Friday, April 29, 2011

Perturbation between two traps in dual-trap optical tweezers

Lin Ling, Fei Zhou, Lu Huang, Honglian Guo, Zhaolin Li, and Zhi-Yuan Li

Dual-trap optical tweezers are widely used in biological sciences and many other areas. The two traps are generally considered to be independent of each other in most situations. But when they are close and even touch side by side, the influence may not be negligible. We calculate the optical force of dielectric spherical particles trapped in dual-trap optical tweezers by means of the discrete dipole approximation method and analyze the perturbation effect between the two traps. We find that the electric field does not change much when it is scattered by the trapped particles. As a result, the scattering light from one sphere has a little perturbation effect on the trapping force upon the other sphere. The perturbation mainly comes from the other trap and is thus affected by the distance between the two traps. In the experiment, the displacement of the sphere trapped in an immovable trap is observed when another trap is moving close. The experiment data of relative displacement match qualitatively with the calculation data.


Optical forces, trapping and strain on extended dielectric objects

M. Sonnleitner, M. Ritsch-Marte and H. Ritsch

We show that the optical properties of an extended dielectric object are reliably reproduced by a large number of thin slices forming a linear array of beam splitters. In the infinite slice number limit this self-consistent approach allows to calculate light forces within a medium directly from the Maxwell stress tensor for any dielectric with prescribed refractive index distribution. For the generic example of a thick slab in counterpropagating fields the effective force and internal strain distribution strongly depend on the object's thickness and the injected field amplitudes. The corresponding trapping dynamics may even change from high-field-seeking to low-field-seeking behaviour while internal forces lead to pressure gradients and thus imply stretching or compression of an elastic object. Our results bear important consequences for a wide scope of applications, ranging from cavity optomechanics with membranes, size selective optical trapping and stretching of biological objects, light-induced pressure gradients in gases, to implementing light control in microfluidic devices.


Photophoretic velocimetry—a new way for the in situ determination of particle size distribution and refractive index of hydrocolloids

Clemens Helmbrecht, Reinhard Niessner and Christoph Haisch

The migration of particles induced by the forces of light is known as photophoresis. The photophoretic velocity of particles under the influence of a strong light source, e.g. a laser beam, is recorded and measured by means of digital image processing which is called photophoretic velocimetry (PPV). The photophoretic velocity depends on the particle size as well as on its refractive index. By applying PPV, we show the determination of the intrinsic properties of polystyrene (PS), melamine resin (MF) and SiO2 particles, deduced from velocity distributions of both monodisperse as well as polydisperse suspensions. Especially the continuous determination of the refractive index of single hydrocolloids is of great interest for quality assurance and the discrimination of polydisperse biological or inorganic samples. Also, PPV is not restricted to in water dispersed samples only.


Improving Signal/Noise Resolution in Single-Molecule Experiments Using Molecular Constructs with Short Handles

N. Forns, S. de Lorenzo, M. Manosas, K. Hayashi, J.M. Huguet and F. Ritort

We investigate unfolding/folding force kinetics in DNA hairpins exhibiting two and three states with newly designed short dsDNA handles (29 bp) using optical tweezers. We show how the higher stiffness of the molecular setup moderately enhances the signal/noise ratio (SNR) in hopping experiments as compared to conventional long-handled constructs (700 bp). The shorter construct results in a signal of higher SNR and slower folding/unfolding kinetics, thereby facilitating the detection of otherwise fast structural transitions. A novel analysis, as far as we are aware, of the elastic properties of the molecular setup, based on high-bandwidth measurements of force fluctuations along the folded branch, reveals that the highest SNR that can be achieved with short handles is potentially limited by the marked reduction of the effective persistence length and stretch modulus of the short linker complex.


Microfluidic production of monodisperse functional o/w droplets and study of their reversible pH dependent aggregation behavior

Wolfgang-Andreas C. Bauer, Jurij Kotar, Pietro Cicuta, Robert T. Woodward, Jonathan V. M. Weaver and Wilhelm T. S. Huck

We report the use of microfluidics for the production of monodisperse oil-in-water droplets functionalized by a pH responsive branched co-polymer surfactant. The droplet functionality facilitates the reversible aggregation of the micron-sized droplets into macroscopic engineered emulsions in response to solution pH changes. Co-injection of dye-loaded and non-dyed droplets into acidic water yields bi-colored dumbbell-shaped aggregates that disassemble into their constituent droplet building blocks upon an increase in pH. Optical tweezers are used to study and quantify the pH dependent interactions of individual droplets.


