Spectroscopy of Scattered Light for the Characterization of Micro and Nanoscale Objects in Biology and Medicine The biomedical uses for the spectroscopy of scattered light by micro and nanoscale objects can broadly be classiﬁed into two areas. The ﬁrst, often called light scattering spectroscopy (LSS), deals with light scattered by dielectric particles, such as cellular and sub-cellular organelles, and is employed to measure their size or other physical characteristics. Examples include the use of LSS to measure the size distributions of nuclei or mitochondria. The native contrast that is achieved with LSS can serve as a non-invasive diagnostic and scientiﬁc tool. The other area for the use of the spectroscopy of scattered light in biology and medicine involves using conducting metal nanoparticles to obtain either contrast or electric ﬁeld enhancement through the effect of the surface plasmon resonance (SPR). Gold and silver metal nanoparticles are non-toxic, they do not photobleach, are relatively inexpensive, are wavelength-tunable, and can be labeled with antibodies. This makes them very promising candidates for spectrally encoded molecular imaging. Metal nanoparticles can also serve as electric ﬁeld enhancers of Raman signals. Surface enhanced Raman spectroscopy (SERS) is a powerful method for detecting and identifying molecules down to single molecule concentrations. In this review, we will concentrate on the common physical principles, which allow one to understand these apparently different areas using similar physical and mathematical approaches. We will also describe the major advancements in each of these areas, as well as some of the exciting recent developments. Index headings: Light scattering; Spectroscopy; Nanoparticle; Surface plasmon; Surface enhanced Raman; SERS.

INTRODUCTION he spectroscopy of scattered light has played an increasingly important role in biology and medicine because it can provide information about subcellular and extracellular biological structures using native contrast, as well as information about nanoparticles that are employed as the exogenous imaging markers or vehicles for the delivery of therapeutic agents. Light scattering by these microscopic objects is

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Received 20 November 2013; Accepted 30 December 2013 * Author to whom correspondence should be sent. E-mail: ltperel@ caregroup.harvard.edu. DOI: 10.1366/13-07395

governed by the very basic principles of electromagnetic wave propagation and interaction with matter developed many decades ago. The impressive advances in biomedical instrumentation that have recently been achieved are examples of the successful applications of these fundamental principles. An analogy can be made between the development of biomedical light scattering and the development of other medical imaging modalities, for example the discovery of the very basic physics of X-rays led to the development of computed tomography decades later, while the initial understanding of another basic physical effect, nuclear magnetic resonance, eventually led to magnetic resonance imaging. Thus it can be argued that the ﬁeld of biomedical

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focal point review optics is primarily concerned with the technological development of new medical applications of electromagnetic wave interactions, described by Maxwell’s equations, with exogenous and endogenous microscopic objects. In particular, the uses of optical spectroscopy of scattered light for quantifying the properties of biological tissue, cells, and cellular organelles have been demonstrated to have unique capabilities of characterizing biological samples without altering them in any way. Important examples of this include the non-invasive detection of diseased tissue by either the characterization of bulk tissue properties, or the assessment of subcellular organelles. The basic understanding that underlies biomedical spectroscopy is the scattering of light by particles and collections of particles. This understanding is used to predict scattering from biological samples, leading to diagnostics or imaging modalities. On the other hand, a seemingly entirely separate ﬁeld is developing in parallel with the spectroscopy of light scattering by cells and tissues—the employment of nanoparticles for use in biomedical applications. This includes, for example, utilizing noble metal nanoparticles as contrast agents and as molecular sensors. The development of new synthesis methods capable of creating functionalized nanoparticles of various size and shape with unique scattering and absorption spectra has greatly advanced the biomedical applications of nanophotonics. The capability of these nanoparticles for enhancing the Raman signals allows for single molecule level sensitivity and identiﬁcation by utilizing the effect called surface enhanced Raman spectroscopy (SERS). What is important to realize is that the interaction of light with conducting metal nanoparticles is described with the same set of equations and similar approaches as the interaction of light with dielectric particles of biological origin. The fundamental tools for the study of how nanoparticles interact with light are all based on Maxwell’s equations in media with complex refractive indices and their approximations. This review will provide an overview of the role of spectroscopy in describing and identifying small dielectric and conducting particles for biomedical applications. A brief theoretical background for light scattering at the micro- and nanoscales is reviewed, followed by a discussion of recent nanoscale spectroscopy accomplishments in the areas of cellular organelle characterization, nanoparticles as contrast agents for imaging, and SERS methods applied to biomedical problems.

BASIC PRINCIPLES OF LIGHT SCATTERING BY A PARTICLE Exact Solution for Light Scattering from Particles. An electromagnetic wave, interacting with a dielectric or conducting particle (by a particle we mean any bounded region with a complex refractive index different from the refractive index of the surrounding medium) induces oscillations of bound and free charges in that particle,

