Highly nonlinear integrated waveguides play a key role in ultra-fast all-optical signal processing. A large number of nonlinear optics phenomena and applications have been demonstrated, in a variety of complementary metal–oxide–semiconductor (CMOS) compatible nonlinear integrated waveguides^[1-11], as these integrated optical circuit platforms provide strong optical field confinement, thereby enhancing Kerr nonlinearity. To further enhance the nonlinearity of the integrated waveguides, a popular approach is to embed a highly nonlinear material, such as a silicon rich layer or a two-dimensional layer such as graphene^{[12, 13]} in the waveguide. Although these silicon rich waveguides have higher nonlinearity, they also suffer from higher linear losses, resulting in a medium nonlinear figure-of-merit (FOM)^[14]. Realizing both high nonlinearity and low propagation loss remain challenging. Low loss is essential in order to achieve compatibility with other linear elements in the circuit.

One platform that has drawn the attention of researchers in the field of nonlinear optics over the past decade involves the use of high-index doped silica glass^[14-18]. The platform is CMOS-compatible with a mature fabrication process that is also suitable for mass production^[14]. It features low linear and nonlinear losses, and is easily monolithically integrated with other linear components, so that both linear and nonlinear components can be fabricated on the same chip. However, due to the lower index of the doped silica, it has a lower nonlinearity than silicon-rich platforms such as silicon and silicon nitride. It is therefore desirable to increase the nonlinearity of the doped silica platform, while maintaining its low loss property. We have discovered that by applying a strip of silicon-rich film, such as SiN, or a low dimensional high index layer such as silicon or silicon nanocrystal (Si-nc), in the core of the high-index doped silica waveguide, the nonlinearity can be increased to a large extent, resulting in only a slight alteration to the mode field distribution^[19].

In this paper, a series of 49 GHz Si-nc embedded micro-ring resonators (MRRs) are fabricated and their nonlinear properties characterized. The waveguide structure of the MRR consists of a thin layer of Si-nc, embedded in a high-index doped silica glass core. The main advantages of using Si-nc are its CMOS-compatiblility, relatively high nonlinearity, and negligible two-photon absorption (TPA)^[20]. In the design of the waveguide structure, the dimension of the waveguide is optimized to achieve a stronger nonlinear interaction while keeping the propagation loss at a manageable level. In our experiment, we observe wavelength conversion from the four-wave mixing (FWM) process near 1550 nm under continuous-wave (CW) pump, at a power below 1 mW. The addition of a 20 nm thick Si-nc layer in the center of the core, results in a twofold increase in nonlinearity. CMOS-compatible integrated microchips with this modified structure have potential applications in high bandwidth optical communications.

Other than the deposition of a thin layer of Si-nc film in the middle of the core, the devices were fabricated using CMOS-compatible processes similar to those described in Refs. [14, 15, 21]. Plasma-enhanced chemical vapor deposition (PECVD) was employed in the deposition of the Si-nc embedded core waveguide films, beginning with a 1 μm n = 1.60 high-index doped silica layer on the SiO₂ lower cladding, followed by a ~ 50 nm thick amorphous silicon (a-Si) and finally another 1 μm n = 1.60 high-index doped silica layer to complete the deposition process. The deposited core film was then patterned, etched and clad with SiO₂ to form the waveguide. It is important to note that in addition to nonlinearity enhancement, the inclusion of an a-Si film will also increase the propagation and potentially TPA losses if its thickness is too great. On the basis of existing research into the dependency of the Si-nc layer location on waveguide nonlinearity and dispersion^[19], we know that the level of nonlinear enhancement is highest when the Si-nc layer is positioned at the center of the core where the optical mode field is the strongest, however it will also induce the highest propagation loss. Although one can reduce the propagation loss by placing the Si-nc layer away from the center, e.g., on the surface of the waveguide core^[22], this will also decrease its effect on nonlinear enhancement, and will require a longer waveguide to produce the same nonlinear effect. One advantage of placing the Si-nc film at the core center is that it enables the flattening of the waveguide dispersion, which is a highly desirable property in nonlinear applications. Along with the simulation of waveguide losses with different silicon rich materials^[19], it has been found that a layer of 50 nm thick a-Si film located at the center of the core, results in optimal nonlinearity, loss and dispersion. To create the Si-nc film, the device was annealed at a high temperature to facilitate the crystallization of the a-Si film, and the formation of Si-nc grains. The size of Si-nc is dependent on the fabrication process, as well as the annealing conditions (atmosphere composition and temperature). The size and density of Si-nc can affect the effective index, which influences the nonlinear properties. Given that smaller Si-nc size tends to produce higher nonlinearity^{[23, 24]}, the objective is to control the production of Si-nc with respect to their dimension and size distribution. Design parameters and fabrication processes of different waveguides are shown in Table 1.

