A method for obtaining optical properties of crystal materials

Abstract

The present invention discloses a method for obtaining the optical properties of a crystal material, comprising obtaining the wave function and electronic structure of the crystal material; constructing a position matrix element of the crystal material based on the wave function and electronic structure; and calculating at least one of the linear optical polarizability, nonlinear optical polarizability, and the contribution of a single atom in the crystal material to the nonlinear optical polarizability of the crystal material based on the position matrix element. The present invention can accurately determine the linear and nonlinear optical polarizability of the crystal material, as well as the contribution of each atom in the crystal material to the nonlinear optical polarizability, and distinguish the contributions of the element's conduction band and valence band. This method not only facilitates the classification of functional elements of NLO materials and the search for new high-performance NLO materials, but also provides important insights into the nature of the interaction between optical fields and matter.

Description

Technical Field

[0001] The present application relates to a method for obtaining the optical properties of a crystal material, and belongs to the technical field of crystal material preparation. Background Art

[0002] Laser technology is one of the most important inventions after atomic energy, computers, and semiconductors. It is widely used in fields such as laser radar and weapons, laser scanning and ranging, and fiber-optic communications. However, the available laser wavelengths are limited, necessitating the use of laser frequency conversion media to broaden the laser wavelength range and meet the required wavelength. Nonlinear optical (NLO) materials, which utilize the NLO effect to achieve laser frequency conversion, are indispensable advanced laser materials and have garnered considerable attention in recent years.

[0003] Due to the complexity of the interaction between lasers and nonlinear optical materials, the methods currently used can only qualitatively describe the functional elements at work in the materials and cannot provide better guidance for chemical synthesis, which has a significant impact on the development cycle and cost of new optical materials. Summary of the Invention

[0004] The purpose of this application is to provide a method for obtaining the optical properties of a crystal material, which can accurately obtain the linear and nonlinear optical polarizabilities of the crystal material and the contribution of each atom in the crystal material to the nonlinear optical polarizability.

[0005] An embodiment of the present invention discloses a method for obtaining optical properties of a crystal material, comprising:

[0006] Obtain the wave function and electronic structure of crystalline materials;

[0007] constructing a position matrix element of the crystal material according to the wave function and the electronic structure;

[0008] At least one of the linear optical susceptibility, the nonlinear optical susceptibility, and the contribution of a single atom in the crystal material to the nonlinear optical susceptibility of the crystal material is calculated based on the position matrix elements.

[0009] Preferably, calculating at least one of the linear optical susceptibility, the nonlinear optical susceptibility, and the contribution of a single atom in the crystal material to the nonlinear optical susceptibility of the crystal material according to the position matrix element comprises:

[0010] The contribution of a single atom in the crystal material to the nonlinear optical susceptibility of the crystal material is calculated according to the position matrix element, specifically:

[0011] The contribution of a single atom in the crystal material to the nonlinear optical susceptibility of the crystal material is calculated according to a first formula, wherein the first formula is:

[0012]

[0013] Among them, A τ is the contribution of a single atom to the nonlinear optical susceptibility of the crystalline material, VB A τ is the contribution of the valence band of a single atom to the nonlinear optical susceptibility of the crystalline material, CB A τ is the contribution of the conduction band of a single atom to the nonlinear optical susceptibility of the crystalline material.

[0014] Preferably, the contribution of the valence band of the single atom to the nonlinear optical susceptibility of the crystalline material is calculated according to a second formula, which is:

[0015]

[0016] Wherein, τ is a single atom in the crystal material, Ω is the volume of the unit cell of the crystal material, L is the number of atomic orbitals of the single atom, j is the valence band of the single atom, Wave vector The orbital coefficient at equal is the partial response function of the valence band, Determined according to the third formula, the third formula is:

[0017]

[0018] in:

[0019]

[0020]

[0021] Where, H(vI s ) is a step function, r vc is the position matrix element, ω cv is the electron vibration frequency.

[0022] Preferably, the contribution of the conduction band of the single atom to the nonlinear optical susceptibility of the crystalline material is determined according to a fourth formula, which is:

[0023]

[0024] Wherein, τ is a single atom in the crystal material, Ω is the volume of the unit cell of the crystal material, L is the number of atomic orbitals of the single atom, j is the conduction band of the single atom, Wave vector The orbital coefficient at equal is the partial response function of the conduction band, Determined according to the fifth formula, the fifth formula is:

[0025]

[0026] in,

[0027]

[0028]

[0029] Where, H(cI s ) is a step function, r vc is the position matrix element, ω cv is the electron vibration frequency.

