光學同調斷層掃描(OCT)是一種具有微米級的解析度和高速三維成像的重要診斷工具。OCT系統通過測量反射光和背向散射光之間的干涉來獲取訊號，主要應用於眼科、牙科、皮膚病學和血管造影等醫學領域。儘管OCT具有即時和高解析度檢測功能，但整個系統體積龐大且昂貴。隨著矽光子學的發展，光學元件的進一步微小化和積體化可以降低成本並大量生產。
本文於絕緣層上覆矽(SOI)基板上，設計傅立葉域OCT中的被動元件。由於SOI
基板上的OCT元件易受製程誤差影響，因此我們應用了一種稱為色散補償和反相測量(DCOPM)的數位校準程序。此方法可以從重新取樣中的誤差和系統的不平衡色散中，檢測出非線性相位，從而維持OCT訊號的縱向解析度，且可優化DCOPM方法中的校準長度，以在數位的相位檢測法中，獲得最小相位誤差。
為了設計積體化干涉儀，我們使用了串聯型Mach-Zehnder方向耦合器 (TMZDC)配置。與傳統的方向耦合器相比，TMZDC有更多的參數，以優化為具有寬頻且平坦的波長響應。我們比較了採用疊代法和粒子群最佳化演算法(PSO)設計的TMZDC，最佳化之TMZDC可以進一步將耦合器的寬頻平坦響應擴展到 200nm (中心波長為1310nm)。由於OCT中的干涉儀為麥克森配置，因此我們設計了基於PSO的雙向寬頻耦合器，如此可提供平坦的傳輸和反射響應。在類似OCT訊號之雙向寬頻耦合器模擬結果表明，該耦合器的性能優於常規的基於PSO的單向TMDZC。
光譜儀是SD-OCT系統的另一個主要組成部分，SD-OCT系統的縱向解析度、最大成像範圍和訊號衰減皆取決於光譜儀的設計。為了維持SD-OCT的性能，陣列波導光柵(AWG)之FSR需與光源光譜相似且具有較高的波長解析度。直接設計與光源光譜相似之AWG的FSR是不切實際的，因為焦距過長以致超過晶片尺寸，為此，串聯AWG能夠最小化10倍以上的尺寸，同時保持SD-OCT性能。通常基於光柵的輸出強度會因其遠場響應而有類似高斯曲線，此響應會降低SD-OCT之縱向解析度，因此在系統中導入另一種基於PSO的U形頻譜輸出之MZDC耦合器，並置於AWG輸入之前，如此可以補償AWG內部的高斯遠場波長強度，從而保持晶片型SD-OCT之縱向解析度的性能。

Optical Coherence Tomography (OCT) is an important diagnostic tool with micrometer resolution and high-speed three-dimensional imaging. OCT system gets the signal by measuring the interference between reflected light and back-scattered light. OCT is mainly used in medical fields such as ophthalmology, dentistry, dermatology, and angiography. Although OCT has real-time and high-resolution detection functions, the entire system is bulky and expensive. With the development of silicon photonics, the further miniaturization and integration of optical components can reduce costs and support mass production.

In this thesis, passive devices in Fourier-domain OCT are designed to be operated on a SOI (silicon-on-insulator)-platform. Since the SOI-based platform OCT is susceptible to fabrication error, a digital calibration procedure is experimentally demonstrated through dispersion compensation by opposite phase measurement (DCOPM), which could detect the phase non-linearity from error in resample and unbalance dispersion from the system, hence maintaining axial resolution from the OCT signal. The calibration length in the DCOPM method can also be optimized to obtain a minimum phase error in digital phase detection.

To design the integrated interferometer, we used a tandem Mach-Zehnder directional coupler (TMZDC) based configuration. In contrast with the traditional directional coupler, TMZDC has more parameters to be easily optimized to achieve a flat wavelength response in a broadband wavelength region. A TMZDC with the iteration approach is compared with an optimization-based method. The optimization-based TMZDC could further extend the broadband flatness response of the coupler up to 200 nm in a 1310 nm wavelength range. Since the OCT interferometer is using the Michelson configuration, we developed a PSO (particle swarm optimization)-based bidirectional broadband coupler to provide flat transmission and reflection response. The simulation result of OCT-like signal in bidirectional broadband coupler is better than the regular unidirectional PSO-based TMDZC.

