Intermode reactive coupling induced by waveguide-resonator interaction

Abstract

We report on a joint theoretical and experimental study of an integrated photonic device consisting of a single mode waveguide vertically coupled to a disk-shaped microresonator. Starting from the general theory of open systems, we show how the presence of a neighboring waveguide induces reactive inter-mode coupling in the resonator, analogous to an off-diagonal Lamb shift from atomic physics. Observable consequences of this coupling manifest as peculiar Fano lineshapes in the waveguide transmission spectra. The theoretical predictions are validated by full vectorial 3D finite element numerical simulations and are confirmed by the experiments.PACS numbers: 42.25. Hz, 42.60.Da, 42.82.Gw,31.30.jf The study of the consequences of coupling a physical system to an environment constitutes the central problem in the theory of open systems [1]. This coupling, on one hand, allows the system to dissipate energy through active decay channels. On the other hand, its reactive component leads to a shift of energy levels and oscillation frequencies of the system. Most celebrated examples of this physics involve an atom coupled to the bath of electromagnetic modes [8], namely, the (dissipative) spontaneous emission of photons from an excited state [2-4] and the (reactive) Lamb shift of transition frequencies [5][6][7].Pioneering experimental studies in late 1970's [9] showed that destructive interference of different decay paths, leading to the same final continuum, can suppress absorption by a multilevel atom via the so-called Coherent Population Trapping (CPT) [10] and Electromagnetically Induced Transparency (EIT) [11,12] mechanisms. While originally these phenomena were discovered in the atomic physics context, a continuous interest has been devoted to analogous effects in solid-state systems [13], photonic devices [14][15][16][17][18][19][20], and, very recently, optomechanical systems [21]. Though in most experiments only the dissipative features are affected by the interference, the theory predicts that a similar phenomenon should also occur on the reactive coupling side [1].In photonics, the presence of a waveguide in the vicinity of a resonator activates new radiative decay channels for the resonator modes via emission of light into the waveguide mode [22][23][24]. The corresponding reactive effect is a shift of the resonator mode frequencies, which can be interpreted as the photonic analogue of the atomic Lamb shift. In this Letter, we report on a joint theoretical and experimental study of a photonic device in which pairs of modes of very similar frequencies are coupled simultaneously to the same waveguide mode. Both the dissipative and the reactive couplings of the cavity modes to the waveguide turn out to be modulated by interference phenomena between the two modes, which can be summarized as environment-induced inter-mode cou-

Complete crossing of Fano resonances in an optical microcavity via nonlinear tuning

“…The asymmetric Fano lineshape may vary abruptly with changing the detuning due to the fine interplay of the phases of individual resonances. For example, there exists a unique spectral point on one side of the composite resonance, where a particular destructive interference leads to a full suppression of one of the transmission features in the spectrum [18,21]. This situation may be observed experimentally in very fortuitous cases for which a given ∆F SR 12 exactly satisfies the necessary condition.…”

“…Having couples of modes of two radial families with different relative detuning permits to monitor the coupling between the two radial families when changing the M with a discrete step of ∆F SR 12 just by changing M . This has been studied in detail in our previous work [18].…”

“…The theory described in the previous sections is supported by experimental results. The samples studied in this work were realized using standard silicon microfabrication tools, as detailed in our previous works [18,24,25]. The resonator is realized in silicon nitride material and is coupled vertically to the underlaying waveguide.…”

“…Here we propose an all-optical approach to detune relatively the resonances within a microresonator by exploiting the thermo-optical effect at a local level. The effect is demonstrated by applying it to a Whispering Gallery * Corresponding author: martino.bernard@unitn.it resonator -waveguide system which exhibits Fano interference features [6,[13][14][15][16][17][18]. The continuous detuning is used to explore complete mode crossings between two resonances.…”

Off-diagonal photonic Lamb shift in reactively coupled waveguide-resonator system

“…As stated before, we will focus on a system with two modes j = 1, 2 interacting with a single (transverse) mode waveguide with a continuum of (K) modes, although generalization to n modes for the resonant system is possible. 30 The transmission of a waveguide which is coupled to a resonator reads then…”