# Foundry-Processed Compact and Broadband Adiabatic Optical Power Splitters with Strong Fabrication Tolerance

^{*}

## Abstract

**:**

## 1. Introduction

^{2}[13]. However, this device was designed for a 300 nm-thick Si layer, which is not commonly used by industrial foundries. More-successful implementations of MMI power splitters have been achieved by modifying the profile of the MMI region, yielding a very compact and low-loss operation [14,15]. One downside of MMI power splitters is that the profile of the device between the MMI region and the output waveguides changes abruptly. This abrupt change constitutes a source for reflections and imbalance in the output, where a slight imbalance in the output waveguides can cause imperfect splitting or increased losses, as we demonstrated a similar effect in previous work [16].

## 2. The 1 × 2 Y-Junction Optical Power Splitters

#### 2.1. Design Methodology for 1 × 2 Y-Junction Power Splitters

_{tip}, and the gaps are denoted by w

_{gap,1}and w

_{gap,2}. The first stage of the Y-junction splitter is an adiabatically tapered region that gradually splits the input power from the middle waveguide to the upper and lower waveguides. The middle waveguide varies from 500 nm to w

_{tip}, while the upper and lower waveguides vary from w

_{tip}to 500 nm over the taper length (L

_{Y}). The value of w

_{tip}is the smallest feature in this design. A smaller w

_{tip}results in shorter devices, but it is typically limited by the minimum feature that is allowed by the foundry. The values of w

_{gap,1}and w

_{gap,2}are the widths of the lower and uppers gaps, respectively, and they are always chosen to be at least 20 nm wider than w

_{tip}to reduce potential reflections due to the abrupt changes at the two ends of the tapers. After the adiabatic coupling region, the waveguides are separated by 4 $\mathsf{\mu}$m by using two 15 $\mathsf{\mu}$m-long S-bends, whose lengths were chosen generously to ensure the losses are predominantly due to the coupling region.

_{gap,1}and w

_{gap,2}are equal, the Y-junction power splitter has a 50:50 splitting ratio. An imbalance between w

_{gap,1}and w

_{gap,2}causes the splitting ratio to vary. Here, we designed four devices with 50:50 splitting ratios with minimum feature sizes (i.e., w

_{tip}) of 140 nm, 160 nm, 180 nm, and 200 nm. The designs with different w

_{tip}allowed us to observe the effect of the minimum feature size on the performance of the Y-junction power splitters. For these devices, w

_{gap,1}and w

_{gap,2}were equal, and they were 20 nm wider than w

_{tip}. To realize Y-junctions with arbitrary splitting ratios, we kept w

_{tip}and w

_{gap,1}fixed at 180 nm and 200 nm, respectively, and varied w

_{gap,2}depending on the power splitting ratio we wished to achieve.

_{n}is the power of the nth term and c

_{n}is the coefficient of the nth term. The chosen p-values were [0, 0.3, 0.5, 0.7, 1, 2, 5, 10], and c

_{n}values were to be determined by the optimization. The normalized length (z

_{norm}) is defined as z

_{norm}= z/L

_{Y}and was limited by the bounds of [0, 1]. Using the polynomial function in Equation (1) allowed great freedom in modifying the shape of the taper. The selection of the p-values was made by considering how rapidly or gradually the tapers were desired to vary in width along the z-axis. For example, for a p-value of 0.3, the taper became wider quickly, then the width changed slowly. On the other hand, for a p-value of 10, the shape of the taper changed very slowly until the end of the taper, where the width started changing rapidly. We chose the p-values of 0.3 and 10 by trial, where we ensured that the taper shape did not vary too quickly, hence disturbing the adiabatic evolution at the beginning or at the end of the taper. Then, we added five more p-values between 0.3 and 10 to ensure that the taper could take shape freely between the two extremes. To satisfy the boundary conditions (i.e., ${w}^{up}\left(0\right)$ = w

_{tip}and ${w}^{up}\left(1\right)$ = 500 nm), we ensured that

_{n}values were chosen prior to the optimization, and the taper profiles were optimized by optimizing the c

_{n}values. A wide range of p-values was chosen to allow for a wide range of taper shapes. Small p-values (p < 1) allowed for a rapid change of shape at the beginning of the taper, followed by a more-gradual change towards the end of the taper, while larger p-values (p > 1) caused the taper shape to vary slowly, followed by a rapid change of width. The c

_{n}values determined to what degree these shapes should be included in the optimized structure. A particle swarm optimization algorithm was used to optimize the c

_{n}values. The optimization goal was set to minimize the taper losses at the wavelength of 1550 nm for the TE, or the TM mode, whichever was higher, so as to achieve polarization-insensitive operation. The number of particles was selected to be 45, and the optimization was run for 25 generations, or until the result had not improved for 3 consecutive generations, whichever happened first. After the optimization, we simulated the devices with the -D finite-difference time-domain (FDTD) method to ensure the accuracy of the results. The field profiles along an optimized 1 × 2 50:50 Y-junction power splitter for a minimum feature size of 180 nm (i.e., w

_{tip}= 180 nm, w

_{gap,1}= w

_{gap,2}= 200 nm) are shown for the TE and TM modes in Figure 1b and Figure 1c, respectively.

