JP5032178B2 - Wave field analysis method and apparatus, and computer-readable recording medium storing a program for causing a computer to execute the wave field analysis method - Google Patents

Description

  The present invention relates to a wave field analysis method and apparatus, and a computer-readable recording medium on which a program for causing a computer to execute the wave field analysis method is recorded. More specifically, the present invention relates to an FDTD method (Finite Difference Time Domain method). ), A wave field analysis method, a wave field analysis device, and a computer program for executing a wave field analysis method for numerically analyzing the propagation of a wave such as an electromagnetic wave, that is, a temporal change of a wave field such as an electromagnetic field (electromagnetic field). The present invention relates to a computer-readable recording medium on which is recorded.

  In recent years, various optical components such as optical disks, lenses, especially micro lenses, optical communication components such as optical connectors, optical waveguides, optical fibers, antennas, laser devices, microscopes, semiconductor integrated circuits (ICs), piezoelectric elements, structures As a design method of wave analysis in fluids and solids, for example, analyze temporal changes in wave propagation, including electromagnetic waves including light and X-rays, sound waves, and elastic waves. As a simulation method, the FDTD method has been used.

This FDTD method is particularly used as an analysis tool for temporal changes in propagation of electromagnetic waves according to the Maxwell equation. Using this FDTD method, by solving the Maxwell equation numerically with a computer in the target propagation system, that is, in the analysis region, an electromagnetic field propagates in the analysis region, for example, in the air. It is possible to theoretically predict a propagation state that is reflected on the surface of a substance existing in the analysis region to be refracted or refracted and transmitted.
Such logical prediction of the propagation state of electromagnetic waves gives extremely useful information and necessary information for the design of the above-described optical components, optical communication components, various components including antennas, and the like.

An electromagnetic field analysis apparatus and method using such an FDTD method is proposed in Patent Document 1. In this Patent Document 1, an excitation part that generates incident light is set in a part of the analysis region, with an electromagnetic field in the entire analysis region (all spaces) being zero “0” as an initial state. It is disclosed that a continuous wave, a pulse wave, or the like is generated from a part and a time change of an electromagnetic field in an analysis region is calculated by an FDTD method. Also, in Patent Document 1, information on an incident wave is input, the incident wave is calculated based on the input information, and the error of the incident wave is accurately reproduced, and a value including the reproduced error is calculated. It is disclosed that by calculating an electromagnetic field based on the calculated incident wave, an error due to the FDTD method can be canceled and a calculation result without an error due to the FDTD method can be output.

FIG. 12 shows a flowchart of a conventional electromagnetic field analysis method using the FDTD method as disclosed in Patent Document 1. In this example, a calculation model of the FDTD method calculation program used in the conventional electromagnetic field analysis method is set.
First, in step S200, a refractive index spatial distribution is defined for the entire space in the analysis region of the calculation model.
Further, in step S202, the spatial calculation range of this calculation model is set to the entire space of the analysis region (total spatial discretization number: S ₀ ), for example, the spatial discretization number (1 to S ₀ ) of the analysis region (spatial discrete (State and condition), boundary conditions and other analysis areas (state and condition) settings, incident wave (input electromagnetic wave) (state and condition) settings, and other calculation steps (N ₀ ) for electromagnetic field calculation Enter the calculation conditions to set the necessary conditions.
Here, the refractive index spatial distribution definition step S200 and the calculation condition input step S202 may be performed first or simultaneously. Thus, first, before starting the electromagnetic field calculation, it is necessary to define the spatial distribution of the refractive index of the analysis region that is the target of the electromagnetic field calculation in this calculation model and to set the entire space of the analysis region as the spatial calculation range. Calculation conditions are set.

Thereafter, in steps S204 and S206, based on the definition of the spatial distribution of the refractive index of the analysis region and the setting of the necessary calculation conditions, the FDTD method calculation program is used to set the state in which no electromagnetic field is present as the initial state. Maxwell's equations until the time (j = N ₀ ) in which electromagnetic waves from the excitation part defined on the space are incident (j = 1) and the electromagnetic waves propagate through the entire space (i = 1 to S ₀ ) of the analysis space The electromagnetic field is solved numerically by a computer, and the temporal and spatial changes of the electromagnetic field are calculated. That is, each time calculation step (j) is fixed using the FDTD method calculation program based on the electromagnetic field distribution in the entire space (1 to S ₀ ) of the analysis region of the previous calculation step (j-1). and the space calculation range entire space analysis region is (1~S ₀₎ (1~S ₀₎ by calculating the temporal variation of the electromagnetic field, the entire space (1 analysis region of the calculating step (j) S ₀ to seek distribution of electromagnetic field), repeated for all time steps until the electromagnetic wave propagates through the entire space (1 to S ₀₎ of the analysis space (j = 1 to N _0), the entire space of the analysis region ( 1 to S ₀ ) of the electromagnetic field in time and space.

Specifically, for each time calculation step (j), in step S204, based on the distribution of the electromagnetic field in the entire analysis area of the calculation step (j-1) before this time step (j), the FDTD method using the calculation program, it calculates a temporal change of the electromagnetic field for all spatial analysis region (1 to S _0), the distribution of the electromagnetic field of the entire space of the analysis region of the calculating step _(j) (1~S 0) Ask for.
When j-1 is 0 (j-1 = 0), the distribution of the electromagnetic field in the entire analysis region in the previous calculation step (j-1) is set to an initial state, for example, 0. .
Next, in step S206, it is determined whether or not the calculation of the all time calculation step is completed. In the illustrated example, it is determined whether the calculation step is the total time calculation step number N ₀ (j = N ₀ ) or greater than N ₀ (j> N ₀ ). If the calculation of all the calculation steps has been completed (in the illustrated example, if j is equal to or greater than N ₀ (j ≧ N ₀ )), the process proceeds to step S208 as Yes, and post-calculation processing is performed. On the other hand, if the calculation of all the calculation steps is not completed (in the illustrated example, if j is less than N ₀ (j <N ₀ )), S ₀ : j = j + 1 is set, and the process returns to step S 204.

Subsequently, for the calculation step (j + 1), in step S204, based on the distribution of the electromagnetic field in the entire analysis area in the previous calculation step (j), the entire space in the analysis area is similarly calculated using the FDTD method calculation program. (1 to S ₀₎ to calculate the temporal change of the electromagnetic field for, it obtains the distribution of the electromagnetic field of the entire space (1 to S ₀₎ of the analysis region of the calculating step (j + 1), then, in step S206, It is determined whether or not the calculation of all calculation steps is completed (j + 1 ≧ N ₀ ). If not completed (j + 1 <N ₀ ), the process returns to step S204, and the above step S204 is repeated until the calculation of all calculation steps is completed. Steps S206 to S206 are repeated, and if completed (j + 1 ≧ N ₀ ), the process proceeds to step S208 to perform post-calculation processing.

Subsequently, in step S208, as post-calculation processing, a physical quantity corresponding to the analysis purpose is calculated based on the time and spatial distribution of the electromagnetic field thus calculated. In addition, the calculation result is displayed as a graphic on the display of the display device, or is hard-copied to a printer.
Thereafter, in step S210 (END), the electromagnetic field analysis is terminated.
Thus, the electromagnetic field calculation for the electromagnetic wave propagated through the entire analysis area of the calculation model is completed.
In such a conventional electromagnetic field analysis technique, for one calculation model, the calculation of the electromagnetic field in the entire space (1 to S ₀ ) of the analysis region is simply performed in each calculation step (j), that is, all the time calculation steps. (J = 1 to N ₀ ) is performed sequentially.

