1. Introduction

Confining photons in a tiny dielectric volume of an ultra-high-Q (UHQ) cavity increases dramatically light-matter interactions. For this reason, high-Q resonators have been used for a number of fundamental investigations [1–5] and applications [6–8]. In particular, UHQ resonators have been employed for a vast spectrum of studies in quantum photonics [1, 9], lasing [7, 8], nonlinear optics [3, 10, 11], telecommunications [12–14], and sensing [15, 16].

Engineering of UHQ’s in whispering-gallery type resonators has become an enticing objective. One of the challenges to reach such Q values relies on reducing the light scattering at the interface between the resonator and the environment. This way UHQ’s were achieved by reflowing the resonator material, as it has been demonstrated for silica-based microspheres [17] and microtoroids [18]. The non-planarity, however, is the drawback which limits their integration with dielectric waveguides and, consequently, into planar photonic circuits. Another approach for achieving UHQ’s is to engineer the geometry of the planar microdisk resonators by realizing a shallow-angle wedge at its rim [19,20]. As a result, the fundamental modes of the wedge-resonator are pushed far away from the scattering edge of the device and, hence, suffer less from surface-induced losses. Very recently, record UHQ’s of ∼ 10⁹ have been reported for large diameter (5 mm) and relatively thick (10 μm) silica wedge resonators [21].

The planarity of wedge resonators, their CMOS-compatibility and accurate control of the processing entail an important step forward towards a full integration of UHQ devices into planar lightwave circuits. However, a last quest in this direction – the integration with on-chip dielectric waveguides – is still open. The mode retraction from the cavity rim precludes intrinsically the realization of side-coupled waveguides in the close proximity of the resonator in order to provide an appropriate mode coupling (Fig. 1(a),(b)). In this work, we show that this important milestone can be reached by opting for a vertical coupling scheme between the wedge microresonator and a bus-integrated waveguide (Fig. 1(c),(d)). Thereby, this study focuses on the proof-of-concept demonstration of the all-on-chip complete integration of wedge resonators.

 

Fig. 1 Evanescent field coupling schemes in integrated photonics. (a) A nanometric gap, d₁, between a microdisk resonator and a dielectric waveguide defines a side-coupling rate of γ₁ ∼ exp(−d₁). (b) Such coupling becomes increasingly inefficient when the pre-defined cavity/waveguide distance, d₂, increases during the formation of the shallow-angle wedge. In a realistic fabrication process also the waveguide retracts forming a wedge-shape (the dashed inclined line), thus, quenching completely the coupling. Because of this, typically, an off-chip technique (tapered-fiber) is used. (c) The vertical coupling allows for both engineering arbitrarily the evanescent field coupling by controlling the vertical gap, d_v, and aligning horizontally the waveguide to the resonator mode. (d) More importantly, this configuration enables the integrated photonics technology to access UHQ wedge resonators with buried dielectric waveguides. The vertical coupling scheme, in fact, permits to realize independently the wedge resonator, maintaining an appropriate coupling rate, γ_v ∼ exp(−d_v). It allows for a direct access of devices through integrated waveguides and has the flexibility to engineer free-standing devices [22].

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Recently, the feasibility of this technology in realizing free-standing microdisk and spider-web resonators coupled vertically to integrated waveguides through an air gap has been demonstrated [22]. The resonator-waveguide vertical coupling does not require expensive lithographic techniques for the gap definition at a desired precision and allows for an independent choice of materials and thicknesses for optical components. Owing to the separation of the resonator and the waveguide into different planes, our approach enables, on one side, to realize the waveguide and the shallow-angle wedge resonator in different technological steps, and on the other side, to define arbitrary and independently the vertical coupling gap size. Moreover, the degree of coupling between the optical components for a fixed vertical gap can be still engineered on a wafer-scale by tuning the lateral (in-plane) resonator-waveguide alignment within a few hundreds of nanometers (as demonstrated in Ref. [22]).

These advantages can be of great utility in a number of applications to cavity optomechanics [4], label-free sensing [15,16] as well as to integrated photonics. In the first case ultra-high Q’s (> 10⁶) are essential, whereas for integrated photonics only moderate Q’s (∼ 10⁴) are required. The reason for this last is that optical logic operations should be guaranteed by a fast response time, τ, of devices, while they are slowed down significantly when ultra-high Q’s are used (τ ∼ Q).

