SECTION 1

Silicon photonics in mid-infrared (mid-IR), of 2–6 $\mu\hbox{m}$, have attracted a great interest because of their potential applications in chemical sensing, infrared spectroscopy and free-space communications [1], [2]. Moreover, due to the absence of two-photon absorption (TPA) in mid-IR range, the applications of optical nonlinearities in silicon can be faster and more efficient because of the absence of free-carriers generated by TPA [3], [4], [5], [6], [7]. Unfortunately, the conventional silicon-on-insulator (SOI) based devices are not suitable for mid-IR, because the buried oxide (BOX) layer has high absorption at wavelengths between 2.6–6.0 $\mu\hbox{m}$ (with a narrow transparent window around 3.2 $\mu \hbox{m}$) [1], [8], [9]. Nevertheless, silicon-on-sapphire (SOS) provides an alternative potential platform for mid-IR devices due to the high transparency of sapphire in mid-IR [1]. SOS based waveguides have been proposed and demonstrated experimentally in the wavelength range of 1.5–5.6 $\mu\hbox{m}$ [10], [11]. Recently, microring resonators were reported operating in the 5.5 $\mu\hbox{m}$ wavelength range [12].

In the 2.6–3.0 $\mu\hbox{m}$ range, there are a number of potential applications of microresonators for chemical sensing and nonlinear generation of mid-IR light. The vibrational and rotational resonances of most gas molecules fall within the mid-IR spectral range: for example the hydroxyl (OH) group have strong absorption peaks spectrum around 2.7 $\mu \hbox{m}$ [13], and thus the sensitivity of evanescent optical waveguide based sensors [14], [15], may be sufficient to detect trace concentrations. Nonlinearities in the mid-IR are also of interest for use in generating different mid-IR wavelengths such as mid-IR silicon Raman amplifier/laser [4], [5], or optical parametric amplifiers [6], [7]. High-$Q$ microresonators can build up high electric energy density in the cavity, which can thus enhance the effective nonlinearity of microresonators. At telecom wavelengths, TPA in silicon and the long lived free-carriers produced by TPA will lead to shifts in resonances which limit the possible enhancement of optical nonlinearities in silicon microresonators. As mentioned previously, TPA is absent in silicon at mid-IR wavelengths and thus the measurement of $Q$ in microresonators at mid-IR wavelengths is of interest for possible applications in nonlinear mid-IR devices. However, the measurement method of $Q$ at mid-IR is limited. In the 2.6–3.0 $\mu\hbox{m}$ range, there is a lack of narrow linewidth tunable laser sources. In the 3–6 $\mu\hbox{m}$ range, the conventional quantum cascade lasers (QCLs) provide limited spectral resolution in the order of 0.1 nm and set a limit on the maximum measurable $Q$ using this source. In order to overcome the limitation of the laser source, there is a need of an alternative $Q$ measurement method with narrow linewidth laser sources such as a mid-IR He-Ne laser.

For high-$Q$ resonator based devices, thermal stability is crucial in practical usage. The thermo-optic coefficient of silicon is higher than silica, and has a value of $(1.86 \pm 0.08) \times 10^{-4}\ \hbox{K}^{-1}$ at 1.5 $\mu\hbox{m}$ wavelength [16]. Silicon waveguide devices are thus more sensitive to temperature than devices based on silica [17]. The thermo-optic coefficient of bulk silicon has been measured in mid-IR range up to 6.0 $\mu\hbox{m}$ [18]. However, the value of strained silicon thin film such as epitaxial layer of SOS have not been studied in mid-IR range as it is difficult to form a conventional etalon (such as described in [16]) since the thickness of the silicon layer can be less than the wavelength in the mid-IR range.

