Alumina coating for dispersion management in ultra-high Q microresonators

Despite the consistent progress in mitigating optical losses within integrated photonics microcavities,^1,2 fused-silica microspheres still rank among the highest optical quality factor microresonators ever fabricated.³ These ultra-high Q-factors, reported above 10⁹ at visible and near-infrared^4,5 and around 10⁸ at telecom wavelengths,^6–8 result from silica’s low material absorption and atomic-level surface roughness achieved by the standard thermal-fusion fabrication process. Those properties, combined with a relatively small modal volume, allowed microspheres to host pioneer low-power nonlinear optical phenomena, such as Raman lasing,^6,9 third-harmonic generation,^10–12 Kerr optical frequency combs,^8,13 and optomechanical effects.¹⁴ The efficiency of many nonlinear processes also depends on momentum conservation (phase-matching), which requires control over the group-velocity dispersion (GVD) of resonator modes. While other types of microresonators offer more geometric degrees of freedom for GVD control, e.g., height or width,¹⁵ sidewall angle,^16,17 or circumference shape control,^18–20 the diameter is the only geometric degree of freedom in microspheres. Despite the outstanding possibilities explored so far,²¹ changing the diameter of microspheres fabricated with glass fusion techniques has critical challenges, such as pre-tapering of an optical fiber or extremely fine control over an electrical arc discharge or laser fusion processing.^22,23 A straightforward approach to overcome this lack of geometrical parameters is to use dielectric coatings, as has already been demonstrated experimentally^24–26 and numerically investigated in multi-layer coated spheres.^27–29 Nevertheless, experiments with coated microspheres have been hindered by rather low optical Q-factors, which have not exceeded the 10⁵ range.³⁰ 

Here, we demonstrate unprecedented control of GVD in silica microspheres coated with alumina (Al₂O₃) while still achieving high Q-factors of 10⁶–10⁷. A smooth alumina layer is obtained using atomic layer deposition (ALD) with nanometer-level thickness control. The optical power handling of the coated microspheres was also preserved and allowed the generation of broadband (250 nm-wide) optical frequency combs. Given the conformal characteristics of the ALD technique, the demonstrated approach could be readily extended to other high-Q resonator geometries and material platforms.

Despite the large index contrast of such microsphere resonators, further insight is possible if we break down total GVD into independent waveguide (geometric) and material dispersion contributions, $β2≈β2(wg)+β2(mat)$⁠, an approximation commonly used in low index contrast waveguides.³² The intuition of such decomposition and the impact of the alumina layer is confirmed in Fig. 1(d), where the total GVD of a microsphere is numerically calculated for three distinct alumina thicknesses (colored solid lines). Increasing from 50 nm to 150 nm-thick alumina layer, the microsphere’s zero-dispersion wavelength can be tuned across ≈200 nm. To confirm that the waveguide contribution (i.e., the surface confinement induced by the alumina’s higher refractive index) is mostly responsible for the observed dispersion tuning, we show corresponding GVD curves where material dispersion of both silica (n = 1.4446) and alumina (n = 1.6171) was neglected. For reference, Fig. 1(d) also includes the material GVD of both alumina (gray solid) and silica (gray dashed-dotted), where it is clear that the zero total GVD position is roughly given by the sum of silica’s and waveguide contributions. As we will discuss later, the role of alumina dispersion is negligible. In Fig. 1(e), we show the usual cavity residual dispersion curves, d_int = ν(μ) − ν₀ − d₁μ, corresponding to the overall dispersion curves of Fig. 1(d). In these polynomial curves, the zero-GVD wavelength manifests as inflection points, while positive (negative) concavity corresponds to anomalous (normal) dispersion. It is worth noting that the GVD curve of a bare silica resonator would be very close to a 50 nm alumina coated one [blue curves in Figs. 1(d) and 1(e)], which are not shown. The details on the numerical simulations are given in 2.B of the supplementary material.

