A method for designing a partially reflective bandwidth-weighted polymer reflector film

Abstract

This invention relates to the fields of optical thin film design and polymer multilayer interference reflective films, and particularly to a method for designing polymer reflective films with local reflection bandwidth weighting. The method acquires target reflection bands, the number of effective layer pairs, and refractive index dispersion data of high and low refractive index polymer materials to establish a dispersion design parameter set; calculates the local normalized reflection bandwidth and the local absolute reflection bandwidth, and takes the reciprocal of the local absolute reflection bandwidth to form a central reflection wavelength distribution weight sequence; accumulates the distribution weights, equally divides the total accumulated weights according to the number of effective layer pairs, and inversely solves the nonlinear central reflection wavelength sequence; reads the high and low refractive indices at each central reflection wavelength, calculates the physical thickness of the film layer according to the quarter-wave optical thickness condition, and generates a polymer multilayer reflective film structural parameter set. This invention matches the distribution density of finite layer pairs with the local reflection coverage width, reducing layer pair redundancy and insufficient local distribution.

Description

Technical Field

[0001] This invention relates to the fields of optical thin film design and polymer multilayer interference reflective film technology, and particularly to a method for designing polymer reflective films with local reflection bandwidth weighting. Background Technology

[0002] In the field of optical thin film design technology, polymer multilayer reflective films are typically composed of alternating high-refractive-index polymer layers and low-refractive-index polymer layers, with reflection bands formed by optical interference at the interfaces of adjacent layers. To extend the reflection band, existing schemes usually employ multiple layer pairs with different central reflection wavelengths, and configure the physical thickness of the layers in a linear, exponential, piecewise, or chirped manner. Some schemes also combine film system design software, the transfer matrix method, or numerical search methods to adjust the number and thickness distribution of layers according to the target reflection band.

[0003] The refractive index of polymer materials varies with wavelength, and the refractive index contrast between high- and low-refractive-index polymers also changes within the target reflection band, resulting in different local reflection bandwidths corresponding to different central reflection wavelengths. Existing linear, exponential, or preset chirp distributions typically configure the central reflection wavelength mainly based on wavelength position, layer pair number, or empirical parameters, failing to fully reflect the actual reflection coverage width at each wavelength position. When the number of effective layer pairs is limited, layer pair redundancy may occur in bands with wider local reflection bandwidths, while insufficient layer pair distribution may occur in bands with narrower local reflection bandwidths.

[0004] The aforementioned allocation method easily leads to a mismatch between the layer pair distribution density within the target reflection band and the refractive index dispersion of the polymer material, resulting in local reflection valleys or reflectivity fluctuations. Furthermore, given a limited number of central reflection wavelengths, existing solutions struggle to transform continuously varying local reflection coverage characteristics into a fixed-number, clearly ordered sequence of central reflection wavelengths. Therefore, it is necessary to address the difficulty in matching local reflection bandwidth with the central reflection wavelength distribution, particularly in design scenarios where the number of effective layer pairs is limited and the polymer material's refractive index varies with wavelength. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides a method for designing a polymer reflective film with localized reflection bandwidth weighting, comprising: S100: Obtain target reflection band, number of effective layer pairs, and refractive index dispersion data of high and low refractive index polymer materials; associate the refractive indices of the two polymer materials with the target wavelength to generate a dispersion design parameter set; S200. Based on the dispersion design parameter set, calculate the local normalized reflection bandwidth at each target wavelength; take the product of the target wavelength and the local normalized reflection bandwidth as the local absolute reflection bandwidth, and take the reciprocal of the local absolute reflection bandwidth to generate the center reflection wavelength distribution weight sequence. S300. Accumulate the distribution weight of the center reflection wavelength from the shortwave boundary of the target reflection band to generate an accumulated weight sequence; divide the total accumulated weight according to the number of effective layer pairs with equal weight, and interpolate and inversely solve the center reflection wavelength corresponding to each equal weight position in the accumulated weight sequence to generate a nonlinear center reflection wavelength sequence. S400. Based on the nonlinear central reflection wavelength sequence, read the high and low refractive indices at each central reflection wavelength from the refractive index dispersion data; calculate the physical thickness of the corresponding high and low refractive index polymer layers according to the quarter-wave optical thickness condition; alternately arrange the high and low refractive index polymer layers according to the nonlinear central reflection wavelength sequence to generate a polymer multilayer reflective film structure parameter set.

[0006] Furthermore, the generated dispersion design parameter set includes: Verify that the target reflection band is within the effective band of the refractive index dispersion data; Establish a common wavelength grid within the target reflection band; The refractive index dispersion data of the two polymer materials are fitted using the Cauchy formula or the Sellmeier formula, respectively, or piecewise interpolation is used to obtain the high and low refractive indices corresponding to each target wavelength in the common wavelength grid.