In this paper, we report on the measurement of the thermo-optic coefficient of SOS waveguides and $Q$ factor measurement of microresonators at a wavelength of 2.75 $\mu\hbox{m}$. We fabricated mid-IR microring resonators which support a fundamental quasi-transverse electric (quasi-TE) mode. The devices were characterized by thermal tuning using a fixed wavelength Er/Pr-codoped $\hbox{ZrF}_{4}\hbox{-BaF}_{2} \hbox{-LaF}_{3}\hbox{-AlF}_{3}\hbox{-NaF}$ (ZBLAN) fiber laser at 2.75 $\mu\hbox{m}$ [19]. A method of $Q$ factor estimation from temperature scanning transmission curve is proposed, which is different from the method used in our previous work [20] as it does not need any curve fitting. Similar results are obtained if we assume the ratio of resonant period (in temperature) to the full-width-half-maximum (FWHM) of resonant dip/peak, $\Delta T/\delta T$, is equal to the cavity finesse [21]. Finally, the thermo-optic coefficient of the epitaxial silicon layer of SOS is also estimated by perturbation method [22], [23]. The measurement techniques were verified with conventional SOI microring resonators in near**-**infrared (near-IR).

SECTION 2

The silicon strip waveguides were fabricated on SOS with 600 nm thickness and 950 nm width which satisfy the single mode condition of quasi-TE mode at 2.75 $\mu\hbox{m}$. The corresponding electric field mode profile are calculated by finite element method (FEM), shown as Fig. 1(c), with refractive indices of 3.44 (silicon), 1.72 (sapphire) and 1 (air) in mid-IR at room temperature [24]. For microring resonators, in order to have a better control of the coupling between the ring cavities and the bus waveguides, the race-track type geometry was used. They were fabricated with 45 $\mu\hbox{m}$ coupling length and 150 $\mu\hbox{m}$ bending radius and, thus, with 1032 $\mu\hbox{m}$ round-trip length. According to simulations using beam propagation method, the bending loss of the waveguides with 150 $\mu\hbox{m}$ bending radius is theoretically negligible compared to the propagation loss of the waveguides. In this paper, microring resonators with two bus waveguides were used. In order to simply the design, the two bus waveguides of each resonator have identical coupling lengths and separation from the ring waveguide.

Grating couplers are used for coupling mid-IR light between the SOS waveguides and single mode ZBLAN fibers with a 10° off-vertical orientation [25], as shown in Fig. 2(b). The uniform-1-D gratings were 360 nm shallow-etched in a period of 1.055 $\mu \hbox{m}$ and 0.31 fill factor. They also ensure the light polarization of waveguides and rings in quasi-TE mode. The microring resonators and grating couplers were patterned by electron beam lithography with ZEP520A resist and then dry etched by reactive-ion etching with $\hbox{C}_{4} \hbox{F}_{8}$ and $\hbox{SF}_{6}$ mixture. The scanning electron microscope (SEM) images of the fabricated microring resonator and the strip waveguide cross-section are shown in Fig. 1(a) and (b).

For comparison in near-IR, a SOI microring resonator (quasi-TE mode) was fabricated on a wafer with 220 nm top silicon layer and 2 $\mu\hbox{m}$ BOX by deep-UV lithography. The waveguide width and round-trip length are 500 nm and 264 $\mu\hbox{m}$, respectively.

SECTION 3

The experimental setup is shown in Fig. 2. The Er/Pr-codoped ZBLAN fiber laser with lasing wavelength at 2.75 $\mu\hbox{m}$ and linewidth < 0.12 nm was pumped by a high power 975 nm diode laser. The mid-IR light from the laser was coupled to an undoped ZBLAN fiber. And then the light is coupled from undoped ZBLAN fiber to the input of the resonator through grating coupler. Another fiber collected the output light from either the throughput port or the drop port of the resonator by grating couplers. Finally, the output light was captured by a mid-IR photovoltaic detector. In order to increase the signal-to-noise ratio, the signal of the mid-IR detector was measured by a lock-in amplifier with a mechanical chopper modulating the pump laser. The SOS chip was mounted on top of a thermoelectric cooler (TEC) for temperature tuning. A thermal detector was directly attached on the epitaxial silicon for monitoring the temperature and TEC control feedback. The light from the throughput port and drop port was measured at 25–65 °C. The received signal is finally normalized by the output of a reference straight waveguide in order to remove the temperature dependence of the coupling efficiency of the grating couplers. In the case of SOI microring measurement, the fibers, laser source, and detector were replaced by fused silica single-mode fibers, a tunable laser, and an optical power meter for near-IR.

