Efficient topology optimization of optical waveguide devices utilizing semi-vectorial finite-difference beam propagation method

Recently published literature has highlighted on the great potentials of topology optimal design method, that can be exploited to further miniaturize the optical waveguide devices and improve the devices performance. Moreover, the applications of the topology optimal design to optical devices have been reported and their effectiveness has been demonstrated far and wide. At present, the topology design methods discussed, so far, utilize; a finite element method, a finite-difference time-domain technique or a finite-difference frequency-domain method for wave propagation analysis. Application of beam propagation method for designing devices whose device length is too long to analyze characteristics with the techniques stated above has also been undertaken. Unfortunately, the latter approach has only been applied for 2D design problems.

Mr. Akito Iguchi (PhD Student) and Professor Yasuhide Tsuji from Muroran Institute of Technology in collaboration with Professor Takashi Yasui and Professor Koichi Hirayama from Kitami Institute of Technology in Japan developed a design approach where the beam propagation method was extended for the case of a semi-vectorial 3-D design problem. The team purposed to employ the semi-vectorial finite-difference beam propagation method(SVFD-BPM) based on an alternating direction implicit method for efficient calculation. Their work is currently published in the research journal, Optics Express.

The researchers commenced the experimental setup by extending the adjoint variable method previously reported for the case of using the density method and the SVFD-BPM based on the alternating direction implicit method. The researchers then advanced to employ the 3-D scalar Helmholtz equation after which they reviewed the basic equations for SVFD-BPM based on the alternating direction implicit method. A good description of the sensitivity analysis technique was then laid out for the case of employing the SVFD-BPM and the density method. Eventually, the research team designed several weakly guiding waveguide devices so as to verify the validity of the sensitivity analysis and their design approach.

The authors observed that the properties of the devices were improved after every iteration in the optimization process. Additionally, they noted that the binarized optimized structures were almost similar, and the difference of the output properties was not substantial even though mosaic-like structures emerged slightly. More so, numerical results directed that the beam propagation method was available when refractive index difference was very low even though waveguide structure was complicated to some extent.

The Yasuhide Tsuji and colleagues study has presented an efficient topology optimal design approach using the SVFD-BPM in which the adjoint variable method has been employed for the first time. In this study, the validity of the novel developed design approach has been confirmed for the case of weakly guiding waveguides. However, the possibility of applying this novel approach is not recommended for strongly guiding waveguides as it necessitates the use of constraint conditions which prohibits appearance of the structure thereby becoming cumbersome to analyze using the beam propagation method.