Nghiên cứu, thiết kế cấu trúc tinh thể quang tử 1d và 2d ứng dụng cho linh kiện lưỡng trạng thái ổn

BỘ GIÁO DỤC VÀ ĐÀO TẠO VIỆN HÀN LÂM KHOA HỌC VÀ CÔNG NGHỆ VIỆT NAM HỌC VIỆN KHOA HỌC VÀ CƠNG NGHỆ -*** - Hồng Thu Trang NGHIÊN CỨU, THIẾT KẾ CẤU TRÚC TINH THỂ QUANG TỬ 1D VÀ 2D ỨNG DỤNG CHO LINH KIỆN LƯỠNG TRẠNG THÁI ỔN ĐỊNH LUẬN ÁN TIẾN SĨ KHOA HỌC VẬT LIỆU Hà Nội - 2020 BỘ GIÁO DỤC VÀ ĐÀO TẠO VIỆN HÀN LÂM KHOA HỌC VÀ CÔNG NGHỆ VIỆT NAM HỌC VIỆN KHOA HỌC VÀ CÔNG NGHỆ -*** - Hoàng Thu Trang NGHIÊN CỨU, THIẾT KẾ CẤU TRÚC TINH THỂ QUANG TỬ 1D VÀ 2D ỨNG DỤNG CHO LINH KIỆN LƯỠNG TRẠNG THÁI ỔN ĐỊNH Chuyên ngành: Vật liệu quang học, quang điện tử quang tử Mã số: 9.44.01.27 LUẬN ÁN TIẾN SĨ KHOA HỌC VẬT LIỆU NGƯỜI HƯỚNG DẪN KHOA HỌC: PGS.TS Ngô Quang Minh GS.TS Arnan Mitchell Hà Nội - 2020 i LỜI CAM ĐOAN Tôi xin cam đoan cơng trình nghiên cứu tơi, hướng dẫn PGS.TS Ngô Quang Minh GS.TS Arnan Mitchell Các số liệu, kết nêu luận án trung thực chưa công bố công trình khác NGHIÊN CỨU SINH HỒNG THU TRANG ii LỜI CẢM ƠN Trước tiên, xin bày tỏ lời cảm ơn sâu sắc hướng dẫn tận tình hai thầy giáo hướng dẫn: PGS.TS Ngô Quang Minh GS.TS Arnan Mitchell Các thầy ln tận tình hướng dẫn, định hướng kịp thời tạo điều kiện thuận lợi để tơi hồn thành luận án Tơi xin cảm ơn giúp đỡ khích lệ GS.TS Vũ Đình Lãm, TS Lê Quang Khải dành cho năm qua Tôi xin chân thành cảm ơn cộng tác giúp đỡ anh chị đồng nghiệp Phòng Vật liệu Ứng dụng Quang sợi, Viện Khoa học Vật liệu, Viện Hàn lâm Khoa học Công nghệ Việt Nam, nơi tơi hồn thành luận án Tơi xin trân trọng cảm ơn giúp đỡ tạo điều kiện thuận lợi sở đào tạo Học viện Khoa học Công nghệ Viện Khoa học Vật liệu – Viện Hàn lâm Khoa học Công nghệ Việt Nam, quan mà tơi cơng tác, q trình thực luận án Sau cùng, muốn gửi lời cảm ơn tới người thân gia đình bạn bè động viên, giúp đỡ tạo điều kiện để tơi hồn thành luận án NGHIÊN CỨU SINH HOÀNG THU TRANG iii MỤC LỤC Trang LỜI CAM ĐOAN i LỜI CẢM ƠN ii MỤC LỤC iii Danh mục chữ viết tắt vii Danh mục ký hiệu ix Danh mục hình vẽ, đồ thị x Danh mục bảng xix MỞ ĐẦU CHƯƠNG TỔNG QUAN 1.1 Cấu trúc tinh thể quang tử 1.1.1 Tổng quan cấu trúc tinh thể quang tử 1.1.2 Cấu trúc tinh thể quang tử chiều cách tử dẫn sóng 1.1.2.1 Khái niệm cấu trúc tinh thể quang tử chiều 1.1.2.2 Giản đồ vùng cấm quang 1.1.2.3 Buồng cộng hưởng 10 1.1.2.4 Cấu trúc cách tử dẫn sóng 11 1.1.3 Cấu trúc tinh thể quang tử hai chiều 13 1.1.3.1 Khái niệm 13 1.1.3.2 Vùng Brillouin 13 1.1.3.3 Mode dẫn sóng: điện trường ngang (TE) từ trường ngang (TM) 14 1.1.3.4 Giản đồ lượng 15 iv 1.1.3.5 Giam giữ ánh sáng cấu trúc tinh thể quang tử hai chiều 16 1.1.4 Ứng dụng cấu trúc tinh thể quang tử 23 1.2 Linh kiện lưỡng trạng thái quang ổn định 27 1.2.1 Khái niệm chung chuyển mạch quang 27 1.2.2 Nguyên lý lưỡng ổn định quang học 28 1.2.3 Ứng dụng linh kiện lưỡng trạng thái quang ổn định 31 1.3 Kết luận chương 32 CHƯƠNG PHƯƠNG PHÁP TÍNH TỐN VÀ MƠ PHỎNG 33 2.1 Lý thuyết ghép cặp mode theo thời gian 33 2.2 Phương pháp khai triển sóng phẳng 37 2.3 Phương pháp đạo hàm hữu hạn miền thời gian 41 2.4 Kết luận chương 50 CHƯƠNG TỐI ƯU HÓA HỆ SỐ PHẨM CHẤT VÀ PHỔ CỘNG HƯỞNG CỦA CẤU TRÚC CÁCH TỬ DẪN SÓNG 3.1 Cộng hưởng dẫn sóng cấu trúc cách tử lý thuyết dẫn sóng cộng hưởng 52 52 3.1.1 Cộng hưởng dẫn sóng cấu trúc cách tử 52 3.1.2 Lý thuyết dẫn sóng cộng hưởng 54 3.2 Cộng hưởng bất đối xứng dạng Fano 57 3.2.1 Cơ sở lý thuyết 57 3.2.2 Cộng hưởng dạng Fano cấu trúc quang tử 59 3.3 Tối ưu hóa hệ số phẩm chất phổ cộng hưởng cấu trúc cách tử dẫn sóng 3.3.1 Cấu trúc đơn cách tử dẫn sóng kết hợp với màng mỏng kim loại 62 64 v 3.3.1.1 Đặc trưng phản xạ màng mỏng kim loại cấu trúc đơn cách tử dẫn sóng 3.3.1.2 Đặc trưng cộng hưởng cấu trúc đơn cách tử dẫn sóng nhờ có mặt hiệu ứng cộng hưởng plasmon bề mặt 64 66 3.3.2 Cấu trúc ghép hai đơn cách tử dẫn sóng 69 3.3.3 Cấu trúc cách tử dẫn sóng dựa màng mỏng đa lớp 72 3.4 Kết luận chương 76 CHƯƠNG LƯỠNG TRẠNG THÁI QUANG ỔN ĐỊNH TRONG CẤU TRÚC CÁCH TỬ DẪN SÓNG 4.1 Lưỡng trạng thái quang ổn định cấu trúc cách tử dẫn sóng kết hợp với màng mỏng kim loại 78 78 4.1.1 Hiệu ứng tăng cường phản xạ màng mỏng kim loại 78 4.1.2 Hiệu ứng cộng hưởng plasmon bề mặt 81 4.2 Lưỡng trạng thái quang ổn định cấu trúc ghép hai đơn cách tử dẫn sóng 4.3 Lưỡng trạng thái quang ổn định cấu trúc cách tử