In addition, changes in waves such as electromagnetic waves propagating at a finite speed according to Maxwell's equations, such as the FDTD method, transmission line matrix method, spatial network method, and finite element time domain method, can be performed sequentially and transiently. A conventional wave analysis method and apparatus using a calculation method of wave data to be calculated is disclosed in Patent Document 2.
In this Patent Document 2, the analysis region is divided into a plurality of blocks, and whether or not the wave data of a predetermined determination discrete point among the discrete points to be calculated in each block is larger than a predetermined value is determined for each block. By determining for each block and calculating the spatial and temporal changes of the wave data of all the discrete points included in the block only for the block where the wave data of the determined discrete point is larger than a predetermined value, It discloses that calculation time can be shortened.
Further, in Patent Document 2, data necessary for calculation of wave data of a calculation target block, that is, wave data of all discrete points included in the block and necessary wave data in the vicinity thereof are stored in the main memory, The wave data of discrete points included in all the blocks are stored in the auxiliary storage unit, and when the calculation of the calculation target block is completed, the calculation result is stored in the auxiliary storage unit, and the other calculation target It is disclosed that the main storage capacity of the computer required for the calculation can be reduced by reading out the data necessary for calculating the wave data of the block from the auxiliary storage means and storing it in the main storage means.

JP 2000-227450 A Japanese Patent Laid-Open No. 9-16548

By the way, in the technique as disclosed in Patent Document 1, as described above, for the propagation model of the electromagnetic wave in the predetermined analysis region, when the time change of the propagation of the electromagnetic wave is sequentially calculated by the FDTD method for each time calculation step, Calculation is performed for the entire analysis area.
For this reason, in any calculation step, that is, regardless of the calculation step, the electromagnetic field of the entire space in the analysis region is calculated, so that there is a problem that the region (space) where the electromagnetic wave at the initial calculation does not reach is also calculated.
Further, in the technique disclosed in Patent Document 2, as described above, the analysis region to be calculated is divided into a plurality of blocks, and only blocks whose wave data at a predetermined point is larger than a predetermined value are calculated. As a result, the amount of calculation can be reduced. However, in this case, it is necessary to check the magnitude of the wave data at a predetermined point in each block and the prescribed value for each block at each calculation step, and there is a problem that a calculation load corresponding to that is generated.

  An object of the present invention is to solve the above-mentioned problems of the prior art and calculate a temporal change of a wave field propagating through an analysis region of one wave analysis model using a wave data calculation method such as the FDTD method. In this case, in the initial stage of wave propagation, that is, in the initial stage of wave field calculation, the amount of calculation while the incident wave does not reach the entire region can be reduced, and the wave field analysis method and apparatus capable of speeding up the calculation Another object of the present invention is to provide a computer-readable recording medium in which a program for causing a computer to execute a wave field analysis method is recorded.

In order to solve the above problems, a first aspect of the present invention, the computer is sequentially performed continuously calculate the wavefield time change of the analysis region the wave propagates from the first period state for each calculation step the computer is a wave field analysis method of the analysis region is the wave to analyze the propagation conditions for propagating the computer, the arrival area of the wave in advance on the analysis area has reached it predict, the computer, the calculation of the time variation of the wave field in a predetermined calculation step, the said calculation step predicted the arrival area was the wave has reached of the calculation the analysis region in step line Ukoto as a spatial calculation range is intended to provide a wave field analysis method according to claim.

Here, it is preferable that the wave propagates in a predetermined axial direction of the analysis region from one end of the analysis region.
Moreover, it is preferable that the arrival region of the wave is predicted by predicting a propagation speed of the wave propagating through the analysis region.
Further, it is preferable that the arrival region of the wave is predicted based on information on a refractive index distribution in the analysis region.
Further, the refractive index distribution in the analysis region has a representative value of the refractive index of the surface orthogonal to the wave propagation direction in the arrival region, and the smallest refractive index in the surface orthogonal to the wave propagation direction. It is preferable that it is obtained by.
Further, it is preferable that the arrival region of the wave is predicted on the assumption that the refractive index in the analysis region is 1.
In addition, it is preferable that the arrival region of the wave is predicted by calculating a propagation length in which the wave propagates from the one end of the analysis region.
The wave is preferably an electromagnetic wave, and the wave field is preferably an electromagnetic field.

  In order to solve the above-mentioned problem, the second aspect of the present invention performs the calculation of the time change of the wave field in the analysis region in which the wave propagates continuously from the initial state for each calculation step, A wave field analyzer for analyzing a propagation state in which the wave propagates in an analysis region, wherein the wave field calculation means calculates a time change of the wave field in the analysis region in which the wave propagates continuously from an initial state. And a prediction means for predicting an arrival area where the wave has reached in the analysis area, and the wave field calculation means in advance calculate the time change of the wave field in a predetermined calculation step. The wave field analysis apparatus is characterized in that the arrival region predicted to have reached the wave in the analysis region reaches the calculation step as a spatial calculation range of the calculation step.

Here, the wave propagates from one end of the analysis region to a predetermined axial direction of the analysis region, and the wave field calculation means changes the time of the wave field along the predetermined axial direction. Is preferably calculated.
Moreover, it is preferable that the said prediction means predicts the said arrival area | region of the said wave by predicting the propagation speed of the said wave which propagates the said analysis area | region.
Moreover, it is preferable that the said prediction means performs the prediction of the said arrival area | region of the said wave based on the information of the refractive index distribution in the said analysis area | region.
Further, the prediction means sets the representative value of the refractive index of the surface orthogonal to the propagation direction of the wave in the arrival region as the smallest refractive index in the surface orthogonal to the propagation direction of the wave. It is preferable to predict the arrival region of the wave based on the obtained refractive index distribution in the analysis region.
Moreover, it is preferable that the said prediction means performs the prediction of the said arrival area | region of the said wave, assuming that the refractive index in the said analysis area | region is 1.
Moreover, it is preferable that the said prediction means performs the prediction of the said arrival area | region of the said wave by calculating the propagation length which the said wave propagates from the said one end of the said analysis area | region.
The wave is preferably an electromagnetic wave, and the wave field is preferably an electromagnetic field.

  In order to solve the above-mentioned problem, a third aspect of the present invention is a computer-readable recording medium in which a program for causing a computer to execute the wave field analysis method of the first aspect is recorded. Is to provide.

According to the present invention, with the above configuration, the temporal change of the wave field propagating through the analysis region of one wave analysis model is calculated for each time calculation step using a wave data calculation method such as the FDTD method. In some cases, in a certain calculation step, the reachable region where the incident wave can reach in the analysis region is calculated in advance, and the spatial calculation range that is the target region for the wave field calculation is changed for each calculation step. By limiting the spatial calculation range for iterative calculation of the field to the reaching region where the incident wave can reach in the time step, the calculation of the wave field in the unreachable region where the incident wave has not reached in the analysis region can be performed. Since it can be omitted, the amount of calculation can be reduced and the calculation speeded up.
Further, according to the present invention, the prediction of the reachable region where the incident wave can reach and the prediction of the unreached region where the incident wave has not reached can be performed simply before calculating the wave field such as the electromagnetic field. Therefore, the load in determining the calculation area for each time calculation step is small.
As a result, according to the present invention, it is possible to enjoy the effect of reducing the amount of calculation and the effect of speeding up the calculation by omitting the calculation of the wave field in the unreached region where the incident wave has not reached in the analysis region.

  Hereinafter, a wave field analysis method and apparatus according to the present invention and a computer-readable recording medium storing a program for causing the computer to execute the wave field analysis method will be described in detail based on preferred embodiments shown in the accompanying drawings. To do.

