Browsing by Author "El-Ganainy, R."
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- ItemResolvent expansion for discrete non-Hermitian resonant systems [Invited](Washington, DC : Optica, 2022) Simonson, L.; Özdemir, S.K.; Busch, K.; El-Ganainy, R.The linear response of non-Hermitian resonant systems demonstrates various intriguing features such as the emergence of non-Lorentzian lineshapes. Recently, we have developed a systematic theory to understand the scattering lineshapes in such systems and, in doing so, established the connection with the input/output scattering channels. Here, we follow up on that work by presenting a different, more transparent derivation of the resolvent operator associated with a non-Hermitian system under general conditions and highlight the connection with the structure of the underlying eigenspace decomposition. Finally, we also present a simple solution to the problem of self-orthogonality associated with the left and right Jordan canonical vectors and show how the left basis can be constructed in a systematic fashion. Our work provides a unifying mathematical framework for studying non-Hermitian systems such as those implemented using dielectric cavities, metamaterials, and plasmonic resonators.
- ItemUniform optical gain as a non-Hermitian control knob(College Park, MD : APS, 2022) Hashemi, A.; Busch, K.; Ozdemir, S.K.; El-Ganainy, R.Non-Hermitian optics utilizes judicious engineering of the spatial and spectral distribution of gain and loss in order to tailor the behavior of photonic systems in ways that could not be achieved by modulating only the real part of the refractive index. In this respect, a question that has never been addressed is whether a uniform distribution of gain or loss can also lead to nontrivial non-Hermitian effects in linear systems, beyond just signal amplification or decay. Here, we investigate this problem and demonstrate that the application of uniform gain to a symmetric photonic molecule (PM) can reverse the optical energy distribution inside the structure. For a PM composed of two coupled resonators, this translates into changing the optical energy distribution inside the resonators. For a PM formed through scattering or defect-induced intermodal coupling in a ring resonator, the applied gain, despite being uniform and symmetric, can impose a strong chirality and switch the direction of light propagation from dominantly clockwise to dominantly counterclockwise. These predictions are confirmed by using both coupled mode formalism and full-wave finite-element simulations. Our work establishes a different direction in the field of non-Hermitian optics where interesting behavior can be engineered not only by unbalancing the non-Hermitian parameter but also by changing its average value - a feature that was overlooked in previous works.