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.
Highlights
Ring microresonators break through the traditional barriers of frequency conversion in terms of power efficiency, generated bandwidth, and compactness [1,2]
References [3,4,5,6] have been among the first ones to demonstrate frequency conversion in high-quality factor whispering gallery microresonators with quadratic nonlinearity
Results on bright parametric down conversion (PDC) solitons in the resonators with group velocity offset published two decades ago [27] provided a conceptual answer, that the compensation of the group velocity difference is achieved via the balancing interplay between the dissipative and nonlinear effects
Summary
Ring microresonators break through the traditional barriers of frequency conversion in terms of power efficiency, generated bandwidth, and compactness [1,2]. References [3,4,5,6] have been among the first ones to demonstrate frequency conversion in high-quality factor whispering gallery microresonators with quadratic nonlinearity Since this area has made significant progress As we have reported recently [23] and investigate in depth below, this makes the frequency conversion and soliton generation mechanisms depart significantly from what has been known about these effects in the relatively low finesse resonators, F ∼ 102, which often have no resonator feedback at one of the generated harmonics One of the prime results included below is the demonstration of bright soliton pulses in a microresonator which has a large repetition rate difference between the fundamental, ωp, and second-harmonic frequencies, 2ωp (see Sec. XIII). The content of what follows is much wider than just reporting the soliton mode locking, and it is useful to give it a brief overview
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