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Abstract
We propose a novel optical 1×2 power splitter based on an asymmetric ladder-shaped multimode interference (MMI) coupler in silicon-on-insulator (SOI) which has an ultra-compact size of 3.3 µm×2.4 µm. A trapezoid with a small region is removed from the bottom left corner of the MMI coupler to achieve variable splitting ratio. The comparison with the asymmetric rectangular 1×2 splitter is numerically analyzed. By carefully optimizing the width of input taper, the proposed splitter shows a low phase deviation for the two output ports while keeping both of a low-loss performance and feasible splitting ratio. The simulated results show that the splitter can operate with an insertion loss less than 0.67 dB, a large range of splitting ratio from 50:50 to 11:89 and an ultra-low phase deviation less than 2.8° among the C band spectra.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical power splitter with variable splitting ratio is an attractive component in photonic integrated circuits, which is important to the applications such as lasers with optical feedback circuits [1], tap-based power monitoring [2,3], asymmetric Mach-Zehnder interferometer [4] and nanophotonic phased arrays [5]. As one of the fundamental building blocks in integrated photonics, multimode interference (MMI) coupler is a kind of multi-port optical component which performs the basic function of beam splitting and combining with advantages of compactness, reliability, large optical bandwidth and relaxed fabrication tolerance [6–8]. To achieve power splitters with a tunable splitting ratio, different structures based on the MMI couplers have been reported such as butterfly geometrical design [9], planar holograms [10,11], cascaded MMI couplers [12,13], asymmetric rectangular coupler [14] and meta-material structures [15,16].
Though many devices with superior performance which can achieve different optical power splitting ratios have been reported, there were few investigations which focus on the phase characteristics of a specified splitter with unequal power output, to the best of our knowledge. The power splitting ratio is undoubtedly an intuitive parameter for an optical splitter which can measure the amplitude-related performance in many advanced applications requiring nonuniform power splitting [17]. However, the phase characteristic is also a vital characteristic which is instructive to applications such as linearity improvement for silicon-based Mach-Zehnder modulators [18,19], on-chip photonic biosensors with coherent detection of phase [20] and optical quantizer based on unbalanced Mach-Zehnder modulator [21] in the multi-wavelength system.
Devices based on silicon-on-insulator (SOI) platform are attractive for electronic-photonics integrated chips due to the compatibility with complementary metal-oxide semiconductors (CMOS) process. Here we focus on the phase-related characteristics of 1$\times$2 power splitter in 220-nm SOI platform along with the splitting ratio. Compared with the previously reported 1$\times$2 power splitter based on asymmetric rectangular MMI coupler [14], an asymmetric ladder-shaped 1$\times$2 MMI coupler with a removed section from the bottom left corner is investigated, which exhibits a lower phase deviation than the rectangular MMI coupler while maintaining a low insertion loss and large range of splitting ratio. By carefully optimizing the width of input taper, the asymmetric ladder-shaped 1$\times$2 splitter shows a low phase deviation less than 2.8$^{\circ }$ and a large splitting ratio ranging from 50:50 to 11:89 within a size of 3.3 µm$\times$2.4 µm, which is a significant improvement related to the common rectangular coupler.
2. Design for the shape of asymmetric 1$\times$2 splitter
As shown in Fig. 1(a), the common 1$\times$2 power splitter is based on an asymmetric rectangular MMI coupler. The width of the coupler and input waveguide is 1.5 µm ($W$) and 500 nm ($width$) respectively. The distance forming two self-images of input light is sharply decreased so the structure can achieve a 1$\times$2 power splitter with an ultra-compact size. Furthermore, only a few lower-order modes are excited in the lateral direction due to the small value of coupler width, which can satisfy the relation of
where $\beta _{1}$ and $\beta _{m}$ are the first and m-th order mode excited in the MMI coupler. Above equation is an essential requirement for high-quality performance of power splitting [22], which can be achieved by such a compact rectangular 1$\times$2 MMI coupler. However, there is still potential improvement for the splitter when the phase characteristics are considered. Figure 1(b) shows the proposed asymmetric splitter based on a linear-tapered 1$\times$2 MMI coupler. The width of MMI coupler is gradually increased along the propagation direction which gives insight to lower the phase deviation of two output light especially for the splitter with unequal power splitting ratio. A small trapezoid is removed from the bottom left corner with length of $x$ and width of $y$. The input width of the tapered MMI coupler is set to be 1.5 µm ($W1$) which is the same as asymmetric rectangular MMI coupler. Then a further optimization is investigated for the linear-tapered 1$\times$2 MMI coupler which is shown in Fig. 1(c). A noticeable difference between two trapezoid-based coupler is the width ($intwidth$) of input taper. By optimizing the value of $intwidth$ which satisfies the relation of $intwidth+2y=W1$, the bottom left corner (point B in Fig. 1(b)) can be eliminated and the optical mismatch caused by the sudden change of effective index can be effectively suppressed. Therefore the light propagation from input taper to the bottom left of MMI coupler can be smoothed which is shown along the line of A-B-C shown in Fig. 1(c) and this optimization can further decrease the phase deviation of the tapered 1$\times$2 MMI. In the following sections, the three optical splitters are called rectangle-based, trapezoid-based and optimized trapezoid-based splitter respectively.
