Two Spot Coupled Ring Resonators

Nguyen Duy Cuong, Dinh Xuan Khoa, Cao Long Van, Le Canh Trung, Bui Dinh Thuan, Marek Trippenbach


Abstract. We consider a model of two coupled ring waveguides with constant linear gain and nonlinear absorption with space-dependent coupling. This system can be implemented in various physical situations as optical waveguides, atomic Bose-Einstein condensates, polarization condensates, etc. It is described by two coupled nonlinear Schrödinger equation. For numerical simulations, we take local two-gaussian coupling.

It is found in our previous papers that, depending on the values of involved parameters, we can obtain several interesting nonlinear phenomena, which include spontaneous symmetry breaking, modulational instability leading to generation of stable circular flows with various vorticities, stable inhomogeneous states with interesting structure of currents flowing between rings, as well as dynamical regimes having signatures of chaotic behavior.

This research will be associated with experimental investigation planned in Freie Universität Berlin, in the group of prof. Michael Giersig.


Bose Einstein condensates, nonlinear optical systems, ring resonators

Full Text:




Peng, B.; Özdemir, ¸S.K.; Lei, F.; Monifi, F.; Gianfreda, M.; Lu, G.; Long, L.G.; Fan, S.; Nori, F.; Bender, C.M.; et al. Parity–time-symmetric whispering-gallery microcavities. Nat. Phys. 2014, 10, 394–398

Chang, L.; Jiang, X.; Hua, S.; Yang, C.; Wen, J.; Jiang, L.; Li, G.; Wang, G.; Xiao, M. Parity-time symmetry and variable optical isolation in active-passive-coupled microresonators. Nat. Photon. 2014, 8, 524–529.

Peng, B.; Özdemir, ¸S.K.; Rotter, S.; Yilmaz, H.; Liertzer, M.; Monifi, F.; Bender C.M.; Nori, F.; Yang, L. Loss-induced suppression and revival of lasing. Science 2014, 346, 328–332.

Liertzer, M.; Ge, L.; Cerjan, A.; Stone, A.D.; Tuüreci, H.E.; Rotter, S. Pump-Induced Exceptional Points in Lasers. Phys. Rev. Lett. 2012, 108, 173901.

Hodaei, H.; Miri, M.-A.; Heinrich, M.; Christodoulides, D.N.; Khajavikhan, M. Parity-time-symmetric microring lasers. Science 2014, 346, 975–978.

Li Y.; Abolmaali, F.; Allen, K.W.; Limberopoulos, N.I.; Urbas, A.; Rakovich, Y.; Maslov, A.V.; Astratov, V.N. Whispering gallery mode hybridization in photonic molecules. Laser Photon. Rev. 2017, 11, 1600278.

Ryu, C. et al. Observation of Persistent Flow of a Bose-Einstein Condensate in a Toroidal Trap. Phys. Rev. Lett. 99, 260401 (2007).

Weiler, C. N. et al. Spontaneous vortices in the formation of Bose Einstein condensates. Nature (London) 455, 948 (2008).

Henderson, K., Ryu, C., MacCormick, C. & Boshier, M. G. Experimental demonstration of painting arbitrary and dynamic potentials for Bose-Einstein condensates. New J. Phys. 11, 043030 (2009).

Murphy, B. et al. Superflow in a Toroidal Bose-Einstein Condensate: An Atom Circuit with a Tunable Weak Link. Phys. Rev. Lett. 106, 130401 (2011).

Eckel, S. et al. Hysteresis in a quantized superfluid’atomtronic’ circuit. Nature 506, 200 (2014).

Komineas, S. & Brand, J. Collisions of Solitons and Vortex Rings in Cylindrical Bose-Einstein Condensates. Phys. Rev. Lett. 95, 110401 (2005).

Halkyard, P. L., Jones, M. P. A. & Gardiner, S. A. Rotational response of two-component Bose-Einstein condensates in ring traps. Phys. Rev. A 81, 061602 (2010).

Agrawal, G.P. Nonlinear Fiber Optics, 3rd ed.; Academic Press: San Diego, CA, USA, 2001; ISBN 0-12-045143-3.

Kosiorek, A.; Kandulski, W.; Chudzinski, P.; Kempa, K.; Giersig, M. Shadow nanosphere lithography: Simulation and experiment. Nano Lett. 2004, 47, 1359–1363.

Saito, H. & Ueda, M. Bloch Structures in a Rotating Bose-Einstein Condensate. Phys. Rev. Lett. 93, 220402 (2004).-nằm trong tài liệu bài 2017

Gao, T.; Li, G.; Estrecho, E.; Liew, T.C.H.; Comber-Todd, D.; Nalitov, A.; Steger, M.; West, K.; Pfeiffer, L.; Snoke, D.W.; et al. Chiral Modes at Exceptional Points in Exciton-Polariton Quantum Fluids. Phys. Rev. Lett. 2018, 120.

Hung, N.V.; Zegadlo, K.B.; Ramaniuk, A.; Konotop, V.V.; Trippenbach, M. Modulational instability of coupled ring waveguides with linear gain and nonlinear loss. Sci. Rep. 2017, 7, 4089.

Sigler, A.; Malomed, B.A. Solitary pulses in linearly coupled cubic-quintic Ginzburg-Landau equations. Phys. D Nonlinear Phenom. 2005, 212, 305–316.

Aleksandr Ramaniuk; Nguyen Viet Hung; Michael Giersig; Krzysztof Kempa; Vladimir V. Konotop and Marek Trippenbach. Vortex Creation without Stirring in Coupled Ring Resonators with Gain and Loss. Symmetry 2018, 10, 195

Chembo, Y.K.; Menyuk, C.R. Spatiotemporal Lugiato-Lefever fromalism for Kerr-comb generation in whispering-gallery-mode resonators. Phys. Rev. A 2013, 87, 053852.

Saito, H.; Ueda, M. Bloch Structures in a Rotating Bose-Einstein Condensate. Phys. Rev. Lett. 2004, 93, 220402.

Bludov, Y.V.; Konotop, V.V. Acceleration and localization of matter in a ring trap. Phys. Rev. A 2007, 75, 053614.

JianKe Yang; Nonlinear Waves in Integrable and Nonintegrable Systems, Monographs on Mathematical Modeling and Computation, (2010).

DOI: Display counter: Abstract : 247 views. PDF : 94 views.


  • There are currently no refbacks.

Editorial Office:

Communications in Physics

1st Floor, A16 Building, 18B Hoang Quoc Viet Street, Cau Giay District, Hanoi, Vietnam

Tel: (+84) 024 3791 7102 


Copyright by