It is thus clear that thin alumina layers can lead to an efficient dispersion control, especially when a reduction of anomalous dispersion is desired, such as in broadband Kerr frequency comb generation^33,34 or higher-order dispersion control.³⁵ It remains elusive, however, whether this technique is indeed more effective than simply controlling the radius of microspheres. We investigate the interplay between these two dispersion control parameters in Figs. 1(f)–1(h), where we focus on the transverse electric (TE) fundamental optical mode. The GVD color map for TE-mode displayed in Fig. 1(f) shows that either parameter is effective to access both normal and anomalous regimes. Actually, GVD varies more uniformly with radius than it varies with alumina thickness, e.g., below t = 80 nm, the GVD slope in Fig. 1(h) is rather flat. However, despite this apparent advantage of radius control, its imprecision level achieved with the thermal fusion technique is often on the order of tens of μm range (see 2.A. of the supplementary material), while the degree of control over alumina thickness is readily available at the nm-level using an ALD process. The alumina coating has the property of minimally affecting the FSR itself; for instance, we verified in our simulations that the FSR is impacted in less than 1% when the alumina thickness increases from zero up to 150 nm. This fine control knob is a key aspect to enable dispersion engineering when coating microresonators.

Despite recent demonstrations of coated microspheres for sensing applications^30,36,37 and GVD control,²⁴ their high optical loss—associated with the sol–gel coating—hinders their usage in the context of nonlinear optics. Here, we fabricated a series of silica microspheres with a high-quality factor (Q ∼ 10⁷) coated with a conformal alumina layer. They were fabricated using an arc-fusion fusion process of a standard optical fiber and coated using an atomic layer deposition technique. A typical microsphere obtained using this technique is shown in Fig. 2(a) (see 2.A of the supplementary material for details). The alumina deposition using atomic layer deposition was performed using the BENEQ TFS 200 tool. The ALD technique ensures nm-level thickness control and conformal covering of the spherical surfaces³⁸ (see 2.B of the supplementary material for details). We directly characterized the microsphere’s surface quality using atomic force microscopy (AFM), as shown in Figs. 2(b) and 2(c). From these representative roughness maps, it is possible to obtain the root-mean-square (rms) roughness σ = 0.4 nm (σ = 4 nm) and correlation length B = 90.6 nm (B = 70.7 nm) for uncoated (alumina-coated) microspheres. Despite the rougher surfaces of the alumina-coated spheres, an analytical scattering-limited quality factor estimate based on a homogeneous sphere model predicts⁵ the roughness-limited Q-factors of 2 × 10⁷ for the coated microsphere, in contrast with 3 × 10⁹ for a pure silica microsphere with the same 250 μm diameter at λ = 1550 nm. It is also worth noting that water adsorption often limits bare silica microsphere quality factors to the 10⁸ level^5,39 (see 2.B of the supplementary material for details).

Another important aspect of nm-thick alumina layers is their thickness-dependent refractive index.⁴⁰ Although this could hinder our dispersion management approach, we verify it to have minimal impact by coating plain silicon wafer pieces simultaneously with each ALD deposition process. These coated pieces were used to perform optical ellipsometry and characterize the alumina layer thickness and refractive index. The refractive index frequency dependence is shown in Fig. 2(d) for four alumina layers with different thicknesses, 48 nm, 73 nm, 88 nm, and 120 nm, as measured by ellipsometry (see 2.B of the supplementary material for details). The material refractive index Sellmeyer’s fittings corresponding to each thickness are shown in Fig. 2(d). Indeed, there is a large variation of material GVD associated with each film, as shown by the colored solid curves of Fig. 2(e). Despite this substantial variation, the alumina material contribution only marginally affects the overall resonator GVD due to the small fraction of optical energy confined to the alumina layer (∼4% according to numerical simulation). We confirm this negligible GVD impact by simulating an alumina coated microsphere with fixed R = 130 μm and t = 60 nm but varying the alumina refractive index dispersion according to the measured curves shown in Fig. 2(d); the total GVD curves for these resonators are so similar that they would visually overlap in the wide vertical scale of Fig. 2(e). We highlight their small differences by subtracting from each total GVD curve the one obtained using the refractive curve of the thinnest (48 nm, blue curve) alumina; the variation is at most ±0.05 ps²/km. Based on the dispersion slope of Fig. 1(d), |∂_λβ₂| ≈ 0.1 ps²/km/nm, and the corresponding zero-GVD wavelength shift is ≈0.5 nm, which confirms that alumina’s GVD thickness dependence can indeed be neglected for the thin layers explored in this work. Yet, it should be accounted for if thicker layers (or shorter wavelengths) are of interest.

