Abstract

Mutual coupling and injection locking of semiconductor lasers is of great interest in non-linear dynamics and its applications for instance in secure data communication and photonic reservoir computing. Despite its importance, it has hardly been studied in microlasers operating at μW light levels. In this context, vertically emitting quantum dot micropillar lasers are of high interest. Usually, their light emission is bimodal, and the gain competition of the associated linearly polarized fundamental emission modes results in complex switching dynamics. We report on selective optical injection into either one of the two fundamental mode components of a bimodal micropillar laser. Both modes can lock to the master laser and influence the non-injected mode by reducing the available gain. We demonstrate that the switching dynamics can be tailored externally via optical injection in very good agreement with our theory based on semi-classical rate equations.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2019 (2)

S. Kreinberg, X. Porte, D. Schicke, B. Lingnau, C. Schneider, S. Höfling, I. Kanter, K. Lüdge, and S. Reitzenstein, “Mutual coupling and synchronization of optically coupled quantum-dot micropillar lasers at ultra-low light levels,” Nat. Commun. 10, 1539 (2019).
[Crossref] [PubMed]

M. Lindemann, G. Xu, T. Pusch, R. Michalzik, M. R. Hofmann, I. Žutić, and N. C. Gerhardt, “Ultrafast spin-lasers,” Nature 568, 212 (2019).
[Crossref] [PubMed]

2018 (4)

T. Heuser, J. Große, A. Kaganskiy, D. Brunner, and S. Reitzenstein, “Fabrication of dense diameter-tuned quantum dot micropillar arrays for applications in photonic information processing,” APL Photonics 3, 116103 (2018).
[Crossref]

F. Denis-le Coarer, A. Quirce, A. Valle, L. Pesquera, M. A. Rodríguez, K. Panajotov, and M. Sciamanna, “Attractor hopping between polarization dynamical states in a vertical-cavity surface-emitting laser subject to parallel optical injection,” Phys. Rev. E 97, 032201 (2018).
[Crossref] [PubMed]

W. W. Chow and S. Reitzenstein, “Quantum-optical influences in optoelectronics—an introduction,” Appl. Phys. Rev. 5, 041302 (2018).
[Crossref]

M. Marconi, J. Javaloyes, P. Hamel, F. Raineri, A. Levenson, and A. M. Yacomotti, “Far-from-equilibrium route to superthermal light in bimodal nanolasers,” Phys. Rev. X 8, 011013 (2018).

2017 (3)

S. Meinecke, B. Lingnau, A. Röhm, and K. Lüdge, “Stability of optically injected two-state quantum-dot lasers,” Ann. Phys. 529, 1600279 (2017).
[Crossref]

H. Lin, S. Ourari, T. Huang, A. Jha, A. Briggs, and N. Bigagli, “Photonic microwave generation in multimode vcsels subject to orthogonal optical injection,” J. Opt. Soc. Am. B 34, 2381–2389 (2017).
[Crossref]

N. Lörch, S. E. Nigg, A. Nunnenkamp, R. P. Tiwari, and C. Bruder, “Quantum synchronization blockade: Energy quantization hinders synchronization of identical oscillators,” Phys. Rev. Lett. 118, 243602 (2017).
[Crossref] [PubMed]

2016 (2)

E. Viktorov, I. Dubinkin, N. Fedorov, T. Erneux, B. Tykalewicz, S. Hegarty, G. Huyet, D. Goulding, and B. Kelleher, “Injection-induced, tunable all-optical gating in a two-state quantum dot laser,” Opt. Lett. 41, 3555–3558 (2016).
[Crossref] [PubMed]

C. Redlich, B. Lingnau, S. Holzinger, E. Schlottmann, S. Kreinberg, C. Schneider, M. Kamp, S. Höfling, J. Wolters, S. Reitzenstein, and K. Lüdge, “Mode-switching induced super-thermal bunching in quantum-dot microlasers,” New J. Phys. 18, 063011 (2016).
[Crossref]

2015 (5)

M. Sciamanna and K. A. Shore, “Physics and applications of laser diode chaos,” Nat. Photonics 9, 151 (2015).
[Crossref]

D. Brunner and I. Fischer, “Reconfigurable semiconductor laser networks based on diffractive coupling,” Opt. Lett. 40, 3854–3857 (2015).
[Crossref] [PubMed]