[0007] Furthermore, the local normalized reflection bandwidth and the local absolute reflection bandwidth are calculated according to the following formula:

[0008] in, For target wavelength Local refractive index contrast factor at that location For the high refractive index polymer material at the target wavelength The refractive index at that point, For the low refractive index polymer material at the target wavelength The refractive index at that point, The local normalized reflection bandwidth, The local absolute reflection bandwidth is given.

[0009] Furthermore, the weight of the central reflection wavelength distribution is calculated according to the following formula:

[0010] in, For target wavelength Weighting of the center reflection wavelength distribution at the location; When the weight of the center reflection wavelength distribution is greater than the preset weight limit, the preset weight limit shall be used as the weight of the center reflection wavelength distribution at the corresponding target wavelength. The center reflection wavelength distribution weight sequence is updated by dividing the center reflection wavelength distribution weight at each target wavelength by the sum of the center reflection wavelength distribution weights at all target wavelengths.

[0011] Furthermore, the target wavelengths in the common wavelength grid are sequentially denoted as... The corresponding center reflection wavelength distribution weights are denoted as follows: ; The cumulative weight sequence is calculated according to the following formula:

[0012] in, , For target wavelength The corresponding cumulative weight, This represents the total cumulative weight.

[0013] Furthermore, the number of effective layer pairs is denoted as... , No. The cumulative target weight corresponding to each equally weighted position is calculated according to the following formula:

[0014] in, ; Searching for the condition in the cumulative weight sequence Adjacent cumulative weights and And solve the inverse solution according to the following formula. One center reflection wavelength:

[0015] in, For the first One center reflection wavelength.

[0016] Furthermore, the high-refractive-index polymer material and the low-refractive-index polymer material are anisotropic polymer materials; The refractive index dispersion data includes the principal axis refractive indices of the two polymer materials along multiple principal axis directions; The principal axis refractive index is selected according to the target polarization direction, and the principal axis refractive index corresponding to the same target polarization direction is used when calculating the local normalized reflection bandwidth and the physical thickness.

[0017] Furthermore, the polymer multilayer reflective film structure parameter set includes multiple layer pair records, each layer pair record including layer pair number, central reflection wavelength, high refractive index, low refractive index, physical thickness of high refractive index polymer layer, physical thickness of low refractive index polymer layer, and arrangement order; Multiple layer pairs are recorded in ascending or descending order of the central reflection wavelength, and the high refractive index polymer layer and the low refractive index polymer layer are alternately arranged in the order of arrangement.

[0018] Furthermore, it also includes: calculating the reflectivity spectrum within the target reflection band using the transfer matrix method based on the set of structural parameters of the polymer multilayer reflective film; The continuous wavelength range with reflectivity below a preset reflectivity threshold is marked as the insufficient reflectivity range; The weight of the center reflection wavelength distribution within the insufficient reflection range is multiplied by a weight correction factor to update the center reflection wavelength distribution weight sequence. Based on the updated center reflection wavelength distribution weight sequence, the cumulative weight sequence is regenerated, the nonlinear center reflection wavelength sequence is solved, and the physical thickness of the corresponding high and low refractive index polymer layers is calculated.

[0019] Furthermore, the weight correction coefficient is calculated based on the difference between the preset reflectivity threshold and the reflectivity within the insufficient reflectivity range; Each time the set of structural parameters of the polymer multilayer reflective film is updated, the reflectance spectrum is recalculated. When the insufficient reflection region is not present in the reflectivity spectrum, or when the number of updates reaches the preset maximum correction number, the update of the center reflection wavelength distribution weight sequence ends.

[0020] The key innovations of this invention include: (1) Compare the refractive indices of high and low refractive index polymer materials at each target wavelength and combine them with the target wavelength to form a local absolute reflection bandwidth. Construct a center reflection wavelength distribution weight sequence with the reciprocal of the local absolute reflection bandwidth so that the local reflection coverage width directly participates in the distribution of effective layer pairs in the target reflection band.

[0021] (2) Accumulate the weight of the center reflection wavelength distribution along the target reflection band, divide the total accumulated weight according to the number of effective layer pairs, and interpolate each weighted position from the accumulated weight coordinates to the wavelength coordinates to form a nonlinear center reflection wavelength sequence with the same number as the number of effective layer pairs.

[0022] (3) Using the same refractive index dispersion data to participate in the calculation of local reflection bandwidth and film physical thickness, read the corresponding high and low refractive indices at each central reflection wavelength, and form the physical thickness and alternating arrangement relationship of high and low refractive index polymer layers according to the quarter-wave optical thickness condition.

