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Register a new userElectromagnetic fields in a time-varying medium: Exceptional points and operator symmetries
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In this paper, we study the interactions of electromagnetic waves with a non-dispersive dynamic medium that is temporally dependent. Electromagnetic fields under material time-modulation conserve their momentum but not their energy. We assume a time-variation of the permittivity, permeability and conductivity and derive the appropriate time-domain solutions based on the causality state at a past observation time. We formulate a time-transitioning state matrix and connect the unusual energy transitions of electromagnetic fields in time-varying media with the exceptional point theory. This state-matrix approach allows us to analyze further the electromagnetic waves in terms of parity and time-reversal symmetries and signify parity-time symmetric wave-states without the presence of a spatially symmetric distribution of gain and loss, or any inhomogeneities and material periodicity. This paper provides a useful arsenal to study electromagnetic wave phenomena under time-varying media and points out novel physical insights connecting the resulting energy transitions and electromagnetic modes with exceptional point physics and operator symmetries.
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Exceptional points (EPs), at which both eigenvalues and eigenvectors coalesce, are ubiquitous and unique features of non-Hermitian systems. Second-order EPs are by far the most studied due to their abundance, requiring only the tuning of two real parameters, which is less than the three parameters needed to generically find ordinary Hermitian eigenvalue degeneracies. Higher-order EPs generically require more fine-tuning, and are thus assumed to play a much less prominent role. Here, however, we illuminate how physically relevant symmetries make higher-order EPs dramatically more abundant and conceptually richer. More saliently, third-order EPs generically require only two real tuning parameters in presence of either $PT$ symmetry or a generalized chiral symmetry. Remarkably, we find that these different symmetries yield topologically distinct types of EPs. We illustrate our findings in simple models, and show how third-order EPs with a generic $sim k^{1/3}$ dispersion are protected by PT-symmetry, while third-order EPs with a $sim k^{1/2}$ dispersion are protected by the chiral symmetry emerging in non-Hermitian Lieb lattice models. More generally, we identify stable, weak, and fragile aspects of symmetry-protected higher-order EPs, and tease out their concomitant phenomenology.
Planar microcavities allow the control and manipulation of spin-polarization, manifested in phenomena like the optical spin Hall effect due to the intrinsic polarization mode splitting. Here, we study a transparent microcavity with broken rotational symmetry, realized by aligning the optical axis of a uniaxial cavity material in the cavity plane. We demonstrate that the in-plane optical anisotropy gives rise to exceptional points in the dispersion relation, which occur pair-wise, are circularly polarized, and are cores of polarization vortices. These exceptional points are a result of the non-Hermitian character of the system, and are in close relationship to singular optical axes in absorptive biaxial systems.
The scattering of electromagnetic pulses is described using a non-singular boundary integral method to solve directly for the field components in the frequency domain, and Fourier transform is then used to obtain the complete space-time behavior. This approach is stable for wavelengths both small and large relative to characteristic length scales. Amplitudes and phases of field values can be obtained accurately on or near material boundaries. Local field enhancement effects due to multiple scattering of interest to applications in microphotonics are demonstrated.
We uncover the existence of Dirac and exceptional points in waveguides made of anisotropic materials, and study the transition between them. Dirac points in the dispersion diagram appear at propagation directions where the matrix describing the eigenvalue problem for bound states splits into two blocks, sorting the eigenmodes either by polarization or by inner mode symmetry. Introducing a non-Hermitian channel via a suitable leakage mechanism causes the Dirac points to transform into exceptional points connected by a Fermi arc. The exceptional points arise as improper hybrid leaky states and, importantly, are found to occur always out of the anisotropy symmetry planes.
The finite gain-bandwidth product is a fundamental figure of merit that restricts the operation of standard optical amplifiers. In microcavity setups, this becomes a serious problem due to the narrow bandwidth of the device. Here we introduce a new design paradigm based on exceptional points, that relaxes this limitation and allows for building a new generation of optical amplifiers that exhibits better gain-bandwidth scaling relations. Importantly, our results can be extended to other physical systems such as acoustics and microwaves.
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