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Low-loss tantalum pentoxide photonics with a CMOS-compatible process

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Abstract

We report a Ta2O5 photonic platform with a propagation loss of 0.49 dB/cm at 1550 nm, of 0.86 dB/cm at 780 nm, and of 3.76 dB/cm at 2000 nm. The thermal bistability measurement is conducted in the entire C-band for the first time to reveal the absorption loss of Ta2O5 waveguides, offering guidelines for further reduction of the waveguide loss. We also characterize the Ta2O5 waveguide temperature response, which shows favorable thermal stability. The fabrication process temperature is below 350°C, which is friendly to integration with active optoelectronic components.

© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

1. Introduction

Over the past two decades, integrated photonics has witnessed remarkable progress, owing to its ability to capitalize on mainstream microelectronic processing technology. Complementary metal-oxide-semiconductor (CMOS) manufacturing processes and materials have facilitated the development of integrated photonics towards wafer-scale and high-density production, akin to electronics. Among the numerous promising silicon-compatible materials in photonic research, tantalum pentoxide (Ta2O5) has garnered attention due to its excellent optical properties for linear and nonlinear optics [1,2]: a broad transparency range spanning from visible to infrared (300-8000 nm), a moderately high nonlinear refractive index (7.2 × 10−19 m2/W) [3], which is three times larger than silicon nitride (2.4 × 10−19 m2/W) [4], and a low thermo-optic coefficient (2.3 × 10−6 /K) [5] which is an order of magnitude smaller than silicon nitride (2.5 × 10−5 /K) [6]. In addition, Ta2O5 is compatible with CMOS processes [7,8] making it promising for heterogeneous electronic photonic integration. These excellent properties render the Ta2O5 integrated photonic platform suitable for several application fields, such as quantum computing [9], nonlinear optics [2,10,11], free-space beams [12] and rare earth ion doped waveguide lasers [13].

In this work, we present a CMOS-compatible and low-loss Ta2O5 integrated photonic platform using a wafer-scale low-temperature process. We commence with a detailed fabrication process, where the maximum temperature is below 350°C, reducing the thermal budget and making it electronics-friendly. We then measure a loaded Q factor of 4.2 × 105 from a 2 mm radius Ta2O5 micro-ring resonator at 1550 nm, corresponding to a propagation loss of 0.49 dB/cm. The results correlate well with the measurements from spiral waveguides using the cut-back method. To further explore the loss origins, we conduct the thermal bistability measurements on the Ta2O5 photonic platform in the entire C-band for the first time, to the best of the authors’ knowledge, revealing that the absorption loss is dominant. In addition, we characterized the waveguide propagation loss in visible and infrared wavelengths, which opens possibilities for potential applications in quantum photonics and spectroscopy. The waveguide temperature sensitivity is also reported, demonstrating the superior thermal stability of Ta2O5.

2. Fabrication

Figure 1(a) presents the cross-section of the fabricated waveguide. The waveguide core has a nominal width of 2.8 µm and a height of 90 nm, which ensures single TE mode operation in the C-band (Fig. 1(b), inset). The entire fabrication process starts with a 4-inch silicon substrate with a 5-µm-thick wet thermal oxide. A 90-nm-thick Ta2O5 film is commercially deposited on the substrate (FiveNine Optics). Then, a 1.2-µm-thick photoresist (RZJ304.10) is spun on the Ta2O5 film and is exposed by an ultraviolet contact lithography machine (Karl SUSS MA6). The exposed photoresist is developed in an alkaline developer (RZX3038) followed by the hard baking. The hard baking is utilized by placing the wafer on a hotplate which is already set at 120°C. The time and temperature (90 s, 120°C, marked with a blue star in Fig. 1(c)) for hard baking are carefully chosen to harden the photoresist and to smoothen the photoresist sidewalls in the meantime, thus reducing the scattering loss of the final Ta2O5 waveguide [14]. Figure 1(c) illustrates the scanning electron microscope (SEM) images of different time of hard baking the photoresist at the temperature of 120°C. One can see that as the hard baking time increases, the photoresist reflows and its sidewall surfaces become smooth. However, over-baking ($\ge $150 s) leads to photoresist being stretched laterally, thinning the thickness of the photoresist which weakens its protection capability during the dry etching step. The dry etching is performed in an inductively coupled plasma (ICP) etcher to transfer the waveguide patterns from the photoresist mask to the Ta2O5 layer. The ICP etcher has CHF3/O2 gas flows of 50/5 sccm, a pressure of 5 mTorr, a RF source power of 150 W, and a RF bias power of 50 W. The geometry of the etched waveguide core is similar to that of the processed photoresist. The remaining photoresist is then stripped by O2 ashing followed by n-methyl-2-pyrrolidone (NMP) soaking. Figure 1(d) shows top-view atomic force microscopy (AFM) measurement of an etched waveguide. The line edge roughness is extracted to be σ = 2.7 nm (Fig. 1(e)) with an autocorrection length exponentially fitted to be Lc = 124 nm (Fig. 1(f)). Finally, a 5-µm-thick SiO2 upper cladding is deposited using 350°C plasma enhanced chemical vapor deposition (PECVD). PECVD deposition method is chosen in this work because of its fast deposition capability at relatively lower temperature, which enables thick cladding deposition upon the waveguides and better protection. A 5-µm-thick thermal oxide as the lower cladding and a 5-µm-thick PECVD oxide as the upper cladding are sufficient to guide the optical wave and prevent the wave leakage to the Si substrate. The process steps mentioned above are operated below 350°C and are compatible with CMOS electronics.