2. Device fabrication and optical characterization

We realized 400 nm-thick and 50 μm-diameter silicon nitride (SiN_x) wedge resonators vertically coupled to silicon oxynitride (SiO_xN_y) waveguides using standard silicon microfabrication tools (Fig. 2(a),(c)). Here, the choice for using SiN_x and SiO_xN_y for the resonator and the waveguide, respectively, has the aim to demonstrate the flexibility of the vertical coupling approach in using different materials for optical components. We note that, in principle, this technology can be feasible for a variety of material platforms where layer-by-layer deposition or growth is applicable.

 

Fig. 2 Fully integrated wedge and conventional microdisk resonators with vertical coupling to bus waveguides on a silicon chip. (a,b) Top-view optical images of the resonators. (a) Concentric Newton’s rings of different color at the edge of the wedge resonator indicate to a gradually decreasing layer thickness towards the outer rim. (b) A homogeneous color is observed across the entire disk surface of the dry-etched resonator. Panels (c) and (d) show the bird’s-eye-view SEM images of the wet- and dry-etched devices, respectively. The calculated intensities of first and second-order radial modes for both (e,f) the wedge and (g,h) the disk resonators around the wavelength of 1575 nm are shown. These panels illustrate how the wedge resonator modes are pushed away from the device external periphery into an ≈ 2.2 μm smaller effective radius trajectory due to the shallow-angled (θ ∼ 7°) confining wedge.

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In order to prove the suppression of surface-induced losses in a fully integrated device, we also realized devices identical to wedge resonators with the only difference of using a conventional dry ion-etching step for the resonator definition (Fig. 2(b),(d)). Spectroscopic characterization and numerical mode analysis were thus performed for both types of devices (see the next Section).

The process flow is sketched in Fig. 3. The devices were fabricated starting from the growth of 2.5 μm-thick thermal oxide on top of crystalline Si wafers. Next, a 300 nm-thick silicon oxynitride layer was deposited by using plasma-enhanced CVD technique and the strip waveguides defined through standard lithography and reactive ion etching (RIE). These were cladded by a borophosphosilicate silica glass (BPSG) and reflowed at high temperature. The BPSG deposition-and-reflow procedure was repeated for two cycles in order to reach an accurate planarization (96% degree of planarization). Afterwards, the cladding height was decreased using a RIE in order to define the vertical coupling gap (730 nm’s for a critical coupling at 1.55 μm wavelength). Next, 400 nm’s of silicon nitride was deposited using PECVD and patterned lithographically.

 

Fig. 3 The schematics of a typical process flow for the realization of vertically coupled wedge resonator/waveguide system. (a) An oxynitride (SiON) layer is deposited in a PECVD chamber on top of a thermally grown silica cladding. (b) SiON strip waveguides are defined using standard lithographic and reactive ion etching (RIE) techniques and, afterwards, cladded by a doped borophosphosilicate glass (BPSG). (c) A high-degree of planarization is achieved by using a two-cycle BPSG deposition-and-reflow procedure. (d) By using RIE the BPSG thickness is reduced in order to achieve the desired thickness (vertical coupling gap) on top of the SiON waveguide. (e) Silicon nitride layer is deposited using the PECVD technique and (f), finally, the wedge resonator is defined using a wet chemical etch in a buffered HF solution. (g) The cross-sectional sketch of the final device. This technology allows also for the realization of air-suspended wedge resonators. After the definition of the coupling gap, (e*) a sacrificial layer, such as amorphous silicon, is deposited on top of BPSG. (f*) Following the deposition of top SiN_x layer and (g*) the definition of the wedge resonator, (h*) the sacrificial layer is partially removed using an isotropic selective etching step (see Ref. [22]).

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The wedge resonator was formed during the transfer of the circular photoresist pattern into the SiN_x layer by using a wet etch in buffered HF solution. Due to the adhesion properties of the photoresist a θ = 7° sharp angle wedge is formed by the end of etching. Numerical calculations show that the fundamental mode is retracted to a 2.2 μm smaller effective radius, r_eff, with respect to the dry-etched (microdisk, hereafter) resonator (Fig. 2(e),(g)). These last were realized by transferring the photoresist to the SiN_x using dry reactive-ion etching step.

The devices were characterized in waveguide transmission experiments realized over a broad near-infrared wavelength range between 1350 nm and 1600 nm exploiting the setup described in Fig. 4(a). The monolithic integration of waveguides permits to use a simple, typical for waveguides characterization experimental setup. A near-infrared tunable laser source was butt-coupled to the bus waveguide, the signal polarization was controlled at the waveguide input and the transmitted power was recorded in a photodiode. For a fast monitoring of spectra and pre-alignment of input fibers a broadband ASE source was also used and the signal was monitored in a optical spectrum analyzer. All the setup was remote controlled by a computer.

