Crosstalk Analysis between Optical Waveguides in Photonic Integrated Circuits PICs by Hybrid Coupled Mode Theory 157173044 CU iThesis 5671443021 dissertation / recv: 31072562 13:33:19 / seq: 8 Mr. Quan Trong Le Hoang A Dissertation Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Electrical Engineering Department of Electrical Engineering Faculty of Engineering Chulalongkorn University Academic Year 2018 Copyright of Chulalongkorn University การวิเคราะห์สัญญาณแทรกข้ามระหว่างท่อนาคลื่นแสงในวงจรรวมโฟโต้นิกส์ด้วยวิธีผสมของระเบียบ วิธีเชิงตัวเลขและทฤษฎีโมดควบกลา 157173044 CU iThesis 5671443021 dissertation / recv: 31072562 13:33:19 / seq: 8 นายกวาน ตรอง เล ฮวาง วิทยานิพนธ์นีเป็นส่วนหนึ่งของการศึกษาตามหลักสูตรปริญญาวิศวกรรมศาสตรดุษฎีบัณฑิต สาขาวิชาวิศวกรรมไฟฟ้า ภาควิชาวิศวกรรมไฟฟ้า คณะวิศวกรรมศาสตร์ จุฬาลงกรณ์มหาวิทยาลัย ปีการศึกษา 2561 ลิขสิทธิ์ของจุฬาลงกรณ์มหาวิทยาลัย Thesis Title Crosstalk Analysis between Optical Waveguides in Photonic Integrated Circuits PICs by Hybrid Coupled Mode Theory By Mr. Quan Trong Le Hoang Field of Study Electrical Engineering Thesis Advisor Tuptim Angkaew 157173044 Accepted by the Faculty of Engineering, Chulalongkorn University in Partial Fulfillment of the Requirement for the Doctor of Philosophy CU iThesis 5671443021 dissertation / recv: 31072562 13:33:19 / seq: 8 Dean of the Faculty of Engineering (Professor SUPOT TEACHAVORASINSKUN, D.) DISSERTATION COMMITTEE Chairman (Professor Prayoot Akkaraekthalin, Ph.) Thesis Advisor (Tuptim Angkaew) Examiner (Associate Professor Somchai Ratanathammaphan, Ph.) Examiner (Associate Professor Duang-rudee Worasucheep, Ph.) External Examiner (Associate Professor Athikom Roeksabutr, Ph.ที่ปรึกษาหลัก : ทับทิม อ่างแก้ว ในวิทยานิพนธ์เล่มนี ได้นาเทคนิคการคานวณเชิงตัวเลขมาอธิบายรูปแบบของแม่เหล็กไฟฟ้าใน รูปแบบท่อนาคลื่นของพลานาร์หลายชันและรวมกับทฤษฏีของคัปเปลอร์โหมดในการตรวจสอบครอส 157173044 ทอล์ค(crosstalk) ระหว่างท่อนาคลื่นทังสองที่ขนานกัน ซึ่งในวิทยานิพนธ์นีได้เสนอการวิธีการคานวณเชิง ตัวเลขที่แม่นยาในการกาหนดค่าคงที่การกระจายตัวในท่อนาคลื่นแบบพลานาร์ ที่ไม่มีการสูญเสียพลังงาน และมีการสูญ เสียพลังงาน โดยใช้ วิธีการของมุลเลอร์ (Muller) เพื่ อแก้สมการดิ สเพอร์ชัน และสมการ CU iThesis 5671443021 dissertation / recv: 31072562 13:33:19 / seq: 8 อนุพันธ์ของดิสเพอร์ชันในโครงสร้างของท่อนาคลื่น โดยข้อดีของวิธีการนีช่วยในการเพิ่มความแม่นยาและ ลดเวลาการคานวณของซี พี ยู ซึ่ งได้ ผ ลลัพ ธ์การจาลองทั งแบบโหมดคี่และโหมดคู่จากการคานวณค่ า สัมประสิทธิ์การคัปปลิงและค่าระยะการคัปปลิง ในการตรวจสอบการถ่ายเทพลังงานจากท่อนาคลื่นหนึ่ง ไปยังอีกท่อนาคลื่นหนึ่ง โดยได้ครอสทอล์คระหว่างท่อนาคลื่นที่ขนานกัน ในปัจจุบันอุปกรณ์ทางแสงและท่อนาคลื่นที่มี การใช้งานร่วมกันบนวงจรรวมซิลิกอนโฟโตนิคต้องการท่อนาคลื่นยาวแบบขนาน ดังนันครอสทอล์คหรื อการสูญเสียพลังงาน ที่เกิดขึนจากการคัปปลิงของคลื่นแสง โดยครอสทอล์คจะมีค่าเพิ่มขึนเมื่อระยะ ระหว่างท่อนาคลื่นลดลง ในงานวิจัยนีได้ตรวจสอบเกี่ยวกับครอสทอล์คและการลดปัญหาของครอสทอล์ค ในท่อนาคลื่นของพลานาร์หลายชัน สาขาวิชา วิศวกรรมไฟฟ้า ลายมือชื่อนิสิต. iv # # 5671443021 : MAJOR ELECTRICAL ENGINEERING KEYWORD: Transfer Matrix Method, Muller's Method, Coupled Mode Theory, ABSTRACT (ENGLISH) Coupling Length, Coupling Coefficient, Crosstalk Quan Trong Le Hoang : Crosstalk Analysis between Optical Waveguides in Photonic Integrated Circuits PICs by Hybrid Coupled Mode Theory.
