Since the first demonstrations of frequency conversion through second-harmonic generation in the early 1960s [1], applications based on nonlinear optics have not stopped flourishing. In particular, the generation of new frequencies led to the development of novel technologies in a multitude of domains. Nonlinear interaction of light with matter is responsible for a myriad of effects resulting in frequency conversion. An important breakthrough was the conception of Kerr frequency comb sources. Such a system is based on the nonlinear interaction of light waves, resulting in the generation of spectral rays equally spaced in the frequency domain. In particular, frequency comb sources based on microresonators pumped by a continuous wave (CW) laser were rapidly developed and showed the possibility of generating broadband comb sources. More generally, nonlinear optical effects can be exploited in different ways, giving a number of possibilities to achieve frequency conversion and broadband spectrum generation. Among them lies supercontinuum generation (SCG), consisting in an important spectral broadening from a narrowband pulsed light source. This nonlinear phenomenon is strongly related to the dispersion of the medium in which light propagates. For that reason, it has gained a great deal of interest in photonic crystal fibers (PCFs). Indeed, the design of the microstructure of PCFs permits tailoring the confinement and the dispersion of the optical mode propagating inside the fiber, allowing one to study and exploit SCG. Researchers have then made strong efforts to unravel the complex physical mechanisms responsible for SCG, involving several nonlinear processes, soliton dynamics, and linear propagation properties [2–9]. The strong development of this technology led to the emergence of novel applications based on SCG [10], such as ultrashort pulse generation, broadband sources for optical coherence tomography (OCT), octave spanning frequency comb generation for precise frequency metrology or for optical communications, and spectroscopy. Nevertheless, it is of particular interest to integrate such technology in compact and cost-effective photonic circuits. By doing so, it is possible to include SCG with other components on a single chip and so to build complex integrated photonics systems with reduced footprint and cost. As a matter of fact, integrated waveguides are very well adapted for SCG, as they permit tight confinement of light, interesting for nonlinear efficiency, and they offer many degrees of freedom for dispersion engineering via the choice of materials, the geometry, and the dimensions of the waveguide. The choice of materials is critical, as it determines the working wavelength range, the efficiency of nonlinear effects, and the fabrication methods. In general, silicon (Si) technology is under the spotlight in the photonics industry, as it is based on the same fabrication process flows as that of complementary-metal-oxide-semiconductor (CMOS) electronics. Si photonics has seen a rapid evolution, now showing exceptional performance. Modulators [11], all types of passive optical components [12–14], as well as detectors [15], have already been demonstrated using Si and/or Si-compatible materials. Therefore, there is now a trend to develop efficient nonlinear devices using materials compatible with Si technology. This review article aims at giving an overview of SCG in Si photonics platforms. A high number of materials have been investigated, but for the sake of conciseness, this article is focused on three main Si compatible platforms, which are Si, silicon nitride (${\mathrm{SiN}}_x$), and silicon germanium (SiGe). This list is not exhaustive, but it gives a good and broad summary of the evolution of SCG in Si photonics. This review paper is organized in three main parts: first, a brief description of the main applications of SCG is given, followed by the theory behind this phenomenon, and finally, a state-of-the-art of SCG in Si photonics platforms is presented.

Many applications can benefit from the impressive features of SCG.

Spectroscopy:

First, in a quite simple way, SCG can be used as a broadband light source for absorption spectroscopy. In this case, the spectrum does not need to be coherent, as the method is only based on absorption phenomena in the tested samples, and the bandwidth of the supercontinuum determines the range of chemical species that can be identified: the broader the spectrum, the more species tested. By integrating an SCG source, it is possible to build a “lab-on-a-chip.” The SCG source generates a broadband spectrum, an analyte can be deposited on a dedicated part on the chip, and a spectrometer can be used to obtain the absorbance spectrum, all on the same chip, for example. Also, more advanced techniques can be employed, such as dual comb spectroscopy, which this time requires the SCG source to be coherent.

Imaging:

SCG is also found useful for imaging techniques that require broadband light sources, such as confocal microscopy [16] or OCT [5,17,18]. To give an example, in the case of time-domain OCT, the bandwidth of the pulsed light source determines the performance of the imaging techniques: a broader spectrum means a faster, more sensitive and higher resolution imaging technique. For better performance, it is also desirable to work with coherent spectra (so with low-intensity noise due to pulse-to-pulse fluctuations) for OCT to minimize the integration time needed to perform an acquisition [19,20].

Optical communications:

The rapid evolution of demand in communication leads to new technological requirements. The use of optical communication answers several bottlenecks thanks to wavelength division multiplexing schemes. Such a method requires many optical carriers. These carriers can be obtained by using several CW laser sources (one for each carrier), or in a more cost-effective and practical way, with a frequency comb source [7,21–24]. SCG is an efficient way to generate broadband frequency combs: a high repetition rate pulsed laser source (from a mode-locked laser for example) can be used to trigger SCG in a waveguide, creating a broad frequency comb with a free spectral range determined by the repetition rate of the source. SCG could be an interesting alternative for the use of dense wavelength division multiplexing in telecommunication systems.

Frequency metrology:

In the frame of the frequency comb, SCG covering more than one octave is of prime interest. Indeed, it permits one to stabilize the comb through the precise determination of the carrier envelope offset frequency by mean of $f$-to-$2f$ interferometry. Since this technique requires interfering between the supercontinuum spectra and its second harmonic, the spectrum must cover at least one octave and be coherent. A feedback loop can then be implemented to stabilize the frequency comb. This technique allows one to determine the position of the frequency comb teeth, achieving excellent precision for frequency metrology [25,26]. In particular, it is especially used in the field of optical clocks, as it gives extremely high resolution in frequency measurement [27].