[0030] Preferably, the linear optical susceptibility of the crystal material is calculated according to the position matrix element, specifically:

[0031] The linear optical susceptibility of the crystal material is calculated according to the sixth formula, which is:

[0032]

[0033] Wherein, Ω is the volume of the unit cell in the crystal material, W k Represents the weight of different k points, k point is the high symmetry point in the Brillouin zone, f nm (k) = f n (k)-f m (k), f n (k) represents the Fermi distribution of electrons at energy band n, r nm represents the position matrix element, ω m represents the vibration frequency of electrons in energy band m, and ω represents the vibration frequency of the photoelectric field.

[0034] Preferably, the nonlinear optical susceptibility of the crystal material is calculated according to the position matrix element, specifically:

[0035] The interband transition term in the nonlinear optical susceptibility of the crystal material is calculated according to the seventh formula, which is:

[0036]

[0037] Wherein, Ω is the volume of the unit cell in the crystal material, W k Represents the weight of different k points, k point is the high symmetry point in the Brillouin zone, f nm (k) = f n (k)-f m (k), f n (k) represents the Fermi distribution of electrons at energy band n, r represents the position matrix element, ω m represents the vibration frequency of electrons in energy band m, and ω represents the vibration frequency of the photoelectric field.

[0038] Preferably, calculating the nonlinear optical susceptibility of the crystal material according to the position matrix element further comprises:

[0039] The intra-band transition term in the nonlinear optical susceptibility of the crystal material is calculated according to the eighth formula, which is:

[0040]

[0041] Preferably, calculating the nonlinear optical susceptibility of the crystal material according to the position matrix element further comprises:

[0042] The modulation term of the intra-band transition to the inter-band transition in the nonlinear optical polarizability of the crystal material is calculated according to the ninth formula, and the ninth formula is:

[0043]

[0044] in,

[0045] Compared with the prior art, the method for obtaining the optical properties of crystal materials of the present invention has the following beneficial effects:

[0046] This invention accurately determines the linear and nonlinear optical susceptibilities of crystalline materials, as well as the contribution of each atom in the crystalline material to the nonlinear optical susceptibilities, and distinguishes the contributions of the conduction band and valence band of an element. This not only helps to classify the functional elements of NLO materials and identify new high-performance NLO materials, but also provides important insights into the nature of the interaction between optical fields and matter. Furthermore, the ARTATOP program is compatible with electronic structure information provided by VASP or ABINIT, and can be used to calculate the linear and second-order nonlinear optical susceptibilities of materials based on this information. The program is simple to operate, comprehensive in functionality, and has a large number of adjustable parameters, making it a valuable aid for scholars and researchers in the design and development of nonlinear optical materials. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 A flow chart of a method for obtaining optical properties of a crystal material according to the present invention;

[0048] Figure 2 (a) is the overall response ζ tot ; Figure 2 (b) is the response functional ζ from part of the valence band to all conduction bands V (E B ) and the energy E in the valence band B Contribution of the energy band to the conduction band 6ζ V (E B ); Figure 2 (c) is the response functional ζ from all valence bands to part of the conduction band C (E B ) and the contribution of the energy band at energy EB in the valence band to the conduction band δζ C (E B );

[0049] Figure 3 The graph of the refractive index (n), reflectivity (R), extinction coefficient (κ), and absorption coefficient (α) of ZnS versus the energy of the optical field;

[0050] Figure 4 The curves of the real part ε1 and imaginary part ε2 of the linear optical polarizability of ZnS changing with the optical electric field energy;

[0051] Figure 5 is the second-order nonlinear optical susceptibility of ZnS The inter-band term, intra-band term, and inter-band to intra-band correction term vary with the energy of the optical field;

[0052] Figure 6 is the second-order nonlinear optical susceptibility of ZnS Curve graph showing changes with the energy of the optical field;

[0053] Figure 7 is the second-order nonlinear optical coefficient of ZnS The partial response functional diagram of ; where (a)ζ V (E B )-vs-E B , (b)ζ C (E B )-vs-E B , (c)δζ V (E B )-vs-E B and (d)δζ C (E B )-vs-E B ′. DETAILED DESCRIPTION

[0054] In the following description, specific details such as particular system structures and techniques are provided for purposes of illustration, not limitation, to facilitate a thorough understanding of the embodiments of the present invention. However, it will be apparent to those skilled in the art that the present invention may be practiced in other embodiments without these specific details. In other cases, detailed descriptions of well-known systems, devices, circuits, and methods are omitted so as not to obscure the description of the present invention with unnecessary detail.

[0055] The present invention is described in detail below with reference to the embodiments, but the present invention is not limited to these embodiments.

[0056] The method for obtaining the optical properties of a crystal material provided by the present invention comprises:

[0057] Step 1: Obtain the wave function and electronic structure of the crystal material;

[0058] Step 2: construct the position matrix element of the crystal material according to the wave function and electronic structure;

[0059] Step 3: Calculate at least one of the linear optical susceptibility, the nonlinear optical susceptibility, and the contribution of a single atom in the crystal material to the nonlinear optical susceptibility of the crystal material based on the position matrix elements.

