Characterization of electromagnetic and light scattering by nano scaled objects

CHARACTERIZATION OF ELECTROMAGNETIC AND LIGHT SCATTERING BY NANO-SCALED OBJECTS SHE HAOYUAN B. Eng, Harbin Institute of Technology, 2005 Submitted for the degree of PhD of Engineering in joint program by Nanoscience and Nanotechnology Initiative & Department of Electrical and Computer Engineering National University of Singapore 2009 Acknowledgement Firstly, I would like to take this opportunity express my most sincere gratitude to my supervisor Professor Le-Wei Li, for his guidance, strong supports, and understandings throughout my postgraduate program. Also I want to thank Professor Chua Soo Jin for his guidance and invaluable discussions. The author also wants to thank Dr. Wei Bin Ewe, Dr. Cheng-Wei Qiu and Dr. Hai-Ying Yao for their helpful discussions on code development. The author’s appreciation also goes to the other Radar and Signal Processing Lab and Microwave Lab members: Dr. Kai Kang, Mr. Tan Hwee Siang, Mr. Tao Yuan, Mr. Li Hu, Miss Ya-Nan Li, Miss Yu-Ming Wu and the senior lab officers Mr. Ng and Mr. Sing. Most importantly, the author is also grateful to his parents for their always understandings, supports and love. Without you, I could never finish this tough job successfully. Thank you so much! i Publication List 1. L.-W. Li, H.-Y. She, W.-B. Ewe, S. J. Chua, Olivier J. F. Martin, and Juan R. Mosig, ”Optical Shielding Nano-Systems Achieved by Multiple Metallic NanoCylinders under Plasmon Resonances”, to be submitted to Journal of Applied Physics, 2009 2. H.-Y. She, L.-W. Li, W.-B. Ewe, S. J. Chua, Olivier J. F. Martin, and Juan R. Mosig, ”Resonance of Cylindrical Structures with High Relative Permittivities– Enhancement of the Field and Applications in Optical Waveguide”, to be submitted to Physical Review B, 2009 3. H.-Y. She, L.-W. Li, S. J. Chua, W.-B. Ewe, Olivier J.F. Martin, and Juan R. Mosig, ”Enhanced Backscattering by Multiple NanoCylinders Illuminated by TE Plane Wave”, Journal of Applied Physics, vol. 104, no. 1, pp. 064310, September 2008 4. L.-W. Li, Z.-C. Li, H.-Y. She, S. Zouhdi, Juan R. Mosig, and Olivier J.F. Martin, ”A New Closed Form Solution to Light Scattering by Spherical Nanoshells”, Accepted by IEEE Transactions on Nanotechnology, vol. 7, 2008 ii Publication List iii 5. L.-W. Li and H.-Y. She, ”High Energy Scattered by Silver Coated Nano Structures”, International Journal of Microwave and Optical Technology, pp. 150156, 2008-5-38 6. H.-Y. She, L.-W. Li, Olivier J.F. Martin, and Juan R. Mosig, ”Surface Polaritons of Coated Cylinders Illuminated by Normal-Incident TM and TE Plane Waves ”, Optics Express, vol. 16, no. 2, pp. 1007-1019, January 2008 Summary In nano-scale, the conducting materials are found to behave the dielectric properties with negative real part of the relative permittivities (known as plasmonic materials with the effective dimensions ranging from 20 nm to 200 nm) and the dielectric materials are found to have different optical properties compared to the bulk properties (such as Si and Ge). Due to their peculiar optical properties, nanoscaled materials can be applied in optical coating, optical communications (optical waveguides), surface cleaning, etching, scattering enhancement equipment, and data storage. In this thesis, I have studied the optical properties including the enhancement of the scattering, the transmission properties of silicon nanorods, the control of shifting the frequencies of the plasmon resonances by coated nanostructures, and the potential applications of plasmonic materials, from simple to complex structures (for both single and multiple scatterers). Further more, various numerical and theoretical investigation methods are used for analyzing the electromagnetic and light scattering problems. Before studying the physical properties of the nano-objects, the basic studies of the electromagnetic wave propagation, scattering and resonances of cylinders and iv SUMMARY v spheres are conducted. These studies help to understand the physical characteristics of the nano-objects better. For example, light scattering by a single sphere and a single cylinder is studied using the exact scattering theory–Mie theory and the resonance properties for electrically small structures are presented. The scattered near-field energy intensity is found to be significantly enhanced. Next, the coated nanostructures are studied and their effects on resonance shifts according to different frequencies are shown. The results are helpful in enhancing the scattered fields of coated nanostructures. The surface