dẫn sóng dựa màng mỏng đa lớp 4.4 Kết luận chương 83 87 89 CHƯƠNG LƯỠNG TRẠNG THÁI QUANG ỔN ĐỊNH DỰA TRÊN SỰ TƯƠNG TÁC GIỮA CỘNG HƯỞNG VÀ DẪN SÓNG KHE HẸP 91 TRONG CẤU TRÚC TINH THỂ QUANG TỬ HAI CHIỀU 5.1 Linh kiện quang tử cấu trúc tinh thể quang tử hai chiều vật liệu silic 91 5.1.1 Vật liệu quang tử silic 91 5.1.2 Sự cần thiết vật liệu lai silic hữu 96 5.2 Kênh dẫn sóng buồng cộng hưởng dạng khe hẹp 97 5.2.1 Kênh dẫn sóng dạng khe hẹp 97 5.2.2 Buồng cộng hưởng dạng khe hẹp 101 vi 5.2.2.1 Thể tích mode cộng hưởng 101 5.2.2.2 Buồng cộng hưởng dạng khe hẹp 102 5.3 Sự tương tác buồng cộng hưởng kênh dẫn sóng dạng khe hẹp 104 5.3.1 Cấu trúc ghép trực tiếp nhiều buồng cộng hưởng qua kênh dẫn sóng dạng khe hẹp 105 5.3.1.1 Mơ hình lý thuyết 105 5.3.1.2 Kết mơ 107 5.3.2 Cấu trúc ghép gián tiếp nhiều buồng cộng hưởng qua kênh dẫn sóng dạng khe hẹp 110 5.3.2.1 Mơ hình lý thuyết 110 5.3.2.2 Kết mơ 114 5.4 Lưỡng trạng thái quang ổn định 116 5.5 Kết luận chương 118 KẾT LUẬN CHUNG 119 HƯỚNG NGHIÊN CỨU TIẾP THEO 121 DANH MỤC CÁC CƠNG TRÌNH CƠNG BỐ CỦA LUẬN ÁN 122 TÀI LIỆU THAM KHẢO 124 vii DANH MỤC CÁC CHỮ VIẾT TẮT Tiếng Anh Auxiliary Differential Equation Available Highly Effective Boundary Conditions Carbon Nanotubes Complementary Metal Oxide Semiconductor Chữ viết tắt Tiếng Việt ADE Phương trình vi phân phụ trợ ABCs Biên hấp thụ CNTs Ống nano bon CMOS Công nghệ CMOS Lý thuyết ghép cặp mode theo Coupled Mode Theory in Time CMT Cross Phase Modulation XPM Điều biến pha chéo Distributed Bragg Reflectors DBR Gương phản xạ Bragg Figure of Merit FOM Hệ số phẩm chất Finite-Difference Time-Domain FDTD Four Wave Mixing FWM Trộn bốn bước sóng Free Carrier Absorption FCA Hiệu ứng hấp thụ hạt tải tự FWHM Bán độ rộng phổ cộng hưởng Full-Width at Half-Maximum One Dimensional 1D thời gian Đạo hàm hữu hạn miền thời gian Một chiều Perfect Matched Layer PML Biên hấp thụ hoàn hảo Photonic Band Gap PBG Vùng cấm quang Photonic Crystals PhCs Tinh thể quang tử Photonic Integrated Circuits PICs Mạch quang tích hợp Plane Wave Expansion PWE Khai triển sóng phẳng Recursive Convolution RC Rigorous Coupled-Wave Theory RCWT Kỹ thuật đệ quy Lý thuyết dẫn sóng cộng hưởng Self Phase Modulation SPM Tự điều biến Silicon Organic Hybrid SOH Vật liệu tích hợp lai silic-hữu Silicon On Insulator SOI Phiến SOI Surface Plasmon Polaritons SPPs Hiệu ứng cộng hưởng plasmon viii bề mặt Stimulated Raman Scattering SRS Tán xạ Raman kích thích Three Dimensional 3D Ba chiều Transverse Electric TE Điện trường ngang Two Dimensional 2D Hai chiều Transverse Magnetic TM Từ trường ngang Two Photon Absorption TPA Hiệu ứng hấp thụ hai photon 125 [14] Lê Quý Thông, Lê Ngọc Minh, Lê Thị Bảo Ngọc (2015), Nghiên cứu cấu trúc vùng tinh thể quang tử hai chiều phương pháp FDTD, Tạp chí Khoa học Cơng nghệ, Đại học Khoa học Huế, 3: pp 25-33 [15] B Huy, P V Hoi, P H Khoi, N T Van, and D T Chi (2011), Porous silicon as a promising material for photonics, International Journal of Nanotechnology, 8: pp 360-370 [15] T C Do, H Bui, T V Nguyen, T A Nguyen, T H Nguyen and V H Pham (2011), A microcavity based on a porous silicon multilayer, Advances in Natural Sciences: Nanoscience Nanotechnology, 2: pp 5:035001 [16] D T Chi, B Huy, N T Van and P V Hoi (2011), Investigation of 1D Photonic Crystal Based on Nano-porous Silicon Multilayer for Optical Filtering, Communications in Physics, 21: pp 89-96 [17] P T Nga, V D Chinh, P T Cuong, N X Nghia, N V Huy, N N Đạt, D N Thuan, C V Ha, D T Chi, L L Anh, C Barthou, P Benalloul, M Romaneli, A Maitre (2007), Experimental study of 3D self – assembled photonic crystal and colloidal core-shell semiconductor quantum dots, Asean Journal on Science and Technology for development, 24: pp 161-170 [18] T T Hoang, Q M Ngo, D L Vu, and H P T Nguyen (2018), Controlling Fano resonances in multilayer dielectric gratings towards optical bistable devices, Scientific Reports, pp 8:16404 [19] T T Hoang, Q M Ngo, D L Vu, K Q Le, T K Nguyen, and H P T Nguyen (2018), Induced high-order resonance linewidth shrinking with multiple coupled resonators in silicon-organic hybrid slotted two-dimensional photonic crystals for reduced optical switching power in bistable devices, Journal of Nanophotonics, 12: p 016014 [20] V H Pham, H Bui, T V Nguyen, T A Nguyen, T