# Connected hidden singularities and toward successive state flipping in degenerate optical microcavities

01 Feb 2017-Journal of The Optical Society of America B-optical Physics (Optical Society of America)-Vol. 34, Iss: 2, pp 238-244

TL;DR: In this article, the formation of a special hidden singular line connecting multiple second-order hidden singular points, in a non-uniformly pumped degenerate optical microcavity, is reported.

Abstract: Using scattering matrix formalism, we report the formation of a special hidden singular line connecting multiple second-order hidden singular points, in a non-uniformly pumped degenerate optical microcavity. Such singularities are known as exceptional points (EPs), and the line is proposed as an exceptional line. Exploring the unconventional behavior of cavity resonances created by a spatially imbalanced gain–loss profile, we have established the adiabatic state-flipping mechanism of coupled resonances encountering such EPs. Various interesting encircling situations, incorporating smooth as well as fluctuating variations of the control parameters, have been analyzed. We exploit the above scheme for the first time, to the best of our knowledge, to analyze the optical performance and stability of the cascaded flip-of-state phenomenon assisted by successive encirclement of either single or multiple singularities following the exceptional line in the context of optical mode converters.

Citations

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Arnab Laha

^{1}, Arnab Laha^{2}, Sibnath Dey^{2}, Harsh K. Gandhi^{2}, Abhijit Biswas^{1}, Somnath Ghosh^{2}•TL;DR: In this paper, the dynamical encirclement of non-Hermitian EPs has been studied in a non-hermitian system with state-flipping and peculiar phase accumulation features.

Abstract: Exceptional points (EPs) in non-Hermitian systems have recently attracted considerable attention owing to unique state-flipping and peculiar phase accumulation features. The dynamical encirclement ...

19 citations

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TL;DR: In this article, the effect of interplay between the proposed resonance interactions and the incorporated non-Hermiticity in the microcavity is analyzed drawing a special attention to the existence of hidden singularities, namely exceptional points (EPs), where at least two coupled resonances coalesce.

Abstract: We report a specially configured open optical microcavity, imposing a spatially imbalanced gain–loss profile, to host an exclusively proposed next-nearest-neighbor resonance coupling scheme. Adopting the scattering matrix (S-matrix) formalism, the effect of interplay between such proposed resonance interactions and the incorporated non-Hermiticity in the microcavity is analyzed drawing a special attention to the existence of hidden singularities, namely exceptional points (EPs), where at least two coupled resonances coalesce. We establish adiabatic flip-of-state phenomenon of the coupled resonances in the complex frequency plane (k-plane), which is essentially an outcome of the fact that the respective EP is being encircled in the system parameter plane. Encountering such multiple EPs, the robustness of flip-of-states phenomena has been analyzed via continuous tuning of coupling parameters along a special hidden singular line which connects all the EPs in the cavity. Such a numerically devised cavity, incorporating the exclusive next neighbor coupling scheme, has been designed for the first time to study the unconventional optical phenomena in the vicinity of EPs.

15 citations

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TL;DR: In this paper, an all-lossy dual-mode planar waveguide structure is proposed for topological control of light signals, where the topological properties of an EP are achieved by patterning the longitudinal loss profile only.

Abstract: Recent technological advances have boosted research related to $e\phantom{\rule{0}{0ex}}x\phantom{\rule{0}{0ex}}c\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}p\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}l$ $p\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}s$ (EPs), singularities arising in non-Hermitian quantum mechanics that once seemed purely mathematical. Device-level implementation of EPs has been primarily in gain-loss-balanced toroidal optical microcavities, but too much gain can cause such a system to become unstable. This study proposes an all-lossy dual-mode planar waveguide structure, in which the topological properties of an EP are achieved by patterning the longitudinal loss profile only. This scheme needs no active pumping, is accessible to many conventional optical elements, and offers a platform for topological control of light signals.

15 citations

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TL;DR: In this paper, a 1D planar optical waveguide with transverse distribution of inhomogeneous loss profile, which exhibits an exceptional point (EP), is presented, where the interaction between them in the vicinity of the EP is controlled by proper adjustment of the inhomogeneity in attenuation profile only.

Abstract: We report a 1D planar optical waveguide with transverse distribution of inhomogeneous loss profile, which exhibits an exceptional point (EP). The waveguide hosts two leaky resonant modes; where the interaction between them in the vicinity of the EP is controlled by proper adjustment of the inhomogeneity in attenuation profile only. We study the adiabatic dynamics of propagation constants of the coupled modes by quasi-static encirclement of control parameters around the EP. Realizing such an encirclement with the inhomogeneous loss distribution along the direction of light propagation, we report the breakdown of adiabatic evolution of two coupled modes through the waveguide in presence of an EP. Here, during conversion the output mode is irrespective of the choice of input excited mode but depends on the direction of light transportation. This topologically controlled, robust scheme of asymmetric mode conversion in the platform of the proposed all-lossy waveguide structure may open up an extensive way-out for implementation of state-transfer applications in chirality driven waveguide-based devices.

