Abstract

Optical logic has the potential to replace electronics with photonic circuits in applications for which optic-to-electronic conversion is impractical and for integrated all-optical circuits. Nonlinear optics in whispering gallery mode resonators provides low power, scalable methods to achieve optical logic. We demonstrate, for the first time, an all-optical, universal logic gate using counterpropagating light in which all signals have the same operating optical frequency. Such a device would make possible the routing of optical signals without the need for conversion into the electronic domain, thus reducing latency. The operating principle of the device is based on the Kerr interaction between counter-propagating beams in a whispering gallery mode resonator which induces a splitting between the resonance frequencies for the two propagating directions. Our gate uses a fused silica microrod resonator with a Q-factor of $2 \times 10^8$ . This method of optical logic gives a practical solution to the on-chip routing of light.

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2019 (3)

S. Zhang, “Sub-milliwatt-level microresonator solitons with extended access range using an auxiliary laser,” Optica, vol. 6, no. 2, pp. 206–212, 2019.

Z. I. W. Ang, “On-chip single-mode high-Q terahertz whispering gallery mode resonator,” Opt. Lett., vol. 44, no. 11, pp. 3–6, 2019.

F. Copie, M. T. M. Woodley, L. Del Bino, J. M. Silver, S. Zhang, and P. Del’Haye, “Interplay of polarization and time-reversal symmetry breaking in synchronously pumped ring resonators,” Phys. Rev. Lett., vol. 122, no. 1, 2019, Art. no. .

2018 (3)

L. Del Bino, J. M. Silver, M. T. M. Woodley, S. L. Stebbings, X. Xhao, and P. Del’Haye, “Microresonator isolators and circulators based on the intrinsic nonreciprocity of the kerr effect,” Optica, vol. 5, no. 3, pp. 279–282, 2018.

M. T. M. Woodley, “Universal symmetry-breaking dynamics for the Kerr interaction of counterpropagating light in dielectric ring resonators,” Phys. Rev. A, vol. 98, no. 5, 2018, Art. no. .

Y. Tian, “Experimental demonstration of an optical Feynman gate for reversible logic operation using silicon micro-ring resonators,” Nanophotonics, vol. 7, no. 1, pp. 333–337, 2018.

2017 (4)

L. Del Bino, J. M. Silver, S. L. Stebbings, and P. Del’Haye, “Symmetry breaking of counter-propagating light in a nonlinear resonator,” Sci. Rep., vol. 7, no. 43142, pp. 1–6, 2017.

T. Hett, S. Krämmer, U. Hilleringmann, H. Kalt, and A. Zrenner, “High-Q whispering gallery microdisk resonators based on silicon oxynitride,” J. Lumin., vol. 191, pp. 131–134, 2017.

G. Lin, C. Aurélien, and Y. K. Chembo, “Nonlinear photonics with high- Q resonators,” Adv. Opt. Photon., vol. 9, no. 4, pp. 828–890, 2017.

D. Gostimirovic and W. N. Ye, “Ultracompact CMOS-compatible optical logic using carrier depletion in microdisk resonators,” Sci. Rep., vol. 7, no. 12603, pp. 1–10, 2017.

2016 (4)

A. Godbole, P. P. Dali, V. Janyani, T. Tanabe, and G. Singh, “All optical scalable logic gates using Si$_3$N$_4$ microring resonators,” IEEE J. Sel. Top. Quant. Electron., vol. 22, no. 6, pp. 326–333,  2016.

E. Agrell, “Roadmap of optical communications,” J. Opt., vol. 18, no. 063002, pp. 1–40, 2016.

W. Liu, “A fully reconfigurable photonic integrated signal processor,” Nat. Photon., vol. 10, pp. 190–195, 2016.

O. Alibart, “Nonlinear and quantum optics with whispering gallery resonators,” J. Opt., vol. 18, pp. 1–44, 2016.

2014 (3)

C. Qiu, W. Gao, R. Soref, J. T. Robinson, and Q. Xu, “Reconfigurable electro-optical directed-logic circuit using carrier-depletion micro-ring resonators,” Opt. Lett., vol. 39, no. 24, pp. 6767–6770, 2014.

P. Sethi and S. Roy, “All-optical ultrafast XOR/XNOR logic gates, binary counter, and double-bit comparator with silicon microring resonators,” Appl. Opt., vol. 53, no. 28, 2014, Art. no. .

A. Fushimi and T. Tanabe, “All-optical logic gate operating with single wavelength,” Opt. Express, vol. 22, no. 4, 2014, Art. no. .

