JP5168051B2 - Electromagnetic field analysis program and electromagnetic field analysis apparatus - Google Patents

Description

  The present invention relates to an electromagnetic field analysis program and an electromagnetic field analysis apparatus that provide electromagnetic field simulation.

Electromagnetic field analysis programs are widely known. The electromagnetic field analysis program provides electromagnetic field simulation. A finite difference time domain (FDTD) method is used to realize the simulation. According to such simulation, changes in the electromagnetic field distribution can be imaged in time series for a specific calculation model.
JP 2008-82849 A JP 2006-3287 A JP 2000-227450 A Kane S. Yee, “Numerical Solution of Initial Boundary Value Values Involving Maxwell's Expressions in Isotropic Media, Month of IEEE TRANSACTIONS ONANTOPON I NON. AP-14, NO. 8, p. 302-307 Satoshi Uno, “Electromagnetic field and antenna analysis by FDTD method”, Corona, March 20, 1998 Taflove, Allen, et al. , “Computational electrodynamics”, Arttech House, Inc.

  The use of an electromagnetic field analysis program is sought for the analysis of so-called near-field light. However, in the FDTD method, the analysis region is limited to about several times the wavelength of light. As a result, for example, modeling of a condensing system such as a condensing lens could not be realized. In the FDTD method, for example, a calculation formula for Fraunhofer diffraction is used for introducing a condensing system. Even if the focused light is introduced into the FDTD method based on the calculation result of such a calculation formula, the focused light cannot be reproduced with high accuracy in the virtual space of the analysis region.

  The present invention has been made in view of the above circumstances, and an object thereof is to provide an electromagnetic field analysis program and an electromagnetic field analysis apparatus that can reproduce focused light with high accuracy when using the FDTD method.

  In order to achieve the above object, the electromagnetic field analysis program specifies a procedure for constructing a calculation model for specifying a three-dimensional distribution of electric field characteristics and magnetic field characteristics in a virtual three-dimensional space, and specifies a wave source in the virtual three-dimensional space. And, based on the finite difference time domain method, for each unit cell partitioned in the virtual three-dimensional space and adjacent to each other, the spatial distribution of the electromagnetic field at the next time is calculated based on the spatial distribution of the electromagnetic field at the current time. In the calculation procedure, in the calculation of the spatial distribution, the procedure of establishing the excitation of the electric field at the wave source based on the predetermined excitation amplitude, and in the calculation of the excitation amplitude, the electric field component perpendicular to the light beam of the focused light is applied to the wave source surface. Compile the procedure for correcting the electric field amplitude of the focused light based on the projection and the procedure for calculating the Fraunhofer diffraction calculation formula based on the corrected electric field amplitude and calculating the excitation amplitude based on the calculation result. To be executed by the Ta. According to these processing operations, the spatial distribution of the electromagnetic field can be reproduced with high accuracy based on the finite difference time domain method.

  In addition, the electromagnetic field analyzer establishes excitation of an electric field with a wave source based on a calculation model input unit that acquires a calculation model for specifying a three-dimensional distribution of electric field characteristics and magnetic field characteristics in a virtual three-dimensional space, and a predetermined excitation amplitude. However, for each unit cell partitioned in the virtual three-dimensional space and adjacent to each other, the spatial distribution of the electromagnetic field at the next time is calculated based on the spatial distribution of the electromagnetic field at the current time based on the finite difference time domain method. The finite-difference time-domain calculation unit that corrects the electric field amplitude of the focused light based on the projection of the electric field component perpendicular to the light beam of the focused light onto the wave source surface, and calculates the calculation formula for Fraunhofer diffraction based on the corrected electric field amplitude And a condensing system reproduction unit that derives the excitation amplitude based on the calculation result.

  As described above, according to the present invention, an electromagnetic field analysis program and an electromagnetic field analysis apparatus capable of reproducing focused light with high accuracy when using the FDTD method are provided.

  Hereinafter, an embodiment of the present invention will be described with reference to the accompanying drawings.