Thursday, April 28, 2011

Correlation between tissue oxygenation and erythrocytes elasticity

Yu-Tsung Wu, Arthur Chiou, Chia-Wei Sun

In this paper, near-infrared spectroscopy (NIRS) and jumping optical tweezers were used to measure the tissue oxygenation and the elasticity of erythrocytes, respectively. The correlation between tissue oxygenation induced by arterial occlusion test (AOT) and the mechanical properties of individual erythrocytes from a blood sample obtained after AOT was studied. The experimental results show a linear correlation between the oxygenation signal caused by AOT and the elasticity of erythrocytes.


Long-distance optical guiding of colloidal particles using holographic axilens

Sunita Ahlawat, Ravi Shanker Verma, Raktim Dasgupta, and Pradeep Kumar Gupta

We report the use of an aspheric holographic optical element (axilens) that essentially combines the properties of the long focal depth of an axicon and the high energy concentration of a conventional spherical lens for long-distance guiding of microscopic objects. With the use of the axilens, polystyrene spheres (~6 μm diameter) could be transported over a distance of ~16 mm that was ∼3 times longer compared with that obtained using a spherical lens of focal length identical to the mean focal length of the axilens. Further, due to the availability of good on-axis power density, even objects having very marginally higher refractive index than the medium (differing only at third decimal place) could be guided with a guiding speed of ~5 μm/s.


Wednesday, April 27, 2011

Characterization of bacterial spore germination using phase-contrast and fluorescence microscopy, Raman spectroscopy and optical tweezers

Lingbo Kong, Pengfei Zhang, Guiwen Wang, Jing Yu, Peter Setlow & Yong-qing Li

This protocol describes a method combining phase-contrast and fluorescence microscopy, Raman spectroscopy and optical tweezers to characterize the germination of single bacterial spores. The characterization consists of the following steps: (i) loading heat-activated dormant spores into a temperature-controlled microscope sample holder containing a germinant solution plus a nucleic acid stain; (ii) capturing a single spore with optical tweezers; (iii) simultaneously measuring phase-contrast images, Raman spectra and fluorescence images of the optically captured spore at 2- to 10-s intervals; and (iv) analyzing the acquired data for the loss of spore refractility, changes in spore-specific molecules (in particular, dipicolinic acid) and uptake of the nucleic acid stain. This information leads to precise correlations between various germination events, and takes 1–2 h to complete. The method can also be adapted to use multi-trap Raman spectroscopy or phase-contrast microscopy of spores adhered on a cover slip to simultaneously obtain germination parameters for multiple individual spores.


Micro-rheology on (polymer-grafted) colloids using optical tweezers

C Gutsche, M M Elmahdy, K Kegler, I Semenov, T Stangner, O Otto, O Ueberschär, U F Keyser, M Krueger, M Rauscher, R Weeber, J Harting, Y W Kim, V Lobaskin, R R Netz and F Kremer
Optical tweezers are experimental tools with extraordinary resolution in positioning (± 1 nm) a micron-sized colloid and in the measurement of forces (± 50 fN) acting on it—without any mechanical contact. This enables one to carry out a multitude of novel experiments in nano- and microfluidics, of which the following will be presented in this review: (i) forces within singlepairs of colloids in media of varying concentration and valency of the surrounding ionic solution, (ii) measurements of the electrophoretic mobility of single colloids in different solvents (concentration, valency of the ionic solution and pH), (iii) similar experiments as in (i) with DNA-grafted colloids, (iv) the nonlinear response of single DNA-grafted colloids in shear flow and (v) the drag force on single colloids pulled through a polymer solution. The experiments will be described in detail and their analysis discussed.


