Fabrication tolerant and wavelength independent arbitrary power splitters on a monolithic silicon photonics platform

Marios Papadovasilakis; Marios Papadovasilakis; Sujith Chandran; Sujith Chandran; Yonas Gebregiorgis; Yusheng Bian; Yusheng Bian; Michal Rakowski; Subramanian Krishnamurthy; Abdelsalam Aboketaf; Rod Augur; Jaime Viegas

doi:10.1364/OE.463721

1. Introduction

Optical couplers (combiners/splitters) are essential building blocks in integrated photonics. They are generally used as power splitting or combining elements in optical routing circuits and in any functional structure consisting of interferometers or resonators. The most common types of optical power splitters/combiners are directional couplers (DCs) [1] and multimode interference (MMI) devices [2,3]. The principle of operation of a DC relies on evanescent field coupling between two waveguides spaced closely, which can be described by coupled mode theory [4,5]. They are typically compact and exhibit low insertion loss (IL). However, the power splitting ratio (SR) of a DC-based coupler is strongly wavelength dependent [6] such that they are not a suitable option for broadband applications. In contrast, MMI splitters rely on the self-imaging principle [2] and provide fabrication tolerant and nearly wavelength independent response. However, the major drawback of the MMI splitter is the poor transmission efficiency for asymmetric power splitting. Though structural modifications of the conventional MMI splitters exhibit arbitrary splitting ratios, they suffer due to significantly higher IL in comparison to DCs [7]. There are various schemes in the literature which utilize DCs in order to achieve broadband SR. One solution that has been widely studied is the introduction of asymmetric arms, i.e. arms consisting of regions of varying cross sections and waveguide widths [8–11]. These devices are very compact, with moderate IL ranging from 0.3 to 1 dB. One particular design [12] demonstrated simulated results with IL as low as 0.05 dB and 0.02 dB for silicon and silicon nitride platform, respectively. Modifying the straight parallel waveguides of a DC to a curved geometry [13–16] has shown to offer good spectral stability, however these studies only demonstrate a 3-dB power splitting ratio. Another solution that has been suggested utilizes sub-wavelength gratings (SWGs) to achieve broadband splitting ratios [17–19]. These couplers show low IL and good spectral stability of less than $\pm$5% from the intended power division. However, these devices also only demonstrate 3-dB splitting. Lastly, another method [20] utilizes highly compact parameterized Y-junctions to achieve arbitrary splitting ratios, however the IL ranged from 0.36 to less than 0.5 dB.

In this work, we designed, simulated, and experimentally demonstrated a Mach-Zehnder Interferometer (MZI) based wavelength-independent coupler (WIC) operating in the O-band. The device configuration is designed to obtain arbitrary SRs, with high fabrication tolerance, very low IL of 0.16 dB and a standard deviation of only 0.6% at $\lambda =1310$ nm. This WIC is basically an MZI consisting of asymmetric arm lengths, and two DCs of different lengths as theoretically suggested in [21]. The DC consists of narrow waveguides, which are separated by a short gap. The narrow waveguide width enables highly delocalized guided modes, which have weak interaction with the waveguide sidewalls, thus providing robust performance with respect to inevitable fabrication variations. Additionally, the weak mode confinement and the short gap facilitates strong coupling, leading to short DC lengths. Moreover, excluding waveguide propagation loss, any loss will only be contributed by radiative modes from the waveguide bends. The main advantage of this $2\times 2$-port device is that any arbitrary power SR can be achieved by adjusting the two DC lengths, as well as the delay length of the MZI. DCs are inherently wavelength dependent; thus, to achieve wavelength independent response we employ an MZI configuration. The delay length of the MZI is chosen to achieve wavelength independent SR by controlling the free spectral range (FSR) and center wavelength. The device is demonstrated on a monolithic CMOS-compatible SOI platform with a thin (160 nm) device layer [22–27]. This platform enables the photonic devices to be seamlessly integrated with technologies consisting of electronic and silicon nitride photonic components on the same chip. The thin device layer typically reduces the modal confinement, which in turn can compromise the device footprint, however we have methodically engineered the geometrical features of the device to obtain compact footprint.