 

Fig. 4 Optical characterization of wedge resonators. (a) The optical spectroscopic setup used for waveguide transmission measurements. (b) The measured broad range spectrum of the wedge resonator shows a series of 1st and 2nd order radial family modes of TE-polarization. Some of the these are labeled as (p, m) according to their radial p and azimuthal m mode numbers. (c) The high-resolution spectra taken around a wavelength of 1576 nm are shown for the wedge (top panel) and the microdisk (bottom panel) resonators. In both cases the 1st radial family mode is critically coupled to the bus waveguide and has a −15 dB transmission. Lorentzian fits to the resonances reveals a an almost fourfold increase in the 1st order mode’s Q for the wedge resonator. (d) The mode Q-factors of both the wedge and dry-etched resonators are compared in a 65 nm range around the wavelength of 1570 nm, showing a three- to fourfold difference for the first order radial families and almost no difference for the second order ones. (e) At a shorter wavelength the wedge resonator’s fundamental mode is split into a doublet due to degeneracy lift-off between clockwise and counter-clockwise propagating modes. A reduction in scattering loss of the wedge device and larger transparency of the SiN_x material provide intrinsic Q’s higher than the scattering Q_s, allowing for doublet observation. Meanwhile, the stronger scattering in the dry-etched device results into a lossy non-split lineshape.

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3. Results and discussion

Figure 4(b) shows a series of sharp and broad resonances corresponding to first- (fundamental) and second-order radial mode families of the wedge resonator. A blow-up of the spectrum around a fundamental mode with −15 dB of transmission suppression is shown in the top panel of Fig. 4(c). By accounting for the critical coupling of this mode to the waveguide, an intrinsic Q_i ≈ 7.6 × 10⁴ is found from a Lorentzian fit. Interestingly, the fundamental mode of the disk device at the very similar wavelength shows an intrinsic Q_i of only 1.8 × 10⁴ (bottom panel in Fig. 4(c)). A similar three to fourfold difference in quality factors of the fundamental modes in the wedge and the disk resonators is observed over a broad spectral range (Fig. 4(d)). Contrary, the second order mode families show much lower and close Q’s over the analyzed spectral range.

At a shorter wavelength (∼ 1370.5 nm) we observe that the transmission curve at the wedge resonator’s undercoupled fundamental mode M_w = 166 is split into a doublet of symmetric and antisymmetric modes due to scattering. The individual resonances have Q₁ = 2 × 10⁵ and Q₂ = 1.56 × 10⁵, respectively (Fig. 4(e), top panel). A fit to the spectrum, using the model for a coherent sum of Lorentzian lineshapes [23], shows that the Q’s of the individual modes are narrower than the scattering-related Q_s = ω₀/γ_s (ω₀ is the uncoupled mode frequency and γ_s is the scattering rate). This indicates to the formation of largely separated standing wave modes. Contrary, no doublet was observed for the disk’s (similarly undercoupled) fundamental mode at λ ≈1368.7 nm (M_d = 186) (Fig. 4(e), bottom panel). In this case, an important linewidth broadening (Q_1,2 ∼ 3.5 × 10⁴) and no observable doublet splitting (Q_1,2 << Q_s) were found from the sum-Lorentzian fit.

Numerical simulations of the resonators have been performed using the COM-SOL/FEMLAB’s PDE-solver to calculate the fields and frequencies of axisymmetric dielectric resonators. In particular, in order to calculate the resonant frequencies of real devices, the following procedure was used; First, the cross-sectional geometry of the resonator and the real refractive index (found from ellipsometric measurements, n = 1.959 for SiN_x at 1.55 μm) were set. The resonator’s radius was adjusted each time within few nm’s around 25 μm, to allow for processing-induced variations, and the numerical code was run. This procedure was repeated until the calculated mode wavelength coincides with the measured one. Afterwards, the radius was fixed and the rest of the mode wavelengths were obtained changing the azimuthal mode number M only. Such calculated values match to the experimental ones with a sub-nm precision (Fig. 5(a)).