Tuptim Angkaew 157173044 In this thesis, a numerical method has been introduced to describe electromagnetic mode in multilayer planar slab waveguides and combine with Couple Mode Theory to investigate the crosstalk between two parallel waveguides. On this CU iThesis 5671443021 dissertation / recv: 31072562 13:33:19 / seq: 8 dissertation, our purpose aims to build a useful and accurate numerical method in order to determine the propagation constants in planar lossless, lossy and active optical waveguides. By using this method contributes to Muller’s method, we can solve the dispersion equations and derivative of dispersion equations in a guided waveguide structure. The benefits of these methods are improved accuracy and reduced CPU time.
The results have been checked with several results published in the papers. Furthermore, after mode field has been found, we can obtain the even and odd mode to calculate the Coupling Coefficient and Coupling Length in order to monitor power exchanges from one waveguide to another waveguide. Finally, we can understand the crosstalk between two parallel waveguides. Nowadays, many devices and waveguides stay close together on silicon photonic integrated circuits and some applications require long parallel waveguides up to several millimeters for connecting devices.
Therefore, crosstalk, or loss, is created by the interaction of coupling light combined back and forth between parallel waveguides. The waveguides are closer and more interaction between parallel waveguides. Because of the following reasons, this research investigates about crosstalk and have solutions to reduce crosstalk in multilayer planar slab waveguides. Field of Study: Electrical Engineering Student's Signature.
Academic Year: 2018 Advisor's Signature. v ACKNOWLEDGE MENTS ACKNOWLEDGEMENTS This work has been done at Telecommunications System Research Laboratory, Department of Electrical Engineering, Chulalongkorn University. The financial support by the 100th Anniversary Chulalongkorn University for Doctoral Scholarship. I am very thankful to Kingdom of Thailand and Chulalongkorn University for giving me an opportunity to do my Ph.
and to achieve one of my life goals. 157173044 I would like to express my deep appreciation for the invaluable guidance, continuous support and adequate patience I have received from my supervisor, CU iThesis 5671443021 dissertation / recv: 31072562 13:33:19 / seq: 8 Assistant Professor Dr. The research and thesis could never be completed without her precious advice and encouragement. I am truly thankful to all the Professors in Electrical Engineering department, Chulalongkorn University for sharing the useful background knowledge for me to understand the difficult theories and concepts very easily.