  FIG. 1 schematically shows a configuration of an electromagnetic field analysis apparatus according to an embodiment of the present invention. The electromagnetic field analysis device 11 includes a computer 12 such as an engineering workstation and a display device 13 connected to the computer 12. For example, input devices such as a keyboard 14 and a mouse 15 are connected to the computer 12.

  The computer 12 includes a box-shaped housing 16. A so-called mother board is accommodated in the housing 16. As is well known, electronic circuit elements such as a CPU (Central Processing Unit) and a memory are mounted on the motherboard. The user can input various data and commands from the keyboard 14 and mouse 15 to the CPU.

  An FDD (flexible disk drive) 17 and a recording disk drive 18 are further incorporated in the housing 16. The FDD 17 and the recording disk drive device 18 can receive a diskette (FD), a CD-ROM, and a DVD-ROM from each front receiving port. The FDD 17 and the recording disk drive device 18 can read, for example, data and software programs from the received FD and CD-ROM.

  The display device 13 includes a display housing 19. The display casing 19 accommodates a flat display panel such as a liquid crystal display (LCD) panel. A rectangular window hole 21 is defined in the display housing 19. An LCD panel display screen faces the window 21. Graphics and text are displayed on the display screen of the LCD panel based on the arithmetic processing of the CPU.

  As shown in FIG. 2, the CPU 21 is connected to a system controller 22 that controls the operation of the computer 12, that is, a chip set. In addition to the keyboard 14, mouse 15, FDD 17, and recording disk drive device 18, the system controller 22 is connected with a system memory 23, an HDD (Hard Disk Drive Device) 24, and a graphic board 25. For example, an OS (operating system) and other software programs are temporarily taken into the system memory 23 from the HDD 24. The CPU 21 executes arithmetic processing based on a software program that is temporarily loaded into the system memory 23. A software program may be transferred to the HDD 24 in advance from, for example, the FD 26 or the CD-ROM 27 described above. The display device 13 is connected to the graphic board 25. The graphic board 25 sends an image signal to the display device 13 based on a command from the CPU 21.

  In addition, a LAN (local area network) board 28 and a modem 29 may be connected to the system controller 22. The LAN board 28 and the modem 29 connect, for example, the CPU 21 in the electromagnetic field analyzer 11 and a CPU (not shown) in another computer system. The CPU 21 in the electromagnetic field analysis device 11 can exchange signals with other CPUs via a LAN or the Internet.

  The HDD 24 stores an electromagnetic field analysis program according to a specific example of the present invention. This software program may be taken into the HDD 24 from, for example, the FD 26, the CD-ROM 27, or another portable recording medium, or may be taken into the HDD 24 from a computer network such as a LAN or the Internet. The CPU 21 can realize a predetermined processing operation according to the description of the electromagnetic field analysis program.

  FIG. 3 schematically shows functional blocks of the electromagnetic field analysis apparatus 11 according to the first embodiment constructed in the CPU 21. The electromagnetic field analysis apparatus 11 includes a finite difference time domain (FDTD) method calculation unit 33. As shown in FIG. 4, the FDTD method calculation unit 33 specifies a cubic unit cell CE in the virtual three-dimensional space. In specifying the unit cell CE, lattice lines are drawn for each of the xz plane, the yz plane, and the xy plane in the virtual three-dimensional space. The intervals Δx, Δy, Δz between the lattice lines are all set to a constant value. A cubic unit cell CE is established by the action of the lattice lines. The virtual three-dimensional space is grasped as an aggregate of unit cells CE. A coordinate value (i, j, k) is attached to each unit cell CE. In addition, the intervals Δx, Δy, Δz between the lattice lines may change for each unit cell CE.

  The FDTD method calculation unit 33 calculates the x component Ex, the y component Ey, and the z component Ez of the electric field E for each unit cell CE according to the following equation.

