Abstract

We report in this paper the wavelength switching features of semiconductor ring lasers that are wavelength tunable based on filtered optical feedback. The filtered feedback provides a wavelength dependent loss mechanism in these devices with which a particular longitudinal mode, and thus a particular wavelength, can be selected by changing the filter characteristics of the feedback channel. We investigate how the wavelength switching speed depends on the amplitude of the modulation of the switching driving signal and on the different phase factors within the filtering branches of the SRL. We compare qualitatively the experimental results with numerical simulations based on a travelling wave model. We also investigate the dynamical behavior of the lasing and nonlasing longitudinal modes in the two channels of the clockwise and the counter-clockwise directions. We show the crucial importance of various phase relation factors on the wavelength switching behavior. Finally, we discuss what limits the switching speed and how we can accelerate it.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (5)

2017 (1)

G. Verschaffelt, M. Khoder, and G. Van der Sande, “Random number generator based on an integrated laser with on-chip optical feedback,” Chaos 27, 114310 (2017).
[Crossref] [PubMed]

2016 (1)

M. Khoder, G. Van der Sande, J. Danckaert, and G. Verschaffelt, “Effect of external optical feedback on tunable micro-ring lasers using on chip filtered feedback,” IEEE Photon. Technol. Lett. 28, 959–962 (2016).
[Crossref]

2014 (3)

M. Khoder, R. M. Nguimdo, J. Bolk, X. J. M. Leijtens, J. Danckaert, and G. Verschaffelt, “Wavelength switching speed in semiconductor ring lasers with on-chip filtered optical feedback,” IEEE Photon. Technol. Lett. 26, 520–523 (2014).
[Crossref]

A. Perez-Serrano, J. Javaloyes, and S. Balle, “Directional reversals and multimode dynamics in semiconductor ring lasers,” Phys. Rev. A 89, 023818 (2014).
[Crossref]

F. Kong, B. Romeira, J. Zhang, W. Li, and J. Yao, “A dual-wavelength fiber ring laser incorporating an injection-coupled optoelectronic oscillator and its application to transverse load sensing,” J. Lightwave Technol. 32, 1784–1793 (2014).
[Crossref]

2013 (6)

N. Li, W. Pan, S. Xiang, B. Luo, L. Yan, and X. Zou, “Hybrid chaos-based communication system consisting of three chaotic semiconductor ring lasers,” Appl. Opt. 52, 1523–1530 (2013).
[Crossref] [PubMed]

M. Khoder, G. Verschaffelt, R. M. Nguimdo, J. Bolk, X. J. M. Leijtens, and J. Danckaert, “Controlled multiwavelength emission using semiconductor ring lasers with on-chip filtered optical feedback,” Opt. Lett. 38, 2608–2610 (2013).
[Crossref] [PubMed]

G. Morthier and P. Mechet, “Theoretical analysis of unidirectional operation and reflection sensitivity of semiconductor ring or disk lasers,” IEEE J. Quantum Electron. 49, 1097–1101 (2013).
[Crossref]

M. Khoder, G. Verschaffelt, R. M. Nguimdo, J. Bolk, X. J. M. Leijtens, and J. Danckaert, “Digitally tunable dual wavelength emission from semiconductor ring lasers with filtered optical feedback,” Laser Phys. Lett.  10, 075804 (2013).
[Crossref]

A. Perez-Serrano, J. Javaloyes, and S. Balle, “Multichannel wavelength conversion using four-wave mixing in semiconductor ring lasers,” IEEE Photon. Technol. Lett. 25, 476–479 (2013).
[Crossref]

A. Trita, G. Mezosi, M. Sorel, and G. Giuliani, “All-optical toggle flip-flop based on monolithic semiconductor ring laser,” IEEE Photon. Technol. Lett. 26, 96–99 (2013).
[Crossref]

2012 (2)

I. V. Ermakov, S. Beri, M. Ashour, J. Danckaert, B. Docter, J. Bolk, X. J. M. Leijtens, and G. Verschaffelt, “Semiconductor ring laser with on-chip filtered optical feedback for discrete wavelength tuning,” IEEE J. Quantum Electron. 48, 129–136 (2012).
[Crossref]

J. Zhao, D. Lenstra, R. Santos, M. J. Wale, M. K. Smit, and X. J. M. Leijtens, “Stability of a monolithic integrated filtered feedback laser,” Opt. Express 20, B270–B278 (2012).
[Crossref] [PubMed]

2011 (2)

2010 (1)

B. Docter, J. Pozo, S. Beri, I. V. Ermakov, J. Danckaert, M. K. Smit, and F. Karouta, “Discretely tunable laser based on filtered feedback for telecommunication applications,” IEEE J. Sel. Top. Quantum Electron. 16, 1405–1412 (2010).
[Crossref]

2009 (1)

J. Javaloyes and S. Balle, “Emission directionality of semiconductor ring lasers: a traveling-wave description,” IEEE J. Quantum Electron. 45, 431–438 (2009).
[Crossref]

2008 (2)

S. Fürst, S. Yu, and M. Sorel, “Fast and digitally wavelength-tunable semiconductor ring laser using a monolithically integrated distributed Bragg reflector,” IEEE Photon. Technol. Lett. 20, 1926–1928 (2008).
[Crossref]

G. Yuan and S. Yu, “Bistability and switching properties of semiconductor ring lasers with external optical injection,” IEEE J. Quantum Electron. 44, 41–48 (2008).
[Crossref]

2007 (1)

2006 (1)

2004 (1)

M. T. Hill, H. J. S. Dorren, T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[Crossref] [PubMed]

2002 (2)

M. Sorel, P. J. R. Laybourn, G. Giuliani, and S. Donati, “Unidirectional bistability in semiconductor waveguide ring lasers,” Appl. Phys. Lett. 80, 3051–3053 (2002).
[Crossref]

M. Sorel, J. P. R. Laybourn, A. Scirè, S. Balle, G. Giuliani, R. Miglierina, and S. Donati, “Alternate oscillations in semiconductor ring lasers,” Opt. Lett. 27, 1992–1994 (2002).
[Crossref]

2000 (3)