Many thanks to all the friends I met in TSRL lab and a special thanks goes to Dr.Thien Le, Dr. Son Nguyen, Dr. Do Tien Sy Dr. Pham Quang Hoa for their encouragement and support all the way through my study.
Most importantly, I will not complete or even start my study without the support of my father and my mother. It is impossible for me to reach this step without your love, caring, sacrifice and understanding. I am grateful to my parents and my brother for their unconditional support. Quan Trong Le Hoang TABLE OF CONTENTS Page ABSTRACT (THAI) .v 157173044 TABLE OF CONTENTS .vi LIST OF TABLES.
viii CU iThesis 5671443021 dissertation / recv: 31072562 13:33:19 / seq: 8 LIST OF FIGURES. ix LIST OF ABBREVIATIONS AND NOTATIONS .2 Motivations for the research .4 Outline of the dissertation. 9 CHAPTER 2 LITERATURE REVIEW .2 Integrated photonics circuits.3 Integrated photonics circuits technology .4 Basic integrated photonic components.5 Silicon photonic waveguides. 16 CHAPTER 3 RESEARCH METHODOLOGY.1 Planar slab waveguide .2 Propagation characteristics of guided waves along with a dielectric guide .3 Transfer Matrix Method .1 Three-layer guiding structure for TE mode:.2 Maxwell’s Equations and TE field solutions .3 Maxwell’s Equations and TM field solutions: .5 Coupled mode theory.
42 CU iThesis 5671443021 dissertation / recv: 31072562 13:33:19 / seq: 8 3.2 The parallel directional coupler .3 Crosstalk between two parallel waveguides: .4 Power flow between waveguides: .6 Methodology in this research. 58 CHAPTER 4 RESULTS AND DISCUSSIONS ON INVESTIGATION .3 Coupling between two parallel dielectric slab waveguides. 66 CHAPTER 5 CONCLUSION AND RECOMMENDATION. 92 LIST OF TABLES Page Table 3-1 Refractive index and thickness of three layers waveguide structure.
32 Table 4-1 Structure with a six-layer lossless dielectric waveguide. 60 Table 4-2 Propagation constants of the lossless waveguide structure. 61 157173044 Table 4-3 Structure of a six-layer lossy dielectric waveguide. 62 Table 4-4 Propagation constants of a six-layer lossy dielectric waveguide structure 63 CU iThesis 5671443021 dissertation / recv: 31072562 13:33:19 / seq: 8 Table 4-5 Structure of a five-layer dielectric waveguide with both gain and losses.
64 Table 4-6 Propagation constants for a five-layer dielectric waveguide. 64 Table 4-7 Data of even and odd modes. 74 Table 4-8 Mode Coupling Coefficient and Coupling Length. 75 Table 4-9 Coupling Length and Coupling Coefficient with distance d.
82 Table 4-10 Output power of 1st core and 2nd core and values of crosstalk. 85 LIST OF FIGURES Page Figure 1-1 The crosstalk mitigation waveguide model with an air gap. (Angkaew, Umezawa et al. 5 Figure 2-1 (a) planar waveguide, (b) channel waveguide, (c) optical waveguide.
11 157173044 Figure 2-2 Cross-section of basic SOI waveguide structures: (a) planar waveguide, (b) strip waveguide, (c) rib waveguide. 15 CU iThesis 5671443021 dissertation / recv: 31072562 13:33:19 / seq: 8 Figure 2-3 Optical waveguide measurement 1. 16 Figure 2-4 Lensed fibers. 17 Figure 2-5 Optical waveguide measurement 2.
17 Figure 2-6 Optical waveguide measurement 3. 18 Figure 2-7 Waveguides with different length, bend radius and various shapes. 19 Figure 3-1 Basic structure of three-layer optical waveguide. 20 Figure 3-2 Slab Optical waveguide.
20 Figure 3-3 The field along the y-direction and = 0. 22 y Figure 3-4 Structure of three layers waveguide. 26 Figure 3-5 Example of the first cutoff and second cut off. 26 Figure 3-6 At a normalized value V=12.065 there are three values of b = 0.
