本論文將絕熱地圖(Adiabaticity Map)運用於矽光子元件設計，在1550nm的波長下，以氮化矽(Silicon Nitride)波導結構，透過更改波導參數，計算出絕熱係數以得到絕熱地圖，並依絕熱地圖選取地圖上之不同路徑，得到相應的絕熱參數分布，進而透過絕熱參數與耦合係數之間的關係，以此設計不同元件，並能以耦合模態理論進行計算並得出此元件各長度之光功率分布情形，進而與光波行進之模擬結果進行比較。
基於絕熱地圖所得出之不同路徑，對相對應之元件進行了光功率分析，並且發現在TE和TM模態下，絕熱係數於近乎0處先降反升一點對光功率所造成之影響。本篇論文發現除了在特定情況以外，利用絕熱地圖可以根據其絕熱參數分布，使用耦合模態理論得出所希望分配之絕熱參數之元件的光功率。

We present a study that the Adiabaticity Map to the design of silicon photonic components. Using a silicon nitride waveguide structure at a wavelength of 1550 nm, the corresponding adiabatic map is obtained by calculating the adiabatic coefficients. Different components are then designed by selecting various paths on the map, allowing for a rapid determination of the optical power distribution along each length of these components.
A power analysis was conducted on the components corresponding to different paths derived from the adiabatic map. It was found that in TE and TM modes, the adiabatic coefficient initially decreases and then slightly increases near zero, affecting the optical power. This paper demonstrates that, except in specific situations, the adiabatic map can be used to quickly determine the optical power of components based on the distribution of their adiabatic parameters.

[1] L. C. Kimerling, D. Ahn, A. B. Apsel, M. Beals, D. Carothers, Y.-K. Chen, T. Conway, D. M. Gill, M. Grove, C.-Y. Hong, M. Lipson, J. Liu, J. Michel, D. Pan, S. S. Patel, A. T. Pomerene, M. Rasras, D. K. Sparacin, K.-Y. Tu, A. E. White, and C. W. Wong, “Electronic-photonic integrated circuits on the CMOS platform,”in Silicon Photonics, J. A. Kubby and G. T. Reed, Eds., vol. 6125, International Society for Optics and Photonics. SPIE, 2006, p. 612502. [Online]. Available: https://doi.org/10.1117/12.654455
[2] W. Stutius and W. Streifer, “Silicon nitride films on silicon for optical waveguides,”Appl. Opt., vol. 16, no. 12, pp. 3218–3222, Dec 1977.
[3] Q. Li, A. A. Eftekhar, A. H. Atabaki, and A. Adibi, “3-d integration of silicon nitride on silicon-on-insulator platform,” in Conference on Lasers and Electro-Optics 2012. Optica Publishing Group, 2012, p. CM3A.5. [Online]. Available: https://opg.optica.org/abstract.cfm?URI=CLEO_SI-2012-CM3A.5
[4] A. Arbabi and L. L. Goddard, “Measurements of the refractive indices and thermo-optic coefficients of si3n4 and siox using microring resonances,” Opt. Lett., vol. 38, no. 19, pp. 3878–3881, Oct 2013. [Online]. Available: https: //opg.optica.org/ol/abstract.cfm?URI=ol-38-19-3878
[5] R. Baets, A. Z. Subramanian, S. Clemmen, B. Kuyken, P. Bienstman, N. Le Thomas, G. Roelkens, D. Van Thourhout, P. Helin, and S. Severi, “Silicon photonics: Silicon nitride versus silicon-on-insulator,” in 2016 Optical Fiber Communications Conference and Exhibition (OFC), 2016, pp. 1–3.
[6] D. J. Blumenthal, R. Heideman, D. Geuzebroek, A. Leinse, and C. Roeloffzen, “Silicon nitride in silicon photonics,” vol. 106, no. 12, 2018, pp. 2209–2231.
[7] A. Rahim, E. Ryckeboer, A. Z. Subramanian, S. Clemmen, B. Kuyken, A. Dhakal, A. Raza, A. Hermans, M. Muneeb, S. Dhoore, Y. Li, U. Dave, P. Bienstman, N. Le Thomas, G. Roelkens, D. Van Thourhout, P. Helin, S. Severi, X. Rottenberg, and R. Baets, “Expanding the silicon photonics portfolio with silicon nitride photonic integrated circuits,” Journal of Lightwave Technology, vol. 35, no. 4, pp. 639–649, 2017.
[8] S. Longhi, “Quantum‐optical analogies using photonic structures,” Laser photonics reviews., vol. 3, no. 3, 2009.
[9] E. Torrontegui, S. Ibáñez, S. Martínez-Garaot, M. Modugno, A. del Campo, D. Guéry-Odelin, A. Ruschhaupt, X. Chen, and J. G. Muga, “Chapter 2 - shortcuts to adiabaticity,” in Advances in Atomic, Molecular, and Optical Physics, ser. Advances In Atomic, Molecular, and Optical Physics, E. Arimondo, P. R. Berman, and C. C. Lin, Eds. Academic Press, 2013, vol. 62, pp. 117–169. [Online]. Available: https://www.sciencedirect.com/science/article/pii/B9780124080904000025
[10] D. Guéry-Odelin, A. Ruschhaupt, A. Kiely, E. Torrontegui, S. Martínez-Garaot, and J. G. Muga, “Shortcuts to adiabaticity: Concepts, methods, and applications,” Rev. Mod. Phys., vol. 91, p. 045001, Oct 2019. [Online]. Available: https: //link.aps.org/doi/10.1103/RevModPhys.91.045001
[11] L. D. d. C. A. K. K. An, Shuoming, “Shortcuts to adiabaticity by counterdiabatic driving for trapped-ion displacement in phase space,” Nature Communications, vol. 7, 09 2016.