This section aims at giving the essential elements of the theory behind SCG. For deeper details, several articles and books give a complete theory of SCG and pulse propagation in nonlinear media [4,28,29]. Nevertheless, this part should give the reader enough information to understand the origin and conditions of SCG.

We consider an electric field $\mathbf{E}$ in the form of a short optical pulse, $$\mathbf{E}(x,y,z,t)=\frac{1}{2}[A(z,t)\mathbf{F}(x,y)\exp (i{\beta }_{0}z-i{\omega }_{0}t)+\text{c.c.}]\mathrm{.}$$(1)

Here, $x$, $y$ are the transverse coordinates, respectively, to the propagation axis $z$, $A(z,t)$ is the temporal envelope of the pulse, $\mathbf{F}(x,y)$ is the transverse modal distribution, and ${\beta }_0$ and ${\omega }_0$ are the propagation constant and the angular frequency of the carrier wave, respectively. The abbreviation “c.c.” stands for “complex conjugate.”

Such a short pulse can reach very high peak intensity, which enables one to trigger strong nonlinear effects. Nonlinear optical phenomena then arise from the creation of a nonlinear dielectric polarization, which then modifies the way in which the optical pulse propagates.

Under the hypothesis of a slowly varying envelope, the propagation of an optical pulse in a material exhibiting third-order nonlinearity only (modeled by the third-order susceptibility tensor ${\chi }^{(3)}$) is ruled by the generalized nonlinear Schrödinger equation (GNLSE), describing the evolution of the pulse envelope during propagation [29], $$\begin{gathered} \frac{\partial A}{\partial z}+\frac{\alpha }{2}A-i\sum _{k\ge 2}{\beta }_k\frac{i^k}{k!}\frac{{\partial }^{k}A}{\partial T^k}=i\gamma (1+i{\tau }_s\frac{\partial }{\partial T})[(1-f_r){|A|}^{2}A \\ +f_{r}A{\int }_0^{\infty }{h}_r(T^{\prime })|A(z,T-T^{\prime }{)|}^2\mathrm{d}{T}^{\prime }]. \end{gathered}$$(2)

Here, $\alpha$ is the linear propagation loss coefficient, $T$ represents a time frame moving alongside the pulse at the group velocity ($T=t-z/v_g$), and ${\beta }_k$ are the dispersion coefficients defined by the Taylor series of the propagation constant around the center frequency $\beta (\omega )$. It is of great importance to consider this frequency dependence of $\beta$, since we consider optical fields with broad spectra. The coefficient ${\beta }_2$ is called group velocity dispersion (GVD), a key parameter in pulse propagation, and ${\beta }_{k>2}$ are referred to as higher-order dispersion (HOD). On the right-hand side of Eq. (2), $\gamma$ is the nonlinear coefficient defined as $\gamma ={\omega }_0{n}_2/(c{A}_{\mathrm{eff}})$, with $n_2$ being the nonlinear refractive index (proportional to ${\chi }^{(3)}$) and $A_{\mathrm{eff}}$ being the nonlinear effective mode area. The time constant ${\tau }_s$ models the frequency dependence of $\gamma$ to the first order, and the integral term is related to the delayed nonlinear response due to the Raman effect, modeled by its temporal response $h_r(t)$ and its fractional contribution $f_r$. Here, the terms corresponding to multiphoton absorption are omitted for clarity, but they can be added depending on the type of nonlinear absorption. In the case of multiphoton absorption, an additional term of linear loss can also be added to model the associated free-carrier absorption.

To better understand the different regimes of pulse propagation, it is interesting to first focus on the contributions of self-phase modulation (SPM) (related to $\gamma$) and GVD (related to ${\beta }_2$).

The main nonlinear effect contributing to SCG is SPM. It is based on the intensity-dependent refractive index of the nonlinear material $n$ [29], $$n=n_0+n_{2}I,$$(3)where $n_0$ is the linear refractive index, $I$ is the optical intensity, and $n_2$ is the nonlinear index ($n_2>0$ in most of the cases), related to ${\chi }^{(3)}$. This causes the optical wave to acquire an intensity-dependent phase: at higher intensity, the refractive index is higher, meaning that the carrier wave travels more slowly, while it travels faster in the tails of the envelope, as depicted in Fig. 1. In the frequency domain, sidelobes appear within the spectrum around the center frequency, while accumulating a frequency-dependent phase during propagation. Qualitatively, it can be interpreted as the appearance of fast lower-frequency components and slow higher-frequency components. The importance of SPM during propagation is commonly characterized by the so-called nonlinear length $L_{\mathrm{nl}}=1/(\gamma P_0)$ [29], with $P_0$ being the peak power of the optical pulse. $L_{\mathrm{nl}}$ corresponds to the length at which the center of the pulse accumulates a phase shift of 1 rad.

By definition, GVD is responsible for a frequency-dependent group velocity. More practically, it means that at a given distance, each frequency component of the initial pulse has a different delay, or phase, with respect to the center frequency. In the temporal domain, the pulse duration increases, while the peak intensity decreases during propagation. Note that in the literature, GVD is also often described by the dispersion parameter defined by $D=-{\omega }_0^2{\beta }_2/(2\pi c)$. Based on the sign of the GVD, two different regimes are possible, as shown in Fig. 1(b): •a normal dispersion regime when ${\beta }_2>0$ ($D<0$), meaning that higher-frequency components travel more slowly than lower-frequency ones;•an anomalous dispersion regime when ${\beta }_2<0$ ($D>0$), meaning that higher-frequency components travel faster than lower-frequency ones.

Similarly, as for SPM, a characteristic length is defined for the GVD, $L_d=T_0^2/|{\beta }_2|$, with $T_0$ being the pulse duration [29]. It corresponds to the distance at which a Gaussian optical pulse undergoes a temporal broadening of a factor $\sqrt{2}$.