S Pham, V D Pham, T C Tran, T T Hoang, and Q M Ngo (2016), Progress in the research and development of photonic structure devices, Advances in Natural Sciences: Nanoscience Nanotechnology, 7: p 015003 126 [21] T T Hoang, K Q Le, and Q M Ngo (2015), Surface plasmon-assisted optical switching/bistability at telecommunication wavelengths in nonlinear dielectric gratings, Current Applied Physics, 15: pp 987-992 [22] Q M Ngo, K Q Le, T T Hoang, D L Vu, and V H Pham (2015), Numerical investigation of tunable Fano-based optical bistability in coupled nonlinear gratings, Optics Communications, 338: pp 528-533 [23] Q M Ngo, T T Hoang, D L Nguyen, D L Vu, and V H Pham (2013), Metallic assisted guided-mode resonances in slab waveguide gratings for reduced optical switching intensity in bistable devices, Journal of Optics, 15: pp 055503 [24] B Mamri and O Barkat (2019), Design of a Selective Filter Based on Onedimensional Supercondutor Photonic Crystal, Journal of Superconductivity and Novel Magnetism, 32: pp 3397-3405 [25] S Ma and S M Anlage (2020), Microwave applications of photonic topological insulators, Applied Physics Letters, 116: p 250502 [26] M Sharma, V Dhasarathan, J S Skibina, M S ManiRajan, S Konar, T T Hoang, and Q M Ngo (2019), Giant Nonlinear AlGaAs-Doped Glass Photonic Crystal Fibers for Efficient Soliton Generation at Femtojoule Energy, IEEE Photonics Journal, 11: pp 7102411 (11 pp) [27] I A Sukhoivanov, I V Guryev (2009), Photonic Crystals: Physics and Practical Modeling [28] S Iwahashi, Y Kurosaka, K Sakai, K Kitamura, N Takayama, S Noda (2011), Higher-order vector beams produced by photonic-crytal lasers, Optical Society of America, 19: pp 11963-11968 [29] K Ashida, M Okano, M Ohtsuka, M Seki, N Yokoyama, K Koshino, M Mori, T Asano, S Noda, and Y Takahashi (2017), Ultrahigh-Q photonic crystal nanocavities fabricated by CMOS process technologies, Optics Express, 25: pp 18165-18174 [30] H S Nalwa (2001), Silicon Based Materials and Devices [31] P R Villeneuve and M Pich´e (1992), Photonic band gaps in two-dimensional square and hexagonal lattices, Physical Review B, 46: pp 4969–4972 127 [32] J D Joannopoulos, S G Johnson, MIT (2003), Introduction to Photonic Crystals: Bloch’s Theorem, Band Diagrams, and Gaps [33] R D Meade, A Devenyi, J D Joannopoulos, O L Alerhand, D A Smith, and K Kash (1994), Novel applications of photonic bandgap materials: Low-loss bands and high Q cavities, Journal of Applied Physics, 75: pp 4753–4755 [34] J D Jackson (1975), Classical electrodynamics [35] O Painter, R K Lee, A Scherer, A Yariv, J D O’Brien, P D Dapkus, and I Kim (1999), Two-dimensional photonic band-gap defect mode laser, Bibliography, 158: pp 1819-1821 [36] O J Painter, A Husain, A Scherer, J D O’Brien, I Kim, and P D Dapkus (1999), Room temperature photonic crystal defect lasers at near-infrared wavelengths in InGaAsP, Journal of Lightwave Technology, 17: pp 2082–2088 [37] A A Siraji, Y Zhao (2015), High-sensitivity and high-Q-factor glass photonic crystal cavity and its applications as sensors, Optics Letters, 40: pp 1508-1511 [38] Z L Bushell, M Florescu, S J Sweeney (2017), High-Q photonic crystal cavities in all-semiconductor photonic crystal heterostructures, Physical Review B, 95: p 235303 [39] D Dodane, J Bourderionnet, S Combrié, and A D Ross (2017), Fully embedded photonic crystal cavity with Q=0.6 million fabricated within a fullprocess CMOS multiproject wafer, Optics Express, 26: pp 20868-20877 [40] T Asano, Y Ochi, Y Takahashi, K Kishimoto, and S Noda (2017), Photonic crystal nanocavity with a Q factor exceeding eleven million, Optics Express, 25: p 1769 [41] Z Zhang and M Qiu (2004), Small-volume waveguide-section high Q microcavities in 2D photonic crystal slabs, Optics Express, 12: pp 3988–3995 [42] K Srinivasan, P E Barklay, O Painter, J Chen, A Y Cho, and C Gmachl (2003), Experimental demonstration of a high quality factor photonic crystal microcavity, Applied Physics Letters, 83: pp.1915–1917 128 [43] K Srinivasan, O Painter (2003), Fourier space design of high-Q cavities in standard and compressed hexagonal lattice photonic crystals, Optics Express, 11: pp 579–593 [44] U P Dharanipathy, M Minkov, M Tonin, V Savona, and R Houdré (2014), High-Q silicon photonic crystal