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Measuring and Modelling the Absolute Optical Cross-Sections of Individual MEASURINGANDMODELLINGTHE ABSOLUTEOPTICALCROSS-SECTIONS OFINDIVIDUALNANO-OBJECTS attilio zilli Thesis submitted to Cardiff University for the degree of Doctor of Philosophy february 2018 supervisors Prof. Paola Borri, School of Biosciences Prof. Wolfgang Langbein, School of Physics and Astronomy This document was typeset using the typographical look-and- feel classicthesis developed by André Miede. The style was inspired by Robert Bringhurst’s seminal book on typography “The Elements of Typographic Style”. classicthesis is available for both LATEX and LYX at the following url: https://bitbucket.org/amiede/classicthesis/ Attilio Zilli, Measuring and modelling the absolute optical cross- sections of individual nano-objects. © February 2018 Attilio Zilli Dedicated to the memory of my friend and colleague Juris¯ Kiškis When I am laid in earth May my wrongs create No trouble in thy breast; Remember me, remember me, But ah! forget my fate. —Henry Purcell, Dido and Aeneas ABSTRACT Nanoparticles are ubiquitous in nature, and the number of tech- nological applications exploiting nano-objects, either synthes- ized chemically or fabricated lithographically, is in steady rise. In particular, metal nano-objects exhibit resonant modes corres- ponding to an enhanced coupling to electromagnetic radiation. The interaction of light with a nano-object is wholly described by its cross-sections for absorption and elastic scattering. In this thesis we present a method to measure the absolute amplitude of the cross-sections. Differently from currently available tech- niques, we account for the finite angular collection of the ob- jective via an analytical model of the scattering process, thereby rendering our method accurate also for objects dominated by scattering and high numerical aperture detection. The model of scattering assumes that the nano-object is placed at a planar dielectric interface, representing the substrate, and a homogen- eous optical environment is obtained as a limiting case. The ac- curacy of the quantitative method was tested on several model systems using two widespread experimental techniques: Micro- spectroscopy and widefield imaging, which are both implemen- ted with a simple experimental set-up, constituted by a com- mercial microscope equipped with an imaging spectrometer or a camera. In order to quantitatively simulate microscopy experi- ments, a realistic description of the excitation must be included in numerical models. In this thesis we describe novel modelling practices which reproduce typical coherent or incoherent micro- scope illumination. Comparison of quantitative experimental and numerical results is used to estimate parameters describ- ing the geometry of a nano-object, such as the diameter or iii the aspect ratio. In conjunction with the high-throughput cap- abilities of widefield image analysis, quantitative cross-section measurements and optical characterization of the geometry can provide a thorough statistical appraisal of the dispersity of the structural and optical properties of a sample. Therefore, this thesis represents a significant step towards an ‘all-optical’ char- acterization of nano-objects, complementing costly and time- consuming electron microscopy techniques. iv ACKNOWLEDGEMENTS When embarking onto a PhD degree, formal supervision is always granted and therefore should not need to be acknow- ledged. However, many other cases I have witnessed have shown me that supervision of good quality is on the contrary far from common: With their wise guidance — and occasionally a gentle push — Paola Borri and Wolfgang Langbein have led me to achievements I never knew I was capable of. I am also indebted to many members of our Quantum Op- toelectronics & Biophotonics group, particularly to all those in the School of Biosciences where I have been based over the four years of my PhD. I would like to mention first Lukas Payne, who patiently assisted me with his image analysis software and was willing to tweak it overnight in order to fulfil every odd request of mine. George Zoriniants introduced me to the mar- vels of the Ettore set-up, and was always available to open his Landau with me whenever I turned to him with my poor un- derstanding of electromagnetic theory. Whenever you cannot make sense of the set-up behaviour, or you are looking for that particular filter which has always been in that box (and now is not), Iestyn Pope is actually who you should be looking for: He came to my aid in countless occasions. Thanks to Yisu Wang for his practical help in sample preparation, and for elegantly pre- tending not to know I have been using his chemicals all along. And last but not least, thanks to Naya Giannakopoulou for the many conversations — sometimes we also talked about science. I am grateful to the two examiners sitting in my viva, Otto Muskens (external) and Egor Muljarov (internal), for the time they spent reading through this thesis; their valuable recom- v mendations helped me to improve the clarity of many figures and the readability of a few