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Abstract
We demonstrate a method for measuring on-chip waveguide losses using a single microring resonator with a tunable coupler. By tuning the power coupling to the microring and measuring the microring’s through-port transmission at each power coupling, one can separate the waveguide propagation loss and the effects of the coupling to the microring. This method is tolerant of fiber-chip coupling/alignment errors and does not require the use of expensive instruments for phase response measurements. In addition, this method offers a compact solution for measuring waveguide propagation losses, only using a single microring (230 µm×190 µm, including the metal pads). We demonstrate this method by measuring the propagation losses of silicon-on-insulator rib waveguides, yielding propagation losses of 3.1-1.3 dB/cm for core widths varying from 400-600 nm.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical waveguides are fundamental building blocks of photonic integrated circuits (PICs). They form on-chip modulators, switches, filters, sensors, and many other devices [1]. The design of these devices require modeling of the components used to construct the devices, including the optical waveguides. For instance, designing micro-ring resonators (MRRs) with certain bandwidths/extinction ratios/quality factors for quantum and nonlinear optics [2,3], telecommunications [4–10], analog signal processing [11,12], and biosensing applications [13,14] require knowledge of the waveguide propagation losses a priori in the design process. Finite difference eigenmode (FDE) solvers can compute the absorption losses (given an accurate model of the waveguide material’s refractive index), however, for waveguides fabricated on the siliconon-insulator (SOI) platform, absorption losses are negligible. In fact, fabrication-associated waveguide sidewall roughness, which results in light scattering remains the dominant source of power loss in straight SOI waveguides [15–18]. While there are methods to model fabrication-associated losses [15,17,19–23], these methods require a knowledge of the root-mean-square deviation from a flat surface and the correlation length of the waveguide sidewall roughness, which requires metrology using expensive instruments, such as scanning electron microscopes [17] or atomic force microscopes [24]. Alternative to modeling, measuring a fabricated waveguide’s propagation loss is simpler, more straightforward, and provides a more accurate value of the propagation loss [16].
Methods to measure the propagation loss include measuring the transmission through waveguides with a known differential length (known as the the cut-back method) [25–27], using direct camera imaging of the decay length [28], and using interferometers. The cut-back method is simple and straightforward, however, it requires several spirals (as shown in Fig. 1(a) and Fig. 1(b)), which consume a large footprint (e.g. 630 µm$\times$400 µm for 3 Archimedean spirals waveguides [29]). In addition, to accurately measure very small propagation losses, the lengths of these waveguides should be even longer to resolve the small differences between the waveguides’ transmissions, making this method impractical for measuring waveguides with small propagation losses [16]. Furthermore, measuring several waveguides means that this method is susceptible to chip-fiber coupling/alignment errors, limiting the loss measurement range. Direct camera imaging is another simple technique, however, the decay length must be on the order of the camera window size, limiting the range of the measured propagation loss [16,28]. To overcome these limitations, interferometers can be used. Such interferometers include an imbalanced Mach- Zehnder interferometer (MZI) [30], a straight waveguide with air-terminated endfacets [31–34], or several weakly-coupled MRRs [16]. Using an imbalanced MZI [30] can result in a very small measurement error and uncertainty. Using straight waveguides with air-terminated endfacets is sensitive to errors in the observed fringe contrast and requires rigorous consideration of the waveguide facets’ reflection coefficients [16]. Such rigorous consideration is especially important for high-index-contrast waveguides [28], which is the case for SOI waveguides. Although a technique was developed to avoid needing a priori knowledge of the waveguide endfacets’ reflection coefficients [33], it was shown that the range of validity of this technique is limited and difficult to verify [34]. Using several weakly-coupled MRRs is an alternative method, which can be compact (similar to the one shown in Fig. 1(c)), offers propagation loss measurement over a large range without being limited by fiber/chip coupling-alignment errors, and has proven to be a reliable method to measure very small propagation losses on various platforms, such as silicon and silicon nitride [16]. Here, instead of using several MRRs, we demonstrate a method to measure on-chip propagation losses using a single MRR with a tunable-coupler.