2013 (4)

M. Xiong, “All-optical 10 Gb/s AND logic gate in a silicon microring resonator,” Opt. Express, vol. 21, no. 22, pp. 25772–25779, 2013.

D. J. Moss, R. Morandotti, A. L. Gaeta, and M. Lipson, “New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics,” Nat. Photon., vol. 7, pp. 597–607, 2013.

Y. Tian, L. Zhang, and L. Yang, “Directed XOR/XNOR logic gates using U-to-U waveguides and two microring resonators,” IEEE Photon. Technol. Lett., vol. 25, no. 1, pp. 18–21,  2013.

P. Del’Haye, S. A. Diddams, and S. B. Papp, “Laser-machined ultra-high-Q microrod resonators for nonlinear optics,” Appl. Phys. Lett., vol. 102, no. 221119, pp. 221119–221119-4, 2013.

2012 (1)

F. Monifi, J. Friedlein, S. K. Ozdemir, and L. Yang, “A robust and tunable add-drop filter using whispering gallery mode microtoroid resonator,” J. Light. Technol., vol. 30, no. 21, pp. 3306–3315,  2012.

2011 (1)

2010 (2)

M. Pöllinger, “All-optical signal processing at ultra-low powers in bottle microresonators using the Kerr effect Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Opt. Express, vol. 18, no. 17, pp. 17 764–17 775, 2010.

L. Zhang, “Demonstration of directed XOR / XNOR logic gates using two cascaded microring resonators,” Opt. Lett., vol. 35, no. 10, pp. 1620–1622, 2010.

2007 (1)

Q. Xu and M. Lipson, “All-optical logic based on silicon micro-ring resonators,” Opt. Express, vol. 15, no. 3, 2007, Art. no. .

2005 (2)

A. Jajszczyk, “Optical networks - the electro-optic reality,” Opt. Switching Netw., vol. 1, no. 1, pp. 3–18,  2005.

S. Mikroulis, H. Simos, E. Roditi, and D. Syvridis, “Ultrafast all-optical AND logic operation based on four-wave mixing in a passive InGaAsP-InP microring resonator,” IEEE Photon. Technol. Lett., vol. 17, no. 9, pp. 1878–1880,  2005.

2004 (1)

T. A. Ibrahim, K. Amarnath, L. C. Kuo, R. Grover, V. Van, and P.-T. Ho, “Photonic logic NOR gate based on two symmetric microring resonators,” Opt. Lett., vol. 29, no. 23, 2004, Art. no. .

2003 (1)

T. A. Ibrahim, R. Grover, L.-C. Kuo, S. Kanakaraju, L. C. Calhoun, and P.-T. Ho, “All-optical AND/NAND logic gates using semiconductor microresonators,” IEEE Photon. Technol. Lett., vol. 15, no. 10, pp. 1422–1424,  2003.

1989 (1)

L. Gorodetsky, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A, vol. 137, no. 7, pp. 393–397, 1989.

1981 (1)

A. E. Kaplan and P. Meystre, “Enhancement of the Sagnac effect due to nonlinearly induced nonreciprocity,” Opt. Lett., vol. 6, no. 12, 1981, Art. no. .

1973 (1)

R. H. Stolen and A. Ashkin, “Optical Kerr effect in glass waveguide,” Appl. Phys. Lett, vol. 22, pp. 294–296, 1973.

Agrell, E.

E. Agrell, “Roadmap of optical communications,” J. Opt., vol. 18, no. 063002, pp. 1–40, 2016.

Alibart, O.

O. Alibart, “Nonlinear and quantum optics with whispering gallery resonators,” J. Opt., vol. 18, pp. 1–44, 2016.

Amarnath, K.

T. A. Ibrahim, K. Amarnath, L. C. Kuo, R. Grover, V. Van, and P.-T. Ho, “Photonic logic NOR gate based on two symmetric microring resonators,” Opt. Lett., vol. 29, no. 23, 2004, Art. no. .

Ang, Z. I. W.

Z. I. W. Ang, “On-chip single-mode high-Q terahertz whispering gallery mode resonator,” Opt. Lett., vol. 44, no. 11, pp. 3–6, 2019.

Ashkin, A.

R. H. Stolen and A. Ashkin, “Optical Kerr effect in glass waveguide,” Appl. Phys. Lett, vol. 22, pp. 294–296, 1973.

Aurélien, C.

Bino, L. Del

F. Copie, M. T. M. Woodley, L. Del Bino, J. M. Silver, S. Zhang, and P. Del’Haye, “Interplay of polarization and time-reversal symmetry breaking in synchronously pumped ring resonators,” Phys. Rev. Lett., vol. 122, no. 1, 2019, Art. no. .