 figure: Fig. 1.

Fig. 1. (a) The schematics of the cross-section of the fabricated waveguide. (b) SEM image of the cross-section of the fabricated waveguide. The inset shows the TE00 mode profile. (c) SEM images of patterned photoresist with different hard baking time. (d) The 2D AFM image of an etched Ta2O5 waveguide sidewall. (e) The waveguide sidewall edge is extracted from an AFM measurement. The roughness of the sidewall is calculated to be σ = 2.7 nm. (f) The autocorrelation length Lc of the sidewall roughness using exponential fitting.

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3. Characterization

3.1 Waveguide propagation loss and ring resonator quality factor

The waveguide propagation loss is characterized by two methods, the Q measurement on ring resonators as well as the cut-back measurement on spiral waveguides and straight waveguides. The schematic of the experimental setup for Q measurement and cut-back measurement is shown in Fig. 2(a) and Fig. 3(a). The Q measurement on ring resonators is performed using an Keysight 8164A Lightwave Measurement System, including an Keysight 81680A tunable laser and an Keysight 81635A power sensor. A program written in Python controls the laser wavelength sweeping with a resolution of 0.1 pm while synchronously makes the power sensor receive the power. An all-pass ring resonator with a 2 mm radius and a 1.25 µm ring-bus waveguide coupling gap is measured to obtain the transmission spectrum. The measured transmission spectra are fitted with Lorentzian curves to extract the loaded Q factors, as shown in Fig. 2(b) and (d). At 1550 nm, the free spectral range (FSR) is 0.1199 nm, corresponding to a group index of ng = 1.595. The full width at half maximum (FWHM) of one resonance (Fig. 2(c)) is fitted to be Δλ = 3.69 pm, yielding a loaded Q factor to be Ql = λresλ = 4.2 × 105. The propagation loss and the intrinsic Q factor are derived to be 0.49 dB/cm and Qi = 5.7 × 105, respectively. The loss at 1572 nm is slightly less than that at 1550 nm. At 1572 nm, the FSR is 0.1253 nm, corresponding to a group index of 1.569. The FWHM of one resonance (Fig. 2(e)) is fitted to be Δλ = 3.42 pm, yielding a loaded Q factor to be Ql = λresλ = 4.6 × 105. The propagation loss and the intrinsic Q factor are thus derived to be 0.39 dB/cm and Qi = 7.0 × 105, respectively. The spectral scan at 1572 nm suggests this resonance is nearly at critical coupling. For resonators with bending radii less than 0.5 mm (Fig. 2(f)), we observe a sharp increase in the propagation loss as the radius becomes smaller. The critical bending radius of the waveguide at 1550 nm is estimated to be 0.35 mm as illustrated in Fig. 2(g). Therefore, the bending loss is assumed to be negligible for the purposes of the treatment here.

 figure: Fig. 2.