B. Lingnau and K. Lüdge, “Analytic characterization of the dynamic regimes of quantum-dot lasers,” Photonics 2, 402–413 (2015).
[Crossref]

T. Wang, G. Puccioni, and G. Lippi, “Dynamical buildup of lasing in mesoscale devices,” Sci. Rep. 5, 15858 (2015).
[Crossref] [PubMed]

S. Walter, A. Nunnenkamp, and C. Bruder, “Quantum synchronization of two Van der Pol oscillators,” Ann. Phys. 527, 131–138 (2015).
[Crossref]

2014 (4)

P. Moser, J. A. Lott, G. Larisch, and D. Bimberg, “Impact of the oxide-aperture diameter on the energy efficiency, bandwidth, and temperature stability of 980-nm vcsels,” J. Light. Technol. 33, 825–831 (2014).
[Crossref]

S. M. Hein, F. Schulze, A. Carmele, and A. Knorr, “Optical feedback-enhanced photon entanglement from a biexciton cascade,” Phys. Rev. Lett. 113, 027401 (2014).
[Crossref] [PubMed]

D. O’Shea, S. Osborne, N. Blackbeard, D. Goulding, B. Kelleher, and A. Amann, “Experimental classification of dynamical regimes in optically injected lasers,” Opt. Express 22, 21701–21710 (2014).
[Crossref]

B. Lingnau, W. W. Chow, and K. Lüdge, “Amplitude-phase coupling and chirp in quantum-dot lasers: influence of charge carrier scattering dynamics,” Opt. Express 22, 4867–4879 (2014).
[Crossref] [PubMed]

2013 (5)

M. Virte, K. Panajotov, H. Thienpont, and M. Sciamanna, “Deterministic polarization chaos from a laser diode,” Nat. Photonics 7, 1–6 (2013).
[Crossref]

M. C. Soriano, J. García-Ojalvo, C. R. Mirasso, and I. Fischer, “Complex photonics: Dynamics and applications of delay-coupled semiconductors lasers,” Rev. Mod. Phys. 85, 421 (2013).
[Crossref]

M. Virte, K. Panajotov, and M. Sciamanna, “Bifurcation to nonlinear polarization dynamics and chaos in vertical-cavity surface-emitting lasers,” Phys. Rev. A 87, 013834 (2013).
[Crossref]

A. Carmele, J. Kabuss, F. Schulze, S. Reitzenstein, and A. Knorr, “Single photon delayed feedback: A way to stabilize intrinsic quantum cavity electrodynamics,” Phys. Rev. Lett. 110, 013601 (2013).
[Crossref] [PubMed]

H. A. M. Leymann, C. Hopfmann, F. Albert, A. Foerster, M. Khanbekyan, C. Schneider, S. Höfling, A. Forchel, M. Kamp, J. Wiersig, and S. Reitzenstein, “Intensity fluctuations in bimodal micropillar lasers enhanced by quantum-dot gain competition,” Phys. Rev. A 87, 053819 (2013).
[Crossref]

2012 (2)

M. Khajavikhan, A. Simic, M. Katz, J. H. Lee, B. Slutsky, A. Mizrahi, V. Lomakin, and Y. Fainman, “Thresholdless nanoscale coaxial lasers,” Nature 482, 204–207 (2012).
[Crossref] [PubMed]

M. Lermer, N. Gregersen, F. Dunzer, S. Reitzenstein, S. Höfling, J. Mørk, L. Worschech, M. Kamp, and A. Forchel, “Bloch-wave engineering of quantum dot micropillars for cavity quantum electrodynamics experiments,” Phys. Rev. Lett. 108, 057402 (2012).
[Crossref] [PubMed]

2010 (2)

M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, “Laser oscillation in a strongly coupled single-quantum-dot-nanocavity system,” Nat. Phys. 6, 279–283 (2010).
[Crossref]

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 Photonic Tech. L. 22, 1759–1761 (2010).
[Crossref]

2009 (3)

R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629 (2009).
[Crossref] [PubMed]