L. Del Bino, N. Moroney, and P. Del’Haye, “Optical memories and switching dynamics of counterpropagating light states in microresonators,” 2020. [Online]. Available: https://arxiv.org/abs/2002.02954

Boyd, R. W.

R. W. Boyd, Nonlinear Optics. New York, NY, USA: Academic, 2008.

Calhoun, L. C.

T. A. Ibrahim, R. Grover, L.-C. Kuo, S. Kanakaraju, L. C. Calhoun, and P.-T. Ho, “All-optical AND/NAND logic gates using semiconductor microresonators,” IEEE Photon. Technol. Lett., vol. 15, no. 10, pp. 1422–1424,  2003.

Chembo, Y. K.

Copie, F.

F. Copie, M. T. M. Woodley, L. Del Bino, J. M. Silver, S. Zhang, and P. Del’Haye, “Interplay of polarization and time-reversal symmetry breaking in synchronously pumped ring resonators,” Phys. Rev. Lett., vol. 122, no. 1, 2019, Art. no. .

Dali, P. P.

A. Godbole, P. P. Dali, V. Janyani, T. Tanabe, and G. Singh, “All optical scalable logic gates using Si$_3$N$_4$ microring resonators,” IEEE J. Sel. Top. Quant. Electron., vol. 22, no. 6, pp. 326–333,  2016.

P. P. Dali, A. Godbole, S. Sahu, G. Singh, and T. Tanabe, “Microring resonator based all optical NAND and NOT gate with higher output power,” in Proc. Asia Commun. Photon. Conf., Washington, DC, USA, Nov. 2015, p. ASu2A.28.

Del Bino, L.

L. Del Bino, J. M. Silver, M. T. M. Woodley, S. L. Stebbings, X. Xhao, and P. Del’Haye, “Microresonator isolators and circulators based on the intrinsic nonreciprocity of the kerr effect,” Optica, vol. 5, no. 3, pp. 279–282, 2018.

L. Del Bino, J. M. Silver, S. L. Stebbings, and P. Del’Haye, “Symmetry breaking of counter-propagating light in a nonlinear resonator,” Sci. Rep., vol. 7, no. 43142, pp. 1–6, 2017.

Del’Haye, P.

F. Copie, M. T. M. Woodley, L. Del Bino, J. M. Silver, S. Zhang, and P. Del’Haye, “Interplay of polarization and time-reversal symmetry breaking in synchronously pumped ring resonators,” Phys. Rev. Lett., vol. 122, no. 1, 2019, Art. no. .

L. Del Bino, J. M. Silver, M. T. M. Woodley, S. L. Stebbings, X. Xhao, and P. Del’Haye, “Microresonator isolators and circulators based on the intrinsic nonreciprocity of the kerr effect,” Optica, vol. 5, no. 3, pp. 279–282, 2018.

L. Del Bino, J. M. Silver, S. L. Stebbings, and P. Del’Haye, “Symmetry breaking of counter-propagating light in a nonlinear resonator,” Sci. Rep., vol. 7, no. 43142, pp. 1–6, 2017.

P. Del’Haye, S. A. Diddams, and S. B. Papp, “Laser-machined ultra-high-Q microrod resonators for nonlinear optics,” Appl. Phys. Lett., vol. 102, no. 221119, pp. 221119–221119-4, 2013.

L. Del Bino, N. Moroney, and P. Del’Haye, “Optical memories and switching dynamics of counterpropagating light states in microresonators,” 2020. [Online]. Available: https://arxiv.org/abs/2002.02954

Diddams, S. A.

P. Del’Haye, S. A. Diddams, and S. B. Papp, “Laser-machined ultra-high-Q microrod resonators for nonlinear optics,” Appl. Phys. Lett., vol. 102, no. 221119, pp. 221119–221119-4, 2013.

Friedlein, J.

F. Monifi, J. Friedlein, S. K. Ozdemir, and L. Yang, “A robust and tunable add-drop filter using whispering gallery mode microtoroid resonator,” J. Light. Technol., vol. 30, no. 21, pp. 3306–3315,  2012.

Fushimi, A.

A. Fushimi and T. Tanabe, “All-optical logic gate operating with single wavelength,” Opt. Express, vol. 22, no. 4, 2014, Art. no. .

Gaeta, A. L.

D. J. Moss, R. Morandotti, A. L. Gaeta, and M. Lipson, “New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics,” Nat. Photon., vol. 7, pp. 597–607, 2013.

Gao, W.

Godbole, A.

