Modulational instability and frequency combs in whispering-gallery-mode microresonators with backscattering

Abstract

We introduce the first principle model describing frequency comb generation in a WGM microresonator with the backscattering-induced coupling between the counter-propagating waves. Elaborated model provides deep insight and accurate description of the complex dynamics of nonlinear processes in such systems. We analyse the backscattering impact on the splitting and reshaping of the nonlinear resonances, demonstrate backscattering-induced modulational instability in the normal dispersion regime and subsequent frequency comb generation. We present and discuss novel features of the soliton comb dynamics induced by the backward wave.

Numerical study of solitonic pulse generation in the self-injection locking regime at normal and anomalous group velocity dispersion

“…The generation of dark solitons or platicons by the free-running laser was found to be practically impossible due to the absence of the modulational instability (MI), so that the system remained in the cw solution during the scanning. In our earlier work we showed that the presence of the backward wave can induce MI [40]. In our opinion this fact in combination with nontrivial tuning curve in the SIL regime [see Fig.…”

“…The field amplitudes are normalized to photon concentration using the same laser-referred coefficient to simplify the expressions. We modify accordingly the equation system for the SIL effect from [12], thus combining it with the results of [40] for the high-finesse microresonator and obtain the coupled mode equation system (CMES) [41] in the form…”

“…For analysis of the frequency comb generation process it is more convenient to control the normalized pump coefficient = √︃ [18,40]. This coefficient encapsulates the microresonator and coupler parameters, such as nonlinearity 3 , mode volume 0 , coupling coefficient 0 , mode and coupler cross-section and refractive index ratios (which is usually assumed to be unity).…”

“…To provide more insight and analogy with the known systems we perform the transformation of the CMES into the LLE. The transformation of the microresonator part of the system to the LLE-type is straightforward [40,45]. We define the spacial fields as ( ) =…”

Soliton blockade in bidirectional microresonators

“…These shifts are different for '+' and '−' waves. In the high repetition rate devices, the phase dependent four-wave mixing terms inside the XPM part of the Kerr response, |ψ ∓ | 2 ψ ± , oscillate with the fast rate ∼ 2D 1 [16][17][18]. If finesse F = D 1 /κ 1, then the fast oscillations can be disregarded and this is why the XPM nonlinearity in Eq.…”