Abstract
A single closed-form analytical solution of the driven nonlinear Schrödinger equation is developed, reproducing a large class of the behaviors in Kerr-comb systems, including bright-solitons, dark-solitons, and a large class of periodic wavetrains. From this analytical framework, a Kerr-comb area theorem and a pump-detuning relation are developed, providing new insights into soliton- and wavetrain-based combs along with concrete design guidelines for both. This new area theorem reveals significant deviation from the conventional soliton area theorem, which is crucial to understanding cavity solitons in certain limits. Moreover, these closed-form solutions represent the first step towards an analytical framework for wavetrain formation, and reveal new parameter regimes for enhanced Kerr-comb performance.
Highlights
A single closed-form analytical solution of the driven nonlinear Schrödinger equation is developed, reproducing a large class of the behaviors in Kerr-comb systems, including bright-solitons, darksolitons, and a large class of periodic wavetrains
To elucidate the dynamics of comb formation, Kerr combs have been modeled with coupled-field[17,18,19,20] and single-field[16,21,22,23,24,25,26,27] formulations of the damped-driven Nonlinear Schrodinger equation (NLSE), termed the Lugiato-Lefever equation[22,28,29]
We derive a modified area theorem that relates the pulse duration to the peak powers within Kerr-comb systems for both soliton and wavetrain solutions, revealing significant deviation from the conventional soliton area theorem and tremendous opportunity for wideband comb formation using wavetrains
Summary
Pump detuning (δ) represents the frequency deviation of the pump light from a cavity resonance This model is strictly valid for bandwidths supporting pulses 50 fs and longer and is expanded to higher order dispersion and nonlinearities[23]. An exact soliton solution is known for this driven NLSE30, and in 200540 a broader class of solutions was discovered; these solutions are of the form E = (G + Kf (T )2)/(1 + Lf (T )2), where f are the Jacobi Elliptic functions. This solution serves as the starting point for our analysis. Where cn is the Jacobi Elliptic function and G, K, L, τ and m are real pulse parameters which are determined by the system parameter, h
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