[0060] The present invention will be described in detail below with reference to more detailed embodiments.

[0061] Existing research often encounters two technical challenges: accurately calculating the linear and nonlinear optical susceptibilities of a material; and determining the contribution of each atom to the nonlinear optical susceptibility. The present invention designs ARTATOP (Atom Response Theory Analysis Toolkits for Optical Properties) to address these two challenges. The following describes the theoretical principles by which ARTATOP addresses these two technical challenges.

[0062] 1. Calculation principle

[0063] 1.1 Linear and nonlinear optical susceptibilities

[0064] The formula for calculating the nonlinear optical polarizability tensor can be derived from Maxwell's equations combined with the equation of motion for the charge density operator ρ in quantum mechanics. The present invention uses a formula first proposed by J.E. Sipe, with an improved summation method by S. Sharma, to obtain the linear and nonlinear optical polarizability of a material.

[0065] Linear susceptibility tensor It is calculated by the following formula:

[0066]

[0067] Among them, Ω represents the unit cell volume, W k represents the weights at different k points, f nm (k) = f n (k) - f m (k), f n (k) represents the Fermi distribution of electrons at energy band n, r nm represents the position matrix element, ω m represents the vibration frequency of electrons at energy band m, and ω represents the vibration frequency of the optical electric field. The k points are the high symmetry points in the Brillouin zone.

[0068] The second-order nonlinear susceptibility is divided into an interband transition term χ(2ω, ω, ω), an intraband transition term η(2ω, ω, ω), and a modulation term σ(2ω, ω, ω) of the intraband transition on the interband transition:

[0069]

[0070]

[0071]

[0072] Among them

[0073] 1.2. Contribution of a single atom to the nonlinear optical susceptibility

[0074] For any response function F(x), the adjustable range of its variable x is -∞ < x < +∞, and the remaining parameters of F(x) are omitted here. Then, the partial response functional in the range x0 ≤ x < +∞ can be defined as:

[0075]

[0076] Among them, H(x - x0) is the Heaviside step function. And the partial response functional in the range -∞ < x ≤ x0 can be defined as:

[0077]

[0078] The corresponding derivative δζ(x0, F) with respect to x0 can be written as:

[0079]

[0080] When we define x as the continuous variable energy E, in Figure 1 we define x0 as E BThe value range of variable E can be regarded as -∞<x<+∞, and F(E) is defined as the contribution of the energy band to the second-order nonlinear optical polarizability, and the partial response equation is defined as Formula (1) describes the relationship between the valence band energy E and the second-order nonlinear optical polarizability ζ V (E B ), use formula (2) to describe the relationship between the conduction band CBs energy E and the second-order nonlinear optical polarizability ζ C (E B ), and respectively by Figure 1 b and Figure 1 c indicates. When E B Changes to E min or E max When V (E B ),ζ C (E B ) represent the total second-order nonlinear optical susceptibility.

[0081] The energy band number I is an integer, and its value range is 1<I<N tot , starting from the lowest energy of 1 to N tot The highest energy point increases with the increase of energy. x0 can be defined as the energy band number Is, and ζ V (I s ) and ζ G (I s ) is used to describe the variation of the second-order nonlinear optical polarizability with energy. V (I s ) describes the energy band I at the valence band s Contribution to the second-order nonlinear optical susceptibility, δζ C (I s ) describes the energy band I at the conduction band s Contribution to the second-order nonlinear optical susceptibility. Figure 2 As shown, Figure 2 is a diagram of the partial response functional method, where Figure 2 (a) is the overall response ζ tot , (b) is the response functional ζ from part of the valence band to all conduction bands V (E B ) and the energy E in the valence band B Contribution δζ from the energy band to the conduction band V (E B ), (c) is the response functional ζ from all valence bands to part of the conduction band C (E B ) and the energy E from the valence band to the conduction band B The contribution of the energy band at C (E B ).

[0082] For the valence band, the partial response function ζ opq (I s ) are:

[0083]

[0084]

[0085] For the conduction band, the partial response function ζ opq (I s ) is divided into the inter-band part and the inner part of the band:

[0086]

[0087]

[0088] Thus, the partial response functions of the valence band and conduction band are obtained respectively.