Fig. 2. (a) The schematic of the experimental setup for Q measurement. (b) The transmission spectrum of a 2 mm radius all-pass ring resonator in the spectral range from 1549.5 nm to 1550.5 nm reveals the TE mode operation only. (c) The Lorentzian fit to the resonance circled in (b) shows a loaded Q factor of 4.2 × 105 and an intrinsic Q factor of 5.7 × 105. (d) The transmission spectrum of the same ring resonator in the spectral range from 1571 nm to 1572 nm reveals the TE mode operation only. (e) Lorentzian fit to the resonance circled in (d) shows a loaded Q factor of 4.6 × 105 and an intrinsic Q factor of 7.0 × 105. (f) Optical microscope image of a ring resonator. (g) The loss as a function of ring radius.

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 figure: Fig. 3.

Fig. 3. (a) The schematic of the experimental setup for cut-back method. (b) The loaded Q factor and propagation loss as a function of wavelength in a range from 1460 nm to 1580 nm. (c) Relationship between the waveguide length (L) and the insertion loss (IL) for Ta2O5 spiral waveguides at 1550 nm. The inset shows the layout of the spiral waveguides.

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The propagation loss and the loaded Q factor in a 2 mm radius ring resonator exhibit wavelength dependency as shown in Fig. 3(b). The propagation loss is above 1 dB/cm when the wavelength is shorter than 1500 nm, but decreases as the wavelength increases, and reaches down to 0.39 dB/cm at 1572 nm. The loaded Q factor shows the opposite trend as expected. This trend is due to the hydrogen absorption in the PECVD SiO2 cladding around 1380 nm [15]. We also conduct cut-back experiments on spiral waveguides to validate the propagation loss. The 1550 nm continuous-wave (CW) laser (Keysight 81680A) is coupled into and out of the waveguide through the lensed fibers. The polarization of the laser is adjusted by the polarization controller (PC) to facilitate maximum coupling. For each waveguide length, the insertion loss of the spiral waveguide is measured three times and the maximum variation per measurement is below 0.2 dB. The averaged insertion losses are linearly fitted with respect to the waveguide length shown in Fig. 3(c). The propagation loss is extracted to be 0.66 ± 0.01 dB/cm from the slope. The intercept on the y-axis indicates that the coupling loss is 2.91 ± 0.25 dB/facet. The slight difference in the propagation loss between the Q measurements and cut-back measurements may arise from the nonuniformity of the PECVD SiO2 cladding and systematic measurement errors.

3.2 Thermal response

We characterize the waveguide temperature sensitivity by tracking the ring resonator’s resonance at different temperatures (Fig. 4(a)), extracting a temperature dependent wavelength shift (TDWS) to be 9.69 pm/K. The TDWS can be attributed to both the thermal expansion (TE) effect and the thermorefractive (TR) effect according to Eq. (1) [16]:

$$\frac{{d{\lambda _{\textrm{res}}}}}{{dT}} = \frac{{{\lambda _{\textrm{res}}}}}{{{n_{\textrm{eff}}}}}\frac{{d{n_{\textrm{eff}}}}}{{dT}} + \frac{{{\lambda _{\textrm{res}}}}}{R}\frac{{dR}}{{dT}}$$
where $\frac{{d{n_{\textrm{eff}}}}}{{dT}}$ is the effective thermo-optic coefficient (TOCeff); $\frac{1}{R}\frac{{dR}}{{dT}}$ is the effective linear thermal expansion coefficient. The first term on the right-hand side of Eq. (1), $\frac{{{\lambda _{\textrm{res}}}}}{{{n_{\textrm{eff}}}}}\frac{{d{n_{\textrm{eff}}}}}{{dT}}$, represents the thermorefractive effect; the second term on the right-hand side of Eq. (1), $\frac{{{\lambda _{\textrm{res}}}}}{R}\frac{{dR}}{{dT}}$, represents the thermal expansion effect. To quantify the impact of the thermal expansion effect and the thermorefractive effect, we build a finite-element-method (FEM) model that involves optical, thermal and mechanical physics. The parameters used in the simulation are based on our measurements as well as the values reported in the literature. The measured and simulated results are shown in Fig. 4(b). The experimental results and simulation show a good correlation under the circumstance of considering both thermal expansion effect and thermorefractive effect. Through the scrutiny of the slope of the curve, one can note that the thermorefractive effect is the dominant factor for the temperature dependent wavelength shift. The contribution of the thermorefractive effect to the TDWS is 8.73 pm/K. The TOC of the Ta2O5 material is extracted to be 2.3 × 10−6 /K [17].

 figure: Fig. 4.

