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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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 ...
35 citations
TL;DR: In this paper, the authors studied the simultaneous interactions between three successive coupled states via avoided-resonance-crossing (ARC) phenomena, and identified two EP2s near two ARC regimes.
Abstract: One of the most intriguing topological features of open systems is that they exhibit exceptional point (EP) singularities. Apart from the widely explored second-order EPs (EP2s), the exploration of higher-order EPs in any system requires more complex topology, which is still a challenge. Here, we encounter a third-order EP (EP3) with the simultaneous presence of multiple second-order EPs in a simple fabrication feasible gain-loss assisted trilayer optical microcavity. Using the scattering-matrix formalism, we study the simultaneous interactions between three successive coupled states via avoided-resonance-crossing (ARC) phenomena, and we identify two EP2s near two ARC regimes. Such an occurrence of two EP2s inside a closed two-dimensional parametric space associated with an unbalanced gain-loss profile leads to the functionality of a cube-root branch point, i.e., an EP3. Following an adiabatic variation of two control parameters around the embedded EP3 in the presence of two identified EP2s, we present a robust successive-state-conversion mechanism among three coupled states. The proposed scheme indeed opens up a unique platform to manipulate light in integrated photonic devices.
20 citations
Cites background from "Connected hidden singularities and ..."
...[15] A....
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...Such unique topological features of EPs have been exploited in-depth to meet a wide range of technological challenges like, asymmetric-mode-conversion [10–14], topological state-switching [15–17], lasing-control [18], unidirectional propagation with enhanced nonreciprocity [19, 20], sensitivity enhancement [21–23], etc....
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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.
18 citations
Cites background from "Connected hidden singularities and ..."
...states of resonances of the Hamiltonian corresponding to the real system are calculated in terms of poles of the associated S-matrix [12, 14]....
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...An EP leads to crucial modifications on associated coupled eigenvalues’ behavior under the influence of coupling parameters; where the phenomenon of flipping of states in the complex eigenvalue plane is the most significant in the context of optical mode converter [12,13]....
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...Adopting scattering matrix (S-matrix) formalism, the effect of interplay between such proposed resonance interactions and the incorporated nonHermiticity in the microcavity is analyzed drawing a special attention to the existence of hidden singularities, namely exceptional points (EP s); where at least two coupled resonances coalesce....
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...Previously, this formation of exceptional line has been reported for the first time by the authors while considering the nearest neighbor coupling situations between the consecutive poles to explore EP s in a different class of Fabry-Perot microcavities [12]....
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...Here, in k-plane each point on the red blue and black trajectories indicate the point-to-point evolution of S-matrix poles from their starting positions (represented by the brown circles) with associated encircling process (following green circle at the inset) around the respective singularity (denoted by red cross at the inset) in (γ, τ)-plane....
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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.
16 citations
References
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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.
776 citations
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.
708 citations
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.
628 citations
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.
327 citations
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.
306 citations