Fig. 1. Various devices for measuring on-chip waveguide losses: (a) rectangular spirals to measure the losses using the cut-back method, (b) Archimedean spirals to measure the losses using the cut-back method, (c) several MRRs where each MRR has a different bus-ring coupling gap, (d) our proposed single, two-point coupled microring resonator.
The through-port response of an all-pass MRR (shown in Fig. 2) is ideally (with a symmetric lossless coupler) given by
In the following paper, we show how the coupling to the ring and propagation losses of a single MRR can be separated using a tunable coupler, enabling us to measure waveguide propagation losses directly using this single device. The tunable coupler is an MZI with a two-point coupling scheme, with a heater above one of the coupler arms (Fig. 1(d)). Through extracting the coupling and propagation losses at various heater powers, a distinction between both parameters can be made. This is similar to the case of fabricating multiple MRRs with various coupling gaps except that only a single MRR is required here.
2. Device design, propagation loss extraction methodology, and simulations
2.1 Device design
Tunable coupling is achieved using a two-point MZI coupler as shown in Fig. 3. Figure 3(a) illustrates the masks layout of the coupling-tunable MRR. This design preserves the compact MRR round structure, thus minimizing mode mismatch losses that could otherwise have been introduced [16]. To tune the coupling to the ring, a TiN heater is placed above the longer arm of the tunable coupler, which changes the phase of the light and thus the output power from the tunable coupler to the ring. The separation between the TiN heater and the top of the silicon waveguide is 2 µm, at such a distance the induced optical loss due to the heater is minimal [39]. The lengths of the tunable coupler arms are selected such that $L_1 = L_2 + \pi R$, where $L_2$ is the length of the shorter arm of the MZI that is shared with the ring, and $L_1$ is the longer arm length. This sets the free-spectral range (FSR) of the coupling-tunable MRR to be twice that of the ring [10,16]. Although this is not a strict constraint, however, it makes it easier to measure the FSR of the isolated ring, which is required for extracting the propagation loss, as shown in subsection 2.2. We used the same arc radius, $R$, for each curved section of the tunable coupler’s longer arm, and $\theta$ was calculated accordingly.
Fig. 3. (a) Schematic of the two-point coupled MRR. The design parameters are shown within the figure. The electric field intensity pattern for the fundamental TE-mode is also shown for the two oppositely rotating arcs forming the longer arm of the tunable coupler. (b) A model of the asymmetric coupling-tunable MRR. (c) Simulation of the MRR radiation loss (in dB/cm) as functions of the bend radius for various Si rib waveguide core width, $W=400$-$600$ nm. The markers are the simulation results and the dotted lines are exponential fittings of the results [40,41]. The figure in the left shows the cross-section of the waveguide geometry and the simulated electric field intensity pattern.
To select a MRR radius with minimal radiation loss (to approximate a straight waveguide) and footprint, we conducted FDE simulations using Lumerical MODE solutions (according to methods described in [18]). Figure 3(c) (left) shows a cross-section of the simulated waveguide that forms the MRR. The waveguide is formed using a rib waveguide with a 90 nm-thick slab and a 220 nm-thick Si waveguide core. Figure 3(c) (right) shows the radiation loss in dB/cm for the waveguide core widths that we aim to measure the propagation loss for ($W=400$-$600$ nm) as functions of the MRR radius. From Fig. 3, we can see that a radius of 20 µm results in a negligible radiation loss (<$10^{-4}$ dB/cm for $W\geq 400$ nm), which is much smaller than the expected propagation loss of Si rib waveguides fabricated using a similar fabrication process [42].
