KR20110007969A - Simulation of electromagnetic wave propagation - Google Patents

Abstract

PURPOSE: An electromagnetic wave propagation simulation method is provided to calculate an electromagnetic wave which is emitted to a part by using a calculator. CONSTITUTION: An aggregate is composed of a media including a plurality of particles. An electromagnetic wave is emitted to the aggregate. An electromagnetic wave propagation simulation method calculates an electromagnetic wave conduct. A method uses a FDTD method and a radiative transfer equation. The radiative transfer equation is a radiative transfer equation of at least 4 speed of light.

Description

Simulation method of electromagnetic wave {SIMULATION OF ELECTROMAGNETIC WAVE PROPAGATION}

The present invention relates to an electromagnetic wave propagation simulation method for calculating, by a calculator, the behavior when electromagnetic waves are incident on a medium containing a large number of particles.

The electromagnetic wave propagation simulation method which calculates the behavior of the light in the case of electromagnetic wave incident in the medium containing a large number of particles using a calculator includes the design of a diffuser plate, a color filter, a color filter, ink, paint, plastic, dyeing, etc. It is useful for the design of various measuring devices in the coloring industry, remote sensing, meteorological science, or medical field.

In particular, since the liquid crystal display is provided with a diffusion plate and a color filter, and the color filter is formed by dispersing pigment particles in a medium made of a transparent resin, a pigment when light is irradiated in a resin medium containing a plurality of pigment particles. It was required to calculate the behavior of light such as scattering, diffraction and absorption of light by particles using a calculator to obtain data for designing a diffuser plate or color filter that is optimal for display.

In the electromagnetic wave propagation simulation method which calculates the behavior when the electromagnetic wave enters into the medium containing a large number of particle | grains using a calculator, the simulation by the scattering (Mie) has conventionally been performed. However, calculation was not possible when the particle concentration in the medium was large or when the thickness of the medium was large or one multiple scattering could not be ignored.

Therefore, the simulation method by the MOM method (Moment method) which calculates a statistical mean with respect to the position and the attribute of the particle disperse | distributed statistically previously is proposed (for example, the nonpatent literature 1 " Monte Carlo Simulation of Electromagnetic Wave Propagation in Dense Random Media with Dielectric Spheroids '', IEICE Trans. Electron., Vol.E83-C, No.12, December 2000, p1797-1801 The precision when it applied to this large particle was inadequate.

In addition, there is a radiative transfer (RT method) as a calculation method of multiple scattering. It is a method of calculating the electromagnetic wave propagation characteristics of a target space by expressing the scattering characteristics of individual scattering particles or the minute regions of the space as a phase function. In the case where the scattering particles are spherical, a phase function can be obtained using a Mie formula or the like, but there is a problem that the application becomes difficult due to an error in the case of non-spherical particles, aggregates or nonuniformity of distribution.

Accordingly, an object of the present invention is an electromagnetic wave propagation simulation method which calculates, using a calculator, electromagnetic wave behavior when an electromagnetic wave is incident on an aggregate comprising a plurality of particles, and when the particles are non-spherical, particles are aggregated. It is an object of the present invention to provide a new electromagnetic wave propagation simulation method that can be simulated even if the distribution is unevenly distributed.

MEANS TO SOLVE THE PROBLEM In order to solve the said subject, as a result of continuing earnest examination about the electromagnetic wave propagation simulation method which calculates the behavior when the electromagnetic wave enters in the medium containing a large number of particle | grains using a calculator, the specific multiple calculation is carried out. By assembling the method into the simulation, it has been found that when the particles are non-spherical, it becomes an electromagnetic wave propagation simulation method that can be simulated even when the particles are aggregated or are unevenly distributed, thereby completing the present invention. That is, this invention provides the invention of following <1>-<5>.

<1>

An electromagnetic wave propagation simulation method for calculating electromagnetic wave behavior when an electromagnetic wave is incident on an aggregate comprising a plurality of particles by using a calculator, wherein the electromagnetic wave is incident on an aggregate in which particles are randomly distributed according to a certain rule. Electromagnetic propagation simulation method that calculates electromagnetic behavior using FDTD method and radiation transfer equation.

<2>

The electromagnetic wave propagation simulation method according to <1>, wherein the radiation transfer equation is a radiation transfer equation of 4 light beams or more.

<3>

The electromagnetic wave propagation simulation method according to <1> or <2>, wherein the space to be calculated has a constant thickness and is a flat plate of infinite width.