As the FWM conversion efficiency depends strongly on the Q-factor of the ring resonator, MRRs with different Q-factors are compared, so as to identify the maximum conversion efficiency of the Si-nc embedded waveguide structure. The Q-factor of the ring resonator can be varied by adjusting the gap separation between the bus waveguide and the ring. In our experiment, there are eight MRRs on one chip within a footprint of ~ 1 × 1 cm². In addition, MRRs with different dimensions are compared. For waveguides with a width of 2 μm, gap separations vary from 1.2 to 1.6 μm with a step of 0.1 μm, while for waveguides with a width of 3 μm, gap separations vary from 0.8 to 1.2 μm with a step of 0.2 μm. Further details of these parameters are listed in Table 2. Generally, larger waveguide cross-sections result in weaker mode distribution confinement, while propagation loss would be lower.

Transmission electron microscope (TEM) images of the annealed a-Si thin films reveal the Si-nc grain sizes and distributions throughout the whole wafer, and are shown in Fig. 1(a). From the TEM images we can conclude that after annealing under an N₂ atmosphere, Si-nc grains with a diameter of about 3 nm are obtained and the nanocrystal grains distribute uniformly across the wafer.

The designed cross-section geometries for Si-nc embedded waveguide are 2 × 2 μm² and 3 × 2 μm² with 50 nm Si-nc sandwiched in the core center. However, the cross-sectional dimensions of the as-deposited waveguides shrank by 13%−15% after the annealing process, as shown in the SEM images in Figs. 1(c) and 1(e). The actual dimensions of the two sets of waveguides are 1.75 × 1.75 μm² (w/20 nm Si-nc - D1) and 2.55 × 1.75 μm² (w/20 nm Si-nc - D6), respectively, with the thickness of the Si-nc layer being ~ 20 nm.

The mode profiles shown in Figs. 1(d) and 1(f) reveal that the electric field is tightly confined in the high-index doped silica core region. The zero-dispersion wavelengths of the transverse electric (TE) modes for the four waveguides are 1590 nm (w/o Si-nc - D6), 1520 nm (w/20 nm Si-nc - D6), 1520 nm (w/o Si-nc - D1), and 1340 nm (w/20 nm Si-nc - D1), respectively. With the exception of the waveguide with a cross-section of 2.55 × 1.75 μm² and without the Si-nc layer (w/o Si-nc - D6), all waveguides exhibit normal dispersion in the telecommunication window, due to the shrinkage of the cross-section, which shifted the dispersion towards the shorter wavelength direction. Normal dispersion will decrease the FWM conversion efficiency, but as our goal is to enhance the nonlinearity by introducing the Si-nc thin film, we can still compare our results among these waveguides. Moreover, for waveguides with marginally smaller normal dispersion, we demonstrate their applications in all-optical analog-to-digital conversion^[25].

Optical intensity in the micro-ring is much higher than in the bus waveguide if the round-trip gain is larger than the loss. In an MRR with a configuration as shown in Fig. 2(a), the intensity enhancement factor B on resonance (with loss α < 1) is given by

 (1)

where κ and t are the coupling parameters of MRR. The * represents the conjugated complex value of κ and t. α denotes the loss coefficient in the micro-ring (α = 1 for zero loss).

The intensity enhancement factor B as a function of coupling coefficient κ was simulated for different propagation losses and various ring radii, results of which are presented in Figs. 2(b) and 2(c), respectively. Intensity enhancement in the ring is a function of round-trip loss and coupling coefficient. At a given round-trip loss, there is an optimal coupling coefficient located on the under coupled side of the critical coupling point, where the intensity enhancement is at its maximum. For a lossless resonator, intensity enhancement factor B is equal to the inverse of the power coupling coefficient. As a function of radius, enhancement increases with decreased radius. This is due mainly to the reduction of the mode volume and round-trip loss. Enhancement B can increase Kerr nonlinearity, which is beneficial in nonlinear processes, such as FWM.

The linear properties of the fabricated ring resonators with the conventional waveguide structure are shown in Table 3 and for the MRRs with the Si-nc waveguide in Table 4. It can be seen that the loaded Q-factors for both the conventional and the Si-nc embedded MRRs increase as a function of gap separation from 1.2 to 1.6 μm for the 1.75 × 1.75 μm² MRRs and from 0.8 to 1.2 μm for the 2.55 × 1.75 μm² MRRs, indicating that the MRRs are not loss limited. With the field enhancement factor in the resonator proportional to its finesse, the amount of stored power in the resonator is higher for resonators with a higher Q value, for a given input power. However, as the gap separation increases, the Q value will saturate once the intrinsic loss is larger than the coupling between the resonator and the bus waveguide. At that point, the power in the resonator decreases and the efficiency will subsequently decrease. With increasing gap separation, Q increases, while κ and B decrease. With increasing waveguide width, Q value increases, while κ, α and B decrease. Intensity enhancement factor B is obtained by fitting the curve of the through port and the drop port. As the thickness of the Si-nc film is more than an order of magnitude smaller than the wavelength, it has almost no effect on the effective index of the MRRs so that the FSRs of the MRRs with and without the Si-nc layers are similar.

