Researching | Higher-order exceptional points in waveguide-coupled microcavities: perturbation induced frequency splitting and mode patterns

Journals >Photonics Research >Volume 11 >Issue 10 >Page A54 > Article

Photonics Research
Vol. 11, Issue 10, A54 (2023)

Higher-order exceptional points in waveguide-coupled microcavities: perturbation induced frequency splitting and mode patterns

Julius Kullig^1、*, Daniel Grom^1、3, Sebastian Klembt², and Jan Wiersig¹

Author Affiliations

¹Institut für Physik, Otto-von-Guericke-Universität Magdeburg, 39106 Magdeburg, Germany

²Technische Physik and Würzburg-Dresden Cluster of Excellence ct.qmat, Physikalisches Institut and Wilhelm-Conrad-Röntgen-Research Center for Complex Material Systems, Am Hubland, University of Würzburg, 97070 Würzburg, Germany

³e-mail: daniel.grom@ovgu.de

show less

DOI: 10.1364/PRJ.496414 Cite this Article Set citation alerts

Julius Kullig, Daniel Grom, Sebastian Klembt, Jan Wiersig. Higher-order exceptional points in waveguide-coupled microcavities: perturbation induced frequency splitting and mode patterns[J]. Photonics Research, 2023, 11(10): A54 Copy Citation Text

show less

References

[1] T. Kato. Perturbation Theory for Linear Operators(1966).

[2] M. V. Berry. Physics of nonhermitian degeneracies. Czech. J. Phys., 54, 1039-1047(2004).

[3] W. D. Heiss. The physics of exceptional points. J. Phys. A Math. Theor., 45, 444016(2012).

[4] H. Cao, J. Wiersig. Dielectric microcavities: model systems for wave chaos and non-Hermitian physics. Rev. Mod. Phys., 87, 61-111(2015).

[5] M.-A. Miri, A. Alù. Exceptional points in optics and photonics. Science, 363, eaar7709(2019).

[6] E. J. Bergholtz, J. C. Budich, F. K. Kunst. Exceptional topology of non-Hermitian systems. Rev. Mod. Phys., 93, 015005(2021).

[7] R. El-Ganainy, K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, D. N. Christodoulides. Non-Hermitian physics and PT symmetry. Nat. Phys., 14, 11-19(2018).

[8] J. Wiersig. Chiral and nonorthogonal eigenstate pairs in open quantum systems with weak backscattering between counterpropagating traveling waves. Phys. Rev. A, 89, 012119(2014).

[9] J. Wiersig. Sensors operating at exceptional points: general theory. Phys. Rev. A, 93, 033809(2016).

[10] W. Chen, Ş. K. Özdemir, G. Zhao, J. Wiersig, L. Yang. Exceptional points enhance sensing in an optical microcavity. Nature, 548, 192-196(2017).

[11] H. Hodaei, A. Hassan, S. Wittek, H. Carcia-Cracia, R. El-Ganainy, D. N. Christodoulides, M. Khajavikhan. Enhanced sensitivity at higher-order exceptional points. Nature, 548, 187-191(2017).

[12] Y.-H. Lai, Y.-K. Lu, M.-G. Suh, Z. Yuan, K. Vahala. Observation of the exceptional-point-enhanced Sagnac effect. Nature, 576, 65-69(2019).

[13] C. Zeng, Y. Sun, G. Li, Y. Li, H. Jiang, Y. Yang, H. Chen. Enhanced sensitivity at high-order exceptional points in a passive wireless sensing system. Opt. Express, 27, 27562-27572(2019).

[14] J. Wiersig. Review of exceptional point-based sensors. Photonics Res., 8, 1457-1467(2020).

[15] R. Kononchuk, J. Cai, F. Ellis, R. Thevamaran, T. Kottos. Exceptional-point-based accelerometers with enhanced signal-to-noise ratio. Nature, 607, 697-702(2022).

[16] B. Peng, Ş. K. Özdemir, S. Rotter, H. Yilmaz, M. Liertzer, F. Monfi, C. M. Bender, F. Nori, L. Yang. Loss-induced suppression and revival of lasing. Science, 346, 328-332(2014).

[17] P. Miao, Z. Zhang, J. Sun, W. Walasik, S. Longhi, N. M. Litchinitser, L. Feng. Orbital angular momentum microlaser. Science, 353, 464-467(2016).