M. Radziunas, H.-J. Wünsche, B. Sartorius, O. Brox, D. Hoffmann, K. Schneider, and D. Marcenac, “Modeling self-pulsating DFB lasers with an integrated phase tuning section,” IEEE J. Quantum Electron. 36, 1026–1034 (2000).
[Crossref]

L. A. Coldren, “Monolithic tunable diode lasers,” IEEE J. Sel. Top. Quantum Electron. 6, 988–999 (2000).
[Crossref]

A. P. A. Fischer, O. K. Andersen, M. Yousefi, S. Stolte, and D. Lenstra, “Experimental and theoretical study of filtered optical feedback in a semiconductor laser,” IEEE J. Quantum Electron. 36, 375–384 (2000).
[Crossref]

1999 (1)

N. J. C. Libatique and R. K. Jain, “Precisely and rapidly wavelength-switchable narrow-linewidth 1.5-µ m laser source for wavelength division multiplexing applications,” IEEE Photon. Technol. Lett. 11, 1584–1586 (1999).
[Crossref]

1996 (1)

Y. Tachikawa and K. Okamoto, “Arrayed-waveguide grating lasers and their applications to tuning-free wavelength routing,” IEE Proc. Optoelectron. 143, 322–328 (1996).
[Crossref]

Andersen, O. K.

A. P. A. Fischer, O. K. Andersen, M. Yousefi, S. Stolte, and D. Lenstra, “Experimental and theoretical study of filtered optical feedback in a semiconductor laser,” IEEE J. Quantum Electron. 36, 375–384 (2000).
[Crossref]

Arai, K.

Ashour, M.

I. V. Ermakov, S. Beri, M. Ashour, J. Danckaert, B. Docter, J. Bolk, X. J. M. Leijtens, and G. Verschaffelt, “Semiconductor ring laser with on-chip filtered optical feedback for discrete wavelength tuning,” IEEE J. Quantum Electron. 48, 129–136 (2012).
[Crossref]

Balle, S.

A. Perez-Serrano, J. Javaloyes, and S. Balle, “Directional reversals and multimode dynamics in semiconductor ring lasers,” Phys. Rev. A 89, 023818 (2014).
[Crossref]

A. Perez-Serrano, J. Javaloyes, and S. Balle, “Multichannel wavelength conversion using four-wave mixing in semiconductor ring lasers,” IEEE Photon. Technol. Lett. 25, 476–479 (2013).
[Crossref]

J. Javaloyes and S. Balle, “Emission directionality of semiconductor ring lasers: a traveling-wave description,” IEEE J. Quantum Electron. 45, 431–438 (2009).
[Crossref]

M. Sorel, J. P. R. Laybourn, A. Scirè, S. Balle, G. Giuliani, R. Miglierina, and S. Donati, “Alternate oscillations in semiconductor ring lasers,” Opt. Lett. 27, 1992–1994 (2002).
[Crossref]

Beri, S.

I. V. Ermakov, S. Beri, M. Ashour, J. Danckaert, B. Docter, J. Bolk, X. J. M. Leijtens, and G. Verschaffelt, “Semiconductor ring laser with on-chip filtered optical feedback for discrete wavelength tuning,” IEEE J. Quantum Electron. 48, 129–136 (2012).
[Crossref]

B. Docter, J. Pozo, S. Beri, I. V. Ermakov, J. Danckaert, M. K. Smit, and F. Karouta, “Discretely tunable laser based on filtered feedback for telecommunication applications,” IEEE J. Sel. Top. Quantum Electron. 16, 1405–1412 (2010).
[Crossref]

Binsma, H.

M. T. Hill, H. J. S. Dorren, T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[Crossref] [PubMed]

Bolk, J.

M. Khoder, R. M. Nguimdo, J. Bolk, X. J. M. Leijtens, J. Danckaert, and G. Verschaffelt, “Wavelength switching speed in semiconductor ring lasers with on-chip filtered optical feedback,” IEEE Photon. Technol. Lett. 26, 520–523 (2014).
[Crossref]

M. Khoder, G. Verschaffelt, R. M. Nguimdo, J. Bolk, X. J. M. Leijtens, and J. Danckaert, “Digitally tunable dual wavelength emission from semiconductor ring lasers with filtered optical feedback,” Laser Phys. Lett.  10, 075804 (2013).
[Crossref]

M. Khoder, G. Verschaffelt, R. M. Nguimdo, J. Bolk, X. J. M. Leijtens, and J. Danckaert, “Controlled multiwavelength emission using semiconductor ring lasers with on-chip filtered optical feedback,” Opt. Lett. 38, 2608–2610 (2013).
[Crossref] [PubMed]

I. V. Ermakov, S. Beri, M. Ashour, J. Danckaert, B. Docter, J. Bolk, X. J. M. Leijtens, and G. Verschaffelt, “Semiconductor ring laser with on-chip filtered optical feedback for discrete wavelength tuning,” IEEE J. Quantum Electron. 48, 129–136 (2012).
[Crossref]

Brox, O.

M. Radziunas, H.-J. Wünsche, B. Sartorius, O. Brox, D. Hoffmann, K. Schneider, and D. Marcenac, “Modeling self-pulsating DFB lasers with an integrated phase tuning section,” IEEE J. Quantum Electron. 36, 1026–1034 (2000).
[Crossref]

Buus, J.

Chan, S.-C.

Coldren, L. A.

L. A. Coldren, “Monolithic tunable diode lasers,” IEEE J. Sel. Top. Quantum Electron. 6, 988–999 (2000).
[Crossref]

Colet, P.

Danckaert, J.