#### 2.2. Profile-optimized 1 × 2 Y-Junction Power Splitters

_{tip}and w

_{gap,1}fixed at 180 nm and 200 nm, respectively, while varying w

_{gap,2}. For each value of w

_{gap,2}, we optimized the profile of the device to minimize the taper losses for the TE mode. Although arbitrary splitting ratios were achievable for both modes, for a given w

_{gap,2}value, Y-junctions will have different splitting ratios for the TE and TM modes. To prove the effectiveness of this structure, we designed our devices for the TE mode only, although the same optimization can be performed for the TM mode. The ratio of the transmitted power to the lower arm of the Y-junction power splitter is shown in Figure 3a for the TE mode as a function w

_{gap,2}. Power splitting ratios from 50:50 to 98:2 could be achieved by varying the w

_{gap,2}from 200 nm to 520 nm.

_{gap,2}of 200 nm, 220 nm, 250 nm, 290 nm, and 355 nm, which resulted in power splitting ratios of 50:50, 58:42, 68:32, 77:23, and 89:11, respectively. The spectra of the power ratios at the lower arm are shown in Figure 3b. The spectral variations in the splitting ratios were within ±1% for all the Y-junction power splitters throughout the wavelength range of 1450 nm to 1650 nm. The excess losses for these devices are shown in Figure 3c, where the excess losses were below 0.2 dB for wavelengths longer than 1500 nm. The electric field profiles (|E|) along the Y-junction splitters showed that the power splitting took place with little radiation losses at a 1550 nm wavelength for a w

_{gap,2}of 250 nm and 355, as shown in Figure 3d and Figure 3e, respectively. The geometrical parameters of the designed devices are presented in Table A1.

#### 2.3. Experimental Results for 1 × 2 Y-Junction Power Splitters

_{2}cladding layer. The edges of the chips were deeply etched to allow access to the edge couplers. Scanning electron microscope images of the resultant Y-junctions with 50:50 and 89:11 power splitting ratios are shown in Figure 4a and Figure 4b, respectively, for a minimum feature size of 180 nm.

_{gap,2}. All the devices we analyzed here had excess losses lower than 0.6 dB for wavelengths longer than 1490 nm, indicating that the varying of the splitting ratio did not affect the bandwidth significantly. Figure 6b shows the spectra of the average power ratio at the lower arm of the Y-junction power splitter along with the simulated results shown as dashed lines. For the power splitters with designed splitting ratios of 50:50, and 58:42, the experimental results were in excellent agreement with the simulated splitting ratios. For the splitters with designed splitting ratios of 68:32, 77:23, and 89:11, however, the differences were 3%, 7%, and 5%, respectively, in the C-band. This discrepancy might have been caused by the gaps between the waveguides being affected disproportionately by the fabrication errors. Such fabrication errors typically do not affect the results for splitting ratios close to 50:50, thanks to the inherent fabrication tolerance of the adiabatic power splitters, but they are more pronounced when the asymmetry in the structure is higher.

_{gap,2}values. The standard deviations ranged between 2% and 4% with the exception of a w

_{gap,2}of 290 nm, where the deviation was around 6%.

## 3. Broadband 2 × 2 50:50 Optical Power Splitters on 90 nm Slab

#### 3.1. Design of 2 × 2 50:50 Power Splitters

_{n}values were [0, 0.1, 0.3, 0.5, 0.7, 1, 3, 5]. These values were smaller than the ones for the 1 × 2 Y-junction power splitter. This was because the 2 × 2 50:50 power splitters performed better with smaller p-values, and including 0.1 in the p-values reduced the times to find the optimal structures. To satisfy the boundary conditions (i.e., w