<4>

The electromagnetic wave propagation simulation method in any one of <1>-<3> whose incident wave is an electromagnetic wave with low coherence.

<5>

An electromagnetic wave propagation simulation method for calculating electromagnetic wave behavior when an electromagnetic wave enters an aggregate comprising a plurality of particles by using a calculator, wherein the scattering characteristics of the aggregate in which particles are randomly distributed according to a certain rule are determined by the FDTD method. A computer readable recording medium having stored therein a program for executing electromagnetic wave simulations, wherein the electromagnetic wave propagation characteristics of a space in which a plurality of the aggregates exist are calculated by a radiation transfer equation using the scattering characteristics of the aggregates.

According to the present invention, when the electromagnetic wave propagation simulation is performed by using a calculator to calculate the behavior when an electromagnetic wave enters an aggregate comprising a plurality of particles, the particles are agglomerated or non-uniform. Simulation is possible even in the case of distribution, and simulation is possible within a realistic time range even when the particle concentration in the medium is high. In particular, the behavior of reflection, transmission, absorption, scattering, etc. of electromagnetic waves when the size and shape of particles are arbitrarily set can be simulated even if the electromagnetic waves are coherent or not coherent. Therefore, it can be used for the design of optical members such as color filters for display and diffusion plates, notch filters having absorption or transmission performance in a narrow wavelength range, and novel optical members having special optical performance, and also remote sensing. In addition, the present invention is very useful industrially because it can be applied to measurement and inspection related to medical care.

BRIEF DESCRIPTION OF THE DRAWINGS Fig. 1 shows a model in which spherical silver particles having a radius of 10 nm are randomly distributed using a Monte Carlo method to form clusters having a radius of 100 nm in a medium having a refractive index of 1.5 nm.
FIG. 2 is a diagram showing results of change according to the wavelength of absorbance cross-sectional area and scattering cross-sectional area in Example 1, which was simulated by the method of the present invention with a model in which a spherical silver particle having a radius of 10 nm formed a cluster. FIG. .
FIG. 3 is a diagram illustrating a model in which columnar silver particles having a radius of 10 nm and a height of 30 nm form clusters according to the wavelength of absorbing cross-sectional area and scattering cross-sectional area. A diagram showing the change result.
FIG. 4 is a graph showing the light absorption cross-sectional area and scattering cross-sectional area in Example 3, which is simulated by the method of the present invention in a model in which columnar silver particles having a radius of 10 nm and a height of 30 nm form clusters. A diagram showing the change result.
Fig. 5 is a diagram showing the results of change according to the wavelength of the attenuation cross-sectional area and the scattering cross-sectional area in Comparative Example 1, in which a simulation was applied to a spherical silver particle and a cylindrical silver particle by applying a conventional Mie theory.
6 shows that a reflecting plate having a reflectance of 0.8 is present on the side opposite to the incident surface of a 100 μm-thick plate, and the scattered light amount and the absorbed light amount when the incident light is incident perpendicularly to the incident surface of the flat plate are simulated in the method of the present invention. In Example 4 performed by the figure, the figure which shows the result of a change with the wavelength of a scattered light quantity and the absorbed light quantity.
Fig. 7 is a model in which spherical silver particles having a radius of 100 nm are contained in a 3 μm thick plate made of a resin having a refractive index of 1.5, and coherent light and incoherent light are mixed in equal parts. The figure which shows the result of Example 5 which performed the simulation of this invention with respect to the case where the light which entered the said board | substrate perpendicularly | vertically entered.
Fig. 8 is a light in which coherent light and non-coherent light are equally mixed in a model in which a spherical silver particle having a radius of 10 nm forms a cluster in a 3 μm thick plate made of a resin having a refractive index of 1.5. The figure which shows the result of Example 6 which performed the simulation of this invention about the case where it injected perpendicular | vertical to this plate.
Fig. 9 illustrates a model in which columnar silver particles having a radius of 10 nm and a length of 30 nm form clusters in a 3 μm thick plate made of a resin having a refractive index of 1.5. The figure which shows the result of Example 7 which performed the simulation of this invention with respect to the case where the light mixed in equal parts perpendicularly incident on the flat plate.
FIG. 10 is a model in which spherical silver particles having a radius of 100 nm are randomly dispersed so that the concentration of silver particles is 1% by volume on a 3 μm thick plate made of a resin having a refractive index of 1.5. The figure which shows the result of Example 8 which simulated this invention with respect to the two beams whose angle with respect to the repair of the flat plate of the light which non-coherent light was mixed equally is 30.556 degree | times and 70.124 degree | times.
Fig. 11 shows a model in which a randomly distributed model of 10 nm-thick spherical silver particles having a radius of 100 nm is formed using a Monte Carlo method on a flat plate having a refractive index of 1.5 to form a cluster. Fig. 9 shows the results of the ninth example in which the simulation of the present invention was performed with respect to two beams of which angles with respect to the repair of the flat plate of the light mixed with the sex light and the non-coherent light are equal to 30.556 degrees and 70.124 degrees.
FIG. 12 is a model in which randomly distributed circular Monterian particles of 10 nm in diameter and 30 nm in length are formed by resin of refractive index 1.5 using Monte Carlo method to form clusters having a radius of 100 nm. The figure which shows the result of Example 10 which performed simulation of this invention with respect to the two beams of which the angle with respect to the repair of the flat plate of the light which the coherent light and the non-coherent light were mixed equally is 30.556 degree | times and 70.124 degree | times.
It is a schematic block diagram of the calculator for implementing the electromagnetic wave propagation simulation method which concerns on one Embodiment of this invention.

