. Santos and H. Lamela, “Experimental observation of chaotic dynamics in two coupled diode lasers through lateral model locking,” IEEE J. Quantum Electron. 45, 1490–1494 (2009).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (6)

H. Lamela, M. Leones, G. Carpintero, C. Simmendinger, and O. Hess, “Analysis of the dynamics behavior and short-pulse modulation scheme for laterally coupled diode lasers,” IEEE J. Sel. Top. Quantum Electron. 7, 192–200 (2001).
[Crossref]

L. Chrostowski, B. Faraji, W. Hofmann, M. C. Amann, S. Wieczorek, and W. W. Chow, “40  GHz bandwidth and 64  GHz resonance frequency in injection-locked 1.55  μm VCSELs,” IEEE J. Sel. Top. Quantum Electron. 13, 1200–1208 (2007).
[Crossref]

C. Z. Sun, D. Liu, B. Xiong, Y. Luo, J. Wang, Z. B. Hao, Y. J. Han, L. Wang, and H. T. Li, “Modulation characteristics enhancement of monolithically integrated laser diodes under mutual injection locking,” IEEE J. Sel. Top. Quantum Electron. 21, 1802008 (2015).
[Crossref]

S. T. M. Fryslie, Z. H. Gao, H. Dave, B. J. Thompson, K. Lakomy, S. Y. Lin, P. J. Decker, D. K. McElfresh, J. E. Schutt-Ainé, and K. D. Choquette, “Modulation of coherently coupled phased photonic crystal vertical cavity laser arrays,” IEEE J. Sel. Top. Quantum Electron. 23, 1700409 (2017).
[Crossref]

M. Radziunas, A. Glitzky, U. Bandelow, M. Wolfrum, U. Troppenz, J. Kreissl, and W. Rehbein, “Improving the modulation bandwidth in semiconductor lasers by passive feedback,” IEEE J. Sel. Top. Quantum Electron. 13, 136–142 (2007).
[Crossref]

J. M. Sarraute, K. Schires, S. LaRochelle, and F. Grillot, “Enhancement of the modulation dynamics of an optically injection-locked semiconductor laser using gain lever,” IEEE J. Sel. Top. Quantum Electron. 21, 1801408 (2015).
[Crossref]

IEEE Photon. J. (1)

H. Han and K. A. Shore, “Zero crosstalk regime direct modulation of mutually coupled nanolasers,” IEEE Photon. J. 9, 1503412 (2017).
[Crossref]

IEEE Photon. Technol. Lett. (1)

S. T. M. Fryslie, M. P. Tan, D. F. Siriani, M. T. Johnson, and K. D. Choquette, “37-GHz modulation via resonance tuning in single-mode coherent vertical-cavity laser arrays,” IEEE Photon. Technol. Lett. 27, 415–418 (2015).
[Crossref]

J. Lightwave Technol. (4)

J. Opt. Soc. Am. B (1)

Laser Photon. Rev. (2)

X. M. Lv, Y. Z. Huang, L. X. Zou, H. Long, and Y. Du, “Optimization of direct modulation rate for circular microlasers by adjusting mode Q factor,” Laser Photon. Rev. 7, 818–829 (2013).
[Crossref]

K. Ding, J. O. Diaz, D. Bimberg, and C. Z. Ning, “Modulation bandwidth and energy efficiency of metallic cavity semiconductor nanolasers with inclusion of noise effects,” Laser Photon. Rev. 9, 488–497 (2015).
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Opt. Commun. (1)

J. Mercier and M. McCall, “Stability and dynamics of an injection-locked semiconductor laser array,” Opt. Commun. 138, 200–210 (1997).
[Crossref]

Opt. Express (5)

Opt. Lett. (3)

Optica (1)

Photon. Res. (2)

Phys. Rev. A (3)

M. J. Adams, N. Q. Li, B. R. Cemlyn, H. Susanto, and I. D. Henning, “Effects of detuning, gain-guiding and index antiguiding on the dynamics of two laterally-coupled semiconductor lasers,” Phys. Rev. A 95, 053869 (2017).
[Crossref]

Y. Kominis, V. Kovanis, and T. Bountis, “Controllable asymmetric phase-locked states of the fundamental active photonic dimer,” Phys. Rev. A 96, 043836 (2017).
[Crossref]

N. Q. Li, H. Susanto, B. R. Cemlyn, I. D. Henning, and M. J. Adams, “Stability and bifurcation analysis of spin-polarized vertical-cavity surface-emitting lasers,” Phys. Rev. A 96, 013840 (2017).
[Crossref]