The spectrometer is another main component in a spectral-domain OCT (SD-OCT) system. The axial resolution, maximum imaging range, and signal fall-off of the SD- OCT system depend on the spectrometer design. To maintain SD-OCT performance, we need to design an arrayed waveguide grating (AWG) FSR similar to the light source spectrum, and a small wavelength resolution is required. The direct design of AWG is impractical since the focal length size is too long, exceeding the size of the chip. A cascaded AWG can minimize the size more than ten times while maintaining the OCT performance. Typically, a grating-based output intensity has a gaussian-like envelope due to its far-field response, which will degrade the axial resolution performance in SD-OCT. Thus, another PSO-based coupler is introduced. This coupler uses a MZDC configuration with a U-shaped spectrum output. This coupler is implemented right before the AWG and its U-shaped spectrum coupler can compensate the Gaussian far-field wavelength intensity inside the AWG, hence maintaining the performance of axial resolution in on-chip SD-OCT.

[1] D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte,K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical coherence tomography,” Science, vol. 254,pp. 1178–1181, 1991.
[2] W. Drexler and J. G. Fujimoto, eds., Optical Coherence Tomography. Springer International Publishing,2015.
[3] J. Zhu, C. W. Merkle, M. T. Bernucci, S. P. Chong, and V. J. Srinivasan, “Can oct angiography be made a quantitative blood measurement tool?,” Applied Sciences (Switzerland), vol. 7, 7 2017.
[4] J. F. de Boer, C. K. Hitzenberger, and Y. Yasuno, “Polarization sensitive optical coherence tomography–a review [invited],” Biomedical Optics Express, vol. 8, p. 1838, 3 2017.
[5] M. Zhou, H. Roodaki, A. Eslami, G. Chen, K. Huang, M. Maier, C. P. Lohmann, A. Knoll, and M. A.Nasseri, “Needle segmentation in volumetric optical coherence tomography images for ophthalmic microsurgery, Applied Sciences (Switzerland), vol. 7, 7 2017.
[6] A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Optics Communications, vol. 117, pp. 43–48, 1995.
[7] M. A. Choma, M. V. Sarunic, C. Yang, and J. A. Izatt, “Sensitivity advantage of swept source and fourier domain optical coherence tomography,” Opt. Express, vol. 11, pp. 2183–2189, Sep 2003.
[8] G. T. Reed and A. P. Knights, Silicon Photonics. Wiley, 2008.
[9] D. Culemann, A. Knuettel, and E. Voges, “Integrated optical sensor in glass for optical coherence tomography (oct),” IEEE Journal of Selected Topics in Quantum Electronics, vol. 6, no. 5, pp. 730–734, 2000.
[10] G. Yurtsever, K. Komorowska, and R. Baets, “Low dispersion integrated michelson interferometer on silicon on insulator for optical coherence tomography,” in Optical Coherence Tomography and Coherence Techniques V, p. 80910T, Optical Society of America, 2011.
[11] V. D. Nguyen, N. Weiss, W. Beeker, M. Hoekman, A. Leinse, R. G. Heideman, T. G. van Leeuwen, and J. Kalkman, “Integrated-optics-based swept-source optical coherence tomography,” Opt. Lett., vol. 37, pp. 4820–4822, Dec 2012.
[12] B. I. Akca, B. Považay, A. Alex, K. Wörhoff, R. M. de Ridder, W. Drexler, and M. Pollnau, “Miniature spectrometer and beam splitter for an optical coherence tomography on a silicon chip,” Optics Express, vol. 21, p. 16648, 7 2013.