S. Osborne, K. Buckley, A. Amann, and S. O’Brien, “All-optical memory based on the injection locking bistability of a two-color laser diode,” Opt. Express 17, 6293–6300 (2009).
[Crossref] [PubMed]

K. Lüdge and E. Schöll, “Quantum-dot lasers – desynchronized nonlinear dynamics of electrons and holes,” IEEE J. Quantum Elect. 45, 1396–1403 (2009).
[Crossref]

2008 (3)

C. Böckler, S. Reitzenstein, C. Kistner, R. Debusmann, A. Löffler, T. Kida, S. Höfling, A. Forchel, L. Grenouillet, J. Claudon, and J. M. Gérard, “Electrically driven high-q quantum dot-micropillar cavities,” Appl. Phys. Lett. 92, 091107 (2008).
[Crossref]

A. Uchida, K. Amano, M. Inoue, K. Hirano, S. Naito, H. Someya, I. Oowada, T. Kurashige, M. Shiki, S. Yoshimori, K. Yoshimura, and P. Davis, “Fast physical random bit generation with chaotic semiconductor lasers,” Nat. Photonics 2, 728 (2008).
[Crossref]

S. Reitzenstein, T. Heindel, C. Kistner, A. Rahimi-Iman, C. Schneider, S. Höfling, and A. Forchel, “Low threshold electrically pumped quantum dot-micropillar lasers,” Appl. Phys. Lett. 93, 061104 (2008).
[Crossref]

2007 (1)

S. Reitzenstein, C. Hofmann, A. Gorbunov, M. Strauß, S. H. Kwon, C. Schneider, A. Löffler, S. Höfling, M. Kamp, and A. Forchel, “AIAs/GaAs micropillar cavities with quality factors exceeding 150.000,” Appl. Phys. Lett. 90, 1–4 (2007).
[Crossref]

2006 (5)

Y. D. Jeong, J. S. Cho, Y. H. Won, H. J. Lee, and H. Yoo, “All-optical flip-flop based on the bistability of injection locked fabry-perot laser diode,” Opt. Express 14, 4058–4063 (2006).
[Crossref] [PubMed]

T. Mori, Y. Yamayoshi, and H. Kawaguchi, “Low-switching-energy and high-repetition-frequency all-optical flip-flop operations of a polarization bistable vertical-cavity surface-emitting laser,” Appl. Phys. Lett. 88, 10–13 (2006).
[Crossref]

H. Altug, D. Englund, and J. Vučković, “Ultrafast photonic crystal nanocavity laser,” Nat. Phys. 2, 484 (2006).
[Crossref]

I. Gatare, M. Sciamanna, J. Buesa, H. Thienpont, and K. Panajotov, “Nonlinear dynamics accompanying polarization switching in vertical-cavity surface-emitting lasers with orthogonal optical injection,” Appl. Phys. Lett. 88, 101106 (2006).
[Crossref]

S. Reitzenstein, A. Bazhenov, A. Gorbunov, C. Hofmann, S. Münch, A. Löffler, M. Kamp, J. P. Reithmaier, V. D. Kulakovskii, and A. Forchel, “Lasing in high-q quantum-dot micropillar cavities,” Appl. Phys. Lett. 89, 051107 (2006).
[Crossref]

2005 (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]

2003 (1)

K. J. Vahala, “Optical microcavities,” Nature 424, 839–846 (2003).
[Crossref] [PubMed]

2001 (1)

1999 (1)

O. Painter, R. K. Lee, A. Scherer, A. Yariv, J. D. O’Brien, P. D. Dapkus, and I. Kim, “Two-dimensional photonic band-gap defect mode laser,” Science 284, 1819–1821 (1999).
[Crossref] [PubMed]

1994 (1)

G. Björk, A. Karlsson, and Y. Yamamoto, “Definition of a laser threshold,” Phys. Rev. A 50, 1675–1680 (1994).
[Crossref] [PubMed]

1993 (1)

Z. G. Pan, S. Jiang, M. Dagenais, R. A. Morgan, K. Kojima, M. T. Asom, R. E. Leibenguth, G. D. Guth, and M. W. Focht, “Optical injection induced polarization bistability in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63, 2999–3001 (1993).
[Crossref]

1992 (1)

