Coherent and incoherent reflection and transmission of multilayer structures

Harbecke, B.

doi:10.1007/bf00697414

Cited by 301 publications

(123 citation statements)

References 4 publications

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“…[27][28][29][30] This method allows calculation of the complex-amplitude reflection and transmission coefficients ͑r and t͒ for a pile of faced absorbent layers. The main goal of the procedure is that it is able to eliminate the interference fringes of thick layers from the concept of the coherent and incoherent multiple reflections within the layers.…”

Section: Geometrical Effects In Layered Systems: Simulation Analysismentioning

confidence: 99%

“…However, for p polarization there are additional terms dependent on Im͑Ϫ1/⑀͒ so, other maxima or minima occur in T pol p and R pol p when Im͑Ϫ1/⑀͒ is in its maximum, i.e., at the zeros of the complex dielectric function that are related to the LO modes. 5,27,32 Both LO and TO modes are affected by angular factors. If, for simplicity, we take the substrate as the vacuum, the angular dependence of the intensity of the LO and TO modes in T pol p is TOϰcos ␣ and LOϰ͑sin ␣͒ 2 /cos ␣.…”

Section: ͑16͒mentioning

confidence: 99%

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Analysis of geometrical effects on the behavior of transverse and longitudinal modes of amorphous silicon compounds

Moreno

Garrido

Samitier

et al. 1997

Journal of Applied Physics

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The peak frequency, width, and shape of the transverse-optical ͑TO͒ and longitudinal-optical ͑LO͒ infrared absorption modes of silicon oxides ͑SiO 2 , SiO x ͒, silicon nitrides ͑Si 3 N 4 , SiN x ͒, silicon oxynitrides ͑SiO x N y ͒, and other silicon compounds have often been connected with stress, stoichiometry, defects, structural order, and other properties of the layers. However, certain geometrical effects strongly influence the spectral response of the material independent of its physical or structural properties. The influence of layer thickness, multilayer configuration, substrate effects, angles, and polarization on the behavior of TO and LO bands are presented and discussed. Some corrections are suggested to reduce experimental error and for the reliable measurement of stress, composition, disorder, and structure.

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Section: Geometrical Effects In Layered Systems: Simulation Analysismentioning

confidence: 99%

Section: ͑16͒mentioning

confidence: 99%

Analysis of geometrical effects on the behavior of transverse and longitudinal modes of amorphous silicon compounds

Moreno

Garrido

Samitier

et al. 1997

Journal of Applied Physics

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“…Within the most frequent definition (Harbecke 1986, Pfrommer 1995) the transfer matrix ( ) relates external ( -front) and internal ( -back) irradiance ( ) and radiosity ( ) as ( , ) = ( , ) , where superscript t indicates the transpose matrix. Solar irradiance incidence defines the external side of the glazing.…”

Section: Summary Of the Model (Operational Aspects)mentioning

confidence: 99%

“…The propagation of solar radiation through complex optical systems with planoparallel optical interfaces has been previously studied by Baenas and Machado (2009), with a basis on the classical transfer matrix methods (Harbecke 1986, Maestre 2000, Pfrommer et al 1995, Van Nijnatten 1994. The physical description is based on irradiance -incoming energy flux -and radiosity -outcoming energy flux -under the approximation of incoherent superposition of radiation waves, due to the fact that radiation wavelengths are negligible with respect to thickness in the case of glass substrates.…”

Section: Introductionmentioning

confidence: 99%

Optical model for multilayer glazing systems: Application to laminated glass and photovoltaic modules

Baenas

Machado

2016

Solar Energy

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This article provides theoretical developments broadening the scope of previous optical simulation models for multilayer glazing systems. The applicability of existing models will be extended through additional characterization of the multilayer optical components from global spectrophotometric (UV-Vis-NIR) measurements. A more complete interlayer film characterization, including reflectivity in the film-glass interface, will be provided. Singular solutions of the related equation systems will be derived for situations involving components with very low or null transmissivity. As a contribution to the fundamentals of the formalism, the condition relating the symmetry of the transmittance of the system with the symmetry of the transmissivity of its optical components will be studied. Finally, with the extension for the calculation of energy fluxes through the components of a multilayer system, analytical expressions for the components absorptivity will be derived. These results are particularly useful to quantify differences in energy absorption of the constituents of a laminated glass, as a tool to define, from the glazing design phase, the thermal and mechanical processing needed for each glazing component. Additionally, the model provides a procedure for the calculation of the absorptivity of encapsulated photovoltaic cells, which is directly related to cell efficiency in each particular configuration.

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“…In the first step, for the optical study of excitation in multilayered materials we have used the approach of Harbecke, 20 which we have extensively developed and previously used in the study of vibrational spectra of multilayered systems. 21 This method allows the calculation of the complex-amplitude reflection and transmission coefficients ͑r and t͒ for a stack of planar absorbent layers.…”

Section: Simulation Of Optical Modulation Effects On Si-nc Pl Spementioning

confidence: 99%

Optical-geometrical effects on the photoluminescence spectra of Si nanocrystals embedded in SiO2

Ferré

Garrido

Pellegrino

et al. 2005

Journal of Applied Physics

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We demonstrate that thickness, optical constants, and details of the multilayer stack, together with the detection setting, strongly influence the photoluminescence spectra of Si nanocrystals embedded in SiO 2 . Due to multiple reflections of the visible light against the opaque silicon substrate, an interference pattern is built inside the oxide layer, which is responsible for the modifications in the measured spectra. This interference effect is complicated by the depth dependence of ͑i͒ the intensity of the excitation laser and ͑ii͒ the concentration of the emitting nanocrystals. These variations can give rise to apparent features in the recorded spectra, such as peak shifts, satellite shoulders, and even splittings, which can be mistaken as intrinsic material features. Thus, they can give rise to an erroneous attribution of optical bands or estimate of the average particle size, while they are only optical-geometrical artifacts. We have analyzed these effects as a function of material composition ͑Si excess fraction͒ and thickness, and also evaluated how the geometry of the detection setup affects the measurements. To correct the experimental photoluminescence spectra and extract the true spectral shape of the emission from Si nanocrystals, we have developed an algorithm based on a modulation function, which depends on both the multilayer sequence and the experimental configuration. This procedure can be easily extended to other heterogeneous systems.

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Coherent and incoherent reflection and transmission of multilayer structures

Cited by 301 publications

References 4 publications

Analysis of geometrical effects on the behavior of transverse and longitudinal modes of amorphous silicon compounds

Analysis of geometrical effects on the behavior of transverse and longitudinal modes of amorphous silicon compounds

Optical model for multilayer glazing systems: Application to laminated glass and photovoltaic modules

Optical-geometrical effects on the photoluminescence spectra of Si nanocrystals embedded in SiO2

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