Optical tweezers based active microrheology of sodium polystyrene sulfonate (NaPSS)

Chia-Chun Chiang, Ming-Tzo Wei, Yin-Quan Chen, Pei-Wen Yen,Yi-Chiao Huang, Jun-Yeh Chen, Olivier Lavastre, Husson Guillaume, Darsy Guillaume, and Arthur Chiou
We used oscillatory optical tweezers to investigate the microrheological properties of Sodium polystyrene sulfonate (NaPSS; Mw = 70kDa) polymer solutions with different concentrations from 0.001mM to 10mM in terms of elastic modulus G’(ω) and loss modulus G”(ω) as a function of angular frequency (ω) in the range of 6rad/s to 6000rad/s. The viscoelastic properties (including zero-shear-rate viscosity, crossing frequency and transition frequency) as a function of polymer concentration, deduced from our primary data, reveal the subtle structural changes in the polymer solutions as the polymer concentration increases from dilute to semi-dilute regimes, passing through the critical micelle formation concentration and the polymer overlapping concentration. The experimental results are consistent with the Maxwell model in some regime, and with the Rouse model in other, indicating the transient network character and the micelles formation in different regimes.


Optical trapping of synaptic vesicles in neurons

Chie Hosokawa, Suguru N. Kudoh, Ai Kiyohara, and Takahisa Taguchi

We demonstrate intracellular manipulation of synaptic vesicles in living neurons by optical trapping. When an infrared trapping laser is focused on synapses of a neuronal cell labeled with a fluorescent endocytic marker, fluorescence is observed at the focal spot. The fluorescence spectrum is attributed to fluorescent dye in the synaptic vesicles, indicating excitation by two-photon absorption of the trapping laser. The fluorescence intensity increases gradually within ∼ 100 s of laser irradiation, suggesting that trapping force causes vesicles assembly at the focus. Our method can be applied to manipulate synaptic transmission of a particular neuron in a neuronal network.


Thursday, April 21, 2011

Optical trapping of microrods: variation with size and refractive index

Stephen H. Simpson and Simon Hanna

Optical traps can be characterized in terms of two simple parameters: the stiffness, given by the gradient of the force at mechanical equilibrium, and the strength, as expressed by the maximum restoring force available for displacement in a given direction. We present numerical calculations of these quantities for dielectric microrods of varying radius and refractive index held horizontally in pairs of holographically generated Gaussian beams. The resulting variations are seen to be influenced by optical resonances, as well as by the relative sizes of the beam waist and rod diameter. In addition, it is shown that trapping in these systems is sensitive to the polarization state of the incident field; i.e., for certain rods, trapping will occur for beams polarized perpendicular to the long axis of the rod, but not for beams polarized parallel to the long axis. Finally, friction coefficients are evaluated and used to estimate the maximum rates at which the rods may be dragged through the ambient medium.


Monday, April 18, 2011

Dynamic steering beams for efficient force measurement in optical manipulation

Xiaocong Yuan, Yuquan Zhang, Rui Cao, Xing Zhao, Jing Bu, and Siwei Zhu

An efficient and inexpensive method that uses a glass plate mounted onto a motorized rotating stage as a beam-steering device for the generation of dynamic optical traps is reported. Force analysis reveals that there are drag and trapping forces imposed on the bead in the opposite directions, respectively, in a viscous medium. The trapped bead will be rotated following the beam's motion before it reaches the critical escape velocity when the drag force is equal to the optical trapping force. The equilibrium condition facilitates the experimental measurement of the drag force with potential extensions to the determination of the viscosity of the medium or the refractive index of the bead. The proposed technique can easily be integrated into conventional optical microscopic systems with minimum modifications.


Radiation forces of a focused partially coherent flattened vortex beam on a Rayleigh spherical particle

Ke Cheng and Baida Lü

A focused partially coherent flattened vortex beam used to trap a Rayleigh dielectric spherical particle with relative refractive index p < 1 is studied. The dependence of radiation forces (RFs) on the beam order N, waist width w0, correlation length σ0, particle radius a and focal length f is analyzed and illustrated by numerical examples. By a suitable choice of N, w0, σ0 and f a stable trap of the Rayleigh particle is achievable. In particular, there exist critical values w0,c, σ0,c for a partially coherent flattened vortex beam the particle can be trapped by the beam with w0 less than w0,c and σ0 larger than σ0,c. A comparison with the previous work is made.


