Over the last few decades, silicon photonics has been extensively studied to operate near the telecommunication band in the near-infrared (NIR) wavelength region. Recently, mid-infrared (MIR) silicon photonics has also attracted considerable attention due to the relatively low intrinsic loss of silicon in this waveband range typically from 2 to 8 μm and to the existence of various application areas ^[1–6], including sensing, medical diagnostics, thermal imaging, and free-space communications ^[7]. It is thus interesting and significant to bridge these two wavelength bands through nonlinear wavelength conversion, such as generation of MIR light with a telecom-band pump source ^[8]. Another motivation for this lies in the challenges related to the detection of MIR waves. The size of detectors is usually bulky, or a cryogenic environment is often needed, which limits the development of the integration level and hinders the low-power consumption of MIR systems. A MIR-to-NIR conversion then allows circumventing these drawbacks by detecting the converted waves using mature telecom-band photodetectors ^[9,10].

To date, MIR-to-NIR proposed converters in silicon photonics have mostly exploited nonlinear four-wave mixing processes in silicon itself ^[10,11]. However, improvements in the performance of nonlinear mechanisms by introducing plasmonic structures or highly nonlinear materials such as organic polymers (NPs) into the silicon photonics platform have also been envisaged as a key option ^[12–19]. Plasmonic structures indeed support strong local-enhanced confinement of light in subwavelength scales and ultrafast responses ^[12,20], and NPs usually have nonlinear susceptibilities exceeding those of silicon or even have large second-order nonlinear susceptibilities that vanish in silicon ^[18,19]. Microring resonators (MRRs) have also been proposed to be attractive components in silicon photonics to further reinforce optical nonlinearities and realize efficient and compact nonlinear frequency conversions because of the large field enhancements around resonant wavelengths provided by MRRs ^[21–28]. The combination of hybrid plasmonic waveguides (HPWs) and MRRs has been proposed in several works in which the HPW-based MRRs support subwavelength or even submicrometer radii and large field enhancements in the low-index slot area ^[29–33]. However, most of these works were focused on the linear response of the MRR. In this work, we apply the HPW of Ref. ^[15] into a MRR configuration. By setting both the fundamental frequency (FF) and the second harmonic frequency (SHF) at two different resonant wavelengths, an enhancement factor of second harmonic generation (SHG) efficiency by almost two orders of magnitude is predicted.

The remainder of this paper is organized as follows. In Section 2, we describe the structure of the proposed HPW-MRR device and the detailed design to take the phase matching, resonance, and optical losses of the MRR into account. In Section 3, results related to SHG in the proposed configuration are presented. Finally, we conclude in Section 4.

The proposed silicon-organic hybrid plasmonic microring resonator (SOHPMR) is shown in Fig. 1. The straight access waveguide with width wa is coupled with the ring through a gap distance of g. The radius and width of the bended waveguide are R and w, respectively. The cross section of the HPW is characterized by a NP with a thickness of hp=70nm, well suited to find a phase-matching point in a bended waveguide, as shown hereafter. The thicknesses of the Ag and Si layers are hm=100nm and hSi=480nm, respectively. The polymer is chosen as the doped, cross-linked NP with a refractive index of n=1.643 and a nonlinear susceptibility of χ111(2)=619pm/V at the wavelength of 1550 nm ^[19]. The pump light at the FF of λ1=3.1μm is coupled into the SOHPMR with reasonable powers (values are given hereafter). The expected SHF at λ2=λ1/2=1.55μm is generated and outputs from the through port of the SOHPMR.

Such a device can be fabricated by classical technological processes. First, the polymer can be spin-coated onto the silicon layer, and then by defining a mask on the wafer and etching through, the MRR configuration can be defined. Following this, metallic layers can be deposited on top through a lift-off process.

Using the modal phase-matching method, the needed phase-matching condition (PMC) to enhance the nonlinear SHG process can be realized between the fundamental (zeroth) mode at the FF and the second-order (first) mode at the SHF in the straight HPW ^[15]. Based on the same mechanism, the new phase-matching points in the bend-waveguide configuration have been searched. The modal properties of bended waveguides have been analyzed by 2D axisymmetric simulation in COMSOL. Material dispersion for modeling the refractive index of SiO2, Si, and Ag was taken from Refs. ^[34,35], and ^[36], respectively. Figure 2 shows the difference of the effective refractive index between the interacting two modes as a function of the radius R and width w of the bended waveguide. Note that the fundamental mode of the SHF was not considered in this study. The black line marks out the zero value, i.e., the phase-matching line. One can see that the PMC can be fulfilled in the bended HPW as well and that for most of the radius values, two phase-matching points can be found.

