[en] The effect of a Kerr nonlinearity on dynamical tunneling is studied, using coupled whispering gallery modes in an optical microcavity. The model system that we have chosen is the “add-drop filter,” which is comprised of an optical microcavity and two waveguides coupled to the cavity. Due to the evanescent fields scattering on the waveguide, the whispering gallery modes in the microcavity form doublets, which manifest themselves as splittings in the spectrum. As these doublets can be regarded as a spectral feature of dynamical tunneling between two different dynamical states with a spatial overlap, the effect of a Kerr nonlinearity on the doublets is numerically investigated in the more general context of the relationship between cubic nonlinearity and dynamical tunneling. Within the numerical realization of the model system, it is observed that the doublets show a bistable transition in their transmission curve as the Kerr nonlinearity in the cavity is increased. At the same time, one rotational mode becomes dominant over the other one in the transmission, since the two states in the doublet have uneven linewidths. By using coupled-mode theory, the underlying mode dynamics of the phenomena is theoretically modeled and clarified.
Disciplines :
Physics
Author, co-author :
Shim, Jeong -Bo ; Université de Liège > Département de physique > Physique quantique statistique
Schlagheck, Peter ; Université de Liège > Département de physique > Physique quantique statistique
Hentschel, Martina
Wiersig, Jan
Language :
English
Title :
Nonlinear dynamical tunneling of optical whispering gallery modes in the presence of a Kerr nonlinearity
Publication date :
November 2016
Journal title :
Physical Review. A, Atomic, molecular, and optical physics
R. W. Boyd, Nonlinear Optics, 3rd ed. (Academic, New York, 2008).
P. Del'Haye, A. Schliesser, O. Arcizet, T. Wilken, R. Holzwarth, and T. J. Kippenberg, Nature (London) 450, 1214 (2007). NATUAS 0028-0836 10.1038/nature06401
P. Del'Haye, O. Arcizet, A. Schliesser, R. Holzwarth, and T. J. Kippenberg, Phys. Rev. Lett. 101, 053903 (2008). PRLTAO 0031-9007 10.1103/PhysRevLett.101.053903
T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, Opt. Lett. 27, 1669 (2002). OPLEDP 0146-9592 10.1364/OL.27.001669
A. Rodriguez, M. Soljacic, J. D. Joannopoulos, and S. G. Johnson, Opt. Express 15, 7303 (2007). OPEXFF 1094-4087 10.1364/OE.15.007303
Dynamical Tunneling: Theory and Experiment, edited by S. Keshavamurthy and P. Schlagheck (CRC, Boca Raton, FL, 2011).
M. J. Davis and E. J. Heller, J. Chem. Phys. 75, 246 (1981). JCPSA6 0021-9606 10.1063/1.441832
C. Dembowski, H.-D. Gräf, A. Heine, R. Hofferbert, H. Rehfeld, and A. Richter, Phys. Rev. Lett. 84, 867 (2000). PRLTAO 0031-9007 10.1103/PhysRevLett.84.867
H. Kwak, Y. Shin, S. Moon, S.-B. Lee, J. Yang, and K. An, Sci. Rep. 5, 9010 (2015). 2045-2322 10.1038/srep09010
J. Yang, S.-B. Lee, S. Moon, S.-Y. Lee, S. W. Kim, Truong Thi Anh Dao, J.-H. Lee, and K. An, Phys. Rev. Lett. 104, 243601 (2010). PRLTAO 0031-9007 10.1103/PhysRevLett.104.243601
S. Gehler, S. Löck, S. Shinohara, A. Bäcker, R. Ketzmerick, U. Kuhl, and H.-J. Stöckmann, Phys. Rev. Lett. 115, 104101 (2015). PRLTAO 0031-9007 10.1103/PhysRevLett.115.104101
W. K. Hensinger, H. Haffner, A. Browaeys, N. R. Heckenberg, K. Helmerson, C. McKenzie, G. J. Milburn, W. D. Phillips, S. L. Rolston, H. Rubinsztein-Dunlop, and B. Upcroft, Nature (London) 412, 52 (2001). NATUAS 0028-0836 10.1038/35083510
D. A. Steck, W. H. Oskay, and M. G. Raizen, Science 293, 274 (2001). SCIEAS 0036-8075 10.1126/science.1061569
A. Mazzei, S. Götzinger, L. de S. Menezes, G. Zumofen, O. Benson, and V. Sandoghdar, Phys. Rev. Lett. 99, 173603 (2007). PRLTAO 0031-9007 10.1103/PhysRevLett.99.173603
F. Treussart, V. S. Ilchenko, J.-F. Roch, J. Hare, V. Lefevre-Seguin, J.-M. Raimond, and S. Haroche, Eur. Phys. J. D 1, 235 (1998). EPJDF6 1434-6060 10.1007/s100530050087
