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.

Geometrical optimization of nanostrips for surface plasmon excitation: an analytical approach.

We give a simple tool for the optimization of the dimensions of a metallic nanostrip illuminated at a given wavelength under normal incidence, to get a maximum of the electromagnetic field amplitude in the nanostrip. We propose an analytical formula that gives the widths and heights of the series of nanostrips that produce field enhancement. The validity of the analytical formula is checked by using the finite element method. This design of a nanostrip could be useful for sensors and thermally active components.

Propagation of uncertainties and applications in numerical modeling: tutorial.

Some inputs of computational models are commonly retrieved from external sources (handbooks, articles, dedicated measurements), and therefore are subject to uncertainties. The known experimental dispersion of the inputs can be propagated through the numerical models to produce samples of outputs. The stemming propagation of uncertainties is already significant in metrology but also has applications in optimization and inverse problem resolution of the modeled physical system. Moreover, the information on uncertainties can be used to characterize and compare models, and to deduce behavior laws. This tutorial gives tools and applications of the propagation of experimental uncertainties through models. To illustrate the method and its applications, we propose to investigate the scattering of light by gold nanoparticles, which also enables the comparison of the full Mie theory and the dipole approximation. The position of the localized surface plasmon resonance and the corresponding value of the scattering efficiency are more specifically studied.

Lycurgus Cup: inverse problem using photographs for characterization of matter.

Photographs of the Lycurgus Cup with a source light inside and outside exhibit purple and green colors, respectively (dichroism). A model relying on the scattering of light to colors in the photographs is proposed and used within an inverse problem algorithm, to deduce radius and composition of metallic particles, and the refractive index of the surrounding glass medium. The inverse problem algorithm is based on a hybridization of particle swarm optimization and of the simulated annealing methods. The results are compared to experimental measurements on a small sample of glass. The linear laws that are deduced from sets of possible parameters producing the same color in the photographs help simplify the understanding of phenomena. The proportion of silver to gold in nanoparticles is found to be in agreement, but a large proportion of copper is also found. The retrieved refractive index of the surrounding glass is close to 2.

Recovering the size of nanoparticles by digital in-line holography.

The development of methods to measure the size of nanoparticles is a challenging topic of research. The proposed method is based on the metrology of the stable vapor bubble created by thermal coupling between a laser pulse and the nanoparticle in a droplet. The measurement is realized by digital in-line holography. The size of the nanoparticle is deduced from numerical simulations computed with a photo-thermal finite element method.

Numerical study of plasmonic efficiency of gold nanostripes for molecule detection.

In plasmonics, the accurate computation of the electromagnetic field enhancement is necessary in determining the amplitude and the spatial extension of the field around nanostructures. Here, the problem of the interaction between an electromagnetic excitation and gold nanostripes is solved. An optimization scheme, including an adaptive remeshing process with error estimator, is used to solve the problem through a finite element method. The variations of the electromagnetic field amplitude and the plasmonic active zones around nanostructures for molecule detection are studied in this paper taking into account the physical and geometrical parameters of the nanostripes. The evolution between the sizes and number of nanostripes is shown.

Numerical modeling of the photothermal processing for bubble forming around nanowire in a liquid.

An accurate computation of the temperature is an important factor in determining the shape of a bubble around a nanowire immersed in a liquid. The study of the physical phenomenon consists in solving a photothermic coupled problem between light and nanowire. The numerical multiphysic model is used to study the variations of the temperature and the shape of the created bubble by illumination of the nanowire. The optimization process, including an adaptive remeshing scheme, is used to solve the problem through a finite element method. The study of the shape evolution of the bubble is made taking into account the physical and geometrical parameters of the nanowire. The relation between the sizes and shapes of the bubble and nanowire is deduced.

Nanobubble evolution around nanowire in liquid.