Friday, April 15, 2011

Optically driven Archimedes micro-screws for micropump application

Chih-Lang Lin, Guy Vitrant, Michel Bouriau, Roger Casalegno, and Patrice L. Baldeck

Archimedes micro-screws have been fabricated by three-dimensional two-photon polymerization using a Nd:YAG Q-switched microchip laser at 532nm. Due to their small sizes they can be easily manipulated, and made to rotate using low power optical tweezers. Rotation rates up to 40 Hz are obtained with a laser power of 200 mW, i.e. 0.2 Hz/mW. A photo-driven micropump action in a microfluidic channel is demonstrated with a non-optimized flow rate of 6pL/min. The optofluidic properties of such type of Archimedes micro-screws are quantitatively described by the conservation of momentum that occurs when the laser photons are reflected on the helical micro-screw surface.


Thursday, April 14, 2011

Algorithm for diffractive optical element of array optical tweezers

Sun, Q., Ren, Y., Yao, K., Li, Y., Lu, R.

As one of the most important techniques in optical tweezers, two-dimensional array optical tweezers have the widespread applications in nanofabrication and biochip manufacturing. Diffractive optical element is the key device to design array optical tweezers. Combined theoretical simulations using pseudo-random phases encoding through Gerchberg-Saxton (G-S) algorithm with experimental measurements, we find that obvious background noise appears when the regular output distribution is array points. A double amplitude filter is adopted to effectively suppress the background noise and improve the quality of diffraction images. These findings are helpful for designing array optical tweezers in the near future.


Ensemble method to measure the potential energy of nanoparticles in an optical trap

Joseph Junio, Jack Ng, Joel A. Cohen, Zhifang Lin, and H. Daniel Ou-Yang

A method is described for measuring the potential energy of nanoparticles in an optical trap by trapping an ensemble of particles with a focused laser beam. The force balance between repulsive osmotic and confining gradient-force pressures determines the single-particle trapping potential independent of interactions between the particles. The ensemble nature of the measurement permits evaluation of single-particle trapping energies much smaller than kBT. Energies obtained by this method are compared to those of single-particle methods as well as to theoretical calculations based on classical electromagnetic optics.


Trapping and transporting aerosols with a single optical bottle beam generated by moiré techniques

Peng Zhang, Ze Zhang, Jai Prakash, Simon Huang, Daniel Hernandez, Matthew Salazar, Demetrios N. Christodoulides, and Zhigang Chen

We demonstrate optical trapping and manipulation of aerosols with an optical bottle beam generated by the moiré techniques. We observe stable trapping and back-and-forth transportation of a variety of absorbing carbon particles suspended in air, ranging from clusters of nanosized buckminsterfullerene C60 to micrometer-sized carbon powders.


Wednesday, April 13, 2011

Electroporation dependence on cell size: an optical tweezers study

Brian E Henslee , Andrew Morss , Xin Hu , Gregory Lafyatis , and L. James Lee

Electropermeabilization or electroporation is the electrical disruption of a cell’s membrane to introduce drugs, DNA/RNA, proteins or other therapies into the cell. Despite four decades of study, the fundamental science of the process remains poorly understood and controversial. We measured the minimum applied electric field required for permeabilization of suspended spherical cells as a function of cell radius for three cell lines. Key to this work is our using optical tweezers to precisely position individual cells and enable well-defined, repeatable measurements on cells in suspension. Our findings call into question fundamental assumptions common to all theoretical treatments that we know of. It is generally expected that for individual cells from a particular cell line, large cells should be easier to electroporate than small ones: the minimum electric field to cause electropermeabilization should scale inversely with cell diameter. We found instead, that each cell line has its own characteristic field that will, on average, cause permeabilization in cells of that line. Electropermeabilization is a stochastic process: two cells which appear identical may have different permeabilization thresholds. However for all three cell lines, we found that the minimum permeabilization field for any given cell does not depend on its size.

Tuesday, April 12, 2011

In situ observations of freezing processes of single micrometer-sized aqueous ammonium sulfate droplets in air

Shoji Ishizaka, Teruhide Wada and Noboru Kitamura
The freezing processes of single micrometer-sized aqueous ammonium sulfate droplets levitated in air were observed by means of laser trapping and spectroscopy techniques. Single micrometer-sized aqueous ammonium sulfate droplets were levitated by radiation pressure in air. When a levitated droplet was cooled below 213 K, a supercooled droplet was turned from the liquid to solid state. To the best of our knowledge, this is the first observation of the freezing processes of single micrometer-sized supercooled aqueous solution droplets in air by means of laser trapping and spectroscopy techniques.