A. Godbole, P. P. Dali, V. Janyani, T. Tanabe, and G. Singh, “All optical scalable logic gates using Si$_3$N$_4$ microring resonators,” IEEE J. Sel. Top. Quant. Electron., vol. 22, no. 6, pp. 326–333,  2016.

P. P. Dali, A. Godbole, S. Sahu, G. Singh, and T. Tanabe, “Microring resonator based all optical NAND and NOT gate with higher output power,” in Proc. Asia Commun. Photon. Conf., Washington, DC, USA, Nov. 2015, p. ASu2A.28.

Gorodetsky, L.

L. Gorodetsky, “Quality-factor and nonlinear properties of optical whispering-gallery modes,” Phys. Lett. A, vol. 137, no. 7, pp. 393–397, 1989.

Gostimirovic, D.

D. Gostimirovic and W. N. Ye, “Ultracompact CMOS-compatible optical logic using carrier depletion in microdisk resonators,” Sci. Rep., vol. 7, no. 12603, pp. 1–10, 2017.

Grover, R.

T. A. Ibrahim, K. Amarnath, L. C. Kuo, R. Grover, V. Van, and P.-T. Ho, “Photonic logic NOR gate based on two symmetric microring resonators,” Opt. Lett., vol. 29, no. 23, 2004, Art. no. .

T. A. Ibrahim, R. Grover, L.-C. Kuo, S. Kanakaraju, L. C. Calhoun, and P.-T. Ho, “All-optical AND/NAND logic gates using semiconductor microresonators,” IEEE Photon. Technol. Lett., vol. 15, no. 10, pp. 1422–1424,  2003.

Hett, T.

T. Hett, S. Krämmer, U. Hilleringmann, H. Kalt, and A. Zrenner, “High-Q whispering gallery microdisk resonators based on silicon oxynitride,” J. Lumin., vol. 191, pp. 131–134, 2017.

Hilleringmann, U.

T. Hett, S. Krämmer, U. Hilleringmann, H. Kalt, and A. Zrenner, “High-Q whispering gallery microdisk resonators based on silicon oxynitride,” J. Lumin., vol. 191, pp. 131–134, 2017.

Ho, P.-T.

T. A. Ibrahim, K. Amarnath, L. C. Kuo, R. Grover, V. Van, and P.-T. Ho, “Photonic logic NOR gate based on two symmetric microring resonators,” Opt. Lett., vol. 29, no. 23, 2004, Art. no. .

T. A. Ibrahim, R. Grover, L.-C. Kuo, S. Kanakaraju, L. C. Calhoun, and P.-T. Ho, “All-optical AND/NAND logic gates using semiconductor microresonators,” IEEE Photon. Technol. Lett., vol. 15, no. 10, pp. 1422–1424,  2003.

Ibrahim, T. A.

T. A. Ibrahim, K. Amarnath, L. C. Kuo, R. Grover, V. Van, and P.-T. Ho, “Photonic logic NOR gate based on two symmetric microring resonators,” Opt. Lett., vol. 29, no. 23, 2004, Art. no. .

T. A. Ibrahim, R. Grover, L.-C. Kuo, S. Kanakaraju, L. C. Calhoun, and P.-T. Ho, “All-optical AND/NAND logic gates using semiconductor microresonators,” IEEE Photon. Technol. Lett., vol. 15, no. 10, pp. 1422–1424,  2003.

Jajszczyk, A.

A. Jajszczyk, “Optical networks - the electro-optic reality,” Opt. Switching Netw., vol. 1, no. 1, pp. 3–18,  2005.

Janyani, V.

A. Godbole, P. P. Dali, V. Janyani, T. Tanabe, and G. Singh, “All optical scalable logic gates using Si$_3$N$_4$ microring resonators,” IEEE J. Sel. Top. Quant. Electron., vol. 22, no. 6, pp. 326–333,  2016.

Kalt, H.

T. Hett, S. Krämmer, U. Hilleringmann, H. Kalt, and A. Zrenner, “High-Q whispering gallery microdisk resonators based on silicon oxynitride,” J. Lumin., vol. 191, pp. 131–134, 2017.

Kanakaraju, S.

T. A. Ibrahim, R. Grover, L.-C. Kuo, S. Kanakaraju, L. C. Calhoun, and P.-T. Ho, “All-optical AND/NAND logic gates using semiconductor microresonators,” IEEE Photon. Technol. Lett., vol. 15, no. 10, pp. 1422–1424,  2003.

Kaplan, A. E.

