Unconventional optical microcavities hosting multiple exceptional points

Recently, presence of hidden singularities known as exceptional points (EPs) in non-Hermitian quantum systems has opened up a tremendous interest in different domains of physics owing to their unique unconventional physical effects. Effectively for such systems an EP appears as a fascinating topological defect where two mutually interacting eigenstates of the system coalesce. In this work, we report occurrence of EP via avoided crossing between coupled resonance states in an optical microcavity with spatially varying gain loss profile, an optical analogue of non-Hermitian system. With suitably tailored system openness and coupling strength, internally coupled resonances can exhibit EP in a medium with simultaneous presence of loss and gain. We explore the characteristics behaviors of energy eigenvalues in complex energy plane and corresponding eigenstates when the control parameters of the system are adiabatically changed, such a way that they encircle the EP. In this letter, we first ever exploit the above scheme to analyze the optical performance in terms of stability and rigidity of a microcavity simultaneously hosting such multiple EPs.Comment: 5 pages 6 figure

Unconventional next nearest neighbor resonance coupling and states flipping mechanism in degenerate optical microcavities

We report a specially configured non-Hermitian optical microcavity, imposing spatially imbalanced gain-loss profile, to host an exclusively proposed next nearest neighbor resonances coupling scheme. Adopting 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-states phenomena 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 system parameter plane. Encountering such multiple EPs, the robustness of flip-of-states phenomena have 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, have been designed for the first time to study the unconventional optical phenomena in the vicinity of EPs.Comment: 15 pages, 7 figure

Non-adiabatic Modal Dynamics around Exceptional Points in an All-Lossy Dual-Mode Optical Waveguide: Towards Chirality Driven Asymmetric Mode-Conversion

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.Comment: 15 pages, 7 figure

Three State Quantum System Exhibiting Third Order Exceptional Singularities and Flip-of-States

A quantum inspired open optical system is mathematically implemented with an analogous three state non-Hermitian Hamiltonian exhibiting two special avoided-resonance-crossings; where interesting characteristics alongside a third-order exceptional point is explored towards robust ultra-selective state switching.Comment: 2 pages one figur

Exceptional Points in an Specialty Microcavity: Interplay between State-Conversion and Cavity Control Parameters

Exploiting scattering-matrix in a gain-loss assisted optical-microcavity, interplay between asymmetric-state-conversion and cavity-control parameters around exceptional points is analyzed; where occupying a least area by coupled states during switching, maximum conversion-efficiency with minimal asymmetry is achieved.Comment: 2 pages 1 figur

Realization of Third Order Exceptional Singularities in a Three level non-Hermitian System: Towards Cascaded State Conversion

The appearance of topological singularities, namely exceptional points (EPs) is an intriguing feature of parameter-dependent open quantum or wave systems. EPs are the special type of nonHermitian degeneracies where two (or more) eigenstates of the underlying system coalesce. In this paper, we present a three level non-Hermitian Hamiltonian which hosts three interacting eigenstates. The matrix elements are optimized in such a way that the intermediate eigenstate interacts with both the other states and the underlying system hosts at least two different second order EPs. The impact of quasi-static parameter variation along a cyclic contour around the embedded EPs on the dynamics of interacting eigenvalues is well investigated in the context of cascaded state conversion. Such dynamics of the eigenvalues shows a clear signature of the third order EP with a combined effect of both the second order EPs. Moreover, we examine the accumulation of phases around the identified EPs and study the hallmark of phase exchange during cascaded state conversions accompanied by the parametric encirclement of the third order EP

All-Lossy Quasi-Guided Dual-Mode Optical Waveguide Exhibiting Exceptional Singularities

We explore exceptional points (EP) in a dual-mode symmetric planar optical waveguide with transverse variation of inhomogeneous loss profile; where modal evolution alongside an EP is reported in the context of selective optical mode conversion.Comment: 2 pages 1 figur

Origin of third order exceptional singularities and its signature in successive state conversion

We report an open three-state perturbed system with quasi-statically varying Hamiltonian depending on the topological parameters. The effective system hosts two second order exceptional points (EP2s). Here a third order exceptional point (EP3) is explored with simultaneous encirclement of two EP2s by adiabatic variation of topological parameters. We study the robust successive state-exchange around the EP3. Applying adiabatic theorem, we estimate the evolution of total phase accumulated by each state during encirclement; where interestingly, the state-common to the pairs of coupled state picks up three times phase shift of 2{\pi}. Such an exclusively reported scheme can be exploited in potential applications of exceptional points, manipulating fewer topological parameters in various non-Hermitian systems.Comment: 11 pages 5 figure

Exceptional Point and Toward Mode Selective Optical Isolation

Dynamical encirclement of an Exceptional Point (EP) and corresponding time-asymmetric mode evolution properties due to breakdown in adiabatic theorem have been a key to range of exotic physical effects in various open atomic, molecular and optical systems. Here, exploiting a gain-loss assisted dual-mode optical waveguide that hosts a dynamical EP-encirclement scheme, we have explored enhanced nonreciprocal effect in the dynamics of light with onset of saturable nonlinearity in the optical medium. We propose a prototype waveguide-based isolation scheme with judicious tuning of nonlinearity level where one can pass only a chosen mode in any of the desired directions as per device requirement. The deliberate presence of EP enormously enhances the nonreciprocal transmission contrast even up to 40 dB over the proposed device length with a scope of further scalability. This exclusive topologically robust mode selective all-optical isolation scheme will certainly offer opportunities in integrated photonic circuits for efficient coupling operation from external sources and improve device performances.Comment: 5 pages, 6 figure

Nonlinearity Induced Anomalous Mode Collapsing and Non-chiral Asymmetric Mode Switching around multiple Exceptional Points

The dynamical encirclement around a second order exceptional point (EP) and corresponding chirality driven nonadiabatic modal dynamics have attracted enormous attention in the topological study of various non-Hermitian systems. However, dynamical encirclement around multiple second-order EPs in a multi-state system is yet to be explored. Here, exploiting an exclusive design of a planar gain-loss assisted three-mode supported optical waveguide with local Kerr-nonlinearity, we encounter multiple second-order EPs. Judiciously, choosing a specific parameter space by varying the unbalanced gain-loss profile, we encircle multiple EPs simultaneously, and explore the beam-dynamics toward corresponding chiral or non-chiral aspects of the device. While propagating through the designed waveguide, three coupled modes are collapsed into a specific dominating mode, owing to corresponding nonadiabatic corrections around multiple EPs. Even in the absence of chirality, here, the same amount of focusing and de-focusing type nonlinearity gives different dominating output, irrespective of the choice of inputs, for the same topological structure of the waveguide. This exclusive topologically robust compact scheme of nonlinearity induced asymmetric and non-chiral light dynamics should provide a promising opportunity to switch or retrieve a selective mode from a multi-mode signal in integrated devices.Comment: 5 pages, 4 figure