2. Theory and simulation results

2.1 Directional coupler

In this section, the theoretical background and simulation results will be presented. Figure 1(a) shows an isometric view of a directional coupler. Assuming negligible losses and $\left |E_{\textrm {in}}\right |^{2}=1$, the electric field of the cross port $E_{\textrm {cross}}$ will be equal to the field coupling coefficient $\kappa$ [4,5]:

(1)$$\kappa = \sin\left(\dfrac{\pi \Delta n}{\lambda} L_{\mathrm{DC}} + \theta_0\right)$$

In Eq. (1), $\Delta n$ is the effective index difference of the symmetric and anti-symmetric supermode of the DC, $L_{\textrm {DC}}$ is the DC length, and $\lambda$ is the wavelength. $\Delta n$ is calculated using Lumerical’s Finite Difference Eigenmode (FDE) solver [28]. The term $\theta _0$ refers to the additional coupling induced at the input and output bends of the DC. This quantity is first simulated by Lumerical’s 3D-Finite Difference Time Domain (FDTD) solver, and then converted to a wavelength-dependent phase term. Figure 1(b) shows the cross-section SEM image of the DC, which is illustrated in the bottom image of Fig. 1(c). However, the calculated $\Delta n$ of Eq. (1) refers to geometrically symmetric waveguides as shown in the top image of Fig. 1(c). Realistically, the case of geometrically symmetric waveguides (i.e., having identical dimensions) is not feasible which means Eq. (1) cannot be applied. Since the geometrical deviations from the symmetric case are impossible to predict, we need to tune the parameters (waveguide width, and gap) such that, when considering the deviations observed on the SEM image, the supported mode is analogous to the mode in the symmetric case.

Fig. 1. (a) Schematic illustration of a directional coupler of length $\mathrm {L_{DC}}$; (b) SEM cross section image of the fabricated directional coupler depicting the fabrication induced geometries, where $w, \, t,\,\theta$ correspond to waveguide width, thickness, and sidewall angles of each waveguide, respectively; (c) cross section illustration of the symmetric and asymmetric cases. (d), (e) Modal analysis of a symmetric (top row) and asymmetric (bottom row) DC cross section. In the case of wider waveguide and longer gap (d), the deviation $\mathbf{\delta }$ between the difference of the fundamental and first order mode (symmetric and anti-symmetric mode) $\Delta n$ of the DC is approximately 10 times higher than the case of narrower waveguides and shorter gap (e). The larger value of $\Delta n$ in (e) compared to (d) indicates the stronger evanescent coupling in the case of the narrower waveguides.

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The confinement factor $\Gamma$ shown in Eq. (2) expresses the fraction of power of a propagating mode that is contained in the waveguide core [29]:

(2)$$\Gamma = \dfrac{\int_{{-}w/2}^{w/2}\int_{{-}t/2}^{t/2} E^{2}(x,y) \,\mathop{}\!\mathrm{d} y\mathop{}\!\mathrm{d} x}{\int_{-\infty}^{\infty} \int_{-\infty}^{\infty} E^{2}(x,y) \,\mathop{}\!\mathrm{d} y\mathop{}\!\mathrm{d} x},$$

where x and y are the directions along the width (w) and thickness (t) of the waveguide, respectively. $\Gamma$ becomes larger with increasing width, which means that a larger percentage of the mode power will interact with the silicon core. Thus, any imperfections of the waveguide geometry will have a higher effect on the propagating mode for larger widths. In other words, narrow waveguides are more insensitive to waveguide fabrication errors, which can also be seen in the comparison presented in Figs. 1(d), (e). Additionally, as the gap increases, the power coupling coefficient $\left | \kappa \right |^{2}$ is decreased exponentially [30], leading to a longer DC length. Consequently, any fabrication-induced errors significantly impact the device’s performance as phase error is accumulated along the length of the DC. In order to reduce the effect of fabrication errors, we have designed the DCs with narrow width and short gap. The short gap enables stronger mode interaction/coupling and the narrow waveguide weekly confines the modes. Figures 1(d), (e) shows a comparison of the fundamental TE mode of the DC between geometrically symmetric and asymmetric DC cross sections. The two cases compared are for waveguide widths of 400 and 300 nm and gaps of 250 and 200 nm, respectively. The confinement factor relation for these two cases as obtained from Lumerical’s FDE solver is $\Gamma _{400}\simeq 2\Gamma _{300}$. We first assume a symmetric cross-section on our designs and then the perturbations depicted in Fig. 1(b) are applied for waveguide width, height, and sidewall angles. We notice that for the case of wider waveguides, when in presence of fabrication induced cross-section asymmetry, (Fig. 1(d)), the electric field of the fundamental mode is not symmetrically distributed between the two waveguides as in the geometrically symmetric case. Additionally, the value of $\Delta n$ deviates by 45.7%, which results in significant change in the expected splitting ratio. Whereas, in the case of DCs with narrow width and separation, mode profiles (symmetric and anti-symmetric) remain nearly identical as the $\Delta n$ deviation is only 4.3% (Fig. 1(e)). It is noted that the SEM image of Fig. 1(b) corresponds to a DC of 400 nm width, and 250 nm gap. In order to study the effect of the fabrication process on the DC of 300 nm width and 200 nm gap, the same perturbations depicted on the SEM image were applied to this design as well.