[0089]

[0090]

[0091] Energy in E min and VBM, the derivative of the valence band is:

[0092]

[0093] Energy in CBM and E max In the range of , the derivative of the conduction band is:

[0094]

[0095] In order to make the expression clearer, when evaluating the contribution of each atom to the SHG component, Simplified to Simplified to I s Assume that a particular atom τ has L atomic orbitals, in the valence band j, wave vector The orbital coefficient at is defined as The contribution of the valence band of the atom to the SHG coefficient is VB A τ It can be expressed as:

[0096]

[0097] In the above formula, Ω represents the volume of the calculation model. Similarly, assuming that a specific atom τ has L atomic orbitals, in the conduction band j, the wave vector The orbital coefficient at is The contribution of the conduction band of the atom to the SHG coefficient is CB A τ It can be expressed as:

[0098]

[0099] The total contribution of the valence band and conduction band of a single atom to the SHG coefficient is A τ It can be expressed as:

[0100]

[0101] The calculation of the valence band orbital contribution uses the conduction band orbital component; similarly, the calculation of the conduction band orbital contribution uses the valence band orbital component. This is because the atomic contribution to the SHG coefficient comes from the electron transition between the conduction band and the valence band. Therefore, the 1 / 2 in the above formula is to eliminate this duplication.

[0102] Using this method, we can determine the contribution of individual atoms in a material to the SHG component. Further calculations reveal the contributions of different orbital components of individual atoms to the SHG component, thereby revealing the origin of the SHG coefficient of nonlinear optical materials at the atomic scale. This theory provides a method for quantitatively analyzing the origin of a material's nonlinear optical response and has universal applicability. It provides important insights into the structure-activity relationship of nonlinear optical materials and their atomic-scale "material genes."

[0103] 2. Program design, see the flowchart for Figure 1 .

[0104] 3. Installation of ARTATOP package

[0105] The ARTATOP package runs on Linux and Windows, as well as MacOS and UNIX systems. If you use the GNU compiler suite on Windows, you must have Cygwin or MinGW installed. Compiling in a Linux environment is recommended.

[0106] 3.1 Compiler

[0107] Compiling source code requires a Fortran compiler and a C compiler. Currently, only gfortran and gcc are supported. Specify the compiler in the makefile as follows:

[0108] FC = gfortran

[0109] CC=gcc.

[0110] 3.2 Mathematical and Crystal Symmetry Libraries

[0111] Before compiling ARTATOP, you need to install the LAPACK library and the crystal symmetry library Spglib. You can download them from the following methods.

[0112] LAPCK: http: / / www.netlib.org / lapack /

[0113] Spglib: https: / / atztogo.github.io / spglib /

[0114] After compiling separately, specify the library path in the makefile file in the following way:

[0115] LIBDIR=-L / <lib_path>

[0116] LIBS=$(LIBDIR)-lrefblas-llapack-lsymspg-lm.

[0117] 3.3 Compilation method

[0118] Unzip the package, modify the makefile to suit your environment, and then compile using the make command. The initial compilation takes approximately 1-3 minutes. You will get the executable file artatop.

[0119] 4. Calculation Example 1 (Optical Module Output Based on VASP)

[0120] Calculation of ZnS using ARTATOP The linear and nonlinear optical polarizabilities of ZnS are investigated, and the contribution of single atoms to the non-optical polarizability in ZnS is obtained.

[0121] 4.1 VASP optical module calculation

[0122] Use VASP to optimize the material structure and perform self-consistent calculations. Read the wave functions from the self-consistent calculations, calculate optical properties, and obtain relevant electronic structure and transition matrix information.

[0123] Taking ZnS as an example, when VASP calculates the optical properties, the parameters that need to be specified in INCAR are (for reference):

[0124] SYSTEM=ZnS

[0125] ENCUT=500

[0126] ISMEAR=-5

[0127] NELMDL=-5

[0128] NELMIN=4

[0129] EDIFF=0.00001

[0130] EDIFFG=-0.0001

[0131] NSW=0

[0132] ISIF=0

[0133] IBRION=-1

[0134] POTIM=0.4

[0135] LORBIT=10

[0136] LREAL=.FALSE.

[0137] KSPACING=0.1

[0138] KGAMMA=.TRUE.

[0139] NBANDS=64

[0140] LOPTICS=.TRUE.

[0141] CSHIFT=0.1

[0142] NEDOS=3000

[0143] NPAR=1

[0144] It is important to note that the NBANDS parameter values ​​need to be expanded by at least a factor of 3 based on the self-consistent calculation to obtain converged optical properties. NPAR=1 also needs to be set to output the OPTIC file.

[0145] 4.2 ARTATOP calculation of linear optical properties

[0146] In the VASP optical property calculation directory, create a file, input_lin, to specify the program input. In addition, create a folder, out_lin, to store the output files.