sections. My position has been part of a network called finon, gath- ering twelve PhD projects in several institutions throughout Europe. I would like to give credit to the whole finonship for being such an amazing team against many odds, and always being there for each other when in need: Juris¯ Kiškis, Caro- lina Rendón Barraza, Alberto Lombardini, Marie Didier, Alex- andra Paul, Michael Stührenberg, Diana Ribeiro, Amala Eliza- beth, Xiao Ling, Vitalijs Zubkovs, Siyuan Wang, Steffi Jung, and our indefatigable representative Naya Giannakopoulou. Within the framework of the finon, my secondment at the Institut Fresnel in Marseille was a great experience, rich in sci- entific and human content. I am grateful to Sophie Brasselet for hosting me in the mosaic group, to Carolina Rendón Barraza for taking good care of me during my stay (inside and outside the lab), and to Naveen K. Balla, my last resort to operate the set-up when I eventually put myself to do some measurements. This work was supported by the European Commission, Re- search Executive Agency — Marie Curie Actions 607842 finon itn-2013 vi OUTLINE Scattering and absorption of light by small particles underpin ch. 1 several everyday-life natural phenomena, such as the colours of the sky and the clouds, the hues of rainbows and irides, and the opalescence of some precious stones. Much attention has been drawn in particular to the optical properties of metal nano-objects (nos), which are ruled by the presence of plas- mon resonances and display a rich phenomenology. The fun- damental concepts and the main results of the electromagnetic theory describing the interaction of light with nos are presen- ted in ch. 1. Further discussion is devoted to the case of a no near a planar dielectric interface, which corresponds to a com- mon experimental configuration in microscopy, where nos are placed on a transparent substrate for imaging. The strong coupling of metal nos with electromagnetic radi- ch. 2 ation at the plasmon resonance offers ample potential to mould the flow of light at the nanoscale. sec. 2.1 reviews the oper- ating principles of a few relevant technological applications selected amongst the numerous proposed. Now, the sensitive dependence of the optical properties on the size, shape, and material composition of the no provides the opportunity to tailor these properties to the needs of a specific application. Over the last few decades the capability to fabricate nos — via either chemical synthesis or lithographic techniques — has in fact reached a high degree of control; on the other hand, the ex- perimental means to characterize accurately their optical prop- erties are still defective to some extent. Specifically, the optical properties are fully described by the optical cross-sections (ocs) spectra for the active optical processes (here scattering and ab- vii sorption), but to date only a handful of techniques have been proposed which can measure the ocs amplitude in absolute units at the single no level. As highlighted in sec. 2.2, all these techniques require costly equipment, as well as significant ex- pertise to operate it and to extract the ocs amplitude from the data. As a result, while much effort has been devoted to invest- igating the effect of the size and shape of the no on the spectral features of the ocs (that is, the position and width of the plas- mon resonances), only a few experimental measurements of absolute ocs amplitude have been reported so far. ch. 5 The core content of this thesis, presented in ch. 5, is a novel data analysis procedure to retrieve the absolute ocs from micro- spectroscopy or widefield imaging measurements. These two techniques are somewhat complementary: Micro-spectroscopy yields detailed spectral information, whereas widefield ima- ging provides a high-sensitivity and high-throughput charac- terization, e. g. of a colloidal sample. The quantitative analysis relies on the knowledge of the angular distribution of the radi- ation scattered by the no. Essentially, this is required because only a fraction of the total scattering falls within the acceptance of the objective and is thereby detected. Such angular distribu- tion can be computed through either numerical or analytical models. In order to minimize the amount of work demanded to the end user of our quantitative method, we developed an analytical model of scattering by a no placed on a dielectric substrate under incoherent microscope illumination. The two main assumptions of the model — which are reasonably well met in many cases of interest — require that the no is much smaller than the wavelength of the exciting light, and that the mismatch between the refractive indices of the substrate and the medium where the no is immersed is not too large. The full derivation is provided for various forms of the polarizability tensor representing the most commonly encountered geomet- viii ries of plasmonic modes. Although the analytical calculations involved are rather cumbersome, these have been automated into a stand-alone executable which only requires a few exper- imental parameters as user input.
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