Low-Loss Low Thermo-Optic Coefficient Ta2O5 on Crystal Quartz Planar Optical Waveguides

Optical resonator-based frequency stabilization plays a critical role in ultra-low linewidth laser emission and precision sensing, atom clocks and quantum applications. However, there has been limited success in translating traditional bench-top stabilization cavities to compact on-chip integrated waveguide structures that are compatible with photonic integration. The challenge lies in realizing waveguides that not only deliver low optical loss but that also exhibit a low thermo-optic coefficient and frequency noise stability. Given the problematic sources of frequency noise within dielectrics, such as thermorefractive noise, resonators with small thermo-optic response are desirable for on-chip reference cavities. We report the first demonstration of a Ta2O5 (tantala) waveguide core fabricated on a crystal quartz substrate lower cladding with TEOS-PECVD SiO2 upper cladding. This waveguide offers significant advantages over other waveguides in terms of its low thermo-optic coefficient and reduced thermorefractive-related frequency noise. We describe the waveguide structure and key design parameters as well as fabrication considerations for processing tantala on quartz waveguides. We report a waveguide thermo-optic coefficient of -1.14×10 RIU/K, a value that is over 6 times smaller in magnitude than SiO2-substrate tantala waveguides, with a propagation loss of 1.19 dB/cm at 1550 nm and <1.33 dB/cm across the 1525 nm to 1610 nm wavelength range. Within a 1.6 mm radius ring resonator, we demonstrate a 2.54×10 intrinsic Q factor. With the potential for very low loss and the ability to control the thermal response, this waveguide platform takes a key step towards creating thermally stable integrated resonators for on-chip laser frequency stabilization and other applications.

resonators suffer more severely from the thermodynamic fluctuations [9] due to their small mode volumes and nontrivial thermal sensitivities caused by thermorefractive and thermal expansion effects. While thermal expansion can be controlled by attaching resonators to substrates with zero or negative thermal expansion coefficients [10,11], thermorefractive effects still produce undesired frequency instability within dielectric resonators.
The thermorefractive frequency noise of an integrated reference cavity is directly tied to the waveguide thermo-optic coefficient [12] as well as the optical mode volume [13][14][15]. Through proper waveguide material choice and design, the effective thermo-optic coefficient (TOC eff ) and mode volume can be optimized to reduce the thermorefractive frequency noise components [16]. For this purpose, crystal quartz has attractive optical and thermal properties such as a wide transparency window (0.2 μm to 2 μm), optical birefringence, and a negative thermo-optic coefficient, e.g. -7.94×10 -6 RIU/K (RIU: refractive index unit) at 1550 nm for ordinary waves [17]. Bulk-optic quartz has been used to fabricate high performance whispering-gallery-mode resonators [18,19], but these systems are environmentally sensitive, costly to fabricate and package, and are incompatible with photonic integration. In the past, efforts to realize quartz-based integrated waveguides [20][21][22][23] resulted in propagation loss as high as 10 dB/cm [20,22] and they could not support the waveguide bends required for waveguide ring resonators. Additionally, the negative TOC property of quartz has not been demonstrated in a composite integrated waveguide. As a result, the realization of low-loss integrated waveguides on quartz substrates will enable novel photonic devices with extraordinary thermo-optic properties, opening new possibilities for photonic integrated reference cavities.
In this work we report the first demonstration of Ta 2 O 5 (tantala) core strip waveguides on a crystal quartz substrate with SiO 2 upper cladding. We measure a low propagation loss of 1. 19 dB/cm at 1550 nm wavelength for a 4 μm-wide 125 nm-thick Ta 2 O 5 -core waveguide. With this waveguide design we fabricated a 1.6 mm-radius resonator and measured an intrinsic Q-factor of 2.54×10 5 and a loaded Q-factor of 1.95×10 5 . In addition, we show that the waveguide effective thermo-optic coefficient is -1.14×10 -6 RIU/K, 6 times smaller than a comparison waveguide that has thermal oxide as substrate. The small and negative thermo-optic coefficient demonstrates that using crystal quartz as a waveguide substrate can enable control of the waveguide thermo-optic coefficient with the potential to suppress thermorefractive frequency noise. Combined with other techniques [10,11] to suppress the thermal expansion, this technology promises a new approach to low thermorefractive noise, low-loss waveguide optical reference cavities for frequency precision applications such as low-energy data center interconnects [24] and ultra-narrow-linewidth on-chip stimulated Brillouin lasers [25].