The electromagnetic wave propagation simulation method of the present invention is an electromagnetic wave propagation simulation method for calculating, using a calculator, electromagnetic wave behavior when an electromagnetic wave is incident on an aggregate comprising a plurality of particles, and the particles are randomly distributed according to a certain rule. The electromagnetic behavior when the electromagnetic wave is incident on the aggregated body is calculated using the FDTD method and the radiation transfer equation method.

EMBODIMENT OF THE INVENTION Hereinafter, one Embodiment of this invention is described in detail.

The electromagnetic wave propagation simulation method according to the present embodiment is an electromagnetic wave propagation simulation method calculated using a calculator, the recording medium 11 storing a program P for executing the calculation, and the program P from the recording medium 11. ) Is executed by a computer 10 having a device 12 for reading the program 12, a storage device 13 for temporarily storing a program P or a calculation result, a CPU 14, and an output device 15 (Fig. 13). Reference).

In this embodiment, the model of the aggregate used as a calculation object is created first. In order to distribute the particles randomly in the medium, it is convenient to use the Monte Carlo method. The Monte Carlo method is a method of generating a random number having a predetermined statistical property. In this embodiment, the Monte Carlo method is used to generate particles dispersed in a medium having a predetermined statistical property in a calculation. Coordinates of the particles can be set in the space to be calculated by using a function that generates a random number that is usually used. The predetermined statistical property corresponds to a state in which there is a certain number of particle aggregates at a specific uniformity and at a specific ratio.

In the present embodiment, the particles can be implemented not only in the case of random distribution in the medium but also in the case of distribution according to a certain rule.

The FDTD (Finite Difference Time Domain) method (finite difference time domain method) used in the present embodiment is, for example, the disclosure described in "Analytical Fields and Antennas by the FDTD Method", 1998, Corona Co., Ltd. It is a simulation method that separates the Maxwell equation spatially and temporally, approximates the spatial and temporal derivatives by finite difference, and tracks and calculates the time change of the electromagnetic field.

In addition, the FDTD method can be applied to any structure where infinite assumptions can be made, even in structures where finite size assumptions with irregular boundaries are valid.

Usually, incident light (electromagnetic waves) in any polarization state can be divided into two orthogonal polarization states, namely TM mode and TE mode.

In addition, in the FDTD method used in this embodiment, calculation can be efficiently advanced by using an inductive interpolation method. As for the TE mode in the electromagnetic wave, the first electromagnetic field equation obtained by applying the inductive interpolation method to the wave equation derived from the Maxwell equation is solved by a computer using the inductive relation equation. A second electromagnetic field analysis equation obtained by applying the inductive interpolation method is solved by a computer using an inductive relational equation, and the electromagnetic field in the spatial and temporal division of the FDTD method is calculated based on the electromagnetic field obtained for the TM mode and the TE mode. It is preferable to set it as an aspect (refer Unexamined-Japanese-Patent No. 2009-223669).

In the FDTD method, the following Maxwell equation can be used.

Where μ is the magnetic permeability, E is the field strength, and H is the magnetic field strength.

Is the derivative operator,

And

And

When is taken as the unit vector of the x-axis direction and the y-axis direction and the z-axis direction,

Differential operator defined by.