14 citations

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References

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C. Dembowski

^{1}, Hans-Dieter Gräf^{1}, Hanns Ludwig Harney^{2}, Andreas Heine^{1}, W. D. Heiss^{3}, H. Rehfeld^{1}, Achim Richter^{1}•TL;DR: A microwave cavity experiment where exceptional points (EPs), which are square root singularities of the eigenvalues as function of a complex interaction parameter, are encircled in the laboratory and one of the Eigenvectors undergoes a sign change which can be discerned in the field patterns.

Abstract: We report on a microwave cavity experiment where exceptional points (EPs), which are square root singularities of the eigenvalues as function of a complex interaction parameter, are encircled in the laboratory. The real and imaginary parts of an eigenvalue are given by the frequency and width of a resonance and the eigenvectors by the field distributions. Repulsion of eigenvalues--always associated with EPs--implies frequency anticrossing (crossing) whenever width crossing (anticrossing) is present. The eigenvalues and eigenvectors are interchanged while encircling an EP, but one of the eigenvectors undergoes a sign change which can be discerned in the field patterns.

523 citations

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J. Doppler

^{1}, Alexei A. Mailybaev^{2}, Julian Böhm^{3}, Ulrich Kuhl^{3}, Adrian Girschik^{1}, Florian Libisch^{1}, Thomas J. Milburn^{1}, Peter Rabl^{1}, Nimrod Moiseyev^{4}, Stefan Rotter^{1}•TL;DR: It is demonstrated that a dynamical encircling of an exceptional point is analogous to the scattering through a two-mode waveguide with suitably designed boundaries and losses, and mode transitions are induced that transform this device into a robust and asymmetric switch between different waveguide modes.

Abstract: Physical systems with loss or gain have resonant modes that decay or grow exponentially with time. Whenever two such modes coalesce both in their resonant frequency and their rate of decay or growth, an 'exceptional point' occurs, giving rise to fascinating phenomena that defy our physical intuition. Particularly intriguing behaviour is predicted to appear when an exceptional point is encircled sufficiently slowly, such as a state-flip or the accumulation of a geometric phase. The topological structure of exceptional points has been experimentally explored, but a full dynamical encircling of such a point and the associated breakdown of adiabaticity have remained out of reach of measurement. Here we demonstrate that a dynamical encircling of an exceptional point is analogous to the scattering through a two-mode waveguide with suitably designed boundaries and losses. We present experimental results from a corresponding waveguide structure that steers incoming waves around an exceptional point during the transmission process. In this way, mode transitions are induced that transform this device into a robust and asymmetric switch between different waveguide modes. This work will enable the exploration of exceptional point physics in system control and state transfer schemes at the crossroads between fundamental research and practical applications.

506 citations

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TL;DR: So-called exceptional points, degenerate quantum states, allow higher energy splitting under the same perturbation conditions, greatly improving the detection sensitivity of sensors as mentioned in this paper, and thus improving the performance of sensors.

Abstract: So-called exceptional points, degenerate quantum states, allow higher energy splitting under the same perturbation conditions, greatly improving the detection sensitivity of sensors.

482 citations

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TL;DR: It is shown that an encircling of an exceptional point induces a phase change of one wave function but not of the other, and it is argued that level anticrossing (crossing) must imply crossing of the corresponding widths of the resonance states.

Abstract: Level repulsion is associated with exceptional points which are square root singularities of the energies as functions of a (complex) interaction parameter. This is also valid for resonance state energies. Using this concept it is argued that level anticrossing (crossing) must imply crossing (anticrossing) of the corresponding widths of the resonance states. Further, it is shown that an encircling of an exceptional point induces a phase change of one wave function but not of the other. An experimental setup is discussed where this phase behavior, which differs from the one encountered at a diabolic point, can be observed.

272 citations

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TL;DR: In this paper, a general theory of sensors based on the detection of splittings of resonant frequencies or energy levels operating at so-called exceptional points is presented, where the complex-square-root topology near such non-Hermitian degeneracies has a great potential for enhanced sensitivity.

Abstract: A general theory of sensors based on the detection of splittings of resonant frequencies or energy levels operating at so-called exceptional points is presented. Exploiting the complex-square-root topology near such non-Hermitian degeneracies has a great potential for enhanced sensitivity. Passive and active systems are discussed. The theory is specified for whispering-gallery microcavity sensors for particle detection. As example, a microdisk with two holes is studied numerically. The theory and numerical simulations demonstrate a sevenfold enhancement of the sensitivity.

229 citations