Device design and fabrication
The waveguide design and conceptual figure of a spiral waveguide and a ring resonator are depicted in Fig.1 (a). We use a z-cut crystal quartz substrate (with c-axis normal to the surface) to ensure the refractive index is independent of waveguide direction. A tantala strip core is deposited and etched on a crystal quartz substrate and cladded with a TEOS-PECVD SiO 2 upper cladding as described in the Methods Section. This process is compatible with wafer-scale lowtemperature fabrication. We employ a high-aspect-ratio weakly guiding waveguide geometry similar to those used in ultra-low loss silicon nitride [26] and tantala on oxide substrate designs [27], with its fundamental TE mode shown in Fig. 1(b). Material absorption-induced temperature variations (Fig.1(c)) perturb the optical constants and mechanical expansion, which will translate into frequency noise in resonators when optical power fluctuates. With the objective to suppress the thermorefractive fluctuations, this designed waveguide geometry has a large optical mode overlap with the quartz substrate, yielding a slightly negative but close-tozero TOC eff , which reduces the overall sensitivity of the mode effective index to temperature variations.
This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset. The Ta 2 O 5 -core on crystal quartz waveguides are fabricated in a similar approach as reported in our previous work [27] except without thermal annealing after Ta 2 O 5 film deposition and after TEOS-PECVD SiO 2 upper cladding deposition (see Methods for fabrication details). High temperature thermal annealing was not used in the fabrication process for two reasons: (1) to avoid thermal shock and film peeling caused by the large thermal expansion coefficient mismatch between the crystal quartz substrate (13.2×10 -6 /K perpendicular to the optical axis [28]) and the deposited films (3.6×10 -6 /K for Ta 2 O 5 [29] and 0.56×10 -6 /K for amorphous SiO 2 [30]) and (2) because quartz changes from αto β-phase, with positive thermo-optic coefficient, as the temperature increases beyond 573℃ [31].

Waveguide propagation loss and resonator Q-factors
The waveguide propagation loss is characterized by using both Q factor measurements in a ring-bus resonator and the optical frequency domain reflectometry (OFDR) method in a waveguide spiral structure. All-pass ring resonators are designed with a radius of 1.6 mm and a 0.5 μm ring-bus waveguide coupling gap. The loaded Q factors of the resonances are measured and verified using two different experiment setups, a RF calibrated Mach-Zehnder interferometer (MZI) setup and a direct laser tuning transmission setup (see Methods sections for more details). In the former approach, the full width at half maximum (FWHM) of the resonance is Δ =991.43 MHz obtained through Lorentzian curve fitting ( Fig.2 (b)), giving a loaded Q factor = / =1.95×10 5 at 1550 nm, where is the resonant frequency. The power coupling coefficient is measured to be 8% between the ring and the bus waveguides by using the ring-bus coupling test structures on the same die. Correspondingly, the propagation loss of the waveguide is derived to be 1.18 dB/cm and the intrinsic Q factor is estimated to be 2.54×10 5 (See Methods for propagation loss and intrinsic Q-factor calculation details). In the second Q factor measurement approach, the input wavelength is precisely controlled by a tunable laser source, and the transmitted power is recorded by a photodetector. Fig. 2(a) shows the transmission spectrum of the fundamental TE mode by varying the laser wavelength. The measured free spectral range (FSR) of the resonator is 0.1393 nm, corresponding to 17.37 GHz at 1550 nm. The slight fluctuations of the transmission spectrum are due to the weakly resonant higher order transverse electric mode. The high order TE mode has distinct resonant line shapes (broad resonance and small extinction ratio) from the fundamental TE mode. It has negligible impact on the Lorentzian fitting on the fundamental TE mode resonance, and thus does not affect the characterization of the fundamental TE mode. The FWHM of one resonance is found to be =6.76 pm (equivalent to 842.6 MHz) through Lorentzian curve fitting ( Fig.2 (c)), and the loaded Q factor is = / =2.29×10 5 . Thus, the propagation loss and the intrinsic Q factor are derived to be 0.96 dB/cm and Q inc =3.15×10 5 , respectively. The waveguide propagation loss is also measured by using optical frequency domain reflectometry (OFDR). The tested waveguide is a 4 μm-wide and 0.2 m-long spiral delay line as shown in Fig. 3(b). The spiral delay line has a minimum bend radius of 800 μm, well above the critical bend radius of 320 μm at which the bending loss is simulated to be 1 dB/m. The measured propagation loss from the OFDR experiment is 1.19 dB/cm at 1550 nm and is lower than 1.33 dB/cm across the 1525 nm to 1610 nm spectrum range shown in Fig.3(a). Waveguide propagation losses measured using OFDR and derived from the MZI-based Q-factor measurements agree well with less than 0.9% difference. The experiment details can be found in Methods.
This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