[0147] vi input_lin

[0148] mkdir out_lin

[0149] Enter the following in input_lin,

[0150] LO 77

[0151] $dft_src lvasp=T$end

[0152] $opc maxomega=1.167domega=0.01167scissor=1.7929ecutmin=0.03smear=0.03$end

[0153] Related parameter description:

[0154] (1) The first two letters LO in the first line of the input_lin file represent the calculations related to linear optical properties. The following two numbers represent the components of the linear polarizability tensor that need to be calculated. For example, there are 9 linear response components, namely xx, xy, xz, yx, yy, yz, zx, zy, zz. In the program, 1 represents the x direction, 2 represents the y direction, 3 = 1 + 2 represents the x and y directions, 4 represents the z direction, 5 = 1 + 4 represents the x and z directions, 6 = 2 + 4 represents the y and z directions, and 7 = 1 + 2 + 4 represents the x, y, and z directions. If the three components xx, xy, and xz are to be calculated, the first digit is 1 for the x direction only, and the second digit is 7 for the x, y, and z directions. In the example file, 77 means calculating all 9 components.

[0155] (2)$dft_src labi=T$end

[0156] Used to specify the data source for first principle calculations. Currently two software packages are supported:

[0157] labi=.TRUE. represents the selection of ABINIT.

[0158] lvasp=.TRUE. represents the selection of VASP.

[0159] Tags are mutually exclusive. Only one tag can be selected at a time.

[0160] (3) Other parameters

[0161] maxomega represents the maximum frequency of the incident optical electric field for calculating the optical susceptibility.

[0162] domega represents the step length of the incident optical field frequency.

[0163] The scissor method is used to correct the band gap. It is expressed in eV. Because density functional theory band gaps are often lower than experimental band gaps, the scissor method is used to correct for these gaps. The scissor value is typically equal to the experimental band gap minus the band gap calculated by self-consistent calculations.

[0164] Ecutmin refers to the minimum allowed energy between two energy bands m and n. When |Em - En| < Ecutmin, rmn = 0 because Em - En appears as the denominator in the calculation formula, and when the difference between these two values is too small, it will cause the data to be extremely large, so truncation is required.

[0165] Smear controls the Gaussian broadening of the optical polarizability coefficient.

[0166] Default values of the above parameters:

[0167] maxomega = 27.21 eV = 1 Ha

[0168] domega = 0.00272 eV = 0.0001 Ha

[0169] scissor = 0.0 eV = 0 Ha

[0170] ecutmin = 0.02721 eV = 0.001 Ha

[0171] smear = 0.16326 eV = 0.006 Ha

[0172] where 1 Ha = 27.21138386 eV.

[0173] Input command:

[0174] artatop <input_lin> re_lin

[0175] You can then perform the ARTATOP calculation to obtain the linear optical properties.

[0176] The output results are stored in the created folder out_lin in the naming format "lin_component.dat". The naming of all 9 components is as follows:

[0177] lin_xx.dat lin_xy.dat lin_xz.dat

[0178] lin_yx.dat lin_yy.dat lin_yz.dat

[0179] lin_zx.dat lin_zy.dat lin_zz.dat <000053​

[0181]

[0182]

[0183] According to the above data, the relevant linear optical properties of ZnS can be obtained as a function of energy, such as Figure 3 and Figure 4 As shown:

[0184] Figure 3 The graph shows the refractive index (n), reflectivity (R), extinction coefficient (κ), and absorption coefficient (α) of ZnS as a function of the optical field energy.

[0185] 4.3 ARTATOP calculation of second-order nonlinear optical susceptibility

[0186] In the VASP optical property calculation directory, create a file, input_nlin, to specify the program input. In addition, create a folder, out_nonlin, to store the output files.

[0187] mkdir out_nonlin

[0188] vi input_nlin

[0189] Enter the following in input_nlin,

[0190] NO 777

[0191] $dft_src lvasp=T$end

[0192] $opc maxomega=1.167domega=0.01167scissor=1.7929ecutmin=0.03smear=0.03$end

[0193] The "NO" in the first line of the input_nlin file indicates the calculation of the second-order nonlinear optical susceptibility. Because the second-order susceptibility is a third-order tensor, it must be represented using three digits. The "777" in the example indicates that all 27 components are calculated. To specify specific components, refer to the instructions in 4.3.

[0194] Execute Command

[0195] artatop<input_nlin> re_nlin

[0196] 27 components of the second-order nonlinear optical polarizability can be obtained.

[0197] The output information when the program is running is stored in re_nlin.

