Interferometric method to estimate the eigenvalues of a non-Hermitian two-level optical system

Stefano Biasi; Riccardo Franchi; Filippo Mione; Lorenzo Pavesi

doi:10.1364/PRJ.450402

[1] 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).

[2] Y. Ashida, Z. Gong, M. Ueda. Non-Hermitian physics. Adv. Phys., 69, 249-435(2020).

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

[4] M. Berry, R. Bhandari, S. Klein. Black plastic sandwiches demonstrating biaxial anisotropy. Eur. J. Phys., 20, 1-14(1999).

[5] Ş. K. Özdemir, S. Rotter, F. Nori, L. Yang. Parity-time symmetry and exceptional points in photonics. Nat. Mater., 18, 783-798(2019).

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

[7] L. Feng, X. Zhu, S. Yang, H. Zhu, P. Zhang, X. Yin, Y. Wang, X. Zhang. Demonstration of a large-scale optical exceptional point structure. Opt. Express, 22, 1760-1767(2014).

[8] A. Calabrese, F. Ramiro-Manzano, H. M. Price, S. Biasi, M. Bernard, M. Ghulinyan, I. Carusotto, L. Pavesi. Unidirectional reflection from an integrated ‘taiji’ microresonator. Photon. Res., 8, 1333-1341(2020).

[9] Z. Lin, H. Ramezani, T. Eichelkraut, T. Kottos, H. Cao, D. N. Christodoulides. Unidirectional invisibility induced by PT-symmetric periodic structures. Phys. Rev. Lett., 106, 213901(2011).

[10] A. Guo, G. J. Salamo, D. Duchesne, R. Morandotti, M. Volatier-Ravat, V. Aimez, G. A. Siviloglou, D. N. Christodoulides. Observation of PT-symmetry breaking in complex optical potentials. Phys. Rev. Lett., 103, 093902(2009).

[11] B. Peng, Ş. K. Özdemir, M. Liertzer, W. Chen, J. Kramer, H. Ylmaz, J. Wiersig, S. Rotter, L. Yang. Chiral modes and directional lasing at exceptional points. Proc. Natl. Acad. Sci. USA, 113, 6845-6850(2016).

[12] A. M. de las Heras, I. Carusotto. Unidirectional lasing in nonlinear taiji micro-ring resonators. Photon. Res., 8, 1333-1341(2020).

[13] L. Jin, Z. Song. Incident direction independent wave propagation and unidirectional lasing. Phys. Rev. Lett., 121, 073901(2018).

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

[15] C. Wang, W. R. Sweeney, A. D. Stone, L. Yang. Coherent perfect absorption at an exceptional point. Science, 373, 1261-1265(2021).

[16] A. Li, T. Van Vaerenbergh, P. De Heyn, P. Bienstman, W. Bogaerts. Backscattering in silicon microring resonators: a quantitative analysis. Laser Photon. Rev., 10, 420-431(2016).

[17] A. M. de las Heras, R. Franchi, S. Biasi, M. Ghulinyan, L. Pavesi, I. Carusotto. Nonlinearity-induced reciprocity breaking in a single nonmagnetic taiji resonator. Phys. Rev. Appl., 15, 054044(2021).

[18] Y. G. N. Liu, O. Hemmatyar, A. U. Hassan, P. S. Jung, J.-H. Choi, D. N. Christodoulides, M. Khajavikhan. Engineering interaction dynamics in active resonant photonic structures. APL Photon., 6, 050804(2021).

[19] S. Fan, W. Suh, J. D. Joannopoulos. Temporal coupled-mode theory for the Fano resonance in optical resonators. J. Opt. Soc. Am. A, 20, 569-572(2003).

[20] W. Suh, Z. Wang, S. Fan. Temporal coupled-mode theory and the presence of non-orthogonal modes in lossless multimode cavities. IEEE J. Quantum Electron., 40, 1511-1518(2004).