[13] T. G. V. Leeuwen, I. B. Akca, N. Angelou, N. Weiss, M. Hoekman, A. Leinse, and R. G. Heideman, “Onchip mach-zehnder interferometer for oct systems,” Advanced Optical Technologies, vol. 7, pp. 103–106, 4 2018.
[14] M. S. Eggleston, F. Pardo, C. Bolle, B. Farah, N. Fontaine, H. Safar, M. Cappuzzo, C. Pollock, D. J.Bishop, and M. P. Earnshaw, “90db sensitivity in a chip-scale swept-source optical coherence tomography system,” in 2018 Conference on Lasers and Electro-Optics (CLEO), pp. 1–2, 2018.
[15] G. Lan and G. Li, “Design of a k-space spectrometer for ultra-broad waveband spectral domain optical coherence tomography,” Scientific Reports, vol. 7, 3 2017.
[16] T. Wu, S. Sun, X. Wang, H. Zhang, C. He, J. Wang, X. Gu, and Y. Liu, “Optimization of linearwavenumber spectrometer for high-resolution spectral domain optical coherence tomography,” Optics Communications, vol. 405, pp. 171–176, 12 2017.
[17] W. Eickhoff and R. Ulrich, “Optical frequency-domain reflectometry in single-mode fibers,” in Integrated Optics and Optical Fiber Communication, p. WF3, Optical Society of America, 1981.
[18] K. Iizuka, Y. Imai, A. P. Freundorfer, R. James, R. Wong, and S. Fujii, “Optical step frequency reflectometer,”Journal of Applied Physics, vol. 68, pp. 932–936, 1990.
[19] J. Nakayama, K. Iizuka, and J. Nielsen, “Optical fiber fault locator by the step frequency method,” Appl.Opt., vol. 26, pp. 440–443, Feb 1987.
[20] M. Nazarathy, D. W. Dolfi, and S. A. Newton, “5 mm resolution optical frequency domain reflectometry using coded phase reversal modulator,” in Optical Fiber Sensors, p. WDD7, Optical Society of America, 1988.
[21] K. IIZUKA, Y. IMAI, A. P. FREUNDORFER, R. JAMES, R. WONG, and S. FUJII, “Optical step frequency reflectometry,” in Conference on Lasers and Electro-Optics, p. CTHP4, Optical Society of America,1990.
[22] U. Glombitza and E. Brinkmeyer, “Coherent frequency-domain reflectometry for characterization of single-mode integrated-optical waveguides,” Journal of Lightwave Technology, vol. 11, no. 8, pp. 1377–1384, 1993.
[23] E. A. Swanson, D. Huang, M. R. Hee, J. G. Fujimoto, C. P. Lin, and C. A. Puliafito, “High-speed optical coherence domain reflectometry,” Opt. Lett., vol. 17, pp. 151–153, Jan 1992.
[24] C. Akcay, P. Parrein, and J. P. Rolland, “Estimation of longitudinal resolution in optical coherence imaging,”Appl. Opt., vol. 41, pp. 5256–5262, Sep 2002.
[25] Z. Hu, Y. Pan, and A. M. Rollins, “Analytical model of spectrometer-based two-beam spectral interferometry,”Appl. Opt., vol. 46, pp. 8499–8505, Dec 2007.
[26] R. Leitgeb, C. K. Hitzenberger, and A. F. Fercher, “Performance of fourier domain vs. time domain optical coherence tomography,” Opt. Express, vol. 11, pp. 889–894, Apr 2003.
[27] M. A. Choma, M. V. Sarunic, C. Yang, and J. A. Izatt, “Sensitivity advantage of swept source and fourier domain optical coherence tomography,” Opt. Express, vol. 11, pp. 2183–2189, Sep 2003.
[28] J. F. de Boer, B. Cense, B. H. Park, M. C. Pierce, G. J. Tearney, and B. E. Bouma, “Improved signalto-noise ratio in spectral-domain compared with time-domain optical coherence tomography,” Opt. Lett.,vol. 28, pp. 2067–2069, Nov 2003.
