本論文利用超絕熱捷徑（counterdiabatic shortcut to adiabaticity）消除了波導中的非絕熱耦合，並設計了短而穩定的軸彎曲定向耦合器。相位不匹配符號翻轉(sign flip of the phase mismatch，SFPM)模型的耦合係數為雙曲正割函數(hyperbolic secant)，而波導之間的相位不匹配在最大耦合處具有符號翻轉，符號翻轉可通過彎曲波導的二階導數x ̈_0 (z)的不連續性來實現的，不再需要不同的折射率波導來達成符號翻轉。
我們設計兩波導間距及軸彎曲形狀，以符合超絕熱捷徑協議，並且對耦合強度和相位不匹配的變化具有穩定性。根據模擬結果顯示，所提出的波導耦合器可以縮短至0.444mm，在波長為1550nm下，波導寬度為3.4μm時，耦合效率為98%。將波導寬度固定為3.4μm時，頻寬可達350nm；將波長固定為1550nm時，製程容忍度為-0.6μm ~+0.8μm。

We use the counterdiabatic shortcut to adiabaticity to cancel non-adiabatic coupling in the waveguide couplers, and we design short and robust couplers by bending the axis of the waveguide couplers.
The SFPM (Sign Flip of the Phase Mismatch) model has a hyperbolic-secant spatial shape while the phase mismatch is constant, with a sign flip at the coupling maximum. The sign flip is achieved by a discontinuity in the second derivative of the bending profile, x ̈_0 (z), without the need of different index waveguides.
In this thesis, we engineer the spacing and bending profile of waveguide couplers to implement the counterdiabatic driving protocol. The coupled waveguides have robustness against variations in experimental parameter. From the result of simulation, we design a waveguide coupler with a reduced length of 0.444mm, coupling efficiency of 98% in wavelength 1550nm. When the wavelength is fixed at 1550nm, the fabrication tolerance is -0.6μm~+0.8μm.

1. R. R. A. Syms, The digital directional coupler: improved design, IEEE Photonics Technol. Lett. vol. 4, no. 10, pp. 1135–1138 (1992).
2. X. Sun, H.-C. Liu, and A. Yariv, Adiabaticity criterion and the shortest adiabatic mode transformer in a coupled waveguide system, Opt. Lett. vol. 34, no. 10, pp. 280–282 (2009).
3. M. R. Watts, H. A. Haus, and E. P. Ippen, Integrated mode-evolution-based polarization splitter, Opt. Lett. vol. 30, no. 9, pp. 967–969 (2005).
4. G. M. Nikolopoulos, Directional coupling for quantum computing and communication, Phys. Rev. Lett. vol.101, no.20, pp. 200502-1-4 (2008).
5. K. Okamoto, Fundamentals of Optical Waveguides, 2nd ed. (Academic Press, New York, 2006).
6. A. Yariv, Quantum Electronics, 3rd ed. (Wiley, New York, 1989).
7. S. Longhi, Coherent destruction of tunneling in waveguide directional couplers, Phys. Rev. A, vol. 7, no. 6, pp. 065801-1-4 (2005).
8. S. Longhi, Quantum-optical analogies using photonic structures, Laser Photon. Rev. 3, no. 3, pp. 243–61 (2009).
9. A. A. Rangelov, E. Kyoseva, Broadband composite polarization rotator, Opt. Commun., vol. 338, pp. 574–577 (2015).
10. S. Longhi , Landau–Zener dynamics in a curved optical directional coupler, J. Opt. B, Quantum and semiclassical optics, vol. 7, no. 6, pp. 9-12 (2005).
11. S. Longhi, G. D. Valle, M. Ornigotti, and P. Laporta, Coherent tunneling by adiabatic passage in an optical waveguide system, Phys. Rev. B, Condens. Matter, vol. 76, no. 20, Art. no. 201101 (2007).
12. Paul K and Sarma A K, Shortcut to adiabatic passage in a waveguide coupler with a complex-hyperbolic-secant scheme. Phys. Rev. A, vol. 91, no. 5, pp. 053406-1-5 (2015).
13. W. Huang, A. A. Rangelov and E. Kyoseva, Complete achromatic optical switching between two waveguides with a sign flip of the phase mismatch, Phys. Rev. A, vol. 90, no. 053837, pp. 1-5 (2014).
14. B. T. Torosov and N. V. Vitanov, Coherent control of a quantum transition by a phase jump, Phys. Rev. A, Gen. Phys., vol. 76, no. 5, pp. 053404 (2007).
15. W. Huang, L.-K. Ang, and E. Kyoseva, Shortcut to adiabatic light transfer in waveguide couplers with a sign flip in the phase mismatch, J. Phys. D: Appl. Phys. vol. 53, pp. 035104 (2020).
16. C. R. Doerr,M. Cappuzzo, E.Chen, A.Wong-Foy, L.Gomez, A.Griffin, and L. Buhl, Bending of a planar lightwave circuit 2×2 coupler to desensitize it to wavelength, polarization, and fabrication changes, IEEE Photonics Technol. Lett., vol. 17, pp. 1211–1213 (2005).
17. H. Morino, T. Maruyama, and K. Iiyama, Reduction of wavelength dependence of coupling characteristics using Si optical waveguide curved directional coupler, J. Light. Technol., vol. 32, pp. 2188–2192 (2014).
18. S.-Y. Tseng, Robust Light Coupling in a Quadratically Bent Directional Coupler, IEEE Photonics Technology Letters, Vol. 33, no. 7, pp. 343-346 (2021).
19. E. A. J. Marcatili, Dielectric rectangular waveguide and directional coupler for integrated optics, Bell Syst. Tech. J. vol. 48, no. 7, pp. 2071-2102 (1969).
20. David J. Griffiths, and Darrell F. Schroeter, Introduction to Quantum Mechanics, 3rd ed. (Cambridge University Press, USA, pp. 402-408, 2018).
21. N. V. Vitanov, T. Halfmann, B. W. Shore, and K. Bergmann, Laser-induced population transfer by adiabatic passage techniques, Annu. Rev. Phys. Chem. vol. 52, no. 1, pp. 763–809 (2001).
22. S.-Y. Tseng, Counterdiabatic mode-evolution based coupled-waveguide devices, Opt. Express, vol. 21, no. 18, pp. 21224-21235 (2013).
23. S.-Y. Tseng, R.-D. Wen, Y.-F. Chiu, and X. Chen, Short and robust directional couplers designed by shortcuts to adiabaticity, Opt. Express, vol. 22, no. 16, pp. 18849-18859 (2014).
24. Kenji Kawano, Tsutomu Kitoh, Introduction to Optical Waveguide Analysis, (John Wiley & Sons, Inc., USA, pp. 20-23& pp.180-203, 2001).