A. E. Kaplan and P. Meystre, “Enhancement of the Sagnac effect due to nonlinearly induced nonreciprocity,” Opt. Lett., vol. 6, no. 12, 1981, Art. no. .

Krämmer, S.

T. Hett, S. Krämmer, U. Hilleringmann, H. Kalt, and A. Zrenner, “High-Q whispering gallery microdisk resonators based on silicon oxynitride,” J. Lumin., vol. 191, pp. 131–134, 2017.

Kuo, L. C.

T. A. Ibrahim, K. Amarnath, L. C. Kuo, R. Grover, V. Van, and P.-T. Ho, “Photonic logic NOR gate based on two symmetric microring resonators,” Opt. Lett., vol. 29, no. 23, 2004, Art. no. .

Kuo, L.-C.

T. A. Ibrahim, R. Grover, L.-C. Kuo, S. Kanakaraju, L. C. Calhoun, and P.-T. Ho, “All-optical AND/NAND logic gates using semiconductor microresonators,” IEEE Photon. Technol. Lett., vol. 15, no. 10, pp. 1422–1424,  2003.

Lin, G.

Lipson, M.

D. J. Moss, R. Morandotti, A. L. Gaeta, and M. Lipson, “New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics,” Nat. Photon., vol. 7, pp. 597–607, 2013.

Q. Xu and M. Lipson, “All-optical logic based on silicon micro-ring resonators,” Opt. Express, vol. 15, no. 3, 2007, Art. no. .

Liu, W.

W. Liu, “A fully reconfigurable photonic integrated signal processor,” Nat. Photon., vol. 10, pp. 190–195, 2016.

Meystre, P.

A. E. Kaplan and P. Meystre, “Enhancement of the Sagnac effect due to nonlinearly induced nonreciprocity,” Opt. Lett., vol. 6, no. 12, 1981, Art. no. .

Mikroulis, S.

S. Mikroulis, H. Simos, E. Roditi, and D. Syvridis, “Ultrafast all-optical AND logic operation based on four-wave mixing in a passive InGaAsP-InP microring resonator,” IEEE Photon. Technol. Lett., vol. 17, no. 9, pp. 1878–1880,  2005.

Monifi, F.

F. Monifi, J. Friedlein, S. K. Ozdemir, and L. Yang, “A robust and tunable add-drop filter using whispering gallery mode microtoroid resonator,” J. Light. Technol., vol. 30, no. 21, pp. 3306–3315,  2012.

Morandotti, R.

D. J. Moss, R. Morandotti, A. L. Gaeta, and M. Lipson, “New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics,” Nat. Photon., vol. 7, pp. 597–607, 2013.

Moroney, N.

N. Moroney, “Logic gates based on interaction of counterpropagating light in microresonators,” in Proc. Conf. Lasers Electro-Opt., San Jose, CA, USA, 2019, Paper. STh3J.7.

L. Del Bino, N. Moroney, and P. Del’Haye, “Optical memories and switching dynamics of counterpropagating light states in microresonators,” 2020. [Online]. Available: https://arxiv.org/abs/2002.02954

Moss, D. J.

D. J. Moss, R. Morandotti, A. L. Gaeta, and M. Lipson, “New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics,” Nat. Photon., vol. 7, pp. 597–607, 2013.

Ozdemir, S. K.

F. Monifi, J. Friedlein, S. K. Ozdemir, and L. Yang, “A robust and tunable add-drop filter using whispering gallery mode microtoroid resonator,” J. Light. Technol., vol. 30, no. 21, pp. 3306–3315,  2012.

Papp, S. B.

P. Del’Haye, S. A. Diddams, and S. B. Papp, “Laser-machined ultra-high-Q microrod resonators for nonlinear optics,” Appl. Phys. Lett., vol. 102, no. 221119, pp. 221119–221119-4, 2013.

Pöllinger, M.

M. Pöllinger, “All-optical signal processing at ultra-low powers in bottle microresonators using the Kerr effect Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Opt. Express, vol. 18, no. 17, pp. 17 764–17 775, 2010.

Qiu, C.

Robinson, J. T.

Roditi, E.

S. Mikroulis, H. Simos, E. Roditi, and D. Syvridis, “Ultrafast all-optical AND logic operation based on four-wave mixing in a passive InGaAsP-InP microring resonator,” IEEE Photon. Technol. Lett., vol. 17, no. 9, pp. 1878–1880,  2005.

Roy, S.

P. Sethi and S. Roy, “All-optical ultrafast XOR/XNOR logic gates, binary counter, and double-bit comparator with silicon microring resonators,” Appl. Opt., vol. 53, no. 28, 2014, Art. no. .