plasmon resonances of the coated structures are also shown, while the closed form solutions are given and compared with the exact solutions, which are found to be very effective over a wide range of electrical dimension. The range with a strong scattered energy is given and the formulas for the scattered energy are derived for both plasmonic coated nanospheres and nanocylinders. The results are applicable over a wide range of electrical dimensions and relative permittivities, and they are more accurate than the previous works. Subsequently, the multiple scattering by the plasmonic nanocylinders is discussed. The great backscattering enhancement effect is studied and compared with that of a single plasmonic nanocylinder. The incident wave is assumed to be TE (transverse electric) plane wave which is capable of exciting the plasmon resonance of cylindrical structures. The results can be applied in nanopatterning, surface cleaning and data storage. Finally, with multiple nanocylinders, we can also achieve a shielding nanosystem composed of metallic nanocylinders near plasmon resonances. The shielding effects SUMMARY vi are found to be very good and shielding systems are very flexible and small in size. We have also proposed an optical waveguide composed of silicon nanowires. The transmission is based on the great coupling effects produced by silicon nanowires with high relative permittivities. Enhanced scattering property of multiple silicon nanocylinders has also been discussed for different pattern arrangements. And we have provided some new closed form solutions of the scattering by electrically small cylinders and the results are more accurate than the commonly used one for cylinders with high relative permittivities. Contents Acknowledgement i Publication List ii Summary iv Contents vii List of Figures xi Introduction 1.1 Optical Properties of Nanoscaled Objects . . . . . . . . . . . . . . . . 1.1.1 Optical Constants of Noble Metals . . . . . . . . . . . . . . . 1.1.2 Surface Plasmon Resonances of Metallic Nano-Objects . . . . vii CONTENTS viii 1.2 Optical Constants of Other Dielectric Materials . . . . . . . . . . . . 20 1.3 Thesis Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Optical Properties of Coated Nano-Cylinders 24 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.2 Surface Modes of Plamonic Coated Cylinders . . . . . . . . . . . . . . 26 2.3 2.2.1 Theoretical Foundation . . . . . . . . . . . . . . . . . . . . . . 26 2.2.2 Coated Cylinders Scattered by TM Plane Wave . . . . . . . . 32 2.2.3 Coated Cylinders Scattered by TE Plane Wave . . . . . . . . 40 2.2.4 Peak Values of the Near-Field Energy Intensity . . . . . . . . 42 Energy Intensity Enhancement of Plamonic Coated Cylinders . . . . 43 Optical Properties of Coated Nano-Spheres 47 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.2 Closed Form Solutions to Light Scattering by Coated Spheres . . . . 50 3.2.1 Basic Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . 50 3.2.2 New Closed Form Solution to Intermediate Coefficients An and Bn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 CONTENTS ix 3.2.3 New Closed Form Solutions to Scattering Coefficients an and bn 62 3.3 Energy Intensity Enhancement of Plamonic Coated Nanospheres . . . 72 3.3.1 Parameter Derivation of High Scattered Energy Region for Plasmonic Coated Spheres . . . . . . . . . . . . . . . . . . . . 72 3.3.2 Energy Distribution of a Plasmonic Coated Nanosphere . . . . 77 Multiple Scattering by NanoCylinders 79 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 4.2 Enhanced Backscattering by Multiple NanoCylinders Illuminated by TE Plane Wave . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 4.2.1 Theoretical Foundation . . . . . . . . . . . . . . . . . . . . . . 82 4.2.2 Scattering Properties of a Single Plasmonic Cylinder . . . . . 84 4.2.3 Scattering by Multiple Plasmonic Cylinders in Arrays . . . . . 87 4.2.4 Scattering by Multiple Plasmonic Cylinders with Different Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 4.3 Optical Shielding Nano-systems Achieved by Multiple Metallic Nanocylinders under Plasmon Resonances . . . . . . . . . . . . . . . . . . 93 4.3.1 Shielding Properties of Multiple Plasmonic Cylinders . . . . . 95 BIBLIOGRAPHY 129 [38] D. 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Schuller, and Mark L. Brongersma, “Near-field characterization of guided polariton propagation and cutoff in surface plasmon waveguides”, Physical Review B (Condensed Matter and Materials Physics), vol. 74, no. 16, pp. 165415, 2006. [...]