[0023] The following are its main beneficial effects: (1) To address the problem that the local reflection coverage width varies at different wavelength positions and the preset chirp distribution is difficult to match, the distribution weight is established by the reciprocal of the local absolute reflection bandwidth, so that the band with a narrower local absolute reflection bandwidth corresponds to a larger distribution weight of the center reflection wavelength, thereby reducing the allocation of repeated layer pairs in the wide bandwidth band and the insufficient layer pair distribution in the narrow bandwidth band.

[0024] (2) To address the problem that the continuous reflection coverage characteristics are difficult to convert into discrete center reflection wavelengths when the number of effective layer pairs is fixed, a nonlinear center reflection wavelength sequence with a fixed number, clear order and coverage of the target reflection band is formed by weighted partitioning of cumulative weights and interpolation inverse solution, so that the layer pair spacing changes with the weight of the center reflection wavelength distribution.

[0025] (3) To address the problem of deviation in central reflection wavelength when different refractive index bases are used for refractive index dispersion evaluation and film thickness calculation, the same refractive index dispersion data is called in the two processing stages to maintain the corresponding relationship between the local reflection bandwidth, central reflection wavelength and physical thickness of each layer pair. Attached Figure Description

[0026] Figure 1 A flowchart illustrating a method for designing a polymer reflective film with localized reflection bandwidth weighting, provided in an embodiment of this application; Figure 2 This is a dispersion curve of the refractive index of a high-refractive-index polymer material and a low-refractive-index polymer material as a function of wavelength in an embodiment of the present invention. Figure 3 This is a graph showing the change of normalized cumulative weight with target wavelength in an embodiment of the present invention. Figure 4 This is a comparison diagram showing the changes in the center reflection wavelength as a function of the layer pair number for the weighted distribution, linear distribution, and exponential distribution of this invention. Detailed Implementation

[0027] Example 1: Refer to Figure 1 This is a flowchart illustrating a method for designing a polymer reflective film with localized reflection bandwidth weighting, provided in an embodiment of the present invention. The process may include at least steps S100-S400: S100: Obtain target reflection band, number of effective layer pairs, and refractive index dispersion data of high and low refractive index polymer materials; associate the refractive indices of the two polymer materials with the target wavelength to generate a dispersion design parameter set; S200. Based on the dispersion design parameter set, calculate the local normalized reflection bandwidth at each target wavelength; take the product of the target wavelength and the local normalized reflection bandwidth as the local absolute reflection bandwidth, and take the reciprocal of the local absolute reflection bandwidth to generate the center reflection wavelength distribution weight sequence. S300. Accumulate the distribution weight of the center reflection wavelength from the shortwave boundary of the target reflection band to generate an accumulated weight sequence; divide the total accumulated weight according to the number of effective layer pairs with equal weight, and interpolate and inversely solve the center reflection wavelength corresponding to each equal weight position in the accumulated weight sequence to generate a nonlinear center reflection wavelength sequence. S400. Based on the nonlinear central reflection wavelength sequence, read the high and low refractive indices at each central reflection wavelength from the refractive index dispersion data; calculate the physical thickness of the corresponding high and low refractive index polymer layers according to the quarter-wave optical thickness condition; alternately arrange the high and low refractive index polymer layers according to the nonlinear central reflection wavelength sequence to generate a polymer multilayer reflective film structure parameter set.

[0028] S100: Obtain target reflection band, effective layer pair quantity, and refractive index dispersion data of high- and low-refractive-index polymer materials; associate the refractive indices of the two polymer materials with the target wavelength to generate a dispersion design parameter set: This implementation is executed by an optical film design calculation device, which includes a memory and a processor. The memory stores the refractive index test data of the polymer material, film system design parameters, and calculation programs. After the design task is started, the processor first reads the target reflection band and the number of effective layer pairs, and then calls up the refractive index dispersion data of the high-refractive-index polymer material and the low-refractive-index polymer material. The target reflection band is defined by short-wavelength and long-wavelength boundaries; the number of effective layer pairs represents the number of layer pairs participating in the allocation of the central reflection wavelength. Each layer pair consists of one high-refractive-index polymer layer and one low-refractive-index polymer layer, and corresponds to one central reflection wavelength.

[0029] Refractive index dispersion data can be obtained from ellipsometric measurements, prism-coupled measurements, or a pre-established material optical parameter library. For discrete measurement data, each data point includes the wavelength and the refractive index at that wavelength. When the material has significant absorption, the extinction coefficient can also be saved simultaneously. However, in this embodiment, the target reflection band is selected in the weak absorption range of the two polymer materials, and the local reflection bandwidth and quarter-wave optical thickness are calculated using the real part of the refractive index. The measurement data uses a uniform wavelength unit, and the film physical thickness is calculated using a length unit corresponding to the wavelength to avoid mismatch between the central reflection wavelength and the film thickness due to inconsistent unit conversion.