D in the equation (2) represents the flux density and is given by the following equation.

Ε in Equation 4 is the permittivity of the object (particle) to be calculated.

The FDTD method used in this embodiment is a three-dimensional extension of the FDTD method for the TM mode described in Japanese Patent Application No. 2008-68139 (Japanese Patent Laid-Open No. 2009-223669).

Using the electromagnetic field calculated by the FDTD method, the value of the electromagnetic field at a point far from the particle is calculated using a far-field transformation method.

The value of the far field electromagnetic field is calculated using Equation 5.

(Equation 5) represents the intensity of any one of x, y, and z components of the electromagnetic field. The letter F at the bottom represents the infinite origin (far field). The integral region is the isolated surface S surrounding the scatterer.

Is the unit vector of the outward direction of the normal at each point on S.

Radiative transfer theory used in the present embodiment is a relational equation in which the total amount of reflected, scattered, absorbed, and transmitted light coincides with the amount of absorption (damping) when incident light interacts with the medium or particles. Calculation method using Radiation transfer equations or RTEs derived from the theory are calculations of electromagnetic wave energy propagation in a medium in which particles are distributed, and are capable of handling coherent light, partially coherent light, and diffused light (non-coherent light). It is a calculation. In addition, the calculation method using RTE is RT method. Electromagnetic energy is calculated as the luminous flux. The luminous flux is related to the intensity or illuminance of the light. If the incident light is fully diffused light, it can be calculated using the two-beam RTE as the luminous flux integrated with the output. When the incident light is partially coherent light, the RTE of four light beams and N light beams (4? N) is used. N of the N light beams RTE corresponds to N channels set in the propagation direction. Each channel is typically defined for polar angles θ and azimuth angles φ (see PSMufgett and LWRichards, Multiple Scattering Calculations for Technology, Applied Optics, vol. 10, No. 7, 1971, pp 1485). .

The basic formula of RTE represents the law of energy conservation at any point in the medium.

The distance gradient of the coherent light beam is given by Equation 6.

K in Equation 6 is an absorption rate. K is the absorption rate relative to the sum of the absorption of the medium and the particles. Equation 6 indicates that light is lost from the propagation channel by absorption and scattering of the coherent light flux. The distance gradient of the diffused light flux is represented by equation (7).

The absorption rate K _d in equation (7) relates to the absorption loss of the diffused light flux. S _d is related to the scattering loss of the diffused light flux. S _{d +} f _d indicates that diffused light propagating through another channel is scattered and enters the propagation channel of the target. S _c f _c is the portion scattered from the coherent light channel and entering the diffusion channel. That is, the second term at the back of Equation 7 represents the gain of the diffused light flux. All coefficients of K and S described in Equation 7 can be calculated from the absorption and scattering cross-sectional area and the phase function of the particles. The phase function is the amplitude of the scattering wave field. For spherical particles, the phase function can be calculated from the Mie theory, but for any shaped particles other than spherical, they cannot be derived from the Mie theory. In this embodiment, the absorption cross-sectional area, scattering cross-sectional area, and phase function of arbitrary shaped particles (including aggregated particles) can be calculated using the FDTD method (applied far field conversion method).

Absorption rate K and scattering rate S used in Equations 6 and 7 relate to the absorption and scattering cross-sectional area of one particle. If the incident light is diffuse light, K and S are represented as follows (P. Kubelka, "New contributions to the optics of intensely light-scattering materials.Part I", Journal of Optical Society of America, vol. 38, no. .5, 1948, p. 448.].

Where C _abs is the absorption cross-section and C _scat is the scattering cross-section. In this case, the luminous flux is not divided by the viewing angle, and the calculation method corresponds to the RT method or the Kubelka-Munk method of the two luminous fluxes in the reciprocating direction in one dimension.

In the two-beam method, the reflectance R and the transmittance T are given by the following expressions (10) and (11).

Where d is the thickness of the diffusing plate, ρ _g is the reflectance of the back of the diffusing plate, and a and b are given next.

K and S can be calculated from Equations 8 and 9, respectively.

For fully spherical particles, C _abs and C _scat can be calculated by Mie theory. However, for any type of particle or particle aggregate, C _abs and C _scat cannot make analytical calculations. In the present embodiment, numerical values of C _abs and C _scat are calculated using the FDTD method. That is, C _abs and C _scat and extinction cross-section C _ext are obtained from the following equation (CF Bohren, DR Huffman, "Absorption and scattering of light by small particles", Wiley-VCH Verlag GmbH & Co. KGaA, 2004, Weinheim, Chap. 3-4.].