cavity for enhanced optical nonlinearities, Applied Physics Letters, 105: p 101101 [45] H Y Ryu, M Notomi, and Y H Lee (2003), High-quality-factor and smallmode-volume hexapole modes in photonic-crystal-slab nanocavities, Applied Physics Letters, 83: pp 4294–4296 [46] Y Akahane, T Asano, B S Song, and S Noda (2003), High-Q photonic nanocavity in a two-dimensional photonic crystal, Nature, 425: pp 944–947 [47] B S Song, S Noda, T Asano, and Y Akahane (2005), Ultra-high-Q photonic double-heterostructure nanocavity, Nature Materials, 4: pp 207–210 [48] V R Almeida, Q Xu, C A Barrios, and M Lipson (2004), Guiding and confining light in void nanostructure, Optics Letters, 29: p 1209 [49] J T Robinson, C Manolatou, L Chen, and M Lipson (2005), Ultrasmall Mode Volumes in Dielectric Optical Microcavities, Physics Review Letters, 95: p 143901 [50] T Yamamoto, M Notomi, H Taniyama, E Kuramochi, Y Yoshikawa, Y Torii, and T Kuga (2008), Design of a high-Q air-slot cavity based on a widthmodulated line-defect in a photonic crystal slab, Optics Express, 16: p 13809 [51] A Di Falco, L O’Faolain, and T F Krauss (2009), Chemical sensing in slotted photonic crystal heterostructure cavities, Applied Physics Letters, 94: p 63503 [52] K Li, J Li, Y Song, G Fang, C Li, Z Feng, R Su, B Zeng, X Wang, and C Jin (2014), L n Slot Photonic Crystal Microcavity for Refractive Index Gas Sensing, IEEE Photonics Journal, 6: p 6802509 [53] S Y Lin, E Chow, S G Johnson, and J G Joannopoulos (2000), Demonstration of highly efficient waveguiding in photonic crystal slab at the 1.5 µm wavelength, Optics Letters, 25: pp 1297-1299 129 [54] S Y Lin, E Chow, S G Johnson, and J G Joannopoulos (2000), Demonstration of highly efficient waveguiding in photonic crystal slab at the 1.5 µm wavelength, Optics Letters, 25: pp 1297-1299 [55] M Loncar, D Nedeljkovic, T Doll, and J Vuˇckovi´c (2000), Waveguiding in planar photonic crystals, Applied Physics Letters, 77: pp 1937–1939 [56] K Tsuruda, M Fujita, and T Nagatsuma (2015), Extremely low-loss terahertz waveguide based on silicon photonic-crystal slab, Optics Express, 23: pp 3197731990 [57] A E Erol, H S Sozuer (2015), High transmission through a 90 bend in a polarization-independent single-mode photonic crystal waveguide, Optics Express, 23: pp 32690-32695 [58] T T Zhu, M R C Mahdy, Y Y Cao, H LV, F Sun, Z Jiang, and W Ding (2016), Optical pulling using evanescent mode in subwavelength channels, Optics Express, 24: pp 9:18437 [59] A Di Falco, L O’Faolain, and T F Krauss (2008), Photonic crystal slotted slab waveguides, Photonics Nanostructures - Fundam Applied, 6: pp 38–41 [60] Y Xu, C Caer, D Gao, E Cassan, and X Zhang (2014), High efficiency asymmetric directional coupler for slow light slot photonic crystal waveguides, Optics express, 22: pp 11021-11028 [61] M Zahravi, H Alipour, Banaei, A Andalib (2015), Design of optical band pass filter based on photonic crystal with resonance cavity, IJCSI International Journal of Computer Science Issues, 4: pp 127-132 [62] A Karim, S O Hassan, A S A Mohamed, M M T Maghrabi, and N H Rafat (2015), Optimal design of one-dimensional photonic crystal filters using minimax optimization approach, Applied Optics, 54: pp 1399-1409 [63] Y Long and J Wang (2015), All-optical tuning of a nonlinear silicon microring assisted microwave photonic filter: theory and experiment, Optics Express, 23: pp 17758-17771 [64] B Chen, T Tang, and H Chen (2009), Study on a compact flexible photonic crystal waveguide and its bends, Optics Express, 17: pp 5033-5038 130 [65] A E Erol and H S Sozuer (2015), High transmission through a 90◦ bend in a polarization-independent single-mode photonic crystal waveguide, Optics Express, 23: pp 32690 (6pp) [66] A Ghaffari, M Djavid, and M S Abrishamian (2009), Power splitters with different ouput power levels based on directional coupling, Applied Optics, 48: pp 1606-1609 [67] A Bakhatazad, and A G Kirk (2006), First-band S-vector photonic crystal superism demultiplexer bends, Optics Letter, 31: pp 745-747 (2006) [68] Y Xiong, Z Liu, S Durant, H Lee, C Sun, and X Zhang (2007), Tuning the far-field superlens: from UV to visible, Optics Express, 15: pp 7095-7102 [69] S Kim, I Park, H Lim, C.S Kee (2004), Highly efficient photonic crystalbased