Research On Silicon-based Multimode Photonic Devices Based On Transformation Optics

The silicon-based integrated photonics has the advantages of high integration,low cost,and good compatibility with CMOS processes,and has become one of the best platforms for building the next generation of large-bandwidth optical interconnect systems.To further enhance the communication capacity of silicon-based integrated photonic chips,researchers have developed a variety of multiplexing techniques.Among them,the mode division multiplexing technology uses multiple spatial modes to carry optical information without increasing the complexity of the system,and can be combined with wavelength division multiplexing and polarization multiplexing to significantly increase the on-chip optical interconnect capacity.Therefore,multimode silicon-based photonics has become a research hotspot in recent years.To construct on-chip high-density integrated mode division multiplexing systems,a series of silicon-based multimode photonic devices have been studied.However,traditional integrated optical design methods can only design devices based on single-mode waveguides,and it is difficult to design functional devices that support multiple waveguide modes.Therefore,a method based on transformation optics theory is proposed to realize high-performance multimode photonic devices.Transformation optics design methods utilize spatial coordinate transformation to flexibly control the propagation of light.The transmission characteristics of the photonic device before and after the coordinate transformation are the same,but the spatial distribution of the permittivity and permeability of the material changes.The purpose of this thesis is to design silicon-based integrated photonic devices supporting multimode transmission using transformation optics theory.The main research contents are as follows:（1）Starting from Maxwell’s equations,the theoretical formulas of general transformation optics and conformal transformation optics with simplified dielectric material parameters are deduced.And the construction method of conformal transformation is introduced.（2）A compact and broadband multi-mode waveguide bend capable of supporting four TE modes is designed by the method of transforming optics combined with device boundary shape optimization.The effective radius of the multimode waveguide bend is only 17μm.The three-dimensional FDTD simulation results show that,in the ultra-wideband range of500 nm,the theoretical transmission loss of each mode is lower than 0.1 d B and the crosstalk between modes is lower than-20 d B.The fabrication tolerance of waveguide width can reach±50 nm.We fabricated this multimode waveguide bend on a commercial silicon-on-insulator（SOI）wafer.The test results show that,at the wavelength of 1550 nm,the insertion loss of TE₀-TE₃ modes were all lower than 0.6 d B,and the inter-mode crosstalk was lower than-17 d B.（3）Based on the multi-mode waveguide bend designed by transformation optics,a high-Q multimode micro-ring resonator that supports the resonance of two TE modes is realized.A tensor calculation method for analyzing multimode micro-ring resonators is proposed,and the transmittance formula suitable for multimode micro-ring is deduced.The multimode micro-ring based on the transfer matrix theory method is verified by FDTD simulation.The multimode microring resonator was fabricated on the SOI platform.And the experimentally measured load Q values of the TE₀ and TE₁ modes were 5.43×10⁴ and3.21×10⁴,respectively.（4）A 180°multimode waveguide bend with mode adiabatic evolution is proposed by using transformation optics combined with waveguide shape optimization,which supports three TE waveguide modes.The simulation results show that,at 1550 nm wavelength,the transmission loss of TE₀-TE₂ modes in the shape-optimized 180°multimode waveguide bend are all lower than 0.1 d B,and the inter-mode crosstalk is lower than-28 d B.Two 180°multimode waveguide bends and two multimode straight waveguides are connected to form a multimode racetrack microring resonator.And the selective excitation of each order mode in the resonator is realized by using the curved directional coupler and the asymmetric directional coupler.The device was fabricated on SOI,and the experimentally measured loaded Q values for all three modes exceeded 4.5×10⁴.（5）A series of methods for designing multimode taper waveguides are proposed using the theory of transformation optics.Firstly,a graded-index multimode taper waveguide supporting six TE modes is designed by using conformal transformation and controlling the refractive index range.The simulation results show that the transmission loss of each order mode is less than 0.01 d B at the wavelength of 1550 nm.To avoid the complicated grayscale exposure process,the subwavelength structure is proposed to realize the graded refractive index distribution required by the device.The optical transmission performance of the subwavelength multimode taper waveguide is verified by FDTD simulation.The theoretical transmission loss of the TE₀-TE₂ modes at 1550 nm are all lower than 0.45 d B,and the inter-mode crosstalk is lower than-21 d B.Finally,to further reduce the fabrication difficulty,a method of transforming optics combined with shape optimization is proposed to design a multimode taper waveguide that does not require graded index or subwavelength structures.The simulation results show that,at 1550 nm wavelength,the theoretical transmission losses of TE₀-TE₂ modes are all lower than 0.15 d B,and the inter-mode crosstalk is lower than-26 d B.