Universal Bright-Bright Integrated Soliton Molecule via Parametric Binding

TL;DR

The paper addresses extending on-chip Kerr frequency combs by exploiting multi-pumped DKS to realize a parametric bright-bright bound state between the DKS and an idler, enabling spectral translation toward visible wavelengths. It develops a multi-color soliton framework using a field decomposition $a( heta,t) = a_0 + a_- e^{i\varpi t} + a_+ e^{-i\varpi t}$ under the modified Lugiato-Lefever equation and derives the idler’s spectral translation via four-wave mixing Bragg scattering, $A_+(mu-mu_+) = \frac{2\gamma}{i\kappa/2 + (D_2^{(+)}/2)(\u0003mu-mu_+)^2} F_0 F_-^* A_0(mu,t)$. Numerical and experimental results in a SiN microring validate two regimes, including a parametric bright-bright bound state in which the idler is a replica of the DKS and can appear even under normal dispersion. The findings show dispersion-free bright-idler generation with robust spectral coverage toward near-visible wavelengths and discuss stabilization pathways via Kerr-induced synchronization, expanding the operational parameter space for integrated optical clocks and spectroscopic applications. This work thus enables flexible spectral engineering of microcomb states with potential impact on metrology and quantum system spectroscopy at visible wavelengths.

Abstract

Dissipative Kerr solitons (DKSs) have emerged as the preferred solution for on-chip integrated optical frequency comb (OFC) generation in metrology. A multi-pumped DKS enables either all-optical trapping in the Kerr-induced synchronization regime, or a multi-component OFC with \greg{a locked repetition rate yet with constant frequency offsets between the components} in the multi-color DKS regime. The multi-color DKS regime is of particular interest since nonlinear mixing between the DKS and the secondary pumped component generates idler waves at different frequencies that are useful for spectral extension of the DKS comb. Here, we explore multi-color idler generation at frequencies in which the resonator free spectral range matches that at the DKS. We demonstrate theoretically and experimentally that without phase matching, the idler forms a bright pulse fundamentally bound to the bright DKS through parametric interaction, despite occurring in normal dispersion. Our work can enable new applications in metrology and spectroscopy of quantum systems toward visible wavelengths, as the parametric nature of our bright-bright state eliminates dependence on dispersion regime or visible wavelength pumping.

Figures (4)

• Figure 1: Concept of multi-pumped soliton bound states induced by nonlinearity in microring resonators. a When dual pumping a microring resonator with the main pump generating the soliton and the secondary pump set outside phase matching---occurring when the phase offset $\varpi$ between the DKS and secondary pumped field exceeds the maximum integrated dispersion $D_\mathrm{int}(\mu)$---a bright-DKS/dark-pulse bound state forms. The dark pulses arise from the cross-phase modulation (XPM) frequency shift experienced by the secondary pumped field when the DKS amplitude along the azimuthal coordinate is significant. b The secondary pump field and the soliton can parametrically nonlinearly interact and generate an idler field at equal but opposite phase shift $-\varpi$. Similar to the previous case, if $-\varpi$ is set to prevent phase matching, a bound state idler pulse with the DKS occurs. The idler parametric driving field closely follows the soliton profile, hence only creating new light at the idler for sufficient energy in the soliton profile, resulting in a bright pulse regardless of the dispersion regime at the idler central mode.
• Figure 2: Numerical demonstration of parametric bright pulse formation through secondary pump detuning. a Integrated dispersion profile $D_{\text{int}}(\mu)$ with main pump $F_0$ creating the DKS comb $A_0$ and the secondary pump $F_-$. The integrated dispersion and FSR mismatch curve are computed directly from the finite element method simulated resonance frequencies. The phase offset $\varpi_-$ of the secondary pumped comb with the DKS enables nonlinear phase mixing, creating an idler at an offset $-\varpi_-$ from the DKS comb. The shaded area corresponds to the detuning used in the simulation. b Spectral evolution of the DKS ($A_0$), secondary pump ($A_-$), and idler comb ($A_+$) with the secondary pump detuning from positive (phase-matched idler) to negative (phase-mismatched idler) values across six conditions (i-vi). c Corresponding azimuthal profile of the idler color $|a_+(\theta)|^2$, transforming into a bright $\sech$ pulse as phase matching is prevented. d Idler spectrum showing transition from synthetic dispersive waves at positive detuning to broadband bright pulse at negative detuning. e-f Azimuthal profiles comparing idler intensity of the idler color $|a_+(\theta)|^2$ (e) with the DKS $|a_0(\theta)|^2$ (f), demonstrating that the parametric idler forms a bright pulse co-localized with the soliton when phase matching is prevented.
• Figure 3: Experimental demonstration of the bright-bright parametrically binded pulse regime. a We use an integrated microring resonator designed to support octave-spanning operation of the microcomb with an integrated dispersion $D_\mathrm{int}(\mu)$ (top) presenting two zero-crossing at 199 and 378 when assuming a pump at 285.3. The resulting single-pump DKS, obtained with thermal-stabilization using a cross-polarized cooler pump at 307.7 present two dispersive waves at the expected phase-matched mode from $D_\mathrm{int}$ and spanning over an octave. b We then introduce a secondary pump at 193.5 to explore bright-bright DKS-idler bond state formation. As the theory predicts, the experimental idler comb profile changes with secondary pump detuning based on phase matching presence or absence. c We reproduce the idler comb map experimentally, with striking resemblance to the theoretical finding of \ref{['fig:2']}, highlighting the parametric bright pulse formation when the phase matching is prevented.
• Figure 4: Experimental demonstration of repetition rate binding. a The measured spectrum in the multi-color soliton regime exhibits three distinct comb components equally offset from one another with opposite signs, confirming multi-color soliton theory and phase conservation. b From the spectrum, one extracts the relative offset of each comb tooth against a fixed frequency grid. The DKS matches the grid perfectly, while the secondary pump and idler comb teeth show equal but opposite frequency offsets, as theory predicts. Both exhibit zero slope (dashed lines), indicating identical repetition rates to the DKS, confirming the binding of all three colors. The dotted lines represent the OSA resolution error which is frequency dependent.