Light confinement in a low-refraction-index microcavity bonded on a silicon substrate

LI WANG, SHU-XIN ZHANG, QINGHAI SONG, QIHUANG GONG, AND YUN-FENG XIAO* State Key Laboratory for Mesoscopic Physics and School of Physics, Peking University, Collaborative Innovation Center of Quantum Matter, Beijing 100871, China Integrated Nanoscience Lab, Department of Electrical and Information Engineering, Harbin Institute of Technology, Shenzhen 518055, China Collaborative Innovation Center of Extreme Optics, Taiyuan, 030006 Shanxi, China *Corresponding author: yfxiao@pku.edu.cn

The trapping of photons in low-refraction-index materials is thought to be prohibited in conventional photonic structures that employ total internal reflection. Specifically, the whispering gallery mode (WGM) microcavity, which is an important optical component, has to rely on a high contrast of the refraction index with the surrounding environment to manifest excellent light confinement. Here, we propose and demonstrate experimentally an optical microcavity structure consisting of a low-refraction-index silica microtoroid directly bonded on a high-refraction-index silicon substrate. The resonant structure supports high-Q fundamental WGMs in both visible and communication bands, while higher-order modes are suppressed significantly due to the strong leakage into the silicon substrate at long wavelengths. The highest measured quality factor exceeds ten million and low-threshold microcavity Raman lasing is also realized. Whispering-gallery-mode (WGM) microcavities [1] confine light in a small volume for a long time, thus significantly enhancing the light-matter interaction. Recent efforts have demonstrated that they are an ideal platform for studies of fundamental and applied photonics, such as cavity quantum optomechanics [2], cavity quantum electrodynamics [3,4], and nonlinear optical processes at weak pump [5,6] and single-nanoparticle detection [7][8][9][10][11]. They are also one of the key components in optical interconnection circuits [12], playing a considerable role in generating on-chip laser sources, filters, switches, modulators, and amplifiers, etc. Among the on-chip resonators, silicon-based microcavities usually have quality (Q) factors on the order of a million [13], and III-V semiconductor, such as GaAs, microcavities often support Q-factors around ten thousand [14]. The relatively low Q factors in these high-refraction-index materials become an obstacle to applications in the fields of on-chip nonlinearity and quantum manipulation, etc. Although the Q factor of the silicon microrings made by some research groups has increased to ten million, the employment of electron beam lithography technology incurs a high cost in the practical application [15]. In contrast, low-refraction-index materials have advantages in many aspects, especially in the fabrication of high-Q devices. With the aid of the reflow process, resonators with Q factors exceeding 100 million could be realized through photolithography [16,17]. However, traditional low-refraction-index devices are usually supported by a pedestal [16,18], introducing an extra air layer. Conventionally, these resonators have to be coupled by a tapered fiber, which makes for complications in using them for integrated photonics.
In this work, we propose and demonstrate experimentally a new method to achieve superior light confinement using a structure consisting of a low-refraction-index donut-shaped microcavity bonded on a substrate of a high-refraction-index material. High-Q fundamental modes are observed experimentally, while higher-order modes are suppressed due to a larger energy leakage into the substrate. The highest measured quality factor exceeds ten million, and subsequently low-threshold Raman lasing is demonstrated. The photonic resonant structure is illustrated in Fig. 1(a). A donut-shaped silica microcavity with a circular cross section is directly placed on the smooth silicon substrate. The refraction indices of silicon and silica are 3.48 (3.88), 1.44 (1.46), respectively, in 1550 nm (635 nm) wavelength band. The circular cross section of the microresonator remarkably reduces the electric field distribution area in the vertical direction compared with the traditional rectangular cross section, resulting in a better light confinement in the silica (see Supplement 1). Thus, the donut-shaped structure could support long-lived resonant modes mainly located in the low-refraction-index material, even though it is directly connected to the high-refraction-index substrate.