 

Fig. 5 Numerical analysis of mode confinement and intensity profiles. (a) Numerically calculated peak wavelengths of the first (M1) and the second (M2) order radial modes of the wedge resonator show an excellent agreement with the experimentally measured ones. (b) The calculated mode confinement factors are reported both for the wedge and the dry-etched resonators. (c) The horizontal and (d) the vertical profiles (through field maxima) of the first order radial modes of two types of resonators around λ = 1576 nm. In particular, the mode maximum in the wedge resonator is situated at a ∼ 1μm smaller radius with respect to the dry-etched case, therefore, is more isolated form the physical edge of the device. The vertical profiles show an identical confinement in both cases. Panels (e) and (f) show the situation for the second order radial modes. In this case, the mode M2 in the wedge resonator is closely situated near the physical edges of the resonator. Insets in (c) and (e) show a close-up of the intensity profiles at the resonator/air interface.

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Figure 5(a) compares the measured resonance positions of two radial families of the wedge resonator to the numerically calculated ones. The observed sub-nanometer-precision matching of mode wavelengths permits us to use the numerical model for further analysis of the modal characteristics of the devices. The total intrinsic loss of a whispering-gallery resonator is given as 1/Q_i = 1/Q_r + 1/Q_m + 1/Q_s, where $Q_r^{-1}$ is the radiative loss, $Q_m^{-1}$ is the modal loss related to the material absorption and $Q_s^{-1}$ is the loss contribution accounting for both the surface scattering and surface absorption. The radiative Q’s can be estimated using the ray-optics approach [24] and for 50 μm-diameter devices are beyond 10¹⁹, having therefore an increasingly negligible contribution to the overall Q_i for both types of resonators. The quality factor, related to the material and modal loss is Q_m = λ (ΓαΛr_eff)⁻¹, where α is the bulk material’s absorption coefficient, Λ is the free-spectral range of the cavity modes, λ is the wavelength and Γ is the confinement factor of the mode. Figure 5(b) shows that the first radial family modes of the wedge resonator have a confinement of ∼ 80% while the Γ’s in the disk are slightly (∼ 4%) larger. Considering that the free-spectral ranges are of about 9.1 nm and 8 nm in the wedge and the disk resonators, respectively, the estimated Q_m’s for both devices are very similar.

The last contribution $Q_s^{-1}$ is taking into account the sidewall effects in terms of mode’s interaction with the resonators external rim by scattering due to roughness and absorption by specimen on the surface. The horizontal profiles across the fundamental modes brightest spot (Fig. 5(c)) show that the mode (M_w = 141) in the wedge resonator is retracted from the etched interface by almost 1 μm with respect to the disk’s case (M_d = 158) and, consequently, is better isolated from scattering and absorption. On the other hand, the vertical profiles of these modes coincide (Fig. 5(d)), suggesting that Q_s–contribution from planar interfaces is nearly identical for both cases.

This analysis shows that under the conditions of negligible radiative and very similar material losses the main contribution to the intrinsic Q_i comes from the surface-related Q_s. In view of the experimental results (Fig. 4(d)), the observed differences in Q’s confirm the effective suppression of surface-induced losses in wet-etched devices [19–21]. This conclusions are further supported by the analysis of horizontal (Fig. 5(e)) and vertical (Fig. 5(f)) profiles of the second-order mode families. In this case, the modes in the wedge resonator have a significant overlap with the interfaces as compared to the disk’s case, hence, larger surface-related losses are expected to significantly limit the Q (see the experimental M2 data-sets in Fig. 4(d)).

4. Conclusion

In conclusion, these results show the feasibility of using conventional silicon microfabrication tools for the realization of planar high-Q wedge resonators monolithically integrated with vertically coupled dielectric waveguides. The integration of waveguides simplifies significantly the access to the resonator, avoiding thus the use of complicated tapered-fiber free-space coupling schemes and guaranteeing stable operation of the device. By opting for a vertical evanescent coupling scheme, several critical issues are resolved; (i) the resonator and the waveguide are fabricated in different fabrication steps without influencing one another, (ii) the wedge angle of the resonator can be controlled without interfering with underlaying waveguiding components, (iii) the waveguide can be freely aligned to the mode position in the resonator, and (iv) the vertical gap between the resonator and the waveguide can be defined for engineering an evanescent coupling of arbitrary strength.

In terms of moderately high Q’s, our results offer a versatile approach for improving the functionalities (sensing, optical logic, lasing) of integrated silicon or hybrid photonics as an alternative to the SOI platform or operation at visible wavelengths. Moreover, the results of this study can boost an intensive research towards the complete integration of fully functional ultra-high quality factor planar resonators into planar photonic circuits. For this ultimate scope, all necessary ingredients, such as the transparent silicon-based materials [12, 21] as well as an easily accessible technology to realize integrated free-standing devices [22] are already available.