It can be seen that in the normal dispersion regime, the evolution of the phase is of the same type as the one due to SPM, while in the anomalous dispersion regime, GVD and SPM have opposite consequences. These two cases naturally lead to different behaviors in the process of SCG. Furthermore, a singular feature of anomalous dispersion regime is the unstable nature of solutions of Eq. (2). Indeed, with ${\beta }_2<0$, a small perturbation of the initial conditions, typically due to noise, can be amplified through phase-matched four-wave mixing processes, leading to amplification of the perturbation during propagation. This phenomenon, known as modulation instability (MI), causes phase and intensity fluctuations, which in turn greatly affect the coherence of the supercontinuum spectrum.

Even if in many cases materials exhibit normal dispersion, GVD can be tailored by playing on the waveguide’s geometry and compensate the normal material dispersion with the waveguide dispersion.

In this article, the term coherence refers to the phase stability across the spectrum from one pulse to another. It is commonly described by the modulus of the first order of mutual coherence $g_{12}$, defined as follows [4,29]: $$|g_{12}(\omega )|=\left|\frac{⟨{\tilde{A}}_1^{*}(\omega ){\tilde{A}}_2(\omega )⟩}{\sqrt{⟨|{\tilde{A}}_1(\omega {)|}^2⟩⟨|{\tilde{A}}_2(\omega {)|}^2⟩}}\right|.$$(4)

Here, ${\tilde{A}}_1(\omega )$ and ${\tilde{A}}_2(\omega )$ are the Fourier transform of the temporal envelopes $A_1(t)$ and $A_2(t)$ of two independent pulses. The angle brackets $⟨·⟩$ denote an ensemble average over a high number of pairs of independent spectra. $|g_{12}|$ close to 1 means a high coherence (high phase stability), while $|g_{12}|$ close to 0 means a poor coherence (unstable phase).

Using this definition, the coherence can be theoretically determined through a high number of simulations, and it can be measured using interferometric techniques [30].

By pumping a waveguide in the normal dispersion regime, spectral broadening is obtained through basic SPM. In this case, the bandwidth is generally quite small, since uncompensated GVD gradually reduces the intensity and increases the duration of the optical pulse. Since SPM is proportional to the intensity, spectral broadening is limited by the effect of GVD. Nevertheless, this scenario has the great advantage of imparting a highly coherent spectrum, since it is not sensitive to noise because MI is absent. Propagation of a pulse in the normal dispersion regime is also known to create a linear frequency chirp, which is especially adequate for pulse compression [31,32]. Moreover, the combination of positive GVD and SPM gives rise to an intriguing behavior responsible for the generation of flat supercontinuum spectra [33]: in this situation, the highly frequency-shifted components from the center of the pulse due to SPM can overtake the nonshifted components located at the tails of the temporal pulse in the temporal domain. This phenomenon, called optical wave breaking (OWB), causes oscillations at the pulse edges due to the temporal overlap of two different frequency components interfering. The pulse acquires a flattop shape in the temporal domain. Additionally, it has been shown that when a pulse traveling on a distance long enough for OWB to occur, the spectrum becomes significantly flatter than in the case without OWB. The specific dynamics of pulse propagation in the normal dispersion regime is detailed in Fig. 2(a). In order to enhance OWB, waveguides can be designed in a way that the dispersion length $L_d$ is reduced: the higher $|{\beta }_2|$, the lower $L_d$.

For these reasons, according to the conditions and the application, it can be of great interest to work in the normal dispersion regime, as it can offer flat and coherent broad spectra.

On the other hand, when pumped in the anomalous dispersion regime, GVD and SPM play opposite roles, meaning they can compensate for each other. This particular interplay between both effects is responsible for a particular type of optical pulses: solitons. Indeed, if GVD and SPM perfectly compensate for each other (when $L_d=L_{\mathrm{nl}}$), the initial optical pulse does not see any deformation during propagation. This distortionless wave is called a fundamental soliton. Also, GVD can periodically catch up SPM, resulting in a periodic behavior of the pulse with the propagation distance, corresponding to a higher-order soliton. Such a light pulse is characterized by the so-called soliton order ($N$), which depends on the GVD, the nonlinear parameter of the waveguide, the initial pulse duration $T_0$, and peak power $P_0$ [29], $$N=\sqrt{\frac{L_d}{L_{\mathrm{nl}}}}=\sqrt{\frac{\gamma P_0{T}_0^2}{|{\beta }_2|}}.$$(5)

Without any HOD or other nonlinear effect than SPM, no SCG is obtained, since the pulse constantly alternates between low and high bandwidth, periodically recovering its original shape. However, such solutions are known to be sensitive to perturbations: a change in an $n$th order soliton condition breaks it into $N$ fundamental solitons, covering a much higher bandwidth than the initial pulse. The peak powers $P_j$ and the temporal widths $T_j$ of these solitons can be predicted by the following formulas [34]: $$\begin{gathered} P_j=P_0\frac{{(2N-2j+1)}^2}{N^2}, \\ {T}_j=\frac{T_0}{2N-2j+1}, \end{gathered}$$(6)where $j=1,\dots ,N$. The distance at which soliton fission occurs is difficult to theoretically evaluate, and several definitions can be found in the literature. For instance, Dudley et al. used $L_{\text{fission}}\sim L_d/N$ to approximate the fission length [4]. Perturbations responsible for such soliton fission can be of multiple origins: HOD, self-steepening effect, or stimulated Raman scattering (SRS) are the most common causes of this pulse breakup. Perturbation due to HOD presents an interesting feature: the optical pulse initially evolving in anomalous dispersion regime sees its spectrum overlapping with normal dispersion regions during its broadening. This configuration allows the existence of dispersive waves (DWs) in the normal dispersion regime that are phase-matched with the soliton in the anomalous dispersion regime. Figure 2(b) shows a simulation of the fission of a fifth-order soliton leading to SCG with the generation of two DWs due to third- and fourth-order HOD. The first soliton that is ejected during the fission has the highest peak power and the smallest duration (and so the highest bandwidth). For that reason, in general, DWs are mainly due to this soliton. Note that the frequency of DWs can be predicted by solving a nonlinear phase-matching equation [4], $$\beta ({\omega }_{\mathrm{DW}})-\beta ({\omega }_s)-\frac{{\omega }_{\mathrm{DW}}-{\omega }_s}{v_{g,s}}-\frac{\gamma P_s}{2}=0,$$(7)where ${\omega }_{\mathrm{DW}}$ and ${\omega }_s$ are the angular frequencies of the DWs and the first ejected soliton, respectively, and $v_{g,s}$ and $P_s$ are the group velocity and the peak power of the latter. The center angular frequency ${\omega }_s$ of the soliton is not easy to know, but approximating it with ${\omega }_0$ is generally sufficient. The peak power of the first ejected soliton can be deduced from the order of the initial soliton before fission using Eq. (6) with $j=1$. In some cases, additional perturbation comes from SRS. This interaction of photons with vibrational modes of the nonlinear material continuously redshifts the soliton frequency and reduces the amount of power transferred to DWs. This phenomenon is predominant in optical fibers, but it is usually negligible in integrated waveguides.