  The wave field analysis method and apparatus according to the present invention uses one calculation model of a propagation state of a wave such as an electromagnetic wave in an analysis region according to a wave equation such as Maxwell's equation, by using a wave data calculation method such as the FDTD method. When calculating sequentially for each time calculation step, first, all the calculations are performed by calculating in advance the reachable region where the wave propagating in the analysis region can reach from the initial state where the incident wave was incident in a certain calculation step. The reachable region in the step is obtained, and for each calculation step, the spatial calculation range that is the reachable region of the wave field such as the electromagnetic field is changed, and the space calculation range in which the wave field is repeatedly calculated is changed to the time step. In the analysis area, the calculation of the wave field in the unreached area where the incident wave has not reached has been omitted. Reducing the calculation amount, it calculates the intended speeds.

  In the following, electromagnetic waves including light, electron beams, X-rays, etc. are used as typical examples of waves, electromagnetic fields and Maxwell equations are used as representative examples of wave fields and wave equations, and Maxwell's equations are calculated by computer using the FDTD method. A representative example will be described in which numerical analysis is performed, the space and time distribution of the electromagnetic wave in the target analysis region is calculated, and the electromagnetic field is analyzed by obtaining temporal changes in the electromagnetic field, but the present invention is not limited thereto. It is not done. The present invention solves the wave equation numerically with a computer, calculates the space and time distribution of the wave in the target analysis region, and obtains the temporal change of the wave field to analyze the wave field. Needless to say, the present invention can also be applied to waves other than electromagnetic waves such as sound waves and elastic waves. In addition, the present invention is not limited to the FDTD method as a numerical calculation method for solving a wave equation such as Maxwell's equation, and is not limited to the FDTD method. The transmission line matrix method, the spatial network method, and the finite element time domain method disclosed in Patent Document 2 Of course, other wave data numerical calculation methods can be used.

  That is, the present invention provides a numerical calculation program such as the FDTD method for numerically solving the electromagnetic wave space and time distribution based on the Maxwell equation and using the spatial distribution of refractive index (dielectric constant) as a boundary condition. The simulation method and means used are mainly provided, mainly optical disks, lenses, in particular various optical parts such as microlenses, optical connectors, optical waveguides, optical communication parts such as optical fibers, antennas, laser devices, A method for calculating the time change of electromagnetic waves incident from the outside, with the starting electromagnetic field set to 0, used for analysis of microscopes, semiconductor integrated circuits (ICs), piezoelectric elements, structures, etc., and analysis of optical phenomena in minute regions. Is to provide.

First, a functional configuration of an electromagnetic field analysis apparatus to which a wave field analysis apparatus that performs a wave field analysis method according to an embodiment of the present invention is applied will be described.
FIG. 1 is a block diagram showing an embodiment of a functional configuration of an electromagnetic field analysis apparatus to which the wave field analysis apparatus of the present invention is applied.
The electromagnetic field analysis apparatus 10 of the present invention shown in FIG. 1 includes a program that operates in a computer (computer) environment such as a personal computer or a workstation, and can be configured by a computer.

  As shown in FIG. 1, the electromagnetic field analysis device 10 includes a refractive index distribution definition unit 12 that defines a spatial distribution of refractive indexes for a plurality of calculation models, and conditions necessary for electromagnetic field calculation including an analysis region (all time calculation step). The calculation condition input unit 14 for inputting calculation conditions to set the number and the total number of discretization layers) and the refractive index distribution of the calculation model defined by the refractive index distribution definition unit 12 and the calculation condition input unit 14 Based on the calculated calculation conditions, the arrival area prediction unit 16 that predicts the arrival area where the incident electromagnetic wave in the analysis area reaches in a predetermined calculation step, the refractive index distribution of the calculation model described above, and the calculation conditions described above An electromagnetic field calculation unit 18 that solves the Maxwell equation numerically for each calculation step using the FDTD method and calculates a propagating electromagnetic field; The storage unit 20 that stores and stores the relationship between the predicted arrival region of the incident electromagnetic wave predicted by the area prediction unit 16 and the calculation step; and the writing of the predicted arrival region for each calculation step from the arrival region prediction unit 16 to the storage unit 20 and A write / read control unit 22 that controls reading of the predicted arrival region in a predetermined calculation step from the storage unit 20 to the electromagnetic field calculation unit 18 and the entire space of the analysis region calculated by the electromagnetic field calculation unit 18 are propagated. And a calculation result output unit 24 for outputting the calculation result of the electromagnetic field.

The refractive index distribution defining unit 12 defines the spatial distribution of the refractive index serving as a calculation model based on the shape and material of the analysis region to be analyzed.
The calculation condition input unit 14 is a spatial discretization method (for example, when electromagnetic waves propagate in a predetermined axial direction in the analysis region from one end surface to the other end surface of the analysis region in a plane shape, a discretization layer: 1 to S ₀ ). Calculation range (for example, total spatial discretization layer number S ₀ ), input and setting of analysis region such as boundary condition, input and setting of input electromagnetic wave (incident wave) such as spatial distribution, time distribution, polarization condition, and others The conditions necessary for calculation such as the total number of time calculation steps (N ₀ ) and time discretization conditions (calculation steps: 1 to N ₀ ) are input and set.

The refractive index distribution definition unit 12 and the calculation condition input unit 14 have the refractive index of the analysis region to be subjected to electromagnetic field calculation for one calculation model before the electromagnetic field calculation unit 18 starts the electromagnetic field calculation in the analysis region. Define the spatial distribution of and input and set the necessary calculation conditions.
The spatial distribution definition of the refractive index by the refractive index distribution definition unit 12 and the input and / or setting of the calculation condition by the calculation condition input unit 14 may be performed simultaneously in correspondence with each other, and either one is performed first. It may be performed or may be performed independently.

The arrival area prediction unit 16 is a feature of the present invention, and is set by the refractive index distribution of the calculation model defined by the refractive index distribution definition unit 12 and the refractive index distribution and calculation condition input unit 14. Based on the calculation conditions, an electromagnetic wave incident in the analysis region propagates in the analysis region and reaches a certain time after the incident, that is, an arrival region that reaches in a calculation step (j) from the start of calculation is predicted. To do.
In arrival area predicting unit 16, as shown by the solid line in FIG. 2, previously obtained over the relationship between the predicted arrival area and the calculation step (j) (j = 1~N 0 ) the entire analysis region.

Here, as described above, for example, electromagnetic waves propagate in a planar shape from one end surface of the analysis region to the other end surface in a predetermined axial direction of the analysis region, and the analysis region is separated from the one end surface to the other end surface. That is, 1 to S ₀ layers (total space discretized layer number S ₀ ) are spatially discretized, and the total time calculation step number (N ₀ ) is the total spatial discretized layer number (S ₀ ). Is larger than the predicted reachable region by the reachable region predicting unit 16 may correspond to the same discretization layer in a plurality of calculation steps. For this reason, as indicated by a dotted line in FIG. 2, a calculation step (j) corresponding to the time when the predicted arrival area reaches the discretization layer (i) (i = 1 to S ₀ ) is defined as t (i). It is preferable to obtain the relationship between the predicted arrival area (discretization layer: i = 1 to S ₀ ) and the calculation step t (i) over all the discretization layers. Here, the predicted arrival area (discretization layer: i) and the calculation step t (i) correspond one to one.