[29] R. Stierlin, R. Bättig, P. D. Henchoz, and P. H. Weber, “Excess-noise suppression in a fibre-optic balanced heterodyne detection system,” Optical and Quantum Electronics, vol. 18, p. 445–454, Nov 1986.
[30] W.-C. Kuo, C.-M. Lai, Y.-S. Huang, C.-Y. Chang, and Y.-M. Kuo, “Balanced detection for spectral domain optical coherence tomography,” Opt. Express, vol. 21, pp. 19280–19291, Aug 2013.
[31] E. Bo, X. Liu, S. Chen, X. Yu, X. Wang, and L. Liu, “Spectral-domain optical coherence tomography with dual-balanced detection for auto-correlation artifacts reduction,” Opt. Express, vol. 23, pp. 28050–28058, Oct 2015.
[32] K. Tsuji, K. Shimizu, T. Horiguchi, and Y. Koyamada, “Spatial-resolution improvement in long-range coherent optical frequency domain reflectometry by frequency-sweep linearisation,” Electronics Letters, vol. 33, no. 5, pp. 408–410, 1997.
[33] K. Iiyama, Lu-Tang Wang, and Ken-Ichi Hayashi, “Linearizing optical frequency-sweep of a laser diode for fmcw reflectometry,” Journal of Lightwave Technology, vol. 14, no. 2, pp. 173–178, 1996.
[34] Kao-Yang Huang and G. M. Carter, “Coherent optical frequency domain reflectometry (ofdr) using a fiber grating external cavity laser,” IEEE Photonics Technology Letters, vol. 6, no. 12, pp. 1466–1468, 1994.
[35] T.-J. Ahn and D. Y. Kim, “Analysis of nonlinear frequency sweep in high-speed tunable laser sources using a self-homodyne measurement and hilbert transformation,” Appl. Opt., vol. 46, pp. 2394–2400, May 2007.
[36] E. D. Moore and R. R. McLeod, “Correction of sampling errors due to laser tuning rate fluctuations in swept-wavelength interferometry,” Opt. Express, vol. 16, pp. 13139–13149, Aug 2008.
[37] K. Yüksel, M. Wuilpart, and P. Mégret, “Analysis and suppression of nonlinear frequency modulation in an optical frequency-domain reflectometer,” Opt. Express, vol. 17, pp. 5845–5851, Mar 2009.
[38] H. Rosenfeldt, C. Knothe, J. Cierullies, and E. Brinkmeyer, “Evolution of amplitude and dispersion spectra during fiber bragg grating fabrication,” in Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, p. BWA4, Optical Society of America, 2001.
[39] B. Boashash, “Estimating and interpreting the instantaneous frequency of a signal. i. fundamentals,” Proceedings of the IEEE, vol. 80, no. 4, pp. 520–538, 1992.
[40] B. Cense, N. A. Nassif, T. C. Chen, M. C. Pierce, S.-H. Yun, B. H. Park, B. E. Bouma, G. J. Tearney, and J. F. de Boer, “Ultrahigh-resolution high-speed retinal imaging using spectral-domain optical coherence tomography,” Opt. Express, vol. 12, pp. 2435–2447, May 2004.
[41] M. Wojtkowski, V. J. Srinivasan, T. H. Ko, J. G. Fujimoto, A. Kowalczyk, and J. S. Duker, “Ultrahigh resolution, high-speed, fourier domain optical coherence tomography and methods for dispersion compensation,”Opt. Express, vol. 12, pp. 2404–2422, May 2004.
[42] K. Singh, G. Sharma, and G. J. Tearney, “Estimation and compensation of dispersion for a high-resolution optical coherence tomography system,” Journal of Optics, vol. 20, p. 025301, jan 2018.
[43] N. Lippok, S. Coen, P. Nielsen, and F. Vanholsbeeck, “Dispersion compensation in fourier domain optical coherence tomography using the fractional fourier transform,” Opt. Express, vol. 20, pp. 23398–23413, Oct 2012.
[44] A. Bradu, M. Maria, and A. G. Podoleanu, “Demonstration of tolerance to dispersion of master/slave interferometry,” Opt. Express, vol. 23, pp. 14148–14161, Jun 2015.
