Multilayer four-flux matrix model accounting for directional-diffuse light transfers

Simonot, Lionel; Hersch, Roger D.; Hébert, Mathieu; Mazauric, Serge

doi:10.1364/ao.55.000027

Cited by 25 publications

(14 citation statements)

References 43 publications

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“…The extension of the model to halftone layered materials is therefore the next challenge to address. The four-flux approach [19][20][21], which relies on two directional fluxes and two diffuse fluxes and has been recently formulated with a similar transfer matrix formalism [22] as the one recalled in this paper, is promising since it could enable the combination of the directional and diffused flux propagation through the partly-diffusing and partly-nonscattering layers.…”

Section: Discussionmentioning

confidence: 99%

Assessing the capacity of two-flux models to predict the spectral properties of layered materials

Hébert¹,

Mazauric²,

Simonot³

2016

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A classical way of coloring a surface in order to create a still image is the application of a colored coating. The more recent digital printing systems enable depositing thick coatings or successive ink layers. The color rendering of the surface depends on the optical properties of the coated materials (optical index, spectral scattering and absorption coefficients) and their thickness. In order to predict its spectral reflectance as a function of these parameters, the so-called two-flux approach is to be tested in first since the model is simple and relies on analytical equations. It has a good chance to provide accurate predictions for coatings made of solid layers of strongly scattering or nonscattering media, or even complex stratified coatings obtained by stacking nonsymmetrical components such as printed films. The generalized Kubelka-Munk model summarized in this paper enables treating all these configurations with a unified mathematical formalism. But it has limitations and may provide poor color predictions for certain types of layered materials. We therefore propose a simple method based on parameters of the model to check the precision of the two-flux model for a given type of coating. 0

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Section: Discussionmentioning

confidence: 99%

Assessing the capacity of two-flux models to predict the spectral properties of layered materials

Hébert¹,

Mazauric²,

Simonot³

2016

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“…Applying boundary conditions, in a similar way, for other interfaces we can express the forward and backward wave amplitudes at the output port of the structure in terms of its counterpart at the input port as follows [26][27][28][29]:…”

Section: Figmentioning

confidence: 99%

Highly amplified light transmission in a parity-time symmetric multilayered structure

Deka

Sarma

2018

Appl. Opt.

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We propose a parity-time symmetric dielectric-nanofilm-dielectric multilayered structure that could facilitate highly amplified transmission of optical power in the infrared spectrum. We have theoretically studied our model using the transfer matrix formalism. The reflection and the transmission coefficients of the S-matrix are evaluated. The theoretical results are validated by FDTD numerical simulation. We have shown how the thickness of the layers and the gain/loss coefficient of the active layers could generate spectral singularities in the S-matrix and how these singularities could be exploited to achieve amplified transmission of a single wavelength through the structure.

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“…A four flux multilayer method has been studied before [25], nevertheless in that article the propagation phase matrix was not explicitly done, only continuous equations where presented. Therefore the aim of this section is to present explicitly the matrix formalism for an arbitrary number of layers (a similar approach was used by Simonot et al [31], also at the time of writing another multilayer 4 flux approach was published [32]). Let us assume a system of slabs as presented in diagram figure 2, where the number of layers increases in the z-axis direction; interfaces are labelled as follows: increasing along the z direction, the first interface of each layer is labelled with 0 and the ending interface with Z.…”

Section: Multilayer Formalismmentioning

confidence: 99%

Extending the applicability of the four-flux radiative transfer method

et al. 2017

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A generalized four-flux method capable of modeling and tuning the spectral reflectance of a diverse range of complex composite coatings is presented. An example application is exploring and maximizing the visible and near-infrared (IR) spectral reflectance available from the diverse structures arising from combinations of the many practical paint ingredients that are available or can be made when applied to different substrates. This requires consideration of scatterers that can differ in composition, particle size, size distribution, and fill factor, and are held in place by a variety of organic binders, which typically partially absorb in the near IR. This extended model is further enhanced by an explicit matrix algorithm that allows analysis of diverse multilayer stacks. This is applied to a multilayer and is designed to model useful changes that result from varying the pigment fill factor as a function of depth within a layer. What we believe is a novel feature is the way the scattering affects matrix absorptance. The model includes contributions to total absorptance from the scattering pigments and from the paint binder that can arise in different bands or simultaneously at the same wavelengths. Model accuracy is demonstrated by example results when compared to experimental data on dried single layer paint profiles using imaged cross sections. The model input covering the actual pigment and binder properties used are material, shape, size, and size distributions, mass added, and the measured optical constants from 400 nm to 2,500 nm of the undoped binder resin layer. One interesting result is the comparison of a two-layered stack, with bigger particles in the first layer and smaller ones in the second, to one with the opposite depth profile.

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Multilayer four-flux matrix model accounting for directional-diffuse light transfers

Cited by 25 publications

References 43 publications

Assessing the capacity of two-flux models to predict the spectral properties of layered materials

Assessing the capacity of two-flux models to predict the spectral properties of layered materials

Highly amplified light transmission in a parity-time symmetric multilayered structure

Extending the applicability of the four-flux radiative transfer method

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