Effective thermo-optic coefficient
The crystal quartz substrate enables adjustment of the TOC eff of the optical mode. To obtain the thermo-optic coefficient of the waveguide, we measured the transmission spectrum of the resonator and tracked its resonance at different temperatures (see Fig. 4 where the second term on the right-hand side of Eq. (2),(1/ )( / ), is the effective linear thermal expansion coefficient. To quantify the impact of the thermal expansion and the thermorefractive effects within the waveguide, we use finite-element-method (FEM) models (COMSOL Multiphysics) based on the mechanical, optical, and thermal parameters taken from our measurements as well as values reported in the literature (see supplementary information for simulation model details). Fig. 4(b) shows the simulated resonant wavelengths of a 4 μmwide resonator caused by the thermal expansion (TE) effect, the thermorefractive (TR) effect, and a combination of both (TE+TR). The measured resonant wavelengths in Fig. 4(a) is also added for comparison, demonstrating a good correlation between the simulation and the experiment results. By comparing the slope of the curve, one can find that thermal expansion is the dominant effect in the total temperature dependent wavelength shift. The thermorefractive curve exhibits a negative slope of -1.139 pm/K, from which the TOC eff of the 4 μm-wide waveguide is calculated to be -1.14×10 -6 RIU/K. To illustrate the validity of the models, we also measure and extract the effective thermo-optic coefficient of a Ta 2 O 5 -core thermal oxidesubstrate waveguide. The oxide-substrate waveguide has the same waveguide design and fabrication process except its substrate is thermal oxide that has a positive thermo-optic coefficient (~9.8×10 -6 RIU/K [32]). The waveguide loss is measured to be 0.276 dB/cm and its This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

PLEASE CITE THIS ARTICLE AS DOI:10.1063/5.0024743
loaded Q factor is 0.945×10 6 (see supplementary information). The temperature-dependent transmission spectrum of a 4 μm-wide, 1.6 mm-radius ring resonator is shown in Fig. 4(c).
Owing to a larger core/substrate refractive index contrast (~2/1.45 for thermal oxide-substrate waveguides vs. ~2/1.53 for crystal quartz-substrate waveguides), a higher order optical mode was observed during the measurement with appearance of second resonance in the transmission spectrum shown in the gray highlighted region in Fig.4 (c). We measured the resonance shift of the fundamental mode that has a larger extinction ratio in the green highlighted region in Fig. 4(c). The measured resonant wavelengths are plotted as the scatter points in Fig. 4(d). The TDWS is linearly fitted to be 10.96 pm/K, among which the thermorefractive contribution is 7.42 pm/K. The TOC eff of the oxide-substrate waveguide is derived to be 7.28×10 -6 RIU/K, over 6 times larger than that of the quartz-substrate waveguide in magnitude. The negative and small TOC eff of quartz-substrate waveguide illustrates that crystal quartz can be used to adjust the waveguide thermo-optic coefficient, which may enable thermorefractive noise engineering. Through proper design of the waveguide geometry, the mode overlap with the quartz substrate can be manipulated, and thus the TOC eff of the optical modes can be adjusted to be close-tozero and in-turn the thermorefractive noise of the optical modes will be suppressed as it scales with the square of the TOC eff [9]. This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