ここで、εは単位セルＣＥごとに特定される誘電率を示す。σは単位セルＣＥごとに特定される導電率を示す。算出は個々の単位セルＣＥごとにΔｔの時間間隔で実施される。ｎは時系列の順番を示す。時間間隔Δｔごとにｎ（自然数）は増加する。同時に、ＦＤＴＤ法計算部３３は１つの単位セルＣＥごとに次式に従って磁界Ｈのｘ成分Ｈｘ、ｙ成分Ｈｙおよびｚ成分Ｈｚを算出する。

Here, ε represents a dielectric constant specified for each unit cell CE. σ indicates the conductivity specified for each unit cell CE. The calculation is performed at time intervals of Δt for each unit cell CE. n indicates the order of time series. N (natural number) increases every time interval Δt. At the same time, the FDTD method calculation unit 33 calculates the x component Hx, the y component Hy, and the z component Hz of the magnetic field H according to the following equation for each unit cell CE.

ここで、μは単位セルＣＥごとに特定される透磁率を示す。

Here, μ represents the magnetic permeability specified for each unit cell CE.

  As shown in FIG. 5, the FDTD method calculation unit 33 specifies the wave source SO in the virtual three-dimensional space CO. As will be described later, the wave source SO reproduces the light beam LB focused by the lens LN toward the focal point FC according to the FDTD method. The optical axis OP of the lens LN corresponds to the z axis of the virtual three-dimensional space CO. The wave source SO is assigned to the unit cells CE arranged along the xy plane of the virtual three-dimensional space CO. The FDTD method calculation unit 33 causes electric field excitation in the unit cell CE of the wave source SO according to the following equation.

ここで、Ｅ_０は波源の励振振幅を示す。ωは波源の角周波数を示す。ξｘ、ξｙは波源の初期位相を示す。ここでは、光軸ＯＰがｚ軸に設定されることから、電界Ｅのｚ成分Ｅｚは励振しない。

Here, E ₀ indicates the excitation amplitude of the wave source. ω represents the angular frequency of the wave source. ξx and ξy indicate the initial phase of the wave source. Here, since the optical axis OP is set to the z axis, the z component Ez of the electric field E is not excited.

  As shown in FIG. 3, a calculation result analysis unit 34 is connected to the FDTD method calculation unit 33. The calculation result analysis unit 34 converts the calculation result of the FDTD method calculation unit 33 based on the specific physical quantity. Physical quantities include, for example, electric field strength, phase, and other measurable physical quantities. Specific physical quantity data is generated based on the x component Ex, y component Ey, and z component Ez of the electric field E, and the x component Hx, y component Hy, and z component Hz of the magnetic field H. In the physical quantity data, for example, a time change of the physical quantity is specified. In addition, the frequency spectrum may be calculated based on the Fourier transform of the time change result.

  An analysis result output unit 35 is connected to the calculation result analysis unit 34. The analysis result output unit 35 visualizes the analysis result of the calculation result analysis unit 34. Visualization data is generated based on the physical quantity data. In this visualization data, a moving image may be described based on a temporal change of a physical quantity, or a still image at a specific time may be described. The visualization data is supplied to the graphic board 25, for example. The graphic board 25 displays the analysis result on the screen of the display device 13 based on the visualization data. In addition, the visualization data may be stored in the HDD 24, may be output toward the LAN via the LAN board 28, or may be output toward the Internet via the modem 29.

  A calculation model input unit 37 is connected to the FDTD method calculation unit 33. The calculation model input unit 37 constructs a calculation model in the virtual three-dimensional space CO. The calculation model specifies, for example, a three-dimensional distribution of electric field characteristics and magnetic field characteristics. The electric field characteristics include dielectric constant ε and conductivity σ. Magnetic field characteristics include permeability μ. The calculation model may be taken into the calculation model input unit 37 based on the operation of the keyboard 14 or the mouse 15, for example, or may be taken into the calculation model input unit 37 from the CD-ROM 27 by the action of the recording disk drive device 18. The calculation model input unit 37 may receive the data via a LAN or the Internet. The fetched calculation model may be stored in the HDD 24.