SECTION 4

The temperature dependent transmission of the highest $Q$ ring, with 350 nm separation between bus waveguides and ring, is plotted in Fig. 3. By tuning the temperature between 25–65 °C, we can observe four resonances in both throughput and drop ports with $\sim\!11\ ^{\circ}\hbox{C}$ temperature spacing and extinction ratio of $\sim$10 dB from the drop port. There is $\sim$10 dB loss from the drop port at resonance compared to the reference waveguide (without resonator). The fluctuations of the measurement data in Fig. 3(a) may be due to instability in the fiber laser as there laser longitudinal mode hopping and wavelength drift noise may be present during temperature scanning of the microresonator. The measured results could be improved by reducing the temperature scan range (25–40 °C), as shown in Fig. 3(b).

The measured transmittance was analyzed by a theoretical model of the microresonator [26]: TeX Source $${E_{t}\over E_{i}} = {t (e^{- i\theta} - \alpha)\over e^{- i\theta} - \alpha t^{2}}, \quad {E_{d}\over E_{i}} = {i\sqrt{\alpha} \kappa^{2}e^{i\theta^{\prime}}\over 1 - \alpha t^{2}e^{i\theta}},\quad \theta = {2\pi L_{rt}n_{eff}\over \lambda_{o}}\eqno{&\hbox{(1)}}$$ with temperature, $T$, dependent round-trip phase shift $\theta (T) = \theta(T_{o}) + \Delta \theta(T)$: TeX Source $$\Delta \theta (T) \cong 2\pi L_{rt} \left. {\partial n_{eff}\over \partial T}\right\vert_{\lambda_{o}}{T - T_{o}\over \lambda_{o}}\eqno{\hbox{(2)}}$$ where $E_{i}$, $E_{t}$, and $E_{d}$ are the electric field at input port, throughput port, and drop port, respectively; $\alpha$ is the field round-trip loss factor; $t$ and $\kappa$ are the field coupling coefficients of each bus waveguides and ring with $\vert t\vert^{2} + \vert\kappa\vert^{2} = 1$ where $t = t_{1} = t_{2}$ and $\kappa = \kappa_{1} = \kappa_{2}$. The “1” and “2” subscripts refer to the each bus waveguides, respectively; $\theta^{\prime}$ is the phase shift reached to the drop port with half of the round-trip; $L_{rt}$ is the physical round-trip length; $n_{eff}$ is the effective index of the waveguide mode; $\lambda_{o}$ is the wavelength in vacuum; $T_{o}$ is the reference temperature; $\partial n_{eff}/\partial T$ is the thermo-optic coefficient of the waveguide mode which depends on the waveguide material (air, silicon and sapphire) and the mode field profile. In order to simplify the model, the propagation loss and the coupling efficiency between the waveguides and the ring are assumed to be temperature independent. Moreover, the linear thermal expansion of silicon is in the order of $10^{-6}\ \hbox{K}^{-1}$ [27] which is two orders of magnitude less than the thermo-optic effect of silicon, and therefore neglected in our analysis. The fitting curves of temperature scanning of the microring, shown in Fig. 3(b), agree well with the experimental data with fitting parameters $\alpha = 0.71$, $\vert t\vert = 0.93$ and $n_{eff} = 2.72$. There are fluctuation in the measured values at the drop port, between normalized level −21 dB and −23 dB because of the noise background of the setup.