[45] K. Wang and Z. Ding, “Spectral calibration in spectral domain optical coherence tomography,” Chin. Opt. Lett., vol. 6, pp. 902–904, Dec 2008.
[46] X. Attendu, R. M. Ruis, C. Boudoux, T. G. van Leeuwen, and D. J. Faber, “Simple and robust calibration procedure for k-linearization and dispersion compensation in optical coherence tomography,” Journal of Biomedical Optics, vol. 24, no. 5, pp. 1 – 11, 2019.
[47] A. Reilly, G. Frazer, and B. Boashash, “Analytic signal generation-tips and traps,” IEEE Transactions on Signal Processing, vol. 42, no. 11, pp. 3241–3245, 1994.
[48] K. M. Ratheesh, L. K. Seah, and V. M. Murukeshan, “Spectral phase-based automatic calibration scheme for swept source-based optical coherence tomography systems,” Physics in Medicine and Biology, vol. 61, pp. 7652–7663, oct 2016.
[49] S.-H. Hsu, Y.-C. Yang, Y.-H. Su, S.-M. Wang, S.-A. Huang, and C.-Y. Lin, “Biosensing using microring resonator interferograms,” Sensors, vol. 14, no. 1, pp. 1184–1194, 2014.
[50] Synopsis, “Rsoft.” https://www.synopsys.com/company.html. Accessed: 2020-10-19.
[51] C. K. Madsen and J. H. Zhao, Optical filter design and analysis : a signal processing approach. John Wiley, 1999.
[52] A. Yariv and P. Yeh, Photonics: Optical Electronics in Modern Communications (The Oxford Series in Electrical and Computer Engineering). USA: Oxford University Press, Inc., 2006.
[53] E. Dulkeith, F. Xia, L. Schares, W. M. J. Green, and Y. A. Vlasov, “Group index and group velocity dispersion in silicon-on-insulator photonic wires,” Opt. Express, vol. 14, pp. 3853–3863, May 2006.
[54] J.-M. Jin, The finite element method in electromagnetics, 3rd Edition. Wiley-IEEE Press, 2014.
[55] 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, vol. 29, no. 10, pp. 2639–2649, 1993.
[56] M. Heiblum and J. Harris, “Analysis of curved optical waveguides by conformal transformation,” IEEE Journal of Quantum Electronics, vol. 11, no. 2, pp. 75–83, 1975.
[57] W. A. Gambling, H. Matsumura, and C. M. Ragdale, “Field deformation in a curved single-mode fibre,”Electronics Letters, vol. 14, no. 5, pp. 130–132, 1978.
[58] K. Jinguji, N. Takato, A. Sugita, and M. Kawachi, “Mach-zehnder interferometer type optical waveguide coupler with wavelength-flattened coupling ratio,”Electronics Letters, vol. 26, no. 17, pp. 1326–1327,
1990.
[59] B. E. Little and T. Murphy, “Design rules for maximally flat wavelength-insensitive optical power dividers using mach-zehnder structures,” IEEE Photonics Technology Letters, vol. 9, no. 12, pp. 1607–1609, 1997.
[60] J. Kennedy and R. Eberhart, “Particle swarm optimization,” in Proceedings of ICNN’95 - International Conference on Neural Networks, vol. 4, pp. 1942–1948 vol.4, 1995.
[61] M. Clerc and J. Kennedy, “The particle swarm - explosion, stability, and convergence in a multidimensional complex space,” IEEE Transactions on Evolutionary Computation, vol. 6, no. 1, pp. 58–73, 2002.
[62] Y.-T. Lu, B. Y. B. Widhianto, S.-H. Hsu, and C.-C. Chang, “Tandem mach zehnder directional coupler design and simulation on silicon platform for optical coherence tomography applications,” Sensors, vol. 20, p. 1054, Feb 2020.