PLEASE CITE THIS ARTICLE AS DOI:10.1063/5.0024743
For optical reference cavities, it is desirable to have high Q factors and small thermal noise. In the absence of the cavity's own noise sources, the rms frequency difference of a locked laser relative to the cavity resonance is inversely proportional to its optical Q factors [8]. Thus, high Q cavities enable tight frequency locking and stabilization. The resonator's loaded Q factor is bounded by its intrinsic Q factor, and the intrinsic Q factor is determined by the waveguide propagation loss αw, which includes waveguide surface roughness scattering loss, material bulk absorption loss and waveguide surface absorption loss [33]. Given a high enough Q factor, the stability of the laser frequency is determined by the thermodynamic fluctuations of the cavity resonance that come from thermorefractive and thermal expansion effects. The thermorefractive-related frequency noises are proportional to 2 [9][10][11], where = (1⁄ )( ⁄ ) is the thermorefractive coefficient. Since this study focuses on lowering the thermo-optic coefficient, we define a figure of merit (FOM) to compare the performance of our Ta  (3) where α w is the waveguide propagation loss. This FOM does not take the resonator design into consideration, but only compares waveguide propagation loss and thermo-optic properties among different waveguide platforms. A lower FOM is preferred, meaning tighter frequency locking and smaller thermorefractive-related frequency noise when locked. Table 1 summarizes a few representative designs with respect to this FOM. Our Ta 2 O 5 on quartz resonator outperforms TiO 2 -and polymer-based thermo-engineered resonators. It features a lower FOM than Si 3 N 4 on oxide resonator [12] but not as low as the silica resonator reported in [8] because the silica resonator has ultra-low loss. To further improve the performance of our Ta 2 O 5 on quartz resonator, the waveguide loss needs to be reduced, which will be discussed in the next section. * lower is better.

Discussion and conclusion
In conclusion, we report fabrication and characterization of the first demonstrated Ta 2 O 5core/crystal quartz-substrate waveguides. Low waveguide propagation losses are measured to be 1.19 dB/cm at 1550 nm and lower than 1.33 dB/cm across the 1525 nm to 1610 nm range using the OFDR method, agreeing well with the loss derived from the Q measurement. The loaded Q factors measured from two different setups correlate reasonably well with slight differences that may come from measurement variations. The thermo-optic coefficient of the waveguide is -1.14×10 -6 RIU/K. The platform can be useful to frequency precision applications such as integrated optical reference cavities and optical frequency combs where the close-tozero waveguide thermorefractive coefficient can help mitigate the thermally induced frequency noise in these cavities.
This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

PLEASE CITE THIS ARTICLE AS DOI:10.1063/5.0024743
While the losses in these quartz-substrate waveguides are slightly better than previously reported Ta 2 O 5 waveguides [37], it may be possible to further reduce propagation loss if material absorption can be mitigated. The main contribution of the propagation loss come from the material absorption in the core and upper cladding region. The bottom substrate quartz has low material absorption at 1550 nm since quartz-based whispering-gallery-mode resonators can achieve billion Q factors [18]. The Rayleigh scattering loss is expected to be small and should not be the dominant factor, because the measured sidewall roughness, 2.76 nm rms (see supplementary information), is close to the previously demonstrated ultra-low-loss Ta 2 O 5 waveguides [27] which achieved 3 dB/m performance. Thermal annealing was not applied on the quartz-substrate devices, thus significant absorption loss can happen due to the presence of SiO-H bonds in SiO 2 cladding and oxygen deficiency in the as-grown Ta 2 O 5 films [37]. In fact, the Ta 2 O 5 on thermal oxide resonator, whose transmission spectrum are shown in Fig. 4(c), was annealed after SiO 2 cladding deposition following the same procedure in Ref. [27], and it has a loaded Q factor as high as 0.945×10 6 and an intrinsic Q of 1.07×10 6 . The propagation loss of the oxide-substrate waveguide is 0.276 dB/cm (see supplementary information), 4.34 times smaller than that of the quartz-substrate waveguide, indicating the significant impact from annealing process. The material absorption loss from the top cladding can also be possibly mitigated by using deuterated SiO 2 in a low-temperature deposition method [38].
It is worth noting that the TDWS of the quartz-substrate resonator is larger than that of the oxide-substrate device since crystal quartz has a large thermal expansion coefficient (α o =13.2×10 -6 /K). With thermorefractive effect suppressed in the quartz-substrate resonator, thermal expansion becomes the dominant effect as indicated by Fig. 4(b). To create temperature insensitive optical cavities, both the thermal expansion [39] and thermorefractive effects must be controlled. To mitigate the thermal expansion effect, a thinner Ta 2 O 5 -core waveguide can be designed in favor of a larger mode overlap with the quartz substrate, yielding a more negative TOC eff to compensate the positive thermal expansion coefficient. The demonstrated device has 500 µm-thick quartz bottom cladding and 6 µm-thick SiO 2 upper cladding. Considering the majority mass of the waveguide is from the quartz, it is not surprising that the thermal expansion effect is dominated by the substrate. To further suppress the thermal expansion effect, the quartz layer can be thinned and bonded to an ultra-low-expansion substrate, which will be the subject of future study.