M. Radziunas, M. Khoder, V. Tronciu, J. Danckaert, and G. Verschaffelt, “Tunable semiconductor ring laser with filtered optical feedback: Traveling wave description and experimental validation,” J. Opt. Soc. Am. B 35, 380–390 (2018).
[Crossref]

M. Khoder, G. Van der Sande, J. Danckaert, and G. Verschaffelt, “Effect of external optical feedback on tunable micro-ring lasers using on chip filtered feedback,” IEEE Photon. Technol. Lett. 28, 959–962 (2016).
[Crossref]

M. Khoder, R. M. Nguimdo, J. Bolk, X. J. M. Leijtens, J. Danckaert, and G. Verschaffelt, “Wavelength switching speed in semiconductor ring lasers with on-chip filtered optical feedback,” IEEE Photon. Technol. Lett. 26, 520–523 (2014).
[Crossref]

M. Khoder, G. Verschaffelt, R. M. Nguimdo, J. Bolk, X. J. M. Leijtens, and J. Danckaert, “Controlled multiwavelength emission using semiconductor ring lasers with on-chip filtered optical feedback,” Opt. Lett. 38, 2608–2610 (2013).
[Crossref] [PubMed]

M. Khoder, G. Verschaffelt, R. M. Nguimdo, J. Bolk, X. J. M. Leijtens, and J. Danckaert, “Digitally tunable dual wavelength emission from semiconductor ring lasers with filtered optical feedback,” Laser Phys. Lett.  10, 075804 (2013).
[Crossref]

I. V. Ermakov, S. Beri, M. Ashour, J. Danckaert, B. Docter, J. Bolk, X. J. M. Leijtens, and G. Verschaffelt, “Semiconductor ring laser with on-chip filtered optical feedback for discrete wavelength tuning,” IEEE J. Quantum Electron. 48, 129–136 (2012).
[Crossref]

B. Docter, J. Pozo, S. Beri, I. V. Ermakov, J. Danckaert, M. K. Smit, and F. Karouta, “Discretely tunable laser based on filtered feedback for telecommunication applications,” IEEE J. Sel. Top. Quantum Electron. 16, 1405–1412 (2010).
[Crossref]

Davis, P.

de Vries, T.

M. T. Hill, H. J. S. Dorren, T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[Crossref] [PubMed]

den Besten, J. H.

M. T. Hill, H. J. S. Dorren, T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[Crossref] [PubMed]

Docter, B.

I. V. Ermakov, S. Beri, M. Ashour, J. Danckaert, B. Docter, J. Bolk, X. J. M. Leijtens, and G. Verschaffelt, “Semiconductor ring laser with on-chip filtered optical feedback for discrete wavelength tuning,” IEEE J. Quantum Electron. 48, 129–136 (2012).
[Crossref]

B. Docter, J. Pozo, S. Beri, I. V. Ermakov, J. Danckaert, M. K. Smit, and F. Karouta, “Discretely tunable laser based on filtered feedback for telecommunication applications,” IEEE J. Sel. Top. Quantum Electron. 16, 1405–1412 (2010).
[Crossref]

Donati, S.

M. Sorel, P. J. R. Laybourn, G. Giuliani, and S. Donati, “Unidirectional bistability in semiconductor waveguide ring lasers,” Appl. Phys. Lett. 80, 3051–3053 (2002).
[Crossref]

M. Sorel, J. P. R. Laybourn, A. Scirè, S. Balle, G. Giuliani, R. Miglierina, and S. Donati, “Alternate oscillations in semiconductor ring lasers,” Opt. Lett. 27, 1992–1994 (2002).
[Crossref]

Dorren, H. J. S.

M. T. Hill, H. J. S. Dorren, T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[Crossref] [PubMed]

Ermakov, I. V.

I. V. Ermakov, S. Beri, M. Ashour, J. Danckaert, B. Docter, J. Bolk, X. J. M. Leijtens, and G. Verschaffelt, “Semiconductor ring laser with on-chip filtered optical feedback for discrete wavelength tuning,” IEEE J. Quantum Electron. 48, 129–136 (2012).
[Crossref]

B. Docter, J. Pozo, S. Beri, I. V. Ermakov, J. Danckaert, M. K. Smit, and F. Karouta, “Discretely tunable laser based on filtered feedback for telecommunication applications,” IEEE J. Sel. Top. Quantum Electron. 16, 1405–1412 (2010).
[Crossref]

Fischer, A. P. A.

A. P. A. Fischer, O. K. Andersen, M. Yousefi, S. Stolte, and D. Lenstra, “Experimental and theoretical study of filtered optical feedback in a semiconductor laser,” IEEE J. Quantum Electron. 36, 375–384 (2000).
[Crossref]

Fürst, S.

S. Fürst, S. Yu, and M. Sorel, “Fast and digitally wavelength-tunable semiconductor ring laser using a monolithically integrated distributed Bragg reflector,” IEEE Photon. Technol. Lett. 20, 1926–1928 (2008).
[Crossref]

Giuliani, G.

A. Trita, G. Mezosi, M. Sorel, and G. Giuliani, “All-optical toggle flip-flop based on monolithic semiconductor ring laser,” IEEE Photon. Technol. Lett. 26, 96–99 (2013).
[Crossref]

M. Sorel, P. J. R. Laybourn, G. Giuliani, and S. Donati, “Unidirectional bistability in semiconductor waveguide ring lasers,” Appl. Phys. Lett. 80, 3051–3053 (2002).
[Crossref]

M. Sorel, J. P. R. Laybourn, A. Scirè, S. Balle, G. Giuliani, R. Miglierina, and S. Donati, “Alternate oscillations in semiconductor ring lasers,” Opt. Lett. 27, 1992–1994 (2002).
[Crossref]

Harayama, T.

Hill, M. T.

M. T. Hill, H. J. S. Dorren, T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[Crossref] [PubMed]

Hoffmann, D.

M. Radziunas, H.-J. Wünsche, B. Sartorius, O. Brox, D. Hoffmann, K. Schneider, and D. Marcenac, “Modeling self-pulsating DFB lasers with an integrated phase tuning section,” IEEE J. Quantum Electron. 36, 1026–1034 (2000).
[Crossref]

Jain, R. K.

N. J. C. Libatique and R. K. Jain, “Precisely and rapidly wavelength-switchable narrow-linewidth 1.5-µ m laser source for wavelength division multiplexing applications,” IEEE Photon. Technol. Lett. 11, 1584–1586 (1999).
[Crossref]

Javaloyes, J.

