Bright-soliton frequency combs and dressed states in chi(2) microresonators

TL;DR

This paper develops a theoretical framework for understanding bright soliton frequency combs in chi(2) microresonators with normal dispersion, revealing how sum-frequency processes and dressed states enable comb generation and Turing patterns.

Contribution

The paper introduces a dressed-resonator theoretical approach that incorporates sum-frequency nonlinearity, providing new insights into comb formation and parametric interactions in chi(2) microresonators.

Findings

Bright soliton combs supported by large repetition rate differences.

Sum-frequency matched sidebands influence comb bandwidth and generation.

Distinct parametric down-conversion conditions identified via Rabi splitting.

Abstract

We present a theory of the frequency comb generation in the high-Q ring microresonators with quadratic nonlinearity and normal dispersion and demonstrate that the naturally large difference of the repetition rates at the fundamental and 2nd harmonic frequencies supports a family of the bright soliton frequency combs providing the parametric gain is moderated by tuning the index-matching parameter to exceed the repetition rate difference by a significant factor. This factor equals the sideband number associated with the high-order phase-matched sum-frequency process. The theoretical framework, i.e., the dressed-resonator method, to study the frequency conversion and comb generation is formulated by including the sum-frequency nonlinearity into the definition of the resonator spectrum. The Rabi splitting of the dressed frequencies leads to the four distinct parametric down-conversion conditions (signal-idler-pump photon energy conservation laws). The parametric instability tongues associated with the generation of the sparse, i.e., Turing-pattern-like, frequency combs with varying repetition rates are analysed in details. The sum-frequency matched sideband exhibits the optical Pockels nonlinearity and strongly modified dispersion, which limit the soliton bandwidth and also play a distinct role in the Turing comb generation. Our methodology and data highlight the analogy between the driven multimode resonators and the photon-atom interaction.