Usually, SCG in anomalous dispersion is broader than in the normal dispersion case because of the particular soliton dynamics. However, MI can have a significant impact on the SCG process and spectra often feature important fluctuations. MI can even break the coherence of the spectrum, which can be troublesome, depending on the application. MI can be induced by SPM if the spectral width of the pulse reaches the maximum MI gain zones. For a Gaussian pulse, this happens at a distance $L_{\mathrm{mi},\mathrm{spm}}=\sqrt{2L_d{L}_{\mathrm{nl}}}$ [29]. Important perturbations can also come from noise (quantum shot noise or relative intensity noise of the source, for example), triggering spontaneous MI. Dudley et al. stated that noise amplified by MI significantly perturbs the pulse propagation after a distance $L_{\mathrm{mi},\text{noise}}\sim 16L_{\mathrm{nl}}$ [4]. From this, it can be considered that the condition $N\ll 16$ is adequate for coherent SCG, ensuring $L_{\text{fission}}\ll L_{\mathrm{mi},\text{noise}}$.

It is noteworthy to highlight that SCG in the anomalous dispersion regime can also be obtained with a CW input by taking advantage of MI. MI can transform a CW pump into a train of short pulses, which can then trigger the SCG process [29]: a small perturbation of the CW pump (which can be induced by another CW source) with frequencies within the MI gain sidebands will get amplified during propagation and modulate the carrier CW wave into optical pulses.

To summarize, SCG results from a complex interplay between many physical effects, mainly based on third-order nonlinear effects and dispersion. Several ways exist to achieve SCG, either in the normal or in the anomalous dispersion regimes, with pulsed sources or CW sources. Each method presents different assets and drawbacks in terms of bandwidth, coherence, and integration. Therefore, the type of supercontinuum must be chosen according to the targeted application.

Si is naturally the first choice one can think about for CMOS fabrication techniques compatibility. Moreover, Si possesses a very high nonlinear index ($n_{2,\mathrm{Si}}\approx 6.3\times {10}^{-18}{\mathrm{m}}^2/\mathrm{W}$), 2 orders of magnitude higher than that of ${\mathrm{SiO}}_2$ (commonly used in nonlinear fiber optics) [35], as shown in Fig. 3, and a high refractive index ($n_{\mathrm{Si}}\approx 3.48$ at a wavelength of 1.5 μm), which results in a high index contrast with the surrounding insulator ($n_{{\mathrm{SiO}}_2}\approx 1.45$ at a wavelength of 1.5 μm). This important index contrast leads to a very tight confinement of light in the Si core, interesting to enhance nonlinear effects as the power density in the Si core can then be extremely high. In general, the nonlinear parameter $\gamma$ in Si waveguides is within the order of $100{\mathrm{W}}^{-1}{\mathrm{m}}^{-1}$. The transparency window of Si extends from 1.1 to 8.5 μm, and thanks to the maturity of fabrication processes, linear propagation losses can be reduced to subdecibel per centimeter levels. However, taking into account two photon absorption (TPA), the lower bound of the transparency range is shifted to 2.2 μm [35], which strongly limits the use of Si for SCG when pumping in the classic optical communication bands. This limitation can be seen in the work of Hsieh et al., who experimentally demonstrated for the first time continuum generation in the anomalous dispersion regime in 4.7 mm long Si waveguides in 2007 [36]. The tested waveguide has a cross section of $520\mathrm{nm}\times 220\mathrm{nm}$ and was pumped by a pulsed source with a repetition rate of 250 kHz, a duration of 100 fs, and an average power of 1 W. Although the confinement and dispersion properties of the waveguide resulted in a highly effective nonlinear effect at $\lambda =1.3\mathrm{\mu m}$, TPA limited the bandwidth of the spectrum to a 3/10 octave span. The important influence of TPA on the SCG bandwidth is also confirmed by the numerical work of Yin et al. [37]. For that reason, Si is generally used for SCG in the mid-infrared (mid-IR) region, interesting for spectroscopy applications, as a tremendous number of chemical compounds have absorption signatures in this domain. Mid-IR SCG is also interesting for imaging techniques like OCT, as the penetration depth in a 3D sample increases with the wavelength [17]. Still, some efforts have been made to achieve SCG in the near-IR range despite the effect of TPA.