A. Perez-Serrano, J. Javaloyes, and S. Balle, “Directional reversals and multimode dynamics in semiconductor ring lasers,” Phys. Rev. A 89, 023818 (2014).
[Crossref]

A. Perez-Serrano, J. Javaloyes, and S. Balle, “Multichannel wavelength conversion using four-wave mixing in semiconductor ring lasers,” IEEE Photon. Technol. Lett. 25, 476–479 (2013).
[Crossref]

J. Javaloyes and S. Balle, “Emission directionality of semiconductor ring lasers: a traveling-wave description,” IEEE J. Quantum Electron. 45, 431–438 (2009).
[Crossref]

Karouta, F.

B. Docter, J. Pozo, S. Beri, I. V. Ermakov, J. Danckaert, M. K. Smit, and F. Karouta, “Discretely tunable laser based on filtered feedback for telecommunication applications,” IEEE J. Sel. Top. Quantum Electron. 16, 1405–1412 (2010).
[Crossref]

Khoder, M.

M. Khoder, “Longitudinal modes competition in micro ring laser subject to both self and cross optical feedback,” Commun. Nonlinear Sci. Numer. Simul. 62, 146–156 (2018)
[Crossref]

M. Khoder, G. Van der Sande, and G. Verschaffelt, “Reducing the sensitivity of semiconductor ring lasers to external optical injection using selective optical feedback,” J. Appl. Phys. 124, 133101 (2018).
[Crossref]

M. Radziunas, M. Khoder, V. Tronciu, J. Danckaert, and G. Verschaffelt, “Tunable semiconductor ring laser with filtered optical feedback: Traveling wave description and experimental validation,” J. Opt. Soc. Am. B 35, 380–390 (2018).
[Crossref]

G. Verschaffelt and M. Khoder, “Directional power distribution and mode selection in micro ring lasers by controlling the phase and strength of filtered optical feedback,” Opt. Express 26, 14315–14328 (2018).
[Crossref] [PubMed]

G. Verschaffelt, M. Khoder, and G. Van der Sande, “Random number generator based on an integrated laser with on-chip optical feedback,” Chaos 27, 114310 (2017).
[Crossref] [PubMed]

M. Khoder, G. Van der Sande, J. Danckaert, and G. Verschaffelt, “Effect of external optical feedback on tunable micro-ring lasers using on chip filtered feedback,” IEEE Photon. Technol. Lett. 28, 959–962 (2016).
[Crossref]

M. Khoder, R. M. Nguimdo, J. Bolk, X. J. M. Leijtens, J. Danckaert, and G. Verschaffelt, “Wavelength switching speed in semiconductor ring lasers with on-chip filtered optical feedback,” IEEE Photon. Technol. Lett. 26, 520–523 (2014).
[Crossref]

M. Khoder, G. Verschaffelt, R. M. Nguimdo, J. Bolk, X. J. M. Leijtens, and J. Danckaert, “Digitally tunable dual wavelength emission from semiconductor ring lasers with filtered optical feedback,” Laser Phys. Lett.  10, 075804 (2013).
[Crossref]

M. Khoder, G. Verschaffelt, R. M. Nguimdo, J. Bolk, X. J. M. Leijtens, and J. Danckaert, “Controlled multiwavelength emission using semiconductor ring lasers with on-chip filtered optical feedback,” Opt. Lett. 38, 2608–2610 (2013).
[Crossref] [PubMed]

Khoe, G. D.

M. T. Hill, H. J. S. Dorren, T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[Crossref] [PubMed]

Kong, F.

Laybourn, J. P. R.

Laybourn, P. J. R.

M. Sorel, P. J. R. Laybourn, G. Giuliani, and S. Donati, “Unidirectional bistability in semiconductor waveguide ring lasers,” Appl. Phys. Lett. 80, 3051–3053 (2002).
[Crossref]

Leijtens, X. J. M.

M. Khoder, R. M. Nguimdo, J. Bolk, X. J. M. Leijtens, J. Danckaert, and G. Verschaffelt, “Wavelength switching speed in semiconductor ring lasers with on-chip filtered optical feedback,” IEEE Photon. Technol. Lett. 26, 520–523 (2014).
[Crossref]

M. Khoder, G. Verschaffelt, R. M. Nguimdo, J. Bolk, X. J. M. Leijtens, and J. Danckaert, “Digitally tunable dual wavelength emission from semiconductor ring lasers with filtered optical feedback,” Laser Phys. Lett.  10, 075804 (2013).
[Crossref]

M. Khoder, G. Verschaffelt, R. M. Nguimdo, J. Bolk, X. J. M. Leijtens, and J. Danckaert, “Controlled multiwavelength emission using semiconductor ring lasers with on-chip filtered optical feedback,” Opt. Lett. 38, 2608–2610 (2013).
[Crossref] [PubMed]

J. Zhao, D. Lenstra, R. Santos, M. J. Wale, M. K. Smit, and X. J. M. Leijtens, “Stability of a monolithic integrated filtered feedback laser,” Opt. Express 20, B270–B278 (2012).
[Crossref] [PubMed]

I. V. Ermakov, S. Beri, M. Ashour, J. Danckaert, B. Docter, J. Bolk, X. J. M. Leijtens, and G. Verschaffelt, “Semiconductor ring laser with on-chip filtered optical feedback for discrete wavelength tuning,” IEEE J. Quantum Electron. 48, 129–136 (2012).
[Crossref]

X. J. M. Leijtens, “JePPIX : the platform for indium phosphide-based photonics,” IET Optoelectron. 5, 202–206 (2011).
[Crossref]

M. T. Hill, H. J. S. Dorren, T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[Crossref] [PubMed]

Lenstra, D.

J. Zhao, D. Lenstra, R. Santos, M. J. Wale, M. K. Smit, and X. J. M. Leijtens, “Stability of a monolithic integrated filtered feedback laser,” Opt. Express 20, B270–B278 (2012).
[Crossref] [PubMed]

A. P. A. Fischer, O. K. Andersen, M. Yousefi, S. Stolte, and D. Lenstra, “Experimental and theoretical study of filtered optical feedback in a semiconductor laser,” IEEE J. Quantum Electron. 36, 375–384 (2000).
[Crossref]

Li, N.

Li, S.-S.

Li, W.

Libatique, N. J. C.

N. J. C. Libatique and R. K. Jain, “Precisely and rapidly wavelength-switchable narrow-linewidth 1.5-µ m laser source for wavelength division multiplexing applications,” IEEE Photon. Technol. Lett. 11, 1584–1586 (1999).
[Crossref]

Luo, B.