Optical transmission spectra of the microspheres were obtained by coupling light using a straight tapered fiber with ≈3 μm waist diameter in contact with the sphere surface near the equator, as schematically represented in Fig. 3(a). We tuned the optical resonances extinctions in the transmission spectra by adjusting the taper radius, which is known to significantly reduce the density of optical mode families appearing in transmission spectra⁴¹ (see 1 of the supplementary material for details). Precise positioning and alignment were achieved using translation stages with 50 nm resolution (Suruga Seiki, KXC06020). In order to accurately measure the Q-factor and the relative frequency of the optical resonances, the transmission of a calibrated fiber-based (Corning SMF28) Mach–Zehnder interferometer [MZI d₁ = 137(10) MHz, d₂ = 0.5(1) Hz] and hydrogen cyanide (HCN) gas cell was recorded along with the microsphere transmission spectra using an oscilloscope with a memory length of 20.5M points per channel (Keysight, 9245). The temporal resolution of the acquired traces enabled the resolution of Q-factors up to 10⁸ across the 150 nm tuning range of our external cavity diode laser (Tunics T100R, 200 kHz linewidth). The calibrated fiber-MZI based measurement was shown to be accurate and reliable.^17,18,42

An excerpt of the transmission spectrum for a 73 nm thick alumina-coated microsphere is shown in Fig. 3(b). Consecutive optical mode groups separated by a free spectral range (FSR ≃ 290 GHz) are excited. Each mode is identified by three integer numbers; the radial order (n), polar number (l), and azimuthal number (m). Due to the equatorial position of the tapered fiber, only modes concentrated around the equator (|m| ≲ l) are visible in the transmission spectrum. Figure 3(c) shows the loaded Q-factor for selected high extinction resonances. A typical 1.2 × 10⁷ loaded Q-factor mode centered at 190.96 THz is shown in Fig. 3(d) along with the reference 137 MHz fiber-MZI trace in Fig. 3(e) (see 2.C of the supplementary material).

In order to extract the cavity GVD parameter (d₂) from the frequency-calibrated transmission spectra, we fitted Eq. (1) (up to d₃) to a frequency vs mode number dataset.¹⁷ By removing the offset (ν₀) and subtracting the linear term (d₁), we obtain the experimental residual dispersion d_int in which only the GVD (d₂) and higher-order terms are relevant. This detailed GVD characterization, combined with accurate one-dimensional (1D) finite element simulations, numerical simulations, allow us to clearly identify distinct radial orders, as shown in Figs. 3(f) and 3(g) for the n = 1 and n = 2 radial orders. While the polar order (l − m) is also discernible in such residual dispersion analysis, their dispersion profile is almost degenerate and is more easily resolved from the expected eccentricity splitting easily identified in the transmission spectrum.⁴³ We emphasize that this technique allows us to be certain about the identification of the n = 1 radial order; otherwise, microsphere modes could be misidentified.

The experimental demonstration of GVD tailoring using different alumina-coating thicknesses is shown in Fig. 4(a), where curves corresponding to the measured residual dispersion (d_int) for alumina thickness ranging from 48 nm to 120 nm are shown; for reference, the residual dispersion of a bare silica microsphere is also included. While both polarizations (TE and TM) experience a consistent reduction in the d₂ value [going from an anomalous (d₂ > 0) to a normal (d₂ < 0) dispersion], TE modes are more sensitive; we actually explored this feature to experimentally distinguish between the two polarization states. Interestingly, near-zero GVD can be obtained, e.g., 73 nm (88 nm) for TE (TM) polarization, confirming that ALD alumina can provide the fine control necessary for GVD control in high-Q microresonators. In these regimes, the influence of the higher-order dispersion parameter becomes progressively more important, and an almost pure third-order dispersion (d₃) contribution can be obtained. Such a degree of control could be readily used for higher-order dispersion engineering.^21,44 The roughness impact of the alumina layer could also be noticed at thicker coatings. In Fig. 4(b), the average loaded quality factor for the fundamental mode across the measured range slightly deteriorates, reaching around 5 × 10⁶ for the 120 nm layer. Although this trend is consistent with the previous reports of rougher surfaces in thicker alumina films,⁴⁵ we believe that further optimization of the deposition process could lead to smoother coatings with potentially lower loss. We also highlight that the measured quality factors for TE and TM polarizations are rather close, with slightly larger values for TM polarization (see Table S4 of the supplementary material). Although this trend has been previously suggested, our data do not provide a statistically significant difference between them.