  A calculation condition input unit 38 is connected to the FDTD method calculation unit 33. The calculation condition input unit 38 specifies calculation conditions. This calculation condition is required when calculating the x component Ex, y component Ey, and z component Ez of the electric field E and the x component Hx, y component Hy, and z component Hz of the magnetic field H. The calculation conditions include intervals Δx, Δy, Δz between lattice lines set in the xz plane, the yz plane, and the xy plane, respectively, and a time interval Δt. Based on the intervals Δx, Δy, Δz, the FDTD method calculation unit 33 establishes a cubic unit cell CE. The intervals Δx, Δy, Δz are set to about 1/10 to 1/20 of the wavelength of the focused light, that is, the light beam LB. The intervals Δx, Δy, Δz and the time interval Δt may be taken into the calculation condition input unit 38 based on the operation of the keyboard 14 or the mouse 15, for example, or may be taken into the calculation condition input unit 38 via the LAN or the Internet. Good. The fetched calculation conditions may be stored in the HDD 24.

  A condensing system reproduction unit 39 is connected to the FDTD method calculation unit 33. The condensing system reproduction unit 39 includes a condensing system input unit 41. The condensing system input unit 41 specifies the wavelength λ of incident light and the condensing characteristics and polarization characteristics of the condensing system. The condensing characteristic of the condensing system includes, for example, the pupil diameter α and the focal length f of the lens. The numerical aperture NA may be specified instead of the focal length f. The polarization characteristic of the condensing system is defined by the electric field amplitude Ex in the xz plane and the electric field amplitude Ey in the yz plane.

  In the light collection system reproduction unit 39, an electric field amplitude calculation unit 42 is connected to the light collection system input unit 41. The electric field amplitude calculator 42 calculates electric field amplitudes E′x and E′y based on the input electric field amplitudes Ex and Ey. The calculation method will be described later.

  In the condensing system reproduction unit 39, a Fraunhofer diffraction calculation unit 43 is connected to the electric field amplitude calculation unit 42. The Fraunhofer diffraction calculation unit 43 calculates the excitation amplitude based on the calculation formula of Fraunhofer diffraction. In the calculation, the electric field amplitudes E′x and E′y are applied to the calculation formula of Fraunhofer diffraction. The Fraunhofer diffraction calculation unit 43 performs a fast Fourier transform (FFT) according to the following equation.

ここで、ｇ（ｘ、ｙ）はレンズＬＮに入射する電界の複素振幅を示す。（ｘ、ｙ）はレンズＬＮの開口面上の座標を示す。（ｘ_０，ｙ_０）は焦点面すなわち励振面上の座標を示す。ｕ（ｖｘ、ｖｙ）は焦点面上の電界振幅を示す。ｆはレンズＬＮの焦点距離を示す。λは光の波長を示す。算出結果の振幅ｕは複素数として表現されることから、励振面上の電界振幅すなわち励振振幅Ｅ′ｘ、Ｅ′ｙおよび位相ξｘ、ξｙが特定される。

Here, g (x, y) represents the complex amplitude of the electric field incident on the lens LN. (X, y) indicates coordinates on the aperture surface of the lens LN. (X ₀ , y ₀ ) indicates coordinates on the focal plane, that is, the excitation plane. u (vx, vy) represents the electric field amplitude on the focal plane. f indicates the focal length of the lens LN. λ indicates the wavelength of light. Since the amplitude u of the calculation result is expressed as a complex number, the electric field amplitude on the excitation surface, that is, the excitation amplitudes E′x and E′y and the phases ξx and ξy are specified.

  Here, a procedure for calculating the electric field amplitudes E′x and E′y will be briefly described. Now, a case is assumed where x-polarized light is incident on the condensing system along the optical axis OP of the lens LN, that is, the z-axis. Consider the electric field on the x-axis of the excitation surface. As shown in FIG. 6, the focused light has a light ray incident at a predetermined inclination angle θ toward the focal point FC. The electric field amplitude Ex of the focused light is defined perpendicular to the light beam. On the other hand, since the excitation surface 44 is set parallel to the x-axis, the excitation amplitude E′x on the x-axis is given by the following equation.

