本論文提出了使用多波長絕熱工程優化的任意比例分光器，解決了快速準絕熱動態(fast quasiadiabatic dynamics, FAQUAD)只能針對單一波長進行優化而導致頻寬較小缺點，多波長絕熱工程(multi-wavelength adiabaticity engineering, MAE)是透過選定多個波長並得到相對應的絕熱參數，再將不同波長的絕熱參數做權重分配則可得到MAE 設計的波導寬度變化量，即可設計出相較於 FAQUAD 設計頻寬更佳的元件。
我們透過改變兩波導寬度差設計並模擬了基於絕緣層覆矽(silicon-on-insulator, SOI)的任意比例分光器，以 50%/50%分光器為例，傳統線性設計的耦合長度為64.69µm，使用 MAE 可將耦合長度縮短為 34.74µm，在波長為 1.5µm~1.6µm 時取波長容忍度為 0.5±1dB，其頻寬大於 100nm 且標準差為 4.43%，而線性設計之頻寬和標準差分別為 95nm 和 6.47%，在工作波長為 1.55µm 時取製程容忍度為 0.5±0.5dB，製程誤差寬度和標準差分別為 69.3nm 和 2.26%，而線性設計之製程誤差寬度與標準差分別為 54.4nm 和 2.38%，不僅縮短耦合長度並且有良好的頻寬、波長穩定性、製程容忍度與製程穩定性。再將 MAE 與 FAQUAD 設計的結構取相近耦合長度做波長容忍度與製程容忍度的對比，以 10%/90%分光器為例，MAE 與 FAQUAD 設計的耦合長度分別為13.80µm 和 14.11µm，在波長為 1.5µm~1.6µm 時取波長容忍度為 0.1±1dB，其頻寬分別為 67nm 和 62nm，標準差分別為 1.55%和 1.66%，透過 MAE 優化後使頻寬和波長穩定性有更良好的表現。

We present a broadband silicon arbitrary ratio power splitters using multi-wavelength adiabaticity engineering (MAE). We control the variation to the width of two waveguides to achieve arbitrary ratio power split. First, we redistribute the adiabaticity parameter of 2×2 linear tapered waveguides using fast quasiadiabatic dynamics (FAQUAD). However, the FAQUAD-designed waveguides cannot adapt to the other operating wavelengths. Therefore, we utilize MAE to redistribute the adiabaticity parameter by selecting the wavelengths (1.5, 1.55, 1.6µm) and assigning the respective weights to each wavelength, which adapt to the selected wavelength.
The MAE-designed couplers shorten the coupling length of the devices and ensure that the mode evolutions remain adiabatic. According to our simulations, we shorten the coupling length to 34.74µm, 40.45µm, 13.80 µm and broaden the bandwidth to 100nm、93nm and 67nm for 50%/50%、30%/70% and 10%/90% MAE couplers, respectively.

[1] C. Sun, M. T. Wade, Y. Lee, J. S. Orcutt, L. Alloatti, M. S. Georgas, A. S. Waterman, J. M. Shainline, R. R. Avizienis, and S. Lin, "Single-chip microprocessor that communicates directly using light," Nature 528,
534-538 (2015).
[2] A. Shacham, K. Bergman, and L. P. Carloni, "Photonic networks-onchip for future generations of chip multiprocessors," IEEE Transactions on Computers 57, 1246-1260 (2008).
[3] B. G. Lee, X. Chen, A. Biberman, X. Liu, I.-W. Hsieh, C.-Y. Chou, J. I. Dadap, F. Xia, W. M. Green, and L. Sekaric, "Ultrahigh-bandwidth silicon photonic nanowire waveguides for on-chip networks," IEEE Photonics Technology Letters 20, 398-400 (2008).
[4] C. Gunn, "CMOS photonics for high-speed interconnects," IEEE micro 26, 58-66 (2006).
[5] I. L. Chuang, and Y. Yamamoto, "SIMPLE QUANTUM COMPUTER," Phys. Rev. A 52, 3489-3496 (1995).
[6] J. Biamonte, P. Wittek, N. Pancotti, P. Rebentrost, N. Wiebe, and S. Lloyd, "Quantum machine learning," Nature 549, 195-202 (2017).
[7] C. A. Brackett, "Dense wavelength division multiplexing networks: Principles and applications," IEEE Journal on Selected areas in Communications 8, 948-964 (1990).
[8] F. Horst, W. M. Green, S. Assefa, S. M. Shank, Y. A. Vlasov, and B. J. Offrein, "Cascaded Mach-Zehnder wavelength filters in silicon photonics for low loss and flat pass-band WDM (de-) multiplexing," Opt. Express 21, 11652-11658 (2013).
[9] J. Van Campenhout, W. M. Green, S. Assefa, and Y. A. Vlasov, "Lowpower, 2× 2 silicon electro-optic switch with 110-nm bandwidth for broadband reconfigurable optical networks," Opt. Express 17, 24020-24029 (2009).