multichannel drop filters of three-port system with reflection feedback, Optical Society of America, 12: pp 5518-5525 [70] C M Soukoulis, M Kafesaki, and E N Economou (1998), Temperature effect on the roughness of the formation interface of p-type porous silicon, Journal of Applied Physics, 84: p 3129 [71] T Stomeo, F Vanlaere, M Ayre (2008), Integration of grating couplers with a compact photonic crytal demultilexer on an InP membrance, Optics Letters, 33: pp 884-886 [72] Y Xu, C Caer, D Gao, E Cassan, and X Zhang1 (2014), High efficiency asymmetric directional coupler for slow light slot photonic crystal waveguides, Optics Express, 22: pp 11021-11028 [73] Y Geng, L Wang, Y Xu, A G Kumar, X Tan, and X Li (2018), Wavelength multiplexing of four-wave mixing based fiber temperature sensor with oil-filled photonic crystal fiber, Optics Express, 26: pp 27907-27916 [74] E Lamilla, M S Faria, I Aldara, P F Jarschel, J L Pita, and P Dainese (2018), Characterization of surface-states in a hollow core photonic crystal fiber, Optics Express, 26: pp 32554-32564 131 [75] D N Christodoulides, and N K Efremidis (2002), Discrete tempotal solitions along a chain of nonlinear coupled microcavities embedded in photonic crystals, Optics Letters 27: pp 568-570 [76] K Nozaki, A Lacraz, A Shinya, S Matsuo, T Sato, K Takeda, E Kuramochi, and M Notomi (2015), All-optical switching for 10-Gb/s packet data by using an ultralow-power optical bistability of photonic-crystal nanocavities, Optics Express, 23: pp 30379-30392 [77] J Li, R Yu, C Ding, and Y Wu (2014), Optical bistability and four-wave mixing with a single nitrogen-vacancy center coupled to a photonic crystal nanocavity in the weak-coupling regime, Optics Express, 22: pp 15024-15038 [78] J Guo, L Jiang, Y Jia, X Dai, Y Xiang, and D Fan (2017), Low threshold optical bistability in one-dimensional gratings based on graphene plasmonics, Optics Express, 25: pp 5972-5981 [79] J P Vasco, and V Savona (2019), Slow-Light Frequency Combs and Dissipative Kerr Solitions in Coupled-Cavity Waveguides, Physical Review Applied, 12: pp 064065 [80] T F Khalkhali, R Shiri, H Shahrokhabadi, and A Bananej (2019), Complete photonic band gap characteristics of two-dimensional Kerr nonlinear plasma photonic crystals, Indian Journal of Physics, 93: pp 1537-1544 [81] M R J Azizpour, M Sorooch, N Dalvand, and Y S Kavian (2019), AllOptical Ultra-Fast Graphene-Photonic Crystal Switch, Crystals, 9: p 461 [82] F Azadpour, and A Bahari (2019), All-optical bistability bassed on cavity resonances in nonlinear photonic crystal slab-reflector-based Fabry-Perot cavity, Optics Communications, 437: pp 297-302 [83] G Yan, Z Jianfeng, Z Han, F Yunpeng, C Haobo (2020), Research on Alloptical Switch Based on Nonlinear Effect of Photonic Crystal, Imaging Science and Photochemistry, 38: pp 15-21 132 [84] A Rode, M Samoc, B L Davies (2006), Photo-structuring of As2S3 glass by femtosecond irradiation, Optics Express, 14:pp 7751-7756 [85] B E A Saleh, M C Teich (2001), Fundamentals of Photonics [86] J L Jewell, H M Gibbs, A C Gossard, A Passner, and Wiegmann (1983), Fabrication of GaAs bistable optical devices, Materials Letters, 1: pp 148-151 [87] H M Gibbs (1985), Optical bistability: Controlling Light with Light [88] E Garmire, S D Allen, J Marburger, and C M Verber (1978), Multimode Integrated Optical Bistable Switch, Optics Letters, 3: p 69 [89] M Notomi, A Shinya, K Nozaki, T Tanabe, S Matsuo, E Kuramochi, T Sato, H Taniyama, and H Sumikura (2011), Low-power nanophotonic devices based on photonic crystals towards dense photonic network on chip, IET Circuits Device Systems, 5: pp.84-93 [90] K Srinivasan, P E Barclay, and O Painter (2004), Fabrication-tolerant high quality factor photonic crystal microcavities, Optics Express, 12: pp 1458–1463 [91] Q M Ngo, S Kim, J Lee, and H Lim (2012), All-optical switches based on multiple cascaded resonators with reduced switching intensity-response time products, Journal of Lightwave Technology, 30: pp 3525-3531 [92] Q M Ngo, S Kim, S H Song, and R Magnusson (2009), Optical bistable devives based on guided-mode resonance in slab waveguide grattings, Optics Express, 17:pp 23459-23467 [93] H A Haus (1984), Waves and Fields in optoelectronics (Englewood