Parity–time-symmetric whispering-gallery microcavities

Peng, Bo; Özdemir, Şahin Kaya; Lei, Fuchuan; Monifi, Faraz; Gianfreda, Mariagiovanna; Long, Gui Lu; Fan, Shanhui; Nori, Franco; Bender, Carl M.; Yang, Lan

doi:10.1038/nphys2927

Cited by 2,193 publications

(1,759 citation statements)

References 53 publications

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“…We expect that our predictions can be verified by combining recent advances in shaping complex wave fronts 3 with new techniques to fabricate non-Hermitian scattering structures with gain and loss [7][8][9][10] . As the precise combination of gain and loss in the same device is challenging, we suggest using passive structures with only loss in the first place.…”

Section: Discussionmentioning

confidence: 66%

“…They also remain valid for any sign of Kerr nonlinearity and thus allow us to perform a modulational stability analysis for non-homogeneous potentials. The most appropriate context to study the MI of such solutions is that of PT -symmetric optics [6][7][8][9][10][11]14,[19][20][21][22]24 . We find that in the selffocusing regime, the waves are always unstable, whereas in the defocusing regime the instability appears for specific values of Bloch momenta.…”

Section: Discussionmentioning

confidence: 99%

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Constant-intensity waves and their modulation instability in non-Hermitian potentials

et al. 2015

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In all of the diverse areas of science where waves play an important role, one of the most fundamental solutions of the corresponding wave equation is a stationary wave with constant intensity. The most familiar example is that of a plane wave propagating in free space. In the presence of any Hermitian potential, a wave's constant intensity is, however, immediately destroyed due to scattering. Here we show that this fundamental restriction is conveniently lifted when working with non-Hermitian potentials. In particular, we present a whole class of waves that have constant intensity in the presence of linear as well as of nonlinear inhomogeneous media with gain and loss. These solutions allow us to study the fundamental phenomenon of modulation instability in an inhomogeneous environment. Our results pose a new challenge for the experiments on non-Hermitian scattering that have recently been put forward.

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Section: Discussionmentioning

confidence: 66%

Section: Discussionmentioning

confidence: 99%

Constant-intensity waves and their modulation instability in non-Hermitian potentials

et al. 2015

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“…However, when wave incidents come from the gain side, the nonlinearity kicks in and bends the "backbone" of resonance, resulting in strong asymmetric wave propagation and nonreciprocity at the same frequency without harmonic generation. Such asymmetric transport has already been demonstrated in electronics and optics [36][37][38][39][40]; however, acoustics remains an open area to be explored.…”

Section: Scattering Propertiesmentioning

confidence: 99%

“…Several interesting physical features have been explored, such as power oscillations [28], unidirectional invisibility [29][30][31][32], the reconfigurable Talbot effect [33], and coherent perfect laser absorbers [34,35]. Moreover, in the nonlinear domain, PT symmetry has been used to realize potential optical isolators and circulators [36][37][38][39][40].…”

Section: Introductionmentioning

confidence: 99%

PT-Symmetric Acoustics

et al. 2014

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We introduce here the concept of acoustic parity-time (PT ) symmetry and demonstrate the extraordinary scattering characteristics of the acoustic PT medium. On the basis of exact calculations, we show how an acoustic PT -symmetric medium can become unidirectionally transparent at given frequencies. Combining such a PT -symmetric medium with transformation acoustics, we design two-dimensional symmetric acoustic cloaks that are unidirectionally invisible in a prescribed direction. Our results open new possibilities for designing functional acoustic devices with directional responses.

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“…If the material possesses the property of ε(x) = ε * (−x), the system is PT -symmetric because the system restores itself after simultaneous parity and time-reversal operations. Such systems have been extensively studied recently and a great variety of interesting phenomena have been discovered, including unusual beam dynamics within paraxial approximations [4][5][6], lasing effect [7][8][9], unidirectional transmission [10][11][12], negative refraction [13], single-particle sensors [14], and others [15][16][17][18][19][20]. Since it is not easy to achieve PT symmetry experimentally, several ways have been proposed to avoid the use of gain in a system.…”

Section: Introductionmentioning

confidence: 99%

Coalescence of exceptional points and phase diagrams for one-dimensionalPT-symmetric photonic crystals

2015

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Non-Hermitian systems with parity-time-(PT )-symmetric complex potentials can exhibit a phase transition when the degree of non-Hermiticity is increased. Two eigenstates coalesce at a transition point, which is known as the exceptional point (EP) for a discrete spectrum and spectral singularity for a continuous spectrum. The existence of an EP is known to give rise to a great variety of novel behaviors in various fields of physics. In this work, we study the complex band structures of one-dimensional photonic crystals with PT -symmetric complex potentials by setting up a Hamiltonian using the Bloch states of the photonic crystal without loss or gain as a basis. As a function of the degree of non-Hermiticity, two types of PT symmetry transitions are found. One is that a PT -broken phase can reenter into a PT -exact phase at a higher degree of non-Hermiticity. The other is that two EPs, one originating from the Brillouin zone center and the other from the Brillouin zone boundary, can coalesce at some k point in the interior of the Brillouin zone and create a singularity of higher order. Furthermore, we can induce a band inversion by tuning the filling ratio of the photonic crystal, and we find that the geometric phases of the bands before and after the inversion are independent of the amount of non-Hermiticity as long as the PT -exact phase is not broken. The standard concept of topological transition can hence be extended to non-Hermitian systems.

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Parity–time-symmetric whispering-gallery microcavities

Cited by 2,193 publications

References 53 publications

Constant-intensity waves and their modulation instability in non-Hermitian potentials

Constant-intensity waves and their modulation instability in non-Hermitian potentials

PT-Symmetric Acoustics

Coalescence of exceptional points and phase diagrams for one-dimensionalPT-symmetric photonic crystals

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