Parity-Time-symmetric optics, extraordinary momentum and spinin evanescent waves, optical analog of topological insulators, andthe quantum spin Hall effect of lightFranco Nori
RIKEN, Saitama, Japan, and The University of Michigan, Ann Arbor, USA
Abstract: This talk provides a brief and pedagogical overview to some aspects of parity-timesymmetric optics, extraordinary momentum and spin in evanescent waves, optical analog oftopological insulators, and the quantum spin Hall effect of light.

1. Parity-Time-Symmetric Optics
Optical systems combining balanced loss and gain provide a unique platform toimplement classical analogues of quantum systems described by non-Hermitian parity–time(PT)-symmetric Hamiltonians [1]. Such systems can be used to create synthetic materials
with properties that cannot be attained in materials having only loss or only gain. We reportPT-symmetry breaking in coupled optical resonators. We observed non-reciprocity in thePT-symmetry-breaking phase due to strong field localization, which significantly enhances
nonlinearity. In the linear regime, light transmission is reciprocal regardless of whether thesymmetry is broken or unbroken. We show that in one direction there is a complete
absence of resonance peaks whereas in the other direction the transmission is resonantlyenhanced, which is associated with the use of resonant structures. Our results could lead toa new generation of synthetic optical systems enabling on-chip manipulation and control oflight propagation.
2. The quantum spin Hall effect of light: photonic analog of 3D topological insulators.
Maxwell’s equations, formulated 150 years ago, ultimately describe properties of light,
from classical electromagnetism to quantum and relativistic aspects. The latter ones result
in remarkable geometric and topological phenomena related to the spin-1 massless natureof photons. By analyzing fundamental spin properties of Maxwell waves, we show [2] that
free-space light exhibits an intrinsic quantum spin Hall effect—surface modes with strong
spin-momentum locking. These modes are evanescent waves that form, for example,
surface plasmon-polaritons at vacuum-metal interfaces. Our findings illuminate the unusualtransverse spin in evanescent waves and explain recent experiments that havedemonstrated the transverse spin-direction locking in the excitation of surface opticalmodes. This deepens our understanding of Maxwell’s theory, reveals analogies with

topological insulators for electrons, and offers applications for robust spin-directional
optical interfaces. Related work can be found in [3].

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B. Peng, et al., Loss-induced suppression and revival of lasing, Science 346, 328 (2014).
[PDF][Link][arXiv];
B. Peng, et al., What is and what is not electromagnetically induced transparency in whisperinggallery microcavities, Nature Communications 5, 5082 (2014). [PDF][Link][arXiv];
H. Jing, Ş.K. Özdemir, X.Y. Lu, J. Zhang, L. Yang, F. Nori, PT-Symmetric Phonon Laser, Phys. Rev.
Lett. 113, 053604 (2014). [PDF][Link][arXiv];
F. Monifi, et al., Optomechanically induced stochastic resonance and chaos transfer between opticalfields, Nature Photonics 10, 399–405 (2016). [PDF][Link]. Also its cover story.
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Nature Photonics 12, pp. 479–484 (2018). [PDF][Link][Suppl. Info.]
D. Leykam, K.Y. Bliokh, C. Huang, Y.D. Chong, F. Nori, Edge Modes, Degeneracies, andTopological Numbers in Non-Hermitian Systems, Phys. Rev. Lett. 118, 040401 (2017).
[PDF][Link][arXiv]
S.K. Ozdemir, S. Rotter, F. Nori, L. Yang , Parity–time symmetry and exceptional points inphotonics, Nature Materials, (2019). [PDF][Link_1][Link_2][2] K.Y. Bliokh, D. Smirnova, F. Nori, Quantum spin Hall effect of light, Science 348, 1448-1451(2015). [PDF] [Link] [arXiv]. Highlighted in a Perspectives [Science 348, 1432 (2015)].
[3] K.Y. Bliokh, F. Nori, Transverse spin of a surface polariton, Phys. Rev. A 85, 061801 (2012).
[PDF][Link][arXiv];
K.Y. Bliokh, A.Y. Bekshaev, F. Nori, Dual electromagnetism: helicity, spin, momentum, and angularmomentum, New J. Phys. 15, 033026 (2013). [PDF][Link][arXiv];
K.Y. Bliokh, J. Dressel, F. Nori, Conservation of the spin and orbital angular momenta inelectromagnetism, New J. Phys. 16, 093037 (2014). [PDF][Link][arXiv];
J. Dressel, K.Y. Bliokh, F. Nori, Space-time algebra as a powerful tool for electromagnetism, Physics
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K. Y. Bliokh, Y. S. Kivshar, F. Nori, Magnetoelectric Effects in Local Light-Matter Interactions, Phys.
Rev. Lett. 113, 033601 (2014). [PDF][Link][arXiv];
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Nature Communications 5, 3300 (2014). [PDF][Link][arXiv] ;A.Y. Bekshaev, K.Y. Bliokh, F. Nori, Transverse spin and momentum in two-wave interference,Phys. Rev. X 5, 011039 (2015). [PDF][Link][arXiv];
K.Y. Bliokh and F. Nori, Transverse and longitudinal angular momenta of light, Physics Reports,
Volume 592, 26 (August 2015), Pages 1–38 (2015). A 38-pages review. [PDF][Link][arXiv];
K.Y. Bliokh, F.J. Rodriguez-Fortuno, F. Nori, A.V. Zayats, Spin-orbit interactions of light. NaturePhotonics 9, p. 796–808 (2016). 13-pages review, including our results. [PDF][Link][arXiv];
M. Antognozzi, et al., Direct measurements of the extraordinary optical momentum and transverse
spin-dependent force using a nano-cantilever, Nature Physics 12, 731-735 (2016).
[PDF][Link][arXiv];
K.Y. Bliokh, F. Nori, Transverse spin and surface waves in acoustic metamaterials, Phys. Rev. B 99,020301(R) (2019). [PDF][Link][arXiv];
K.Y. Bliokh, D. Leykam, M. Lein, F. Nori, Topological non-Hermitian origin of surface Maxwell waves,
Nature Communications 10, 580 (2019). [PDF][Link_1][Link_2][arXiv]