In order to develop and verify the method for $Q$ factor estimation from temperature dependent transmission curve, we can start with a conventional SOI microring for near-IR. The transmission spectrum at 25 °C is shown in Fig. 4(a), which shows the free-spectral-range $(FSR)$ as 2.08 ± 0.014 nm. Fig. 4(b) shows the resonant dip of the throughput port centered at 1546 nm with FWHM $\delta\lambda_{o} = 0.08 \pm 0.014\ \hbox{nm}$. The corresponding $Q$ factor is about 19900 ± 3500. The figure also shows the resonant wavelength red (blue) shifted with increasing (decreasing) the temperature. We can see that the shape of the spectral profile of the resonant dip is almost unchanged in this temperature range. For the thermal tuning measurement, we fixed the laser wavelength at the resonant wavelength at 25 °C (1546 nm) and tuned the temperature. When the resonance is shifted by about half of $\delta\lambda_{o}$ at a temperature shift $\delta T/2$, the output power is changed to the half of resonant dip. Therefore, the temperature shift $\delta T$ behaves as the FWHM of the resonance in the temperature tuning domain. The relationship between $\delta T$ and $\delta\lambda_{o}$ can be obtained directly by considering the resonant condition of the resonator at $m$-order resonance of $\lambda_{m}$ at temperature $T$ with waveguide mode group index $n_{g} = n_{eff} - \partial n_{eff}/\partial\lambda_{o}$, the resonant wavelength changes with temperature: TeX Source $${d\lambda_{m}\over dT} = {\lambda_{m}\over n_{g}}\left. {\partial n_{eff}\over \partial T} \right\vert_{\lambda_{m}}, \quad \hbox{then} \quad \delta \lambda_{o} \cong {\lambda_{m}\over n_{g}}\left. {\partial n_{eff}\over \partial T} \right\vert_{\lambda_{m}}\delta T.\eqno{\hbox{(3)}}$$ The thermo-optic coefficient of the waveguide mode can be obtained by considering temperature difference between two resonances in temperature domain, $\Delta T$, of same wavelength $\lambda_{o}$: TeX Source $$\left. {\partial n_{eff}\over \partial T} \right\vert_{\lambda_{o}} \cong {\lambda_{o}\over L_{rt}\Delta T}.\eqno{\hbox{(4)}}$$ By combining (3) and (4), $Q$ can be expressed as TeX Source $$Q = {\lambda_{m}\over \delta \lambda_{o}} \cong {\Delta T\over \delta T}{n_{g}L_{rt}\over \lambda_{m}}.\eqno{\hbox{(5)}}$$ From the thermal transmission curves at 1546 nm, shown in Fig. 4(c) and (d), the resonant period $\Delta T$ is and FWHM $\delta T$ are $24.7 \pm 1.0\ ^{\circ}\hbox{C}$ and $0.74 \pm 0.03\ ^{\circ}\hbox{C}$, respectively. The mode group index is 4.35 which is obtained by $FSR = \lambda_{m}^{2}/n_{g}L_{rt}$. By (5), the resulting $Q$ is about 24800 ± 2000. The measured values of $Q$ from the wavelength scanning and thermal tuning techniques agree to within the error bars of the different measurement techniques.

By combining (5) and $FSR = \lambda_{m}^{2}/n_{g}L_{rt}$ TeX Source $${\Delta T\over \delta T} \cong {FSR\over \delta \lambda_{o}} = F.\eqno{\hbox{(6)}}$$ This gives similar results as obtained by assuming $\Delta T/\delta T$ as being equal to the finesse [21].

As this proposed method works well in near-IR, it was applied in the SOS microring resonators at mid-IR. From Fig. 3(b), the resonant period $\Delta T$ and dip FWHM $\delta T$ are $11.2 \pm 0.4\ ^{\circ}\hbox{C}$ and $1.48 \pm 0.06\ ^{\circ}\hbox{C}$, respectively. The theoretical mode effective index is 4.01 calculated by FEM. The resulting $Q$ is about 11400 ± 800. Since the power stability and the linewidth of the ZBLAN fiber laser is not as good as the commercial tunable laser, the measurement results of our system, in fact, are the convolution of the actual resonator transmission spectral function and the power spectrum of the laser. Therefore, the features would be averaged or broadened. The estimated $Q$ factor may be underestimated. Using this method with a narrow linewidth laser (such as a mid-IR He-Ne laser), the maximum measurable $Q$ can be up to $10^{6}$ by using a temperature controller system with temperature stability and set point resolution in 0.01 °C, which is commercially available. This limit is over 10 times of wavelength scanning with QCLs.