28 Figure 3-7 Simple structure of three layers waveguide. 30 Figure 3-8 Using MATLAB to solve the dispersion equation to find propagation constant. 32 Figure 3-9 Mode field of the three-layer waveguide structure. 33 Figure 3-10 Structure of the multilayer planer optical waveguide.
34 x Figure 3-11 Structure of multilayer waveguide. 44 Figure 3-12 Transmit power from guide 1 to guide 2. 55 Figure 3-13 Power exchange in couplers. 56 Figure 3-14 Directional Coupler rectangular waveguides.
57 Figure 3-15 Coupling Coefficient and Coupling Length with Distance between two parallel waveguides. 58 157173044 Figure 3-16 Flow Chart of summarizing research methodology. 59 Figure 4-1 TE mode field and Power for individual layers of TE 1 and TE 2. 61 CU iThesis 5671443021 dissertation / recv: 31072562 13:33:19 / seq: 8 Figure 4-2 TE mode field and Power for individual layers of TE 3 and TE 4.
61 Figure 4-3 TE mode field and Power for individual layers of TE 1 and TE 2. 63 Figure 4-4 TE mode field and Power for individual layers of TE 3 and TE 4. 63 Figure 4-5 TE mode field TE1 TE2 TE3 TE4 TE5 TE6 for individual layers. 65 Figure 4-6 TE mode field and Power for individual layers of TE 7 , TE 8 and TE 9.
66 Figure 4-7 Structure of lossless waveguide. 67 Figure 4-8 TE modes of structure with gap width = 1 micron. 68 Figure 4-9 TE modes of structure with gap width = 1. 69 Figure 4-10 TE modes of structure with gap width = 2.
70 Figure 4-11 TE modes of structure with gap width = 2. 71 Figure 4-12 TE modes of structure with gap width = 3. 72 Figure 4-13 TE modes of structure with gap width = 4. 73 Figure 4-14 Ratio between Power in each core with total Power.
76 Figure 4-15 Coupling Length = 300um with distance 1 micrometer. 77 Figure 4-16 Coupling Length = 500um with distance 2 micrometer. 77 Figure 4-17 Coupling Length = 900um with distance 3 micrometer. 78 xi Figure 4-18 Coupling Length = 1600um with distance 4 micrometer.
78 Figure 4-19 Coupling Length = 2800um with distance 5 micrometer. 79 Figure 4-20 Coupling Length = 4650um with distance 6 micrometer. 79 Figure 4-21 Coupling Length = 7950um with distance 7 micrometer. 80 Figure 4-22 Coupling Length = 13500um with distance 8 micrometer.
80 157173044 Figure 4-23 Coupling Length = 22800um with distance 9 micrometer. 81 Figure 4-24 Coupling Length = 38000um with distance 10 micrometer. 81 CU iThesis 5671443021 dissertation / recv: 31072562 13:33:19 / seq: 8 Figure 4-25 Structure of lossless waveguide. 82 Figure 4-26 Field mode of the waveguide.
83 Figure 4-27 Coupling with distance 8um. 83 Figure 4-28 Coupling with distance 10um. 84 Figure 4-29 Coupling with distance 15um. 84 Figure 4-30 The relationship between crosstalk and distance.
85 LIST OF ABBREVIATIONS AND NOTATIONS TE Transverse Electric TM Transverse Magnetic FDTD Finite Difference Time Domain Method FEM Finite Element Method TMM Transfer Matrix Method 157173044 CIM Cauchy’s Integral Method 1D One - dimensional CU iThesis 5671443021 dissertation / recv: 31072562 13:33:19 / seq: 8 2D Two - dimensional 3D Three - dimensional E Electric Field vector H Magnetic Field vector D Electric displacement vector B Magnetic flux density vector J Electric current density vector P Electric polarization vector Multi – dimensional spatial partial derivative operator “del” Partial derivative operator with respect to time t Polar incident angle Azimuthal incident angle Kronecker delta function/vector Electric charge density Electric permittivity o Electric permittivity of free space, 8.