^{up}(0) = 400 nm, and w

^{up}(1) = 500 nm), we ensured that

_{c}), along with the linear taper (red solid line) for comparison. The linear taper required approximately a 60 $\mathsf{\mu}$m coupling length to achieve losses lower than 0.1 dB. On the other hand, the profile-optimized tapers could achieve 0.1 dB losses with a coupling length of approximately 12 $\mathsf{\mu}$m and 16 $\mathsf{\mu}$m, depending on the $\alpha $ parameter. Among the $\alpha $ parameters analyzed here, an $\alpha $ of 0.3 achieved the lowest losses with the shortest length; hence, we used an $\alpha $ parameter of 0.3 and a coupling length of 16 $\mathsf{\mu}$m. When the coupling region was simulated with the 3D FDTD method, an excess loss of less than 0.2 dB can be achieved over a bandwidth of 200 nm, as shown in Figure 7c. Moreover, the excess loss difference between the two inputs was less than 0.05 dB throughout the spectrum, indicating a balance in losses seen from both inputs. When we included fabrication errors of ±20 nm in the widths of the two waveguides, the calculated losses varied by less than 0.09 dB within the wavelength range of 1450–1650 nm. This indicated that the designed 2 × 2 Y-junction power splitter was tolerant to fabrication errors. Figure 7d,e show the field profiles of the mode evolution from the inputs to the anti-symmetric and symmetric modes, respectively. The mode profiles showed a successful transition from the inputs to the desired output modes. The geometrical parameters of the device is given in Table A1.

#### 3.2. Experimental Design for the 2 × 2 50:50 Power Splitters

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

Device | Min. Feature Size (nm) | Coupling Length ($\mathsf{\mu}$m) | $\mathit{\alpha}$ | p_{n} | c_{n} |
---|---|---|---|---|---|

1 × 2 50:50 Y-junction | 140 | 10 | 0.5 | [0, 0.3, 0.5, 0.7, 1, 2, 5, 10] | [140, 0, 0, 0, 170, 37, 153] |

160 | 15 | [160, 0, 0, 50, 68, 127, 11, 84] | |||

180 | 20 | [180, 0, 1, 117, 52, 57, 82, 11] | |||

200 | 30 | [200, 0, 7, 73, 71, 33, 16, 100] | |||

1 × 2 58:42 Y-junction | 180 | 20 | 0.5 | [0, 0.3, 0.5, 0.7, 1, 2, 5, 10] | [180, 22, 49, 57, 8, 56, 47, 81] |

1 × 2 68:32 Y-junction | 180 | 20 | [180, 35, 57, 78, 5, 31, 54, 60] | ||

1 × 2 78:22 Y-junction | 180 | 20 | [180, 60, 43, 40, 33, 21, 57, 66] | ||

1 × 2 89:11 Y-junction | 180 | 20 | [180, 60, 79, 9, 13, 16, 56, 87] | ||

2 × 2 50:50 | 200 | 16 | 0.3 | [0, 0.1, 0.3, 0.5, 0.7, 1, 3, 5] | [400, 14, 45, 18, 1, 10, 0, 12] |

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**Figure 1.**(

**a**) Schematic of the 1 × 2 Y-junction power splitters. Electric fields along the Y-junctions for the (

**b**) TE and (

**c**) TM modes at a 1550 nm wavelength.

**Figure 2.**(

**a**) Simulated taper losses for the Y-junction power splitter with a 180 nm minimum feature size for varying $\alpha $ for the TE mode. The optimized taper losses for the (

**b**) TE and (

**c**) TM modes. (

**d**) Spectra of the excess losses for the devices with four minimum feature sizes.

**Figure 3.**(

**a**) Power fraction at the lower arm for varying w

_{gap,2}. (

**b**) Spectra of the splitting ratios for the Y-junction power splitters for varying w

_{gap,2}. (

**c**) Spectra of the excess losses for the devices with arbitrary power splitting ratios. The magnitude of electric fields (|E|) along the Y-junction power splitter with (

**d**) w

_{gap,2}= 250 nm and (

**e**) w

_{gap,2}= 355 nm, at 1550 nm. All figures pertain to the TE mode.

**Figure 4.**Scanning electron microscope images of the (

**a**) 50:50 power splitter and (

**b**) 89:11 power splitter with 180 nm minimum feature sizes.

**Figure 5.**Average excess losses for the 50:50 1 × 2 Y-junction for the (

**a**) TE and (

**b**) TM modes. Average excess losses and standard deviation in losses for the Y-junction with 180 nm minimum feature size for the (

**c**) TE and (

**d**) TM modes. Transmission spectra of the Mach–Zehnder interferometer for the Y-junction with a 180 nm minimum feature size for the (

**e**) TE and (

**f**) TM modes. Spectra of the average extinction ratios for the (

**g**) TE and (

**h**) TM modes.

**Figure 6.**(

**a**) Average excess losses for the 1 × 2 Y-junction with arbitrary splitting ratios. (

**b**) The average power ratio at the lower arm of the Y-junction for the power splitters with different splitting ratios (solid lines) and their corresponding simulation results (dashed lines). (

**c**) Standard deviation in the measured splitting ratios of the 1 × 2 Y-junction power splitters.

**Figure 7.**(

**a**) Schematic of the designed 2 × 2 power splitter. (

**b**) Simulated taper losses in the adiabatic coupling region. (

**c**) Spectra of the simulated excess losses when power is launched from both inputs. The mode field profiles along the coupling region for (

**d**) Input 1 (TE

_{1}mode) and (

**e**) Input 2 (TE

_{2}mode).