[0030] After reading the refractive index and dispersion data, the effective wavelengths of the two polymer materials are first checked. Subsequent correlation processing only proceeds when the target reflection wavelength falls within the effective wavelengths covered by both sets of refractive index and dispersion data. If one set of material data only covers a portion of the target reflection wavelength, the extrapolated value without boundary restrictions is not directly used; instead, the missing wavelength is marked as a dispersion data out-of-bounds interval. For dispersion data out-of-bounds intervals, the measurement data for that interval can be re-imported, or the boundary of the target reflection wavelength can be adjusted. When the target reflection wavelength is inconsistent with the effective wavelengths of the material data, the current design task remains in the dispersion parameter verification stage and does not proceed to local reflection bandwidth calculation.

[0031] After the effective wavelengths of both materials have been verified, a common wavelength grid is established within the target reflection band. The common wavelength grid is arranged from the short-wavelength boundary to the long-wavelength boundary according to a preset wavelength interval, sequentially forming the target wavelength. The wavelength spacing is set according to the degree of change in the material's dispersion curve and the integration accuracy of subsequent cumulative weights. When the refractive index curve changes gently, an equally spaced grid can be used; when there is a large dispersion gradient in a certain band, the wavelength spacing of that band can be reduced. Regardless of whether an equally spaced or non-equally spaced grid is used, all target wavelengths are arranged in ascending order, and subsequent cumulative weight calculations are performed directly in this order.

[0032] The refractive index measurement points for the two polymer materials typically do not completely overlap, therefore it is necessary to map the two sets of refractive indices to a common wavelength grid. In one implementation, the refractive index dispersion data of the two materials are fitted using the Cauchy formula separately. For cases where the target wavelength range is wide or the material dispersion is not suitable for description using the Cauchy formula, the Sellmeier formula can be used. After fitting, each target wavelength is substituted into the corresponding refractive index dispersion function to obtain the high refractive index. and low refractive index In another implementation, instead of establishing an analytical dispersion function, piecewise interpolation is used between adjacent measurement wavelengths to obtain the high and low refractive indices corresponding to each target wavelength in a common wavelength grid.

[0033] When using analytical fitting, the deviation between the fitted curve and the original measurement points needs to be checked. If the fitting deviation at a certain target wavelength exceeds the preset fitting error, measurement points are added near that target wavelength, or the interval is changed to piecewise interpolation. When using piecewise interpolation, if the target wavelength is the same as a certain measurement wavelength, the corresponding refractive index is directly read; if the target wavelength is between two measurement wavelengths, the interpolated refractive index is calculated based on the wavelength distance between the two measurement points. When repeated wavelengths appear in the common wavelength grid, one target wavelength record is retained, and the corresponding refractive index is selected based on the validity of the repeated measurement values ​​to prevent zero wavelength intervals from appearing in subsequent cumulative weight calculations.

[0034] For isotropic polymer materials, the refractive index dispersion data are the scalar refractive indices at each target wavelength. For anisotropic polymer materials formed by stretching and orientation, the refractive index dispersion data include the principal axis refractive indices along multiple principal axis directions. When designing reflective polarizing films, the corresponding principal axis refractive index is selected according to the target polarization direction; both high- and low-refractive-index materials use the refractive index component under the same target polarization direction. If the target polarization direction does not coincide with the material's principal axis, the corresponding effective refractive index can be calculated based on the material's refractive index tensor and the incident light direction, and then the effective refractive index is associated with a common wavelength grid. Subsequent calculations of local reflection bandwidth and film physical thickness continue to use the refractive index corresponding to this polarization direction, without switching the refractive index component between the two calculation stages.

[0035] After wavelength correlation is completed, a set of dispersion design parameters is formed for each target wavelength. These dispersion design parameters include at least the target wavelength, high refractive index, and low refractive index, and together with the target reflection band boundary and the number of effective layer pairs, constitute the dispersion design parameter set. In one embodiment, the material identifier, refractive index data source, and target polarization direction are also retained in the dispersion design parameters; these only participate in the selection of refractive index and the correspondence of subsequent film materials, without changing the calculation relationship of local reflection bandwidth. The dispersion design parameter set is provided to S200 in ascending order of target wavelength, enabling S200 to compare the refractive indices of two polymer materials at the same wavelength position.