... (the first order approximation of Mie scattering) will dominate [17, 18] the field distribution With the recent development of nanotechnologies and some progresses of nanoscience, it becomes desirable and timely demanded to characterize scattering properties of light waves by nanoscaled objects including the nanoparticles Nanoparticles have shown interesting optical properties and are important for modern... LIST OF FIGURES xviii 4.17 Magnetic and electric field distributions of a nanocylinder in the nano shielding system with r = 2 and a = 17.5 nm 102 4.18 Magnetic and electric field distributions of a nanocylinder in the nano shielding system with r = 2 and a = 35 nm 103 4.19 Magnetic and electric field distributions of a nanocylinder in the shielding nanosystem with 5.1 r = 2 and. .. distribution of scattering by a single sphere for q = 0.1 with different relative permittivities and permeabilities The sphere is resonant by the second order mode 13 xi LIST OF FIGURES 1.9 xii Geometry for scattering of a plane wave by a cylinder 13 1.10 Properties of different orders of the scattering coefficient In the case of a lossless cylinder, scattering coefficients of all orders... Introduction With the rapid technological advancements, the size of the objects we can investigate is becoming smaller and smaller, so it becomes possible and desirable to study the properties of the microcosmic world–the nano- objects As is well-known, one nanometer is one billionth of a meter and the concept of nano- technology” was firstly proposed by a physicist Richard Feynman at the American Physical Society... constants of copper, silver and gold with an oblique-incidence thin-film technique [14] and measurements of copper and nickel as a function of temperature were also shown [13] In this thesis, we will use the results obtained in [14] 1.1.2 Surface Plasmon Resonances of the Metallic NanoObjects Surface plasmon resonances of metallic nano- objects occur at where n = 1, 2, · · ·, for spherical structures [28] and. .. permittivity of the nano- objects) It has been found that the near-field energy can be significantly enhanced as well as the scattering and total cross sections (far-field characteristics) In this part, we will illustrate the optical properties of spherical and cylindrical plasmonic structures CHAPTER 1 INTRODUCTION 5 Surface Plasmon Resonances of Nanospheres Scattering of electromagnetic waves by spherical... distribution of a nano shielding system consisting of 28 identical nanocylinders with various incident wavelengths λ0 (two circular layers) 96 4.12 Magnetic and electric field distributions of a shielding nano system consisting of 36 identical nanocylinders (with three circular layers) 97 4.13 Magnetic and electric field distributions of a nano shielding system consisting of 42... accurate measurements and detailed band-structure calculations for Ag and Cu [4,5] Effects of the stress on the optical constants are shown in [6] for Cu, [7] for Ag and [7– 9] for Alloys The optical properties of Au were investigated by means of thin semitransparent films [10] Wavelength modulation spectrum of copper was studied in [11] and the optical properties of gold in [12] P B Johnson and R W Christy... resonances of plasmonic structures possible and practical Dimensions of the nano- objects in which surface plasmon polariton (SPP) happens are usually considered in the range from 20 to 200 nm Some photonic applications such as surface cleaning, etching, imaging, nanopatterning, and bio-sensoring in very small scale can be achieved 1.1 1.1.1 Optical Properties of Nanoscaled Objects Optical Constants of the... possibility of developing a process which can manipulate individual atoms and molecules Over the past half a century, scientists have been making continuous contributions to engineering applications and theoretical research on the objects in nanoscale Now nanotechnology leads to the fields of theoretical sciences and applied technologies whose aim is to investigate the objects with dimensions of 100 nanometers . CHARACTERIZATION OF ELECTROMAGNETIC AND LIGHT SCATTERING BY NANO-SCALED OBJECTS SHE HAOYUAN B. Eng, Harbin Institute of Technology, 2005 Submitted for the degree of PhD of Engineering. studies of the electromagnetic wave propagation, scattering and resonances of cylinders and iv SUMMARY v spheres are conducted. These studies help to understand the physical characteristics of the. various numerical and theoretical in- vestigation methods are used for analyzing the electromagnetic and light scattering problems. Before studying the physical properties of the nano -objects, the