Next, the locations of the resonant wavelengths for the ring have been adjusted in order to match with the two frequencies of interest for the reinforcement of the SHG process. Stating that a resonance into the ring happens when neffkFFR=m (m is an integer and is known as the azimuthal number of the resonance), where neff and kFF are the effective refractive index and propagation constant, respectively, the “neffkFFR” quantity has been plotted as a function of radius in Fig. 3(a). For each radius value, the larger waveguide width on the top phase-matching line has been chosen correspondingly. Combining this condition with the minimization of the 90°-bending HPW losses for the two frequencies of interest [shown in Fig. 3(b)], the m=9 value was finally chosen. Optimal radii near 2.6 and 2 μm were found for the FF and the SHF, respectively, where a minimum loss level was obtained due to the joint contributions from the radiation (increasing exponentially with a radius decrease) and the intrinsic losses of the waveguide resulting from the metal absorption ^[30]. As shown in the inset of Fig. 3(a), the corresponding geometrical parameters for m=9 are R=2.325μm and w=351nm≈350nm, which are the final geometrical parameters that were chosen.

The obtained phase-matched field distributions are shown in Fig. 4, where Figs. 4(a) and 4(b) plot the Ez distributions of the zeroth mode at the FF and the first mode at the SHF, respectively. The effective refractive indices of the two modes are nFF=1.90963+0.00362i and nSH=1.90961+0.00144i, respectively. Figure 4(c) shows the normalized Ez profiles on the center line of the slot along the r direction, as marked in Fig. 4(a). We can see that the peak value of the field is not located at the center of the waveguide because of the bended-waveguide property.

The width of the access waveguide was then designed as wa=358.3nm≈360nm in order to maximize the fraction of FF field coupled into the ring. Then, nFF=1.90968+0.00271i and nSH=1.91268+0.00139i for the access waveguide. Finally, in order to set a comparison benchmark for the SHG efficiency in the ring resonator configuration with previous results, the efficiency of the SHG process in a straight HPW was complementarily estimated (with w=369.2nm≈370nm in this case for PMC consideration).

In this subsection, we derive the enhancement factor for the SHG in a ring resonator when compared to a single waveguide. First, the SHG efficiency in a single lossy waveguide with a length of L is (the detailed derivation is given in Appendix A) η1=PSH(out)PFF(in)=ωFF216cSH2Leff2(L)exp(−αSHL)PFF(0),(1)where PFF(in) and PSH(out) are the input power of the FF and the generated output power of the SHF, respectively. ωFF is the angular frequency of the FF, cSH is the nonlinear coupling coefficient being the overlap integral between the interacting modes in the nonlinear cross-sectional area, and Leff is the effective length defined by Leff(L)=1−exp[−(αFF−αSH/2+iΔβ)L]αFF−αSH/2+iΔβ.(2)Δβ=βSH−2βFF is the phase mismatch. βFF,SH and αFF,SH represent the phase propagation constant and attenuation coefficient, respectively.

For the SHG in a MRR, the conversion efficiency is (Appendix B) η2=PSH(out)PFF(in)=ωFF216cSH2Leff2(L)FFF4FSH2exp(−αSHL)PFF(in).(3)Here L is the circumference of the microring given by L=2πR with R being the radius of the ring measured from the center of the ring to the center of the waveguide. FFF,SH are the field enhancement factors, which can be written as FFF,SH=κFF,SH1−tFF,SHexp[(iβFF,SH−αFF,SH/2)L].(4)κ and t are the coupling and transmission coefficients related to each other by |κ|2+|t|2=1.

Compared to the SHG efficiency in a single waveguide of Eq. (1), the efficiency in a MRR is enhanced by a factor of FFF4FSH2. However, it should be noted that the linear losses of the bended waveguide in the MRR here include the intrinsic loss of the waveguide and the bend radiation loss, which makes them larger than that for a straight waveguide. The real enhancement factor would thus be smaller than FFF4FSH2. Specifically, at the considered phase-matching and resonating point considered in this study, where βSH=2βFF=2m/R with m being an integer, the effective length and field enhancement factor are $$\begin{gathered} Leff(L)=1−exp[−(αFF−αSH/2)L]αFF−αSH/2, \\ FFF,SH=κFF,SH1−tFF,SHexp(−αFF,SH2L). \end{gathered}$$(5)In this circumstance, SHG shows the best performance.