Marcenac, D.

M. Radziunas, H.-J. Wünsche, B. Sartorius, O. Brox, D. Hoffmann, K. Schneider, and D. Marcenac, “Modeling self-pulsating DFB lasers with an integrated phase tuning section,” IEEE J. Quantum Electron. 36, 1026–1034 (2000).
[Crossref]

Mechet, P.

G. Morthier and P. Mechet, “Theoretical analysis of unidirectional operation and reflection sensitivity of semiconductor ring or disk lasers,” IEEE J. Quantum Electron. 49, 1097–1101 (2013).
[Crossref]

Mezosi, G.

A. Trita, G. Mezosi, M. Sorel, and G. Giuliani, “All-optical toggle flip-flop based on monolithic semiconductor ring laser,” IEEE Photon. Technol. Lett. 26, 96–99 (2013).
[Crossref]

Miglierina, R.

Mirasso, C.

Morthier, G.

G. Morthier and P. Mechet, “Theoretical analysis of unidirectional operation and reflection sensitivity of semiconductor ring or disk lasers,” IEEE J. Quantum Electron. 49, 1097–1101 (2013).
[Crossref]

Murphy, E. J.

Nguimdo, R. M.

M. Khoder, R. M. Nguimdo, J. Bolk, X. J. M. Leijtens, J. Danckaert, and G. Verschaffelt, “Wavelength switching speed in semiconductor ring lasers with on-chip filtered optical feedback,” IEEE Photon. Technol. Lett. 26, 520–523 (2014).
[Crossref]

M. Khoder, G. Verschaffelt, R. M. Nguimdo, J. Bolk, X. J. M. Leijtens, and J. Danckaert, “Digitally tunable dual wavelength emission from semiconductor ring lasers with filtered optical feedback,” Laser Phys. Lett.  10, 075804 (2013).
[Crossref]

M. Khoder, G. Verschaffelt, R. M. Nguimdo, J. Bolk, X. J. M. Leijtens, and J. Danckaert, “Controlled multiwavelength emission using semiconductor ring lasers with on-chip filtered optical feedback,” Opt. Lett. 38, 2608–2610 (2013).
[Crossref] [PubMed]

Oei, Y. S.

M. T. Hill, H. J. S. Dorren, T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[Crossref] [PubMed]

Okamoto, K.

Y. Tachikawa and K. Okamoto, “Arrayed-waveguide grating lasers and their applications to tuning-free wavelength routing,” IEE Proc. Optoelectron. 143, 322–328 (1996).
[Crossref]

Pan, W.

Pérez, T.

Perez-Serrano, A.

A. Perez-Serrano, J. Javaloyes, and S. Balle, “Directional reversals and multimode dynamics in semiconductor ring lasers,” Phys. Rev. A 89, 023818 (2014).
[Crossref]

A. Perez-Serrano, J. Javaloyes, and S. Balle, “Multichannel wavelength conversion using four-wave mixing in semiconductor ring lasers,” IEEE Photon. Technol. Lett. 25, 476–479 (2013).
[Crossref]

Pozo, J.

B. Docter, J. Pozo, S. Beri, I. V. Ermakov, J. Danckaert, M. K. Smit, and F. Karouta, “Discretely tunable laser based on filtered feedback for telecommunication applications,” IEEE J. Sel. Top. Quantum Electron. 16, 1405–1412 (2010).
[Crossref]

Pusino, V.

Radziunas, M.

M. Radziunas, M. Khoder, V. Tronciu, J. Danckaert, and G. Verschaffelt, “Tunable semiconductor ring laser with filtered optical feedback: Traveling wave description and experimental validation,” J. Opt. Soc. Am. B 35, 380–390 (2018).
[Crossref]

M. Radziunas, H.-J. Wünsche, B. Sartorius, O. Brox, D. Hoffmann, K. Schneider, and D. Marcenac, “Modeling self-pulsating DFB lasers with an integrated phase tuning section,” IEEE J. Quantum Electron. 36, 1026–1034 (2000).
[Crossref]

M. Radziunas, ‘Traveling wave modeling of nonlinear dynamics in multisection semiconductor laser diodes,” in Handbook of Optoelectronic Device Modeling and Simulation: Lasers, Modulators, Photodetectors, Solar Cells, and Numerical Methods, J. Piprek, ed. (CRC Press, 2017), vol. 2, pp. 153–182.
[Crossref]

Romeira, B.

Santos, R.

Sartorius, B.

M. Radziunas, H.-J. Wünsche, B. Sartorius, O. Brox, D. Hoffmann, K. Schneider, and D. Marcenac, “Modeling self-pulsating DFB lasers with an integrated phase tuning section,” IEEE J. Quantum Electron. 36, 1026–1034 (2000).
[Crossref]

Schneider, K.

M. Radziunas, H.-J. Wünsche, B. Sartorius, O. Brox, D. Hoffmann, K. Schneider, and D. Marcenac, “Modeling self-pulsating DFB lasers with an integrated phase tuning section,” IEEE J. Quantum Electron. 36, 1026–1034 (2000).
[Crossref]

Scirè, A.

Smalbrugge, B.

M. T. Hill, H. J. S. Dorren, T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[Crossref] [PubMed]

Smit, M. K.

J. Zhao, D. Lenstra, R. Santos, M. J. Wale, M. K. Smit, and X. J. M. Leijtens, “Stability of a monolithic integrated filtered feedback laser,” Opt. Express 20, B270–B278 (2012).
[Crossref] [PubMed]

B. Docter, J. Pozo, S. Beri, I. V. Ermakov, J. Danckaert, M. K. Smit, and F. Karouta, “Discretely tunable laser based on filtered feedback for telecommunication applications,” IEEE J. Sel. Top. Quantum Electron. 16, 1405–1412 (2010).
[Crossref]

M. T. Hill, H. J. S. Dorren, T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[Crossref] [PubMed]

Sorel, M.