Fig. 1. Schematic drawing of the 1$\times$2 MMI coupler based on (a) rectangle-based shape, (b) trapezoid-based shape and (c) optimized trapezoid-based shape.
3. Simulation and Numerical Analysis for the coupler
3.1 Analysis of splitting ratio
The splitting ratio of three kinds of splitter is first investigated before the phase deviation. A three-dimensional finite-difference time-domain (3D-FDTD) method is used to optimize and simulate the device.The three kinds of splitters are based on 220-nm silicon-on-insulator (SOI). The length of rectangle-based MMI coupler is 2.14 µm ($Lr$). For the trapezoid-based splitter, the output width and length of MMI coupler are 2.4 µm ($W2$) and 3.3 µm ($Lt$) which is also used for the optimized trapezoid-based coupler. Rib waveguides are used for the coupler with the slab height of 90 nm for the two kinds of trapezoid-based splitter. To compare the performance of three kinds of splitter, the width of removed bottom left corner is set as 0.4 µm ($y$) which is the same value for the previously reported rectangle-based MMI coupler [14].
The splitting ratio between two output ports is defined as $T1/T2$ where $T1$ is the normalized power of the upper output port and $T2$ is the power of the lower output port which is shown in Fig. 1. The splitting ratio of rectangle-based splitter and trapezoid-based splitter related to the length of removed corner is shown Fig. 1(a). Because the length of rectangle-based MMI splitter is 2.14 µm, the range of $x$ is set to be [0 2.1] µm. The simulation is in C band spectra range, so for every value of $x$, there is a range of $T1/T2$ for the wavelength from 1530 nm to 1570 nm which is plotted using a pair of solid circles. For both of the two splitter, the splitting ratio decreases from 50:50 when $x$ increases. The rectangle-based splitter achieves a ratio range from 50:50 to 3:97 which is a little larger than the range from 50:50 to 11:89 for the trapezoid-based splitter. Figure 2(b) shows the splitting ratio of trapezoid-based splitter and optimized trapezoid-based splitter. The tendency of lines for the two kinds of splitter is similar to each other. It can be concluded that the two splitters achieve a range of splitting ratio from 50:50 to 10:90 which means that the optimization of input taper width does not cause significant difference for the splitting ratio based on the trapezoid coupler. The deviation of splitting ratio is shown in Fig. 3 which is calculated by subtracting the minimum ratio from the maximum ratio within C band.
Fig. 2. Splitting ratio related to the length of removed corner. (a) Couplers with rectangle-based shape and trapezoid-based shape. (b) Couplers with trapezoid-based shape and optimized trapezoid-based shape.
Fig. 3. Comparison between the three kinds of MMI coupler for the deviation of power splitting ratio.
The three kinds of splitter shows a similar tendency when $x$ is larger than 0.5 µm and the fluctuation of rectangle-based splitter is larger than that of trapezoid-based splitter. When $x$ is about 0.1 µm, there is a large deviation for the rectangle-based splitter which means the performance of unequal power splitting is deteriorated.
Figure 4 shows the normalized power of rectangle-based splitter and optimized trapezoid-based splitter. For the optimized trapezoid-based splitter, the normalized power of two output port at 1550 nm is 0.51 and 0.46 with the deviation less than 3.7e-3 in the C band. However, for the rectangle-based splitter, the normalized power is about 0.43 and 0.41 and the maximum deviation is 0.0547. It’s clear that the output power of rectangle-based splitter is more wavelength-sensitive when $x$ is 0.1 µm.
Fig. 4. Normalized power of the rectangle-based MMI coupler and optimized trapezoid-based MMI coupler when x=0.1 µm.
