Quantitative comparison of optimized nanorods, nanoshells and hollow nanospheres for photothermal therapy

The purpose of this study is to get more efficient gold nanoparticles, for necrosis of cancer cells, in photothermal therapy. Therefore a numerical maximization of the absorption efficiency of a set of nanoparticles (nanorod, nanoshell and hollow nanosphere) is proposed, assuming that all the absorbed light is converted to heat. Two therapeutic cases (shallow and deep cancer) are considered. The numerical tools used in this study are the full Mie theory, the discrete dipole approximation and the particle swarm optimization. The optimization leads to an improved efficiency of the nanoparticles compared with previous studies. For the shallow cancer therapy, the hollow nanosphere seems to be more efficient than the other nanoparticles, whereas the hollow nanosphere and nanorod, offer comparable absorption efficiencies, for deep cancer therapy. Finally, a study of tolerance for the size parameters to guarantee an absorption efficiency threshold is included.

Gold Nanoparticles as a Photothermal Agent in Cancer Therapy: The Thermal Ablation Characteristic Length

In cancer therapy, the thermal ablation of diseased cells by embedded nanoparticles is one of the known therapies. It is based on the absorption of the energy of the illuminating laser by nanoparticles. The resulting heating of nanoparticles kills the cell where these photothermal agents are embedded. One of the main constraints of this therapy is preserving the surrounding healthy cells. Therefore, two parameters are of interest. The first one is the thermal ablation characteristic length, which corresponds to an action distance around the nanoparticles for which the temperature exceeds the ablation threshold. This critical geometric parameter is related to the expected conservation of the body temperature in the surroundings of the diseased cell. The second parameter is the temperature that should be reached to achieve active thermal agents. The temperature depends on the power of the illuminating laser, on the size of nanoparticles and on their physical properties. The purpose of this paper is to propose behavior laws under the constraints of both the body temperature at the boundary of the cell to preserve surrounding cells and an acceptable range of temperature in the target cell. The behavior laws are deduced from the finite element method, which is able to model aggregates of nanoparticles. We deduce sensitivities to the laser power and to the particle size. We show that the tuning of the temperature elevation and of the distance of action of a single nanoparticle is not significantly affected by variations of the particle size and of the laser power. Aggregates of nanoparticles are much more efficient, but represent a potential risk to the surrounding cells. Fortunately, by tuning the laser power, the thermal ablation characteristic length can be controlled.

Models of near-field spectroscopic studies: comparison between Finite-Element and Finite-Difference methods

We compare the numerical results obtained by the Finite Element Method (FEM) and the Finite Difference Time Domain Method (FDTD) for near-field spectroscopic studies and intensity map computations. We evaluate their respective efficiencies and we show that an accurate description of the dispersion and of the geometry of the material must be included for a realistic modeling. In particular for the nano-objects, we show that a grid size around rhoa approximately 4pia/lambda (expressed in lambda units) as well as a Drude-Lorentz' model of dispersion for FDTD should be used in order to describe more accurately the confinement of the light around the nanostructures (i.e. the high gradients of the electromagnetic field) and to assure the convergence to the physical solution.

Light depolarization induced by metallic tips in apertureless near-field optical microscopy and tip-enhanced Raman spectroscopy

We have investigated the depolarization effects of light scattered by sharp tips used for apertureless near-field optical microscopy. Dielectric and metal coated tips have been investigated and depolarization factors between 5 and 30% have been measured, changing as a function of the incident light polarization and of the tip shape. The experimental results are in good agreement with theoretical calculations performed by the finite element method, giving a near-field depolarization factor close to 10%. The effect of depolarization has been investigated in polarized tip-enhanced Raman spectroscopy (TERS) experiments; the depolarization gives rise to forbidden Raman modes in Si crystals.

New adaptive mesh development for accurate near-field enhancement computation

An accurate computation of the near-field enhancement is a key factor for the optimization of nanostructures in plasmonics. This problem has been addressed for Green's dyadic method but remains open for finite element method (FEM) where the use of non-Cartesian meshes is known to be the most efficient. We present a new adaptive mesh process based on the a posteriori error indicator estimation on the physical solution. This new procedure accelerates drastically the convergence of the solution and minimizes both the memory requirement and the computational time.