[12] H. Li, H. Z. Shen, S. L. Wu, and X. X. Yi, “Shortcuts to adiabaticity in non-hermitian quantum systems without rotating-wave approximation,” Opt. Express, vol. 25, no. 24, pp. 30 135–30 148, Nov 2017. [Online]. Available: https://opg.optica.org/oe/abstract.cfm?URI=oe-25-24-30135
[13] G. Riblet, “A directional coupler with very flat coupling,” IEEE Transactions on Microwave Theory and Techniques, vol. 26, no. 2, pp. 70–74, 1978.
[14] E. A. J. Marcatili, “Dielectric rectangular waveguide and directional coupler for integrated optics,” The Bell System Technical Journal, vol. 48, no. 7, pp. 2071–2102, 1969.
[15] H. Yamada, T. Chu, S. Ishida, and Y. Arakawa, “Optical directional coupler based on si-wire waveguides,” IEEE Photonics Technology Letters, vol. 17, no. 3, pp. 585–587, 2005.
[16] D. Dai, Z. Wang, and J. E. Bowers, “Ultrashort broadband polarization beam splitter based on an asymmetrical directional coupler,” Opt. Lett., vol. 36, no. 13, pp. 2590–2592, Jul 2011. [Online]. Available: https://opg.optica.org/ol/abstract.cfm?URI= ol-36-13-2590
[17] A. W. Snyder and J. Love, Optical Waveguide Theory, 1st ed. Springer, 1983.
[18] R. Bergh, G. Kotler, and H. Shaw, “Single-mode fibre optic directional coupler,” Electronics Letters, vol. 7, no. 16, pp. 260–261, 1980.
[19] A. Ghatak and K. Thyagarajan, An Introduction to Fiber Optics. Cambridge University Press, 1998.
[20] V. Vassilev, V. Belitsky, D. Urbain, and S. Kovtonyuk, “A new 3-db power divider for millimeter-wavelengths,” IEEE Microwave and Wireless Components Letters, vol. 11, no. 1, pp. 30–32, 2001.
[21] F. Anelli, A. Annunziato, A. M. Loconsole, V. Portosi, S. Cozic, P. Teilleul, S. Venck, S. Poulain, and F. Prudenzano, “Low-loss fluoride optical fiber coupler for mid-infrared applications,” Journal of Lightwave Technology, vol. PP, pp. 1–7, 01 2023.
[22] T. A. Ramadan and R. M. Osgood, “Adiabatic couplers: Design rules and optimization,” J. Lightwave Technol., vol. 16, no. 2, p. 277, Feb 1998. [Online]. Available: https://opg.optica.org/jlt/abstract.cfm?URI=jlt-16-2-277
[23] L. Cao, A. Elshaari, A. Aboketaf, and S. Preble, “Adiabatic couplers in soi waveguides,” in Conference on Lasers and Electro-Optics 2010. Optica Publishing Group, 2010, p. CThAA2. [Online]. Available: https://opg.optica.org/abstract.cfm? URI=CLEO-2010-CThAA2
[24] J. Čtyroký, “A simple bi-directional mode expansion propagation algorithm based on modes of a parallel-plate waveguide,” Optical and Quantum Electronics, vol. 38, p. 45– 62, 2006.
[25] D. F. G. Gallagher and T. P. Felici, “Eigenmode expansion methods for simulation of optical propagation in photonics: pros and cons,” in Integrated Optics: Devices, Materials, and Technologies VII, Y. S. Sidorin and A. Tervonen, Eds., vol. 4987, International Society for Optics and Photonics. SPIE, 2003, pp. 69 – 82. [Online]. Available: https://doi.org/10.1117/12.473173
[26] W.-P. Huang, “Coupled-mode theory for optical waveguides: an overview,” J. Opt. Soc. Am. A, vol. 11, no. 3, pp. 963–983, Mar 1994.
[27] S. R. . Y. L. Avron, J.E., “Adiabatic theorems and applications to the quantum hall effect,” Commun.Math. Phys., vol. 110, p. 33–49, 1987. [Online]. Available: https://doi.org/10.1007/BF01209015
[28] WKB and Berry Phase. John Wiley Sons, Ltd, 2001, ch. 6, pp. 171–188.
[29] G. Auletta, M. Fortunato, and G. Parisi, Quantum Mechanics, ser. EBL-Schweitzer. Cambridge University Press, 2009.
[30] S. Martínez-Garaot, J. G. Muga, and S.-Y. Tseng, “Shortcuts to adiabaticity in optical waveguides using fast quasiadiabatic dynamics,” Opt. Express, vol. 25, no. 1, pp. 159–167, Jan 2017. [Online]. Available: https://opg.optica.org/oe/abstract.cfm?URI= oe-25-1-159
[31] H.-C. Chung, Z.-Y. Li, F.-C. Liang, K.-S. Lee, and S.-Y. Tseng, “The fast quasiadiabatic approach to optical waveguide design,” in Integrated Optics: Design, Devices, Systems, and Applications V, P. Cheben, J. Čtyroký, and I. Molina-Fernández, Eds., vol. 11031, International Society for Optics and Photonics. SPIE, 2019, p. 110310Y. [Online]. Available: https://doi.org/10.1117/12.2520346
[32] Y.-L. Wu, F.-C. Liang, H.-C. Chung, and S.-Y. Tseng, “Adiabaticity engineering in optical waveguides,” Opt. Express, vol. 28, no. 20, pp. 30 117–30 129, Sep 2020. [Online]. Available: https://opg.optica.org/oe/abstract.cfm?URI=oe-28-20-30117