Fig. 4. (a) The temperature-dependent transmission spectrum of a 2 mm radius ring resonator. (b) The simulated and measured center resonant wavelengths as a function of temperature.

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3.3 Propagation loss analysis

To analyze the loss origins, we perform thermal bistability measurements [1820] on this resonator. A portion of optical power coupled into the resonator is absorbed and converted into heat, which results in an increment of intracavity temperature and correspondingly a redshift of the resonant wavelength. To quantify the absorption fraction ξ, we measured the power- dependent transmission spectra of the same Ta2O5 resonator, as shown in Fig. 5(a). The power annotated in the figure labels the dropped power ${P_\textrm{d}}$, defined as ${P_\textrm{d}} = {P_{\textrm{in}}}({1 - {T_{\textrm{res}}}} )$, where ${P_{\textrm{in}}}$ is the power in the bus waveguide, ${T_{\textrm{res}}}$ is transmission at the resonance wavelength. It is noted that the transmission spectra at all power levels have the same extinction ratio, indicating that no extra power-dependent loss is present in the Ta2O5 resonators. The absorption fraction ξ can be derived from the Eq. (2),

$$\Delta {f_{\textrm{res}}} = \beta {R_{\textrm{th}}}{P_{\textrm{abs}}} = \beta {R_{\textrm{th}}}\xi {P_\textrm{d}} = {\chi _{\textrm{th}}}{P_\textrm{d}}$$
where $\Delta {f_{\textrm{res}}}$ is the resonance frequency shift, β is the temperature dependent frequency shift, ${R_{\textrm{th}}}$= 28.3 K/W is the thermal resistance obtained from a FEM simulator, ${P_{\textrm{abs}}}$ is the absorbed power, ${\chi _{\textrm{th}}}$ is the thermal susceptibility. Through a linear relationship between the resonance frequency shift $\Delta {f_{\textrm{res}}}$ and the dropped power ${P_\textrm{d}}$, as illustrated in Fig. 5(b), the thermal susceptibility is derived to be 23.27 MHz/mW. With $\beta $ derived from TDWS to be 1.1651 GHz/K, the fraction of the absorbed power is estimated to be 70% at 1550 nm, revealing that a significant amount of optical power is dissipated through material absorption. We conduct the measurements in the entire C-band. The thermal susceptibility as a function of wavelength is depicted in Fig. 5(c). The propagation loss stemmed from material absorption and radiation (non-absorption) in the C-band are decomposed in Fig. 5(e). The absorption-induced propagation loss gets reduced as the wavelength increases, leading to a lower total propagation loss. Based on the measured line edge roughness σ = 2.7 nm and Lc = 124 nm from Section 2, we estimate the scattering loss from the waveguide sidewalls is 1.3 dB/m using the Payne-Lacey Model [21,22], confirming that the scattering loss is less dominant than the absorption loss. The thermal bistability measurements offer important guidance to further reducing the propagation loss, substituting the current materials with lower-absorption materials. For example, the PECVD oxide could be replaced by the sputtered SiO2 [1], the thermal SiO2 (through wafer bonding) [23], the deuterated SiO2 [15] or the SiCl4 based SiO2 [24], to further reduce the total propagation loss down to 0.1 dB/cm. The aforementioned methods do not rely on high-temperature annealing and, concurrently, avoid notorious hydrogen absorption.

 figure: Fig. 5.

Fig. 5. (a) The skewed resonance measured under different power. The power indicated in the figure denotes the dropped power. (b) A linear relation between the resonance frequency shift and the dropped power is measured from (a). (c) The derived thermal susceptibility in the C-band. (d) The simulated heat distribution of the Ta2O5 waveguide. (e) The total and the absorption propagation loss measurement in C-band for the resonator mentioned above.