Measuring colloidal forces from particle position deviations inside an optical trap

Djamel El Masri, Peter van Oostrum, Frank Smallenburg, Teun Vissers, Arnout Imhof, Marjolein Dijkstra and Alfons van Blaaderen
We measure interaction forces between pairs of charged PMMA colloidal particles suspended in a relatively low-polar medium (5 ε 8) directly from the deviations of particle positions inside two time-shared optical traps. The particles are confined to optical point traps; one is held in a stationary trap and the other particle is brought closer in small steps while tracking the particle positions using confocal microscopy. From the observed particle positions inside the traps we calculate the interparticle forces using an ensemble-averaged particle displacement-force relationship. The force measurements are confirmed by independent measurements of the different parameters using electrophoresis and a scaling law for the liquid-solid phase transition. When increasing the salt concentration by exposing the sample to UV light, the force measurements agree well with the classical DLVO theory assuming a constant surface potential. On the other hand, when adding tetrabutylammonium chloride (TBAC) to vary the salt concentration, surface charge regulation seems to play an important role.


Friday, April 8, 2011

Tumour cell identification by means of Raman spectroscopy in combination with optical traps and microfluidic environments

Sebastian Dochow, Christoph Krafft, Ute Neugebauer, Thomas Bocklitz, Thomas Henkel, Günter Mayer, Jens Albert and Jürgen Popp
Raman spectroscopy has been recognized to be a powerful tool for label-free discrimination of cells. Sampling methods are under development to utilize the unique capabilities to identify cells in body fluids such as saliva, urine or blood. The current study applied optical traps in combination with Raman spectroscopy to acquire spectra of single cells in microfluidic glass channels. Optical traps were realized by two 1070 nm single mode fibre lasers. Microflows were controlled by a syringe pump system. A novel microfluidic glass chip was designed to inject single cells, modify the flow speed, accommodate the laser fibres and sort cells after Raman based identification. Whereas the integrated microchip setup used 514 nm for excitation of Raman spectra, a quartz capillary setup excited spectra with 785 nm laser wavelength. Classification models were trained using linear discriminant analysis to differentiate erythrocytes, leukocytes, acute myeloid leukaemia cells (OCI-AML3), and breast tumour cells BT-20 and MCF-7 with accuracies that are comparable with previous Raman experiments of dried cells and fixed cells in a Petri dish. Implementation into microfluidic environments enables a high degree of automation that is required to improve the throughput of the approach for Raman activated cell sorting.


Thursday, April 7, 2011

Optical orientation and rotation of trapped red blood cells with Laguerre-Gaussian mode

Raktim Dasgupta, Sunita Ahlawat, Ravi Shankar Verma, and Pradeep Kumar Gupta

We report the use of Laguerre-Gaussian (LG) modes for controlled orientation and rotation of optically trapped red blood cells (RBCs). For LG modes with increasing topological charge the resulting increase in size of the intensity annulas led to trapping of the cells at larger tilt angle with respect to the beam axis and thus provided additional control on the stable orientation of the cells under trap. Further, the RBCs could also be driven as micro-rotors by a transfer of orbital angular momentum from the LG trapping beam having large topological charge or by rotating the profile of LG mode having fractional topological charge.


Manipulation and Raman Spectroscopy with Optically Trapped Metal Nanoparticles Obtained by Pulsed Laser Ablation in Liquids

E. Messina, E. Cavallaro, A. Cacciola, R. Saija, F. Borghese, P. Denti, B. Fazio, C. D’Andrea, P. G. Gucciardi, M. A. Iat, M. Meneghetti, G. Compagnini, V. Amendola, and O. M. Marag

We investigate experimentally and theoretically optical trapping of metal nanoparticles and aggregates. In particular, we show how light forces can be used to trap individual gold nanoaggregates of controlled size and structure obtained by laser ablation synthesis in solution. Due to their surface charge, no agglomeration of isolated nanoparticles was observed during trapping experiments and reliable optical force measurements of isolated and aggregated nanoparticles was possible through an analysis of the Brownian motion in the trap. We show how the field-enhancement properties of these nanostructures enables surface-enhanced Raman spectroscopy of molecules adsorbed on aggregates optically trapped in a Raman tweezers setup. We finally discuss calculations of extinction and optical forces based on a full electromagnetic scattering theory for aggregated gold nanostructures where the occurrence of plasmon resonances at longer wavelength play a crucial role in the enhancement of the trapping forces.