The thermo-optic coefficient of the waveguide mode, from (4), can be used to estimate the thermo-optic coefficient of the epitaxial silicon core, $\partial n_{Si}/\partial T$, of SOS by the perturbation method [22], [23]. This method is more accurate than conventional mode weighted average method for high index contrast waveguide [28]. A small perturbation of the waveguide materials refractive indices induces the small change of effective index in waveguide mode $\delta n_{eff}$: TeX Source $$\eqalignno{\delta n_{eff} \cong &\, {\int\limits_{\infty} \left({\partial n (r)\over \partial T}\delta T\right)n (r) \left\vert E \right\vert^{2}dr\over Z_{o}\int\limits_{\infty} {\rm Re} \{E\times H^{\ast}\} \cdot e_{z}dr} \cong \Gamma_{Si}{n_{g}\over n_{Si}}{\partial n_{Si}\over \partial T}\delta T, \ \hbox{with}\ \Gamma_{Si} = {\int\limits_{Si} n (r)^{2}\left\vert E \right\vert^{2}dr\over \int\limits_{\infty} n (r)^{2}\left\vert E \right\vert^{2}dr}&\hbox{(7)}\cr {\partial n_{eff}\over \partial T} \cong &\, {\delta n_{eff}\over \delta T} \cong \Gamma_{Si}{n_{g}\over n_{Si}}{\partial n_{Si}\over \partial T}&\hbox{(8)}}$$ where $Z_{o}$ is the impedance of vacuum, and $\Gamma_{Si}$ is defined as the conventional electric field confinement factor of the mode in silicon core region. In (7), because of the thermo-optic coefficients of sapphire and air is much smaller than silicon [29], [30], and the electric field is highly confined in the silicon core, we can neglect the contribution of them. Moreover, the high thermal conductivity of silicon ensures the temperature can be approximately constant in the core. Again, we start from the SOI counterpart in near-IR. The $\partial n_{eff}/\partial T$ is obtained as $2.37 \pm 0.10 \times 10^{-4}\ \hbox{K}^{-1}$ and then the resulting $\partial n_{Si}/\partial T$ of silicon core of SOI is $2.07 \pm 0.08 \times 10^{-4}\ \hbox{K}^{-1}$ which agrees well to the result in [16]. The value is smaller than the waveguide mode thermo-optic coefficient since $\Gamma_{Si}\cdot n_{g}/n_{Si}$ is larger than 1. It is because $n_{g}$ is larger than $n_{Si}$ while $\Gamma_{Si}$ is close 1. It indicates that the light in guided mode with large group index spends more time, therefore, experience higher thermo-optic effect than in bulk material for given a length [23].

In case of SOS microring, $\partial n_{eff}/\partial T$ and theoretical group index are obtained as $2.38 \pm 0.08\, \times 10^{-4}\ \hbox{K}^{-1}$ and 4.01, respectively. Then $\partial n_{Si}/ \partial T$ of epitaxial silicon on SOS is $2.11 \pm 0.08\, \times 10^{-4}\ \hbox{K}^{-1}$. We can see that the resulting value of epitaxial silicon on SOS is similar to the bulk silicon.

SECTION 5

In conclusion, we have fabricated and characterized microring resonators on SOS at wavelength of 2.75 $\mu\hbox{m}$ by thermal tuning. The measured $Q$ factor was about 11400 ± 800 under normal ($\sim$60% relative humidity) atmospheric condition. The thermo-optic coefficient of epitaxial silicon on SOS is estimated as $2.11 \pm 0.08 \times 10^{-4}\ \hbox{K}^{-1}$ by perturbation method. The characterization methods have been verified by SOI microring in near-IR with comparable results. The thermal tuning technique for $Q$ factor measurement is of practical use for characterizing resonator at wavelengths where there is limited tunability and spectral resolution of laser source and the technique may find applications for other types of cavities such as Fabry–Pérot cavities in mid-IR.

We thank Bookham (now Oclaro Inc) for the 975 nm pump laser.

This work was supported by Hong Kong UGC Special Equipment Grant CUHK-SEG01 Grant and direct Grant 2050508. Corresponding author: C. Y. Wong (e-mail: cywong@ee.cuhk.edu.hk).

The authors are with the Department of Electronic Engineering, The Chinese University of Hong Kong, Shatin Hong Kong.

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