TERAHERTZ TIME-DOMAIN SPECTROSCOPY OF LOW- DIMENSIONAL MATERIALS AND PHOTONIC STRUCTURES by CHEN XIA Submitted in partial fulfillment of the requirements For the degree of Doctor of Philosophy Thesis advisor: Dr. Jie Shan Department of Physics Case Western Reserve University January, 2013 CASE WESTERN RESERVE UNIVERSITY SCHOOL OF GRADUATE STUDIES We hereby approve the thesis/dissertation of Chen Xia ______________________________________________________ Doctor of Philosophy candidate for the ________________________________degree *. Jie Shan (signed)_______________________________________________ (chair of the committee) Kenneth D. Singer ________________________________________________ Xuan Gao ________________________________________________ Lei Zhu ________________________________________________ ________________________________________________ ________________________________________________ (date) ____08/10/2012__________________ *We also certify that written approval has been obtained for any proprietary material contained therein. TABLE OF CONTENTS LIST OF FIGURES ............................................................................................... 5 ABSTRACT ........................................................................................................ 13 CHAPTER 1 ....................................................................................................... 15 1.1 DEVELOPMENT OF THZ SOURCES ..................................................... 17 1.2 THZ SOURCES BASED ON ULTRAFAST LASERS .................................... 18 1.3 NOVEL THZ SOURCES ...................................................................... 23 1.4 THZ SPECTROMETER ....................................................................... 24 1.5 OUTLINE OF THIS THESIS .................................................................. 30 CHAPTER 2 ....................................................................................................... 32 2.1 INTRODUCTION ................................................................................ 32 2.2 FILMS FABRICATION AND CHARACTERIZATION METHODS ..................... 34 2.2.1 Preparation of BaTiO3/PMMA nanocomposite films ............... 34 2.2.2 Fabrication of THz photonic crystals ...................................... 35 2.2.3 Scanning electron microscopy ............................................... 35 2.2.4 Terahertz Transmission Spectroscopy ................................... 36 2 2.3 TRANSFER MATRIX METHOD............................................................. 37 2.3.1 Matrix form in wave propagation ............................................ 38 2.3.2 Wave propagation in layered system ..................................... 43 2.3.3 Transfer matrix of photonic crystal ......................................... 47 2.4 LOCAL FIELD AND EFFECT-MEDIUM THEORY ........................................ 51 2.4.1 Homogenous system ............................................................. 51 2.4.2 Two-phase system ................................................................. 53 2.4.3 Layered structure ................................................................... 56 2.5 STUDY OF ALL POLYMERIC THZ PHOTONIC CRYSTAL ......................... 58 2.5.1 Polymer films incorporated with nanoparticles ....................... 58 2.5.2 THz properties of polymer films ............................................. 61 2.5.3 Polymeric THz photonic crystal .............................................. 66 2.6 CONCLUSION ................................................................................... 69 CHAPTER 3 ....................................................................................................... 70 3.1 INTRODUCTION ................................................................................ 70 3.2 EXPERIMENTAL SETUP ..................................................................... 73 3.3 THZ EMISSION FROM GRAPHITE SURFACES ....................................... 74 3.4 FLUENCE DEPENDENCE OF THZ EMISSION FROM GRAPHITE BASAL PLANES .......... 77 3.5 CORRELATION DYNAMICS OF THZ EMISSION FROM GRAPHITE SURFACES ............. 83 3.6 POLARIZATION RESOLVED THZ EMISSION FROM BASAL AND EDGE PLANES OF GRAPHITE ....... 87 3.7 CONCLUSION ................................................................................... 92 3 CHAPTER 4 ....................................................................................................... 93 4.1 INTRODUCTION ................................................................................ 93 4.2 EXPERIMENT ................................................................................... 95 4.3 EXPERIMENTAL RESULTS ................................................................. 