Cliffs, NJ: Prentice-Hall [94] M Plihal, and A A Maradudin (1991), Photonic band structure of twodimensional systems: The triangular lattice, Physics Review B, 44: pp 8565-8571 [95] P R Villeneuve, and M Piché (1992), Photoinc band gaps in two-dimensional square and hexagonal lattices, Physics Review B, 46: pp 4969-4972 [96] R D Meade, K D Brommer, A M Rappe, and J D Joannopoulos (1992), Existence of a photonic band gap in two dimensions, Applied Physics Letters, 61: pp 495-497 133 [97] K M Ho, C T Chan, and C M Soukoulis (1990), Existence of a photonic gap in periodic dielectric structures, Physic Review Letters, 65: pp 3152-3155 [98] H S Sözüer and J W Haus (1992), Photonic bands: Convergence problems with the plane-wave method, Physics Review B, 45: pp 13962-13972 [99] M Plihal and A A Maradudin (1991), Photonic band structure of twodimensional systems: The triangular lattice, Physics Review B, 44: pp 8565-8571 (1991) [100] K Sakoda (2001), Optical Properties of Photonic Crystals [101] A Barra, D Cassagne, and C Jouanin (1998), Existence of two-dimensional absolute photonic band gaps in the visible, Applied Physics Letters, 72: pp 627629 [102] N Yokouchi, A J Danner, and K D Choquette (2002), Effective index model of 2D photonic crystal confined VCSELs, presented at LEOS VCSEL Summer Topical, Mont Tremblant, Quebec [103] J C Knight, T A Birks, R F Cregan, P Russell and J.-P de Sandro (1998), Photonic crystals as optical fibres - physics and applications, Optical Materials, 11: pp 143-151 [104] K Yee (1966), Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media, IEEE Transactions on Antennas and Propagation, 14: pp 302-307 [105] A Deinega, S Belousov and I Valuev (2009), Hybrid transfer-matrix FDTD method for layered periodic structures, Optics Letters, 34: pp 860 [106] Y Hao and R Mittra (2009), FDTD Medeling of Metamaterials: Theory and Applications [107] J D Jackson (1998), Classical Electrodynamics Wiley, New York, 3rd edn [108] S Fan, P R Villeneuve, J D Joannopoulos, and H A Haus (1998), Channel drop filters in photonic crystals, Optics Express, 3: pp 4-11 134 [109] S Kim, I Park, H Lim, and C S Kee (2004), Highly efficient photonic crystal-based multichanel drop filters of three-port system with reflection feedback, Optics Express, 12: pp 5518-25 [110] H S Bark and T I Jeon (2018), Tunable terahertz guided-mode resonance filter with a variable grating period, Optics Express, 26: pp 29353 -29362 [111] D A Bykov, L L Doskolovich, and V A Soifer (2017), Coupled mode theory and Fano resonances in guided mode resonant gratings: the conical diffraction mounting, Optics Express, 25: pp 1151 – 1164 [112] W K Kuo, and C J Hsu (2017), Two dimensional grating guided mode resonance tunable filter, Optics Express, 25: pp 29642 – 29649 [113] H Ahmadpanahi, R Vismara, O Isabella, and M Zeman (2018), Distinguishing Fabry Perot from guided resonances in thin periodically textured silicon absorbes, Optics Express, 26: pp 737-749 [114] H A Lin, H Y Hsu, C W Chang, and C S Huang (2016), Compact spectrometer system based on a gradient grating period guide mode resonance filter, Optics Express, 24: pp 10972-10979 [115] C P Stumberg, K B Dossou, L C Botten, R C Mcphedran, and C Martijn (2015), Fano resonances of dielectric gratings: symmetries and broadband filtering, Optics Express, 23: pp 1672-1686 [116] Z Wang, R Zhang, and J Guo (2018), Quadrupole mode plasmon resonance enabled subwavelength metal dielectric grating optical reflection filters, Optics Express, 26: pp 496-504 [117] Y Liang, W Peng, M Lu, and S Chu (2015), Narrow band wavelength tunable filter based on asymmetric double layer metallic grating, Optics Express, 23: pp 14434-14445 135 [118] H S Bark and T I Jeon (2018), Dielectric film sensing with TE mode of terahertz guided mode resonance, Optics Express, 26: pp 34547-34556 [119] R Magnusson, and S S Wang (1992), New principle for optical filters, Applied Physics Letters, 61: pp 1022-1024 [120] A E Miroshnichenko, S Flach, and Y S Kivshar (2009), Fano resonances in nanoscale structures [121] Breit, G., and E Wigner (1936), Capture of Slow Neutrons, Physical Review Journals, 49: pp 519–531 [122] U Fano (1935), Sullo spettro di assorbimento dei gas nobili presso il limite dello spettro