Phys. Rev. E (1)

H. Erzgräber, S. Wieczorek, and B. Krauskopf, “Dynamics of two laterally coupled semiconductor lasers: strong- and weak-coupling theory,” Phys. Rev. E 78, 066201 (2008).
[Crossref]

Phys. Rev. Lett. (1)

H. G. Winful and L. Rahman, “Synchronized chaos and spatiotemporal chaos in arrays of coupled lasers,” Phys. Rev. Lett. 65, 1575–1578 (1990).
[Crossref]

Physica D (1)

O. Hess and E. Scholl, “Spatio-temporal dynamics in twin-stripe semiconductor lasers,” Physica D 70, 165–177 (1994).
[Crossref]

Proc. SPIE (1)

N. Q. Li, H. Susanto, B. R. Cemlyn, I. D. Henning, and M. J. Adams, “Injection locking of two laterally-coupled semiconductor laser arrays,” Proc. SPIE 10682, 106820Z (2018).
[Crossref]

Sci. Rep. (2)

N. Q. Li, H. Susanto, B. R. Cemlyn, I. D. Henning, and M. J. Adams, “Locking bandwidth of two laterally-coupled lasers subjected to optical injection,” Sci. Rep. 8, 109 (2018).
[Crossref]

J. Shena, J. Hizanidis, V. Kovanis, and G. P. Tsironis, “Turbulent chimeras in large semiconductor laser arrays,” Sci. Rep. 7, 42116 (2016).
[Crossref]

SIAM J. Appl. Dyn. Syst. (1)

N. Blackbeard, H. Erzgräber, and S. Wieczorek, “Shear-induced bifurcations and chaos in models of three coupled lasers,” SIAM J. Appl. Dyn. Syst. 10, 469–509 (2011).
[Crossref]

Other (1)

D. Botez and D. R. Scifres, Diode Laser Arrays (Cambridge University, 1994).

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Figures (12)

Fig. 1.
Fig. 1. (a) Schematic of a phased array consisting of two laser waveguides, A and B, with each of width 2a and an edge-to-edge separation of 2d. (b) More details about the distribution of refractive indices n1,2, where g represents gain per unit length and α the background attenuation coefficient per unit length due to effects such as scattering and intervalence band absorption [43].
Fig. 2.
Fig. 2. Stability diagrams of the solitary phased array in the (d/a, γNΔΩ/2π) plane for (a)–(d) P=1.1Pth and (e)–(h) P=2Pth. (a), (e) Purely real index, (b), (f) positive index guiding with gain-guiding, (c), (g) pure gain-guiding, and (d), (h) index antiguiding with gain-guiding. Blue (yellow) stands for stability (instability).
Fig. 3.
Fig. 3. Modulation frequency response of the solitary phased array at P=1.1Pth. (a) Purely real index with d/a=2.4, (b) positive index guiding with gain-guiding with d/a=1.35, (c) pure gain-guiding with d/a=1.25, and (d) index antiguiding with gain-guiding with d/a=1.01. Red (blue) represents in-phase (out-of-phase) modulation.
Fig. 4.
Fig. 4. Modulation frequency response of the solitary phased array at P=2Pth. (a) Purely real index with d/a=1.75, (b) positive index guiding with gain-guiding with d/a=1.3, (c) pure gain-guiding with d/a=1.05, and (d) index antiguiding with gain-guiding with d/a=0.91. Red (blue) represents in-phase (out-of-phase) modulation.
Fig. 5.
Fig. 5. Modulation frequency response of the solitary phased array at (a), (b) P=1.1Pth and (c), (d) P=2Pth for index antiguiding with gain-guiding. (a), (b) d/a, 0.5–1.01 and (c), (d) d/a, 0.5–0.91. (a), (c) In-phase modulation and (b), (d) out-of-phase modulation.
Fig. 6.
Fig. 6. Modulation frequency response of the solitary phased array for (a), (b)P=1.1Pth and d/a=0.97, as well as (c), (d) P=2Pth and d/a=0.87 in the case of index antiguiding with gain-guiding. (a), (b) γNΔΩ/2π, 0  to  9  GHz and (c), (d) γNΔΩ/2π, 0  to  10  GHz. (a), (c) In-phase modulation and (b), (d) out-of-phase modulation.
Fig. 7.
Fig. 7. Modulation frequency response of the solitary phased array for (a) P=1.1Pth and d/a=1.01, as well as (b) P=2Pth and d/a=0.91 in the case of index antiguiding with gain-guiding. Red (blue) represents laser A (B). Here only laser A is modulated.
Fig. 8.
Fig. 8. Stability diagrams of the optically injected phased array in the (K, Δf) plane for (a) P=1.1Pth and d/a=1.01, as well as for (b) P=2Pth and d/a=0.91 in the case of index antiguiding with gain-guiding. Blue (yellow) stands for stability (instability).
Fig. 9.
Fig. 9. Modulation frequency response of the optically injected phased array for different detuning frequencies Δf and a fixed injection ratio K=200 in the case of index antiguiding with gain-guiding, where (a), (b) P=1.1Pth and d/a=1.01, as well as (c), (d) P=2Pth and d/a=0.91. (a), (c) In-phase modulation and (b), (d) out-of-phase modulation.
Fig. 10.
Fig. 10. Modulation frequency response of the optically injected phased array for different injection ratios K and a fixed detuning frequency Δf=0  GHz in the case of index antiguiding with gain-guiding, where P=2Pth and d/a=0.91. (a) In-phase modulation and (b) out-of-phase modulation.
Fig. 11.
Fig. 11. Modulation frequency response of the optically injected phased array for (a) P=2Pth and (b) P=5Pth in the case of index antiguiding with gain-guiding. (a) K=160 and (b) K=250. Other parameters are d/a=0.91 and Δf=20  GHz. Red (blue) represents in-phase (out-of-phase) modulation. Horizontal dashed line corresponds to the 3  dB level.
Fig. 12.
Fig. 12. Modulation frequency response of the master-amplitude-modulated optically injected phased array for different injection ratios K and a fixed detuning frequency Δf=20  GHz in the case of index antiguiding with gain-guiding. Other parameters are P=2Pth and d/a=0.91. Horizontal dashed line corresponds to the 3  dB level.

