Abstract
Abstract The Vernier effect and harmonic Vernier effect have attracted ever-increasing interest due to their freely tailored spectrum envelope in tunable laser, modulator, and precision sensing. Most explorations have mainly focused on configuring two isolated optical resonators, namely the reference and tunable resonator. However, this configuration requires a stable reference resonator to guarantee robust readout, posing a significant challenge in applications. Here, we discover the coupled-resonators configuration enabling a reference-free envelope modulation to address this problem. Specifically, all parameters of one resonator theoretically span a hypersurface. When the resonator couples to another one, photon coupling merit an escaped solution from the hypersurface, resulting in an envelope modulation independent of reference. We have first experimentally verified this mechanism in a coupled air resonator and polydimethylsiloxane resonator by inserting a semi-transparent 2-mercaptobenzimidazole-modified silver nanowire network. In addition, this novel mechanism provides a new degree of freedom in the reciprocal space, suggesting alternative multiplexing to combine more envelope modulations simultaneously. This study facilitates the fundamental research in envelope multiplexing. More importantly, the combination of silver nanowire network and flexible microcavity experimentally progress the spectral envelope modulation in optoelectronic integration inside resonators.
Highlights
The Vernier effect is a ubiquitous physical phenomenon to applications ranging from accurate sensing [1,2,3] to modulators in integrated photonics [4, 5] and microwave technology [6, 7]
To avoid the theoretical conflict, several groups mathematically treated two coupled resonators as three reflectors [32, 36]. Such treatment must assume that the counter-propagating light does not contribute to the output, breaking the Lorentz reciprocity [37]. This current study has clarified the elusive envelope modulation mechanism in the coupled resonators, and we spectacularly discovered that the photon coupling features a reference-free spectral envelope modulation, addressing the difficulty of the susceptible reference resonator
This current work presents that the coupled resonator endows a new mechanism of the Vernier effect and harmonic Vernier effect
Summary
The Vernier effect is a ubiquitous physical phenomenon to applications ranging from accurate sensing [1,2,3] to modulators in integrated photonics [4, 5] and microwave technology [6, 7]. There are two mainstream configurations, i.e., parallel and series, commonly used to introduce the Vernier effect and harmonic Vernier effect [22] The former provides an advantage in interference visibility due to their crosstalk-free light intensities [23, 24]; the latter contributes a more compact packaging, widely used in space-starved chip applications [25, 26]. To avoid the theoretical conflict, several groups mathematically treated two coupled resonators as three reflectors [32, 36] Such treatment must assume that the counter-propagating light does not contribute to the output, breaking the Lorentz reciprocity [37]. This study has experimentally manifested that the coupled resonators configuration facilitates the optoelectronic integration and provides an extra degree of freedom in the reciprocal space, offering alternative multiplexing to combine and identify more modulated signals
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