[21] Q. Li, T. Wang, Y. Su, M. Yan, M. Qiu. Coupled mode theory analysis of mode-splitting in coupled cavity system. Opt. Express, 18, 8367-8382(2010).

[22] S. Biasi, F. Ramiro-Manzano, F. Turri, P.-E. Larré, M. Ghulinyan, I. Carusotto, L. Pavesi. Hermitian and non-Hermitian mode coupling in a microdisk resonator due to stochastic surface roughness scattering. IEEE Photon. J., 11, 6101114(2019).

[23] R. Franchi, S. Biasi, A. M. de las Heras, M. Ghulinyan, I. Carusotto, L. Pavesi. Influence of the bus waveguide on the linear and nonlinear response of a taiji microresonator. Opt. Express, 29, 29615-29630(2021).

[24] Q. Li, Z. Zhang, J. Wang, M. Qiu, Y. Su. Fast light in silicon ring resonator with resonance-splitting. Opt. Express, 17, 933-940(2009).

[25] R. J. Potton. Reciprocity in optics. Rep. Prog. Phys., 67, 717-754(2004).

[26] D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, H. Renner. What is-and what is not-an optical isolator. Nat. Photonics, 7, 579-582(2013).

[27] S. Biasi, P. Guillemé, A. Volpini, G. Fontana, L. Pavesi. Time response of a microring resonator to a rectangular pulse in different coupling regimes. J. Lightwave Technol., 37, 5091-5099(2019).

[28] J. Heebner, R. Grover, T. Ibrahim. Optical Microresonators: Theory, Fabrication, and Applications, 138(2008).

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

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

[31] M. Borghi, D. Bazzanella, M. Mancinelli, L. Pavesi. On the modeling of thermal and free carrier nonlinearities in silicon-on-insulator microring resonators. Opt. Express, 29, 4363-4377(2021).

[32] R. Marchetti, C. Lacava, A. Khokhar, X. Chen, I. Cristiani, D. J. Richardson, G. T. Reed, P. Petropoulos, P. Minzioni. High-efficiency grating-couplers: demonstration of a new design strategy. Sci. Rep., 7, 16670(2017).

[33] M. Mancinelli, P. Bettotti, J. M. Fedeli, L. Pavesi. Interferometric switching in coupled resonator optical waveguides-based reconfigurable optical device. Opt. Lett., 38, 217-219(2013).

[34] S. V. Boriskina. Photonic Molecules and Spectral Engineering, 393-421(2010).

[35] M. Borghi, A. Trenti, L. Pavesi. Four wave mixing control in a photonic molecule made by silicon microring resonators. Sci. Rep., 9, 408(2019).

[36] 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).

[37] M. A. Quiroz-Juárez, A. Perez-Leija, K. Tschernig, B. M. Rodríguez-Lara, O. S. M. Loaiza, K. Busch, Y. N. Joglekar, R. de J. León-Montiel. Exceptional points of any order in a single, lossy waveguide beam splitter by photon-number-resolved detection. Photon. Res., 7, 862-867(2019).

[38] M. Am-Shallem, R. Kosloff, N. Moiseyev. Parameter estimation in atomic spectroscopy using exceptional points. Phys. Rev. A, 93, 032116(2016).

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

[40] Y. Wu, P. Zhou, T. Li, W. Wan, Y. Zou. High-order exceptional point based optical sensor. Opt. Express, 29, 6080-6091(2021).

[41] B. Little, S. Chu, P. Absil, J. Hryniewicz, F. Johnson, F. Seiferth, D. Gill, V. Van, O. King, M. Trakalo. Very high-order microring resonator filters for WDM applications. IEEE Photon. Technol. Lett., 16, 2263-2265(2004).

[42] T. Lei, A. W. Poon. Modeling of coupled-resonator optical waveguide (crow) based refractive index sensors using pixelized spatial detection at a single wavelength. Opt. Express, 19, 22227-22241(2011).