Tailoring Fano Lineshape in Photonic Local Density of States by Losses Engineering

Non-Hermitian theory in photonics revolutionized the understanding of optical resonators, thanks to the concept of quasi-normal modes (QNM) and to a deep revision of the Purcell factor expression. Counterintuitive effects followed, such as complex modal volumes and non-Lorentzian local density of states (LDOS) of QNMs. One of the fascinating aspects of non-Hermitian theory is the analogy with quantum mechanics for autoionizing electronic levels where the absorption cross'section is characterized by Fano lineshapes, caused by interference between the probability of absorption in the continuum and in the bound states. In photonics Fano lineshapes can arise from QNM normalization through the complex modal volume. The link between Fano lineshapes in photonic LDOS of QNMs and in the case of autoionizing states needs to be clarified. Here, by developing an analytical model based on the role of losses in the QNM normalization, they clarify the meaning of the phase of QNM normalized fields (qFano parameter),linking QNMs normalization to the concept of interference among the resonant and the leaky modes. This inspired the design of photonic crystal (PhC) cavity that exhibits LDOS with Fano character inside the itself, providing a proof of principle on how to mold the radiative lifetime by Purcell effect. Non-Hermitian theories are breaking new ground in quantum photonics applications with their unexpected predictions for the local density of states (LDOS). This paper shows how to mold the Purcell radiative rate by tailoring Fano lineshapes in the LDOS. This approach also highlights the link between the origin of Fano lineshapes in photonics and in quantum mechanics.image