Sahu, S.

P. P. Dali, A. Godbole, S. Sahu, G. Singh, and T. Tanabe, “Microring resonator based all optical NAND and NOT gate with higher output power,” in Proc. Asia Commun. Photon. Conf., Washington, DC, USA, Nov. 2015, p. ASu2A.28.

Sethi, P.

P. Sethi and S. Roy, “All-optical ultrafast XOR/XNOR logic gates, binary counter, and double-bit comparator with silicon microring resonators,” Appl. Opt., vol. 53, no. 28, 2014, Art. no. .

Silver, J. M.

F. Copie, M. T. M. Woodley, L. Del Bino, J. M. Silver, S. Zhang, and P. Del’Haye, “Interplay of polarization and time-reversal symmetry breaking in synchronously pumped ring resonators,” Phys. Rev. Lett., vol. 122, no. 1, 2019, Art. no. .

L. Del Bino, J. M. Silver, M. T. M. Woodley, S. L. Stebbings, X. Xhao, and P. Del’Haye, “Microresonator isolators and circulators based on the intrinsic nonreciprocity of the kerr effect,” Optica, vol. 5, no. 3, pp. 279–282, 2018.

L. Del Bino, J. M. Silver, S. L. Stebbings, and P. Del’Haye, “Symmetry breaking of counter-propagating light in a nonlinear resonator,” Sci. Rep., vol. 7, no. 43142, pp. 1–6, 2017.

Simos, H.

S. Mikroulis, H. Simos, E. Roditi, and D. Syvridis, “Ultrafast all-optical AND logic operation based on four-wave mixing in a passive InGaAsP-InP microring resonator,” IEEE Photon. Technol. Lett., vol. 17, no. 9, pp. 1878–1880,  2005.

Singh, G.

A. Godbole, P. P. Dali, V. Janyani, T. Tanabe, and G. Singh, “All optical scalable logic gates using Si$_3$N$_4$ microring resonators,” IEEE J. Sel. Top. Quant. Electron., vol. 22, no. 6, pp. 326–333,  2016.

P. P. Dali, A. Godbole, S. Sahu, G. Singh, and T. Tanabe, “Microring resonator based all optical NAND and NOT gate with higher output power,” in Proc. Asia Commun. Photon. Conf., Washington, DC, USA, Nov. 2015, p. ASu2A.28.

Soref, R.

Stebbings, S. L.

L. Del Bino, J. M. Silver, M. T. M. Woodley, S. L. Stebbings, X. Xhao, and P. Del’Haye, “Microresonator isolators and circulators based on the intrinsic nonreciprocity of the kerr effect,” Optica, vol. 5, no. 3, pp. 279–282, 2018.

L. Del Bino, J. M. Silver, S. L. Stebbings, and P. Del’Haye, “Symmetry breaking of counter-propagating light in a nonlinear resonator,” Sci. Rep., vol. 7, no. 43142, pp. 1–6, 2017.

Stolen, R. H.

R. H. Stolen and A. Ashkin, “Optical Kerr effect in glass waveguide,” Appl. Phys. Lett, vol. 22, pp. 294–296, 1973.

Syvridis, D.

S. Mikroulis, H. Simos, E. Roditi, and D. Syvridis, “Ultrafast all-optical AND logic operation based on four-wave mixing in a passive InGaAsP-InP microring resonator,” IEEE Photon. Technol. Lett., vol. 17, no. 9, pp. 1878–1880,  2005.

Tanabe, T.

A. Godbole, P. P. Dali, V. Janyani, T. Tanabe, and G. Singh, “All optical scalable logic gates using Si$_3$N$_4$ microring resonators,” IEEE J. Sel. Top. Quant. Electron., vol. 22, no. 6, pp. 326–333,  2016.

A. Fushimi and T. Tanabe, “All-optical logic gate operating with single wavelength,” Opt. Express, vol. 22, no. 4, 2014, Art. no. .

P. P. Dali, A. Godbole, S. Sahu, G. Singh, and T. Tanabe, “Microring resonator based all optical NAND and NOT gate with higher output power,” in Proc. Asia Commun. Photon. Conf., Washington, DC, USA, Nov. 2015, p. ASu2A.28.

Tian, Y.

Y. Tian, “Experimental demonstration of an optical Feynman gate for reversible logic operation using silicon micro-ring resonators,” Nanophotonics, vol. 7, no. 1, pp. 333–337, 2018.

Y. Tian, L. Zhang, and L. Yang, “Directed XOR/XNOR logic gates using U-to-U waveguides and two microring resonators,” IEEE Photon. Technol. Lett., vol. 25, no. 1, pp. 18–21,  2013.