[0036] S200. Based on the dispersion design parameter set, calculate the local normalized reflection bandwidth at each target wavelength; take the product of the target wavelength and the local normalized reflection bandwidth as the local absolute reflection bandwidth, and take the reciprocal of the local absolute reflection bandwidth to generate the center reflection wavelength distribution weight sequence: S200 is executed by the local reflection bandwidth calculation program and the distributed weight calculation program in the optical film design calculation device. This step receives the dispersion design parameter set formed in S100 and reads the target wavelengths one by one in ascending order. High refractive index and low refractive index Since the refractive indices of the two materials have been mapped to a common wavelength grid in S100, this step no longer cross-compares the refractive indices at different wavelengths, but instead forms a set of local refractive index relationships at each target wavelength.

[0037] For target wavelength First, calculate the local refractive index contrast factor according to the following formula. :

[0038] The local refractive index contrast factor reflects the relative refractive index difference between high- and low-refractive-index polymer materials centered on the current target wavelength. The numerator uses the absolute value of the difference between the high and low refractive indices to prevent the calculation result from becoming negative due to changes in the material identification order; the denominator uses the sum of the refractive indices of the two materials to ensure that the refractive index difference at different wavelengths can be compared on the same scale. Normally, the refractive index of the high-refractive-index polymer material is greater than that of the low-refractive-index polymer material throughout the entire target reflection band. If the refractive index curves of the two materials intersect within the target reflection band, the intersection interval is marked near the intersection point. For small intersection intervals, the local refractive index contrast factor can continue to be calculated using absolute values; for intersection intervals that continuously span multiple wavelength grids, the target reflection band can be segmented, and the high-low refractive index relationship of the two materials in each segment can be checked separately.

[0039] The local normalized reflection bandwidth is calculated using the following formula based on the local refractive index contrast factor. :

[0040] The local normalized reflection bandwidth represents the relative reflection bandwidth of a local quarter-wave periodic structure composed of materials with corresponding high and low refractive indices, centered on the current target wavelength. This value is dimensionless and is mainly affected by the refractive index comparison of the two materials at the current wavelength. The local normalized reflection bandwidth is not the measured reflection bandwidth of the final polymer multilayer reflective film, but rather a local bandwidth parameter used when subsequently allocating the central reflection wavelength. The final reflection spectrum is also affected by the number of layer pairs, the layer pair arrangement order, the incident medium, the substrate, the incident angle, and the polarization direction.

[0041] Using only the local normalized reflection bandwidth cannot distinguish the actual wavelength range covered by the same relative bandwidth at different target wavelengths. Therefore, the target wavelength... With local normalized reflection bandwidth Multiplying them together yields the local absolute reflection bandwidth. :

[0042] The local absolute reflection bandwidth uses the same unit of length as the target wavelength, and its value represents the local reflection coverage width near the current target wavelength. When two target wavelengths have the same local normalized reflection bandwidth, the longer target wavelength corresponds to a larger local absolute reflection bandwidth. The allocation of subsequent center reflection wavelengths is controlled by the local absolute reflection bandwidth, not just by the refractive index difference or relative bandwidth.

[0043] For each target wavelength in the common wavelength grid, the reciprocal of the local absolute reflection bandwidth is taken as the weight of the central reflection wavelength distribution:

[0044] When the local absolute reflection bandwidth at a certain target wavelength is small, the corresponding weight of the center reflection wavelength distribution is large; when the local absolute reflection bandwidth is large, the corresponding weight is small. The weight does not directly modify the existing film thickness, nor is it used as a smoothing window for the thickness of adjacent layers. Instead, it is used in S300 as a density parameter for distributing the center reflection wavelength along the target reflection band.

[0045] If the refractive indices of two materials are very similar at a target wavelength, the local absolute reflection bandwidth may approach 0, and directly taking the reciprocal will result in an abnormally large weight. To address this, the calculated weight of the center reflection wavelength distribution is first compared with a preset upper limit. When the weight exceeds the preset upper limit, the preset upper limit replaces the current weight. The preset upper limit can be set based on the target reflection band length, the number of effective layer pairs, and the common wavelength grid density. Weight limiting only applies to abnormally high values ​​and does not change the relative relationships between weights at other target wavelengths.

[0046] In another implementation, a positive lower limit can be set for the local absolute reflection bandwidth before taking the reciprocal. When the local absolute reflection bandwidth is less than the lower limit, the lower limit is used in the reciprocal calculation. This process and the upper limit weighting process can be selected; if both are set simultaneously, the lower limit bandwidthing process is performed first, and then the weights are checked to see if they exceed the upper limit weighting process. Anomalies caused by missing refractive index data, non-numerical fitting results, or negative refractive index data are not masked by amplitude limiting, but instead the process returns to S100 to recheck the refractive index data at the corresponding target wavelength.

