Modulational instability at normal dispersion in microresonators with backscattering Текст научной статьи по специальности «Физика»

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Modulational instability at normal dispersion in microresonators with backscattering

N. Kondratiev1, V. Lobanov1, D. Skryabin1,2

1Russian Quantum Center, Coherent Microoptics and Ragiophotonics, Moscow, Russian Federation

2University of Bath, Department of Physics, Bath, United Kingdom

In recent years, optical whispering gallery modes (WGM) microresonators have found wide application in various fields of science and technology. Due to high quality factor they represent the most promising platform for the creation of miniature, energy-efficient components for photonics and radiophotonics. The discovery of Kerr frequency combs and dissipative Kerr solitons (DKS) generation in microresonators [1] increased the interest to the WGM microresonator field. Several recent works showed that Rayleigh scattering inside a microresonator [2] can generate a backward wave to provide resonant feedback for the laser line stabilization via the self-injection locking effect [3,4]. Furthermore the generation of DKS was demonstrated by the multi-frequency laser locked by high-Q microresonator [5]. However, this backward wave also interacts nonlinearly with the forward wave and influence frequency comb dynamics. It was shown that the cross-phase modulation can lead to modulational instability for the copropagating waves [6-8]. Here we study this effect for the counter-propagating waves using numerical modeling and linear stability analysis.

First, we rigorously derived the coupled mode equations from the ab initio Maxwell equations to describe the resonator. For large enough finesse (the resonance frequency to inter-mode distance ratio) and the equations can be transformed to Lugiat-Lefever-like equations. We found that in the normal dispersion mode, the scanning of the main resonance does not generate additional spectral components. At the same time, modulation instability is observed at the second resonance, which provides a new mechanism for the generation of the frequency comb. While scanning the second branch branch and a certain detuning value is reached, the first sidebands appear, and then due to non-degenerate four-wave interaction, the remaining frequency components rise. Then, a chaotic regime is observed, corresponding to the generation of an incoherent comb, which then passes into a stable low-intensity single-mode mode.

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Fig. 1.

The parameters of the generated frequency comb also depend on the linear coupling coefficient of the forward and backward waves. It can be assumed that such a mechanism of frequency comb generation in the normal dispersion mode may be responsible for the generation of the platicon in

the self-injection locking regime [9]. The linear stability analysis was also performed to get the insight on the system regimes. This allows us to estimate the detuning and mode number at which the first sideband will appear during laser sweeping. We also note that the mode number and second order dispersion parameter appear in formulas as a united term giving out a simple square-root scaling for first sideband with dispersion.

This work was supported by the Russian Science Foundation (Project 17-12-01413).

References

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[9] V.Lobanov, et.al., Frequency combs and platicons in optical microresonators with normal GVD,Opt.Express 23, 77137721 (2015).