Van, V.

T. A. Ibrahim, K. Amarnath, L. C. Kuo, R. Grover, V. Van, and P.-T. Ho, “Photonic logic NOR gate based on two symmetric microring resonators,” Opt. Lett., vol. 29, no. 23, 2004, Art. no. .

Woodley, M. T. M.

F. Copie, M. T. M. Woodley, L. Del Bino, J. M. Silver, S. Zhang, and P. Del’Haye, “Interplay of polarization and time-reversal symmetry breaking in synchronously pumped ring resonators,” Phys. Rev. Lett., vol. 122, no. 1, 2019, Art. no. .

L. Del Bino, J. M. Silver, M. T. M. Woodley, S. L. Stebbings, X. Xhao, and P. Del’Haye, “Microresonator isolators and circulators based on the intrinsic nonreciprocity of the kerr effect,” Optica, vol. 5, no. 3, pp. 279–282, 2018.

M. T. M. Woodley, “Universal symmetry-breaking dynamics for the Kerr interaction of counterpropagating light in dielectric ring resonators,” Phys. Rev. A, vol. 98, no. 5, 2018, Art. no. .

Xhao, X.

Xiong, M.

Xu, Q.

Yang, L.

Y. Tian, L. Zhang, and L. Yang, “Directed XOR/XNOR logic gates using U-to-U waveguides and two microring resonators,” IEEE Photon. Technol. Lett., vol. 25, no. 1, pp. 18–21,  2013.

F. Monifi, J. Friedlein, S. K. Ozdemir, and L. Yang, “A robust and tunable add-drop filter using whispering gallery mode microtoroid resonator,” J. Light. Technol., vol. 30, no. 21, pp. 3306–3315,  2012.

Ye, W. N.

D. Gostimirovic and W. N. Ye, “Ultracompact CMOS-compatible optical logic using carrier depletion in microdisk resonators,” Sci. Rep., vol. 7, no. 12603, pp. 1–10, 2017.

Zhang, L.

Y. Tian, L. Zhang, and L. Yang, “Directed XOR/XNOR logic gates using U-to-U waveguides and two microring resonators,” IEEE Photon. Technol. Lett., vol. 25, no. 1, pp. 18–21,  2013.

L. Zhang, “Demonstration of directed XOR / XNOR logic gates using two cascaded microring resonators,” Opt. Lett., vol. 35, no. 10, pp. 1620–1622, 2010.

Zhang, S.

S. Zhang, “Sub-milliwatt-level microresonator solitons with extended access range using an auxiliary laser,” Optica, vol. 6, no. 2, pp. 206–212, 2019.

F. Copie, M. T. M. Woodley, L. Del Bino, J. M. Silver, S. Zhang, and P. Del’Haye, “Interplay of polarization and time-reversal symmetry breaking in synchronously pumped ring resonators,” Phys. Rev. Lett., vol. 122, no. 1, 2019, Art. no. .

Zrenner, A.

T. Hett, S. Krämmer, U. Hilleringmann, H. Kalt, and A. Zrenner, “High-Q whispering gallery microdisk resonators based on silicon oxynitride,” J. Lumin., vol. 191, pp. 131–134, 2017.

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Appl. Opt. (1)

P. Sethi and S. Roy, “All-optical ultrafast XOR/XNOR logic gates, binary counter, and double-bit comparator with silicon microring resonators,” Appl. Opt., vol. 53, no. 28, 2014, Art. no. .

Appl. Phys. Lett (1)

R. H. Stolen and A. Ashkin, “Optical Kerr effect in glass waveguide,” Appl. Phys. Lett, vol. 22, pp. 294–296, 1973.

Appl. Phys. Lett. (1)

P. Del’Haye, S. A. Diddams, and S. B. Papp, “Laser-machined ultra-high-Q microrod resonators for nonlinear optics,” Appl. Phys. Lett., vol. 102, no. 221119, pp. 221119–221119-4, 2013.

IEEE J. Sel. Top. Quant. Electron. (1)

A. Godbole, P. P. Dali, V. Janyani, T. Tanabe, and G. Singh, “All optical scalable logic gates using Si$_3$N$_4$ microring resonators,” IEEE J. Sel. Top. Quant. Electron., vol. 22, no. 6, pp. 326–333,  2016.

IEEE Photon. Technol. Lett. (3)

S. Mikroulis, H. Simos, E. Roditi, and D. Syvridis, “Ultrafast all-optical AND logic operation based on four-wave mixing in a passive InGaAsP-InP microring resonator,” IEEE Photon. Technol. Lett., vol. 17, no. 9, pp. 1878–1880,  2005.