The silicon on insulator (SOI) platform, composed of a patterned Si core on a buried oxide (BOX) layer made of ${\mathrm{SiO}}_2$, is the most commonly used structure in Si photonics due to its high maturity and low cost. There is a high index contrast between both materials, and low linear loss can be achieved. However, the transparency window of ${\mathrm{SiO}}_2$ stops at about 3.6 μm, hence limiting the range of wavelengths that can be used to pump the waveguide and to achieve spectral broadening. Still, great efforts were made to exploit the SOI platform for SCG due to its high potential of integration. In the early stages of SCG development on the SOI platform, the SCG bandwidth was limited to less than an octave. In 2012, numerical studies showed the possibility to generate an octave-spanning supercontinuum using a dispersion-engineered SOI slot waveguide [38]. In this numerical work, the input optical pulse is arbitrary, taken to have a duration of 120 fs and a peak power of 62 W at a center wavelength of 1810 nm in the anomalous dispersion regime. The authors proposed a way to tailor the dispersion profile in order to create a flat, wide anomalous dispersion window (from 1418 to 2108 nm in their case). This way, it is possible to optimize the waveguide design for octave-spanning supercontinuum. Interestingly, they also showed a drastic pulse compression, resulting in a short pulse with a duration of approximately 10 fs. Such a supercontinuum source on the SOI platform is of prime interest for optical communication applications, offering the possibility to generate a stable frequency comb suitable for wavelength division multiplexing, and also for frequency metrology or pulse compression. In 2018, the first experimental demonstration of a coherent octave-spanning supercontinuum on the SOI platform in the near-IR range was reported by pumping a rib waveguide at a wavelength of 1.9 μm [39]. At this wavelength, TPA is still present, but its effect is reduced compared to shorter wavelengths while the nonlinear index is higher, and the waveguide profile is tailored to exhibit anomalous dispersion. This optimization improves the overall nonlinear behavior of the waveguide, enabling the generation of a broadband coherent supercontinuum extending from 1 to 2.4 μm when pumped by a pulsed laser with a duration between 50 and 100 fs, a coupled average power of 3.6 mW, and a repetition rate of 200 MHz. Moreover, they experimentally measured the coherence of the spectrum, showing a degree of mutual coherence higher than 95% over the whole bandwidth, allowing $f$-to-$2f$ interference for self-referencing of the frequency comb. Figures 4(a) and 4(d) show the geometry of the waveguide and the associated supercontinuum spectrum with its degree of coherence. Recently, the same group showed the possibility of improving the generated spectrum shape by use of Bragg gratings [42]. This method permits one to greatly enhance the generation in low-power spectral regions, which can be a way to generate flatter spectra. These studies show that despite the presence of TPA in Si in the near-IR range and the low upper bound of transparency of ${\mathrm{SiO}}_2$, it is still possible to perform coherent octave-spanning SCG on the SOI platform in the near-IR range.

In order to avoid TPA, it is interesting to work further in the mid-IR domain. Results on SOI were obtained by designing the waveguide cross section so that it operates in the anomalous dispersion regime at wavelengths higher than 2.2 μm, where TPA vanishes. However, the upper limit of the spectrum bandwidth stays limited due to absorption in the BOX layer. To overcome this limitation, researchers investigated other solutions by replacing the ${\mathrm{SiO}}_2$ layer with different materials exhibiting a wider transparency window. In 2015, Singh et al. proposed using sapphire as a substrate, which is transparent up to 6 μm [43]. Thanks to this approach, they achieved the widest SCG in Si waveguides at that time, extending from 1.9 to 6 μm. To obtain this result, they pumped a strip waveguide of a cross section $2400\mathrm{nm}\times 480\mathrm{nm}$ with a 320 fs pulsed source centered at 3.7 μm with a repetition rate of 20 MHz and a peak power up to 2.5 kW. More recently, in 2018, Nader et al. reported mid-IR dual-comb spectroscopy on a gas sample using Si-on-sapphire (SOS) waveguides based on SCG covering wavelengths from 2.5 to 6.2 μm through the use of notch waveguides, a design that provides more degrees of freedom for dispersion engineering than simple strip waveguides [40] [Figs. 4(b) and 4(e)]. The center wavelength was chosen to be 3.06 μm, using a source with a pulse duration of 100 fs, a coupled average power of 12 mW, and a repetition rate of 100 MHz. These demonstrations show promising possibilities of the Si-on-sapphire platform for SCG, but fabrication techniques still need to be improved to reduce propagation losses caused by lattice mismatch between Si and sapphire, which are still in the order of 5 dB/cm.

Another solution to remove the barrier caused by the absorption in the bottom cladding is to use suspended Si waveguides. In these structures, the BOX is removed around the waveguide’s core, which is then surrounded only by air, as shown in Fig. 4(c). This approach offers two main advantages: it totally removes the issue of material absorption in the BOX, and it increases the confinement of light in the Si core, enhancing the nonlinear effect. This platform is more challenging in terms of fabrication, as it requires precise selective etching of the BOX and specific design of the Si core to create the suspended structure, but it also shows great advantages for SCG. In 2018, Kou et al. realized Si suspended waveguides designed in order to exhibit anomalous dispersion around a wavelength of 4 μm [44]. They pumped 7 to 12 mm long waveguides with 300 fs short optical pulses and a few microwatts of average power coupled in the waveguides and a repetition rate of 150 kHz. They obtained a spectrum covering a wide range of wavelength from 2 to 5 μm, which can be used for absorption spectroscopy, for example. For instance, their experiment results clearly show the absorption of ${\mathrm{CO}}_2$ at $\sim 4.25\mathrm{\mu m}$. Later, in 2019, there was also a demonstration of coherent SCG in a suspended Si waveguide fabricated through wafer bonding to create the suspended structure [45]. They measured a wider spectrum (2 to 7.7 μm) by pumping the waveguide at a wavelength of 3.06 μm with 85 fs pulses and a coupled peak power of 1.1 kW. They used it to perform dual-comb spectroscopy of atmospheric water vapor, methanol, and isopropanol, giving results in excellent agreement with the predicted absorption spectra and performances at the level of current state-of-the-art devices. Very recently, similar results in terms of bandwidth were obtained with suspended Si waveguides fabricated with more standard wet-etching techniques instead of complex wafer bonding methods [Fig. 4(f)] [41].