To gain a deeper understanding of the resonant modes in this photonic structure, we intend to vary the refraction index of the substrate n sub while keeping the refraction index of the silica microcavity unchanged. Figure 1(b) plots the imaginary part of the effective mode index [Imn eff ], which reflects the leakage rate depending on n sub . It is noted that the leakage into the substrate dominates the whole decay given that the radiation into the air is trivial for a large-sized WGM microcavity. In contrast to the intuitive understanding that more energy will leak into the substrate with larger n sub , the numerical result shows that Imn eff has a maximum value when n sub is around the refraction index of the silica microcavity. This phenomenon results from the trade-off between the density of states and leakage strength [19,20]. Figure 1(c) shows the real part of the effective mode index Ren eff , calculated by l λ∕2πR, which characterizes the mode resonance wavelength λ. It is found that Ren eff relies on not only the ratio of energy distributed in the substrate to that in the cavity part, which is related to Imn eff , but also the location of the mode field in the substrate, which moves inward as n sub increases [insets of Fig. 1(c)]. The peak in Fig. 1(c) is the trade-off between these two factors (see Supplement 1).
According to the coupled-mode theory [21], the resonant mode, to the first approximation, can be given as a "superposition" of the WGM in the donut-shaped microcavity (free microcavity) and the "leaky mode" in the silicon substrate (without bonding to the microcavity), where a d and b d are the amplitudes of the constituent WGM ψ WGM d f1; 0g T and leaky mode ψ lea d f0; 1g T basis respectively, d is the minor diameter of the microcavity. The square modulus of the WGM amplitude ja d j 2 is a measure of the 'character' of the resonant mode, that is, the degree to which it is WGM-like: Here n WGM d , n lea d and n eff d are the effective indices of WGM, leaky mode and resonant mode. The finite element method simulation results show that n eff d ≅ n WGM d (with or without substrate bonding, the resonant frequencies of modes are almost the same), leading to ja d j 2 ≅ 1. Thus we could just treat the resonant modes as WGMs, which shows high-Q property.
Next, to demonstrate the concept of light confinement in the photonic microstructure studied above, we bond a silica toroidal microcavity directly to the silicon substrate. To this end, first, the microtoroid is fabricated by optical lithography, buffered HF wet etching, XeF 2 gas etching and CO 2 laser pulse irradiation successively. Then, a second XeF 2 dry etching process is applied to create very tiny silicon pillar [17]. Subsequently, the microtoroid is separated from the supporting pillar and transferred onto a silicon substrate surface, using a tapered fiber tip controlled by a three-dimensional translation stage [22]. Finally, a second pulse of CO 2 laser slightly melts the microtoroid, firmly bonding the cavity with the silicon substrate [inset of Fig. 3(b)]. It is noted that the microtoroid includes an extra disk part compared with the structure in Fig. 1. The disk part does not affect the resonant mode which is distributed in the toroidal part, as confirmed by the numerical simulation (see Supplement 1).
To study the properties of the resonant modes, a fiber-taper waveguide is used to couple with the silica microtoroid, and the transmission spectra are obtained by scanning the probe light wavelength. A polarization controller is used to adjust the polarization of the probe light, exciting transverse magnetic (TM) and transverse electric (TE) modes separately. The fiber-cavity gap is optimized to ensure the concerned modes falling in undercoupling regime, and the pump power is kept below 2.5 μW to greatly reduce the thermal noise. The transmission spectra are shown in Figs. 2(a) and 2(b), in which several mode families with certain free spectral range can be clearly seen. We denote the modes by TE q l;m and TM q l;m , with q the radial number, l the angular number, and m the azimuthal number. Through the finite element method simulation, the mode numbers of the exited resonances shown in the transmission spectra could be determined by comparing resonant wavelengths and Q factors [23]. In Fig. 2(a), only three mode families TE 1 l;l , TE 1 l;l−1 , and TE 1 l;l−2 , "survive", with corresponding free spectral ranges of about 6.53, 6.52, and 6.55 nm. 220;218 ) pertain to the second (third)-order mode family, which hold two (three) maximum values of field density in the azimuthal direction. The higher-order azimuthal modes have larger field distribution areas in the vertical direction that suffer from much lower Q factors due to the increasing energy leakage to the silicon substrate (see Supplement 1).
Similarly, we could identify four TM mode families TM 1 l;l , TM 1 l;l−1 , TM 1 l;l−2 , and TM 2 l;l from the transmission spectrum in Fig. 2(b). Differing from TE polarization, TM-polarized probe light could excite the second-order radial mode family TM 2 223;223 and TM 2 224;224 with two maximum values of field density in the radial direction. The higher-order radial mode possesses a much lower Q factor than the azimuthal modes, which is ascribed to the larger field distribution area in the radial direction, decreasing Letter the Q factor more tremendously. Moreover, several low-Q modes with low coupling efficiency appear in the transmission spectrum, in contrast to the cleaner spectrum in Fig. 2(a), because of the better light confinement for TM-polarized high-order modes.