Note that the arrival area prediction in the analysis area in the predetermined calculation step (j) by the arrival area prediction unit 16 is performed before the electromagnetic field calculation in the analysis area by the electromagnetic field calculation unit 18 is started.
Thus, the predicted arrival area determined before the start of the electromagnetic field calculation (e.g., discretized layers: i = 1 to S ₀₎ relationship between the calculation step (t (i)) is, LUT (lookup table) and, The relational expression is stored and stored in the storage unit 20 by the writing / reading control unit 22.
In the example described above, the arrival area prediction unit 16 obtains the relationship between the predicted arrival area and the calculation step over the entire space of the analysis area, stores this relationship in the storage unit 20, and calculates the electromagnetic field as described later. The unit 18 reads out this relational expression and sets the spatial calculation range in which the electromagnetic field calculation is to be performed. However, the present invention is not limited to this, and the arrival area prediction unit 16 performs the calculation step (j) A spatial calculation range to be calculated in the calculation step (j) is set, the relationship between the calculation step (j) and the spatial calculation range is stored in the storage unit 20 as an LUT or the like, and the electromagnetic field calculation unit 18 stores the relationship. The space calculation range to be calculated in the calculation step (j) may be directly read from the unit 20.

In the present invention, it is preferable that the arrival area prediction unit 16 predicts the arrival area by predicting the propagation speed of the electromagnetic wave propagating through the analysis area. The propagation speed (v) of the electromagnetic wave is inversely proportional to the refractive index n of the medium through which the electromagnetic wave propagates (v = c ₀ / n: where c ₀ is the speed of light in vacuum (c ₀ = 2.998 × 10 ⁸ m / s)), the reaching region prediction unit 16 may perform prediction of the reaching region based on information on the refractive index distribution in the analysis region. The refractive index n is a function of the dielectric constant ε and the magnetic permeability μ (n = √ (εμ / ε ₀ μ ₀ ): ε ₀ and μ ₀ are the dielectric constant (10 ⁷ / 4πc _{0 in} vacuum), respectively. ² ) and the magnetic permeability (4π × 10 ⁻⁷ )), the reaching region prediction unit 16 performs the prediction of the reaching region based on the information on the dielectric constant ε and the permeability μ of the medium in the analysis region. Also good.

Specifically, the arrival area prediction unit 16 has the smallest value in the plane orthogonal to the propagation direction of the electromagnetic wave as a representative value of the refractive index representing the plane orthogonal to the propagation direction of the electromagnetic wave in the arrival area in the analysis area. It is preferable to adopt a refractive index, obtain a refractive index distribution in the propagation direction of the electromagnetic wave in the analysis region, and predict an arrival region of the electromagnetic wave based on the obtained refractive index distribution.
The reason for this is that, as described above, the propagation speed (v) of the electromagnetic wave is inversely proportional to the refractive index n. Therefore, by adopting the smallest refractive index in the plane perpendicular to the propagation direction of the electromagnetic wave, The predicted propagation speed is a little faster than the actual propagation speed, and the predicted arrival area is a little larger than the actual arrival area, that is, an area that has reached a little farther, effectively and reliably This is because a region including the reaching region can be predicted.

The arrival area prediction unit 16 may also predict the arrival area of the electromagnetic wave assuming that the refractive index in the analysis area is 1 instead of the refractive index distribution in the propagation direction of the electromagnetic wave in the analysis area. it can. The reason for this is that, as described above, the refractive index of the vacuum is 1 by definition, and there is no substance having a refractive index smaller than 1, that is, no medium, and the refractive index of air is close to 1. This is because a region including the actual reachable region can be predicted more easily and surely when a vacuum or air is included therein.
In the present invention, it is preferable that the electromagnetic wave propagates substantially from one end of the analysis region in a predetermined axial direction of the analysis region. Of course, in this case, the electromagnetic field calculation unit 18 calculates the time change of the electromagnetic field along the predetermined axial direction.
Moreover, it is preferable that the reach | attainment area | region prediction part 16 performs the prediction of the reach | attainment area of electromagnetic waves by calculating the propagation length which electromagnetic waves propagate from one end of an analysis area | region.
Details and specific examples of the prediction of the arrival area will be described later.

The electromagnetic field calculation unit 18 uses the FDTD method calculation program to calculate the Maxwell equation based on the refractive index distribution of the calculation model defined by the refractive index distribution definition unit 12 and the calculation conditions set by the calculation condition input unit 14. It is numerically solved by a computer such as a workstation, and calculates temporal and spatial changes of the electromagnetic field in the analysis region (analysis space).
At this time, in the present invention, before starting the electromagnetic field calculation of the predetermined calculation step, the electromagnetic field calculation unit 18 performs the calculation in the calculation step based on the relationship between the predicted arrival area stored in the storage unit 20 and the calculation step. A spatial calculation range in the analysis region to be set is set, and the electromagnetic field calculation of the calculation step is performed within the set spatial calculation range. Alternatively, before starting the electromagnetic field calculation of a predetermined calculation step, the electromagnetic field calculation unit 18 directly determines the space to be calculated in the calculation step from the relationship between the calculation step stored in the storage unit 20 and the space calculation range. The calculation range may be read, and the electromagnetic field calculation of the calculation step may be performed within the read space calculation range.

That is, in the present invention, the electromagnetic field calculation unit 18 starts the calculation of the electromagnetic field in the calculation step (j = N), and the predicted arrival region (for example, discretization layer: i = 1 to S ₀ ) and the calculation step (t (i)) are read out via the writing / reading control unit 22, and the predicted arrival region (discretization layer) in the calculation step (N) is read using the read relationship. (I)) is obtained. Specifically, the electromagnetic field calculation unit 18 reads out the relational expression or the LUT as shown in FIG. 2, and the minimum calculation step t (S) in the calculation step t (i) larger than the calculation step (N), That is, the minimum discretization layer S is obtained, and the discretization layers 1 to S are set as the spatial calculation range S in the calculation step (N).
In the present invention, it is possible to set only the predicted arrival region of the electromagnetic wave as the spatial calculation range S immediately after the start of the electromagnetic field calculation immediately after the incident wave is incident, and the electromagnetic field in the region where the incident wave does not reach is This is because it can be omitted because it remains 0 as in the initial state and does not require calculation.
Thereafter, the electromagnetic field calculation unit 18 performs the calculation of the electromagnetic field in the calculation step (N) by limiting to the spatial calculation range of the discretization layers 1 to S. As a result, in the present invention, in the calculation step (N), it is possible to omit the electromagnetic field calculations for the remaining discrete layer S + 1 to S _0, to reduce the calculation amount of the electromagnetic field by the electromagnetic field calculation unit 18, This calculation can be speeded up.

  The FDTD calculation program executed by the electromagnetic field calculation unit 18 is one method for numerically solving the Maxwell equation representing the physical phenomenon of the electromagnetic field by a computer. This is a simulation technique in which an electromagnetic wave from an excitation part (wave source) defined in space is incident and calculation is performed while sequentially updating the time change of the electromagnetic field. (For the FDTD method and the FDTD method calculation program, reference can be made to documents published by Satoshi Uno, Corona Co., Ltd., “Electromagnetic field and antenna analysis by FDTD method”.)

As for the FDTD method and the FDTD method calculation program, the techniques disclosed in various conventionally known documents including the above-mentioned documents may be used, and detailed description thereof will be omitted. An example of the FDTD method will be briefly described.
The FDTD method is a numerical calculation method of an electromagnetic field obtained by differentiating Maxwell's equations shown in the following formulas (1) and (2) in time and space directions.
In the electromagnetic field calculation, the Maxwell equation shown in the following equations (1) and (2) is converted into a difference equation by discretizing time and space, that is, the electromagnetic field calculation difference equation shown in the following equations (3) and (4) (as an example) Only one component of the electromagnetic field is shown).

  In the FDTD method applied to the present invention, as shown in FIG. 3, an analysis space (region) into which incident light (electromagnetic field E and magnetic field H) is incident is divided into a mesh shape and discretized. A refractive index n (dielectric constant ε) is assigned to each lattice (microcell) point according to the shape and material. In FIG. 3, as shown by extracting one lattice (unit cell) from the analysis space, x, y, z components of the electric and magnetic fields, that is, Ex, Ey, Ez, Hx, Hy, and Hz are defined.

