Fabrication tolerances for coupled waveguide

As previously stated in section D.1, variations during the fabrication process can have an effect on the performance of the coupling waveguide. Also, based on equation D.12, the dimensions of the waveguide as well as the separation between them influence the coupling coefficient.

One of the issues faced with fabricating a vertical coupling waveguide is the capability to control the thickness of each layer. Therefore, if there are variations in the thickness of each layer, the coupling effect changes. In this section we analyse the effect of a change in the thickness of core as well as the thickness of the core separation layer on the power output and the coupling between the two waveguides.

In the first scenario, we vary the thickness of each core from 150 nm to 450 nm. The simulation results show that in order to have >90% coupling from the lower waveguide to the upper waveguide, the thickness of each core can only be within a ±60 nm tolerance as shown in Fig. D.5. On the other hand, the coupling efficiency show that even if core thickness ranges from 150 nm to 450 nm, the coupling efficiency is still greater than 2dB as seen in Fig D.6.

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Fig. D.5: Normalized power output of the upper waveguide when the core thickness is varied from 150 nm to 450 nm. The blue highlighted area indicate >90% normalized power output of the upper waveguide.

Fig. D.6: Coupling efficiency (dB) when the core thickness is varied from 150 nm to 450 nm.

0.15 0.20 0.25 0.30 0.35 0.40 0.45

Coupling efficiency [dB]

Core thickness [m]

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In the second scenario, we vary the thickness of the core separation layer from 1.0 µm to 2.5 µm and the simulation results show that for >80% power coupling, the fabrication tolerance allows for a core separation thickness to vary from 1.32 m to 1.72 m as shown in Fig. D.7 below. Similarly, the coupling efficiency as shown in Fig. D.8 indicate that the coupling efficiency is lower than zero for if the thickness goes thinner than 1.25 m or thicker than 1.9 m. Therefore, the fabrication tolerance of ±0.2 m is acceptable for fabricating the core separation layer.

Fig. D.7: Normalized power output of the upper waveguide when the core separation thickness is varied from 1.0 m to 2.5 m. The blue highlighted area indicate >80% power output of the upper waveguide.

0.0 0.2 0.4 0.6 0.8 1.0 1.2

1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5

Normalized power output

Core separation thickness [m]

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Fig. D.8: Coupling efficiency (dB) when the core separation thickness is varied from 1.0 m to 2.5 m.

One assumption that is held throughout the simulation process is that each layer is consistent throughout the entire waveguide. In actuality, this may not be the exact case during the fabrication process. Imperfections such as cracks, voids, and diffusion of one layer into the other can have an adverse effect on the performance of the vertical coupler and will reduce the coupling efficiency further. Some of the imperfections seen during the fabrication process and methods to overcome them are described in detail in the next chapter.

-10 -5 0 5 10 15

1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5

Coupling efficiency [dB]

Core separation thickness [m]

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D. 5. Conclusion

In conclusion, in this chapter we have shown an overview of the coupled mode theory for the coupling waveguide. Calculation and simulation done through BPM have shown a coupling length of around 55 m is achieved for our designed dimensions. Further simulation data show that the fabrication tolerance for variations in both the core thickness and the core separation thickness where data indicates that >90% power coupling can be achieved if the core thickness is kept within a ±60 nm tolerance. For variation in the core separation, a ±200 nm fabrication tolerance is acceptable for a >80%

power coupling. The lower size of the design can enable it to be integrated with other photonic devices in a photonic integrated circuit. It is expected that by making use of the multi-layer sol-gel SiO2 fabrication technique in conjunction with a suitable core material, a vertical coupling waveguide can be achieved.

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D. 6. References

[1] R. G. Hunsperger, “Coupling Between Waveguides,” in Integrated Optics: Theory and Technology, Springer New York, pp. 153–169, 2009.

[2] W.-P. Huang, “Coupled-mode theory for optical waveguides: an overview,” J. Opt. Soc. Am. A, vol. 11, no. 3, p. 963, 1994.

[3] H. A. Haus, W.-P. Huang, S. Kawakami, and N. A. Whitaker, “Coupled-Mode Theory of Optical Waveguides,” J. Light. Technol., vol. 5, no. 1, pp.

16–23, 1987.

[4] T. Tamir, "Guided-Wave Optoelectronics," 2nd ed., vol. 26. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988.

[5] K. Okamoto, "Fundamentals of Optical Waveguides," 2nd ed. Elsevier, 2006.

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Acknowledgements

All praise to Allah for giving me the blessing, the opportunity, the support, the strength and the perseverance in completing this thesis. My deepest gratitude first and foremost goes to Professor Kiichi Hamamoto for allowing me the chance to fulfil my lifelong dream of pursuing this study. I am also greatly indebted to Professor Hiroshi Nakashima and Professor Shiyoshi Yokoyama for reviewing my thesis carefully and for their kind suggestions.

I would like to say my deepest gratitude and love to my wife Siti Fauziah and my three lovely and understanding children. Thank you Adam Haiqal, Aisyah Raihan and Alya Khadijah for giving me joy and happiness even during the busiest of times. I would also like to thank my parents, Mohd. Idris and Jamilah Ibrahim for their constant support and understanding for I would not be here if not for them and for my whole family.

Thank you also to Dr. Jiang Haisong, Dr. Qui Feng, Dr. Hinokuma and all of the lab members, Ryosuke Sakata, Syota Enami, Ryan Imansyah, Hong Bingzhou, Li Wenying, Han Yu, Takuya Kitano, Hatem Elserafy, Sampad Ghosh, Shota Oe, Tomotaka Mori, Mahmoud Nasef, Satoshi Ogawa and all of the rest for the lovely experiences.

I would also like to express my sincerest gratitude to the Japan Government for the Monbukagakusho (MEXT) scholarship and to Kyushu University for their support throughout my stay here in Japan.

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