The coupling coefficients κ₁, κ₂, and the propagation loss in the ring α in Tables 3 and 4 are extracted from the measured responses by fitting the measured responses with the analytical formulas^[27]. At 1550 nm, the extracted propagation loss of the ring embedded with 20 nm Si-nc strip is ~ 0.1 dB/cm higher than for a case without the strip. The α values of these two wafers are below 0.32 dB/cm. Although the low propagation loss in the ring indicates the promise of these devices for use in nonlinear experiments, it is important to point out that as the Q-factor of the MRR is highly dependent on the propagation loss, the increased loss with the additional layer of Si-nc film reduces the Q-factor of the MRRs by a factor of approximately half. Furthermore, due to the high propagation loss of transverse magnetic (TM) polarization, we only study the linear and nonlinear properties of TE polarization.

The fiber to waveguide coupling loss for the MRRs devices is around 5 dB/facet. Figs. 3(a)–3(d) show the measured responses from through port and drop port across the C-band for TE mode of the 49 GHz FSR. The 3 dB bandwidth for the four waveguides from Fig. 3(e) to Fig. 3(h) is 269, 288, 367, and 379 MHz, respectively.

The nonlinear parameter γ was measured for the 49 GHz MRRs, based on the conversion efficiency η of the FWM process, with the field enhancement from the micro-ring also taken into consideration, in accordance with^{[15, 28]}:

 (2)

 (3)

 (4)

where R denotes the radius of the MRR. Here, FE_p, FE_s and FE_i represent the field enhancement at the pump, signal and idler wavelengths, respectively. The product corresponds to the overall power enhancement of the MRR. is the mode linear loss of the μ-th order of the mode. is the self-coupling coefficient between the bus waveguide and the ring. is the finesse of the MRR filter, which is given by the ratio of FSR and 3 dB width for the mode μ. Using the MRRs, we measured the nonlinear parameter γ by exciting the pump and the signal power from the input and add ports, respectively^[15]. Pump and signal wavelengths are tuned carefully to align with two resonances to utilize the maximum cavity enhancement.

When a laser with high pump power is launched into the waveguide, the generated heat will shift the resonances. Thermal shift rate of the high-index doped silica glass is approximately 17 pm/°C at 1550 nm^[29]. Taking into account the fact that cold resonance can shift to longer wavelength by almost a half-line width with a temperature change of as little as 0.1 °C^[30], we use a thermoelectric cooler (TEC) stage with thermocouple feedback to maintain thermal balance, as shown in Fig. 4(a). Both the drop and the through responses are measured using the same OSA with the aid of an optical switch.

The generated first and second idler signals from the FWM process in the MRRs are shown in Figs. 4(b)–4(e). When aligning the pump and signal wavelengths with the resonances, idler peaks can be recorded on both sides with the frequencies satisfying the energy conservation or . The recorded idler peaks are all aligned on resonances, indicating that the dispersion at these wavelengths is negligible.

We note that while both the 1.75 × 1.75 μm² and 2.55 × 1.75 μm² MRRs have similar Q-factors, but the 1.75 × 1.75 μm² MRR has a higher FWM converson efficiency due to the higher power density, shown in Fig. 5(a). The measured nonlinear parameter γ extracted from the FWM measurement for the MRRs is shown in Table 5. It can be seen that γ increased from 0.144 to 0.366 W⁻¹m⁻¹ for the 1.75 × 1.75 μm² MRR and from 0.120 to 0.212 W⁻¹m⁻¹ for the 2.55 × 1.75 μm² MRR with the addition of the Si-nc film. The increase of the nonlinear parameter γ by adding the Si-nc film is with the tradeoff of additional propagation loss, resulting in a lower Q-factor and intensity enhancement of the MRRs, which results in the low FWM conversion efficiency. Fig. 5(b) plots the linear relationship of the idler power versus the square of the pump power and reveals a quadratic dependence, demonstrating that the Si-nc film exhibits no TPA and 3PA absorption under input pump powers up to 15 mW, and which is limited by the available CW pump source. Moreover, using long path length spiral waveguides with the same embedded Si-nc thin film, we observed that the TPA is negligible, derived from measured reciprocal transmission as a function of the coupled peak power^[25].

In conclusion, we have fabricated a series of 49 GHz MRRs with embedded Si-nc layers and measured their FWM efficiency. The Si-nc film is formed by the deposition of a thin layer of a-Si film in the middle of the core waveguide, and subsequently crystallized at a high temperature. We found that the addition of the Si-nc film increased the propagation loss by approximately 0.11 to 0.15 dB/cm and reduced the Q-factor of the MRRs by one half, however the Si-nc film doubles the nonlinear parameter γ. By adding a thin layer of Si-nc film, it is possible to enhance the nonlinearity of the waveguide and to improve these waveguide circuits for all optical signal processing applications.

This work is supported by the Research Grants Council, University Grants Committee (GRF 11213618), and the Strategic Priority Research Program of the Chinese Academy of Sciences (XDB24030300).