Here, as is clear from the above equation (3), the change (difference) in the magnetic field (magnetic field) is a constant multiple of the sum and difference of the surrounding electric fields (electric fields), that is, as shown in FIG. As shown in the above equation (4), the change (difference) in the electric field is represented by a constant multiple of the sum and difference of the surrounding magnetic fields, ie, FIG. Thus, it is expressed as a constant multiple of the vortex formed by the surrounding magnetic field.
For this reason, in the FDTD method, in each Yee cell, the magnetic field is calculated from the electric field at a certain time by the above equation (3), and the magnetic field obtained by this is substituted into the above equation (4) to obtain the electric field at the next time. Then, the electric field obtained by this is substituted again in the above equation (3) to calculate the magnetic field, or the electric field is calculated from the magnetic field of a certain time by the above equation (4), and the electric field obtained by this Is substituted into the above equation (3) to calculate the magnetic field for the next time, and the magnetic field obtained by this is substituted into the above equation (4) again to calculate the electric field.

In the FDTD method, generally, the calculation is repeatedly performed for the entire space of the analysis region, and in the present invention, all Yee cells in the space calculation range of the analysis region corresponding to the predicted arrival region of the electromagnetic wave in the calculation step (j). Thus, the time change of the electromagnetic field can be calculated. That is, first, the spatial distribution of the magnetic field after a half step is calculated from the spatial distribution of the electric field in the analysis space at a certain time. Subsequently, the electric field after the half step is calculated from the magnetic field distribution in the analysis space, and the electric field after one step is updated. In this way, the time change of the electromagnetic field is calculated while alternately updating the electric field and the magnetic field.
Therefore, in the FDTD method, the calculation of the electromagnetic field can be performed in time series by repeating the calculation procedure (leap frog algorithm) for alternately calculating the electric field and the magnetic field.

From the above, in the present invention, in the FDTD method, an excitation source (wave source) is determined in the analysis region, an incident wave is given, and the state in which the electromagnetic field in the entire space in the analysis region is zero is defined as the initial (start) state. By repeating the calculations according to the equations (3) and (4), it is possible to calculate how the incident wave propagates through the calculation model.
In the present invention, a continuous wave can be given as the incident wave, and the calculation can be continued until the change converges, or a pulse wave can be given. In the present invention, an absorption boundary condition, a periodic boundary condition, or the like can be set as the boundary.
In the present invention, as described above, the FDTD method and the FDTD method calculation program can be applied.

The storage unit 20 includes a calculation step (j) (j = 1 to N ₀ ) or (t (i)) and a predicted arrival region (for example, a discretization layer: i = 1 to S ₀ ) by the arrival region prediction unit 16. Are stored and saved as a relational expression over the entire analysis region, a one-dimensional LUT, or the like. Alternatively, the storage unit 20 may store and save the relationship between the calculation step (j) and the space calculation range as a relational expression over the entire analysis region, a one-dimensional LUT, or the like.
The write / read control unit 22 stores and saves the relationship between the calculation step and the predicted arrival area or the space calculation range in the storage unit 20 as a relational expression or LUT indicating such a relationship. In addition to writing to the storage unit 20, the writing control is performed, and the relationship between the predicted calculation step stored in the storage unit 20 and stored in the storage unit 20 by the electromagnetic field calculation unit 18 and the predicted arrival area or the spatial calculation range is read from the storage unit 20. At the same time, the readout control is performed.

  The calculation result output unit 24 is based on the calculation result of the internal time and spatial distribution of the magnetic field in the analysis region performed by the electromagnetic field calculation unit 18 as post-processing after completion of the electromagnetic field calculation of one calculation model by the electromagnetic field calculation unit 18. Then, the physical quantities according to the analysis purpose such as reflectance, transmittance, absorptivity, and far-field radiation distribution are calculated. The calculation result output unit 24 may be provided with a function for displaying the calculated physical quantity and the calculation result such as the time and space distribution of the electromagnetic field on the display of the display device. A function of outputting a copy may be provided.

Next, the hardware configuration of the electromagnetic field analyzer shown in FIG. 1 will be described.
FIG. 5 is a block diagram showing an embodiment of the hardware configuration of the electromagnetic field analysis apparatus shown in FIG.
The electromagnetic field analysis device 30 shown in FIG. 5 has the functional configuration of the electromagnetic field analysis device 10 shown in FIG. 1 as a hardware configuration. As described above, the electromagnetic field analysis device 10 of the present invention shown in FIG. This is an embodiment in the case of a computer such as a computer or a workstation.

  An electromagnetic field analysis device 30 shown in FIG. 5 includes an input device 32 for inputting data such as an analysis region, a refractive index, and calculation conditions, a program for executing the electromagnetic field analysis method of the present invention on a computer, and the FDTD method calculation program. And a reading / writing device 34 that reads data from a removable data recording medium storing data such as a program such as analysis area, refractive index, and calculation conditions, and writes data to the data recording medium, and features of the present invention Predict the arrival area of the electromagnetic wave propagating in the analysis area and determine the relationship between the time or time calculation step and the prediction arrival area or spatial calculation range, or the spatial calculation range from the relationship between the calculation step and the prediction arrival area Calculations such as calculation and calculation of temporal and spatial changes of electromagnetic field by executing FDTD method calculation program And an arithmetic processing unit (for example, CPU) 36 for controlling the entire process including the control of writing / reading of the relationship between the time or the time calculation step and the predicted arrival area or the space calculation range, and the features of the present invention A memory for storing data such as a relationship between a time or a time calculation step and a predicted arrival area or a spatial calculation range, a program such as an FDTD calculation program, an execution program for an electromagnetic field analysis method of the present invention, and necessary calculation conditions 38, a display device 40 for displaying calculation results and the like, a recording device (printer) 42 for recording the calculation results and the like, and a bus 44 for connecting these devices.

Here, the input device 32 includes a keyboard and a mouse such as a computer, and the read / write device 34 includes a media drive that reads and writes various data recording media. Further, the input device 32 and the reading / writing device 34 perform the electromagnetic field calculation including the refractive index distribution defining unit 12 and the analysis region for defining the spatial distribution of the refractive index for a plurality of calculation models of the electromagnetic field analysis device 10 shown in FIG. A function as a calculation condition input unit 14 for inputting calculation conditions (for example, the total number of discretization layers (S ₀ ) and the total number of time calculation steps (N ₀ )) in order to set necessary conditions is included.
The arithmetic processing unit 36 is constituted by a CPU (Central Processing Unit) such as a computer, for example, and predicts the relationship between the time or time calculation step and the predicted arrival area or space calculation range of the electromagnetic wave in the analysis area. Controls the reaching region prediction unit 16 to be obtained and the electromagnetic field calculation unit 18 that numerically solves the Maxwell equation by executing the FDTD method program, and the writing of the relationship to the storage unit 20 and the reading of the relationship from the storage unit 20 The function as the writing / reading control unit 22 performed in this manner is included. Note that the arithmetic processing unit 36 may include a function of the calculation result output unit 24 such as calculation of a physical quantity according to the purpose after the electromagnetic field calculation by the electromagnetic field calculation unit 18.

The memory 38 includes a hard disk such as a computer and various built-in or external memories, and the relationship between the time or time calculation step and the predicted arrival area or space calculation range of the electromagnetic wave in the analysis region, and before the calculation step. A function as a storage unit 20 for storing and saving step electromagnetic field data (time, spatial distribution) and the like is included.
The display device 40 is for displaying calculation results on a display screen, and includes a liquid crystal display device such as a computer, a display such as a CRT, and a monitor. The recording device 42 displays the calculation results and the like on paper. Output a hard copy recorded on the printer, including a so-called printer. The display device 40 and the recording device (printer) 42 have a function as a calculation result output unit 24 that outputs a calculation result of an electromagnetic field that has propagated through the entire space started from one end face of the analysis region and ended at the other end face. Have.