Are the polar and azimuth angles, respectively. Ψ ₀ used in equations (14) and (15) results from the following equation.

Ψ _F in Equation 16 is calculated using Equation 5. Ψ _i is the field strength of incident light. Absorption cross-sectional area C _abs is obtained by equation (17).

The RTE can be executed for more than two fluxes by setting a plurality of propagation channels. The scattering rates S and S _{d ±} are determined by the scattering cross section C _scat and the phase function. The phase function is the amplitude of the scattering field in any direction. If the phase function is developed using the Regendre polynomial, the coefficient of each term can be calculated as follows.

here,

는 1차 계수이고, p(θ)는 위상 함수이며, P_i는 1차 르장드르 다항식을 나타낸다. p(θ)는 어떤 상태에 따라서 미(Mie) 이론 또는 FDTD 방법을 이용하여 계산할 수 있다.

Is the first order coefficient, p (θ) is the phase function, and P _i represents the first order genre polynomial. p (θ) can be calculated using Mie theory or FDTD method depending on the state.

In this embodiment, it is preferable to use combining the three calculation methods of FDTD method, Monte Carlo method, and RTE method.

In addition, in the RTE method, it is preferable to use the RTE method of four or more luminous fluxes because it is suitable for the simulation when coherent light is included. The number of light beams is usually 4 or more and 12 or less, and the case of 4 and 6 is particularly preferable because the calculation speed is fast.

In the present embodiment, the particles to be simulated can be arbitrarily set in shape. As particle shape, it can be set to arbitrary shapes, for example, spherical shape, columnar shape, foot shape, polyhedron other than footnote, flaky shape, donut shape, and hollow columnar shape. Moreover, when some 2 particle | grains are associated, it can set also when particle | grains aggregate. In addition, when the shape and substance of particle | grains are mixed 2 or more types, when there is distribution in a size, it can set also when there exists a bias in particle distribution in a medium.

Moreover, it can set also when the particle | grain density | concentration in a medium turns into high density | concentration of 5 volume% or more. This embodiment can be preferably applied when the particle concentration in the medium is 5 to 90% by volume, more preferably 5 to 50% by volume, and even more preferably when 6 to 20% by volume. Can be.

In the present embodiment, the medium to be simulated can be set in any of vacuum, air, water, organic solvent, solution, glass, and resin by setting light transmittance and refractive index as constants as long as the medium passes through light and is uniform. Can be. The present invention can be suitably applied particularly in the case of using glass or resin which does not cause particle movement as a medium.

In the present embodiment, the aggregate to be calculated in the simulation is a case where the space occupied by the medium and the particles is generally a flat plate, a flat plate having a constant thickness and having an infinite width. The space occupied by the medium and the particles is a flat plate, i.e., the medium and the particles exist in a space existing between two parallel planes at regular intervals.

The light source of the light to be simulated in this embodiment is any one of a laser light source (light source emitting high coherence), a normal light source (light source emitting low coherence), a continuous light source and a pulsed light source. Also, for display design, the present invention can be preferably applied in the case of a continuous light source as a normal light source, and is preferable in the case of a parallel light source, since the calculation is simple.

Next, specific embodiments of the present embodiment will be described.

[1] setting of particle dispersing media

As a medium to be calculated, an appropriate light transmittance (or light absorptivity) and a refractive index are set to represent a uniform and light-transmitting material (including vacuum). A flat plate is set as a medium shape, two parallel surfaces of predetermined intervals corresponding to the flat plate thickness are set, and an infinite space existing therebetween is set as an approximate shape to the flat plate.

The shape of the particles to be dispersed is determined. Appropriate light transmittance (or absorbance) and refractive index are set to represent the material constituting the particles.

As a light source, in order to use for design of a display, the parallel ray of light is normally set.

The particles are distributed at random to a predetermined concentration in the medium by the Monte Carlo method.

[2] running the simulation

Scattering and absorption cross-sectional areas of aggregates in which a plurality of particles are randomly distributed according to certain rules are calculated using the FDTD method.

[3] Calculate the propagation of electromagnetic fields in a medium randomly distributed by a certain set of rules or by radiative transfer equations (or radiative transfer method).

<Examples>

The present invention will be described in more detail with reference to the following Examples, but the present invention is not limited to these Examples.

