Transmission of a thin film of spherical particles on a dielectric substrate: the concept of effective medium revisited

Bosi, G.

doi:10.1364/josab.9.000208

Cited by 10 publications

(4 citation statements)

References 14 publications

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“…The problem of reflection and transmission of light by a monolayer of very small particles, either supported by a flat interface or embedded in a transparent medium, has received extensive attention over the years [5][6][7][8][9][10][11][12][13][14][15][16][17]. In most of these works an effective-medium approach has been developed and used.…”

Section: Introductionmentioning

confidence: 99%

“…In most of these works an effective-medium approach has been developed and used. If the particles are small, but not sufficiently small, the effective-medium approach requires an extension [10][11][12]. But when the size of the particles is comparable to or larger than the wavelength of the incident radiation the rewards from effective-medium theories are lost in many respects and a multiple-scattering approach is required [18,19,20].…”

Section: Introductionmentioning

confidence: 99%

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Multiple-scattering model for the coherent reflection and transmission of light from a disordered monolayer of particles

2012

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Using a multiple-scattering formalism, we derive closed-form expressions for the coherent reflection and transmission coefficients of monochromatic electromagnetic plane waves incident upon a two-dimensional array of randomly located spherical particles. The calculation is performed within the quasi-crystalline approximation, and the statistical correlation among the particles is assumed to be given simply by a correlation hole. In the resulting model, the size of the spheres and the angle of incidence are both unrestricted. The final formulas are relatively simple, making the model suitable for a straightforward interpretation of optical-sensing measurements.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Multiple-scattering model for the coherent reflection and transmission of light from a disordered monolayer of particles

2012

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“…The behavior of a film of metallic nanometer-scale spheres [3] and rings [4] has been investigated at optical frequencies. The behavior of thin metallic layers at microwave frequencies has been studied in [5], where the authors showed that even a very thin layer can absorb up to 50 % of the energy of an electromagnetic wave.…”

Section: Introductionmentioning

confidence: 99%

Microwave Reflectivity From Gold Sputtered Nanolayer

Buchar

Macháč

Zehentner

2007

IEEE Trans. Nanotechnology

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Abstract-This paper deals with reflectivity of a gold layer of nanometer-scale thickness sputtered on a dielectric foil at microwave frequencies. A model of nanometer-scale spheres characterizes the behavior of the layer. For short sputtering times, these spheres are separated, and later they touch each other to form a continuous layer. The structure is analyzed in several ways. The first model, as suggested in the literature, replaces the spheres by their electric dipole moments, while the second, newly proposed model replaces them by their mutual capacities. The structure is also being investigated by the CST Microwave Studio software. The data provided by the models is compared with the data obtained from measurements carried out and published by the authors previously. The reduction in effective conductivity of the layer due to microscopic phenomena in thin films is taken into account in the models. The measured conductivity is compared with values taken from the literature, and the differences are discussed.

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“…The behavior of a layer of metallic nanometer-scale spheres [3] and rings [4] has been investigated at optical frequencies. The response of thin metallic layers at microwave frequencies has been investigated by several authors.…”

Section: Introductionmentioning

confidence: 99%

Reflection from a Gold Sputtered Thin Layer

Buchar

Macháč

Zehentner

et al. 2006

2006 International Conference on Microwaves, Radar &Amp; Wireless Communications

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I. INTRODUCTIONThin metallic layers have been gaining significant importance, e.g., in the field of so-called active packaging [1] and electromagnetic shielding [2]. The behavior of a layer of metallic nanometer-scale spheres [3] and rings [4] has been investigated at optical frequencies. The response of thin metallic layers at microwave frequencies has been investigated by several authors. It was shown in [5] that even a very thin layer may absorb up to 50 % of the incident electromagnetic wave energy. The influence of layer thickness on effective conductivity was studied in [6].A thin sputtered gold layer was experimentally investigated at microwave frequencies in [7]. It was found that there is a small reflection from a layer of disconnected gold nano-particles for short sputtering times. For long sputtering times when the gold layer up to tens of nanometers in thickness is homogeneous, the reflection is high. The transition between these two states of reflection was recorded.The thin metallic layer is represented in this paper as a 2D array of spherical gold particles. The process of gradual depositing of metal by sputtering is simulated by decreasing the distance between particles, which is equivalent to increasing their number. Their interaction with an electromagnetic wave is interpreted in four ways. The first model taken from [8] analyses the electromagnetic field interaction with the electric dipole moment of the particles. The second, newly proposed model, is based on the capacities between spheres. Next we consider the layer to be homogeneous, and take into account the effect of decreasing conductivity in very thin films [6], which gives results valid for longer sputtering times. Finally, the layer of gold particles is modeled using the CST Microwave Studio (MWS). Unlike the above-mentioned three models, the MWS model accounts for a random distribution of particles over the analyzed aperture, which gives the most relevant results. All resulting curves of the reflection coefficient with respect to sputtering time are compared with the measured data. The aim of this work is to approximate the measured reflection coefficient [7] for the whole range of investigated sputtering times.

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Transmission of a thin film of spherical particles on a dielectric substrate: the concept of effective medium revisited

Cited by 10 publications

References 14 publications

Multiple-scattering model for the coherent reflection and transmission of light from a disordered monolayer of particles

Multiple-scattering model for the coherent reflection and transmission of light from a disordered monolayer of particles

Microwave Reflectivity From Gold Sputtered Nanolayer

Reflection from a Gold Sputtered Thin Layer

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