3.2 Analysis of phase deviation
The phase characteristics of the three kinds of asymmetric splitter play a key role for the applications requiring low wavelength-sensitive phase deviation while keeping a large range of splitting ratio. Because the removed section from the bottom left corner, the symmetry is broken so the absolute phase of two output ports are actually different which is an important difference from the 1$\times$2 splitter based on the symmetric MMI coupler. In this condition, a low phase deviation is essential for the coupler while maintaining a large range of power splitting ratio. Figure 5(a) shows the simulated phase difference of the two output ports of rectangle-based splitter and trapezoid-based splitter.
Fig. 5. Output phase difference related to the length of removed corner. (a) Couplers with rectangle-based shape and trapezoid-based shape. (b) Couplers with trapezoid-based shape and optimized trapezoid-based shape.
For every value of $x$, the range of output phase difference in C band is presented by a pair of solid circles. It can be seen that the phase of rectangle-based splitter is generally larger than that of the trapezoid-based splitter. When $x$ is less than 1.2 µm, the phase difference of both of the two types of splitter increases gradually with a slop about 20$^{\circ }$/µm. However, a significant difference occurs when $x$ is larger than 1.2 µm, the phase difference of rectangle-based splitter has a sharp increase while the phase of trapezoid-based splitter decreases gradually. When $x$ tends to 2.1 µm, the phase difference of rectangle-based splitter is up to 99.2$^{\circ }$ for the minimum value and 109.1$^{\circ }$ for the maximum value within C band. For the trapezoid-based splitter with $x$=2.1 µm, the phase difference ranges from 19.1$^{\circ }$ to 21.9$^{\circ }$. This phenomenon shows the potential of the trapezoid-based MMI coupler to lower the phase difference of splitter. Furthermore, Fig. 5(b) shows the output phase difference of the trapezoid-based splitter and optimized trapezoid-based splitter. It’s obvious that both of the two splitters have the same tendency when $x$ increases. In addition, there is a further decrease for the phase of optimized trapezoid-based splitter compared with the common trapezoid-based splitter.
It is noted that when $x$ is 0, all of the three kinds of splitter become symmetrical MMI coupler with a power splitting ratio of 50:50, which should have zero phase difference for the two output ports. Based on the examination for simulated data when $x$ is 0, the maximum absolute values of output phase difference are 0.0036$^{\circ }$ (rectangle-based splitter), 0.0057$^{\circ }$ (trapezoid-based splitter) and 0.0067$^{\circ }$ (optimized trapezoid-based splitter) respectively. These values are well close to 0 which shows that the simulation error of phase is less than 0.007$^{\circ }$. The calculated phase deviation for the three kinds of splitter is shown in Fig. 6 which represents the fluctuation of phase difference of two output ports, showing the wavelength-related characteristic in C band spectra.
When $x$ increase from 0, the three lines go up with different tendency. For the rectangle-based splitter, there are two sharp increase of phase deviation larger than 8.2$^{\circ }$ for the value of $x$=0.2 µm and x=2.1 µm corresponding to the splitting ratio near 50:50 and 3:97. For the $x$ between these two values, the phase deviation is larger than 2.1$^{\circ }$ and the line shows some fluctuation. The trapezoid-based splitter exhibits a lower deviation compared with the rectangle-based splitter within the whole range and the value increases gradually from 0 to 2.8$^{\circ }$. Then the optimized trapezoid-based splitter shows an even lower deviation than the trapezoid-based splitter due to the optimization for the width of input taper. When $x$ tends to 2.1 µm, the lines of two kinds of trapezoid-based splitter converge near 3.0$^{\circ }$. Also there is a difference larger than 0.4$^{\circ }$ when $x$ is from 0.7 µm to 1.4 µm. When $x$ is from 0.1 µm to 0.7 µm, the optimized trapezoid-based splitter exhibits a significant improvement with an ultra-low phase deviation less than 0.22$^{\circ }$, which is almost an order of magnitude smaller than the deviation of rectangle-based splitter which is larger than 2.1$^{\circ }$. It is noted that there is no sharp increase for both of the two trapezoid-based splitters, which is contributed by the introduction of trapezoidal shape of MMI coupler.
As a comparation, Fig. 7 shows the phase characteristics of rectangle-based splitter and optimized trapezoid-based splitter when $x$ is 0.6 µm. For the rectangle-based splitter, the output phase of two output ports at 1570 nm are -44.73$^{\circ }$ and -65.14$^{\circ }$ with the maximum difference of 20.41$^{\circ }$ while for the optimized trapezoid-based splitter, the output phase at 1570 nm is -158.90$^{\circ }$ and -171.29$^{\circ }$ with the minimum difference of 12.39$^{\circ }$. The minimum phase difference of rectangle-based splitter occurs at 1545 nm with 18.27$^{\circ }$ and the fluctuation of phase difference is 2.14$^{\circ }$. The maximum phase difference of optimized trapezoid-based splitter occurs at 1540 nm with 12.49$^{\circ }$ so the corresponding fluctuation of phase difference is 0.10$^{\circ }$, which compares well to the points in Fig. 6 when $x$ is 0.6 µm.