[0047] After obtaining the center reflection wavelength distribution weights at each target wavelength, each weight is divided by the sum of the weights at all target wavelengths to normalize the weight sequence. The sum of the normalized weights is 1, but S300 still integrates the normalized weights according to the target wavelength interval. Therefore, the weight value at each target wavelength and the interval between adjacent wavelengths jointly determine the cumulative weight increment. For non-equally spaced wavelength grids, the cumulative distribution cannot be determined solely based on the sum of discrete weights; the actual interval between each target wavelength must be retained.

[0048] This step ultimately forms the center reflection wavelength distribution weight sequence. The sequence stores the target wavelength, its corresponding local normalized reflection bandwidth, local absolute reflection bandwidth, and the normalized center reflection wavelength distribution weight in ascending order of target wavelength. S300 directly reads the target wavelength and the center reflection wavelength distribution weight, constructing a cumulative weight sequence starting from the shortwave boundary of the target reflection band; local bandwidth data is retained in the current design task for locating the weight source during reflection spectrum feedback correction.

[0049] S300. Accumulate the distribution weight of the center reflection wavelength starting from the shortwave boundary of the target reflection band to generate an accumulated weight sequence; divide the total accumulated weight according to the number of effective layer pairs with equal weights, and interpolate and inversely solve the center reflection wavelength corresponding to each equal weight position in the accumulated weight sequence to generate a nonlinear center reflection wavelength sequence: S300 receives the center reflection wavelength distribution weight sequence output by S200 and reads the number of effective layer pairs determined in S100. The center reflection wavelength distribution weight is a density parameter that changes continuously along the target reflection band. Since polymer multilayer reflective films require a certain number of layer pairs, this step converts the continuous weight distribution into a discrete center reflection wavelength that is consistent with the number of effective layer pairs.

[0050] The target wavelengths in the common wavelength grid are denoted as follows: The weights of the corresponding center reflection wavelength distribution are denoted as follows: ,in The shortwave boundary of the target reflection band. This represents the longwave boundary. The cumulative weighting starts from the shortwave boundary and is set accordingly. The remaining cumulative weights are calculated recursively based on the trapezoidal area between adjacent wavelength grids:

[0051] in, , For target wavelength The corresponding cumulative weight, This represents the total cumulative weight at the long-wavelength boundary. This accumulation method considers both the weights at adjacent grids and the wavelength spacing. When using non-equally spaced wavelength grids, it is not necessary to remap the weights to equally spaced grids.

[0052] Under normal circumstances, the weight of the central reflection wavelength distribution is greater than 0, and the target wavelengths are strictly increasing; therefore, the cumulative weight sequence is monotonically increasing. Before calculation, check the differences between adjacent target wavelengths; if any... equal If duplicate target wavelengths are not found, the duplicate target wavelengths are deleted, or the two target wavelength records are merged and the corresponding weights are recalculated. If a weight becomes a non-numerical value due to an input anomaly, the current cumulative calculation stops before that target wavelength and returns to S200 to check the local absolute reflection bandwidth. If the weights at multiple consecutive target wavelengths are 0, the corresponding cumulative weights remain unchanged, and subsequent inverse solutions skip intervals with the same cumulative weights.

[0053] The number of effective layer pairs is denoted as Since both the short-wave and long-wave boundaries of the target reflection band must correspond to the center reflection wavelength, in this embodiment... Not less than 2. If the number of valid layer pairs input is less than 2, a center reflection wavelength sequence containing two boundaries cannot be formed according to the following formula, and the current task returns to the valid layer pair number configuration stage. For The effective layer pair, the first The target cumulative weight corresponding to each equally weighted position Calculate according to the following formula:

[0054] in, .thus, An equal value of 0 corresponds to the shortwave boundary of the target's reflection band; equal The corresponding target's longwave boundary in the reflection band; the cumulative weight of other targets is between 0 and... The wavelengths are evenly distributed. The equal weighting is applied to the cumulative weight coordinates, not the wavelength coordinates; therefore, the center reflection wavelengths obtained from the inverse solution are usually not evenly spaced.

[0055] Accumulated weights for each target Searching for the condition in the cumulative weight sequence Adjacent cumulative weights and When the cumulative weight sequence is monotonically increasing, sequential search, binary search, or a progressive search that retains the position of the previous search can be used. Since the target cumulative weight... The elements are arranged in ascending order. During the progressive search, the first element... The starting point for searching the cumulative weight of each target can be the first... The interval corresponding to the cumulative weight of each objective does not need to be calculated from each time. Search again.