S.-S. Li, V. Pusino, S.-C. Chan, and M. Sorel, “Experimental investigation on feedback insensitivity in semiconductor ring lasers,” Opt. Lett. 43, 1974–1977 (2018)
[Crossref] [PubMed]

A. Trita, G. Mezosi, M. Sorel, and G. Giuliani, “All-optical toggle flip-flop based on monolithic semiconductor ring laser,” IEEE Photon. Technol. Lett. 26, 96–99 (2013).
[Crossref]

S. Fürst, S. Yu, and M. Sorel, “Fast and digitally wavelength-tunable semiconductor ring laser using a monolithically integrated distributed Bragg reflector,” IEEE Photon. Technol. Lett. 20, 1926–1928 (2008).
[Crossref]

M. Sorel, P. J. R. Laybourn, G. Giuliani, and S. Donati, “Unidirectional bistability in semiconductor waveguide ring lasers,” Appl. Phys. Lett. 80, 3051–3053 (2002).
[Crossref]

M. Sorel, J. P. R. Laybourn, A. Scirè, S. Balle, G. Giuliani, R. Miglierina, and S. Donati, “Alternate oscillations in semiconductor ring lasers,” Opt. Lett. 27, 1992–1994 (2002).
[Crossref]

Stolte, S.

A. P. A. Fischer, O. K. Andersen, M. Yousefi, S. Stolte, and D. Lenstra, “Experimental and theoretical study of filtered optical feedback in a semiconductor laser,” IEEE J. Quantum Electron. 36, 375–384 (2000).
[Crossref]

Sunada, S.

Tachikawa, Y.

Y. Tachikawa and K. Okamoto, “Arrayed-waveguide grating lasers and their applications to tuning-free wavelength routing,” IEE Proc. Optoelectron. 143, 322–328 (1996).
[Crossref]

Trita, A.

A. Trita, G. Mezosi, M. Sorel, and G. Giuliani, “All-optical toggle flip-flop based on monolithic semiconductor ring laser,” IEEE Photon. Technol. Lett. 26, 96–99 (2013).
[Crossref]

Tronciu, V.

Tsuzuki, K.

Uchida, A.

Van der Sande, G.

M. Khoder, G. Van der Sande, and G. Verschaffelt, “Reducing the sensitivity of semiconductor ring lasers to external optical injection using selective optical feedback,” J. Appl. Phys. 124, 133101 (2018).
[Crossref]

G. Verschaffelt, M. Khoder, and G. Van der Sande, “Random number generator based on an integrated laser with on-chip optical feedback,” Chaos 27, 114310 (2017).
[Crossref] [PubMed]

M. Khoder, G. Van der Sande, J. Danckaert, and G. Verschaffelt, “Effect of external optical feedback on tunable micro-ring lasers using on chip filtered feedback,” IEEE Photon. Technol. Lett. 28, 959–962 (2016).
[Crossref]

T. Pérez, A. Scirè, G. Van der Sande, P. Colet, and C. Mirasso, “Bistability and all-optical switching in semiconductor ring lasers,” Opt. Express 15, 12941–12948 (2007).
[Crossref] [PubMed]

Verschaffelt, G.

M. Khoder, G. Van der Sande, and G. Verschaffelt, “Reducing the sensitivity of semiconductor ring lasers to external optical injection using selective optical feedback,” J. Appl. Phys. 124, 133101 (2018).
[Crossref]

G. Verschaffelt and M. Khoder, “Directional power distribution and mode selection in micro ring lasers by controlling the phase and strength of filtered optical feedback,” Opt. Express 26, 14315–14328 (2018).
[Crossref] [PubMed]

M. Radziunas, M. Khoder, V. Tronciu, J. Danckaert, and G. Verschaffelt, “Tunable semiconductor ring laser with filtered optical feedback: Traveling wave description and experimental validation,” J. Opt. Soc. Am. B 35, 380–390 (2018).
[Crossref]

G. Verschaffelt, M. Khoder, and G. Van der Sande, “Random number generator based on an integrated laser with on-chip optical feedback,” Chaos 27, 114310 (2017).
[Crossref] [PubMed]

M. Khoder, G. Van der Sande, J. Danckaert, and G. Verschaffelt, “Effect of external optical feedback on tunable micro-ring lasers using on chip filtered feedback,” IEEE Photon. Technol. Lett. 28, 959–962 (2016).
[Crossref]

M. Khoder, R. M. Nguimdo, J. Bolk, X. J. M. Leijtens, J. Danckaert, and G. Verschaffelt, “Wavelength switching speed in semiconductor ring lasers with on-chip filtered optical feedback,” IEEE Photon. Technol. Lett. 26, 520–523 (2014).
[Crossref]

M. Khoder, G. Verschaffelt, R. M. Nguimdo, J. Bolk, X. J. M. Leijtens, and J. Danckaert, “Controlled multiwavelength emission using semiconductor ring lasers with on-chip filtered optical feedback,” Opt. Lett. 38, 2608–2610 (2013).
[Crossref] [PubMed]

M. Khoder, G. Verschaffelt, R. M. Nguimdo, J. Bolk, X. J. M. Leijtens, and J. Danckaert, “Digitally tunable dual wavelength emission from semiconductor ring lasers with filtered optical feedback,” Laser Phys. Lett.  10, 075804 (2013).
[Crossref]

I. V. Ermakov, S. Beri, M. Ashour, J. Danckaert, B. Docter, J. Bolk, X. J. M. Leijtens, and G. Verschaffelt, “Semiconductor ring laser with on-chip filtered optical feedback for discrete wavelength tuning,” IEEE J. Quantum Electron. 48, 129–136 (2012).
[Crossref]

Wale, M. J.

Wünsche, H.-J.

M. Radziunas, H.-J. Wünsche, B. Sartorius, O. Brox, D. Hoffmann, K. Schneider, and D. Marcenac, “Modeling self-pulsating DFB lasers with an integrated phase tuning section,” IEEE J. Quantum Electron. 36, 1026–1034 (2000).
[Crossref]

Xiang, S.

Yan, L.

Yao, J.

Yoshimura, K.

Yousefi, M.

A. P. A. Fischer, O. K. Andersen, M. Yousefi, S. Stolte, and D. Lenstra, “Experimental and theoretical study of filtered optical feedback in a semiconductor laser,” IEEE J. Quantum Electron. 36, 375–384 (2000).
[Crossref]

Yu, S.

