Studying The Extinction Properties Of Silver Nanoparticles Using A Method Known As The DDA Calculate

The optical properties of metal nanoparticles have longbeen of interest in physical chemistry, starting withFaraday's investigations of colloidal gold in the middle1800s. In 1908, Mie presented a solution to Maxwell'sequations that describes the extinction spectra (extinction= scattering + absorption) of spherical particles ofarbitrary size. Mie's solution remains of great interestto this day, it is the only simple, exact solution toMaxwell's equations that is relevant to particles. Inaddition, most of the standard colloidal preparations yieldparticles that are approximately spherical, and most of theoptical methods for characterizing nanoparticle spectraprobe a large ensemble of these particles. This leads toresults that can be modeled reasonably well using Mie-theory.More recently, new lithographic techniques as well asimprovements to classical wet chemistry methods have madeit possible to synthesize noble metal nanoparticles with awide range of sizes, shapes, and dielectric environments.There has been growing interest in characterizing theoptical properties of metal nanoparticles that are madeusing lithographic methods such as nanosphere lithography,e-beam lithography, and other methods, which producewell-defined sizes and nonspherical shapes withoutaggregation. In addition, variations on classical wetchemistry techniques have been developed that give highyields of nonspherical particles, especially rods andtriangles. The modern generation of metal nanoparticlescience, including applications to medical diagnostics andnanooptics, has provided new challenges for theory. All ofthese factors motivate the need for theory that can describethe electrodynamics of nanoparticles of arbitrary shape andsize subject to a complex external dielectric environment.In this feature article, we describe recent progress inthe theory of nanoparticle optical properties, emphasizingespecially the linear optical properties (extinction,absorption, scattering) of isolated silver particles ofarbitrary shape with sizes up to a few hundred nanometers.This paper begins with a qualitative discussion of the useof simple electrostatic theories and models-Mie theory andM-G theory. We then give a brief description of modernnumerical techniques that can treat arbitrary particles andenvironments, and then, we describe applications of thesetechniques to problems of recent interest, using a methodknown as the discrete dipole approximation (DDA). Ourapplications include studies of the particle size and shapedependence of absorption, extinction, and scatteringefficiencies, which can be directly compared withexperiments. In this work, the main features in the opticalspectra have been investigated depending of the geometry andsize of the nanoparticles. The origins of the optical spectraare discussed in terms of the size, shape, and materialproperties of each nanoparticle, showing that a nanoparticlecan be distinguish by its optical signature. In most cases,we have clearly identified the main optical signatureassociated to each geometry. We find, as it might have beenexpected, that the spectra are more complex as the particlehas less symmetry and/or has more vertexes.Our main goal is 2-fold: first we show how the main peaksof the optical spectra can be associated to the shape andsize of the nanoparticle, as well as its material propertiesand second, we show in all these spectra the relativeimportance of absorption and scattering processes. We attacha multipolar character to the different excitationsresponsible for the characteristic features of the spectraby comparing results for particles with the same shape butwith different size. We have also paid a particular attentionto the accuracy of our calculations showing explicitly theconditions under which they might become numericallyunstable. We believe that this study can be very useful todetermine and optimize some of the physical properties ofnanoparticles by controlling their shape and size during andafter a growth process another goal is to motivate futuremeasurements of extinction and absorption spectra ofnanoparticles.