The electromagnetic field analysis device to which the wave field analysis device of the present invention is applied basically has the above-described functional configuration and hardware configuration. Hereinafter, the operation and electromagnetic field analysis of the electromagnetic field analysis device described above will be described. The electromagnetic field analysis method to which the wave field analysis method of the present invention is applied will be described by explaining the embodiment.
FIG. 6 is a flowchart showing an example of an electromagnetic field analysis method to which the wave field analysis method of the present invention is applied. The electromagnetic field analysis method shown in FIG. 6 is carried out by the electromagnetic field analysis apparatus shown in FIG.

  In the following, when a cylindrical lens array 54 arranged on the glass substrate 52 as shown in FIG. 7 is present in the air 56, incident light is incident on the air layer 56, and the air layer 56, cylindrical lens array. A calculation model 50 that sequentially propagates 54 and the glass substrate 52 is taken as an example. In this calculation model 50, the thickness of the air layer 56 has a refractive index n of 1 (n = 1), 1 μm at the apex of each cylindrical lens 54a of the cylindrical lens array 54, and its base (adjacent). 2 μm at the connecting portion of the cylindrical lens 54a). That is, in this calculation model 50, each cylindrical lens 54a is a semi-cylindrical member with a refractive index n of 1.5 (n = 1.5) and a radius of 1 μm, and a refractive index n of 1.5 ( n = 1.5), and connected to a glass substrate having a thickness of 3 μm. In the calculation model 50, it is assumed that the same structure is infinitely continuous in a direction perpendicular to the paper surface.

In the present embodiment, as shown in FIG. 8, the analysis region 50a of the calculation model 50 includes one cylindrical lens 54a constituting a cylindrical lens array 54, and an air layer 56a exists above the cylindrical lens 54a, and the cylindrical lens 54a. A space of 2 μm × 5 μm in which the glass substrate 52a exists is set in the lower part of the screen. In this analysis region 50a, a periodic boundary condition is set in the direction perpendicular to the paper surface, assuming that the same structure is infinitely continuous, and an absorbing boundary condition is set at the boundary in the upper limit direction.
In the following, as shown in FIGS. 7 and 8, a calculation model 50 and an analysis region 50a in which incident light is incident on a cylindrical lens array 54 supported by a glass substrate 52 and exists in the air and propagates from the air layer 56 are transmitted. However, it goes without saying that the present invention is not limited to this.

First, in the electromagnetic field analysis method shown in FIG. 6, the electromagnetic field calculation is performed using the FDTD method calculation program. In step S100, the refractive index distribution defining unit 12 of the apparatus 10 shown in FIG. For a 5 μm analysis region (space) 50a, a spatial distribution of refractive indexes having different refractive indexes in each region is defined.
For example, as shown in FIG. 8, in the analysis region (space) 50a of 2 μm × 5 μm, the air layer 56a with the minimum thickness of 1 μm at the upper part has a refractive index n of 1.0, and a semi-cylindrical shape with a radius of 1 μm below it. In the cylindrical lens 54a, the refractive index n is 1.5, and the refractive index distribution in which the refractive index n is 1.5 is defined in the lower 3 μm thick glass substrate that supports the cylindrical lens 54a.

In step S102, the calculation condition input unit 14 sets the analysis region (space) 50a of 2 μm × 5 μm as the calculation range of the analysis region 50a, and the spatial grid Δd is set to 20 nm as the spatial discretization method. As a unit cell (lattice) of 20 nm × 20 nm × 20 nm is set.
Further, as an incident light (electromagnetic wave) condition, one end surface of the analysis region 50a (the upper end surface of the air layer 56a in the calculation model 50 and the analysis region 50a in FIGS. 7 and 8) is used as the excitation unit 58. A plane wave having a wavelength of 500 nm is incident as a continuous wave and propagates from the upper end surface of the air layer 56a in the analysis region 50a to the lower end surface of the glass substrate 52a.
Accordingly, since the electromagnetic wave is uniform in the direction orthogonal to the traveling direction from the upper end surface to the lower end surface of the analysis region 50a in which the electromagnetic wave propagates, the analysis region 50a has a predicted arrival region for predicting the arrival of the electromagnetic wave. The spatial discretization layer having a spatial grid Δd of 20 nm in the traveling direction can be set to 250 (total spatial discretization layer number S ₀ = 250).
As other calculation conditions, the above-described periodic boundary condition is set in the direction perpendicular to the paper surface, and the above-described absorption boundary condition is set in the upper limit direction boundary.

In step S102, as an initial state, the electromagnetic field in the entire space of the analysis region 50a is set to 0, and the excitation by the excitation unit 58 is set to start simultaneously with the calculation by the electromagnetic field calculation unit 18 of the present invention. Is done.
Furthermore, in the electromagnetic field calculation of the present invention, the time per one calculation step (j) for updating the electromagnetic field by the FDTD method calculation program is Δt. Δt is a constant set below the upper limit value called the Courant condition. In this embodiment, for example, Δt = 0.02978 [fs / step], and the total number of calculation steps N ₀ is 1000 [step]. ] Is set.
Thus, in step S102, necessary calculation conditions are input.
Here, either step S100 or step S102 may be performed first or simultaneously. Through these steps S100 and S102, before starting the electromagnetic field calculation, first, for each calculation model, the definition of the spatial distribution of the refractive index of the analysis region to be subjected to the electromagnetic field calculation and the setting of the necessary calculation conditions are made.

Next, before the electromagnetic field calculation is started by the electromagnetic field calculation unit 18, the arrival region of the electromagnetic wave is predicted for each time calculation step (j) by the arrival region prediction unit 16 in step S104.
Specifically, in the arrival area prediction unit 16, first, in the analysis area 50a shown in FIG. 8, the minimum value n (i) of the refractive index for each plane (i) of the grating crossing the traveling direction of the incident wave. Ask for. As a result, only the air layer 56a exists in a region having a thickness of 1 μm from the excitation portion 58 to 1 μm, i.e., i = 1 to 50 [grid] (i = 0 to 49 layers as a spatial discretization layer). Therefore, the minimum value n (i) of the refractive index is 1.0. Next, a cylindrical lens 54a with a refractive index n = 1.5 and air with a refractive index n = 1.0 are provided in a region (i = 50-99 layers) having a thickness of 1 μm to 2 μm from the excitation portion 58. Since the layer 56a is mixed, the minimum value n (i) of the refractive index in this region is also 1.0. Next, since there is only a glass substrate having a refractive index n = 1.5 in the 3 μm thick region (i = 100 to 250 layers) from the excitation part 58 to 2 μm to 5 μm, the refractive index of this region is The minimum value n (i) is 1.5.
That is, in the analysis region 50a, when i = 0 to 99, n (i) = 1.0, and when i = 100 to 250, n (i) = 1.5.

Next, the fastest arrival calculation step t (i) to each surface (each spatial discretization layer) (i) is calculated according to the following equation (5).
Here, n (k) and d (k) are the minimum value of the refractive index of the spatial discretization layer (k) and the mesh distance (grid interval) (n (0)) of the spatial discretization layer (k). ˜n (99) = 1.0, d (0) ˜d (249) = 20 nm), c ₀ is the speed of light in vacuum (c ₀ = 2.998 × 10 ⁸ m / s), As described above, Δt is the time per calculation step (j) for updating the electromagnetic field by the FDTD method calculation program, and is, for example, Δt = 0.02978 [fs / step].

