本論文致力於研究絕緣層覆矽(silicon-on-insulator, SOI)超絕熱方向耦合器之理論分析與數值模擬。首先，我們介紹耦合波導系統之基本理論，並比較弱耦合波導系統與近共振電磁場下兩能階系統之量子–光學相似性，藉此將量子系統中之超絕熱協定(counterdiabatic protocol)應用到耦合波導系統中，以抵銷絕熱模態間之非絕熱耦合以避免其干擾模態轉換，如此，即使裝置長度短至無法滿足絕熱條件，也能使耦合器達到良好的功率轉換效率，亦即我們能藉由此協定設計長度更為縮減的耦合器。此外，我們著重於利用絕緣層覆矽材料以具體實現超絕熱協定之設計，因為絕緣層覆矽材料所具有的高折射率對比(high-index-contrast)特性，耦合器的長度可望更為縮減。我們藉由實際模擬的結果，驗證了超絕熱協定在絕緣層覆矽材料上之適用性。模擬結果與理論預測相符合，並顯示了絕緣層覆矽超絕熱方向耦合器在極短裝置長度下依然具有良好的寬頻特性。

This thesis is devoted to the theoretical investigation and numerical simulations of a counterdiabatic directional coupler based on silicon-on-insulator (SOI). We begin by introducing the theory of coupled-waveguide system and the quantum‐optical analogies between weakly-coupled waveguide structure and two-level system driven by near-resonant laser light. By means of the analogies, the counterdiabatic protocol is introduced into coupled-waveguide system to cancel the nonadiabatic coupling between adiabatic modes and achieve high-fidelity power coupling even when the device length is too short to satisfy the adiabatic condition. The device length can hence be shorten. We emphasize the applicability of the counterdiabatic protocol to the SOI material system, the high-index contrast of SOI also allows devices to be more compact. The simulation results agree with the theoretical predictions, and show that the counterdiabatic coupler has the desired broadband characteristics at a short device length.

1. X. Sun, H.-C. Liu, and A. Yariv, Adiabaticity criterion and the shortest adiabatic mode transformer in a coupled-waveguide system. Optics Letters. 34(3): p. 280-282 (2009).

2. K. Okamoto, Fundamentals of Optical Waveguides, 2nd ed. (Academic Press, New York, 2006).

3. M. Demirplak and S. A. Rice, Adiabatic Population Transfer with Control Fields. Journal of Physical Chemistry A. 107(46): p. 9937-9945 (2003).

4. S.-Y. Tseng, Counterdiabatic mode-evolution based coupled-waveguide devices. Optics Express. 21(18): p. 21224-21235 (2013).

5. T.-Y. Lin, F.-C. Hsiao, Y.-W. Jhang, C. Hu, and S.-Y. Tseng, Mode conversion using optical analogy of shortcut to adiabatic passage in engineered multimode waveguides. Optics Express. 20(21): p. 24085-24092 (2012).

6. A. M. Prabhu, A. Tsay, Z. Han, and V. Van, Ultracompact SOI microring add-drop filter with wide bandwidth and wide FSR. IEEE Photonics Technology Letters. 21(10): p. 651-653 (2009).

7. S. Longhi, Quantum-optical analogies using photonic structures. Laser & Photonics Reviews. 3(3): p. 243-261 (2009).

8. R. G. Unanyan, L. P. Yatsenko, K. Bergmann, and B. W. Shore, Laser-induced adiabatic atomic reorientation with control of diabatic losses. Optics Communications. 139(1–3): p. 48-54 (1997).

9. M. Demirplak and S. A. Rice, Assisted Adiabatic Passage Revisited†. Journal of Physical Chemistry B. 109(14): p. 6838-6844 (2005).

10. M. V. Berry, Transitionless quantum driving. Journal of Physics A: Mathematical and Theoretical. 42(36): p. 365303 (2009).

11. X. Chen, I. Lizuain, A. Ruschhaupt, D. Guéry-Odelin, and J. G. Muga, Shortcut to Adiabatic Passage in Two- and Three-Level Atoms. Physical Review Letters. 105(12): p. 123003 (2010).

12. S.-Y. Tseng, Development of linear and nonlinear components for integrated optical signal processing. Ph.D. dissertation (University of Maryland, College Park, USA, 2006).

13. T. E. Murphy, Design, fabrication and measurement of integrated Bragg grating optical filters. Ph.D. dissertation (Massachusetts Institute of Technology, USA, 2000).

14. C.-L. Xu, W.-P. Huang, M. S. Stern, and S. K. Chaudhuri, Full-vectorial mode calculations by finite difference method. IEE Proceedings - Optoelectronics. 141(5): p. 281-286 (1994).

15. W.-P. Huang and C.-L. Xu, Simulation of three-dimensional optical waveguides by a full-vector beam propagation method. IEEE Journal of Quantum Electronics. 29(10): p. 2639-2649 (1993).

16. D. F. G. Gallagher and T. P. Felici, Eigenmode expansion methods for simulation of optical propagation in photonics: pros and cons. Proceedings of SPIE. 4987: p. 69-82 (2003).

17. W.-P. Huang, Coupled-mode theory for optical waveguides: an overview. Journal of the Optical Society of America A. 11(3): p. 963-983 (1994).

18. N. V. Vitanov, T. Halfmann, B. W. Shore, and K. Bergmann, Laser-induced population transfer by adiabatic passage techniques. Annual Review of Physical Chemistry. 52(1): p. 763-809 (2001).

19. K. Bergmann, H. Theuer, and B. W. Shore, Coherent population transfer among quantum states of atoms and molecules. Reviews of Modern Physics. 70(3): p. 1003-1025 (1998).

20. S. K. Korotky, Three-space representation of phase-mismatch switching in coupled two-state optical systems. IEEE Journal of Quantum Electronics. 22(6): p. 952-958 (1986).

21. S. Ibáñez, X. Chen, E. Torrontegui, J. G. Muga, and A. Ruschhaupt, Multiple Schrödinger Pictures and Dynamics in Shortcuts to Adiabaticity. Physical Review Letters. 109(10): p. 100403 (2012).

22. R. R. A. Syms, The digital directional coupler: improved design. IEEE Photonics Technology Letters. 4(10): p. 1135-1138 (1992).

23. K. Jinguji, N. Takato, A. Sugita, and M. Kawachi, Mach–Zehnder interferometer type optical waveguide coupler with wavelength-flattened coupling ratio. Electronics Letters. 26(17): p. 1326-1327 (1990).

24. X. Xiong, C.-L. Zou, X.-F. Ren, and G.-C. Guo, Integrated polarization rotator/converter by stimulated Raman adiabatic passage. Optics Express. 21(14): p. 17097-17107 (2013).