S. Fürst, S. Yu, and M. Sorel, “Fast and digitally wavelength-tunable semiconductor ring laser using a monolithically integrated distributed Bragg reflector,” IEEE Photon. Technol. Lett. 20, 1926–1928 (2008).
[Crossref]

G. Yuan and S. Yu, “Bistability and switching properties of semiconductor ring lasers with external optical injection,” IEEE J. Quantum Electron. 44, 41–48 (2008).
[Crossref]

Yuan, G.

G. Yuan and S. Yu, “Bistability and switching properties of semiconductor ring lasers with external optical injection,” IEEE J. Quantum Electron. 44, 41–48 (2008).
[Crossref]

Zhang, J.

Zhao, J.

Zou, X.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

M. Sorel, P. J. R. Laybourn, G. Giuliani, and S. Donati, “Unidirectional bistability in semiconductor waveguide ring lasers,” Appl. Phys. Lett. 80, 3051–3053 (2002).
[Crossref]

Chaos (1)

G. Verschaffelt, M. Khoder, and G. Van der Sande, “Random number generator based on an integrated laser with on-chip optical feedback,” Chaos 27, 114310 (2017).
[Crossref] [PubMed]

Commun. Nonlinear Sci. Numer. Simul. (1)

M. Khoder, “Longitudinal modes competition in micro ring laser subject to both self and cross optical feedback,” Commun. Nonlinear Sci. Numer. Simul. 62, 146–156 (2018)
[Crossref]

IEE Proc. Optoelectron. (1)

Y. Tachikawa and K. Okamoto, “Arrayed-waveguide grating lasers and their applications to tuning-free wavelength routing,” IEE Proc. Optoelectron. 143, 322–328 (1996).
[Crossref]

IEEE J. Quantum Electron. (6)

A. P. A. Fischer, O. K. Andersen, M. Yousefi, S. Stolte, and D. Lenstra, “Experimental and theoretical study of filtered optical feedback in a semiconductor laser,” IEEE J. Quantum Electron. 36, 375–384 (2000).
[Crossref]

G. Yuan and S. Yu, “Bistability and switching properties of semiconductor ring lasers with external optical injection,” IEEE J. Quantum Electron. 44, 41–48 (2008).
[Crossref]

G. Morthier and P. Mechet, “Theoretical analysis of unidirectional operation and reflection sensitivity of semiconductor ring or disk lasers,” IEEE J. Quantum Electron. 49, 1097–1101 (2013).
[Crossref]

J. Javaloyes and S. Balle, “Emission directionality of semiconductor ring lasers: a traveling-wave description,” IEEE J. Quantum Electron. 45, 431–438 (2009).
[Crossref]

I. V. Ermakov, S. Beri, M. Ashour, J. Danckaert, B. Docter, J. Bolk, X. J. M. Leijtens, and G. Verschaffelt, “Semiconductor ring laser with on-chip filtered optical feedback for discrete wavelength tuning,” IEEE J. Quantum Electron. 48, 129–136 (2012).
[Crossref]

M. Radziunas, H.-J. Wünsche, B. Sartorius, O. Brox, D. Hoffmann, K. Schneider, and D. Marcenac, “Modeling self-pulsating DFB lasers with an integrated phase tuning section,” IEEE J. Quantum Electron. 36, 1026–1034 (2000).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (2)

L. A. Coldren, “Monolithic tunable diode lasers,” IEEE J. Sel. Top. Quantum Electron. 6, 988–999 (2000).
[Crossref]

B. Docter, J. Pozo, S. Beri, I. V. Ermakov, J. Danckaert, M. K. Smit, and F. Karouta, “Discretely tunable laser based on filtered feedback for telecommunication applications,” IEEE J. Sel. Top. Quantum Electron. 16, 1405–1412 (2010).
[Crossref]

IEEE Photon. Technol. Lett. (6)

S. Fürst, S. Yu, and M. Sorel, “Fast and digitally wavelength-tunable semiconductor ring laser using a monolithically integrated distributed Bragg reflector,” IEEE Photon. Technol. Lett. 20, 1926–1928 (2008).
[Crossref]

N. J. C. Libatique and R. K. Jain, “Precisely and rapidly wavelength-switchable narrow-linewidth 1.5-µ m laser source for wavelength division multiplexing applications,” IEEE Photon. Technol. Lett. 11, 1584–1586 (1999).
[Crossref]

A. Trita, G. Mezosi, M. Sorel, and G. Giuliani, “All-optical toggle flip-flop based on monolithic semiconductor ring laser,” IEEE Photon. Technol. Lett. 26, 96–99 (2013).
[Crossref]

A. Perez-Serrano, J. Javaloyes, and S. Balle, “Multichannel wavelength conversion using four-wave mixing in semiconductor ring lasers,” IEEE Photon. Technol. Lett. 25, 476–479 (2013).
[Crossref]

M. Khoder, G. Van der Sande, J. Danckaert, and G. Verschaffelt, “Effect of external optical feedback on tunable micro-ring lasers using on chip filtered feedback,” IEEE Photon. Technol. Lett. 28, 959–962 (2016).
[Crossref]

M. Khoder, R. M. Nguimdo, J. Bolk, X. J. M. Leijtens, J. Danckaert, and G. Verschaffelt, “Wavelength switching speed in semiconductor ring lasers with on-chip filtered optical feedback,” IEEE Photon. Technol. Lett. 26, 520–523 (2014).
[Crossref]

IET Optoelectron. (1)

X. J. M. Leijtens, “JePPIX : the platform for indium phosphide-based photonics,” IET Optoelectron. 5, 202–206 (2011).
[Crossref]

J. Appl. Phys. (1)

M. Khoder, G. Van der Sande, and G. Verschaffelt, “Reducing the sensitivity of semiconductor ring lasers to external optical injection using selective optical feedback,” J. Appl. Phys. 124, 133101 (2018).
[Crossref]

J. Lightwave Technol. (2)

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

Laser Phys. Lett (1)

M. Khoder, G. Verschaffelt, R. M. Nguimdo, J. Bolk, X. J. M. Leijtens, and J. Danckaert, “Digitally tunable dual wavelength emission from semiconductor ring lasers with filtered optical feedback,” Laser Phys. Lett.  10, 075804 (2013).
[Crossref]