One important application of GVD engineering within microspheres is the generation of Kerr optical frequency combs. A key aspect when engineering dispersion for broadband comb generation is the control of the ratio of second-order (d₂) to third-order dispersion (d₃). Indeed, cascaded four-wave mixing can phase match at modes distant from the pump wave giving rise to a dispersive wave (DW) emission, and the azimuthal mode number satisfying this criterion is μ_DW = −3d₂/d₃, also known as Cherenkov radiation in the context of mode-lock soliton Kerr combs.⁴⁶  Figures 4(c) and 4(d) show the residual dispersion curve fitted around the pump frequency (ν_p) of an optical frequency (non-soliton) comb generated in the 73 nm thick alumina-coated microsphere (65 mW CW-pump power). Three changes were made to the experimental setup shown in Fig. 3(a) to demonstrate the OFC: (1) an erbium-doped fiber amplifier (EDFA) was used to increase the laser power, (2) a bandpass filter was used to suppress the EDFA residual amplified spontaneous emission, and (3) an optical waveshaper (FINISAR 4000A) was employed to selectively monitor the total comb power within the telecom C-band; a detailed version of the setup is shown in Fig. S12 of the supplementary material. An increase in the comb intensity near 207.6 THz is in good agreement with the residual dispersion zero crossing (d_int = 0) shown in Fig. 4(c). Indeed, around the pump-mode position (ν_c = 193.87 THz), the dispersion parameters are d₂ = 440(10) kHz and d₃ = −24(1) kHz. If we replace these dispersion parameters values for the spectral position of the Cherenkov radiation peak, we find μ_DW = 55. These results suggest that alumina coating can indeed enable the control of higher-order GVD features, such as dispersive-wave emission. Finally, in Figs. 4(e)–4(g), we show that it is possible to identify the optical pump mode generating the comb, despite the dense optical transmission spectrum of the microspheres. By attenuating the input pump power (120 mW) while simultaneously and independently monitoring both the pump transmission and the comb power (using the optical waveshaper; see Fig. S11 of the supplementary material), we gradually move from a strongly bistable to a linear optical transmission spectrum, confirming the fundamental TM mode as the seed of the observed Kerr microcomb. We also observed comb generation in the other microspheres with anomalous GVD around 150 nm (bare silica and 48 nm coating), but they were not captured under the optimum conditions of Fig. 4(d) and could not be directly compared; they are shown in the supplementary material (Fig. S11).

In summary, we experimentally demonstrated ultra-high quality factors in alumina-coated silica microspheres. Using alumina coatings with roughly 100 nm thickness, we could achieve a large degree of GVD control, significantly reducing the degree of anomalous GVD yet not drastically impacting their high Q-factors. Furthermore, the alumina-coated films could sustain the higher optical intensities necessary for the generation of broadband optical frequency combs, which brings a new degree of freedom for dispersion control in the context of nonlinear photonics. A route to tuning of dispersive-wave emission or engineering higher-order dispersion comb generation is clearly opened.^21,35,47,48 Although a single coating layer does not readily generate blue- and red-shifted dispersive waves, the presented technique could be extended with alternating dielectric layers to achieve a larger range of GVD control.⁴⁹ 

See the supplementary material for simulation details and some experimental considerations, discussion and validation, in summary, of the 1D Maxwell eigenproblem solver, details about the fabrication and characterization of the silica microspheres and alumina coating characterization, a detailed discussion of the fiber-MZI calibration, and direct comparison between simulated and measured residual dispersion curves.

The authors acknowledge Dr. Yovanny Valenzuela for his support with numerical simulations, Dr. Sandro Marcelo Rossi for his help in characterizing the MZI fiber dispersion, and the Center for Research and Development in Telecommunications (CPqD) for providing access to their infrastructure. We also acknowledge the MultiUser Laboratory (LAMULT) at IFGW for support in the AFM measurements and the LCPNano at the Federal University of Minas Gerais (UFMG) for the support with the spectroscopic ellipsometer.

This work was supported by the São Paulo Research Foundation (FAPESP) through Grant Nos. 2012/17610-3, 2012/17765-7, 2018/15580-6, 2018/15577-5, 2018/25339-4, and 2018/21311-8, Coordenação de Aperfeiçoamento de Pessoal de Nível Superior—Brasil (CAPES)—Finance Code 001, the National Council for Scientific and Technological Development (CNPq; Grant Nos. 306297/2017-5 and 435260/2018-9), and the National Institute of Surface Engineering (INES/CNPq; Grant No. 465423/2014-0). A.S.F. is a CNPq fellow.