Supplementary Material
Details of the waveguide sidewall roughness, simulation models and material properties, Ta 2 O 5 on oxide substrate waveguide loss and resonator Q factors, RF calibrated MZI setup to measure Q factors, can be found in the supplementary information.
Fabrication methods. Fabrication of the waveguide starts with sputtering amorphous Ta 2 O 5 film on 0.5 mm-thick, 100 mm-diameter single-side polished z-cut optical-grade crystal quartz wafers. The film thickness is measured to be ~125 nm after deposition. The waveguide structures are patterned using a photoresist mask by a 248 nm ASML stepper lithography tool followed by inductively coupled plasma etching. The etching recipe uses CHF 3 /CF 4 /O 2 gas flow of 25/5/10 sccm, accompanied by a pressure of 0.5 Pa, with a RF source power of 500 W and a RF bias power of 50 W. The photoresist is stripped by O 2 ashing followed by n-methyl-2-pyrrolidone solvent soaking with ultrasonic heat bath and piranha cleaning. A layer of 6 μm TEOS-PECVD SiO 2 is deposited as the upper cladding on the etched wafer. The wafer then undergoes dicing into several die for experiment characterization. Q-factor measurement using a RF calibrated MZI setup. An unbalanced fiberbased MZI was used as a reference frequency spectrum to accurately measure the resonator Q [40]. The free spectral range of the MZI is pre-calibrated to be 5.87 MHz. A tunable laser is connected to both the MZI and the device under test (DUT). The laser frequency was swept in time using a microwave synthesizer and the interferometer FSR was measured by monitoring the transmitted power on a synchronized oscilloscope. By simultaneously scanning the laser frequency through both the MZI and the DUT, the MZI fringe spacing provides a radiofrequency calibrated frequency reference for accurate evaluation of resonator Q factors. The FWHM of the resonator is estimated by fitting the resonator transmission spectrum to a Lorentzian curve. A more detailed discussion and a setup figure can be found in the supplementary information.
Q-factor measurement using direct laser tuning transmission setup. A tunable laser (HP81640A) with a built-in wavelength sweeping functionality is connected to the device under test, and the transmitted power is measured by the power meter (HP81532A). An automation program written in Python controls the laser wavelength with 0.1 pm resolution and synchronizes the power injection and collection process.
where n g is the group index of the waveguide and is derived to be 1.7168 from the measured FSR of the resonator shown in Fig.2 (a), = 2 is the perimeter of the ring resonator and R = 1.6 mm is the radius of the ring, is the resonant wavelength, = √(1 − 2 )is the selfcoupling coefficient where k 2 = 0.08 is the measured power coupling coefficient, a is the singlepass amplitude transmission and is related to the power attenuation coefficient [1/m] as 2 = (− ). With the derived propagation loss, the intrinsic Q of the resonator is estimated to be by the following equation [42], Waveguide loss measurement using OFDR methods. An optical backscatter reflectometer (Luna OBR 4400) injects a pulse that contains a wide spectral range (1525 nm -1610 nm) into the waveguide under test. The reflected signal is collected to map the discontinuities with micron-level spatial resolution along the optical path as shown in the inset of Fig. 3(a). The propagation loss spectrum is obtained by analyzing the backscattered signal in the black region through linear curve fitting at each wavelength, which gives the propagation loss spectrum regardless of the fiber-to-chip coupling loss.