In the results presented in the previous sections, the waveguides consist in fixed width Si channels. Recently, new routes have been explored to enhance SCG performance using more complex designs. Indeed, SCG is strongly dependent on the dispersion, which is very sensitive to the waveguide’s geometry. Therefore, by implementing a variation of the waveguide’s width, it is possible to generate different solitons and DWs along propagation. In 2017, Ciret and Gorza numerically investigated such varying width structures and showed that the SCG process leads to broader, flatter, and more coherent spectra [46]. In 2019, Singh et al. proposed three varying dispersion designs: two-section and three-section cascaded waveguides (discrete variation of width), and tapers (continuously varying width) [47]. In all the cases, they experimentally showed that the supercontinuum is broader and flatter than in single-width configurations, as predicted by the numerical work of Ciret and Gorza, and the coherence is greatly enhanced, in particular for the taper waveguides, since MI cannot build up efficiently in such a structure. Soon after these promising results, Wei et al. proposed a similar approach based on cascaded waveguides [48]. The design they propose contains seven sections. The determination of the widths, lengths, and positions of each section was optimized by the use of a genetic algorithm made to produce broad and flat spectra, as depicted in Fig. 5. They obtained quite flat supercontinuum spectra covering the whole transmission window of the waveguides with a high degree of coherence all over the bandwidth, with a low input pulse energy ($\sim 0.9\mathrm{pJ}$).

Also, it is well known that the effect of noise through the MI process is higher for longer pulses. The use of ultrashort femtosecond pulses is advantageous for SCG but represents a greater challenge for integration using mode-locked lasers. Cheng et al. proposed a design composed of a tapered waveguide optimized for pulse compression, followed by a fixed width section designed for efficient SCG [49]. This technique permits one to use picosecond pulses at the input of the waveguide, which are then compressed into femtosecond pulses by the tapered region, which gives a more appropriate condition for SCG in the following section of the waveguide.

Of course, the methods proposed in these studies are not restricted to Si waveguides, and they can be transposed to any platform. These novel results show very promising perspectives for SCG optimization in integrated waveguides.

The use of Si waveguides for mid-IR applications restricts the upper bound of the spectrum to 8.5 μm. To obtain SCG at higher wavelengths, solutions are investigated through the use of Ge and SiGe alloys, as Ge is transparent from 1.5 up to 14.5 μm [35]. Moreover, Ge is compatible with Si technology, and it has a nonlinear index 1 order of magnitude higher than that of Si (see Fig. 3), making it an excellent candidate for broadband integrated mid-IR supercontinuum sources.

Very recently, SCG was obtained in pure Ge waveguides grown on Si [50]. The use of pure Ge permits one to benefit from the high nonlinear index of the material and its full transparency range, but the lattice mismatch between Si and Ge results in dislocations responsible for propagation loss. In this study, an optimized fabrication process based on epitaxial growth enabled the researchers to strongly reduce the threading dislocation density and to reach linear propagation losses of 1.2 dB/cm. They were able to generate a supercontinuum from 3.4 to 6 μm with a pump wavelength of 4.6 μm, 200 fs duration, up to 22 mW of average coupled power, and a repetition rate of 63 MHz. The limitation in the long wavelength side is attributed to high free-carrier loss, and the authors anticipate that this issue can be overcome by pumping the waveguide at a higher wavelength. Nevertheless, the broadest SCG results were found using SiGe alloys. ${\mathrm{Si}}_{1-x}{\mathrm{Ge}}_x$ combinations have the advantage of reducing dislocations, and so to decrease linear losses. The same group presented results in a SiGe on Si waveguide with 40% of Ge, exhibiting lower propagation losses of 0.23 dB/cm [51]. With the same platform, they also achieved broad all-normal dispersion SCG (from 2.8 to 5.7 μm) [52]. While the spectral broadening is lower than in the anomalous dispersion case, the output spectrum presents a flat, smooth shape and high coherence, as expected when pumping in the normal dispersion regime, and allows one to compress the 200 fs pulse down to 22 fs. However, this platform encounters some inconvenience: the Si substrate imposes the upper limit of the spectrum to approximately 8.5 μm, and the increase of Ge concentration for better confinement and nonlinearity would be at the cost of threading dislocation density responsible for higher losses. Another approach is based on a graded index SiGe alloy. This platform consists in a waveguide presenting a linearly increasing Ge concentration in the SiGe core along the vertical axis, reaching a value of 80% [53]. This way, a high concentration of Ge can be achieved with few dislocations. Moreover, with such a technique, the optical mode is confined in the upper part of the waveguide, where the refractive index is higher due to the high Ge concentration, far away from the Si substrate. The geometry of the waveguide is described in Fig. 6(a). Consequently, this platform avoids absorption losses in the substrate at wavelengths higher than 8.5 μm. Propagation losses were measured to be at decibel per centimeter levels at long wavelengths (up to 9.5 μm), and the nonlinear parameter $\gamma$ is estimated to be around $1{\mathrm{W}}^{-1}{\mathrm{m}}^{-1}$ at a wavelength of 5 μm and $0.5{\mathrm{W}}^{-1}{\mathrm{m}}^{-1}$ at 8 μm. The quite low nonlinear parameter compared to what is usually observed in Si waveguides despite a higher nonlinear index of Ge is due to a high effective modal area and the high wavelength in mid-IR operation. By dispersion engineering, anomalous dispersion is obtained at long wavelengths, and extremely broad supercontinua were measured, covering more than two octaves from 3 to 13 μm. The waveguide was pumped with 200 fs pulses and the wide anomalous dipsersion region permitted one to vary the pump wavelength and study its effect, showing that broad SCG can be obtained on a wide range of pump wavelengths [Figs. 6(b) and 6(d)]. As far as we know, this result evidences the longest wavelengths obtained with SCG in a Si-compatible integrated photonic platform. Furthermore, numerical simulations show a high degree of coherence over the entire bandwidth of the spectrum, as shown in Figs. 6(c) and 6(e). This progress in the mid-IR range points toward a promising future for Ge-based waveguides for nonlinear applications in imaging, spectroscopy, or free-space communications.