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3.4 Propagation loss at 780 nm and 2000 nm

We further characterize the waveguide propagation losses at 780 nm and 2000 nm to uncover its potential usages. We measure the insertion loss at 780 nm on the spiral waveguides and straight waveguides with different lengths. A 780 nm continuous-wave laser (TOPTICA DLPRO780) is coupled into and out of the waveguide through the lensed fibers. The polarization of the laser is adjusted by the polarization controller to facilitate maximum coupling. As illustrated in Fig. 6(a), the propagation loss at 780 nm is measured to be 0.86 ± 0.02 dB/cm on the Ta2O5 waveguides using the cut-back method. For each waveguide length, the insertion loss of the spiral waveguide is measured three times and the maximum variation per measurement is below 1.1 dB. The intercept on the y-axis indicates that the coupling loss is 8.54 ± 0.31 dB/facet. The increased coupling loss compared to that at 1550 nm can be attributed to the larger mode mismatch between the lensed fiber and the waveguide.

 figure: Fig. 6.

Fig. 6. (a) The relationship between the waveguide length (L) and the insertion loss (IL) for Ta2O5 spiral waveguides at 780 nm. (b) The relationship between the waveguide length (L) and the insertion loss (IL) for Ta2O5 spiral waveguides at 2000 nm. (c) The Lorentzian fit to the resonance shows a loaded Q factor of 3.3 × 104 and an intrinsic Q factor of 3.7 × 104 at 2000 nm. (d) The summary of the loss performance of the several material photonic platforms which utilize low-temperature process.

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We conduct similar experiments at 2000 nm wavelength using the cut-back method. As illustrated in Fig. 6(b), the propagation loss at 2000 nm is extracted to be 3.76 ± 0.01 dB/cm using linear curve fitting. The intercept on the y-axis indicates that the coupling loss is 2.6 ± 0.03 dB/facet. For each waveguide length, the insertion loss of the spiral waveguide is measured three times and the maximum variation per measurement is below 0.16 dB. We also deduce the propagation loss at 2000 nm to be 5.6 dB/cm by measuring the quality factor of the Ta2O5 ring resonator using a broadband light source and an optical spectrum analyzer (Yokogawa AQ6375B). The FWHM of the resonance (Fig. 6(c)) is fitted to be Δλ = 60.99 pm, yielding a loaded Q factor to be Ql = λresλ = 3.3 × 104. The intrinsic Q factor is derived to be Qi = 3.7 × 104. Interestingly, the propagation loss extracted through the Q measurement is slightly larger than that measured through the cut-back method. The difference may be attributed to the nonuniformity of the fabrication process across the whole wafer on which the waveguides and the ring resonators are located apart. The largely increased propagation loss compared to that at 1550 nm and 780 nm may result from the increased absorption by SiO2 cladding at longer wavelengths [25].

Figure 6(d) summaries the loss of several material photonic platforms which utilize low-temperature process [1,2634], including silicon nitride (SiN), titanium dioxide (TiO), and tantalum pentoxide (TaO). With the limited thermal budget, we achieve a Ta2O5 photonic platform whose propagation loss is comparable to that of the low-temperature Si3N4 photonic platform. In addition to similar waveguiding capability (the refractive index of Ta2O5 at 1550 nm is nearly the same as Si3N4, ∼2.05), Ta2O5 possesses better thermal stability, larger nonlinearity, and is less vulnerable to stress issues compared to Si3N4, demonstrating the great potential to unlocking a wide array of linear and nonlinear photonic components, seamlessly integrating them with existing photonic platforms and integrated circuits to revolutionize the future of communication, computing, and sensing technologies.

4. Conclusion

In conclusion, our work presents a CMOS-compatible, low-loss, and thermally-stable Ta2O5 integrated photonic platform achieved through a low-temperature fabrication process without the need for advanced lithographic tools. This fabrication process lends itself well to heterogeneous integration with active electronic components, allowing for the realization of powerful on-chip optoelectronic devices. Additionally, our study includes an examination of the material absorption fraction of Ta2O5 waveguides, representing, to the best of the authors’ knowledge, the first such investigation in Ta2O5 photonic platform across the entire C-band. We identify the path to further reduction of waveguide propagation loss by addressing the issue of material absorption in the oxide cladding, which could have great potentials for power delivery and high-Q resonance applications. Furthermore, the low loss and superior thermal stability of Ta2O5 waveguides open up potential applications in the development of on-chip narrow-linewidth lasers [35]. Loss measurements in the visible and infrared wavelengths are also presented, which could fertilize wider applications in quantum photonics and sensing applications.