2.2 Loss extraction methodology
To extract the waveguide propagation loss in dB/cm ($\alpha _{\textrm {dB}}$), first, the total transmission coefficient (which includes both, propagation loss in the ring and loss in the coupler), $\alpha$, is extracted. To extract $\alpha$, the heater is biased at various bias values. For each bias, the power coupling to the ring is varied. The MRR through-port transmission spectrum is then measured using a tunable laser source and a photodetector. From each spectrum, $t$ and $\alpha$ are extracted according to the method described in [35] (this method is revisited and its applicability to the case presented here is discussed in more detail in Appendix A.), where
Here, $\mathcal {F}$ is the Finesse of the MRR, $\mathcal {E}$ is the extinction ratio of the MRR, $\Delta \lambda _{\textrm {FSR}}$ is the FSR of the MRR (in isolation, without the tunable coupler) which can be extracted from the optical spectrum (half the coupling-tunable MRR compound FSR) and is equal to $\lambda _q^2/(2\pi R n_{\textrm {g}})$ (where $\lambda _q$ is the $q^{\textrm {th}}$ resonant wavelength and $n_{\textrm {g}}$ is the waveguide’s group index at the resonant wavelength), $\Delta \lambda _{\textrm {FWHM}}$ is the full width at half maximum (FWHM) of the resonances, and $T_{\textrm {max}}$ and $T_{\textrm {min}}$ are the maximum (off-resonance) and minimum (on-resonance) of the transmission spectrum, respectively. Choosing $\alpha$ to be the larger value among the two solutions given by Eq. (2) results in an interchange between $\alpha$ and $t$ when the MRR is under-coupled. Thus, we interchange $\alpha$ and $t$ when the MRR is under-coupled.
2.3 Extracting the propagation loss, $\alpha _{\textrm {dB}}$, from the total loss, $\alpha$
From [35], $\alpha$ is the transmission loss factor, which includes both, propagation loss in the ring and loss in the coupler, and is expressed as
where ${\vert} {t_r^\prime}{\vert}=10^{(-\alpha _{\textrm {dB}}L_3/20)}$ is the magnitude of the fields transmission through the portion of the MRR not shared with the tunable coupler (i.e., the portion of length $L_3$), and $\alpha _c^\prime$ is the magnitude of the field-transmission through the coupler, which is expressed as [35] The notations used here complement the notations used in [35], where ${\vert}{t_c^\prime }{\vert}$ and ${\vert} {\kappa _c^\prime }{\vert}$ are the magnitudes of the through and cross field transmissions, respectively (see Fig. 3(b)). ${\vert} {t_c^\prime }{\vert}^2+{\vert} {\kappa _c^\prime }{\vert}^2$ can be expressed in terms of the point couplers’ field coupling coefficient ($\kappa$) and the magnitude of the field transmissions in the tunable coupler’s top (${\vert} {\alpha _1}{\vert}$) and bottom (${\vert} {\alpha _2}{\vert}$) arms (see the inset in Fig. 4), where2.4 Numerical simulations
In our designs, we selected point coupler gaps of 200 nm. Table 1 shows $\kappa ^2$ at each waveguide width (simulated using 3D-FDTD simulations according to methods described in [18]). The mode field profiles for each rib waveguide core width was simulated for the two opposing bend orientations (using the FDE solver in Lumerical MODE Solutions according to methods discussed in [18]). The mode mismatch loss at the junctions shown in Fig. 3(a), was then calculated using the overlap integral [43] of the two oppositely propagating bent TE-mode field patterns. The results are tabulated in Table 1.
Table 1. The simulated point couplers’ normalized power coupling coefficient ($\kappa ^2$, for a fixed coupling gap of 200 nm) and the simulated mode mismatch loss, at the junctions of the oppositely oriented arcs, for a 20 µm-radius MRR rib waveguide (see Fig. 3) with core widths of $W=400$-$600$ nm. These parameters were simulated using a wavelength of 1550 nm. The last two columns show the measured ($\alpha _{\textrm {dB}}$) and actual ($\alpha _{\textrm {dB, actual}}$) averaged propagation loss. The standard deviation propagation loss measurement error for each waveguide width is also shown.
3. Device fabrication and experimental results
Coupling-tunable MRRs, with varying waveguides core widths of $W=400$-$600$ nm, were fabricated at the A*STAR IME foundry in Singapore, using 193 nm-deep UV lithography. Figure 4 shows an optical micrograph of the fabricated devices.
Fig. 4. Optical microgragh of the fabricated coupling-tunable MRRs. The waveguide width (mentioned above the respective device) was varied from $W=400$-$600$ nm in steps of 50 nm. The inset shows a zoomed-in view of a single device.