L. Del Bino, J. M. Silver, S. L. Stebbings, and P. Del'Haye, arXiv:1607.01194.
A. Smerzi, S. Fantoni, S. Giovanazzi, and S. R. Shenoy, Phys. Rev. Lett. 79, 4950 (1997) PRLTAO 0031-9007 10.1103/PhysRevLett.79.4950;
M. Albiez, R. Gati, J. Fölling, S. Hunsmann, M. Cristiani, and M. K. Oberthaler, Phys. Rev. Lett. 95, 010402 (2005). PRLTAO 0031-9007 10.1103/PhysRevLett.95.010402
H. Ramezani, T. Kottos, V. Shuvayev, and L. Deych, Phys. Rev. A 83, 053839 (2011). PLRAAN 1050-2947 10.1103/PhysRevA.83.053839
E. Bulgakov, K. Pichugin, and A. Sadreev, J. Phys: Condens. Matter 25, 395304 (2013). JCOMEL 0953-8984 10.1088/0953-8984/25/39/395304
C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, and J. D. Joannopoulos, IEEE J. Quantum Electron. 35, 1322 (1999). IEJQA7 0018-9197 10.1109/3.784592
F. Monifi, J. Friedlein, S. K. Ozdemir, and L. Yang, J. Lightwave Technol. 30, 3306 (2012). JLTEDG 0733-8724 10.1109/JLT.2012.2214026
M. L. Gorodetsky, A. A. Savchenkov, and V. S. Ilchenko, Opt. Lett. 21, 453 (1996). OPLEDP 0146-9592 10.1364/OL.21.000453
M. Cai, O. Painter, and K. J. Vahala, Phys. Rev. Lett. 85, 74 (2000). PRLTAO 0031-9007 10.1103/PhysRevLett.85.74
Q. Chen, Y.-D. Yang, and Y.-Z. Huang, Appl. Phys. Lett. 89, 061118 (2006). APPLAB 0003-6951 10.1063/1.2335966
B. E. Little, S. T. Chu, H. A. Haus, J. Foresi, and J.-P. Laine, J. Lightwave Technol. 15, 998 (1997). JLTEDG 0733-8724 10.1109/50.588673
Z. Qiang, W. Zhou, and R. A. Soref, Opt. Express 15, 1823 (2007). OPEXFF 1094-4087 10.1364/OE.15.001823
Q. Huang and J. Yu, Opt. Express 22, 25171 (2014). OPEXFF 1094-4087 10.1364/OE.22.025171
P. Chak, S. Pereira, and J. E. Sipe, Phys. Rev. B 73, 035105 (2006). PRBMDO 1098-0121 10.1103/PhysRevB.73.035105
E. F. Franchimon, K. R. Hiremath, R. Stoffer, and M. Hammer, J. Opt. Soc. Am. B 30, 1048 (2013). JOBPDE 0740-3224 10.1364/JOSAB.30.001048
Y. K. Chembo and N. Yu, Phys. Rev. A 82, 033801 (2010). PLRAAN 1050-2947 10.1103/PhysRevA.82.033801
Allen Taflove and Susan C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech, London, 2005).
A. F. Oskooi, D. R. M. Ibanescu, P. Bermel, J. D. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010). CPHCBZ 0010-4655 10.1016/j.cpc.2009.11.008
J. Uwe Nöckel, Ph.D. thesis, Yale University, 1997.
Jeong-Bo Shim and Jan Wiersig, Opt. Express 21, 24240 (2013). 10.1364/OE.21.024240
V. Grigoriev and F. Biancalana, J. Opt. Soc. Am. B 28, 2165 (2011). JOBPDE 0740-3224 10.1364/JOSAB.28.002165
E. Ott, Chaos in Dynamical Systems (Cambridge University Press, London, 2002).
N. M. Litchinitser, C. J. McKinstrie, C. Martijn de Sterke, and G. P. Agrawal, J. Opt. Soc. Am. B 18, 45 (2001). JOBPDE 0740-3224 10.1364/JOSAB.18.000045
A. R. Cowan and J. F. Young, Phys. Rev. E 68, 046606 (2003). 1063-651X 10.1103/PhysRevE.68.046606