Tables (1)

Tables Icon

Table 1. Values of Key Parameters for Modeling, Using Material Parameter Values Given in Refs. [43,48]

Equations (18)

Equations on this page are rendered with MathJax. Learn more.

dE˜Adt˜=Γc2ngadiff(N˜AN˜Ath)(1iαH)E˜A+i(ωΩ˜A)E˜A+iηE˜B+kinjE˜injei(ωinjω)t,
dE˜Bdt˜=Γc2ngadiff(N˜BN˜Bth)(1iαH)E˜B+i(ωΩ˜B)E˜B+iηE˜A+kinjE˜injei(ωinjω)t,
dN˜A,Bdt˜=PA,BN˜A,BγNcn[gth+adiff(N˜A,BN˜A,Bth)]|E˜A,B|2.
|η|=Cηexp(2Wrda),arg(η)=Cθ2Wida,
EA,B=E˜A,B|E˜o|;NA,B=N˜A,BN˜th1;t=γNt˜;β=c2ngγNΓadiffN˜th;V=ωγN;ΩA,B=Ω˜A,BγN;κ=ηγN;K=kinjE˜inj|E˜0|γN;Δ=ωinjωγN;Gth=|E˜o|2cnN˜thγNgth;ζ=|E˜o|2cnγNadiff;μA,B=PA,BγNN˜th1,
dEAdt=βNA(1iαH)EA+i(VΩA)EA+iκEB+KeiΔt,
dEBdt=βNB(1iαH)EB+i(VΩB)EB+iκEA+KeiΔt,
dNA,Bdt=μA,BNA,B(Gth+ζNA,B)|EA,B|2.
dExdt=βNA(Ex+αHEy)(VΩA)Ey(EnκR+EmκI)+KΔEy,
dEydt=βNA(EyαHEx)+(VΩA)Ex+(EmκREnκI)+ΔEx,
dEmdt=βNB(Em+αHEn)(VΩB)En(EyκR+ExκI)+KΔEn,
dEndt=βNB(EnαHEm)+(VΩB)Em+(ExκREyκI)+ΔEm,
dNAdt=μANA(Gth+ζNA)(Ex2+Ey2),
dNBdt=μBNB(Gth+ζNB)(Em2+En2),
μ(t)=μA,B[1+mLA,Bsin(2πfmtγN)],
(2πfR)2=μγNτp(CQ+1)γD2,
γD=γN2[1+μ(CQ+1)],
CQ=Noadiffgth.

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