Near-field optical patterning and structuring based on local-field enhancement at the extremity of a metal tip

We present a particular approach and the associated results allowing the nanostructuration of a thin photosensitive polymer film. This approach based on a scanning near-field optical microscopy configuration uses the field-enhancement (FE) effect, a so-called lightning-rod effect appearing at the extremity of a metallic tip when illuminated with an incident light polarized along the tip axis. The local enhancement of the electromagnetic field straight below the tip's apex is observed directly through a photoisomerization reaction, inducing the growth of a topographical nanodot characterized in situ by atomic-force microscopy using the same probe. From a survey of the literature, we first review the different experimental approaches offered to nanostructure materials by near-field optical techniques. We describe more particularly the FE effect approach. An overview of the theoretical approach of this effect is then given before presenting some experimental results so as theoretical results using the finite-element method. These results show the influence on the nanostructuration of the polymer of a few experimental parameters such as the polarization state, the illumination mode and the tip's geometry. Finally, the potentiality of this technique for some applications in the field of lithography and high-density data storage is shown via the fabrication of nano-patterns.

Adaptive Non-Uniform Particle Swarm Application to Plasmonic Design

The metaheuristic approach has become an important tool for the optimization of design in engineering. In that way, its application to the development of the plasmonic based biosensor is apparent. Plasmonics represents a rapidly expanding interdisciplinary field with numerous transducers for physical, biological and medicine applications. Specific problems are related to this domain. The plasmonic structures design depends on a large number of parameters. Second, the way of their fabrication is complex and industrial aspects are in their infancy. In this study, the authors propose a non-uniform adapted Particle Swarm Optimization (PSO) for rapid resolution of plasmonic problem. The method is tested and compared to the standard PSO, the meta-PSO (Veenhuis, 2006) and the ANUHEM (Barchiesi, 2009).These approaches are applied to the specific problem of the optimization of Surface Plasmon Resonance (SPR) Biosensors design. Results show great efficiency of the introduced method.

Nanoshells for photothermal therapy: a Monte-Carlo based numerical study of their design tolerance

The optimization of the coated metallic nanoparticles and nanoshells is a current challenge for biological applications, especially for cancer photothermal therapy, considering both the continuous improvement of their fabrication and the increasing requirement of efficiency. The efficiency of the coupling between illumination with such nanostructures for burning purposes depends unevenly on their geometrical parameters (radius, thickness of the shell) and material parameters (permittivities which depend on the illumination wavelength). Through a Monte-Carlo method, we propose a numerical study of such nanodevice, to evaluate tolerances (or uncertainty) on these parameters, given a threshold of efficiency, to facilitate the design of nanoparticles. The results could help to focus on the relevant parameters of the engineering process for which the absorbed energy is the most dependant. The Monte-Carlo method confirms that the best burning efficiency are obtained for hollow nanospheres and exhibit the sensitivity of the absorbed electromagnetic energy as a function of each parameter. The proposed method is general and could be applied in design and development of new embedded coated nanomaterials used in biomedicine applications.

Design of nanostructures for imaging and biomedical applications by plasmonic optimization

An adapted method of optimization of coated metallic nanoparticles is introduced to perform the optimal choice of material and sizes for better scattering or absorption efficiency. This design of nanoshells, involving plasmon resonance, is achieved to maximize the efficiency factors. The presented method is turned to tune the efficiency of nanoshells for biomedical applications and an increasing of the efficiency factors by 1 or 2 orders of magnitude is predicted with realistic materials.

Use of a scanning near-field optical microscope architecture to study fluorescence and energy transfer near a metal

Fluorescence intensity depends strongly on the distance between the emitting molecule and a metallic interface. We show that a scanning near-field optical microscope (SNOM) is a simple and versatile tool for studying such an effect. The fluorescent molecules are embedded in a layer upon a silica substrate, and metal is coated on the SNOM tip. We present variations of fluorescence intensity versus tip-sample distance from 800 to ~80 nm . A simple model is used to explain the experimental results. The proposed setup could be used to study nonradiative transfer at a nanometric scale. It could also yield to a new type of optical near-field profiler that uses fluorescent signal.