In the examples, programs written in the PG Fortran 90 language were prepared and calculated using Mathcad (trade name) of Masssoft Engineering & Education Inc. manufactured products.

(Example 1)

A model in which spherical silver particles having a radius of 10 nm were randomly distributed using the Monte Carlo method was formed to form one cluster having a radius of 100 nm in a medium having a refractive index of 1.5. The particle content in the cluster was 50% by volume. An image of this model is shown in FIG. 1. Three figures (FIG. 1 (a), (b), (c)) of FIG. 1 show the cross section by XY plane, YZ plane, and XZ plane in order from the left side.

With respect to the model of the aggregate, the incident light was completely scattered light (light completely incoherent), and the amount of scattered light and the amount of absorbed light when the wavelength of the incident light was changed from 400 nm to 700 nm at 20 nm intervals was calculated. The scattering and absorption of light were calculated by Kubelka-Munk method, which is a 2-beam RT method. Scattering and absorption cross sections were calculated using a combination of three-dimensional FDTD and far field transformations. Far field conversion is a calculation method for knowing an electromagnetic field at a point far from a particle. The calculation result is shown in FIG.

Spherical silver particles with a radius of 10 nm, which are much smaller than the wavelength of light, can be inferred to have small interactions with light and less scattering or absorption if they do not form clusters. When dispersed to produce an aggregate, silver particles aggregate to form clusters. This model is a model of its actual aggregate. As a result of the simulation by the method of the present invention, when the concentration is high and close to the actual formation of the cluster, a considerable amount of scattering and absorption occurs, and the shorter the light wavelength, the larger the amount of scattered light and the absorbed light. Thus, it has been found that the simulation method of the present invention can accurately simulate the actual situation.

(Example 2)

A model in which columnar silver particles having a radius of 10 nm and a height of 30 nm was randomly distributed using the Monte Carlo method was formed so as to form one cluster having a radius of 100 nm in a medium having a refractive index of 1.5. The direction of the columnar particles was arranged in a direction perpendicular to the plane in which the axis of the circumference was perpendicular to the advancing direction of the incident light and perpendicular to the polarization direction. The particle content in the cluster was 50% by volume.

Using the model of the aggregate, the amount of scattered light and the amount of absorbed light when the wavelength of incident light was changed at intervals of 20 nm from 400 nm to 700 nm in the same manner as in Example 1 were calculated. The results are shown in FIG.

Cylindrical silver particles with a radius of 10 nm and a height of 30 nm, which are much smaller than the wavelength of light, can be inferred to have little interaction with light and less scattering or absorption if they do not form clusters. When particles are dispersed in a medium at high concentration to prepare an aggregate, silver particles aggregate to form clusters. This model is a model of its actual aggregate. As a result of the simulation by the method of the present invention, when the concentration is high and close to the actual formation of the cluster, a considerable amount of scattering and absorption occurs, and the shorter the light wavelength, the larger the amount of scattered light and the absorbed light. Thus, it has been found that the simulation method of the present invention can accurately simulate the actual situation.

(Example 3)

In the same manner as in Example 2, the model of the aggregate was created so that the axis of the circumference was perpendicular to the plane perpendicular to the advancing direction of the incident light and arranged in a direction parallel to the polarization direction. Using this model, the amount of scattered light and the amount of absorbed light when the wavelength of incident light was changed at intervals of 20 nm from 400 nm to 700 nm in the same manner as in Example 1 was calculated. The results are shown in FIG.

As in Example 2, a considerable amount of scattering and absorption occurred, and the shorter the light wavelength, the larger the amount of scattered light and the absorbed light. Thus, as in Example 2, it was found that the simulation method of the present invention can accurately simulate the actual situation.

(Comparative Example 1)

For the same aggregate model as in Example 1, the incident light is completely scattered (when completely incoherent) by applying the conventional Mie theory, and the wavelength of the incident light is spaced at 20 nm intervals from 400 nm to 700 nm. The amount of scattered light and the amount of absorbed light at the time of change were calculated. In the Mie calculation, since the scattering characteristics of the clusters composed of the particle aggregates cannot be calculated, the clusters having a radius of 100 nm were replaced with homogeneous equivalent particles. The radius of the equivalent particle was 79 nm. The results are shown in FIG.

It was found that the amount of scattered light and the amount of absorbed light also generated a large peak around 420 nm and it was impossible to accurately simulate the actual situation.