次に、集光する光の波面を考察する。図７に示されるように、波面４５は励振面４４に対して所定の傾斜姿勢で観察される。励振面４４への投射像から明らかなように、波面４５上の単位面積に対して励振面４４の投射面積は狭まる。こうした面積の縮小に応じて単位面積当たりの電界強度は調整される。［数５］に鑑み、最終的に、ｘ軸上の励振振幅Ｅ′ｘは次式で与えられる。

Next, consider the wavefront of the collected light. As shown in FIG. 7, the wavefront 45 is observed with a predetermined inclination with respect to the excitation surface 44. As is clear from the projection image on the excitation surface 44, the projection area of the excitation surface 44 is narrower than the unit area on the wave surface 45. The electric field intensity per unit area is adjusted in accordance with the reduction of the area. In view of [Equation 5], the excitation amplitude E′x on the x-axis is finally given by the following equation.

その一方で、ｙ軸上の電界は光線の傾斜に対して偏光方向は垂直に交差する。したがって、ｙ軸上の電界では面積の補正のみが適用される。このとき、ｙ軸上の励振振幅Ｅ′ｘは次式で与えられる。

On the other hand, the direction of polarization of the electric field on the y-axis intersects perpendicularly to the tilt of the light beam. Therefore, only area correction is applied to the electric field on the y-axis. At this time, the excitation amplitude E′x on the y-axis is given by the following equation.

図８に示されるように、軸上の電界以外の電界は平行方向成分Ｅｐと垂直方向成分Ｅｓとに分解される。こういった分解にあたってｚ軸回りに極座標値φが特定される。前述の数式［数５］および［数６］が平行方向成分Ｅｐおよび垂直方向成分Ｅｓにそれぞれ適用される。その結果、平行方向成分Ｅｐおよび垂直方向成分Ｅｓは次式で与えられる。

As shown in FIG. 8, the electric field other than the axial electric field is decomposed into a parallel component Ep and a vertical component Es. In such decomposition, a polar coordinate value φ is specified around the z axis. The above mathematical formulas [Equation 5] and [Equation 6] are applied to the parallel direction component Ep and the vertical direction component Es, respectively. As a result, the parallel direction component Ep and the vertical direction component Es are given by the following equations.

平行方向成分Ｅｐおよび垂直方向成分Ｅｓを合成し、ｘ方向成分Ｅ′ｘおよびｙ方向成分Ｅ′ｙを算出する。

The parallel direction component Ep and the vertical direction component Es are combined to calculate the x direction component E′x and the y direction component E′y.

ｙ偏光は同様に考察される。その結果、次式が与えられる。

y-polarization is considered similarly. As a result, the following equation is given.

ｘ方向成分Ｅ′ｘおよびｙ方向成分Ｅ′ｙが足し合わせられると、一般化された励振振幅の式が与えられる。

When the x-direction component E′x and the y-direction component E′y are added together, a generalized excitation amplitude equation is given.

なお、数式［数１２］で、極座標に基づく三角関数に代えて集光系の入射瞳上の座標（ｘ、ｙ）と焦点距離ｆとが用いられると、次式が与えられる。

In the equation [Equation 12], when the coordinates (x, y) on the entrance pupil of the condensing system and the focal length f are used instead of the trigonometric function based on the polar coordinates, the following equation is given.

ここで、次式が成立する。

Here, the following equation holds.

以上のような機能ブロックは前述の電磁界解析プログラムの実行に基づきＣＰＵ２１内に構築されればよい。その他、こうした機能ブロックは例えば電子デバイスの組み合わせに基づきハードウェアで実現されてもよい。

The functional blocks as described above may be constructed in the CPU 21 based on the execution of the electromagnetic field analysis program described above. In addition, such functional blocks may be realized by hardware based on a combination of electronic devices, for example.

  Next, processing operations realized by the CPU 21 based on the execution of the electromagnetic field analysis program will be described. As shown in FIG. 9, in step S1, the CPU 21 acquires the spatial arrangement of the substance. For example, dielectric constant ε, conductivity σ, and magnetic permeability μ are designated for each substance. Based on the spatial arrangement of the substance, the three-dimensional distribution of the electric field characteristic and the magnetic field characteristic is specified in the virtual three-dimensional space CO as described above. A calculation model is built.