We can verify the above observation for an asymmetric DC by comparing the modeled performance based on Eq. (1) and that of a 3D-FDTD simulation. Figure 2(a) shows a comparison between the 3D-FDTD simulation and the modeled DC for three different DC lengths. The DC cross section is symmetric; thus, the two methods are in complete agreement. However, in the case where we consider asymmetric cross section, the two methods significantly deviate from each other. This is expected because the model only applies to symmetric waveguides, and as it can be seen from Fig. 2(b) the deviation increases as the DC becomes longer. However, in Fig. 2(c) we observe that there is an excellent agreement between the two methods regardless of the DC length even though the cross section is asymmetric. Here, the DCs are designed with closely spaced narrow waveguides to suppress any effects derived from the geometrical asymmetries of the coupler. This implies that regardless of inevitable fabrication variability, the DC performance remains stable across the silicon wafer.

Fig. 2. Comparison of power coupling coefficient (SR) between analytical model and 3D-FDTD for 3 different lengths of 1, 3, and 30 $\mu \mathrm {m}$ for: (a) symmetric cross-section of 400 nm width, and 250 nm gap, (b) asymmetric cross section of 400 nm width, and 250 nm gap, and (c) asymmetric cross-section of 300 nm width, and 200 nm gap. Inset cross section illustrations represent the geometry of each directional coupler.

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2.2 Wavelength independent coupler

As mentioned before, we have designed the WIC using an asymmetric MZI configuration with a length difference of $\Delta L$ between the MZI arms, as can be seen in Fig. 3(a). The transmission characteristics of the WIC are obtained by cascading the transfer functions of the DCs and the asymmetric MZI arms between them:

(3)$$\begin{bmatrix} E_{\textrm{cross}}\\ E_{\textrm{bar}} \end{bmatrix} = \begin{bmatrix} t_2 & \mathrm{i}\kappa_2\\ \mathrm{i}\kappa_2 & t_2 \end{bmatrix} \begin{bmatrix} e^{\mathrm{i}\beta \Delta L} & 0\\ 0 & 1 \end{bmatrix} \begin{bmatrix} t_1 & \mathrm{i}\kappa_1\\ \mathrm{i}\kappa_1 & t_1 \end{bmatrix} \begin{bmatrix} 0\\ E_{\textrm{in}} \end{bmatrix},$$

where $t=\sqrt {1-\kappa ^{2}}$ is the throughput coefficient, assuming lossless transmission. There are three parameters that control the output spectrum of the WIC; $L_{\textrm {{DC}}_1}$, $L_{{\textrm {DC}}_2}$, and $\Delta L$. The DC lengths correspond to specific values of $\kappa$ through Eq. (1). Since the device is considered to be lossless, the cross port power $P_{\textrm {cross}}=\left | E \right |^{2}$ will be equal to the device splitting ratio. For an intended splitting ratio value of SR, we choose the values of these three parameters such that the mean value of $P_{\textrm {cross}}$ (Eq. (3)) across the O-band is approximately equal to the desired SR and $\dfrac {\Delta P_{\textrm {cross}}\left ( \lambda \right )}{\Delta \lambda } \simeq 0$ to ensure that the power remains constant over the entire O-band. The power profile of a WIC with intended SR of 0.5, which is obtained from a 3D FDTD simulation, can be seen in Fig. 3(b). It is apparent that most of the power is coupled to the top arm after the first DC, which can also be seen in Fig. 3(c) ($\mathrm {DC_1}$). Figure 3(c) shows the transmission spectrum of the two individual DCs compared to a WIC with intended SR of 0.5, along with the performance deviation parameter $\sigma$ with respect to the wavelength, which is defined as $\sigma =\sqrt {\dfrac {\sum _{i=1}^{N} \left [ P(\lambda _i)-P_{\mathrm {mean}} \right ]^{2}}{N}}$, where $P(\lambda _i)$ is the cross port power at wavelength $\lambda _i$ and $P_{\mathrm {mean}}$ is the mean cross port power over N wavelength points. We can see that the output power is constant across the O-band with a standard deviation (SD) of only 0.4%. However, it can be observed that the power is equally divided at the output of the WIC. By using the same method, we are able to obtain the parameters for any arbitrary splitting ratios, as shown in Fig. 3(d). This is particularly useful especially in applications where wavelength independent arbitrary ratio power splitters are required [31]. Finally, we simulated the 50:50 WIC configuration for a waveguide width offset of $\pm 10$ nm (Fig. 3(e)), which according to the results has little effect on the output spectrum. The $\pm 10$ nm width offset was tested as it resembles the platform’s lithography margin [22].