**Figure 8.**(

**a**) Scanning electron microscope image of the 2 × 2 3 dB power splitter. Average excess losses and standard deviation in losses when the input power is launched from (

**b**) Input 1 and (

**c**) Input 2. (

**d**) A representative transmission spectra of the Mach–Zehnder interferometer. Spectra of the average extinction ratios when the input power is launched from (

**e**) Input 1 and (

**f**) Input 2.

**Table 1.**Summary of measured performance metrics of the selected power splitters designed in this paper. The excess losses (ELs) and splitting ratios (SRs) are given for the entire bandwidth.

Device | Min. Feature Size (nm) | EL_{TE} ^{1} (dB) | EL_{TM} ^{1} (dB) | SR_{TE} ^{2} | Bandwidth (nm) |
---|---|---|---|---|---|

1 × 2 50:50 Y-junction | 180 | <0.5 | <0.5 | 50 ± 2 | 1480–1585 |

1 × 2 58:42 Y-junction | 180 | <0.6 | - | 58 ± 2 | 1490–1590 |

1 × 2 68:32 Y-junction | 180 | <0.5 | - | 71 ± 3 | 1487–1590 |

1 × 2 78:22 Y-junction | 180 | <0.6 | - | 84 ± 5 | 1490–1590 |

1 × 2 89:11 Y-junction | 180 | <0.6 | - | 94 ± 2 | 1490–1590 |

2 × 2 50:50 | 200 | <0.7 | - | 50 ± 3 | 1465–1590 |

^{1}EL: excess loss.

^{2}SR: splitting ratio.

**Table 2.**A comparison of the adiabatic 50:50 power splitters reported in the literature with our power splitters.

Ref. | Device Type | Length ($\mathsf{\mu}$m) | Min. Feature Size (nm) | EL_{TE} ^{1} (dB) | EL_{TM} ^{1} (dB) | Bandwidth (nm) |
---|---|---|---|---|---|---|

[39] | 1 × 2 | 5 | 30 | 0.19 | 0.14 | 1530–1600 |

[41] | 1 × 2 | 40 | 100 | <1 | <1 | 1260–1650 |

[44] | 1 × 2 | 19 | 200 | ∼0.09 | - | 1510–1560 |

[45] | 1 × 2 | 40 | 200 | ∼0.06 | - | 1470–1570 |

[55] | 1 × 2 | 14 | 120 | 0.25 | 0.23 | 1500–1600 |

This work | 1 × 2 | 20 | 180 | <0.5 | <0.5 | 1480–1585 |

[46] | 2 × 2 | 100 | 200 | NR ^{2} | - | 1500–1600 ^{3} |

[47] | 2 × 2 | 60 | 200 | <0.3 | - | 1500–1600 |

[48] | 2 × 2 | 83 | 200 | <0.15 | - | 1480–1620 |

[49] | 2 × 2 | 26.3 | 200 | NR ^{2} | - | 1470–1620 ^{4} |

[50] | 2 × 2 | 11.7 | 150 | NR ^{2} | - | 1500–1600 ^{4} |

[51] | 2 × 2 | 11.7 | 150 | NR ^{2} | NR ^{2} | 1490–1565 ^{4} |

This work | 2 × 2 | 16 | 200 | <0.7 | - | 1465–1590 |

^{1}EL: Excess loss.

^{2}NR: not reported.

^{3}This is the measurement bandwidth.

^{4}These indicate a 3 ± 0.5 dB bandwidth.

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## Share and Cite

**MDPI and ACS Style**

Ozcan, C.; Aitchison, J.S.; Mojahedi, M.
Foundry-Processed Compact and Broadband Adiabatic Optical Power Splitters with Strong Fabrication Tolerance. *Photonics* **2023**, *10*, 1310.
https://doi.org/10.3390/photonics10121310

**AMA Style**

Ozcan C, Aitchison JS, Mojahedi M.
Foundry-Processed Compact and Broadband Adiabatic Optical Power Splitters with Strong Fabrication Tolerance. *Photonics*. 2023; 10(12):1310.
https://doi.org/10.3390/photonics10121310

**Chicago/Turabian Style**

Ozcan, Can, J. Stewart Aitchison, and Mo Mojahedi.
2023. "Foundry-Processed Compact and Broadband Adiabatic Optical Power Splitters with Strong Fabrication Tolerance" *Photonics* 10, no. 12: 1310.
https://doi.org/10.3390/photonics10121310