To study the dependence of the Q factors on the minor diameter d of the microtoroid, we fabricate a series of microtoroids with different d by adjusting the etching time of the first gas etching process. Figures 3(a) and 3(b) display the Q factors of fundamental modes in the 1550 nm and the 635 nm wavelength band, respectively. As d increases, the Q factors in the 1550 nm wavelength band increase exponentially. With d 9.7 μm, the highest measured Q factor can be even up to ten million. The numerical simulation result shown by the red curve is in good accordance with the experimental data, especially for relatively small d sizes (see Supplement 1). Regarding the relatively large d sizes, the deviation between the experiment and simulation is attributed to the surface scattering introduced during the transfer process (inset of Fig. 3), which could be avoided by better micromaching technology.
In the visible wavelength band, for different d sizes, the measured Q factors maintain large values. The simulated Q factor could exceed 10 million even for a small minor diameter d 4.5 μm. Thus, the measured Q factor is mainly determined by the surface scattering loss for d varying from 5 to 10 μm, and the silica-to-silicon leakage plays a minor role. With a smaller d, a larger proportion of the mode energy is distributed outside the silica toroidal part, suffering stronger scattering loss, which leads to a slightly smaller measured Q. This effect coincides well with the slowly increasing trend of experimental data in Fig. 3(b).
Remarkably, the measured Q factors in the 635 nm wavelength band are greater than that in the 1550 nm wavelength band, in particular for small d . This phenomenon is distinct from that in the conventional microtoroid supported by a tiny silica pillar, where the Q factors of modes at shorter wavelength are lower due to stronger surface scattering effects. With regard to the effects of the principal diameter p on characteristics of the microcavity, it is similar to the case of the microcavity with a supporting pillar. The free spectral range is inversely proportional to p and the Q factor is hardly affected by p for large enough cavities with a p of tens of micrometers.
Finally, we demonstrated microcavity Raman lasing [5] to show the potential of the resonant structure in the low-powerconsumption integrated photonics. To this end, the tapered fiber is attached to the top of the toroidal part during the experiment, which is more stable and does not decrease the Q factor too much. We performed the experiment in a cavity with principal (minor) diameter of 63.4 (9.7) μm. The pump cavity mode has an intrinsic Q factor of about ten million and a loaded Q factor of about six million. The pump laser is locked on the target mode while the pump power is increased to trigger stimulated Raman scattering. Figure 4 shows a typical Raman lasing spectrum of the microtoroid measured by an optical spectrum analyzer (OSA) with a resolution of 0.02 nm [see Fig. 4(a)]. The pump laser is around   Letter 1550.8 nm and Raman lasing occurs at 1653.4 nm. The dependence of the Raman laser power, measured by the OSA, on the loading pump power is shown in Fig. 4(b), from which we can clearly see a Raman lasing threshold of about 56 mW. It should also be noted that when the pump power reaches about 58 mW, the pump-to-Raman conversion efficiency is suddenly reduced. This is due to the first-order Raman laser field acting as a secondary pump field for the generating second-order Raman laser, thus reducing the intensity of the first order Raman laser.
In summary, we have demonstrated experimentally excellent light confinement in low-refraction-index material by using a photonic microstructure consisting of a donut-shaped microcavity bonded on a high-refraction-index substrate. The resonant structure supports high-Q fundamental whispering gallery modes in both visible and communication bands, and possesses weak energy leakage to the substrate, especially for short wavelength and large d . Low-threshold Raman lasing is also demonstrated in the microcavity with a Q factor of ten milliom. This mechanism of light confinement in the photonic microstructure applies to various low-refraction-index materials besides silica, such as polymers. In practical applications, micromachining technology can be adopted to realize bath production instead of a transfering method of microcavity [24][25][26]. As for the attached coupling, a waveguide could be fabricated under the donut-shaped microcavity to replace the tapered fiber, which offers perfect stability and high efficiency without a large decrease of the Q factor. Moreover, the resonant structure shows good tolerance to the geometry deformation of the toroidal cross section, which is particularly needed for industrial applications (see Supplement 1). The present work may open up new possibilities for the investigation of highly integrated photonics and applications in fields including on-chip nonlinearity and quantum manipulation.