Fig. 3. (a) Schematic of a wavelength independent coupler consisting of two directional couplers of lengths $\mathrm {L_{DC_1}}$, $\mathrm {L_{DC_2}}$, and MZI of arm length separation $\mathrm {\Delta L}$; (b) electric field distribution as obtained by 3D-FDTD simulation for a coupler aiming at SR = 0.5; simulated splitting ratio spectra comparison for: (c) each isolated DC and the WIC with SR = 0.5, (d) 4 different WIC configurations aiming at SR of 0.5, 0.3, 0.2, and 0.05. (e) SR = 0.5 for different waveguide widths ($\pm 10$ nm).

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3. Experimental results

3.1 Evaluation of performance stability

In order to test the validity of our assumption regarding the stability of the device with respect to fabrication errors, we fabricated 2 sets of devices. The first set consists of different WIC configurations aiming at 4 splitting ratios. The normalized parameters for these WICs can be seen in Table 1. Additionally, for each configuration, we fabricated 3 different variations, where the different parameter was the waveguide width, i.e., $\Delta w=-10,\,0,\,+10$ nm from the intended width. The experimental results for the spectrum of each coupler are plotted as follows; First we measure the output cross port of each device, and then we normalize the power by subtracting the corresponding IL. The IL of a WIC is measured with the help of the second configuration which will be presented at the next step. Finally, the normalized cross port can be considered as the SR of the WIC.

Table 1. Normalized WIC parameters and experimental SR metrics for WIC configurations aiming at various splitting ratios.^a

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The measurement setup can be seen in Fig. 4(a) [32]. Figure 4(b) shows the spectrum of each of the 3 WIC configurations for 4 intended SRs. Based on these results, we can observe that the performance of the WIC is very consistent for any SR for all waveguide width/gap combinations. We can also observe that as the SR increases from 0.05 to 0.5, the variation of the SR among the 3 devices also increases. This can also be seen in Table 1 which shows the mean and the SD of each splitting ratio across the O-band. Since the cross sections for each DC are different, the deviation of the total accumulated phase between the three cases will be higher as the DC length is increased. Thus, the resulting spectrum will suffer from higher variation. However, the standard deviation (SD) is measured to be only 1.3% even for the WIC with $\mathrm {SR=0.5}$.

Fig. 4. (a) Image of the optical characterization setup [32] used to measure the devices described in this work; (b) experimental results for different splitting ratios obtained for devices of three different waveguide widths ($w=290 ,\,\, 300 ,\,\, 310$ nm) and gaps ($g=210 ,\,\, 200 ,\,\, 190$ nm).

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3.2 Insertion loss and splitting ratio measurement

The second set of measurements were performed on a macro which was designed specifically to evaluate the insertion loss of the WIC, as well as obtain the average splitting ratio for a 3-dB coupler design. The reason we chose this particular WIC is because according to our simulations, the device of $\mathrm {SR}=0.5$ demonstrates the highest spectral variation. This can be seen in Fig. 3(e) and was also proven experimentally in Fig. 4(b). The schematic which helps us obtain the SR and IL can be seen in Fig. 5. It contains a series of 9 cascaded WICs which consist of 5 different outputs. The ports denoted as $\mathrm {P_{B_9}}$ and $\mathrm {P_{C_9}}$ correspond to 9 WICs cascaded through bar and cross ports, respectively. This method helps reduce measurement error, by averaging the performance of 9 identical couplers, which is then normalized as follows; The power at the bar and cross port of a single WIC in dB will be:

(4)$$\begin{array}{l} {\textrm{P}_{\textrm{bar}}} = 10{\log _{10}}\left[ {\left( {1 - {\textrm{L}_\textrm{F}}} \right)\left( {1 - \textrm{SR}} \right)} \right]\\ {\textrm{P}_{\textrm{cross}}} = 10{\log _{10}}\left[ {\left( {1 - {\textrm{L}_\textrm{F}}} \right)\textrm{SR}} \right], \end{array}$$

where SR is the splitting ratio and $\mathrm {L_F}$ is the loss factor, i.e. the normalized fraction of power lost from a single WIC. If we apply Eq. (4) for 9 cascaded WICs the measured power in dB for $\mathrm {P_{B_9}}$ and $\mathrm {P_{C_9}}$ will be:

(5)$$\begin{array}{l} {\textrm{P}_{{\textrm{B}_\textrm{9}}}} = 10{\log _{10}}\left[ {{{\left( {1 - {\textrm{L}_\textrm{F}}} \right)}^9}{{\left( {1 - \textrm{SR}} \right)}^9}} \right]\\ {\textrm{P}_{{\textrm{C}_\textrm{9}}}} = 10{\log _{10}}\left[ {{{\left( {1 - {\textrm{L}_\textrm{F}}} \right)}^9}\textrm{S}{\textrm{R}^\textrm{9}}} \right] \end{array}$$

Solving Eq. (5) for SR produces:

(6)$$\begin{array}{l} SR = \frac{1}{{1 + a}}\\ a = {10^{\frac{{{\textrm{P}_{{\textrm{C}_\textrm{9}}}} - {\textrm{P}_{{\textrm{B}_\textrm{9}}}}}}{{90}}}} \end{array}$$

Equation (6) allow us to calculate the average SR of 9 cascaded WICs. This value will help us calculate the average IL combined with the measured power from the other 3 ports in Fig. 5. These ports are named $\mathrm {P_{{C_8}{B_1}}}$, $\mathrm {P_{{C_4}{B_1}}}$, $\mathrm {P_{{C_2}{B_1}}}$, and correspond to the measured power of 8, 4, and 2 cascaded cross ports and one bar port, respectively. For N cascaded WICs, the measured power of N-1 cascaded cross ports and 1 bar port will be:

(7)$$\begin{array}{l} {\textrm{P}_{{\textrm{C}_{\textrm{N - 1}}}{\textrm{B}_\textrm{1}}}} = 10{\log _{10}}\left[ {{{\left( {1 - {\textrm{L}_\textrm{F}}} \right)}^N}\textrm{S}{\textrm{R}^{N - 1}}\left( {1 - \textrm{SR}} \right)} \right] \Rightarrow \\ {\textrm{P}_{{\textrm{C}_{\textrm{N - 1}}}{\textrm{B}_\textrm{1}}}} = \underbrace{{10{{\log }_{10}}\left[ {\left( {1 - {\textrm{L}_\textrm{F}}} \right)\textrm{SR}} \right]}}_{\textrm{S}} \times \underbrace{N}_{\textrm{X}} + \underbrace{{10{{\log }_{10}}\left[ {\frac{{1 - \textrm{SR}}}{{\textrm{SR}}}} \right]}}_{\textrm{C}} = \textrm{sX + c} \end{array}$$

Lastly, the IL is related to the loss factor as $\mathrm {IL} = 10\log _{10}\left ( 1 - \mathrm {L_F} \right )$ and can be directly obtained by the slope in Eq. (7) as:

(8)$$\mathrm{IL} = \mathrm{s} - 10\log_{10}\left[ \mathrm{SR} \right]$$

Figure 6(a) shows the wavelength dependent splitting ratio extracted using Eq. (7) for 6 different wafer sites with an inset figure showing the magnified view of the plot near the center of the O-band. The SR measurements demonstrate very stable performance across different wafer sites. More specifically, Fig. 6(b) shows the statistics for 9 different wavelengths points equally spaced across the O-band. The maximum deviation ranges from 0.011 to only 0.026 for the displayed wavelength points.

Fig. 5. GDS layout of the cascaded WICs for the experimental estimation of SR and IL. $\mathrm {P_{{C_i}{B_1}}}$: Power obtained at the bar port of the $\mathrm {(i+1)^{th}}$ device in which $i$ devices are cascaded through cross port, $\mathrm {P_{B_9}}$: power obtained at bar port of the $\mathrm {9^{th}}$ device in which 9 devices are cascaded through bar ports, $\mathrm {P_{C_9}}$: power obtained at the cross port of the $\mathrm {9^{th}}$ device in which all the 9 devices are cascaded through the cross port.

