Integrated optical devices based on liquid crystals embedded in polydimethylsiloxane flexible substrates Department of Information, Electronics and Telecommunication Engineering PhD degree in Information and Communication Technology – XXXI Cycle Luca Civita ID number 799451 Thesis Advisor Prof. Antonio d’Alessandro A.A. 2017-2018 A thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Information and Communication Technology This page intentionally left blank Per aspera sic itur ad astra 3 Summary Introduction ...................................................................................................................... 7 Chapter 1: Optofluidics ................................................................................................. 11 1.1 Overview ......................................................................................................... 11 1.1.1 Equation of Flow .................................................................................... 16 1.2 Optofluidic Optical Components................................................................. 20 1.2.1 PDMS ....................................................................................................... 20 1.2.2 Solid core and liquid cladding ............................................................. 24 1.2.3 Liquid core and solid cladding ............................................................ 26 1.2.4 Liquid Core and Liquid Cladding ....................................................... 27 Chapter 2: Liquid Crystals ............................................................................................ 33 2.1 Overview ......................................................................................................... 33 2.2 Types of mesophase ....................................................................................... 33 2.2.1 Thermotropic LC .................................................................................... 34 2.2.2 Main crystalline mesophases ................................................................ 35 2.2.3 Crystalline solid phase .......................................................................... 35 2.2.4 Smectic C phase ...................................................................................... 35 2.2.5 Smectic A phase ...................................................................................... 36 2.2.6 Nematic phase ........................................................................................ 36 2.2.7 Isotropic phase ........................................................................................ 37 2.3 LC interaction with surfaces and modelization ......................................... 37 2.3.1 Surface interaction ................................................................................. 37 2.3.2 Elastic Energy ......................................................................................... 40 2.3.3 Anchoring Energy .................................................................................. 41 2.3.4 Dielectric properties of LC .................................................................... 43 2.3.5 Electro-Optic effect in LC ...................................................................... 46 2.3.6 Free energy and torque by electric and magnetic fields ................... 48 2.3.7 Freedericksz transition revisited .......................................................... 49 2.3.7.1 Case 1: One elastic constant approximation. ...................................... 50 2.3.7.2 Case 2: Freedericksz transition voltage including elastic anisotropies. ............................................................................................................ 52 4 2.3.7.3 Case 3: Freedericksz transition voltage including elastic conductivity. ........................................................................................................... 53 2.4 LC in photonic applications .......................................................................... 54 Conclusions ................................................................................................................. 60 Chapter 3: Fabrication and characterization of LC:PDMS waveguides ................. 61 3.1 Fabrication of LC:PDMS waveguides ......................................................... 61 3.2 Characterization of LC:PDMS guides ......................................................... 64 3.3 Fabrication of co-planar electrodes for electro-optic LC:PDMS waveguides ................................................................................................................. 68 3.3.1 Fabrication of samples by evaporation process ................................. 68 3.3.2 Sample fabrication by sputtering process ........................................... 70 3.3.3 Indium Tin Oxide (ITO) ........................................................................ 70 3.3.4 Chromium (Cr) ....................................................................................... 73 3.3.6 Gold Plating ............................................................................................ 82 3.3.7 Sample fabrication by galvanic process .............................................. 85 Conclusions ................................................................................................................. 90 Chapter 4: Simulations of LC:PDMS waveguides ..................................................... 91 4.1 Overview ......................................................................................................... 91 4.2 Introduction to Finite Element Method ...................................................... 91 4.3 Introduction on Beam Propagation Method .......................................... 92 4.3.1 Monte Carlo Simulations ...................................................................... 96 4.3.2 Alternative-Direction Successive Over-Relaxation (ADSOR) ....... 103 4.3.3 Euler-Lagrange method ...................................................................... 104 4.4 Results of COMSOL simulations ............................................................... 108 4.4.1 Partial Differential Equations ............................................................. 108 4.5 COMSOL Simulations ................................................................................. 110 Conclusions ............................................................................................................... 122 Chapter 5: Directional coupler ................................................................................... 123 5.1 Theory of the coupling modes ................................................................... 123 5.1.1 Couplings between co-propagating modes ...................................... 127 5.1.2 Coupling between counter-propagating modes .................................. 128 5.2 Design of an LC:PDMS based directional coupler .................................. 136 5 5.3 Simulations of Zero Gap Directional Coupler ......................................... 140 Conclusion ................................................................................................................ 144 Chapter 6: Multimode Interferometer ....................................................................... 145 6.1 Theory ............................................................................................................ 146 6.1.1 Self-Image Principle ............................................................................. 146 6.2 Simulations of MMI in SiO2–SiON ............................................................ 154 6.3 Simulation of MMI in LC:PDMS technology ........................................... 156 Conclusions ............................................................................................................... 159 Chapter 7: Conclusions ............................................................................................... 160 Bibliography ................................................................................................................. 164 6 Introduction The contribution of this thesis is to find possible solutions for the creation of interconnections and optical switches to be used in microoptofluidic systems in the frame of the research activities of the Optoelectronic laboratory of the Department of Information Engineering, Electronics and Telecommunications (DIET). The main goal is to explore a new technology for integrated optic based on a low cost technology to produce low driving power devices. Optofluidics is the science which links the field of photonics with microfluidics, for the creation of innovative and state-of-the-art devices. Liquid crystals (LC) can be used for optofluidic applications because they have the possibility to change without external mechanical actions, the average direction of the molecules through the application of electric fields, reorienting the crystal molecules in such a way as to alter their optical properties [1-2]. The research on LC is more than a century old, but only since the ‘80s of the past century these materials were employed in various fields, from flat panel displays used for televisions, tablets, and smartphones, to biomedical and telecommunication applications [3-5]. The results reported in this thesis include simulation, design and preliminary fabrication of optofluidic prototypes based on LC embedded in polydimethylsiloxane (PDMS)