[0198] The output results are stored in the created folder out_nonlin, with the naming format of "nonlin_component.dat". All 27 components are as follows:

[0199] nonlin_xxx.dat nonlin_xxy.dat nonlin_xxz.dat nonlin_xyx.dat

[0200] nonlin_xyy.dat nonlin_xyz.dat nonlin_xzx.dat nonlin_xzy.dat

[0201] nonlin_xzz.dat nonlin_yxx.dat nonlin_yxy.dat nonlin_yxz.dat

[0202] nonlin_yyx.dat nonlin_yyy.dat nonlin_yyz.dat nonlin_yzx.dat

[0203] nonlin_yzy.dat nonlin_yzz.dat nonlin_zxx.dat nonlin_zxy.dat

[0204] nonlin_zxz.dat nonlin_zyx.dat nonlin_zyy.dat nonlin_zyz.dat

[0205] nonlin_zzx.dat nonlin_zzy.dat nonlin_zzz.dat

[0206] The output includes the real part, imaginary part, and absolute value of the second-order nonlinear optical susceptibility, as well as the real part, imaginary part, and absolute value of the inter-band term and intra-band term, as well as the inter-band transition term χ, the intra-band transition term η, and the modulation term σ of the intra-band transition on the inter-band transition. There are two commonly used conversion units for expressing the second-order nonlinear optical susceptibility:

[0207]

[0208] The following are some of the data of the output file and the attached Figure 5 and attached Figure 6 .

[0209]

[0210] 4.4 ARTATOP calculation of the contribution of single atoms to the second-order nonlinear optical response

[0211] In the VASP optical property calculation directory, create a file, input_art, to specify the program input. In addition, create a folder, out_nonlin, to store the output files.

[0212] mkdir out_nonlin

[0213] vi input_art

[0214] Enter the following in input_art,

[0215] AR 124

[0216] $dft_src lvasp=T$end

[0217] $opc maxomega=0 domega=0.1167 scissor=1.7929 ecutmin=0.03 smear=0.03$end

[0218] The first line in the input file, "AR," indicates that the second-order nonlinear optical susceptibility of the material will be analyzed using nonlinear optical atomic response theory. "124" indicates the calculation of the xyz component. The optical field frequency calculated by this module is specified by "maxomega." The remaining parameters are the same as those set in Section 3.2.

[0219] Execute Command

[0220] artatop<input_art> re_art

[0221] The results of the related nonlinear optical atomic response of the second-order polarizability component χ123 can be obtained.

[0222] The output information of the program is stored in re_art. The output result files are stored in the folder out_nonlin:

[0223] arp_dshg-cb_xyz.txt arp_dshg-vb_xyz.txt arp_dshg_xyz.txt arp_nonlin.txt arp_nshg_xyz.txt arp_shg_con_xyz.txt arp_shg_val_xyz.txt

[0224] arp_nonlin.txt: Contribution of each atomic orbital to the second-order nonlinear polarizability component.

[0225] arp_shg_val_xxx.txt: Contribution of the valence band part of each atomic orbital to the corresponding second-order nonlinear polarizability component.

[0226] arp_shg_con_xxx.txt: Contribution of the conduction band portion of each atomic orbital to the corresponding second-order nonlinear polarizability component.

[0227] arp_nshg_xxx.txt: Partial functionals of the energy bands corresponding to the second-order nonlinear polarizability components.

[0228] arp_dshg_xxx.txt: Contributions of different energy bands to the corresponding second-order nonlinear polarizability components.

[0229] arp_dshg-vb_xxx.txt: valence band contribution to the corresponding second-order nonlinear polarizability components.

[0230] arp_dshg-cb_xxx.txt: Conduction band contribution to the corresponding second-order nonlinear susceptibility components.

[0231] The results calculated based on the input file, for example, the data contained in arp_nonlin.txt:

[0232]

[0233] Where orbit corresponds to the 6 spd orbitals of the two atoms in ZnS. Based on the above results, the orbitals of individual atoms in ZnS and their overall contributions (%) can be calculated as follows:

[0234] atom s p d sum Zn 7.7 34.5 -4.9 37.3 S -11.7 74.4 0 62.7

[0235] To obtain the contribution of each atomic orbital in the valence band and conduction band, you need to use the data of arp_shg_val_xyz.txt and arp_shg_con_xyz.txt:

[0236]

[0237]

[0238] Based on the above results, the contribution (%) of the valence band and conduction band of a single atom in ZnS can be calculated:

[0239]

[0240] Using the data in arp_nshg_xyz.txt and arp_dshg_xxx.txt, the partial response functional in any energy range can be obtained. Figure 7 .

[0241] 5. Calculation Example 2 (Optical Module Output Based on ABINIT)

[0242] Calculation using ARTATOP The linear and nonlinear optical polarizabilities of AgGaS2 are investigated, and the contribution of single atoms to the non-optical polarizability is obtained.

[0243] 5.1. Calculation of ABINIT's optical module

[0244] Obtain DDK output information for AgGaS2 using ABINIT calculations. Below is a sample file, opitc_1.in, required for ABINIT optical property calculations. The prtwant and w90iniprj functions must be configured to output wannier orbital information for use in atomic response theory calculations.