Fig. 7. Output phase of the rectangle-based MMI coupler and optimized trapezoid-based MMI coupler when x=0.6 µm.
3.3 Simulation for the insertion loss
The insertion loss is examined after the analysis for splitting ratio and phase deviation. Figure 8 shows the maximum loss of three kinds of splitter related to $x$ in C band spectra.
Fig. 8. Comparison between the three kinds of power splitters for the maximum insertion loss in C band.
For the rectangle-based splitter, the maximum loss is about 0.87 dB when $x$ is 0, which indicates that the splitter will have a larger loss when used for uniform power splitting. The minimum value of 0.17 dB occurs at $x$=0.6 µm. When $x$ is larger than 0.6 µm, the loss gradually increases to 0.44 dB. For the two kinds of trapezoid-based splitter, the tendency of lines are similar to each other. The minimum loss about 0.13 dB occurs near $x$=0.1 µm for the optimized trapezoid-based splitter. The lines increase to the maximum value about 0.67 dB when $x$ is from 0.2 µm to 2.1 µm. Above all, the optimized trapezoid-based 1$\times$2 splitter can achieve a comparable low-loss performance which indicates that the optimization for the width of input taper to achieving an ultra-low phase deviation does not introduce much additional loss for the optical splitter.
4. Numerical analysis of fabrication tolerance
By adjusting the value of x, tunable splitting ratio can be achieved for the three kinds of 1$\times$2 optical splitter. Here the transmittance-related and phase-related fabrication tolerance are analyzed based on the former discussion. According to the simulation result in Fig. 2, the splitting ratios of the three kinds of splitter gradually decrease when the value of $x$ increases. It is noted that the splitting ratio in Fig. 2 ranges from 0:100 to 50:50, which can be transformed into the normalized transmittance ranging from 0 to 0.5 for the lower output port in Fig. 1. So the derivative of transmittance is calculated to evaluate how the splitting ratio changes with the length of removed corner. For every value of $x$, the splitting ratio has a maximum and minimum value in the C band, so the average value is used to calculate the derivative of transmittance which is shown in Fig. 9(a).For the rectangle-based splitter, there is a large fluctuation which reaches the maximum of -0.087%/nm when $x$=0.2 µm. The trapezoid-based splitter comparatively shows a smooth line of transmittance derivative with an absolute value less than 0.039%/nm in the whole range and has a near-zero value when $x$ is about 2.0 µm, which compares well to the simulation result in Fig. 2.
Fig. 9. (a) Derivative of average transmittance with respect to the length of removed corner. (b) Derivative of phase deviation with respect to the length of removed corner.
For the phase-related tolerance, it can be seen that the phase lines of trapezoid-based splitter in Fig. 6 has a smaller slop than that of the rectangle-based splitter, which indicates that the characteristic of trapezoid-based splitter are more robust to the fabrication error. The calculated derivative of phase deviation is plotted in Fig. 9(b), showing how the range of output phase difference changes with the length of removed corner in the C band. It is clear that the rectangle-based splitter has a relative large shock of derivative, especially for the condition near 50:50 splitting ratio ($x\approx 0.1$ µm) and 3:97 splitting ratio ($x\approx 2.0$ µm) ,which can also be deduced by Fig. 6. The optimized trapezoid-based splitter has a smaller variation of phase deviation which is less than $\pm 0.0073^{\circ }$/nm and therefor is weakly sensitive to fabrication imperfections.
5. Conclusion
In this paper, we propose and numerically analyze an ultra-compact 1$\times$2 splitter employing an asymmetric ladder-shaped MMI coupler. The shape of coupler is optimized to be a trapezoid which can achieve a lower phase deviation with a comparable low-loss performance of the rectangle-based splitter. The use of trapezoid shape can effectively eliminate the fluctuation of splitting ratio and phase deviation. What is more, by optimizing the width of input taper for a smooth optical propagation, superior performance is obtained for the optimized trapezoid-based splitter with an ultra-low phase deviation less than 2.8$^{\circ }$, a low insertion loss less than 0.67 dB and a large splitting ratio ranging from 50:50 to 11:89.
Funding
National Key Research and Development Program of China (Grant No. 2018YFB2200202); National Natural Science Foundation of China (Grant No. 61804148).
Disclosures
The authors declare no conflicts of interest.
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