Surface imaging in near-field optical microscopy by using the fluorescence decay rate: a theoretical study

In this paper, we study the fluorescence decay rate of a molecule above a corrugated interface, and particularly the variations of the decay rate as a function of the lateral position of the molecule. As a first step, one has to determine the field diffracted by a corrugated interface when the incident field is the field emitted by a dipole. For this purpose, we have used a perturbative Rayleigh method, and we show that the decay rate variations can be connected to the surface profile via a transfer function. Some numerical calculations of this transfer function and of decay rate variation images are presented for dielectric and metallic samples. The visibility of the theoretical images is up to 20% and, moreover, resolution of the images is good enough to use the fluorescence lifetime of molecules as signal in a life-time scanning near-field optical microscope. The technical problems are discussed briefly.

Electromagnetic beam diffraction by a finite lamellar structure: an aperiodic coupled-wave method

We have developed a new formulation of the coupled-wave method (CWM) to handle aperiodic lamellar structures, and it will be referred to as the aperiodic coupled-wave method (ACWM). The space is still divided into three regions, but the fields are written by use of their Fourier integrals instead of the Fourier series. In the modulated region the relative permittivity is represented by its Fourier transform, and then a set of integro-differential equations is derived. Discretizing the last system leads to a set of ordinary differential equations that is reduced to an eigenvalue problem, as is usually done in the CWM. To assess the method, we compare our results with three independent formalisms: the Rayleigh perturbation method for small samples, the volume integral method, and the finite-element method.

Application of evolution strategies for the solution of an inverse problem in near-field optics

We introduce an inversion procedure for the characterization of a nanostructure from near-field intensity data. The method proposed is based on heuristic arguments and makes use of evolution strategies for the solution of the inverse problem as a nonlinear constrained-optimization problem. By means of some examples we illustrate the performance of our inversion method. We also discuss its possibilities and potential applications.

Localized surface plasmon resonance in arrays of nano-gold cylinders: inverse problem and propagation of uncertainties

The plasmonic nanostructures are widely used to design sensors with improved capabilities. The position of the localized surface plasmon resonance (LSPR) is part of their characteristics and deserves to be specifically studied, according to its importance in sensor tuning, especially for spectroscopic applications. In the visible and near infra-red domain, the LSPR of an array of nano-gold-cylinders is considered as a function of the diameter, height of cylinders and the thickness of chromium adhesion layer and roughness. A numerical experience plan is used to calculate heuristic laws governing the inverse problem and the propagation of uncertainties. Simple linear formulae are deduced from fitting of discrete dipole approximation (DDA) calculations of spectra and a good agreement with various experimental results is found. The size of cylinders can be deduced from a target position of the LSPR and conversely, the approximate position of the LSPR can be simply deduced from the height and diameter of cylinders. The sensitivity coefficients and the propagation of uncertainties on these parameters are evaluated from the fitting of 15500 computations of the DDA model. The case of a grating of nanodisks and of homothetic cylinders is presented and expected trends in the improvement of the fabrication process are proposed.

Image resolution in reflection scanning near-field optical microscopy using shear-force feedback: characterization with a spline and Fourier spectrum

Scanning near-field optical microscopes (SNOM's) actually lead to nanometric lateral resolution. A combination with shear-force feedback is sometimes used to keep the SNOM tip at a constant force from the sample. However, resolutions in shear-force and optical data are different. An estimation of both resolutions is important for characterizing the capabilities of such systems. The basic principle of the measurement is to compare a spline-fitted logarithm of the power spectra calculated with the optical image with that of the shear force image in which resolution is determined a priori. Quantitative results are given in the case of periodic or untested sample and simulated data. Moreover the accuracy and the stability of the method are discussed.