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

[19] A. Stegmaier, S. Imhof, T. Helbig, T. Hofmann, C. H. Lee, M. Kremer, A. Fritzsche, T. Feichtner, S. Klembt, S. Höfling, I. Boettcher, I. C. Fulga, L. Ma, O. G. Schmidt, M. Greiter, T. Kiessling, A. Szameit, R. Thomale. Topological defect engineering and PT symmetry in non-Hermitian electrical circuits. Phys. Rev. Lett., 126, 215302(2021).

[20] Y. Wang, Y. Ren, X. Luo, B. Li, Z. Chen, Z. Liu, F. Liu, Y. Cai, Y. Zhang, J. Liu, F. Li. Manipulating cavity photon dynamics by topologically curved space. Light Sci. Appl., 11, 308(2022).

[21] Y.-K. Lu, P. Peng, Q.-T. Cao, D. Xu, J. Wiersig, Q. Gong, Y.-F. Xiao. Spontaneous T-symmetry breaking and exceptional points in cavity quantum electrodynamics systems. Sci. Bull., 63, 1096-1100(2018).

[22] C. Wang, X. Jiang, G. Zhao, M. Zhang, C. W. Hsu, B. Peng, A. D. Stone, L. Jiang, L. Yang. Electromagnetically induced transparency at a chiral exceptional point. Nat. Phys., 16, 334-340(2020).

[23] F. Zhang, Y. Feng, X. Chen, L. Ge, W. Wan. Synthetic anti-PT symmetry in a single microcavity. Phys. Rev. Lett., 124, 053901(2020).

[24] Q. Zhong, Ş. K. Özdemir, A. Eisfeld, A. Metelmann, R. El-Ganainy. Exceptional-point-based optical amplifiers. Phys. Rev. Appl., 13, 014070(2020).

[25] J. Wiersig. Response strengths of open systems at exceptional points. Phys. Rev. Res., 4, 023121(2022).

[26] J. Kullig, J. Wiersig. High-order exceptional points of counterpropagating waves in weakly deformed microdisk cavities. Phys. Rev. A, 100, 043837(2019).

[27] H. Jing, Ş. K. Özdemir, H. Lü, F. Nori. High-order exceptional points in optomechanics. Sci. Rep., 7, 3386(2017).

[28] W. Xiong, Z. Li, Y. Song, J. Chen, G.-Q. Zhang, M. Wang. Higher-order exceptional point in a pseudo-Hermitian cavity optomechanical system. Phys. Rev. A, 104, 063508(2021).

[29] S. Wang, B. Hou, W. Lu, Y. Chen, Z. Q. Zhang, C. T. Chan. Arbitrary order exceptional point induced by photonic spin–orbit interaction in coupled resonators. Nat. Commun., 10, 832(2019).

[30] Q. Zhong, J. Kou, Ş. K. Özdemir, R. El-Ganainy. Hierarchical construction of higher-order exceptional points. Phys. Rev. Lett., 125, 203602(2020).

[31] J. Wiersig. Revisiting the hierarchical construction of higher-order exceptional points. Phys. Rev. A, 106, 063526(2022).

[32] X.-Y. Wang, F.-F. Wang, X.-Y. Hu. Waveguide-induced coalescence of exceptional points. Phys. Rev. A, 101, 053820(2020).

[33] H. Yang, X. Mao, G.-Q. Qin, M. Wang, H. Zhang, D. Ruan, G.-L. Long. Scalable higher-order exceptional surface with passive resonators. Opt. Lett., 46, 4025-4028(2021).

[34] K. Liao, Y. Zhong, Z. Du, G. Liu, C. Li, X. Wu, C. Deng, C. Lu, X. Wang, C. T. Chan, Q. Song, S. Wang, X. Liu, X. Hu, Q. Gong. On-chip integrated exceptional surface microlaser. Sci. Adv., 9, eadf3470(2023).

[35] Q. Zhong, J. Ren, M. Khajavikhan, D. N. Christodoulides, Ş. K. Özdemir, R. El-Ganainy. Sensing with exceptional surfaces in order to combine sensitivity with robustness. Phys. Rev. Lett., 122, 153902(2019).

[36] Q. Zhong, S. Nelson, Ş. K. Özdemir, R. El-Ganainy. Controlling directional absorption with chiral exceptional surfaces. Opt. Lett., 44, 5242-5245(2019).