Nature (1)

M. T. Hill, H. J. S. Dorren, T. de Vries, X. J. M. Leijtens, J. H. den Besten, B. Smalbrugge, Y. S. Oei, H. Binsma, G. D. Khoe, and M. K. Smit, “A fast low-power optical memory based on coupled micro-ring lasers,” Nature 432, 206–209 (2004).
[Crossref] [PubMed]

Opt. Express (4)

Opt. Lett. (3)

Phys. Rev. A (1)

A. Perez-Serrano, J. Javaloyes, and S. Balle, “Directional reversals and multimode dynamics in semiconductor ring lasers,” Phys. Rev. A 89, 023818 (2014).
[Crossref]

Other (1)

M. Radziunas, ‘Traveling wave modeling of nonlinear dynamics in multisection semiconductor laser diodes,” in Handbook of Optoelectronic Device Modeling and Simulation: Lasers, Modulators, Photodetectors, Solar Cells, and Numerical Methods, J. Piprek, ed. (CRC Press, 2017), vol. 2, pp. 153–182.
[Crossref]

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Figures (13)

Fig. 1
Fig. 1 Top: Microscopic image of the device, bottom: Schematic of the lab setup.
Fig. 2
Fig. 2 Optical spectrum of the output of the SRL in the CW direction when it is pumped at 85 mA and without pumping any gate (without feedback).
Fig. 3
Fig. 3 (left) A schematic representation of the test structure which is used to characterize the SOA gate. (Right) Output power of the SOA amplifier as a function of the injection current (when the SRL is switched off).
Fig. 4
Fig. 4 Spectrum of the SRL’s output in the CW direction when pumping the SRL at 95 mA, gate 1 at 14.2 mA and gate 3 either at 3.55 mA (red) or at 38 mA (blue). A schematic representation of the AWG channels passbands is plotted at the top.
Fig. 5
Fig. 5 (a) Trigger signal from arbitrary waveform generator to the oscilloscope. (b). Device output signal when the tunable bandpass filter is centered at λ1. (c). Zoom in of a single switching event.
Fig. 6
Fig. 6 Histogram of the wavelength switching’s delay time at the falling edge of the gate 1 modulation using Vpp = 0.5 volt.
Fig. 7
Fig. 7 (a). Transition time as function of Vpp. (b). Delay time as function of Vpp. Other experimental settings are ISRL= 95 mA, I1 =27.86 mA and I3 =5.18 mA.
Fig. 8
Fig. 8 Schematic representation of the simulated SRL with four FOF branches. Different colored frames and black segments indicate three different types of SRL sections and interfaces between these sections, respectively. Blue curved arrows represent all nonvanishing field reflections at these interfaces.
Fig. 9
Fig. 9 Simulated SRL operation for continuous pumping of the 1st and 3rd gates. (a): time trace of the emitted CW field after filtering it with digital filters centred at the dominant first and third gate mode wavelengths. (b): optical spectra of this field (bottom) and different gate transmission spectra (above). (c): wavelengths of the dominant (large bullets) and the largest side (small bullets) modes within the two considered gates, and power of the emitted CW field after filtering it with digital filters as functions of I1. (d): same as the previous panel as functions of I3. In all cases, φj = 0, j = 1, , 4.
Fig. 10
Fig. 10 Switchings between channel 1 and channel 3 modes by modulating the first gate with a = 40 mA (a), 20 mA (b) and 5 mA (c), or by modulating the third gate with a = 20 mA (d) and 5 mA (e). Modulation period in all cases was T = 100 ns. Black and red represent the first and the third gates, respectively. Thin: intensities of the central (solid), shorter-wavelength neighbor (dashed) and the longer-wavelength neighbor (dotted) mode within the first and third gates. Black and red bullets indicate beginning and end of the corresponding gate opening and closing. Thick: deviations of the mean carrier density within the ring (blue), within gate 1, and within gate 3 from the steady state densities n ¯R = 1.08 · 1024/m3, n ¯1 = 2.85 · 1024/m3, and n ¯3 = 2.03 · 1024/m3, respectively. Carrier density deviations within modulated gates are shown after dividing them by factor 10. The steady parts of the bias currents are I1 = 29 mA and I3 = 18 mA.
Fig. 11
Fig. 11 Simulated gate switching delay-[(a), (b)] and transition- [(c), (d)] times as functions of the amplitude of the current modulation in the first gate. Switching on of the first gate and switching off of the third gate are considered in panels (a),(c) and (b),(d), respectively. Gray dots and black lines at each bias modulation amplitude represent these times in 40 individual calculations and the mean value of these times, respectively. The steady parts of the bias currents are the same as in Fig. 10.
Fig. 12
Fig. 12 Simulated dominance of the first channel modes (light shading), third channel modes (black), and dual gate operation with < 10 dB suppression of the weaker channel mode (white) for different φ1 and I1 whereas I3 = 18mA and φ3/2π = 0.2 (a) or φ3/2π = 0.9 (b), as well as different φ3 and I3 whereas I1 = 29mA and φ1 = 0 (c) or φ1/2π = 0.8 (d).
Fig. 13
Fig. 13 Study of the phase factors φ1 and φ3. (a): the first (light shading), third (black), or dual (white) channel mode operation for I1 = 29 mA and I3 = 18 mA. (b): the first gate bias I1 giving the upper border of the third channel mode operation regime once I3 = 18 mA. (c): the third gate bias I3 giving the upper border of the first channel mode operation regime once I1 = 29 mA. Horizontal and vertical dashed lines in panels (b) and (c) correspond to the simulations presented in panels (a),(b) and (c),(d) of Fig. 12, respectively.

Equations (4)

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1 v g t E ± ± z E ± = ( i β ± ( N , | E ± | 2 ) D ) E ± + F s p ± ,
β ± = [ δ i α 0 2 ] + [ α H + i 1 + ε S | E ± | 2 + ε c | E | 2 ] g ( N ) 2 .
t N = I q V R ( N ) G ( N , | E ± | ,
δ I = a 2 · s i g n ( s i n ( 2 π t / T ) ) .