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Fig. 6. (a) Experimentally measured splitting ratio spectra of the 50:50 WIC device across different wafer sites; (b) statistical SR analysis for equally spaced wavelengths. The red line denotes the median value, while the blue box corresponds to the range between the $\mathrm {25^{th}}$ and $\mathrm {75^{th}}$ percentile.

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Experimentally extracted SR is used for estimating the insertion loss from the slope of the line representing the output power with respect to the number of cascaded devices, using Eq. (7). For a wavelength dependent insertion loss, linear interpolation is performed for each wavelength by plugging the respective wavelength dependent SR into Eq. (8). Figure 7(a) shows the three output power values obtained by ports $\mathrm {P_{C_{2}B_1}}$, $\mathrm {P_{C_{4}B_1}}$, and $\mathrm {P_{C_{8}B_1}}$, with their corresponding linear fit for three different wavelengths. The inset figure shows the grating couplers’ response, which justifies the lower power obtained for $\lambda =1260$ nm. Obtaining the slope of each wavelength point, and solving for the IL through Eq. (8) produces Fig. 7(b). We can see a clear trend of increasing IL for longer wavelengths ranging from 0.08 dB at $\lambda =1260$ nm up to 0.38 dB at $\lambda =1340$ nm. The reason behind this trend is attributed to the sharp bends in the asymmetric arm length region. The modes of longer wavelengths are more weakly confined in the waveguide core, thus they suffer higher loss due to the radiative modes in the bent regions. Alternatively, the bent loss can be minimized by increasing the bent radius, or by increasing the waveguide width in the bent sections. However, both methods will increase the total footprint. Another way of addressing the increased IL for longer wavelengths is by introducing adiabatic bends in the asymmetric arm length region [33]. These bends enable smoother mode transition compared to circular bends which allow for a more compact MZI design leading to a footprint reduction by a factor of $\sim$24. Table 2 summarizes the key performance metrics of our device compared to the state of the art.

Fig. 7. (a) Linear fit obtained by the measured power of the three ports described in Eq. (7) for three different wavelengths. Inset figure shows the grating coupler’s response; (b) measured insertion loss as a function of wavelength as obtained from the slope of each different wavelength point.

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Table 2. Performance comparison of this work with the state of the art on silicon photonics wavelength independent power splitters

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4. Conclusion

In summary, we designed, simulated, and experimentally measured several wavelength independent coupler designs, aiming at constant splitting ratios over the O-band. The device is fabricated on a state-of-the-art CMOS-compatible monolithic silicon platform, which makes it suitable for implementation in future technologies consisting of on-chip electronics and silicon/silicon nitride photonics for optimized integration density. The WICs consist of narrow waveguides and directional couplers of short gaps, thus ensuring fabrication tolerant performance. We have successfully verified wavelength independent operation for 4 different target splitting ratios with a mean SD of 1.2% for the least stable device, for a waveguide width offset of $\pm 10$ nm. Additionally, we cascaded 9 WICs with intended SR of 0.5 and calculated the normalized SR and IL. The experimental results showed an SD of only 0.6% and a mean IL of $\sim$0.16 dB for $\lambda = 1310$ nm. Regarding the rest of the O-band the maximum deviation is only 1.2% for the best device, while the insertion loss increased from 0.08 to 0.38 dB as the wavelength changes from 1260 to 1340 nm. As a mitigation plan for higher insertion loss at longer wavelengths, we suggest replacing the constant radius waveguide bents with adiabatic bends. This solution is expected to improve not only the insertion loss but also reduce the device footprint by a factor of $\sim$24.

Funding

Semiconductor Research Corporation (2713.001, 2984.001).

Acknowledgments

The authors thank GlobalFoundries for providing silicon fabrication through the MPW university program as well as Ken Giewont, Karen Nummy, Dave Riggs, and the rest of the GlobalFoundries team for the technical support. Additionally, the authors wish to acknowledge the contribution of Khalifa University’s high-performance computing and research computing facilities to the results of this research.

Disclosures

The authors declare no conflicts of interest.