(Example 4)

Spherical silver particles having a radius of 10 nm were randomly distributed using a Monte Carlo method to form a cluster having a radius of 100 nm in a medium having a refractive index of 1.5 μm on a flat plate having a thickness of 1,000 μm. The model and a model in which columnar silver particles having a radius of 10 nm and a height of 30 nm were randomly distributed using the Monte Carlo method to form one cluster having a radius of 100 nm in a medium having a refractive index of 1.5 in the same manner as in Example 2. And three models of models in which spherical silver particles having a radius of 10 nm were randomly distributed using the Monte Carlo method without forming clusters in a medium having a refractive index of 1.5. It is assumed that a reflecting plate with a reflectance of 0.8 exists on the side opposite to the plane of incidence of the flat plate, and the amount of scattered light and the amount of absorbed light when the incident light enters the plane of incidence of the flat plate are calculated.

The incident light was completely scattered (when completely incoherent), and the amount of scattered light and the absorbed light when the wavelength of the incident light was changed from 400 nm to 700 nm was calculated by the Kubelka-Munk method, which is a 2-beam RT method. . Scattering and absorption cross sections were calculated using a combination of three-dimensional FDTD and far field transformations. Simulation results are shown in FIG. 6.

Spherical silver particles with a radius of 10 nm, which are much smaller than the wavelength of light, and columnar silver particles with a radius of 10 nm and a height of 30 nm, have little interaction with light and little scattering or absorption in the absence of clusters. 6 (r), when the concentration is high and close to the reality of forming clusters, the amount of scattered light and absorption is greater in the case of columnar particles (r_cyl in FIG. 6) than in the case of spherical particles (r_sph in FIG. 6). It was found that the amount of light increased.

(Example 5)

The cross-sectional area and phase function of spherical silver particles having a radius of 100 nm were calculated by Mie theory on a 3 μm thick plate made of a resin having a refractive index of 1.5, and coherent light and non-coherent light were mixed in equal parts. The reflectance and transmittance at the time of the incident light perpendicularly to the flat plate were calculated. The density | concentration of silver particle was made into low density | concentration as 1 volume%. The calculation used the RTE of 4 beams which handles electromagnetic waves (light) propagating in one direction and the opposite direction with respect to coherent light and incoherent light.

The results according to wavelengths of the coherent light transmittance, the coherent light reflectance, the non-coherent light transmittance, and the non-coherent light reflectance in the wavelength range of 400 to 700 nm are calculated and shown in FIG. 7. In FIG. 7, the coherent light transmittance is indicated by "x", the coherent light reflectance is indicated by the dotted line "...", the non-coherent light transmittance is indicated by the dashed-dotted line "-...-", and is incoherent. Light reflectance is a solid line ”.

Coherent Luminance Incoherent luminous intensity and transmittance showed little change with wavelength and low values, and much light was reflected or absorbed. The coherent light reflectance was about 4%, and the incoherent light reflectance increased with the wavelength. The coherent light reflectance of 4% is caused by Fresnel reflection of most interfaces.

(Example 6)

Spherical silver particles having a radius of 10 nm were randomly distributed by using the Monte Carlo method to form a cluster having a radius of 100 nm in a flat plate having a thickness of 3 μm made of a resin having a refractive index of 1.5 nm. , The model which distributed a plurality of clusters in the flat plate was created so that the particle concentration in a flat plate might be 1 volume%. The reflectance and transmittance were calculated when the light in which the coherent light and the non-coherent light were equally mixed is incident perpendicularly to the flat plate. In calculation, similarly to Example 5, an RTE of 4 beams was used together with the FDTD method.

The change according to the wavelength of the coherent light transmittance, the coherent light reflectance, the non-coherent light transmittance, and the non-coherent light reflectance in the wavelength range of 400 to 700 nm is calculated and shown in FIG. 8. In FIG. 8, the coherent light transmittance is indicated by "x", the coherent light reflectance is indicated by the dotted line "...", the non-coherent light transmittance is indicated by the dashed-dotted line "-...-," Light reflectance is a solid line ”.

Incoherent Light Incoherence, Transmittance, and Reflectance Even though the change of wavelength is small, the incoherent light has a high transmittance, and then the incoherent light reflectance is high, and the coherent light transmittance and the coherent light are high. The reflectance was lowered. The propagation behavior of the electromagnetic wave was completely different from that of the flat plate in which the 100 nm silver particles in Example 5 were dispersed without forming clusters. Also in the actual flat plate, it was found that the propagation behavior of the light was completely different in the case where the pigments formed clusters and uniformly dispersed.