In the first benchmarking single straight HPW considered configuration, the nonlinear coupled coefficient was calculated to be cSH=134psm−1W−1/2. Then by using Eq. (1), the SHG efficiency was estimated as η1=0.14% for an input pump power PFF(in)=20mW and a waveguide length of 14.6 μm corresponding to the unfolded circumference of the MRR considered in a second step. Similarly, by using Eq. (3), the SHG efficiency was newly obtained in the MRR configuration under the same pumping power condition. The nonlinear coupled coefficient was then cSH=130psm−1W−1/2 for the bended-waveguide case. Figure 5 shows the final MRR-enhanced SHG efficiency η2 as a function of the two waveguide-to-ring transmission coefficients for the FF (tFF) and the SHF (tSH), respectively (see Appendix B for the exact definitions of tFF and tSH, which are in practice controlled by the geometrical sizes of the access and bended waveguides, and the gap g between them). As is visible, a peak efficiency up to η2=21% is realized when the MRR works at the critical coupling point for both the FF and the SHF, i.e., when tFF=exp(−παFFR)=0.898 and tSH=exp(−παSHR)=0.918. A maximum enhancement factor of η2/η1=150 is then expected. However, it is worth noting that it is not possible to let the FF and the SHF work at the critical coupling points at the same time in practice. Usually, tSH is larger than tFF for the same MRR because the waveguide mode at the SHF extends less beyond the waveguide boundary due to a smaller wavelength. In spite of this, an optimal point can be envisaged in practice by adjusting the geometrical parameters of the MRR.

All the other geometrical parameters being fixed, the coupling and transmission coefficients of the MRR are only controlled by the thickness of the gap g between the access waveguide and the ring. Figure 6(a) shows the transmission coefficients for the two wavelengths of interest as a function of the gap parameter g. Here the coupling coefficients are calculated by making use of the coupled mode theory for MRRs ^[37,38]. Figure 6(b) shows the corresponding SHG conversion efficiency for different gap thicknesses. As can be seen, there is an optimal gap of g=175nm, where the SHG efficiency is η2=13.71%. Correspondingly, tFF=0.8088 and tSH=0.9666, respectively. Figure 6(c) shows the SHG enhancement factor described by FFF4FSH2 and the realistic enhancement η2/η1 ratio as functions of g. For the optimal gap of 175 nm, a maximum enhancement up to η2/η1∼100 is thus possible in practice by changing the straight HPW configuration into the MRR one. Another interesting point lies in the critical point for the FF, where no FF light would couple out from the through port. It happens when g=251nm≈250nm. At this point, tFF=0.898 and tSH=0.988. The SHG efficiency is then η2=9.2%, which means a MRR-enhancement factor of still 66.

In order to further confirm the veracity of the proposed scheme, we calculated the transmission spectra of the MRR around the SHF and the FF in a 3D structure and plot them in Fig. 7. FDTD Lumerical software was used to carry out the 3D full-wave simulation. Two resonant wavelengths of 1548.4 and 3099 nm are presented. The slight difference over the previous mode analysis is probably due to the applied different mesh sizes and different calculation methods in the finite-element-based mode analysis and 3D full-wave FDTD simulation. The MRR shows small extinction ratios because it works deviating from the critical points especially at the SHF. Figures 7(b) and 7(d) show the Ez distributions at the SHF and the FF, respectively. As can be seen, the MRR resonates at both the FF and the SHF and the azimuthal numbers at two wavelengths are 9 and 18, respectively. This agrees well with the previous mode analysis.

In the meantime, we finally estimated the robustness of the present results with respect to the additional optical losses due to the side-wall roughness coming from lithographic and etching steps used to define the investigated structure. In this purpose, we considered the last optimized configuration with loss coefficients of the bended HPW at the FF and the SHF given by αFF=638dB/cm and αSH=509dB/cm, respectively, and anticipated from this initial condition an increase of αFF and αSH. The result is plotted in Fig. 8, in which the left bottom corner corresponds to the bottom loss level coming from the absorption of the metallic layer and radiation losses only. As shown here, the SHG efficiency only slightly drops from 13% to 10% even for extremely large extrinsic losses eventually coming from the fabrication process. This point and the quantitative results provided by the 3D performed FDTD simulations (Fig. 7) assess the strong potential of the proposed approach for SHG enhancement in the ultrasmall footprint silicon plasmonic ring resonator structures.

To conclude, a silicon-organic HPW geometry based on a microring configuration is proposed to enhance the SHG process on the silicon photonics platform. By taking the phase matching, resonance, and loss level into consideration, the conversion properties are shown to be improved in three aspects: the needed pump power becomes lower, the size of the device is smaller, and the efficiency of the SHG is larger. In the proposed final geometry, a SHG conversion efficiency of around 13.7% is predicted for a pump power as low as 20 mW and a ring radius of 2.325 μm. This obtained dramatic improvement of the nonlinear efficiency with respect to previous results opens avenues to practical applications using low-power nonlinear SHG-based all-optical on-chip signal processing.