When the spatial discretization layer number (i) obtained in this way and the time calculation step t (i) are plotted, the relationship schematically shown by the dotted line in FIG. 2 is obtained. Here, S ₀ = 250 and N ₀ = 1000.
In step S106, the relationship between the time calculation step indicated by the dotted line in FIG. 2 obtained in step S104 and the number of spatial discretization layers is stored in the storage unit by the write / read control unit 22 as an LUT or a relational expression. 20 is stored and saved.

Next, in step S108, j = 1 is set, and the electromagnetic field calculation unit 18 first stores the dotted line in FIG. 2 stored in the storage unit 20 before starting the calculation of the electromagnetic field in the calculation step (j = 1). Is read out, and the spatial calculation range S in the calculation step (j = 1) is set.
In the present invention, only the predicted arrival area of the electromagnetic wave can be set as the spatial calculation range S because the incident wave is not sufficiently propagated in the initial stage of the electromagnetic field calculation and the incident wave does not reach. This is because the electromagnetic field of 0 remains 0, which is the same as the initial state, and does not need to be calculated. As a result, in the present invention, the amount of calculation of the electromagnetic field by the following electromagnetic field calculation unit 18 can be reduced, and this calculation can be speeded up.

Here, in general, the setting of the space calculation range S in the calculation step (j = N) will be specifically described.
That is, in the present invention, before starting the calculation of the electromagnetic field in the calculation step (j = N), the electromagnetic field calculation unit 18 has the number of spatial discretization layers (predicted arrival region: i = 1 to S ₀₎ shown in FIG. ) And the calculation step (t (i)) are read from the storage unit 20.
In FIG. 2, the minimum calculation step t (S) satisfying Nt <(i) is obtained, and the discretization layers 1 to S are set as the spatial calculation range (S) in the calculation step (N).
FIG. 9 shows the spatial calculation range (S) 60 in the analysis region 50a set in this way.
Note that the i = S + 1 layer of outer space calculation range (S) 60 to S ₀ th layer, at the speed of light limits, the incident wave can not reach all the electromagnetic field is 0, necessary for calculation There is no.
When N ≧ t (S ₀ ), the entire region in the analysis region 50a is set as the space calculation range (S), and the entire region in the analysis region 50a is calculated.

Next, in step S110, assuming that i = 1, the electromagnetic field calculation unit 18 calculates the electromagnetic field of the first layer (i = 1) in the spatial calculation range (S) 60 set in step S108 shown in FIG.
Here, generally, the calculation of the electromagnetic field of the i-th layer (i) of the set space calculation range (S) 60 will be specifically described.
That is, the electromagnetic field calculation unit 18 first converts the spatial calculation range (S) 60 set in step S108 shown in FIG. 9 into the electromagnetic field of the calculation step (N-1) of the i-th layer (i) of the analysis region 50a. Based on this, the change of the electromagnetic field in the calculation step (N) is calculated, and the electromagnetic field in the calculation step (N) is calculated.

  The analysis field 50a shown in FIG. 8 and FIG. 9 is made into an initial state by the electromagnetic field calculation unit 18 using the FDTD method calculation program based on the definition of the spatial distribution of refractive index and the necessary calculation conditions. The incident light from the excitation part 54 determined at the upper end surface of the analysis area is incident, the Maxwell equation is numerically solved by a computer, the electromagnetic field in the set space calculation range (S) is calculated, and the set space calculation is performed. Calculate temporal and spatial changes of the electromagnetic field in the range (S).

In the calculation of the electromagnetic field by the electromagnetic field calculation unit 18, the calculation proceeds with the state where the electromagnetic field in the entire space of the analysis region 50a is 0 as the start state. In the electromagnetic field calculation unit 18, since the incident light (electromagnetic wave) given by the excitation unit 58 gradually propagates in the analysis space 50a, the convergence by the cylindrical lens 54a can be calculated even if it hits the cylindrical lens 54a. In the electromagnetic field calculation unit 18, calculation is performed at a stage where a certain calculation step or an end condition such as a determination condition of a convergence state of the calculation is satisfied, such as a set space calculation range (S) and a full-time calculation step (N ₀ ). End.

Next, in step S112, it is determined whether or not the calculation of the entire space calculation range (S) is completed, that is, whether or not i ≧ S is satisfied. If the calculation of the entire space calculation range (S) has not been completed (in the illustrated example, i <S), No: i = i + 1 is set, and the process returns to step S110, and similarly, the space calculation range (S) The calculation of the electromagnetic field of the 60th (i + 1) layer is repeated until the calculation of the entire space calculation range (S) is completed.
On the other hand, if the calculation of the entire space calculation range (S) has been completed (in the illustrated example, if i ≧ S is satisfied), the process returns to step S114 as Yes.

Next, in step S114, it is determined whether or not the calculation of all the calculation steps (N ₀ ) is completed, that is, whether or not j ≧ N ₀ is satisfied. If the calculation of all the calculation steps (N ₀ ) has not been completed (in the illustrated example, if j <N ₀ ), No: j = j + 1 is set, and the process returns to step S108. Similarly, the calculation step (j + 1) The space calculation range (S) is newly set, and in steps S110 and S112, the calculation of the electromagnetic field by the electromagnetic field calculation unit 18 is performed for the space calculation range S from i = 1 to S layers. The process is repeated until the calculation of the range (S) is completed, and when the calculation of the entire space calculation range (S) is completed, the process returns to step S114 again. In this way, steps S108, S110, S112, and S114 are repeated until the calculation of the electromagnetic field in each spatial calculation range of all the calculation steps (N ₀ ) is completed.

Since N ≧ t (S ₀ ) after a certain time calculation step (N), the entire region in the analysis region 50a is set as the space calculation range (S), and the electromagnetic field calculation unit 18 sets the region in the analysis region 50a. Is calculated.
On the other hand, if the calculation of all the calculation steps (N ₀ ) has been completed (in the illustrated example, if j ≧ N ₀ is satisfied), the process goes to step S116 as Yes.

Next, in step S116, as post-calculation processing, a physical quantity corresponding to the analysis purpose is calculated based on the time and space distribution of the electromagnetic field thus calculated. Further, the calculation result output unit 24 displays the calculation result on the display of the display device as a graphic or outputs it to a printer as a hard copy.
Next, in step S118 (END), the electromagnetic field calculation for the analysis region 50a of one calculation model 50 ends.

In this way, in the present embodiment, the calculation results performed on the analysis region 50a of one calculation model 50 are shown in FIGS. 10A, 10B, and 10B for every 50 propagation steps (N = 50 steps). Shown in (c). FIG. 10D specifically shows the size of the analysis region 50a of the calculation model 50.
FIG. 11 is a graph showing the relationship between the number of time calculation steps (t (i), N) [step] obtained in this embodiment and the space calculation range (calculation area) [grid]. The graph shown in FIG. 11 is the same as the graph shown in FIG. 2 except that the area on the upper side of the graph shows the reduction rate of the calculation amount.

From these figures, in the initial stage (between 0 calculation step and about 730 step), there is a region where the incident light does not reach in the analysis region 50a, and its electromagnetic field is zero. In this calculation step, the calculation of the electromagnetic field in the region where the incident light does not reach can be omitted. Therefore, the calculation of the electromagnetic field in the calculation omitted portion surrounded by the solid line from the 0 calculation step to the 700th step in FIG. Can be omitted.
As a result, in the example shown in FIG. 11, the upper area of the graph indicating the reduced calculation amount indicates that the ratio to the total area indicating the entire calculation amount is about 30%, and the calculation amount reduction is about 30%. Rate can be achieved.

