_{1}

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In this paper, we demonstrated a compact Si-SiO2 waveguide coupler with a footprint of only 2 μm × 3 μm by topology optimization in the communication wavelength. The transmission was increased from 30% to 100%, much higher than other methods. Besides, the optimized structure did not incorporate other dielectric materials, facilitating fabrications and applications.

Photonic integrated circuits (PICs) integrate multiple photonic functional elements (such as waveguides [

In this paper, we first numerically demonstrate that topological optimization could be applied in designing waveguide coupler with near unity efficiency. We designed a new coupler for Si-SiO_{2} waveguide transition with high transmission efficiency. 100% transmission is achieved with the design based on topology optimization while introducing minimum modification in the optimization region. This technique could be potentially used in different areas of photonic device design.

The topology optimization problem for the Si-SiO_{2} waveguide coupler is schematically shown in _{2}. Other scattered light is absorbed by the perfectly matched layer as indicated between the two dashed lines. To get a high transmission from the Si waveguide to the SiO_{2} waveguide, we defined an optimization region of 2 μm × 3 μm in size. The refractive index in this region can vary from 1 to 3.5 according to the following equation.

n R A M P ( η ) = n S i − n a i r 1 + exp [ − 2 p 1 ( η − 0.5 ) ] + n a i r (1)

where η is the parameter to be optimized directly. p_{1} is a control parameter set to be 10 so that over a large range of the value of η, n_{RAMP} is close to either n_{ai}_{r} or n_{Si}. η is constrained to vary between 0 and 1. n_{RAMP} is chosen this way such that n_{RAMP}(η = 0) = n_{ai}_{r} while n_{RAMP}(η = 1) = n_{Si}.

Infrared light with 1550 nm is sent from the left input port and transmission is monitored at the output port. Scattered light is absorbed by the perfectly matched layers (the region between the two dashed box).

On the other hand, we still have possibility to get refractive index that is not close n_{air} or n_{Si}, in which case, it will be difficult to achieve. We impose another constrain by designating a weight function (w) on every point in the optimization region. The integration over the optimization region is set to be lower bounded by 95% of its area, restricting w to be as close to unit as possible.

w = 1 + 1 1 + exp [ − 2 p 2 ( η − 0.6 ) ] − 1 1 + exp [ − 2 p 2 ( η − 0.4 ) ] (2)

The Equation (2) shows that w is determined by η which is shown in _{RAMP} and w.

Lambda | 1550 [nm] | Wavelength |
---|---|---|

W_SiO_{2} | 1.8 [um] | Width of the SiO_{2} waveguide |

W_Si | 430 [nm] | Width of the Si waveguide |

p_{1} | 10 | Control parameter |

p_{2} | 10 | Control parameter |

n_SiO_{2} | 1.5 | Refractive index of SiO_{2} |

n_Si | 3.5 | Refractive index of Si |

n_air | 1 | Refractive index of air |

L_domain | 2 [um] | Length of the optimization region |

W_domain | 3 [nm] | Width of the optimization region |

eta_initial | 0.8 | Initial value of eta |

d_PML | 0.8 [um] | Thickness of the PML region |

to be Si. It is clear that strong scatterings towards unwanted directions and reflection occurs, resulting in only 30% transmission.

Strong light scattering outside the dielectric region can be observed from the distorted wave front. A transmission of 30% is recorded.

A first step to optimize is to simply introduce a transitional tapered region as shown in the left side of _{Si} and n SiO 2 . Simulation results on right side indicate improved transmission to 72%. Though this is more than twice than the original case, much need to be improved for real applications.

Last, we employ the method described in previous section for topology optimization with results shown in _{RAMP} close to n_{air} and w close to unit, fulfilling our initial design goal.

Relatively uniform waveguide mode propagation in the input and output waveguide and some scattering outside the dielectric region is observed. A transmission of 72% is recorded.

Uniform waveguide mode propagation in the input and output waveguide and little scattering outside the dielectric region is observed. A transmission of 100% is recorded.

In conclusion, we have numerically studied a topological optimization problem for a Si-SiO_{2} waveguide coupler in photonic integrated circuits. The design features a compact footprint with minimal region removed. This method could potentially be used in optimization problems of other photonic devices.

Wang, Y.K. (2018) Optimization of a Si-SiO_{2} Waveguide Coupler for Photonic Integrated Circuits. Circuits and Systems, 9, 101-106. https://doi.org/10.4236/cs.2018.97010