A tunable and sweepable (with a 0.5 pm resolution) laser (HP 81682A) and a photodetector (HP 81635A) were used to measure the optical spectrum of the coupling-tunable MRRs using grating couplers as optical I/Os (see Fig. 4). A source-measure unit (Keithley 2602B) was used to bias the heaters on top of each MRR. Fig. 5(a) shows the optical spectra for the resonances nearest to 1550 nm, of the 400 nm-wide rib waveguide MRR as a function of the heater bias. The heater had a 2 µm width, which resulted in a resistance of 580 $\Omega$ at 3.5 V bias. The power consumption varied from 5 mW to 21 mW as the heater bias was changed from 1.7 V to 3.5 V. The expected temperature of the silicon waveguide at maximum bias is $\sim$40 °C [39,44]. The method described in subsection 2.2 was then applied to the resonances of the optical spectra for each device. The measured FWHMs and extinction ratios (ERs) of the resonances as functions of the heater powers are shown in Fig. 5(b). The extracted $t$ and $\alpha$ (from the FWHMs and ERs shown in Fig. 5(b) using Eq. (2)) are shown in Fig. 6(a). $t$ and $\alpha$ are then interchanged for those heater powers for which the MRR is under-coupled (indicated by a dotted circle in Fig. 6(a)). We repeat the above procedure for the other MRRs shown in Fig. 4, for their resonances nearest to 1550 nm. We then use $\kappa$ and $\alpha _{\textrm {m}}$ from Table 1 to solve Eq. (7) numerically in order to obtain $\alpha _{\textrm {dB}}$ at each heater power for $W=400$-$600$ nm. The results are shown in Fig. 6(b) (top plot), and the averaged losses are tabulated in Table 1 and shown in Fig. 6(b) (bottom plot). Since the existence of noise in the spectrum is pronounced when the ring is under-coupled, we only consider measuring the loss from the extracted $\alpha$ values when the ring is over-coupled. The error bars in Fig. 6(b) (bottom plot) indicate the standard deviation ($\pm \sigma$) of the propagation loss at the various heater powers. Although the standard deviation error is less than $0.1$ dB/cm it is worth mentioning that this measurement error is predominantly caused by the use of the method described in subsection 2.2 (as described in Appendix A.) when applied to the device presented here. Other sources that contribute to the error include the quality of the measured through-port optical spectra. Fitting the model given by Eq. (1) (using a least-square algorithm for example [45]) to the through-port optical spectra can reduce the latter errors.
Fig. 5. (a) The through-port optical spectra of the coupling-tunable MRR with $W=400$ nm at various heater biases. (b) The measured FWHMs and ERs from the optical spectra in Fig. 5(a).
Fig. 6. (a) The extracted $t$ and $\alpha$ from the FWHMs and ERs shown in Fig. 5(b) using Eq. (2). $t$ and $\alpha$ are interchanged when the MRR is under-coupled (indicated with a dotted circle). (b) Top plot: the measured propagation losses ($\alpha _{\textrm {dB}}$) obtained using Eq. (7) as functions of the heater power for each MRR waveguide core width. The legend within the figure indicates the corresponding MRR waveguide core width. Bottom plot: The averaged measured ($\alpha _{\textrm {dB}}$) and actual ($\alpha _{\textrm {dB, actual}}$) propagation loss (indicated with markers) and the $\pm \sigma$ measurement error (indicated with error bars) for each waveguide core width.
4. Results analysis and discussion
The method described in subsection 2.2 to separate $t$ and $\alpha$ is applicable to coupling-tunable MRRs with balanced arms, where the through-port optical transmission is symmetric around the resonant wavelength. If the arms of the tunable coupler are imbalanced (unequal length and losses in each arm, as in our case here), the through-port optical transmission is no longer symmetric around the resonant wavelength. This results in a systematic error in the measured $\alpha _{\textrm {dB}}$, which increases with increasing $\kappa$ (see Appendix A.). To correct for this systematic error, we simulate the optical spectra of a coupling-tunable MRR using the transfer function of the device (Eq. (25) in Appendix B.). Then, in the simulations, we assume an $\alpha _{\textrm {dB}}$, which we refer to as the $\alpha _{\textrm {dB, actual}}$, that we adjust until it results in an extracted $\alpha _{\textrm {dB}}$ (from the simulated optical spectra using the method in subsection 2.2 and subsection 2.3) that matches the measured $\alpha _{\textrm {dB}}$. The actual propagation loss ($\alpha _{\textrm {dB, actual}}$) values are tabulated in Table 1 and shown in Fig. 6(b) (bottom plot). A summary of the steps required to measure the propagation loss is shown in Fig. 7.