  In step S2, the CPU 21 acquires the above-described calculation conditions. The intervals Δx, Δy, Δz and the time interval Δt are specified. Similar to the above, the unit cell CE is partitioned in the virtual three-dimensional space CO based on the calculation conditions. A dielectric constant ε, electrical conductivity σ, and magnetic permeability μ are specified for each unit cell CE.

  In step S <b> 3, the CPU 21 acquires the wavelength λ of the incident light and the light collection characteristics and polarization characteristics of the light collection system. Similar to the above, the condensing characteristics of the condensing system include, for example, the pupil diameter α and the focal length f of the lens. The polarization characteristic of the condensing system is defined by the electric field amplitude Ex in the xz plane and the electric field amplitude Ey in the yz plane.

  In step S4, the CPU 21 calculates electric field amplitudes E′x and E′y based on the input electric field amplitudes Ex and Ey. In the calculation, the above-described equation [Equation 12] or [Equation 13] is used. The values of the input electric field amplitudes Ex and Ey are corrected. In subsequent step S5, the CPU 21 calculates the excitation amplitude based on Fraunhofer diffraction. The CPU 21 performs the fast Fourier transform according to the above-described equation [Equation 4]. In calculating the excitation amplitude, the CPU 21 uses correction values of the electric field amplitudes Ex and Ey, that is, electric field amplitudes E′x and E′y.

  After step S6, the CPU 21 calculates the electromagnetic field distribution according to the FDTD method. In calculation, first, in step S6, the CPU 21 initializes a variable t. In subsequent step S7, the CPU 21 sets the current time t. A time interval Δt is added to the previous time t. In step S8, the CPU 21 calculates an electric field for each unit cell CE according to the mathematical formula [Equation 1]. In the calculation, excitation, that is, electric field oscillation is caused in a specific unit cell CE according to the mathematical formula [Equation 3]. The electric field vibration propagates to the surrounding unit cells CE according to the formula [Equation 1]. Thus, the three-dimensional distribution of the electric field is reproduced at the current time t. In the calculation, each calculation result is temporarily stored in the system memory 23.

  In step S9, the CPU 21 calculates a magnetic field for each unit cell CE according to the mathematical formula [Equation 2]. In response to the propagation of the electric field, the magnetic field propagates to the surrounding unit cell CE. Thus, the three-dimensional magnetic field distribution is reproduced at the current time t. In the calculation, each calculation result is temporarily stored in the system memory 23. Therefore, the allowable number of unit cells CE, that is, the size of the virtual three-dimensional space is determined based on the capacity of the system memory 23.

In step S10, the CPU 21 confirms the end time. If the current time t has not reached the end time _tEND , the process returns to step S7. As a result of the processes in steps S7 to S9 being repeated, the three-dimensional distribution of the electric field E and the three-dimensional distribution of the magnetic field H can be specified for each time interval Δt. As a result, light propagation can be reproduced in the virtual three-dimensional space CO.

  When the current time t reaches the end time tEND, the CPU 21 generates physical quantity data in the same manner as described above in step S11. The time change of the three-dimensional distribution of the electric field E and the time change of the three-dimensional distribution of the magnetic field H are expressed by specific physical quantities. In subsequent step S12, the CPU 21 generates visualization data in the same manner as described above. Visualization data is output. Thus, the processing operation of the CPU 21 ends.

  The inventor verified the accuracy of the electromagnetic field analysis apparatus 11 according to the present embodiment. The electromagnetic field analysis program was executed as described above. In this simulation, linearly polarized light LB was collected by a lens LN having a numerical aperture (NA) of 0.7. The inventor prepared a reference example. In the reference example, light was analyzed based on the calculation formula of diffraction under the same conditions. Polarization was taken into account in diffraction calculations. It is known that the propagation of light is reproduced with high accuracy according to such a calculation of diffraction. As shown in FIG. 10, it was confirmed that the calculation result based on the electromagnetic field analysis program approximates to the reference example in the light intensity in the direction parallel to the polarized light. Similarly, as shown in FIG. 11, it was confirmed that the calculation result based on the electromagnetic field analysis program approximates the reference example for the light intensity in the direction orthogonal to the polarization.