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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WIC Parameters			SR Metrics
$L_{D C_{1}} / L_{0}$	$L_{D C_{2}} / L_{0}$	$Δ L / L_{0}$	Target	Mean $(μ)$	SD $(σ)$
$1.12$	0	$0.18$	0.50	0.480	0.013
$0.81$	0	$0.16$	0.30	0.301	0.010
$0.72$	$0.02$	$0.14$	0.20	0.202	0.007
$0.48$	$0.02$	$0.13$	0.05	0.065	0.006

Type	Splitting Ratio (%)	Insertion Loss (dB)	Maximum Deviation (%)	Length $\times$ Width ( $μ m \times μ m$ )	Wavelength Range (nm)	Reference
MMI	Any	$0.4 \pm 0.5$	$5 - 20$	$300 \times 5$	$1450 - 1650$	[7]
Tapered DC	50:50	$0.3 \pm 0.2$	2	$300 \times 80$	$1500 - 1600$	[8]
	50:50	$< 1$	20	$145 \times 40$	$1520 - 1600$	[9]
	Any	$< 1$	10	$41 \times 10$	$1500 - 1600$	[10]
	Any	$\sim 1$	1.6	$240 \times 3$	$1260 - 1360$	[11]
Curved DC	50:50	N/A	2	N/A	$1476 - 1534$	[14]
	50:50	$< 1$	N/A	N/A	$1518 - 1666$	[15]
	50:50	N/A	20	$20 \times 3$	$1520 - 1620$	[16]
SWG	50:50	$< 0.5$	7	$50 \times N / A$	$1490 - 1620$	[17]
	50:50	$< 0.11$	7	$35 \times N / A$	$1200 - 1700$	[18]
	50:50	$0.2$	6	$65 \times N / A$	$1500 - 1600$	[19]
Y-Junction	Any	$< 0.5$	$< 10$	$1.4 \times 2.3$	$1500 - 1600$	[20]
MZI	Any	$0.08 - 0.38$	1.2	$60 \times 40$	$1260 - 1340$	This Work

WIC Parameters			SR Metrics
$L_{D C_{1}} / L_{0}$	$L_{D C_{2}} / L_{0}$	$Δ L / L_{0}$	Target	Mean $(μ)$	SD $(σ)$
$1.12$	0	$0.18$	0.50	0.480	0.013
$0.81$	0	$0.16$	0.30	0.301	0.010
$0.72$	$0.02$	$0.14$	0.20	0.202	0.007
$0.48$	$0.02$	$0.13$	0.05	0.065	0.006

Type	Splitting Ratio (%)	Insertion Loss (dB)	Maximum Deviation (%)	Length $\times$ Width ( $μ m \times μ m$ )	Wavelength Range (nm)	Reference
MMI	Any	$0.4 \pm 0.5$	$5 - 20$	$300 \times 5$	$1450 - 1650$	[7]
Tapered DC	50:50	$0.3 \pm 0.2$	2	$300 \times 80$	$1500 - 1600$	[8]
	50:50	$< 1$	20	$145 \times 40$	$1520 - 1600$	[9]
	Any	$< 1$	10	$41 \times 10$	$1500 - 1600$	[10]
	Any	$\sim 1$	1.6	$240 \times 3$	$1260 - 1360$	[11]
Curved DC	50:50	N/A	2	N/A	$1476 - 1534$	[14]
	50:50	$< 1$	N/A	N/A	$1518 - 1666$	[15]
	50:50	N/A	20	$20 \times 3$	$1520 - 1620$	[16]
SWG	50:50	$< 0.5$	7	$50 \times N / A$	$1490 - 1620$	[17]
	50:50	$< 0.11$	7	$35 \times N / A$	$1200 - 1700$	[18]
	50:50	$0.2$	6	$65 \times N / A$	$1500 - 1600$	[19]
Y-Junction	Any	$< 0.5$	$< 10$	$1.4 \times 2.3$	$1500 - 1600$	[20]
MZI	Any	$0.08 - 0.38$	1.2	$60 \times 40$	$1260 - 1340$	This Work

Fabrication tolerant and wavelength independent arbitrary power splitters on a monolithic silicon photonics platform

Abstract

1. Introduction

2. Theory and simulation results

2.1 Directional coupler

2.2 Wavelength independent coupler

3. Experimental results

3.1 Evaluation of performance stability

3.2 Insertion loss and splitting ratio measurement

4. Conclusion

Funding

Acknowledgments

Disclosures

Data availability

References

Data availability

Cited By

Figures (7)

Tables (2)

Equations (8)

Optics Express