It is worth noting that wafer thickness non-uniformity and/or fabrication errors [10,46] might lead to changes in the MRR’s waveguide dimensions, which in turn results in an actual $\kappa ^2$ and $\alpha _{\textrm {m}}$ values different than that obtained from FDTD and FDE simulations. If the waveguide thickness and width both change by $\pm 3\sigma _{\textrm {H}}$ and $\pm 3\sigma _{\textrm {W}}$, respectively, $\kappa ^2$ can change by $\pm 30\%$ (in the worst case scenario) [10], and $\alpha _{\textrm {m}}$ can change by $0.005$ dB. For the case of $W=600$ nm, this will result in an error of $\pm 0.08$ dB/cm, and $0.05$ dB/cm in $\alpha _{\textrm {dB, actual}}$, for changes in $\kappa ^2$ and $\alpha _{\textrm {m}}$, respectively.
The systematic error between the measured ($\alpha _{\textrm {dB}}$) and actual ($\alpha _{\textrm {dB, actual}}$) propagation loss reduces as $\kappa$ is reduced (as seen in Fig. 6(b) (bottom plot), and explained in Appendix A.). For example, for the case of $W=600$ nm, if $\kappa ^2=0.01$, the systematic error in the propagation loss is less than $0.02$ dB/cm. Strictly speaking, the systematic error increases with increasing the power coupling to the ring, ${\vert} {\kappa _c^\prime}{\vert}^2$, therefore, in future designs, it is recommended to reduce $\kappa$, and extract the propagation loss only from few $\alpha$ values at which the coupling to the ring is close to critical-coupling. Besides reducing the systematic error, there are several other advantages to reducing $\kappa$. First, the dependency of $\alpha _{\textrm {dB}}$ on $\kappa$ and $\alpha _{\textrm {m}}$ is reduced, which reduces the error in $\alpha _{\textrm {dB, actual}}$ due to uncertainties in both parameters (which might occur due to errors in the fabrication as discussed earlier), reduces possible losses/backscattering due to the point-couplers [45] and reduces the contribution of the loss in the top coupler arm to the total propagation loss. The latter is helpful in a process that has a smaller heater and waveguide separation, where the metal heater can increase the optical losses [39]. Second, in practice, it is easier to design point couplers with smaller coupling coefficients by using larger gaps between the couplers’ waveguides. It is worth mentioning that $\kappa$ should not be set to $0$, otherwise, no light will be coupled to the ring and no resonances will be observed in the optical spectrum.
Unfortunately, none of the devices shown in Fig. 1 were fabricated on the same chip to compare our method against, however, the devices shown in Fig. 1(c) were fabricated using a similar process [1,42], and a comparable value for the propagation loss (1.9 dB/cm) for the rib waveguide with 500 nm core width was measured. It is also worth mentioning that light can be backscattered inside the MRR either due to the point-couplers, waveguides sidewall roughness, or the mode mismatch at the junctions in the top coupler. However, while conducting the measurements, no backscattering was observed as revealed by the smooth optical spectra with a single null, as shown in Fig. 5(a). If there is backscattering, then the single resonance will be split and the spectral parameters to separate $\alpha$ and $t$ given by Eq. (2) cannot be used. In such a case, one can increase the coupling to reduce the effect of backscattering [45] up to the point at which a single null appears in the optical spectrum and ignore the points ($\alpha$ values) at which the resonance is split. This is another advantage of using our coupling-tunable MRR compared to the several MRRs shown in Fig. 1(c).