  The inventor reproduced light propagation based on a calculation method according to a comparative example. In this comparative example, in the calculation process based on the FDTD method, the calculation formula of Fraunhofer diffraction was simply used without following the above-described excitation amplitude calculation procedure. As a result, as shown in FIG. 12, in the light intensity in the direction parallel to the polarized light, an error was recognized between the calculation result of the comparative example and the reference example. Similarly, as shown in FIG. 13, an error was recognized between the calculation result of the comparative example and the reference example in the light intensity in the direction orthogonal to the polarized light. As shown in FIG. 14 and FIG. 15, the error is reduced in the calculation result based on the electromagnetic field analysis program in both the light intensity in the direction parallel to the polarization and the light intensity in the orthogonal direction compared to the calculation result according to the comparative example. It was confirmed.

FIG. 16 schematically shows functional blocks of the electromagnetic field analysis apparatus 11 according to the second embodiment. In this electromagnetic field analysis apparatus 11, the condensing system reproduction unit 39 includes a light beam intensity distribution input unit 51. The light beam intensity distribution input unit 51 is connected to the condensing system input unit 41. The light beam intensity distribution input unit 51 specifies the spatial distribution of the intensity of the light beam incident on the entrance pupil. The spatial distribution of the intensity may be given by a coordinate table and a numerical table indicating the intensity corresponding to the coordinate, or may be defined by a spread width based on the assumption of a Gaussian distribution. For example, when the Gaussian distribution is defined by the spread width of the peak intensity 1 / e ² , the electric field amplitude is given by the following equation.

ただし、Ａ_０は振幅のピーク値を示す。ｗ_ｘ、ｗ_ｙは拡がり幅（全幅）を示す。算出結果は電界振幅算出部４２に供給される。電界振幅算出部４２は、供給された電界振幅に基づき前述のように電界振幅Ｅ′ｘ、Ｅ′ｙを算出する。その他、前述の第１実施形態と均等な構成には同一の参照符号が付される。

However, A ₀ represents the peak value of the amplitude. w _x and w _y indicate the spread width (full width). The calculation result is supplied to the electric field amplitude calculation unit 42. The electric field amplitude calculation unit 42 calculates the electric field amplitudes E′x and E′y as described above based on the supplied electric field amplitude. In addition, the same reference numerals are assigned to components equivalent to those in the first embodiment.

  FIG. 17 schematically shows functional blocks of the electromagnetic field analysis apparatus 11 according to the third embodiment. In the electromagnetic field analysis apparatus 11, the condensing system reproduction unit 39 includes an aberration input unit 52. The aberration input unit 52 sets a phase distribution that defines the aberration for each electric field component. Specifically, the electric field amplitudes Ex and Ey are set to complex numbers reflecting the phases in Equations [Equation 12] and [Equation 13]. This complex field amplitude is defined as a function of the coordinates on the entrance pupil. For example, the phase may be given by a Zernike polynomial. Now, if polar coordinates are established on the entrance pupil, the Zernike polynomial is given by

図１８は数式［数１６］に基づく集光スポットを概略的に示す。ここでは、数式［数１６］中、ｎ＝３，ｍ＝１、Ａ_ｎ＝０、Ｂ_ｍｎ＝０、Ｃｎｍ＝０．５が設定された。集光光学系でコマ収差が再現されることができる。

FIG. 18 schematically shows a focused spot based on the formula [Equation 16]. Here, n = 3, m = 1, A _n = 0, B _mn = 0, and Cnm = 0.5 are set in the mathematical formula [Equation 16]. The coma aberration can be reproduced by the condensing optical system.