[37] G.-Q. Qin, R.-R. Xie, H. Zhang, Y.-Q. Hu, M. Wang, G.-Q. Li, H. Xu, F. Lei, D. Ruan, G.-L. Long. Experimental realization of sensitivity enhancement and suppression with exceptional surfaces. Laser Photonics Rev., 15, 2000569(2021).

[38] J. Wiersig, D. Christodoulides, J. Yang. Non-Hermitian effects due to asymmetric backscattering of light in whispering-gallery microcavities. Parity-time Symmetry and Its Applications, 280, 155-184(2018).

[39] J. Wiersig. Structure of whispering-gallery modes in optical microdisks perturbed by nanoparticles. Phys. Rev. A, 84, 063828(2011).

[40] https://www.comsol.com. https://www.comsol.com

[41] A. Hashemi, K. Busch, D. N. Christodoulides, Ş. K. Özdemir, R. El-Ganainy. Linear response theory of open systems with exceptional points. Nat. Commun., 13, 3281(2022).

[42] N. Hatano, D. R. Nelson. Localization transitions in non-Hermitian quantum mechanics. Phys. Rev. Lett., 77, 570-573(1996).

[43] W. D. Heiss, H. L. Harney. The chirality of exceptional points. Eur. Phys. J. D, 17, 149-151(2001).

[44] W. D. Heiss. Chirality of wavefunctions for three coalescing levels. J. Phys. A Math. Theor., 41, 244010(2008).

[45] T. J. Kippenberg, S. M. Spillane, K. J. Vahala. Modal coupling in traveling-wave resonators. Opt. Lett., 27, 1669-1671(2002).

[46] C. Manolatou, M. J. Khan, S. Fan, P. R. Villeneuve, H. A. Haus, J. D. Joannopoulos. Coupling of modes analysis of resonant channel add-drop filters. IEEE J. Quantum Electron., 35, 1322-1331(1999).

[47] M. Khanbekyan, J. Wiersig. Decay suppression of spontaneous emission of a single emitter in a high-Q cavity at exceptional points. Phys. Rev. Res., 2, 023375(2020).

[48] W. D. Heiss. Green’s functions at exceptional points. Int. J. Theor. Phys., 54, 3954-3959(2015).

[49] H.-K. Lau, A. A. Clerk. Fundamental limits and non-reciprocal approaches in non-Hermitian quantum sensing. Nat. Commun., 9, 4320(2018).

[50] W. Langbein. No exceptional precision of exceptional-point sensors. Phys. Rev. A, 98, 023805(2018).

[51] H. Wang, Y.-H. Lai, Z. Yuan, M.-G. Suh, K. Vahala. Petermann-factor sensitivity limit near an exceptional point in a Brillouin ring laser gyroscope. Nat. Commun., 11, 1610(2020).

[52] C. Chen, L. Jin, R.-B. Liu. Sensitivity of parameter estimation near the exceptional point of a non-Hermitian system. New J. Phys., 21, 083002(2019).

[53] M. Zhang, W. Sweeney, C. W. Hsu, L. Yang, A. D. Stone, L. Jiang. Quantum noise theory of exceptional point amplifying sensors. Phys. Rev. Lett., 123, 180501(2019).

[54] L. Feng, Z. J. Wong, R.-M. Ma, Y. Wang, X. Zhang. Single-mode laser by parity-time symmetry breaking. Science, 346, 972-975(2014).

[55] Z.-Q. Yang, Z.-K. Shao, H.-Z. Chen, X.-R. Mao, R.-M. Ma. Spin-momentum-locked edge mode for topological vortex lasing. Phys. Rev. Lett., 125, 013903(2020).

[56] D. Korn, M. Lauermann, S. Koeber, P. Appel, L. Alloatti, R. Palmer, P. Dumon, W. Freude, J. Leuthold, C. Koos. Lasing in silicon–organic hybrid waveguides. Nat. Commun., 7, 10864(2016).

Figures&Tables (15)

References (56)

Copy Citation Text

Julius Kullig, Daniel Grom, Sebastian Klembt, Jan Wiersig. Higher-order exceptional points in waveguide-coupled microcavities: perturbation induced frequency splitting and mode patterns[J]. Photonics Research, 2023, 11(10): A54

Download Citation

Set citation alerts for the article

Set citation alerts for the article

Save the article for my favorites

Paper Information

Recommended Topics

laser devices and laser physics

Lasers and Laser Optics

laser manufacturing

Instrumentation, Measurement and Metrology

Set citation alerts for the article

Please enter your email address