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  • Optimization of broadband optical response of multilayer nanospheres

    Wenjun Qiu,1 Brendan G. DeLacy,2 Steven G. Johnson,3

    John D. Joannopoulos,1 and Marin Soljačić1∗ 1Department of Physics, Massachusetts Institute of Technology

    77 Massachusetts Avenue, Cambridge Massachusetts 02139, USA 2Edgewood Chemical Biological Center, Research & Technology Directorate

    5183 Blackhawk Rd., Aberdeen Proving Ground, MD 21010, USA 3Department of Mathematics, Massachusetts Institute of Technology 77 Massachusetts Avenue, Cambridge Massachusetts 02139, USA

    ∗soljacic@mit.edu

    Abstract: We propose an optimization-based theoretical approach to tailor the optical response of silver/silica multilayer nanospheres over the visible spectrum. We show that the structure that provides the largest cross-section per volume/mass, averaged over a wide frequency range, is the silver coated silica sphere. We also show how properly chosen mixture of several species of different nanospheres can have an even larger minimal cross-section per volume/mass over the entire visible spectrum.

    © 2012 Optical Society of America

    OCIS codes: (290.5825) Scattering theory; (290.2200) Extinction.

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    #169722 - $15.00 USD Received 4 Jun 2012; revised 20 Jul 2012; accepted 23 Jul 2012; published 27 Jul 2012 (C) 2012 OSA 30 July 2012 / Vol. 20, No. 16 / OPTICS EXPRESS 18494

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    1. Introduction

    Nanoparticles with strong optical response, characterized by scattering, absorption and total cross-sections, have wide applications in biomedical imaging, photothermal therapy, and opti- cal obscurance [1–3]. Different applications require different optical response properties. For instance, real-time biomedical imaging is based on large scattering cross-sections, while pho- tothermal therapy requires nanoparticles with large absorption cross-sections and small scatte- ring cross-sections. For obscurance applications [4, 5], the ideal nanoparticle should typically have large total cross-sections over the whole visible spectrum while keeping the volume or mass of nanoparticles as small as possible. The diversity and complexity of these requirements necessitate an engineering approach of nanoparticle design.

    Previous studies on the optical response of nanoparticles are mainly based on parametric ap- proach [6–8], which works well for simple structures. However, when the structure becomes complicated and the number of design parameters increases, optimization becomes the prefer- able approach because it can efficiently explore the whole parameter space. Furthermore, be- cause the optimization objective function can be an arbitrary transformation of the frequency- dependent cross-sections, this approach is very powerful in tailoring the broadband optical response of nanoparticles. For example, some applications may require that the optical reso- nance has both a strong peak value and a wide bandwidth. This can be achieved by maximizing the average cross-section over the bandwidth of interest. For obscurance applications, we want the total cross-section to be consistently large over the whole visible spectrum. This is equiva- lent to maximizing the minimal cross-section over this spectrum. In this paper, we will use an optimization tool to tailor the optical response of multilayer nanospheres over wide frequency range of interest.

    Before we start, we need to select the material system. Nanoparticles composed of metal and dielectric materials support surface plasmons on the metal/dielectric interfaces and can strongly interact with light in the visible range [9–13]. At resonance, the cross-sections of these nanoparticles are much larger than their physical cross-sections, which makes them super- scatterers and super-absorbers [14–17]. Furthermore, the plasmon resonance frequency can be tuned by varying the physical structure of the nanoparticles. In order to be able to tailor the optical response of nanoparticles over a wide frequency range, we choose the metal/dielectric

    #169722 - $15.00 USD Received 4 Jun 2012; revised 20 Jul 2012; accepted 23 Jul 2012; published 27 Jul 2012 (C) 2012 OSA 30 July 2012 / Vol. 20, No. 16 / OPTICS EXPRESS 18495

  • material system. For concreteness, we will focus on the silver/silica material system. In this article, we first formulate the Transfer Matrix Method to calculate the optical response

    of multilayer nanospheres. After briefly reviewing the optical response of bilayer silver/silica nanospheres, we proceed to optimize the average cross-section of various silver/silica multi- layer nanospheres. Our optimization results show that the structure with the maximal average cross-section is the bilayer silver/silica structure with silver as the shell. Finally, we investigate using a mixture of several species of bilayer nanospheres to enhance the minimal cross-sections over the entire visible range.

    2. Calculation of optical response via transfer matrix method

    Fig. 1. Schematic of an n layer nanosphere embedded in infinite dielectric medium. The outer radius and dielectric function of individual layers are (Ri,εi), i = 1,2, ...,n. The di- electric function of the medium is εm. The solid lines represent an incident plane wave which contains incoming and outgoing waves. The da