(Example 7)

The same model as in Example 6 was created except that the silver particles were columnar with a radius of 10 nm and a length of 30 nm. The same calculations as in Example 6 were performed, and the results are shown in FIG. The line of FIG. 9 showed the same thing as FIG. 8 of Example 6. FIG.

Similar results as in Example 6 were obtained, but the non-interfering reflectance increased as the wavelength became longer.

(Example 8)

In the same manner as in Example 5, a model in which spherical silver particles having a radius of 100 nm were randomly dispersed by the Monte Carlo method in a flat plate having a refractive index of 1.5 μm so that the concentration of silver particles was 1% by volume was obtained. Created. In the same manner as in Example 5, the light in which the coherent light and the non-coherent light were mixed in equal parts was used. The transmittance was calculated. One luminous flux was calculated for two luminous fluxes of 30.556 degrees and 70.124 degrees with a range of ± 20 degrees. In the calculation, an RTE of 6 beams that handles electromagnetic waves (light) propagated in one direction and opposite directions of each of the two beams with respect to the coherent light and the non-coherent light was used together with the FDTD method.

Since the light propagated in the medium is totally reflected by being incident on the light emitting slope at an angle of 70.124 degrees with respect to its normal, the calculation result is shown in FIG. 10 only for the channel 1 of 30.556 degrees.

It was found that the transmittance was low and most of the light was reflected or absorbed. The wavelength dependence of the reflectance was small.

(Example 9)

The flat plate model was the same as in Example 6, and randomly distributed using the Monte Carlo method to form clusters having a radius of 100 nm in spherical silver particles having a radius of 10 nm in a 3 μm thick plate made of a resin having a refractive index of 1.5. It was set as a model. About the propagation channel of light, reflectance and transmittance were computed similarly to Example 8. In calculation, the RTE of 6 beams was used similarly to Example 8 with the FDTD method.

Since the light propagated in the medium is totally reflected by entering the light exit surface at an angle of 70.124 degrees with respect to its normal, the calculation result is shown in FIG. 11 only for the channel 1 of 30.556 degrees.

It was found that the transmittance was low and most of the light was reflected or absorbed. The wavelength dependence of the reflectance was small and lower than the case where 100 nm silver particles were uniformly dispersed.

(Example 10)

The flat plate model was the same as that of Example 7, and the model similar to Example 6 was produced except having the columnar shape of a radius of 10 nm and a length of 30 nm. About the propagation channel of light, reflectance and transmittance were computed similarly to Example 8. In calculation, the RTE of 6 beams was used similarly to Example 8 with the FDTD method.

Since the light incident at an angle of 70.124 degrees with respect to the repair of the surface of the flat plate is totally reflected, the calculation result is shown in FIG. 12 only for the channel 1 of 30.556 degrees.

It was found that the transmittance was low and most of the light was reflected or absorbed. The wavelength dependence of the reflectance was small and lower than the case where the 100 nm silver particles were uniformly dispersed, so that there was no significant difference from the case where the silver particles were spherical.

Claims (5)

An electromagnetic wave propagation simulation method for calculating electromagnetic wave behavior when an electromagnetic wave is incident on an aggregate comprising a plurality of particles by using a calculator, wherein the electromagnetic wave is incident on an aggregate in which particles are randomly distributed according to a certain rule. Electromagnetic propagation simulation method that calculates electromagnetic wave behavior using Finite Difference Time Domain (FDTD) and Radiative Transfer Equation. The electromagnetic wave propagation simulation method according to claim 1, wherein the radiation transfer equation is a radiation transfer equation of at least four light beams. The electromagnetic wave propagation simulation method according to claim 1 or 2, wherein the space to be calculated is a flat plate having a constant thickness and of infinite width. The electromagnetic wave propagation simulation method according to claim 1, wherein the incident wave is an electromagnetic wave having low coherence. An electromagnetic wave propagation simulation method for calculating electromagnetic wave behavior when an electromagnetic wave enters an aggregate comprising a plurality of particles by using a calculator, wherein the scattering characteristics of the aggregate in which particles are distributed randomly or according to a certain rule are calculated using the FDTD method ( A program for performing electromagnetic wave propagation simulation, which is obtained by Finite Difference Time Domain and calculates the electromagnetic wave propagation characteristics of the space where a large number of the aggregates exist by using the scattering characteristic of the aggregates. A computer readable recording medium that has been stored.

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