99 4.3.1 Static Properties ..................................................................... 99 4.3.2 Photoconductive properties.................................................. 101 4.4 CONDUCTION IN AMORPHOUS SEMICONDUCTORS ............................. 106 4.4.1 Drude-smith model ............................................................... 107 4.4.2 Quantum mechanical tunneling (QMT) in one-dimensional (1D) systems ........ 114 4.4.3 Resonant Photon Absorption ............................................... 122 4.5 CONCLUSION ................................................................................. 128 APPENDIX: ...................................................................................................... 130 0 ELECTROMAGNETIC MODEL FOR THZ EMISSION FROM SURFACES ..... 130 0.1 THE SNELL’S LAW IN NONLINEAR OPTICS .......................................... 132 0.2 EMISSION FROM NONLINEAR POLARIZATION AT THE SURFACES OR INTERFACES ..... 134 0.2.1 THZ RADIATION FROM ISOTROPIC POLARIZATION SHEET ............. 138 0.2.2 THZ RADIATION FROM ANISOTROPIC SURFACES ......................... 142 0.3 FORMATION OF POLARIZATION SHEET ON GRAPHITE SURFACES ........ 145 REFERENCE…………………………………………………………………………… 147 4 List of Figures 1. Figure 1.1 THz spectrometer based on a Ti:Sapphire femtosecond laser. The THz radiation is generated in a ZnTe emitter through optic rectification and detected by another ZnTe crystal via electro-optic sampling…………………………………………………….24 2. Figure 1.2 Schematics of a THz emitter (left) and detector (right) based on (110) ZnTe. In the generation process, both the pump and the emitted THz fields are polarized in the {y’,z’}-plane. In the detection process, the applied THz field along the y’ axis induces birefringence. The principle axes are along {y”, z”}, rotated by 45° from {y’, z’}. ......................................................................................................... 25 3. Figure 1.3 Electro-optic sampling of THz electric field. ............................................. 27 4. Figure 2.1 A plane wave E1 with wave vector k1 and frequency ω is incident from medium 1 with permittivity ε1 and permeability m1 to medium 2 with permittivity ε 2 and permeability m2 . The reflection and transmission happen at interface of two dielectric media, and the reflected field and transmitted field are observed at ' direction θ1 and θ2 with wave vectors k1 and k 2 , respectively. ............................... 39 5. Figure 2.2 Demonstration of p-polarized plane waves propagation through plane interface between medium i and j inside multilayered system. Ei and E j are fields approaching the interface from medium i (left) and medium j (right), and plane ' ' waves Ei and E j leaving the interface are observed at reflection directions of θi and θ j , respectively. All the electric fields are polarized in the plane of incidence, 5 while all the magnetic fields are perpendicular to the plane to satisfy the vector rules determined by Maxwell equations. .................................................................. 42 6. Figure 2.3 Multilayered structure is fabricated between substrates n0 and nN +1 . The lth layer with dielectric function nl has thickness of dl . The electric field propagating in layer is sum of right-travelling wave Al and left-travelling wave Bl ......................................... 44 7. Figure 2.4 Demonstration of 1D photonic crystal comprising of alternatively stacked layers of index of refraction n1 and n2 . The physical period of crystal is d with neighboring layers to be d1 and d2 in thickness. The amplitude of fields inside nth unit cell are denoted as an , bn , cn , en , respectively. ............................................... 48 8. Figure 2.5 Schematic diagram of two-phase systems that could be applied by a) Maxwell Garnett, b) Bruggeman, and c) layered structure effective medium theory ...................... 58 9. Figure 2.6 Scanning electron microscopy (SEM) images of fractured surfaces of PMMA/BaTiO3 nanocomposites. (a) 6% v/v, particle size 100 nm ; (b) 19% v/v, 100 nm; (c) 3% v/v, 200 nm; (d) 18% v/v, 200 nm. .......................................................... 59 10. Figure 2.7 Scanning electron microscopy images of fractured surfaces of PMMA comprising BaTiO3 nanoparticles: (a) 6% v/v, particle size 100 nm; (b) 3% v/v, particle size 200 nm. The images show occasional zones of aggregated BaTiO3 ...... 60 11. Figure 2.8 Real (n’) and imaginary (n“) parts of the THz refractive index of PMMA/BaTiO3 nanocomposite films containing a) 0%, b) 3%, and c) 18% v/v BaTiO3 (particle size: 200 nm). Solid lines represent effective medium theory calculations ............................................. 63 6 12. Figure 2.9 Real (n’) and imaginary