d’arco, Nuovo Cimento, 12: pp 154–161 [123] U Fano (1961), Effects of Configuration Interaction on Intensities and Phase Shifts, Physical Review, 124: pp 1866–1878 [124] M F Limonov, M V Rybin, A N Poddubny, and Y S Kivshar (2017), Fano resonances in photonics, Nature Photonics, 11: pp 543-554 [125] J Fransson, and A V Balatsky (2007), Exchange interaction and Fano resonances in diatomic molecular systems, Physical Review B, 75: pp 153309 [126] P Kolorenc, V Brems, and J Horacek (2005), Computing resonance positions, widths, and cross sections via the Feshbach-Fano R-matrix method, Application to potential letter, 53: pp 710-713 [127] R Soref and J Larenzo (1986), All-silicon active and passive guide-wave components for λ = 1.3 and 1.6 μm, IEEE Journal of Quantum Electronics, 22: pp 873-879 [128] Y A Vlasov (2008), Silicon photonics for next generation computing systems 136 [129] B G Lee and K Bergmann (2008), Silicon nano-photonic interconnection networks in multicore processor systems [130] W Bogaerts, R Baets, P Dumon, V Wiaux, S Beckx, D Taillaert, B Luyssaert, J VanCampenhout, P Bienstman, and D Van Thourhout (2005), Nanophotonic waveguides in silicon-on-insulator fabricated with CMOS technology, Journal of Lightwave Technology, 23: pp 401-412 [131] J Gao, J F McMillan, M.-C Wu, J Zheng, S Assefa, and C W Wong (2010), Demonstration of an air-slot mode-gap confined photonic crystal slab nanocavity with ultrasmall mode volumes, Applied Physics Letters, 96: p 051123 [132] J Jágerská, H Zhang, Z Diao, N Le Thomas, and R Houdré (2010), Refractive index sensing with an air-slot photonic crystal nanocavity, Optics Letters, 35: pp 2523-2525 [133] A H Safavi-Naeini, T P M Alegre, M Winger, O Painter (2010), Optomechanics in an ultrahigh-Q slotted 2D photonic crystal cavity, Applied Physics Letters, 97: p 181106 [134] C Caër, X Le Roux, and E Cassan (2012), Enhanced localization of light in slow wave slot photonic crystal waveguides, Optics Letters, 37: p 3660 [135] C Caër, X Le Roux, and E Cassan (2013), High-Q silicon-on-insulator slot photonic crystal cavity infiltrated by a liquid, Applied Physics Letters, 103: p 251106 [136] Y Liu, S Wang, D Zhao, W Zhou, and Y Sun (2017), High quality factor photonic crystal filter at k ≈ and its application for refractive index sensing, Optics Express, 25: pp 10536-10545 [137] H K Tsang and Y Liu (2008), Nonlinear optical properties of silicon waveguides, Semiconductor Science and Technology, 23: p 64007 [138] H K Tsang, C S Wong, T K Liang, I E Day, S W Roberts, A Harpin, J Drake, and M Asghari (2002), Optical dispersion, two-photon absorption and selfphase modulation in silicon waveguides at 1.5 μm wavelength, Applied Physics Letters, 80: pp 416–418 137 [139] J Leuthold, C Koos and W Freude (2010), Nonlinear silicon photonics, Nature photonics, 4: pp 535-543 [140] A Khilo, S J Spector, M E Grein, A H Nejadmalayeri, C W Holzwarth, M Y Sander, M S Dahlem, M Y Peng, M W Geis, N A DiLello, J U Yoon, A Motamdi, J S Orcutt, J P Wang, C M Sorace-Agaskar, M A Popović, J Sun (2012), Overcoming the bottleneck of electronic jitter 13, Optics Express, 20: pp 4454 [141] Q Lin, O J Painter, and G P Agrawal (2007), Nonlinear optical phenonmena in silcon waveguides: modeling and applications, Optics express, 15: pp 16604-16644 [142] T Vallaitis (2009), Optical properties of highly nonlinear silicon-organic hybrid (SOH) waveguide geometries, Optics Express, 17: pp 17357–17368 [143] H K Tsang and Y Liu (2008), Nonlinear optical properties of silicon waveguides, Semiconductor Science and Technology, 23: p 064007 [144] R Salem, M A Foster, A C Turner, D F Geraghty, M Lipson, and A L Gaeta (2007), Signal regeneration using low-power four-wave mixing on silicon chip, Natures Photonics, 2: pp 35–38 [145] V Mizrahi, K W DeLong, G I Stegeman, M A Saifi, and M J Andrejco (1989), Two photon absorption as a limitation to all-optical switching, Optics Letters, 14: pp 1140-1142 [146] K W DeLong, K B Rochford, and G I Stegeman (1989), Effect of twophoton absorption on all-optical guidedwave devices, Applied Physics Letters, 55: pp 1823–1825 [147] H Park, A W Fang, S Kodama, and J E Bowers (2005), Hybrid silicon evanescent laser fabricated with a silicon waveguide and III-V offset