As seen in the previous sections, the main obstacles of Si photonics for SCG in the near-IR range are TPA and linear absorption. The ${\mathrm{SiN}}_x$ platform has been intensively studied as a solution that overcomes both matters. Indeed, ${\mathrm{SiN}}_x$ has a high bandgap, corresponding to an absorption edge in the deep-UV region ($\sim 230\mathrm{nm}$). As a consequence, TPA only occurs in the UV and a part of visible ranges. In addition, the transparency window of this material extends up to 7 μm. Also, fabrication processes of ${\mathrm{SiN}}_x$ films via chemical vapor deposition techniques are very mature and are compatible with Si technology. This makes ${\mathrm{SiN}}_x$ a viable candidate for SCG in the visible, near-IR, and partially mid-IR ranges. As for the nonlinear index, it is difficult to give a precise value, as it strongly depends on the stoichiometry: a higher Si/N ratio results in a higher nonlinear index [54]. Nevertheless, a value of $n_{2,\mathrm{SiN}}\sim 2.4\times {10}^{-19}{\mathrm{m}}^2/\mathrm{W}$ is usually considered for stoichiometric ${\mathrm{Si}}_3{\mathrm{N}}_4$ in the near-IR region. This value is 1 order of magnitude lower than that of Si (see Fig. 3), but it is still high enough to achieve efficient nonlinear processes in integrated devices. Indeed, the extremely low propagation losses achieved in the ${\mathrm{SiN}}_x$ platform, even lower than 1 dB/cm, make it possible to work with long structures, increasing the nonlinear interactions in the waveguide, and hence compensating for its reduced nonlinear index. Moreover, the ease of tuning the Si/N ratio during deposition enables wide possibilities to tailor the properties of the material. Eventually, the large transparency window, low temperature sensitivity, ease of fabrication, and good nonlinear properties make ${\mathrm{SiN}}_x$ a particularly interesting choice for integrated nonlinear photonics compatible with Si technology.

A tremendous number of publications about SCG in ${\mathrm{SiN}}_x$ have been published in the last few years, showing important progress. In particular, fabrication techniques to obtain high-quality films were established with two main objectives: to reduce propagation losses as much as possible, and to improve the compatibility with Si fabrication process flows [55–59]. Methods to deposit crack-free ${\mathrm{SiN}}_x$ films have been reported, resulting in subdecibel per centimeter propagation loss in waveguides. While being extremely interesting for the exploitation of efficient nonlinear processes, these methods are only compatible with front-end-of-line (FEOL) CMOS process flows due to a high thermal budget that hinders the cointegration of photonic devices with electronic components. Therefore, efforts were also made to find ways to deposit ${\mathrm{SiN}}_x$ with low temperature so that the technique could be compatible with back-end-of-line (BEOL) CMOS process flows.

From the significant interest allocated to SCG in ${\mathrm{SiN}}_x$ waveguides, many demonstrations of impressive results and novel devices have been published in the last several years [25,60–66]. Ultrabroadband SCG has been measured covering more than two octaves, including the visible range and the near-IR range [67–69]. For example, we experimentally and numerically studied SCG in low-loss ($<1\mathrm{dB}/\mathrm{cm}$) nitrogen-rich ${\mathrm{SiN}}_x$ waveguides, extending from 400 up to 1600 nm (Fig. 7). The $600\mathrm{nm}\times 1200\mathrm{nm}$ waveguides were pumped at a center wavelength of 1.2 μm, with pulses with 130 fs duration, an average coupled power of a few microwatts, and a repetition rate of 1 MHz. The extensive amount of nitrogen in the film was made on purpose in order to reduce the refractive index of the material for better compatibility with fiber-to-chip coupling schemes in the O-band optical communication window (around a wavelength 1330 nm). Dispersion engineering permitted researchers to obtain a wide anomalous dispersion region that led to the extremely broad supercontinuum spectrum. This result also shows the important part played by dispersion engineering. Indeed, while the nonlinear parameter of the waveguide is 2 orders of magnitude lower than what can be obtained in Si-rich ${\mathrm{SiN}}_x$ waveguides, the bandwidth is higher than results in these waveguides, only thanks to a different dispersion profile that covers a broad region and allows for the existence of two DWs that are far away from each other. Furthermore, it is clearly visible in Fig. 7 that the long spiral waveguide exhibits much lower power after 1400 nm than the short straight waveguide. This highlights the influence of losses in the SCG process. Indeed, this difference of power level comes from absorption losses in a region around a wavelength of 1500 nm due to N-H bonds in the ${\mathrm{SiN}}_x$ film. The extension of the spectrum in the visible region also makes it interesting for biosensing, for example. Numerical results also show the ability to generate such a spectrum with a high coherence, near unity over the whole bandwidth.

${\mathrm{SiN}}_x$ waveguides with ultralow loss, under 1 dB/cm, were used to generate light in the mid-IR region up to 4 μm through DW generation with a high conversion efficiency, giving microwatt levels of output power [70]. The efficient conversion of near-IR light into the mid-IR domain is a very appealing approach, and dispersion engineering of low-loss ${\mathrm{SiN}}_x$ waveguides appears to be a promising solution. The same waveguide was then used to demonstrate gas spectroscopy, showing excellent agreement with the theoretical absorption spectra of the tested chemical compounds. Moreover, it was reported that performances of mid-IR dual-comb spectroscopy based on SCG can be enhanced with supermode dispersion engineering in a coupled waveguide [71]. In this study, the use of coupled waveguides offers new advantages to tailor the dispersion and to enhance mid-IR light generation.

