Nonorthogonal pairs of copropagating optical modes in deformed microdisk cavities

Wiersig, Jan; Eberspächer, Alexander; Shim, Jeong-Bo; Ryu, Jung-Wan; Shinohara, Susumu; Hentschel, Martina; Schomerus, Henning

doi:10.1103/physreva.84.023845

Cited by 90 publications

(112 citation statements)

References 55 publications

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“…Also in the vicinity of the EP the mode exhibit an unbalanced contribution of clockwise and counter-clockwise traveling-wave components. This kind of partial chirality has been predicted by Wiersig et al (2011a and Wiersig (2011) and has been confirmed in experiments by Kim et al (2014); see Fig. 31.…”

Section: B Exceptional Pointssupporting

confidence: 50%

“…In a deformed cavity, the CW and CCW waves are often coupled, which lift the degeneracy. The eigenmodes have slightly different frequencies, and the eigenfunctions are standing waves [assuming that a mirror-reflection symmetry is present or that the system is closed (Wiersig et al, 2011a)] approximately described for small deformation by sine or cosine functions. Due to their frequency difference, the eigenmodes cannot superpose to form CW or CCW modes.…”

Section: B Wave Chaos In Rotating Cavitiesmentioning

confidence: 99%

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Dielectric microcavities: Model systems for wave chaos and non-Hermitian physics

2015

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Section: B Exceptional Pointssupporting

confidence: 50%

Section: B Wave Chaos In Rotating Cavitiesmentioning

confidence: 99%

Dielectric microcavities: Model systems for wave chaos and non-Hermitian physics

2015

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“…Consequences of the coalescence of optical modes have been observed in recent theoretical studies on deformed microdisks which lack of mirror symmetries [21][22][23]. The modes in such cavities come in highly nonorthogonal pairs.…”

Section: Introductionmentioning

confidence: 87%

“…It should be emphasized that our usage of the term "chirality" is not related to optical activity in chiral media (see, e.g., [24]). The appearance of nonorthogonal and chiral modes in deformed microdisks has been traced back to the asymmetric transition between CW and CCW propagating waves [22,23].…”

Section: Introductionmentioning

confidence: 99%

Structure of whispering-gallery modes in optical microdisks perturbed by nanoparticles

Wiersig¹

2011

Phys. Rev. A

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It is a well-known fact that a single nanoparticle placed in the evanescent field of an optical microdisk leads to coherent backscattering of light between counterpropagating whispering-gallery modes. This backscattering lifts the spectral degeneracy giving rise to a doublet of standing-wave modes. Here, we show that the evanescent coupling of two or more nanoparticles leads in general to asymmetric backscattering (i.e., the strength of the scattering of light from the clockwise to the counterclockwise propagation direction is different than the other way around). Even if the strength of the backscattering is weak its asymmetry can have a dramatic impact on the mode structure. In the regime of overlapping resonances the modes do not have a standing-wave character. Instead nonorthogonal pairs of mainly copropagating modes are formed. In the extreme case the pair of optical modes coalesce at a so-called exceptional point. We derive an effective Hamiltonian within a two-mode approximation which reveals that this unexpected behavior is due to interference of the scattered waves which can be destructive or constructive depending on the propagation direction of the light.

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“…2 A, iii and B, iii): The reflection shows a pronounced resonance peak for the ccw input, whereas this peak vanishes for the cw input. This asymmetric backscattering (reflection) is the defining hallmark of the desired chiral modes (12,30,31), for which we provide here to our knowledge the first direct measurement in a microcavity (SI Appendix, S4: Chirality Analysis and Comparison Between the Lasing and the Transmission Models and Fig. S9).…”

Section: Modal Chirality and Asymmetric Backscattering At An Epmentioning

confidence: 99%

Chiral modes and directional lasing at exceptional points

Peng

Özdemir

Liertzer

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

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Controlling the emission and the flow of light in micro-and nanostructures is crucial for on-chip information processing. Here we show how to impose a strong chirality and a switchable direction of light propagation in an optical system by steering it to an exceptional point (EP)-a degeneracy universally occurring in all open physical systems when two eigenvalues and the corresponding eigenstates coalesce. In our experiments with a fiber-coupled whispering-gallery-mode (WGM) resonator, we dynamically control the chirality of resonator modes and the emission direction of a WGM microlaser in the vicinity of an EP: Away from the EPs, the resonator modes are nonchiral and laser emission is bidirectional. As the system approaches an EP, the modes become chiral and allow unidirectional emission such that by transiting from one EP to another one the direction of emission can be completely reversed. Our results exemplify a very counterintuitive feature of nonHermitian physics that paves the way to chiral photonics on a chip.exceptional points | asymmetric backscattering | chiral modes | directional lasing | whispering-gallery-mode resonator C hirality lies at the heart of the most fascinating and fundamental phenomena in modern physics like the quantum Hall effect (1), Majorana fermions (2), and the surface conductance in topological insulators (3) as well as in p-wave superconductors (4). In all of these cases chiral edge states exist, which propagate along the surface of a sample in a specific direction. The chirality (or handedness) is secured by specific mechanisms, which prevent the same edge state from propagating in the opposite direction. For example, in topological insulators the backscattering of edge states is prevented by the strong spin-orbit coupling of the underlying material.Transferring such concepts to the optical domain is a challenging endeavor that has recently attracted considerable attention. Quite similar to their electronic counterparts, the electromagnetic realizations of chiral states typically require either a mechanism that breaks time-reversal symmetry (5) or one that gives rise to a spinorbit coupling of light (6-8). Because such mechanisms are often not available or difficult to realize, alternative concepts have recently been proposed, which require, however, a careful arrangement of many optical resonators in structured arrays (9,10).Here, we demonstrate explicitly that the above demanding requirements on the realization of chiral optical states propagating along the surface of a system can all be bypassed by using a single resonator with non-Hermitian scattering. The key insight in this respect is that a judiciously chosen non-Hermitian outcoupling of two near-degenerate resonator modes to the environment leads to an asymmetric backscattering between them [an effect that has been ignored in previous models based on coupled mode theory (11)] and thus to an effective breaking of the time-reversal symmetry that supports chiral behavior (12). More specifically, we show that a strong spatia...

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Nonorthogonal pairs of copropagating optical modes in deformed microdisk cavities

Cited by 90 publications

References 55 publications

Dielectric microcavities: Model systems for wave chaos and non-Hermitian physics

Dielectric microcavities: Model systems for wave chaos and non-Hermitian physics

Structure of whispering-gallery modes in optical microdisks perturbed by nanoparticles

Chiral modes and directional lasing at exceptional points

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