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

Significance 

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.

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

About the author

Akito Iguchi received the B.S. and M.S. degree in information and electronic engineering from Muroran Institute of Technology, Muroran, Japan, in 2015 and 2017, respectively.
He is currently working toward the Ph.D. degree in information and electronic engineering at the same university. He is a Student Member of IEEE and  the Institute of Electronics, Information and Communication Engineers(IEICE).

About the author

Yasuhide Tsuji received the B.S., M.S., and Ph.D. degrees in electronic engineering from Hokkaido University, Sapporo, Japan, in 1991, 1993, and 1996, respectively. In 1996, he joined the Department of Applied Electronic Engineering, Hokkaido Institute of Technology, Sapporo. From 1997 to 2004, he was an Associate Professor in the Division of Electronics and Information Engineering, Hokkaido University. From 2004 to 2011, he was an Associate Professor in the Division of Electrical and Electronic Engineering, Kitami Institute of Technology, Kitami, Japan. Since 2011, he has been a Professor in the Division of Information and Electronic Engineering, Muroran Institute of Technology, Muroran, Japan. His research interest includes wave electronics. Dr. Tsuji is a member of the Institute of Electronics, Information and Communication Engineers (IEICE), the Japan Society of Applied Physics, and the Optical Society of America. In 1997 and 1999, he received the Excellent Paper Award from IEICE. In 2000, he received the Third Millennium Medal from IEEE.

About the author

Takashi Yasui received the B.S. degree in electronic engineering from Fukui University, Fukui, Japan, in 1997, and the M.S. and Ph.D. degrees in electronic engineering from Hokkaido University, Sapporo, Japan, in 1999 and 2001, respectively.
From 1999 to 2002, he was a Research Fellow of the Japan Society for the Promotion of Science. In 2002, he joined Fujitsu Ltd., Chiba, Japan. From 2004 to 2011, he was an Assistant Professor in the Department of Electronic and Control Systems Engineering, Shimane University, Matsue, Japan. Since 2011, he has been an Associate Professor in the Department of Electrical and Electronic Engineering, Kitami Institute of Technology, Kitami, Japan. His research interests include wave electronics.
Dr. Yasui is a Member of the Applied Computational Electromagnetics Society, the Optical Society of America, the Institute of Electronics, Information, and Communication Engineers of Japan, and the Magnetics Society of Japan.

About the author

Koichi Hirayama received the B.S., M.S., and Ph.D. degrees in electronic engineering from Hokkaido University, Sapporo, Japan, in 1984, 1986, and 1989, respectively. In 1989, he joined the Department of Electronic Engineering, Kushiro National College of Technology, Kushiro, Japan. In 1992, he became an Associate Professor of electronic engineering at Kitami Institute of Technology, Kitami, Japan, and since 2004, he has been a Professor. He has been interested in the analysis and optimal design of electromagnetic and optical waveguides. Dr. Hirayama is a Member of the Institute of of Electronics, Information and Communication Engineers of Japan and the Japan Society of Applied Physics.

Reference

Akito Iguchi, Yasuhide Tsuji, Takashi Yasui, Koichi Hirayama. Efficient topology optimization of optical waveguide devices utilizing semi-vectorial finite-difference beam propagation method. Vol. 25, No. 23 | 13 Nov 2017 | Optics Express

 

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