H. Yokoyama, “Physics and device applications of optical microcavities,” Science 256, 66–70 (1992).
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H. A. M. Leymann, C. Hopfmann, F. Albert, A. Foerster, M. Khanbekyan, C. Schneider, S. Höfling, A. Forchel, M. Kamp, J. Wiersig, and S. Reitzenstein, “Intensity fluctuations in bimodal micropillar lasers enhanced by quantum-dot gain competition,” Phys. Rev. A 87, 053819 (2013).
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B. Lingnau, W. W. Chow, and K. Lüdge, “Amplitude-phase coupling and chirp in quantum-dot lasers: influence of charge carrier scattering dynamics,” Opt. Express 22, 4867–4879 (2014).
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E. Schlottmann, S. Holzinger, B. Lingnau, K. Lüdge, C. Schneider, M. Kamp, S. Höfling, J. Wolters, and S. Reitzenstein, “Injection locking of quantum-dot microlasers operating in the few-photon regime,” Phys. Rev. Appl.6 (2016).
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S. Kreinberg, X. Porte, D. Schicke, B. Lingnau, C. Schneider, S. Höfling, I. Kanter, K. Lüdge, and S. Reitzenstein, “Mutual coupling and synchronization of optically coupled quantum-dot micropillar lasers at ultra-low light levels,” Nat. Commun. 10, 1539 (2019).
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Mégret, P.

Meinecke, S.

S. Meinecke, B. Lingnau, A. Röhm, and K. Lüdge, “Stability of optically injected two-state quantum-dot lasers,” Ann. Phys. 529, 1600279 (2017).
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Z. G. Pan, S. Jiang, M. Dagenais, R. A. Morgan, K. Kojima, M. T. Asom, R. E. Leibenguth, G. D. Guth, and M. W. Focht, “Optical injection induced polarization bistability in vertical-cavity surface-emitting lasers,” Appl. Phys. Lett. 63, 2999–3001 (1993).
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T. Mori, Y. Yamayoshi, and H. Kawaguchi, “Low-switching-energy and high-repetition-frequency all-optical flip-flop operations of a polarization bistable vertical-cavity surface-emitting laser,” Appl. Phys. Lett. 88, 10–13 (2006).
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M. Lermer, N. Gregersen, F. Dunzer, S. Reitzenstein, S. Höfling, J. Mørk, L. Worschech, M. Kamp, and A. Forchel, “Bloch-wave engineering of quantum dot micropillars for cavity quantum electrodynamics experiments,” Phys. Rev. Lett. 108, 057402 (2012).
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S. Reitzenstein, A. Bazhenov, A. Gorbunov, C. Hofmann, S. Münch, A. Löffler, M. Kamp, J. P. Reithmaier, V. D. Kulakovskii, and A. Forchel, “Lasing in high-q quantum-dot micropillar cavities,” Appl. Phys. Lett. 89, 051107 (2006).
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N. Lörch, S. E. Nigg, A. Nunnenkamp, R. P. Tiwari, and C. Bruder, “Quantum synchronization blockade: Energy quantization hinders synchronization of identical oscillators,” Phys. Rev. Lett. 118, 243602 (2017).
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M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, “Laser oscillation in a strongly coupled single-quantum-dot-nanocavity system,” Nat. Phys. 6, 279–283 (2010).
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N. Lörch, S. E. Nigg, A. Nunnenkamp, R. P. Tiwari, and C. Bruder, “Quantum synchronization blockade: Energy quantization hinders synchronization of identical oscillators,” Phys. Rev. Lett. 118, 243602 (2017).
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M. Nomura, N. Kumagai, S. Iwamoto, Y. Ota, and Y. Arakawa, “Laser oscillation in a strongly coupled single-quantum-dot-nanocavity system,” Nat. Phys. 6, 279–283 (2010).
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R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bartal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature 461, 629 (2009).
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Figures (5)

