Topological Soliton Frequency Comb in Nanophotonic Lithium Niobate

Abstract

Frequency combs have revolutionized metrology, ranging, and optical clocks, which have motivated substantial efforts on the development of chip-scale comb sources. The on-chip comb sources are currently based on electro-optic modulation, mode-locked lasers, quantum cascade lasers, or soliton formation via Kerr nonlinearity. However, the widespread deployment of on-chip comb sources has remained elusive as they still require RF sources, high-Q resonators, or complex stabilization schemes while facing efficiency challenges. Here, we demonstrate an on-chip source of frequency comb based on the integration of a lithium niobate nanophotonic circuit with a semiconductor laser that can alleviate these challenges. For the first time, we show the formation of temporal topological solitons in a on-chip nanophotonic parametric oscillator with quadratic nonlinearity and low finesse. These solitons, independent of the dispersion regime, consist of phase defects separating two $π$-out-of-phase continuous wave solutions at the signal frequency, which is at half the input pump frequency. We use on-chip cross-correlation for temporal measurements and confirm formation of topological solitons as short as 60 fs around 2 $μ$m, in agreement with a generalized parametrically forced Ginzburg-Landau theory. Moreover, we demonstrate a proof-of-concept turn-key operation of a hybrid-integrated source of topological frequency comb. Topological solitons offer a new paradigm for integrated comb sources, which are dispersion-sign agnostic and do not require high-Q resonators or high-speed modulators and can provide access to hard-to-access spectral regions, including mid-infrared.

Figures (4)

• Figure 1: Topological soliton concept.a, Schematic of the hybrid-integrated topological soliton frequency comb source. A degenerate optical parametric oscillator (DOPO) is pumped by a continuous wave (cw) laser diode. The poled section is phase-matched for degenerate parametric down-conversion, leading to the generation of signal photons at half the pump frequency. Inset: image of the actual chip containing 30 OPOs. b, The cw pumping of a DOPO results in a cw signal in the conventional regime. Owing to a $\pi$ phase indetermination, the signal field sign is either positive ($+A_h^+$) or negative ($-A_h^+$), with equal probability. c, These two fields with opposite signs can coexist through the formation of domain walls connecting the opposite signs. The intensity profiles of these domain walls correspond to dark pulses named topological solitons. At the pump, they coincide with the formation of bright pulse. This dark-bright pulse pair forms a two-color frequency comb.
• Figure 2: Theoretical analysis of temporal topological solitons. a, Phase diagram showing the main bifurcation lines of the system for two values of phase mismatch [$\varrho\approx0$ (gray) and $\varrho=\pi$ (red)], $\eta_1=-1$ and $\eta_2=0.13$. $S_P$: pitchfork bifurcation. $S_f$: fold. The pink (white) area indicates the existence of stable topological solitons (trivial solution). Gray area: modulationally unstable regions, delimited by point-dashed lines (see main text). b, Bifurcation diagram in the supercritical configuration for $\Delta=0$ and $\varrho\approx0$. The purple arrow suggests the formation of domain walls (DWs). Solid (dashed) lines represent stable (unstable) states. We omit the (unstable) trivial solution above the threshold. c, Similar to (b) but for the subcritical regime with $\Delta=4$ and $\varrho=\pi$. Gray arrows: close to $S_p$, the system tends to dynamically converge toward the conventional regime ($A_h^+$or$-A_h^+$) rather than forming DWs ($A_h^+$and$-A_h^+$). d, Schematic representation of a localized domain arising from the locking between two DWs through their oscillatory tails. The interaction function governs the locking distances (see SI, section IV). e, Field envelope and intensity profile (f) of a TS pair in the supercritical regime [see (b)] for $S=2$.
• Figure 3: Temporal and spectral characteristics of topological solitons. a, Pulsed pumping allows the spontaneous formation of an isolated stable topological soliton (TS) from quantum noise ($S=1.6$, $\Delta = 0$, $\rho \approx 0$, $\Delta t = 95\,$fs/roundtrip). b, Theoretical temporal profile of the signal (top) and spectrum (bottom) after 100,000 roundtrips. c, Temporal profile of the pump (light blue) at the same condition as (b). Dark blue: undepleted pump profile. d, Schematic of the experimental setup (see Methods). M: mirror; MM: magnetic mirror; BS: beamsplitter; DM; dichroic mirror. DOPA: degenerate optical parametric amplifier. e, Photograph of the DOPA chip. The green emission corresponds to the second harmonic generation of the gate pulses on the chip. f, Experimental cross-correlation (top) and spectrum (bottom) when the DOPO is synchronously pumped ($\Delta t = 0$) near resonance and perfect phase-matching. g, By detuning the pump from the synchronous condition ($\Delta t \approx 95\,$fs/roundtrip), a 70-fs-long dark pulse is formed in the output signal. Dashed: theoretical spectrum [see (b)]. The dark pulse in the signal coincides with the formation of a bright pulse at the pump (h), resulting from a depletion above 50% (i).
• Figure 4: Integrated topological soliton frequency comb source. a, Experimental setup for the formation and characterization of the topological soliton frequency comb. b, An electrically-driven DBR singly-frequency laser is edge-coupled to a DOPO nanophotonic chip. c, Under cw-pumping, the numerical integration of Eq. \ref{['eq:GLE']} reveals the spontaneous formation of 95-fs-long topological soliton using the experimental parameters ($S=1.1$, $\Delta \approx 0$, $\rho\approx0$). d, Experimental topological soliton frequency comb (red) and theory [light red, see (c)]. Dashed: theoretical spectrum resulting from a pair of 95-fs-long hyperbolic tangents. e, Experimental multi-TS state (orange). Light orange: simulation of a perfect TS crystal with a dark pulse spacing of $D\approx7.75\,$ps. Inset: DBR spectrum and its broadening in the topological soliton regime.