Comparing the proposed method to the alternative methods mentioned earlier, our method has three advantages. First, the method is tolerant of fiber-chip coupling/alignment errors, thus resulting in very small measurement errors ($<\;0.1$ dB/cm). Second, no expensive instruments are required for the phase response measurements. Third, since a single coupling-tunable MRR is used, the footprint is greatly reduced as compared to the spiral waveguides used in the cut-back method, thus saving significant chip area/cost. There are, however, three drawbacks to the method we propose. First, a stable, tunable, narrow-spectral-linewidth laser [47] is required to measure the MRR optical spectra (especially when the MRR is under-coupled); however, such lasers are typically available/accessible to most test groups. Second, our method is an active-based approach that requires a stable power source to bias the heater; however, such power sources are relatively inexpensive and widespread. Also, since electrical probes are required to bias the heaters, this might increase the amount of time required to conduct the measurements. Third, the proposed method is sensitive to uncertainties in $R$, $\kappa$, and $\alpha _{\textrm {m}}$. Although the error in the actual propagation loss due to uncertainties in these parameters is small ($<\;0.1$ dB/cm), we suggested methods to improve the device in future designs to reduce the sensitivity of the proposed method to uncertainties in such parameters.
5. Summary and conclusion
We demonstrated a method for measuring propagation losses in optical waveguides. The method starts with tuning the power coupling of a single two-point coupled MRR, measuring the MRR’s through-port transmission over the three coupling states of the MRR, and extracting the propagation loss using the equations developed herein. By doing so, one can separate the waveguide propagation loss and the effects of the coupling to the ring. We implemented this method to measure the propagation loss of SOI waveguides with core widths varying from $400$ nm to $600$ nm, which resulted in propagation losses varying from $3.1$ to $1.3$ dB/cm, respectively. Since a single and compact coupling-tunable MRR was used, such device can be easily incorporated as a general calibration device in PICs and also at multiple points on a wafer for wafer-scale characterization, without consuming significant area.
Appendix
A. Extracting $t$ and $\alpha$ using a MRR with a lossy coupler
Here we discuss the applicability and the limitation of the method described in [35] to extract the propagation losses using the device we propose. For a single MRR with a lossless coupler and a fixed power coupling (similar to the one shown in Fig. 2), the propagation losses in dB/cm, $\alpha _{\textrm {dB}}$, can be calculated from the extracted round-trip transmission, $\alpha$, where $\alpha _{\textrm {dB}}=-20\log (\alpha )/L$. However, for an MRR with a lossy tunable coupler (as in our case), $\alpha$ includes both losses: losses across the ring as well as the tunable coupler. Thus, an alternative model, similar to the one in [35], which accounts for the coupler losses shall be used to correctly extract $\alpha _{\textrm {dB}}$.
In [35], McKinnon and coauthors describe a method to extract the coupling and MRR loss from the spectral properties of the the resonances in the MRR through-port spectrum. The analysis shown in [35] does assume a lossy coupler, however, the authors make the assumption that
Equations (8) and (9) are a result of power conservation in lossless couplers [48,49], however, these equations do not hold for asymmetric couplers with unequal losses (i.e., $t_c\ne t_c^\prime$), which is supposed to be the general case considered in [35] and our case here, since the imbalanced tunable coupler can be considered as an asymmetric coupler with unequal losses in the top and bottom arms (see Fig. 3(a)). If we consider such a general case and define then the equation relating the through ($b$) to the input ($a$) fields transmission will beThe method described in [35] can, however, still be used in our analysis, if the cross-coupling to the ring, $\kappa _c^\prime$, is minimized. The additional term in Eq. (11) can be written as,
B. Transfer function of a coupling-tunable MRR
The transfer function of the device used here is an expansion of Eq. (12), where the coupler is represented by the MZI transfer function [51],
where $\alpha _1={\vert} {\alpha _1}{\vert}e^{j(\beta L_1+\phi _{\textrm {H}})}$, $\alpha _2={\vert} {\alpha _2}{\vert}e^{j\beta L_2}$, $t_r^\prime ={\vert} {t_r^\prime }{\vert}e^{j\beta L_3}$, $\beta =2\pi n_{\textrm {eff}}/\lambda$ is the waveguide propagation constant, $n_{\textrm {eff}}$ is the waveguide effective index, $\lambda$ is the free-space wavelength, and $\phi _{\textrm {H}}$ is the phase shift in the tunable coupler’s longer arm due to heating.Funding
Natural Sciences and Engineering Research Council of Canada (CREATE); Faculty of Graduate Studies, University of British Columbia; CMC Microsystems.
Disclosures
The authors declare no conflicts of interest.
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