Fig. 1
Fig. 1 (a) Experimental setup: The master laser is optically injected in the electrically driven micropillar laser. After spectral filtering using a monochromator, the micropillar emission is analyzed by either CCD, a Fabry-Pérot interferometer, a fiber-coupled cross-correlation configuration, or by interference measurements of master and microlaser emission. (b) Input-output characteristics of both micropillar modes. The SM (red) shows the typical s-shaped behavior of high-β microlasers while the WM (dark blue) first increases after threshold and reaches a maximum around 20 μA before it decreases in intensity. Inset: Schematic view of an electrically driven QD-micropillar laser. The polarization of the two orthogonal fundamental micropillar modes are indicated by the red and blue arrows.
Fig. 2
Fig. 2 (a) and (b): Experimental phase locking cones obtained with interference of master and microlaser signals. The color scale in (a) and (b) is normalized to the maximum interference amplitude, respectively. (c) – (f): Theoretical mean intensities of the two modes emitted from the micropillar laser as a function of detuning Δ = νmasterνmicrolaser and injection strength (middle and bottom panels) under injection in the SM (a, c, e) and WM (b, d, f) for ±3.5 GHz detuning range.
Fig. 3
Fig. 3 Experimental intensity heatmaps measured with an FPI for spectra with a detuning range between ± 5 GHz. For injection into the SM (left panels) and WM (right panels) at Keff = 0.12 (Keff = 0.066). The response of the SM (a) and WM (c) are shown. In panel (a) the SM is clearly locked for a detuning within ± 1 GHz, where the master laser’s intensity gets strongly enhanced. The broad WM in the center (c) is suppressed in the locking range and is increased at the boundary for negative detuning. The narrow peaks are the incompletely surpressed SM and master laser. In panel (b) the injected WM shows a smaller locking region compared to the corresponding situation for the SM in panel (a), and similar to panel (c) the SM is suppressed (panel (d)). The inset shows the data with logarithmic intensity scale and visualizes the broad WM.
Fig. 4
Fig. 4 (a) Exemplary experimental cross-correlation measurements g WS ( 2 ) ( 0 ) without injection (black curve) and with injection into the WM with Keff = 0.063. Pronounced anti-bunching reveals SM interaction and mode switching under optical injection. (b) Simulated g WS ( 2 ) ( 0 ) under variation of Keff and detuning. Experimental and theoretical g WS ( 2 ) ( 0 ) and correlation time τ for driven Keff (c) and detuning (d).
Fig. 5
Fig. 5 Time series for injection into the WM with Δ = 0 GHz and increasing injection strength. (a) Keff = 0: While the SM is in a stable lasing mode, the WM shows low intensity and is well below the onset of lasing. (b) Keff = 0.05: Both SM and WM fluctuate anti-correlated. (c) Keff = 0.06: The WM is dominating and switching events occur. (d) Keff = 0.09: The WM is stable lasing while the SM is dark. (e) Δ = 1.3 GHz and Keff = 0.07: SM and WM switch often for positive detuning.

Tables (1)

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Table 1 Parameters used for the simulations if not stated otherwise.

Equations (9)

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t E j ( t ) = [ ω 0 bg Z QD V g j ( 2 ρ ( t ) 1 ) κ j ] ( 1 + i α ) E j ( t ) + t E j | sp + t E j | inj
t ρ act ( t ) = j { s , w } g j [ 2 ρ ( t ) 1 ] | E j ( t ) | 2 ρ ( t ) 2 τ sp + S in n r ( t ) [ 1 ρ ( t ) ] ,
t n r ( t ) = η e 0 A ( J J p ) S in n r ( t ) 2 Z QD A [ 1 ρ ( t ) ] n r ( t ) τ r 2 Z inact QD ρ inact A τ sp .
ρ inact ( t ) = ( τ sp S in n r ( t ) ) ( 1 + τ sp S in n r ( t ) ) 1 .
g j = g j 0 ( 1 + ε j s ε ˜ | E s ( t ) | 2 + ε j w ε ˜ | E w ( t ) | 2 ) 1 ,
t E j | sp = β ω 0 bg 2 Z QD V ρ act 2 τ sp ξ j ( t ) ,
ξ i ( t ) = 0 and ξ i ( t 1 ) ξ j ( t 2 ) = δ i , j δ ( t 1 t 2 ) .
t E j inj ( t ) = K j κ j E 0 exp ( 2 π i ( Δ ν inj ν j ( 0 ) ) t ) ,
E 0 = | E s | 2 + | E w | 2 .

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