[0245]

[0246]

[0247]

[0248]

[0249] Since ABINIT has a large degree of freedom in naming its output files, it is necessary to rename some of the wave functions and wannier orbital files output by ABINIT so that they can be read into ARTATOP.

[0250] In this example, the wave function optic_1o_DS3_WFK file output from the third step of the ABINIT calculation is renamed WFK, the wave function optic_1o_DS4_1WF25 file output from the fourth step is renamed DDK1, the wave function optic_1o_DS5_1WF26 file output from the fifth step is renamed DDK2, and the wave function optic_1o_DS6_1WF27 file output from the sixth step is renamed DDK3. The wannier orbital information file optic_1o_DS3_w90.amn output from the third step is renamed wan90.amn

[0251] mv optic_1o_DS2_WFK WFK

[0252] mv optic_1o_DS4_1WF25 WFK

[0253] mv optic_1o_DS5_1WF26 WFK

[0254] mv optic_1o_DS6_1WF27 WFK

[0255] mv optic_1o_DS3_w90.amn wan90.amn

[0256] 5.2 ARTATOP calculation of linear optical properties

[0257] Similar to 4.2, you also need to create a file, input_lin, in the ABINIT optical property calculation directory to specify the program input. In addition, you also need to create a folder, out_lin, to store the output files.

[0258] Enter the following in input_lin,

[0259] LO 77

[0260] $dft_src lvasp=T$end

[0261] $opc maxomega=1.167 domega=0.01167 scissor=1.691 ecutmin=0.03smear=0.03$end

[0262] labi=T represents the program output of reading ABINIT. The rest of the parameters are described in 4.2.

[0263] Enter the command:

[0264] artatop<input_lin> re_lin

[0265] You can then perform ARTATOP calculations to obtain linear optical properties. Refer to 4.2 for analysis.

[0266] 5.3 ARTATOP calculation of second-order nonlinear optical susceptibility

[0267] In the ABINIT optical property calculation directory, create a file, input_nlin, to specify the program input. In addition, create a folder, out_nonlin, to store the output files.

[0268] Enter the following in input_nlin,

[0269] NO 777

[0270] $dft_src lvasp=T$end

[0271] $opc maxomega=1.167domega=0.01167scissor=1.691ecutmin=0.03smear=0.03$end

[0272] Execute the command:

[0273] artatop<input_nlin> re_nlin

[0274] The 27 components of the second-order nonlinear optical susceptibility are obtained. The program output is stored in the file re_nlin. The output files are stored in the folder out_nonlin. Refer to 4.3 for analysis.

[0275] 5.4 ARTATOP calculation of the contribution of single atoms to the second-order nonlinear optical response

[0276] In the ABINIT optical property calculation directory, create a file, input_art, to specify the program input. In addition, create a folder, out_nonlin, to store the output files.

[0277] Enter the following in input_art,

[0278] AR 124

[0279] $dft_src lvasp=T$end

[0280] $opc maxomega=0 domega=0.01167 scissor=1.691 ecutmin=0.03 smear=0.03$end

[0281] Execute Command

[0282] artatop<input_art> re_art

[0283] This function generates the nonlinear optical atomic response associated with the second-order polarizability component χ123. The program output is stored in the file re_art. The output files are stored in the folder out_nonlin. Refer to 4.4 for analysis.

[0284] Based on the output of ABINIT's optical module, the single-atom contribution size (%) of AgGaS2 was calculated using ARTATOP as shown in the following table:

[0285]

[0286]

[0287] To shorten the development cycle and reduce development costs of new optical materials, theoretical research is essential for exploring material properties, predicting properties, and discovering new crystal materials. This theoretical research often requires the use of numerical computational software. In particular, first-principles calculations based on density functional theory are a key type of software for crystal material research. Currently, software specifically focused on calculating optical properties, particularly in the field of nonlinear optical materials, remains largely undeveloped in China. In this context, based on our newly proposed atomic response theory for nonlinear optics and combined with first-principles crystal calculation methods, we have developed ARTATOP, a numerical computational software package for the optical properties of nonlinear optical materials and laser crystals. This software fills the gap in numerical computational software in this field in my country, strengthens numerical research in materials optics, and enriches existing chemical computational software. This program can determine the contribution of each atom to the harmonic generation coefficient in a material and distinguish between the contributions of the conduction band and the valence band. This not only facilitates the classification of functional elements in nonlinear optical materials and the search for new high-performance NLO materials, but also provides important insights into the nature of the interaction between optical fields and matter. Furthermore, the ARTATOP program is compatible with electronic structure information provided by VASP or ABINIT, allowing calculation of linear and second-order nonlinear optical susceptibilities of materials. This program is easy to use, comprehensive in functionality, and offers a wide range of adjustable parameters, making it a valuable aid for academics and researchers in the design and development of nonlinear optical materials.

