Microcomb-driven silicon photonic systems

Microcombs have sparked a surge of applications over the past decade, ranging from optical communications to metrology1–4. Despite their diverse deployment, most microcomb-based systems rely on a large amount of bulky elements and equipment to fulfil their desired functions, which is complicated, expensive and power consuming. By contrast, foundry-based silicon photonics (SiPh) has had remarkable success in providing versatile functionality in a scalable and low-cost manner5–7, but its available chip-based light sources lack the capacity for parallelization, which limits the scope of SiPh applications. Here we combine these two technologies by using a power-efficient and operationally simple aluminium-gallium-arsenide-on-insulator microcomb source to drive complementary metal–oxide–semiconductor SiPh engines. We present two important chip-scale photonic systems for optical data transmission and microwave photonics, respectively. A microcomb-based integrated photonic data link is demonstrated, based on a pulse-amplitude four-level modulation scheme with a two-terabit-per-second aggregate rate, and a highly reconfigurable microwave photonic filter with a high level of integration is constructed using a time-stretch approach. Such synergy of a microcomb and SiPh integrated components is an essential step towards the next generation of fully integrated photonic systems.

To model the self-stimulation of the dark pulse in an optical microcavity, two mode families have to be considered, where one mode family is the dark-pulse-supporting primary (P) mode family and the other is the auxiliary (A) mode family which exerts the avoided-modecrossing (AMX) effect on the primary mode family. Two sets of coupled-mode equations are employed here, where the Kerr effects and the linear coupling between two mode families are included [1].
E (P ) and E (A) respectively stand for the intracavity temporal fields in the primary and the auxiliary modes, α (P ) and α (A) are the roundtrip cavity loss factor, β represent the second-order dispersion coefficients, and δ = ω is the resonance frequency of the primary mode and ω p is the frequency of the pump field. t R is the roundtrip time of the primary mode and L is roundtrip length. The pump filed is coupled into the primary mode by √ θE in , where θ is the waveguide coupling coefficient and E in is the pump field. While the coupling between the pump field and the auxiliary mode is ignored, due to the relatively small coupling rate in the pulley couplers. γ (P ) and γ (A) are the nonlinear coefficients. The linear coupling between two mode families is induced by , where κ is linear coupling strength. ∆ indicates the resonant frequency difference between the two modes, which is equal to t R ω is the resonance frequency, β A 1 and β (P ) 1 are the first-order dispersion coefficients. The spectra of the four points marked in a, in experiment (blue) and in simulation (red).
c, The pulse shapes in simulation of the four points marked in a.
Supplementary Fig. 1 shows the two resonances caused by the AMX around 1551 nm.
According to the coupling mode theory, the resonance frequencies shifted by the avoided mode crossing can be determined by Where ω (P ) and ω (A) are the resonance frequencies without the AMX effect, and K = Lκ is the coupling rate between the two modes. The AMX strength can be effectively tuned by changing the resonance frequency difference ω (P ) − ω (A) between two modes. In experiment,

Supplementary note II: Accessibility analysis under the thermal effects
The thermal analysis in this paper is based on the model proposed in [2]. As the response time of thermal is several magnitudes slower than that of Kerr effects, the Kerr effects and thermal effects can be decoupled into two steps. In step one, the intracavity field evolution can be simulated by Eq. 1 and Eq. 2, as shown in Supplementary Fig. 3a. In step two, the thermal effects can be described by a linear model: Where K ef f = ngKc ωo dn dT , the ω l is the hot cavity resonance frequency, ω o is the cold cavity resonance frequency, ω p is the frequency of the pump laser and n g is the group index. The α thermal is the thermal absorption rate, defined to be equal to P thermal /P inc , where the P thermal is the thermal power and the P inc is the intracavity optical power. dn dT is the thermal-optical coefficient and K c is the thermal conductance of the microring. In the simulation in step one, the influence of thermal effects is ignored, and the x-axis is given by ω p − ω o . For a given α thermal , a line, passing through the highest point on the non-mode-locked region with the slope of k = K eff /α thermal , can be drawn to analyse the accessibility of the mode-locked states. If the line intersects with the mode-locked region, the intracavity state will drop to the intersection. In other words, the mode-locked region is thermal accessible.
For an evolution process of the intracavity field, the thermal tolerance can be analyzed using the line l, that passes through the highest point of non-mode-locked region and is tangent to the mode-locked region. For a larger α thermal , the whole mode-locked region will be under the line. For a smaller α thermal , part of the mode-locked region will be above the line. Thus, the line l represents the highest α thermal under which the mode-locked region is accessible. The highest α thermal , or α max thermal for ease of expression, is selected to assess the thermal tolerance of the dark pulse generation. In experiment, the α thermal can be extracted by fitting the resonance transmission under different pump power, and is estimated to be 0.2α i , where the α i is the intrinsic loss factor. The α max thermal for the dark pulse evolution processes under different pump power P in is shown in Fig. 3b. The region with the α max thermal > 0.2α i indicates the dark pulse state is accessible. As the α thermal is a part of α i , α thermal can be normalized by α i , which is employed in Supplementary Fig.   3b. As shown in Supplementary Fig. 3b, due to a large nonlinear coefficient, P in = 0.45 The theoretical transfer function for the multi-tap delay-line microwave photonic filter (MPF) was calculated by the equation below [3,4]: where ω is the angular velocity of the input microwave signal, p n is the optical power of the nth comb line which can be measured by the optical spectrum analyzer (OSA) during the experiment, N is the total number of the comb lines, T is the time delay unit between the adjacent comb lines.
For the MPF implemented based on non-dispersive (true-time) delay scheme, the theoretical transfer function of the MPF can be directly calculated, based on the measured p n using Eq. 5. The parameter T is equal to the delay value of on-chip spiral delay line which is approximately 59 µs, and the G(ω) here is equal to a unit constant of 1.
For the MPF implemented based on dispersive delay line scheme, the theoretical calculation is a bit more complex, taking the third-order dispersion of the single-mode fibre (SMF) into consideration. The G(ω) here is a frequency-dependent function, which is determined by the modulation type of the high-speed electro-optical modulator (EOM). For the double sideband modulation (DSB) adopted in this work, the approximate expression of the G(ω) is shown as below [4]: where θ 2 = −β 2 L is the second-order fiber dispersion, θ 3 = −β 3 L is the third-order fiber dispersion, ∆ω is the free spectral range (FSR) of the comb lines in the form of angular velocity (rad/s). T is generated by the chromatic dispersion of a spool of single-mode fibre (SMF), which is not a fixed value but as a function of the tap number n, due to the influence of the third-order dispersion. The transfer function H(ω) can be formulated as below: G(ω) · exp jnθ 2 ω∆ω + j 1 6 θ 3 ω 3 + j n 2 2 θ 3 ∆ω 2 ω where the second-order fiber dispersion β 2 and third-order fiber dispersion β 3 are given by: The second-order dispersion parameter D and third-order dispersion parameter S of a standard SMF are ∼17.4 ps/(nm·km) and ∼0.083 ps/nm 2 /km, respectively. Based on the Eqs. 7-9, the theoretical transfer function for arbitrary filter response can be obtained. The calculation was carried out by the numerical calculation software MATLAB.