According to the calculation example described above, the arrival step of incident light is calculated for light that has passed through a region having a low refractive index and a high propagation speed of incident light. The limit calculation area can be set, and the calculation amount can be reduced and the speed can be increased by omitting the electromagnetic field calculation in the unreached area.
In the above-described embodiment, the minimum refractive index in the plane orthogonal to the traveling direction of the incident wave is obtained from the refractive index distribution in the analysis region, and the prediction calculation of the arrival region of the incident wave and the prediction calculation of the unreached region are performed. However, the present invention is not limited to this, and it is possible to simply perform the above-described prediction calculation of the arrival area of the incident wave and the prediction calculation of the non-arrival area assuming that the entire area is air. It is. The refractive index n of a normal medium is 1 or more (n ≧ 1), and the refractive index condition is sufficiently satisfied if air is assumed. When a high refractive index exists, more calculations than necessary are required, but the processing can be simplified.

  As described above, the present invention is a technique for improving the efficiency of calculation by reducing the amount of calculation of the area where the incident wave has not yet reached in the calculation model in which the incident wave travels in a predetermined direction. Of course, the present invention can be applied to technical fields such as detection elements and structures.

  The wave field analysis method described above can also be realized by executing a prepared program on a computer such as a personal computer or a workstation. This program is a program for causing a computer to execute the wave field analysis method, and is recorded on a computer-readable recording medium such as a hard disk, a floppy disk, a CD-ROM, an MO, or a DVD, and is read from the recording medium by the computer. Is executed by. The program can be distributed via the recording medium and a network such as the Internet.

  As described above, the wave field analysis method and apparatus according to the present invention and the computer-readable recording medium storing the program for causing the computer to execute the wave field analysis method have been described in detail. However, the present invention is limited to the above embodiments. However, various improvements and changes may be made without departing from the scope of the present invention.

It is a block diagram which shows one Example of a functional structure of the electromagnetic field analyzer to which the wave field analyzer of this invention is applied. It is a graph which shows an example of the relationship between the prediction arrival area | region obtained by the arrival area prediction part of the wave field analyzer shown in FIG. 1, and a calculation step. It is explanatory drawing explaining the FDTD method applied to this invention. It is explanatory drawing explaining calculation of the magnetic field and electric field by FDTD method applied to this invention. It is a block diagram which shows one Example of the hardware constitutions of the electromagnetic field analyzer shown in FIG. It is a flowchart which shows an example of the electromagnetic field analysis method to which the wave field analysis method of this invention is applied. It is a schematic diagram which shows one Example of the calculation model to which the electromagnetic field analysis method shown in FIG. 6 is applied. It is a schematic diagram for demonstrating the analysis area | region of the calculation model shown in FIG. 7, its refractive index distribution, and minimum refractive index. It is a schematic diagram which shows an example of the space calculation range in the analysis area | region shown in FIG. (A) is a figure which shows the calculation result performed about the analysis area | region shown in FIG. 8 of the calculation model shown in FIG. 7 for every predetermined | prescribed time calculation step number, (b) is an analysis area | region shown in FIG. It is explanatory drawing explaining the specific dimension of. It is explanatory drawing which shows the graph which shows an example of the relationship between the space calculation range and calculation step in the analysis area | region shown in FIG. 8, and a calculation amount reduction rate. It is a flowchart which shows the conventional electromagnetic field analysis method.

Explanation of symbols

DESCRIPTION OF SYMBOLS 10,30 Electromagnetic field analyzer 12 Refractive index distribution definition part 14 Calculation condition input part 16 Arrival area prediction part 18 Electromagnetic field calculation part 20 Storage part 22 Write / read (control) part 24 Calculation result output part 32 Input device 34 Read / write Device 36 Arithmetic processing unit (CPU)
38 Memory 40 Display device 42 Recording device (printer)
44 bus 50 calculation model 50a analysis area 52, 52a glass substrate
54 Cylindrical lens array 54a Cylindrical lens 56, 56a Air layer 58 Excitation part (wave source)
60 Spatial calculation range

Claims (17)

Propagation conditions the computer, sequentially performed continuously calculate the wavefield time change of the analysis region the wave propagates from the first period state for each calculation step, the computer, to the analysis area is the wave propagates the a wave field analysis method of analysis,
The computer, the arrival area of the wave in said analysis area in advance is reached to predict,
The computer calculates the time change of the wave field in a predetermined calculation step, and sets the arrival region where the wave in the analysis region is predicted to reach the calculation step as a spatial calculation range of the calculation step. wave field analysis wherein the line Ukoto as a.   The wave field analysis method according to claim 1, wherein the wave propagates from one end of the analysis region to a predetermined axial direction of the analysis region.   The wave field analysis method according to claim 1 or 2, wherein the arrival region of the wave is predicted by predicting a propagation speed of the wave propagating through the analysis region.   The wave field analysis method according to claim 1, wherein the arrival area of the wave is predicted based on information on a refractive index distribution in the analysis area.   In the refractive index distribution in the analysis region, the representative value of the refractive index of the surface orthogonal to the propagation direction of the wave in the arrival region is set to the smallest refractive index in the surface orthogonal to the propagation direction of the wave. The wave field analysis method according to claim 4, wherein the wave field analysis method is obtained.   The wave field analysis method according to claim 1, wherein the prediction of the arrival region of the wave is performed on the assumption that the refractive index in the analysis region is 1.   The wave field analysis method according to any one of claims 1 to 6, wherein the arrival area of the wave is predicted by calculating a propagation length in which the wave propagates from the one end of the analysis area.   The wave field analysis method according to claim 1, wherein the wave is an electromagnetic wave, and the wave field is an electromagnetic field. A wave field analyzer for calculating the time change of the wave field in the analysis region where the wave propagates sequentially from the initial state for each calculation step and analyzing the propagation state in which the wave propagates in the analysis region. There,
A wave field calculating means for continuously calculating a time change of the wave field in the analysis region in which the wave propagates from an initial state;
Prediction means for predicting the arrival region where the wave has reached in the analysis region in advance,
The wave field calculation means calculates the time change of the wave field in a predetermined calculation step, and calculates the arrival region where the wave in the analysis region is predicted to reach the predetermined calculation step. A wave field analyzer characterized in that it is performed as a spatial calculation range of steps.   The wave propagates from one end of the analysis region to a predetermined axial direction of the analysis region, and the wave field calculation means calculates a time change of the wave field along the predetermined axial direction. The wave field analysis apparatus according to claim 9, which is a thing.   The wave field analysis device according to claim 9 or 10, wherein the prediction means predicts the arrival region of the wave by predicting a propagation speed of the wave propagating in the analysis region.   The wave field analysis device according to any one of claims 9 to 11, wherein the prediction unit performs prediction of the arrival region of the wave based on information on a refractive index distribution in the analysis region.   The prediction means sets the representative value of the refractive index of the surface orthogonal to the propagation direction of the wave in the arrival region as the smallest refractive index in the surface orthogonal to the propagation direction of the wave, The wave field analyzer according to any one of claims 9 to 12, wherein a refractive index distribution is obtained, and the arrival area of the wave is predicted based on the obtained refractive index distribution in the analysis area.   The wave field analysis apparatus according to any one of claims 9 to 12, wherein the prediction unit performs prediction of the arrival region of the wave on the assumption that a refractive index in the analysis region is 1.   The wave field analysis device according to any one of claims 9 to 14, wherein the predicting unit predicts the arrival region of the wave by calculating a propagation length of the wave propagating from the one end of the analysis region. .   The wave field analysis device according to claim 9, wherein the wave is an electromagnetic wave, and the wave field is an electromagnetic field.   A computer-readable recording medium having recorded thereon a computer program for executing the wave field analysis method according to claim 1.