[10] Z. Lu, H. Yun, Y. Wang, Z. Chen, F. Zhang, N. A. F. Jaeger, and L. Chrostowski, "Broadband silicon photonic directional coupler using asymmetric-waveguide based phase control," Opt. Express 23, 3795-3808 (2015).
[11] K. Bergmann, H. Theuer, and B. Shore, "Coherent population transfer among quantum states of atoms and molecules," Reviews of Modern Physics 70, 1003 (1998).
[12] H.-C. Chung, G.-X. Lu, and S.-Y. Tseng, "Shortcut to adiabaticity in a silicon polarization splitter rotator using multi-wavelength adiabaticity engineering," Opt. Express 30, 8115-8125 (2022).
[13] D. Mao, Y. Wang, E. El-Fiky, L. Xu, A. Kumar, M. Jaques, A. Samani, O. Carpentier, S. Bernal, and M. S. Alam, "Adiabatic coupler with design-intended splitting ratio," J. Lightwave Technol. 37, 6147-6155 (2019).
[14] D. Mao, Y. Wang, L. Xu, E. El-Fiky, M. Jacques, J. Zhang, M. S. Alam, A. Kumar, Y. D’Mello, and D. V. Plant, "Adiabatic coupler with nonlinearly tapered mode-evolution region," IEEE Photonics Technology Letters 33, 840-843 (2021).
[15] Z. Lin, and W. Shi, "Broadband, low-loss silicon photonic Y-junction with an arbitrary power splitting ratio," Opt. Express 27, 14338-14343 (2019).
[16] Y. Wang, Z. Lu, M. Ma, H. Yun, F. Zhang, N. A. F. Jaeger, and L. Chrostowski, "Compact Broadband Directional Couplers Using Subwavelength Gratings," IEEE Photonics Journal 8, 1-8 (2016).
[17] J. Niklas Caspers, and M. Mojahedi, "Measurement of a compact colorless 3 dB hybrid plasmonic directional coupler," Opt. Lett. 39, 3262-3265 (2014).
[18] S.-H. Hsu, "Signal power tapped with low polarization dependence and insensitive wavelength on silicon-on-insulator platforms," J. Opt. Soc. Am. B 27, 941-947 (2010).
[19] K. Solehmainen, M. Kapulainen, M. Harjanne, and T. Aalto, "Adiabatic and multimode interference couplers on silicon-on-insulator," IEEE Photonics Technology Letters 18, 2287-2289 (2006).
[20] D. F. 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(SPIE2003), pp. 69-82.
[21] M. Born, and V. Fock, "Beweis des adiabatensatzes," Zeitschrift für Physik 51, 165-180 (1928).
[22] S. Martinez-Garaot, J. G. Muga, and S. Y. Tseng, "Shortcuts to adiabaticity in optical waveguides using fast quasiadiabatic dynamics," Opt. Express 25, 159-167 (2017).
[23] H. C. Chung, and S. Y. Tseng, "Ultrashort and broadband silicon polarization splitter-rotator using fast quasiadiabatic dynamics," Opt. Express 26, 9655-9665 (2018).
[24] H. C. Chung, K. S. Lee, and S. Y. Tseng, "Short and broadband silicon asymmetric Y-junction two-mode (de)multiplexer using fast quasiadiabatic dynamics," Opt. Express 25, 13626-13634 (2017).
[25] Y.-J. Hung, Z.-Y. Li, H.-C. Chung, F.-C. Liang, M.-Y. Jung, T.-H. Yen, and S.-Y. Tseng, "Mode-evolution-based silicon-on-insulator 3 dB coupler using fast quasiadiabatic dynamics," Opt. Lett. 44, 815-818 (2019).
[26] H.-C. Chung, and S.-Y. Tseng, "High fabrication tolerance and broadband silicon polarization beam splitter by point-symmetric cascaded fast quasiadiabatic couplers," OSA Continuum 2, 2795-2808 (2019).
[27] Y. Wang, L. Xu, H. Yun, M. Ma, A. Kumar, E. El-Fiky, R. Li, N. Abadíacalvo, L. Chrostowski, and N. A. Jaeger, "Polarizationindependent mode-evolution-based coupler for the silicon-on-insulator platform," IEEE Photonics Journal 10, 1-10 (2018).
[28] W. Bogaerts, and S. K. Selvaraja, "Compact single-mode silicon hybrid rib/strip waveguide with adiabatic bends," IEEE Photonics Journal 3, 422-432 (2011).
[29] FIMMWAVE/FIMMPROP, https://www.photond.com.
[30] J.-Y. Sie, H.-C. Chung, X. Chen, and S.-Y. Tseng, "Robust arbitrary ratio power splitter by fast quasi-adiabatic elimination in optical waveguides," Opt. Express 27, 37622-37633 (2019).
[31] H. C. J. Gan, G. Maslennikov, K.-W. Tseng, C. Nguyen, and D. Matsukevich, "Hybrid Quantum Computing with Conditional Beam Splitter Gate in Trapped Ion System," Physical Review Letters 124, 170502 (2020).
[32] E. Knill, R. Laflamme, and G. J. Milburn, "A scheme for efficient quantum computation with linear optics," nature 409, 46-52 (2001).