The evolution of the shape and size of a bubble around a nanowire immersed in a liquid can be studied as a light absorption problem and consequently can directly be related to the distribution of the temperature around the nanowire. Such a physical phenomenon can be seen as the photo-thermal coupled problem of nanowire illuminated by an electromagnetic wave. The resolution of the multiphysic model allows to compute the variation of the temperature and consequently the evolution of the created bubble. An advanced adaptive remeshing process is developed to solve the numerical model using Finite Element Method. An optimization process is applied to solve the coupled problem and is used to detect the size of the produced bubble around nanowire under illumination. The adaptive remeshing process permits to control the convergence of the numerical solution relatively to the evolution of the temperature field. The process allows to study the evolution of the shape and size of the bubble. We show the influence of the laser parameters on the evolution of the bubble. The informations about the geometry of the nanowire can be deduced from the size and shape of the bubble.

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.

Numerical retrieval of thin aluminium layer properties from SPR experimental data.

The inverse problem for Surface Plasmon Resonance measurements [1] on a thin layer of aluminium in the Kretschmann configuration, is solved with a Particle Swarm Optimization method. The optical indexes as well as the geometrical parameters are found for the best fit of the experimental reflection coefficient in s and p polarization, for four samples, under three theoretical hypothesis on materials: the metal layer is pure, melted with its oxyde, or coated with oxyde. The influence of the thickness of the metal layer on its optical properties is then investigated.

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.

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.

Toward nanoworld-based secure encryption for enduring data storage.

The generation of encryption secret keys with a high level of security is crucial to ensure secure enduring data storage and is a challenging topic of investigation. We show that the use of nano-objects and optical response permits us to produce a complex optical tomography map, which can be used as a pseudorandom generator that satisfies the basic requirements for encryption based on the secret key.

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.

Scanning near-field optical microscopy signal processing and resolution.

To increase the signal-to-noise ratio and to remove the spatially slow varying signals, a lock-in amplifier is often used in scanning probe microscopy. The signal reconstructed from the lock-in data contains the contributions of the evanescent and homogeneous waves that are mixed in the near-field zone (i.e., at a very short distance). The resolution is determined and a method is given to suppress the useless background information. Experimental images of nanoparticles are processed.

Improved scheme for accurate computation of high electric near-field gradients.

We present an improved adaptive mesh process that allows the accurate control of the numerical solution of interest derived from the solution of the partial differential equation. In the cases of two-dimensional studies, such an adaptive meshing is applied to compute phenomenon involving high field gradients in near-field (electric intensity, Poynting's vector, optical forces,...). We show, that this improved scheme permits to decrease drastically the computational time and the memory requirements.

Tomography of the near-field optical signal.

In near-field optics, measurement of vertical variations of the near field is of great interest for characterizing the efficiency of resonances such as surface plasmon polaritons. The use of the signal obtained through the lock-in amplifier using a feedback on the vertical vibration of the probe is shown to enable the reconstruction of the near field without the use of the slower technique of approach curves. Therefore, a tomography of the near field is directly available.

Scanning near-field optical data contrast measurement: a tomographylike near-field reconstruction.

A method for the reconstruction of near-field optical signals is proposed to produce a tomographylike map of the field above the nanostructures being studied. The data obtained through lock-in detection are processed employing Chebyshev's polynomial function of the distance between the probe and the sample. The method is first applied to numerically generated near-field evanescent data, with three different decreasing lengths, and then applied to an experimental signal. Therefore the contrast of the signal above nanostructures is discussed to underline the discrepancy between the scanning near-field optical microscopy data and the reconstructions.

Signal reconstruction from a scanning near-field optical microscopy approach curve.

Scanning Near-field Optical Microscopies suffer from the low signal to noise ratio, due to the smallness of the diffracting probe used to get images. Therefore a lock-in amplifier is commonly used to perform homodyne detection. From the lock-in data, we reconstruct the near-field intensity diffracted by the probe-end in the case of approach curves. We show that the reconstructed and the detected signals can strongly differ. The reconstruction of the signal is necessary to give physical interpretation.

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.