Indirect optical gripping with triplet traps

Brian Koss, Sagar Chowdhury, Thomas Aabo, S. K. Gupta, and Wolfgang Losert

We describe an indirect optical gripper for noninvasive micromanipulation of sensitive objects, such as cells. Our optical gripper, driven by dynamic holographic optical tweezers, consists of an arrangement of six silica beads, each held in place by an optical trap. The beads are moved so as to grip an object, which itself is not significantly exposed to laser light. Six beads are sufficient to grip an object reliably, consistent with robotics design rules. We find that improved gripping is achieved when beads are arranged into groups of triplets, since each triplet of trapped beads forms a weakly attractive pocket into which other objects are drawn.


Combination of Raman tweezers and quantitative differential interference contrast microscopy for measurement of dynamics and heterogeneity during the germination of individual bacterial spores

Pengfei Zhang, Lingbo Kong, Guiwen Wang, Yong-qing Li, and Peter Setlow

Raman tweezers and quantitative differential interference contrast (DIC) microscopy are combined to monitor the dynamic germination of individual bacterial spores of Bacillusspecies, as well as the heterogeneity in this process. The DIC bias phase is set properly such that the brightness of DIC images of individual spores is proportional to the dipicolinic acid (DPA) level of the spores, and an algorithm is developed to retrieve the phase image of an individual spore from its DIC image. We find that during germination, the rapid drop in both the intensity of the original DIC image and the intensity of the reconstructed phase image precisely corresponds to the release of all DPA from that spore. The summed pixel intensity of the DIC image of individual spores adhered on a microscope coverslip is not sensitive to the drift of the slide in both horizontal and vertical directions, which facilitates observation of the germination of thousands of individual spores for long periods of time. A motorized stage and synchronized image acquisition system is further developed to effectively expand the field of view of the DIC imaging. This quantitative DIC technique is used to track the germination of hundreds or thousands of individual spores simultaneously.


Monday, April 4, 2011

T-matrix method for modelling optical tweezers

Nieminen, Timo; Loke, Vincent; Stilgoe, Alexander; Heckenberg, Norman; Rubinsztein-Dunlop, Halina
We review the use of the T-matrix description of scattering, or the T-matrix method, for the calculation of optical forces and torques, especially for the computational modelling of optical tweezers. We consider both simple particles such as homogeneous isotropic spheres, spherical shells, spheroids, and so on, and complex particles, including anisotropic particles, inhomogenous particles, and geometrically complex particles.


Optical tweezers directed one-bead one-sequence synthesis of oligonucleotides

Tao Wang, Stefan Oehrlein, Mark M. Somoza, Jose R. Sanchez Perez, Ryan Kershner and Franco Cerrina

An optical tweezers directed parallel DNA oligonucleotide synthesis methodology is described in which controlled pore glass (CPG) beads act as solid substrates in a two-stream microfluidic reactor. The reactor contains two parallel sets of physical confinement features that retain beads in the reagent stream for synthetic reaction but allow the beads to be optically trapped and transferred between the reagent and the inert streams for sequence programming. As a demonstration, we synthesized oligonucleotides of target sequence 25-nt, one deletion and one substitution using dimethoxytrityl (DMT) nucleoside phosphoramidite chemistry. In detecting single-nucleotide mismatches, fluorescence in situ hybridization of the bead-conjugated probes showed high specificity and signal-to-noise ratios. These preliminary results suggest further possibilities of creating a novel type of versatile, sensitive and multifunctional reconfigurable one-bead one-compound (OBOC) bead array.


Friday, April 1, 2011

Nonconservative electric and magnetic optical forces on submicron dielectric particles

Raquel Gómez-Medina, Manuel Nieto-Vesperinas, and Juan José Sáenz

We present a study of the total force on a small lossless dielectric particle, which presents both an electric and magnetic response, in a optical vortex wave field. We show that the force is a simple combination of conservative and nonconservative steady forces that can rectify the flow of magnetodielectric particles. In a vortex lattice the electric-magnetic dipolar interaction can spin the particles either in or out of the whirl sites leading to trapping or diffusion. Specifically, we analyze force effects on submicron silicon spheres in the near infrared, proving that the results previously discussed for hypothetical magnetodielectric particles can be observed for these Si particles.