It is a figure showing roughly the composition of the electromagnetic field analysis device concerning one embodiment of the present invention. It is a block diagram which shows roughly the structure of an electromagnetic field analyzer. It is a block diagram which shows roughly the functional block of the electromagnetic field analyzer which concerns on 1st Embodiment. It is a conceptual diagram which shows a unit cell roughly. It is a conceptual diagram which shows the model of a condensing optical system roughly. It is a conceptual diagram which specifies the inclination of a light ray. It is a conceptual diagram which specifies the inclination of a wave front. It is a conceptual diagram which specifies electric fields other than the electric field on an axis | shaft. It is a flowchart which shows the processing operation of an electromagnetic field analyzer. It is a graph which shows the light intensity computed with the electromagnetic field analysis program concerning this embodiment. It is a graph which shows the light intensity computed with the electromagnetic field analysis program concerning this embodiment. It is a graph which shows the light intensity calculated with the electromagnetic field analysis program using the calculation formula of Fraunhofer diffraction in the calculation process based on FDTD method. It is a graph which shows the light intensity calculated with the electromagnetic field analysis program using the calculation formula of Fraunhofer diffraction in the calculation process based on FDTD method. It is a graph which shows the comparison with the error of the light intensity calculated based on this embodiment, and the error of the light intensity calculated based on the comparative example. It is a graph which shows the comparison with the error of the light intensity calculated based on this embodiment, and the error of the light intensity calculated based on the comparative example. It is a block diagram which shows roughly the functional block of the electromagnetic field analyzer which concerns on 2nd Embodiment. It is a block diagram which shows roughly the functional block of the electromagnetic field analyzer which concerns on 3rd Embodiment. It is a figure which shows the simulation result which shows the mode of a condensing spot roughly.

Explanation of symbols

  11 Electromagnetic field analysis device, 33 Finite difference time domain method calculation unit, 37 Calculation model input unit, 39 Condensing system reproduction unit, CE unit cell, CO virtual three-dimensional space, LB ray, SO wave source surface.

Claims (4)

A procedure for constructing a calculation model for specifying a three-dimensional distribution of electric field characteristics and magnetic field characteristics in a virtual three-dimensional space; a procedure for setting a wave source in a virtual plane perpendicular to the optical axis of the lens in the virtual three-dimensional space; A procedure for calculating the spatial distribution of the electromagnetic field at the next time based on the spatial distribution of the electromagnetic field at the current time, based on the finite difference time domain method, for each unit cell partitioned in the virtual three-dimensional space and adjacent to each other. , in calculating the spatial distribution, the procedure for establishing an excitation electric field in the wave source based on a predetermined excitation amplitude, in the calculation of the excitation amplitude, the virtual electric field component perpendicular to the rays of the focused beam in the direction of the light beam a step of setting the electric field amplitude of the focused light by the projection image specified when projected on the plane, a calculation formula of Fraunhofer diffraction based on the electric field amplitude is set to calculate the excited on the basis of the result Electromagnetic field analysis program characterized by executing the steps of calculating the amplitude computer. 2. The electromagnetic field analysis program according to claim 1, wherein the incident is performed according to a polar coordinate system having an electric field amplitude Ex and Ey of the electric field component specified in the xz plane and the yz plane with respect to the optical axis z and an origin at a focal position. Based on the coordinate values (θ, φ) that specify the pupil,

An electromagnetic field analysis program characterized in that the set electric field amplitudes E'x and E'y are specified. The electromagnetic field analysis program according to claim 1, further causing a computer to execute a procedure for setting the aberration of the focused light prior to the procedure for setting the electric field amplitude. A calculation model input unit for acquiring a calculation model for specifying a three-dimensional distribution of electric field characteristics and magnetic field characteristics in a virtual three-dimensional space, and a wave source set in a virtual plane orthogonal to the optical axis of the lens in the virtual three-dimensional space in being established the excitation of the predetermined based feeding circuit boundaries excitation amplitude, the each unit cell is divided into a virtual three-dimensional space adjacent to each other, based on the finite-difference time-domain method, the electromagnetic field at the current time A finite-difference time-domain calculation unit that calculates the spatial distribution of the electromagnetic field at the next time based on the spatial distribution of the current, and specified when an electric field component perpendicular to the light beam of the focused light is projected on the virtual plane in the direction of the light beam set the electric field amplitude of the focused light in the projection image to be, in that it comprises a condensing system reproducing unit calculates the calculation formula of Fraunhofer diffraction based on the electric field amplitude is set, deriving the excitation amplitude based on the calculation result Characteristic electric Field analyzer.

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