Recently, the same group also reported SCG in a ${\mathrm{SiN}}_x$ waveguide with a strong dependence on polarization [72]. The waveguide exhibits opposite GVD for each polarization (transverse electric, TE and transverse magnetic, TM) at a wavelength of 2.1 μm: the TE mode experiences anomalous dispersion leading to an octave-spanning SCG based on soliton fission, whereas the TM mode lies within the normal dispersion regime that results in flat and smooth SPM-driven SCG suitable for postcompression of the pulse for few-cycle pulse generation. This result unveils the versatility of such an approach, showing the possibility to choose between the types of SCG mechanisms only by switching the input polarization, depending on the desired application.

In 2018, a fully self-referenced frequency comb with low electrical power requirements based on SCG in a ${\mathrm{SiN}}_x$ waveguide was reported [73]. Such an achievement shows the high potential of the ${\mathrm{SiN}}_x$ platform for applications based on SCG using low-cost integrated photonic chips.

A high variety of waveguides have been studied for integrated SCG in different wavelength windows. These works show the high potential of Si-compatible platforms for nonlinear applications. As seen in the literature, the most developed applications of integrated SCG at the moment are related to sensing, with impressive results in dual-comb spectroscopy, for example. This application is the most straightforward for SCG, as it does not require unreasonable complexity of the devices and is well adapted for on-chip integration, since the whole system can be built at the same time on the same chip. However, integrated SCG devices currently suffer from an important weakness: the pump laser source. Indeed, most of the studies performed on integrated SCG are done using high volume, expensive pulsed lasers, and optical parametric amplifiers, which is contrary to the initial goal of building compact and cost-efficient nonlinear devices. For example, using an SCG chip for an imaging system would not be so beneficial if it still needed a dedicated fiber-pulsed laser and an optical parametric amplifier. Additionally, while many publications mention optical communications among the potential applications of SCG, it is currently not viable, especially due to the pump repetition rate requirements: all the work presented here is done with sources of quite low repetition rates (in the megahertz range), while even dense wavelength division multiplexing systems use at least 12.5 GHz channel spacing, several orders of magnitude higher than the frequency spacing of the SCG-based combs cited here. In the end, the production of high bandwidth and coherent spectra through SCG puts colossal constraints on the initial light source: high peak power (often in the order of several kilowatts), very short pulses (in the order of a few hundreds of femtoseconds), high repetition rate (more than 10 GHz), and ideally low relative intensity noise. While the final goal would be to achieve SCG with integrated mode-locked lasers, it appears incredibly challenging to achieve such performance at the moment. Nevertheless, in our opinion, the development of novel designs and the rapid evolution of laser technologies go toward the fulfillment of this challenge in the future. For instance, the implementation of a pulse compression stage before the waveguide designed for SCG is an interesting approach to lighten the requirements on the duration and the peak power of the initial pulse; the use of tapered waveguides allows one to reduce the sensitivity to MI triggered by noise, hence reducing the phase and intensity fluctuations of the generated spectrum, and advances in light-coupling schemes permit one to drastically reduce losses at the input and output of the waveguides. Moreover, mode-locked laser chips also have seen some progress, with demonstrations of integrated sources with subpicosecond short pulses and repetition rates between 10 and 100 GHz [74]. The peak power of such laser diodes remains rather low (in the order of a few milliwatts up to 1 W) compared to the needs for SCG, meaning that amplifiers may be necessary. Yet, the progress made in the design of waveguides for SCG and in the laser technologies leads us to believe that compact nonlinear devices still have a bright future.

Diverse photonics platforms compatible with Si technology have been studied during the past two decades to develop on-chip SCG. Performance has not stopped improving; ways to overcome obstacles such as substrate absorption, TPA, or fabrication complexity have been implemented. A summary of SCG performance in Si-compatible platforms is given in Table 1. Si waveguides proved to be suitable for near-IR and mid-IR SCG. To obtain supercontinuum spectra extending farther in the long wavelength side, germanium-based waveguides were envisaged, and outstanding results were observed, both with standard Ge and SiGe alloy waveguides. Also, ${\mathrm{SiN}}_x$ has been extensively studied, as it provides a high potential platform for nonlinear applications. Indeed, it does not suffer from TPA in the optical communication windows, it has a large transparency window, and it offers additional degrees of freedom to play on nonlinearity and dispersion. Many results were published, demonstrating state-of-the-art performance in spectroscopy or in self-referenced frequency combs for optical communications or frequency metrology, for example. Thanks to these studies, it was possible to precisely understand how SCG is formed in integrated waveguides and how to optimize it. Consequently, more complex novel designs are now being investigated to pursue the development of low-cost, highly efficient integrated platforms for SCG.Table 1.

Main Parameters of the Different Platforms for SCG Presented in the Review^a

Acknowledgment. Frédéric Boeuf, Stéphane Monfray, and Charles Baudot from STMicroelectronics and Sylvain Guerber, Quentin Wilmart, and Bertrand Szelag from CEA-Leti are acknowledged for fruitful discussions and fabrication contribution in SiNx. Jacopo Frigerio and Giovanni Isella from Politecnico di Milano are also acknowledged for the SiGe alloy epitaxial growth. All engineers in the C2N cleanroom (PIMENT platform) and especially Jean-René Coudevylle, Etienne Herth, David Bouville, Nathalie Isac, Samson Edmond, and Cédric Villebasse are acknowledged for their fabrication contribution. The fabrication of some reported devices was partially carried out at the Micro-NanoTechnologie platform/C2N, which was partially funded by the Conseil Général de l’Essonne. This work was also partly supported by the French RENATECH network.