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which in turn generates electromagnetic waves inside and outside of the particle. Thus, the problem of light scattering by a single particle can be formulated in the following way: given a particle of known structure, illuminated by a plane wave of particular polarization, ﬁnd the electromagnetic ﬁeld inside and outside the particle. Usually, however, the simpliﬁed formulation of the problem sufﬁces: ﬁnd the electromagnetic ﬁeld at large distances from the particle. Let us consider a particle illuminated by a plane electromagnetic wave E01 Ei1 ð1Þ ¼ e -iðkr-xt Þ Ei2 E02 where Ei1 and E01 are components of the wave amplitude perpendicular to the scattering plane, and Ei2 and E02 are components parallel to the scattering plane, k is the wavevector, and x is the frequency. Then the scattering amplitude matrix relates components of the scattered wave (Es1, Es2) and those of the incident one e -iðkr-xt Þ S2 S3 Es2 Ei2 ¼ ð2Þ Es1 S4 S1 Ei1 ikr where r=r(h,/) is a direction of propagation of the scattered light given by the polar angles h and / in the spherical system of reference associated with the particle, and k = 2p/k is the wavenumber. The scattering amplitude matrix is the fundamental property that gives a complete description of the scattering process. For example, the scattering cross section, rs, is given by Z 2pZ p rs ¼ k -2 ðjS1 þ S4 j2 þ jS1 þ S4 j2 Þsin hd hd u ð3Þ 0

0

The phase function p(h, u), defined as the probability of light scattering as a function of angle, can similarly be obtained from the scattering amplitude matrix. To find the matrix elements of the scattering matrix, one needs to solve Maxwell’s wave equations with proper boundary conditions for electric and magnetic fields. Such a solution is rather difficult to find; in fact there are just a few cases when the analytical solution to the wave equation has been found. One of these rare exact solutions is the famous solution that Gustav Mie obtained in 1908 for the scattering of a plane wave by a uniform sphere.1 Mie rigorously solved Maxwell’s equations for an electromagnetic light wave interacting with a sphere using appropriate boundary conditions. In the Mie solution, the functions S1 and S2 are expressed as an inﬁnite series of Bessel functions of the size parameter x = ka, where a is the sphere diameter, and m, the relative refractive index, is deﬁned as the ratio of the refractive index of the sphere to the refractive index of the surrounding medium. Based on the Mie solution we can plot a composite graph of spectroscopic dependence of the far ﬁeld

FIG. 1. Composite graph of the spectroscopic dependence of the differential scattering coefﬁcient rsp(h) for spherical particles in the range of diameters from 20 nm to 900 nm, and the wavelength range from 400 nm to 800 nm vs. inverse size parameter 1/x. The three lines represent the following combinations of relative refractive index m and scattering angle h: m = 1.06 and h = 1800 (solid curve); m = 1.06 and h = 1550 (dashed curve); m = 1.04 and h = 1800 (dotted curve). The straight dashed line is proportional to k-4 and shows the slope of Rayleigh scattering.

scattering intensity, which provides information about scattering by spherical particles over a wide range of parameters.2 Since the solution depends on the scattering angle, we plot angle-dependent differential scattering cross section rsp(h), where p(h) is the scattering phase function. Also, since the inverse size parameter 1/x is linearly proportional to the wavelength, we plot the differential scattering cross section vs. the inverse size parameter in Fig. 1 in order to agree with the more common way of plotting wavelength-dependent scattering coefﬁcients. Diameters from 20 nm to 900 nm for the wavelength range from 400 nm to 800 nm are included. We plotted three spectra for the following relative refractive indices and scattering angles: m=1.06 and h=1808, m=1.06 and h=1558, m=1.04 and h=1808. Other examples of particles for which the scattering problem has been solved analytically are cylinders, coated spheres, uniform and coated spheroids, strips, and planes. 3 Even for these ‘‘simple’’ cases the amplitudes can be expressed only as inﬁnite series which are often poorly converging. Approximate Solutions for Light Scattering from Particles. Difﬁculties with ﬁnding exact solutions of the wave equations have led to the development of the approximate methods of solving the scattering problem. One class of these approximations was originally found by Lord Rayleigh (John Strutt) in 1871 and is known as

Rayleigh scattering.4-7 Rayleigh scattering describes light scattering by particles that are small compared to the wavelength and is a very important approximation for biomedical optics since a great variety of structures of which cells organelles are built, such as the tubules of endoplasmic reticulum, cisternae of Golgi apparatus, etc., fall into this category. In the Rayleigh limit the electric ﬁeld is considered to be homogenous over the volume of the particle. Therefore, the particle behaves like a dipole and radiates in all directions. In the usual case of isotropic polarizability a of the particle, the scattering amplitude matrix becomes cos h 0 S2 S3 3 ð4Þ ¼ ik a 0 1 S4 S1 The scattering cross section in this case becomes simply 8 rs ¼ pk 4 a2 3

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Since a is proportional to the particle’s volume, the scattering cross section scales with the particle’s linear dimension a as a6 and varies inversely with k4.

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focal point review For larger particles with sizes comparable to the wavelength the Rayleigh approximation does not hold anymore and one can use another solution called the Rayleigh-Gans approximation.3 It is applicable if the relative refractive index of the particle, m, is close to unity while at the same time the phase shift across the particle 2kajm-1j is small. Applying the Rayleigh’s formulas in Eq. 4 to any volume element dV within the particle derives the Rayleigh-Gans approximation. It can be easily shown that ik 3 V cosh 0 S2 S3 > = < sin 2x ðm-1Þ sin x ðm-1Þ 2 @ A ð10Þ þ rs ’ 2pa 1> > x ðm-1Þ x ðm-1Þ ; :

with

It shows that large spheres give rise to a very different type of scattering than do the small particles considered above. Both the intensity of the forward scattering and the scattering cross-section are not monotonic functions of wavelength. Rather, they exhibit oscillations with the wavelength; the frequency of these oscillations is proportional to x(m-1), so it increases with the sphere size and refractive index.