[0056] After determining the adjacent cumulative weights, the inverse interpolation solution is performed according to the following formula. Each center reflection wavelength :

[0057] This formula assigns the cumulative weight of the objective within the interval. Relative positions within the range are mapped to wavelength ranges .when equal hour, Pick ;when equal hour, Pick .like equal If the division is not performed in that interval, then the search proceeds along the cumulative weight sequence to find the first value greater than 1. The cumulative weights are calculated; if no larger cumulative weights are found up to the long-wavelength boundary, the weight sequence and total cumulative weights are rechecked.

[0058] It is obtained by inverse solving the cumulative weights of multiple objectives in sequence. The wavelengths are arranged in ascending order to form a nonlinear central reflection wavelength sequence. For bands with larger weights, the cumulative weight increases faster with wavelength, and the interval between adjacent equally weighted positions on the wavelength coordinate is smaller; for bands with smaller weights, the interval between adjacent central reflection wavelengths is larger. This distribution relationship is naturally formed by the local absolute reflection bandwidth through cumulative weights, without the need to pre-set the linear gradient slope, exponential coefficient, or piecewise chirp coefficient.

[0059] After the inverse kinematics is completed, check whether the number of elements in the central reflection wavelength sequence equals the number of effective layer pairs, and check whether the first and last central reflection wavelengths correspond to the short-wave and long-wave boundaries of the target reflection band, respectively. Since numerical precision may cause slight differences between the first and last central reflection wavelengths and the boundaries, the first central reflection wavelength can be directly set as the short-wave boundary, and the last central reflection wavelength as the long-wave boundary. If adjacent central reflection wavelengths are equal due to numerical rounding, increase the cumulative weight calculation precision or reduce the common wavelength grid spacing before resolving the inverse kinematics, without artificially splitting the wavelengths by arbitrarily increasing the wavelength offset.

[0060] In one implementation, the nonlinear central reflection wavelength sequence is passed to S400 in ascending order; in another implementation, S400 reverses the sequence according to the film stacking direction. Regardless of whether the sequence is ascending or descending, the numerical values ​​of each central reflection wavelength and their correspondence with the local bandwidth weights remain unchanged. S400 reads each central reflection wavelength in the sequence and recalculates the refractive index dispersion data from S100 to calculate the corresponding physical thickness of the film.

[0061] S400. Based on the nonlinear central reflection wavelength sequence, read the high and low refractive indices at each central reflection wavelength from the refractive index dispersion data; calculate the physical thickness of the corresponding high and low refractive index polymer layers according to the quarter-wave optical thickness condition; alternately arrange the high and low refractive index polymer layers according to the nonlinear central reflection wavelength sequence to generate a polymer multilayer reflective film structure parameter set: S400 is executed by the film thickness calculation program and the film structure organization program. This step receives the nonlinear central reflection wavelength sequence output by S300 and calls the refractive index dispersion data established by S100. Since the central reflection wavelength obtained by the inverse solution of S300 is usually located between the two target wavelengths of the common wavelength grid, it is not possible to only read the refractive index of the nearest grid point. Instead, according to the refractive index dispersion function or piecewise interpolation relationship used by S100, the high and low refractive indices at each central reflection wavelength are calculated.

[0062] When S100 uses the Cauchy formula or the Sellmeier formula to establish the refractive index dispersion function, the first... Each center reflection wavelength Substituting the dispersion functions of high- and low-refractive-index polymer materials respectively, we obtain... and When S100 uses piecewise interpolation, it searches within the common wavelength grid. The wavelengths of adjacent targets on both sides are interpolated based on their wavelengths and refractive indices. If... If the refractive index matches a target wavelength in the common wavelength grid, then the refractive index corresponding to that target wavelength is read directly. For anisotropic materials, the principal axis refractive index selected according to the target polarization direction in S100 is continued to be used, and the average refractive index is not used in the film thickness calculation stage.

[0063] For each center reflection wavelength The physical thicknesses of the corresponding high-refractive-index polymer layer and low-refractive-index polymer layer are calculated according to the quarter-wave optical thickness condition:

[0064]

[0065] in, For the first The physical thickness of the high refractive index polymer layer in each layer pair For the first The physical thickness of the low-refractive-index polymer layer in each layer pair. The optical thicknesses of the two materials at the corresponding central reflection wavelengths are respectively... Since each central reflection wavelength uses the actual refractive index at that wavelength, the physical thickness of the film is not obtained by scaling a single reference refractive index.

[0066] After calculating the physical thickness of a layer pair, a corresponding layer pair record is generated. Each layer pair record includes the layer pair number, central reflection wavelength, high refractive index, low refractive index, physical thickness of the high refractive index polymer layer, physical thickness of the low refractive index polymer layer, and their arrangement order. The layer pair number corresponds to its position in the nonlinear central reflection wavelength sequence; the material identification uses the high and low refractive index polymer material identification from S100, enabling subsequent film structure outputs to distinguish between the two materials.

