263488 Optical Sensor for Nanoparticle Identification in Liquids
A method for optical identification of dielectric and metal nanoparticles in a liquid matrix is presented using the maximum entropy method (MEM) for phase retrieval of reflectance with transverse electric (TE) and transverse magnetic (TM) linearly polarized light. The effective dielectric function of the colloid is obtained using phase retrieved complex reflectance components. An excellent accuracy is observed both for dielectric and metallic nanoparticles with volume fractions up to 10 percent. It is believed that such nanoparticle identification will find applications in monitoring systems for identification of nanoparticles and their concentration in water streams.
The study of optical properties of colloids has a rather long history dating back to the start of the 20thcentury and works by Maxwell Garnett who studied colors of glasses containing minute metal spheres . He also presented an elegant theory to predict the optical properties of such effective media that is even nowadays widely used in the description of optical properties of colloids. The spectroscopic properties of colloids have been important in basic research of colloidal physics and chemistry since the optical properties of a colloid depend on the size, shape and structure of the nanoparticles, their complex refractive index, and thermodynamic condition of the ambient host liquid. Much of the research work has been on fundamental optical properties of nanoparticles in liquid environments.
The emergence of nanotechnology and addition of nanoparticles into existing consumer products to improve their performance has extended applications of colloid studies to completely new fields such as nanomedicine and nanotoxicology. For example, colloidal gold nanoparticles have been studied for cancer diagnostics and therapy, and their optical properties such as surface plasmon resonance (SPR) and Raman scattering are important in molecular specific diagnostics and detection of the cancer . Another recent example is addition of functional materials including nanoparticles in food, and issues of nanotoxicology in liquid has been raised . The fundamental properties of such colloids are the intrinsic optical properties of both the host medium and the nanoparticles: the optical properties of the host medium are typically well-known and free of spectroscopic resonances in the frequency range of interest, for example, as in the case of water. On the other hand, nanoparticles can usually be identified with their optical fingerprints. Furthermore, these fundamental properties are independent of the optical process used to access them.
In this study we show that it is possible to obtain the optical properties of both insulating and conducting nanoparticles from the angle-, wavelength-, and polarization-dependent reflectance, which is directly measured from the colloid. This allows us to identify particular nanoparticles and/or to get their concentration in a colloid. In practical measurements one can utilize a polarization maintaining single mode fiber to measure the reflectance at various angles from a colloid containing nanoparticles. A great benefit of reflectance measurement compared to traditional transmission measurement is significantly reduced scattering providing a more accurate identification of nanoparticles.
Here we study the reflectance from the air/nanoparticle colloid interface with spherical dielectric or metal nanoparticles dispersed in a water matrix. From reflectance measurement we get the amplitude of the reflectance but the phase information is lost. Traditionally such phase retrieval problems in reflection spectroscopy have been analyzed using the Kramers-Kronig type dispersion relations  that relate the phase and the amplitude of reflectance to each other. Unfortunately, there are some serious drawbacks in the classical dispersion theory analysis as the integral relation nature of the analysis is based on semi-infinite integration from zero to infinity. This, in principle, requires knowledge of reflectance data over the semi-infinite spectral range. However, in reality, we are always limited to finite spectral range. Therefore, we will utilize here the maximum entropy method (MEM) . In the MEM the entropy is a measure of the uncertainty in the data, and hence, the maximum entropy estimate is the least biased estimate on the given data. The method has been successfully applied in various fields ranging from enhancement of astronomical images  to predict atmospheric CO2 content .
A Maxwell Garnett (MG) type effective medium theory (EMT)  is utilized here to describe the effective dielectric function of colloids with spherical nanoparticles. We assume that the dielectric nanoparticles have a dielectric function given by a single resonance Lorentzian lineshape function  whereas bulk properties of gold  are used for the gold nanoparticles. The dielectric function of non-absorbing water host is given by Partington’s formula .
We analyze the reflectance from arbitrary angle of incidence with two different linear polarizations using well-known Fresnel reflectance coefficients for air/colloid interface. The colloid is described with effective dielectric function. The remarkable feature with TE/TM polarized reflectance is that we can immediately obtain the complex effective dielectric function of the colloid after retrieval of the complex reflectivities for an arbitrary angle of incidence. We have shown before  that it is possible to obtain optical properties of nanoparticles in a liquid matrix in the SPR reflectance configuration with the aid of the MEM for phase retrieval. However, the SPR experimental set-up has drawbacks such as contamination and oxidation of the metal film that supports plasmons. Therefore, the current set-up significantly simplifies the experiments as one can do a similar analysis from the reflectance without the SPR configuration as there is no need for the metal film.
The phase retrieval procedure using the MEM includes fitting the measured reflectance spectrum into the maximum entropy model . The unknown maximum entropy coefficients are obtained from a Toeplitz matrix with autocorrelation functions calculated from a discrete Fourier transform of the measured reflectance. This procedure always fits the maximum entropy phase function of the measured reflectance. The only feature of the actual phase function, which is not captured with the MEM, is the background phase information. This is the error phase function that is typically a much smoother function than the actual phase function of interest i.e. the actual phase function is a sum of the maximum entropy and error phase functions. The main features of the actual phase are always captured by the MEM. For details of the MEM, see Ref . The key feature here is that we can use only the error phase function of the known host liquid similar to the SPR reflectance analysis . Thus we can immediately obtain the effective complex dielectric function once the optical properties of the host liquid are known, i.e. no a priori knowledge is needed about the properties of the constituent nanoparticles.
We have performed phase retrieval from TE/TM-polarized reflectance both for dielectric and insulating nanoparticles. We observe an excellent agreement between the exact values and ME estimates with locations of resonances well reproduced. It is noteworthy that we can always obtain the effective dielectric function of the colloid regardless of the actual colloid composition. Furthermore, we can also obtain the optical properties of individual nanoparticles if the colloid can be modeled with effective medium theory. In the present case we use Maxwell Garnett EMT and obtain both dielectric and metallic nanoparticle dielectric functions with sufficient accuracy. The best accuracy is obtained with large angles of incidence but this is expected as reflectance becomes more sensitive to the optical properties of colloid above Brewster’s angle of incidence.
As a conclusion we have shown that it is possible to obtain the complex dielectric function both for colloids and the individual dielectric or metallic nanoparticles from direct reflectance measurement using two different linear polarizations. The present method for direct reflectance measurement is experimentally simple and accurate for nanoparticle identification. It is worth emphasizing that the results here are applicable any type of colloid independent of the actual colloid composition. We believe that the optical methods will find many applications in nanoparticle identification from a water stream in the future.
This work has been funded by the Academy of Finland (grant no 250 122 & 256 263). JJS wishes to thank the Japan Society for the Promotion of Science (JSPS) for a research grant (L-11537).
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See more of this Group/Topical: Topical 9: Sensors