quantum wells, Optics Express, 13: pp 9460– 9464 [148] G Roelkens, D Van Thourhout, R Baets, R Nötzel, and M Smit (2006), Laser emission and photodetection in an InP/InGaAsP layer integrated on and coupled to a Silicon-on-Insulator waveguide circuit, Optics Express, 14: pp 8154– 8159 138 [149] A W Fang, H Park, O Cohen, R Jones, M J Paniccia, and J E Bowers (2006), Electrically pumped hybrid AlGaInAs-silicon evanescent laser, Optics Express, 14: pp 9203–9210 [150] A W Fang, R Jones, H Park, O Cohen, O Raday, M J Paniccia, and J E Bowers (2007), Integrated AlGaInAs-silicon evanescent racetrack laser and photodetector, Optics Express, 15: pp 2315–2322 [151] J Van Campenhout, P Rojo-Romeo, P Regreny, C Seassal, D Van Thourhout, S Verstuyft, L Di Cioccio, J M Fedeli, C Lagahe, and R Baets (2007), Electrically pumped InP-based microdisk lasers integrated with a nanophotonic silicon-on- insulator waveguide circuit, Optics Express, 15: pp 6744–6749 [152] P E Barclay, K Srinivasan, and O Painter (2005), Nonlinear response of silicon photonic crystal microresonators excited via an integrated waveguide and fiber taper, Optics Express, 13: pp 801–820 [153] E M Purcell (1946), Spontaneous emission probabilities at radio frequencies, Physics Review Journals, 69: p 681 [154] L C Andreani and G Panzarini (1999), Strong-coupling regime for quantum boxes in pillar microcavities: Theory Lucio, Physics Review B, 60: pp 13276– 13279 [155] J T Robinson, C Manolatou, L Chen, and M Lipson (2005), Ultrasmall Mode Volumes in Dielectric Optical Microcavities, Physics Review Letters, 95: pp 143901 [156] D Yang, H Tian, Y Ji (2011), Nanoscale photonic crystal sensor arrays on monolithic substrates using side-coupled resonant cavity arrays, Optics Express, 19: pp 20023-20034 [157] M Mendez-Astudillo, H Okayama,and H Nakajima (2018), Silicon optical filter with transmission peaks in wide stopband obtained by anti-symmetric photonic crystal with defect in multimode, Optics Express, 26: pp 1841-1850 139 [158] Y Liu, F Zhou, and Q Mao (2013), Analytical theory for the nonlinear optical response of a Kerr-type standing-wave cavity side-coupling to a MIM waveguide, Optics Express, 21: pp 23687-23694 [159] D Fitsios, T Alexoudi, A Bazin, P Monnier, R Raj, A Miliou, G.T Kanellos, N Pleros, F Raineri (2016), Ultra-compact III‒V-on-Si photonic crystal memory for flip-flop operation at Gb/s, Optics Express, 24: pp 4270-4277 [160] A E Miroshnichenko, S Flach, and Y S Kivshar (2010), Fano resonances in nanoscale structures, Reviews of Modern Physics, 82: pp 2257 [161] B Maes, P Bienstman, and R Baets (2005), Switching in coupled nonlinear photonic-crystal resonators, Journal of the Optical Society of America, 22: pp 1778-1784 [162] C Husko, A D Rossi, S Combrié, Q V Tran, F Raineri, and C W Wong, (2009), Ultrafast all-optical modulation in GaAs photonic crystal cavities, Applied Physics Letters, 94: pp 021111 (4 pp) [163] Y Yu, M Heuck, H Hu, W Xue, C Peucheret, Y Chen, L K Oxenlowe, K Yvind, and J Mork (2014), Fano resonance control in a photonic crystal structure and its application to ultrafast switching, Applied Physics Letters, 105: pp 061117 [164] H Y Song, S Kim, and R Magnusson (2009), Tunable guided-mode resonances in coupled gratings, Optics Express, 17: pp 23544-23555 [165] H M Nguyen, and T B Thanh (2020), Electroslatic modulation of a photonic crystal resonant filter, Journal of Nanophotonics, 14: pp 026014 [166] S M A Mostaan, and H R Saghai (2019), Optical bistable switch based on the nonlinear Kerr effect of chalcogenide glass in a rectangular defect of a photonic crystal, Journal of Computational Electronics, 18: pp 6785 ... CHƯƠNG TỔNG QUAN 1.1 Cấu trúc tinh thể quang tử 1.1.1 Tổng quan cấu trúc tinh thể quang tử 1.1.2 Cấu trúc tinh thể quang tử chiều cách tử dẫn sóng 1.1.2.1 Khái niệm cấu trúc tinh thể quang tử chiều... xuất cấu trúc, tính tốn mô linh kiện lưỡng trạng thái quang ổn định sử dụng cấu trúc PhCs 1D 2D Ảnh hưởng cấu hình tham số cấu trúc PhCs lên đặc tính hiệu làm việc linh kiện lưỡng trạng thái quang. .. Dựa kết tích cực có thời gian qua gồm lý thuyết, tính tốn mơ [18-26], luận án với tiêu đề: ? ?Nghiên cứu, thiết kế cấu trúc tinh thể quang tử 1D 2D ứng dụng cho linh kiện lưỡng trạng thái ổn định”