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Scientific Reports

Analysis and modeling of Fano resonances using equivalent circuit elements

Bo Lv, Rujiang Li, Jiahui Fu, Qun Wu, Kuang Zhang, Wan Chen, Zhefei Wang, Ruyu Ma

Published Aug 22, 2016• 37 citations
Publisher

Abstract

Fano resonance presents an asymmetric line shape formed by an interference of a continuum coupled with a discrete autoionized state. In this paper, we show several simple circuits for Fano resonances from the stable-input impedance mechanism, where the elements consisting of inductors and capacitors are formulated for various resonant modes, and the resistor represents the damping of the oscillators. By tuning the pole-zero of the input impedance, a simple circuit with only three passive components e.g. two inductors and one capacitor, can exhibit asymmetric resonance with arbitrary Q-factors flexiblely. Meanwhile, four passive components can exhibit various resonances including the Lorentz-like and reversely electromagnetically induced transparency (EIT) formations. Our work not only provides an intuitive understanding of Fano resonances, but also pave the way to realize Fano resonaces using simple circuit elements.

DOI
10.1038/srep31884

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Fano resonance presents an asymmetric line shape formed by an interference of a continuum coupled with a discrete autoionized state. In this paper, we show several simple circuits for Fano resonances from the stable-input impedance mechanism, where the elements consisting of inductors and capacitors are formulated for various resonant modes, and the resistor represents the damping of the oscillators. By tuning the pole-zero of the input impedance, a simple circuit with only three passive components e.g. two inductors and one capacitor, can exhibit asymmetric resonance with arbitrary Q-factors flexiblely. Meanwhile, four passive components can exhibit various resonances including the Lorentz-like and reversely electromagnetically induced transparency (EIT) formations. Our work not only provides an intuitive understanding of Fano resonances, but also pave the way to realize Fano resonaces using simple circuit elements.
In this paper, we realize tunable Fano and electromagnetically induced transparency (EIT)-like resonances in the outputs of a nested feedback ring resonator. Compared with the traditional add-drop ring resonator, the feedback arm introduces interference between different resonance modes. Using coupled mode theory, we reveal that the output Fano resonances are the interference of discrete modes and continuum modes, whereas the EIT-like resonance only appears in the over-coupled state. We experimentally confirm the two effects using optical fiber ring resonators, finding that the Fano effect can be easily controlled with phase shifts in the feedback arm. Moreover, we achieve the double Fano resonance, which displays an ‘X’ type lineshape utilizing one ring resonator, predicting it to be a good candidate in wavelength monitor. The proposed simple configuration provides a platform to study Fano and EIT-like effect, which is useful in the optical filter, fast and slow light, optical switching, and optical sensing.
Abstract The Fano resonance has been a familiar and important feature in atomic and molecular physics for more than half a century. Typically, the combination of a discrete state with one or more continua results in an asymmetric peak in the ionization spectrum. The peak-shape, called the Fano profile, can be expressed by a simple formula derived by Fano in 1935. However, the interpretation of its characteristic parameter q , which represents the asymmetry of the peak in the formula, is not necessarily intuitively transparent. The Fano resonance is not necessarily a quantum effect, but it is a manifestation of a certain physical mechanism in various systems, both quantum and classical. Through the derivation of q from the known classical pictures with the classical coupled oscillator, we interpret the q value with a geometrical view. And further, we introduce a complex valued q parameter for the description of the resonance with a damped oscillator.
Spectroscopic signatures associated with symmetric Lorentzian and asymmetric Fano line shapes are ubiquitous. Distinct features of Fano resonances in contrast with conventional symmetric resonances have found several applications in photonics such as optical switching, sensing, lasing, and nonlinear and slow-light devices. It is therefore important to effectively generate and control these resonances. In this work, we show through ab initio simulations of coupled light–matter systems that Fano interference phenomena can be realized in a multimode photonic environment by strong coupling to the electromagnetic continuum. Specifically, we show that by effectively enhancing the light–matter coupling strength to the photon continuum in an experimentally feasible way, we can achieve a transition from Lorentzian to Fano lines shapes for both electronic and polaritonic excitations. An important outcome of switching between these spectral signatures is the possibility to control the Purcell enhancement of spontaneous emission alongside electromagnetically induced transparency, which is a special case of Fano resonances. Switching from Fano back to a Lorentzian profile can be achieved by physically reducing the coupling strength to the continuum of modes. Our results hold potential for realizing tunable Fano resonances of molecules and materials interacting with the electromagnetic continuum within multimode photonic environments.
We achieve Fano-like resonances in an all-in-fiber structure embedded with an in-line Mach-Zehnder interferometer (MZI). A fiber Bragg grating is inserted into MZI's one arm to form a resonance, which functions as the discrete state of the Fano-like resonance to couple with the continuum propagating mode of MZI in the fiber core. A theoretical model predicts the controllable resonance lineshape by changing the phase difference between the MZI's two interference pathways. Fano-like resonances with an extinction ratio over 20 dB are experimentally observed, which are reliably tuned into Lorentzian and electromagnetically induced transparency-like resonances by versatile methods. The realization of Fano-like resonances with broad tunability in this all-in-fiber structure holds potentials in fiber-based applications of sensing, signal processing and nonlinear optics.
By breaking the symmetrical arrangement of double micro-ring resonator, the formation mechanism and performance of reflection and transmission spectrum and optical field distribution are investigated. The reflection spectrum is Fano shape. The Fano resonance has an asymmetric and sharp resonance peak can be independently tuned by changing the asymmetric coupling factor of the first micro-ring. The transmission spectrum is electromagnetically induced transparency(EIT)-like shape. The (EIT)-like resonance can be independently tuned by changing the absorption factor and the phase shift factor of the second micro-ring. The Fano and EIT-like resonance have low loss and high near-field localization characteristics, our research has promising applications in optical communication and opto-electronic modulators.
We experimentally and theoretically demonstrate electromagnetically induced transparency (EIT)-like and Fano resonance in a single quasi-cylindrical microresonator (QCMR). Stable controlling of the EIT and Fano resonance lineshapes can be achieved by vertically moving the resonator along its axis while in touch with the tapered fiber. Moreover, by horizontally scanning the coupling point along the tapered fiber, asymmetric Fano resonances of the transmission spectra are observed and can be engineered to vary periodically. Interestingly, the two different kinds of mechanisms that induce the Fano or EIT resonances can work on the same mode simultaneously. Our device offers a stable platform for controlling the EIT and Fano resonances and holds unique potential in all-optical switching, quantum information processing and sensitivity-enhanced sensing applications.