[0288] The technical effects achieved by this program package are: accurately obtaining the linear and nonlinear optical polarizability of crystal materials and obtaining the contribution of each atom in the crystal material to the nonlinear optical polarizability.

[0289] The above descriptions are merely a few embodiments of the present application and do not constitute any form of limitation to the present application. Although the present application discloses the preferred embodiments as above, they are not intended to limit the present application. Any technical personnel familiar with the present profession, without departing from the scope of the technical solution of the present application, using the technical content disclosed above to make slight changes or modifications are equivalent to equivalent implementation cases and fall within the scope of the technical solution.

Claims

1. A method for obtaining the optical properties of a crystal material, characterized in that: include: Obtain the wave function and electronic structure of crystalline materials; constructing a position matrix element of the crystal material according to the wave function and the electronic structure; Calculating the linear optical susceptibility, the nonlinear optical susceptibility, and the contribution of a single atom in the crystal material to the nonlinear optical susceptibility of the crystal material according to the position matrix elements; The nonlinear optical susceptibility of the crystal material is calculated according to the position matrix element, specifically: The interband transition term in the nonlinear optical susceptibility of the crystal material is calculated according to the seventh formula, which is: Wherein, Ω is the volume of the unit cell in the crystal material, W k Indicates the weights of different k points, where k points are high symmetry points in the Brillouin zone, and f nm (k) = f n (k)-f m (k), f n (k) represents the Fermi distribution of electrons at energy band n, r represents the position matrix element, ω m represents the vibration frequency of electrons at energy band m, and ω represents the vibration frequency of the optical electric field; The intra-band transition term in the nonlinear optical susceptibility of the crystal material is calculated according to the eighth formula, which is: The modulation term of the intra-band transition to the inter-band transition in the nonlinear optical polarizability of the crystal material is calculated according to the ninth formula, and the ninth formula is: in, 2. The method for obtaining the optical properties of a crystal material according to claim 1, characterized in that: Calculating at least one of a linear optical susceptibility, a nonlinear optical susceptibility, and a contribution of a single atom in the crystal material to the nonlinear optical susceptibility of the crystal material according to the position matrix element, comprising: The contribution of a single atom in the crystal material to the nonlinear optical susceptibility of the crystal material is calculated according to the position matrix element, specifically: The contribution of a single atom in the crystal material to the nonlinear optical susceptibility of the crystal material is calculated according to a first formula, wherein the first formula is: Among them, A r is the contribution of a single atom to the nonlinear optical susceptibility of the crystalline material, VB A τ is the contribution of the valence band of a single atom to the nonlinear optical susceptibility of the crystalline material, CB A τ is the contribution of the conduction band of a single atom to the nonlinear optical susceptibility of the crystalline material.

3. The method for obtaining the optical properties of a crystal material according to claim 2, characterized in that: The contribution of the valence band of the single atom to the nonlinear optical polarizability of the crystal material is calculated according to a second formula, which is: Wherein, τ is a single atom in the crystal material, Ω is the volume of the unit cell of the crystal material, L is the number of atomic orbitals of the single atom, j is the valence band of the single atom, Wave vector The orbital coefficient at VB ζ j equal VB ζ opq (I s ) Partial response function of the valence band, VB ζ opq (I s ) is determined according to a third formula, which is: in: Where, H(vI s ) is a step function, r vc is the position matrix element, ω cv is the electron vibration frequency.

4. The method for obtaining the optical properties of a crystal material according to claim 2, wherein: The contribution of the conduction band of the single atom to the nonlinear optical susceptibility of the crystalline material is determined according to a fourth formula, which is: Wherein, τ is a single atom in the crystal material, Ω is the volume of the unit cell of the crystal material, L is the number of atomic orbitals of the single atom, j is the conduction band of the single atom, Wave vector The orbital coefficient at CB ζ j equal CB ζ opq (I s ) the partial response function of the conduction band, CB ζ opq (I s ) is determined according to the fifth formula, which is: in, Where, H(cI s ) is a step function, r vc is the position matrix element, ω cv is the electron vibration frequency.

5. The method for obtaining optical properties of a crystal material according to claim 1, wherein: The linear optical susceptibility of the crystal material is calculated according to the position matrix element, specifically: The linear optical susceptibility of the crystal material is calculated according to the sixth formula, which is: Wherein, Ω is the volume of the unit cell in the crystal material, W k Indicates the weights of different k points, where k points are high symmetry points in the Brillouin zone, and f nm (k) = f n (k)-f m (k), f n (k) represents the Fermi distribution of electrons at energy band n, r nm represents the position matrix element, ω m represents the vibration frequency of electrons in energy band m, and ω represents the vibration frequency of the photoelectric field.

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