[63] B. Y. B. Widhianto, Y. T. Lu, W. C. Chang, and S. H. Hsu, “Broadband coupler manipulation through particle swarm optimization for arrayed waveguide grating based optical coherence tomography,” IEEE Photonics Journal, vol. 13, no. 1, pp. 1–13, 2021.
[64] C. R. Pollock and M. Lipson, Numerical Methods for Analyzing Optical Waveguides, pp. 209–239. Boston, MA: Springer US, 2003.
[65] B. K. X. J. MLeijtens and M. K. Smit, Arrayed Waveguide Gratings, pp. 125–187. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006.
[66] A. R. Vellekoop and M. K. Smit, “Four-channel integrated-optic wavelength demultiplexer with weak polarization dependence,” Journal of Lightwave Technology, vol. 9, no. 3, pp. 310–314, 1991.
[67] A. R. Vellekoop and M. K. Smit, “Low-loss planar optical polarisation splitter with small dimensions,”Electronics Letters, vol. 25, no. 15, pp. 946–947, 1989.
[68] H. Takahashi, S. Suzuki, K. Kato, and I. Nishi, “Arrayed-waveguide grating for wavelength division multi/demultiplexer with nanometer resolution,” Electronics Letters, vol. 26, no. 2, pp. 87–88, 1990.
[69] H. Takahashi, I. Nishi, and Y. Hibino, “10 ghz spacing optical frequency division multiplexer based on arrayed-waveguide grating,” Electronics Letters, vol. 28, no. 4, pp. 380–380, 1992.
[70] A. Kaneko, T. Goh, H. Yamada, T. Tanaka, and L. Ogawa, “Design and applications of silica-based planar lightwave circuits,” IEEE Journal of Selected Topics in Quantum Electronics, vol. 5, no. 5, pp. 1227–1236,
1999.
[71] L. Eldada, J. Fujita, A. Radojevic, T. Izuhara, R. Gerhardt, J. Shi, D. Pant, F. Wang, and A. Malek, “40-channel ultra-low-power compact plc-based roadm subsystem,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, p. NThC4, Optical Society of America, 2006.
[72] Geun-Young Kim and Yong-Gil Lee, “Simple and reliable bidirectional optical amplifier suitable for variable traffic pattern networks,” IEEE Photonics Technology Letters, vol. 14, no. 4, pp. 552–554, 2002.
[73] R. A. Crocombe, Miniature optical spectrometers: The art of the possible, Part IV: New near-infrared technologies and spectrometers. Advanstar Communications Inc., 2009.
[74] P. Gatkine, S. Veilleux, and M. Dagenais, “Astrophotonic spectrographs,” Applied Sciences, vol. 9, no. 2,2019.
[75] B. I. Akca and C. R. Doerr, “Interleaved silicon nitride awg spectrometers,” IEEE Photonics Technology Letters, vol. 31, no. 1, pp. 90–93, 2019.
[76] R. M. Ruis, A. Leinse, R. Dekker, R. G. Heideman, T. G. van Leeuwen, and D. J. Faber, “Decreasing the size of a spectral domain optical coherence tomography system with cascaded arrayed waveguide gratings in a photonic integrated circuit,” IEEE Journal of Selected Topics in Quantum Electronics, vol. 25, no. 1, pp. 1–9, 2019.
[77] E. A. Rank, R. Sentosa, D. J. Harper, M. Salas, A. Gaugutz, D. Seyringer, S. Nevlacsil, A. Maese-Novo,M. Eggeling, P. Muellner, R. Hainberger, M. Sagmeister, J. Kraft, R. A. Leitgeb, and W. Drexler, “Toward optical coherence tomography on a chip: in vivo three-dimensional human retinal imaging using photonic integrated circuit-based arrayed waveguide gratings,” Light: Science & Applications, vol. 10, p. 6, Jan 2021.
[78] M. K. Smit and C. Van Dam, “Phasar-based wdm-devices: Principles, design and applications,” IEEE Journal of Selected Topics in Quantum Electronics, vol. 2, no. 2, pp. 236–250, 1996.
[79] D. Seyringer, Arrayed waveguide gratings, p. 16. SPIE Press, 2016.