Synthesized soliton crystals

Abstract

Dissipative Kerr soliton (DKS) featuring broadband coherent frequency comb with compact size and low power consumption, provides an unparalleled tool for nonlinear physics investigation and precise measurement applications. However, the complex nonlinear dynamics generally leads to stochastic soliton formation process and makes it highly challenging to manipulate soliton number and temporal distribution in the microcavity. Here, synthesized and reconfigurable soliton crystals (SCs) are demonstrated by constructing a periodic intra-cavity potential field, which allows deterministic SCs synthesis with soliton numbers from 1 to 32 in a monolithic integrated microcavity. The ordered temporal distribution coherently enhanced the soliton crystal comb lines power up to 3 orders of magnitude in comparison to the single-soliton state. The interaction between the traveling potential field and the soliton crystals creates periodic forces on soliton and results in forced soliton oscillation. Our work paves the way to effectively manipulate cavity solitons. The demonstrated synthesized SCs offer reconfigurable temporal and spectral profiles, which provide compelling advantages for practical applications such as photonic radar, satellite communication and radio-frequency filter.

Fig. 1. Conceptual schematic for deterministic SC synthesis and switching in the microcavity.

a Conventional monochromatic pump scheme where solitons are initialized from a flat CW background, which generally results in a multiple-soliton state with a stochastic angular distribution of the solitons and accompanying irregular spectral envelope, such as an 8-soliton state shown in (b). Inset: single comb line exists in each resonance. c Proposed deterministic SC synthesis scheme by introducing an additional control light. The beating of the pump light (blue line) and the control light (green line) constructs a traveling periodic modulated background and draws the soliton into the equally spaced potential wells. To create N soliton crystal, the frequency of the control light shall be N free spectral range (FSR) away from the pump light. d Synthesized SC in the dichromatic pumped system with equal temporal spacing, which corresponds to a smooth sech² envelope in the spectrum. The vibration of soliton will induce modulated sidebands around the main comb lines (inset). e By switching the control light at different mode number μ (μ = 0 for pump mode), the styles of the SC could be reconfigured on demand.

Fig. 2. A library of 1–32 soliton crystals.

a Illustration of the experimental set-up, the wavelength of the pump light is fixed, while the wavelength of the control light is tunable for both SC switching and intracavity thermal balancing. EDFA erbium-doped fiber amplifier, FPC fiber polarization controller, Cir. circulator, PD photodiode, TEC thermoelectric cooler, OSC oscilloscope, ESA electric spectrum analyzer, OSA optical spectrum analyzer, Auto. autocorrelator. b Butterfly-packaged device with a 20.5-mm-diameter Chinese coin for comparison (upper panel). Microscope image of the high-index doped silica glass microring resonators with a diameter of ~1.2 mm (lower panel). c Complete optical spectra for 1–32 synthesized SC with smooth sech² envelope (red dashed line).

Fig. 3. Enhancement of soliton comb line power.

The soliton center line power extracted from experimental spetral envolopes versus square of soliton number N², which shows N² enhancement in comparison to the single-soliton state excited under similar pump conditions.

Fig. 4. Formation dynamics of soliton crystal.

a Measured intracavity power evolution trace. With cavity resonance scanning from longer wavelength to shorter wavelength gradually, the laser-cavity detuning varies from blue detuned to red-detuned regime. Three states are respectively marked as: state i, CW background; state ii, modulated Turing pattern (TP); state iii, soliton crystal (SC). The deterministic "step” in the trace is a characteristic feature of SC formation. b Simulations of the intracavity temporal waveform evolution. Turing combs directly turns to SC state as the pump enters red-detuned regime. c, d Measured temporal (c) and spectral (d) profile in different states: modulated CW background (i), modulated TP (ii), SC (iii). e, f Simulated angular (e) and spectral (f) profile in different states, showing good agreement with the experiment.

Fig. 5. Forced oscillation of SC.

a Illustration showing force applied on SC. The moving potential field imposes a periodic force on soliton pulses, resulting in the forced oscillatory motion of SC. b Simulated intracavity angular position oscillation of 3 lattice sites from a 10-SC state. Simulated intracavity field envelope is shown in (c). The modulated background has a relative moving speed to SC, and SC vibrates around its equilibrium position with oscillating power. d, e Experimental (d) and simulated (e) optical spectrum (left panel), normalized soliton power trace (middle panel, inset: zoom-in of 1–1.1 μs range) and electrical spectrum (right panel) for 10-SC state. Electrical spectra show that the fundamental oscillation frequency is 69 MHz.

Fig. 6. Soliton repetition rate tuning.

a, b The measured beat frequency Δf (i.e., soliton oscillation frequency) and repetition rate of a single soliton as the frequency of the control laser is tuned. c The repetition rate of the single soliton is approximately linearly decreasing with the increasing beat frequency, providing a way for realizing oscillation frequency and repetition rate tuning.