Although the study is conducted on thin-core waveguides, the results can also benefit development of thick-core photonic devices which enable tight mode confinement and anomalous dispersion. The propagation loss of thick waveguides is expected to be lower using the demonstrated fabrication process, since more optical power is confined in the Ta2O5 core region which is hydrogen-free rather than the cladding region that could be contaminated by hydrogen bonds. It has been proved that an air-cladded thick-core Ta2O5 waveguide can have a propagation loss as low as 8 dB/m [2]. The potential of low propagation loss, together with large third-order nonlinearity and cracking-free deposition capability, renders the thick Ta2O5 platforms ideal for nonlinear photonic applications.

Funding

National Natural Science Foundation of China (62205137); Guangdong Provincial Quantum Science Strategic Initiative (GDZX2304009); Basic and Applied Basic Research Foundation of Guangdong Province (2021B1515120074, 2023A1515012141); Wuhan National Laboratory for Optoelectronics (2021WNLOKF001); Shenzhen NSQKJJ (K23799109); State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, China(2024GZKF003).

Acknowledgment

The authors acknowledge the assistance of SUSTech Core Research Facilities. The authors would like to thank Dr. Yi Li from the Southern University of Science and Technology for providing the TOPTICA DLPRO780 laser.

Disclosures

The authors declare that there are no conflicts of interest related to this article.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (6)

Fig. 1.
Fig. 1. (a) The schematics of the cross-section of the fabricated waveguide. (b) SEM image of the cross-section of the fabricated waveguide. The inset shows the TE00 mode profile. (c) SEM images of patterned photoresist with different hard baking time. (d) The 2D AFM image of an etched Ta2O5 waveguide sidewall. (e) The waveguide sidewall edge is extracted from an AFM measurement. The roughness of the sidewall is calculated to be σ = 2.7 nm. (f) The autocorrelation length Lc of the sidewall roughness using exponential fitting.
Fig. 2.
Fig. 2. (a) The schematic of the experimental setup for Q measurement. (b) The transmission spectrum of a 2 mm radius all-pass ring resonator in the spectral range from 1549.5 nm to 1550.5 nm reveals the TE mode operation only. (c) The Lorentzian fit to the resonance circled in (b) shows a loaded Q factor of 4.2 × 105 and an intrinsic Q factor of 5.7 × 105. (d) The transmission spectrum of the same ring resonator in the spectral range from 1571 nm to 1572 nm reveals the TE mode operation only. (e) Lorentzian fit to the resonance circled in (d) shows a loaded Q factor of 4.6 × 105 and an intrinsic Q factor of 7.0 × 105. (f) Optical microscope image of a ring resonator. (g) The loss as a function of ring radius.
Fig. 3.
Fig. 3. (a) The schematic of the experimental setup for cut-back method. (b) The loaded Q factor and propagation loss as a function of wavelength in a range from 1460 nm to 1580 nm. (c) Relationship between the waveguide length (L) and the insertion loss (IL) for Ta2O5 spiral waveguides at 1550 nm. The inset shows the layout of the spiral waveguides.
Fig. 4.
Fig. 4. (a) The temperature-dependent transmission spectrum of a 2 mm radius ring resonator. (b) The simulated and measured center resonant wavelengths as a function of temperature.
Fig. 5.
Fig. 5. (a) The skewed resonance measured under different power. The power indicated in the figure denotes the dropped power. (b) A linear relation between the resonance frequency shift and the dropped power is measured from (a). (c) The derived thermal susceptibility in the C-band. (d) The simulated heat distribution of the Ta2O5 waveguide. (e) The total and the absorption propagation loss measurement in C-band for the resonator mentioned above.
Fig. 6.
Fig. 6. (a) The relationship between the waveguide length (L) and the insertion loss (IL) for Ta2O5 spiral waveguides at 780 nm. (b) The relationship between the waveguide length (L) and the insertion loss (IL) for Ta2O5 spiral waveguides at 2000 nm. (c) The Lorentzian fit to the resonance shows a loaded Q factor of 3.3 × 104 and an intrinsic Q factor of 3.7 × 104 at 2000 nm. (d) The summary of the loss performance of the several material photonic platforms which utilize low-temperature process.

Equations (2)

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d λ res d T = λ res n eff d n eff d T + λ res R d R d T
Δ f res = β R th P abs = β R th ξ P d = χ th P d
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