T. A. Ibrahim, R. Grover, L.-C. Kuo, S. Kanakaraju, L. C. Calhoun, and P.-T. Ho, “All-optical AND/NAND logic gates using semiconductor microresonators,” IEEE Photon. Technol. Lett., vol. 15, no. 10, pp. 1422–1424,  2003.

Y. Tian, L. Zhang, and L. Yang, “Directed XOR/XNOR logic gates using U-to-U waveguides and two microring resonators,” IEEE Photon. Technol. Lett., vol. 25, no. 1, pp. 18–21,  2013.

J. Light. Technol. (1)

F. Monifi, J. Friedlein, S. K. Ozdemir, and L. Yang, “A robust and tunable add-drop filter using whispering gallery mode microtoroid resonator,” J. Light. Technol., vol. 30, no. 21, pp. 3306–3315,  2012.

J. Lumin. (1)

T. Hett, S. Krämmer, U. Hilleringmann, H. Kalt, and A. Zrenner, “High-Q whispering gallery microdisk resonators based on silicon oxynitride,” J. Lumin., vol. 191, pp. 131–134, 2017.

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Y. Tian, “Experimental demonstration of an optical Feynman gate for reversible logic operation using silicon micro-ring resonators,” Nanophotonics, vol. 7, no. 1, pp. 333–337, 2018.

Nat. Photon. (2)

W. Liu, “A fully reconfigurable photonic integrated signal processor,” Nat. Photon., vol. 10, pp. 190–195, 2016.

D. J. Moss, R. Morandotti, A. L. Gaeta, and M. Lipson, “New CMOS-compatible platforms based on silicon nitride and Hydex for nonlinear optics,” Nat. Photon., vol. 7, pp. 597–607, 2013.

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A. Fushimi and T. Tanabe, “All-optical logic gate operating with single wavelength,” Opt. Express, vol. 22, no. 4, 2014, Art. no. .

M. Pöllinger, “All-optical signal processing at ultra-low powers in bottle microresonators using the Kerr effect Observation of critical coupling in a fiber taper to a silica-microsphere whispering-gallery mode system,” Opt. Express, vol. 18, no. 17, pp. 17 764–17 775, 2010.

M. Xiong, “All-optical 10 Gb/s AND logic gate in a silicon microring resonator,” Opt. Express, vol. 21, no. 22, pp. 25772–25779, 2013.

Q. Xu, “Reconfigurable optical directed-logic circuits using microresonator-based optical switches,” Opt. Express, vol. 19, no. 6, pp. 5244–5249, 2011.

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T. A. Ibrahim, K. Amarnath, L. C. Kuo, R. Grover, V. Van, and P.-T. Ho, “Photonic logic NOR gate based on two symmetric microring resonators,” Opt. Lett., vol. 29, no. 23, 2004, Art. no. .

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L. Zhang, “Demonstration of directed XOR / XNOR logic gates using two cascaded microring resonators,” Opt. Lett., vol. 35, no. 10, pp. 1620–1622, 2010.

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F. Copie, M. T. M. Woodley, L. Del Bino, J. M. Silver, S. Zhang, and P. Del’Haye, “Interplay of polarization and time-reversal symmetry breaking in synchronously pumped ring resonators,” Phys. Rev. Lett., vol. 122, no. 1, 2019, Art. no. .

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L. Del Bino, J. M. Silver, S. L. Stebbings, and P. Del’Haye, “Symmetry breaking of counter-propagating light in a nonlinear resonator,” Sci. Rep., vol. 7, no. 43142, pp. 1–6, 2017.

D. Gostimirovic and W. N. Ye, “Ultracompact CMOS-compatible optical logic using carrier depletion in microdisk resonators,” Sci. Rep., vol. 7, no. 12603, pp. 1–10, 2017.

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P. P. Dali, A. Godbole, S. Sahu, G. Singh, and T. Tanabe, “Microring resonator based all optical NAND and NOT gate with higher output power,” in Proc. Asia Commun. Photon. Conf., Washington, DC, USA, Nov. 2015, p. ASu2A.28.

L. Del Bino, N. Moroney, and P. Del’Haye, “Optical memories and switching dynamics of counterpropagating light states in microresonators,” 2020. [Online]. Available: https://arxiv.org/abs/2002.02954

N. Moroney, “Logic gates based on interaction of counterpropagating light in microresonators,” in Proc. Conf. Lasers Electro-Opt., San Jose, CA, USA, 2019, Paper. STh3J.7.

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