[0067] In one embodiment, multiple layer pairs are arranged in ascending order of central reflection wavelength, with short-wavelength central reflection layer pairs located on one side of the film structure and long-wavelength central reflection layer pairs arranged sequentially to the other side. In another embodiment, multiple layer pairs are arranged in descending order of central reflection wavelength. The arrangement direction can be selected based on the incident direction, substrate location, and subsequent manufacturing processes, but it does not change the correspondence between the central reflection wavelength and the physical thickness. Within each layer pair, high-refractive-index polymer layers are alternately arranged in the order of low-refractive-index polymer layers; in another layer-end configuration, they can also be alternately arranged starting from the low-refractive-index polymer layer, and the specific end layer order is recorded in the film structure parameter set.

[0068] If the design object is a 500-layer polymer multilayer reflective film, the effective layer pair number can be set to 250. S300 outputs 250 center reflection wavelengths, and S400 accordingly calculates the physical thicknesses of 250 high-refractive-index polymer layers and 250 low-refractive-index polymer layers. If the film structure also includes an outer protective layer, adhesive layer, or substrate layer, these layers are not included in the effective layer pair number, and their physical thickness and materials can be configured separately from the layer pair records in the polymer multilayer reflective film structure parameter set; these additional layers do not participate in the local absolute reflection bandwidth weighting and center reflection wavelength inverse solution.

[0069] After generating all layer pair records, each layer pair is unfolded in the order of arrangement to form a set of structural parameters for the polymer multilayer reflective film layer by layer. This set of structural parameters includes at least the layer number, material identifier, and physical thickness of each film layer, and retains the layer pair to which the film layer belongs and its central reflection wavelength. In subsequent conversion of multilayer co-extrusion or stacking process parameters, the layer-by-layer physical thickness can be converted into the corresponding flow channel allocation ratio, layer multiplication parameter, or thickness before stretching; this conversion is part of the manufacturing process configuration and does not change the central reflection wavelength and quarter-wave optical thickness relationship determined in this step.

[0070] In one implementation, after the initial set of parameters for the polymer multilayer reflective film structure is formed, the reflectivity spectrum within the target reflection band is calculated using the transfer matrix method. During the calculation, characteristic matrices are established for each high- and low-refractive-index polymer layer according to the layer arrangement order, and then multiplied sequentially by the incident medium refractive index, substrate refractive index, incident angle, and polarization direction to obtain the reflectivity at each calculated wavelength. If the design condition is normal incidence, the characteristic matrix uses the normal incidence condition; if the design condition includes oblique incidence, the optical admittance and phase thickness under the corresponding polarization direction are used respectively.

[0071] After the reflectance spectrum calculation is completed, the reflectance at each calculated wavelength is compared with a preset reflectance threshold. If the reflectance at multiple consecutive calculated wavelengths is lower than the preset reflectance threshold, the continuous wavelength range is marked as an insufficient reflectance interval. If a single discrete calculated point is lower than the threshold while adjacent calculated points are not lower than the threshold, the spectral sampling density near that point can be increased and the calculation can be recalculated; if a continuous low reflectance range is still formed after recalculation, it can then be included as an insufficient reflectance interval in the weight correction.

[0072] For the insufficient reflection range, the weights of the center reflection wavelength distributions corresponding to each target wavelength within this range are multiplied by a weight correction factor. The weight correction factor is calculated based on the difference between a preset reflectivity threshold and the reflectivity within the insufficient reflection range. In one embodiment, the lowest reflectivity within the insufficient reflection range is first calculated. and preset reflectivity threshold The difference between them is then used to calculate the weight correction factor according to the following formula. :

[0073] in, This is a positive correction coefficient. The larger the reflectivity difference, the larger the weight correction coefficient. The weight correction only applies to the target wavelengths corresponding to the insufficient reflectivity interval; the weights of the center reflectivity wavelength distribution outside the interval remain at their current values. After the modification is completed, the weights at all target wavelengths are normalized again, and the updated center reflectivity wavelength distribution weight sequence is sent back to the cumulative weight calculation process.

[0074] After each weight update, the nonlinear center reflection wavelength sequence is regenerated according to the cumulative, equal-weight division, and interpolation inverse relationship of S300. Then, the physical thickness of the high and low refractive index polymer layers is recalculated according to the quarter-wave optical thickness condition of this step. The newly formed film structure parameter set replaces the previous structure in the reflectivity spectrum calculation. To avoid the weights repeatedly exceeding the same numerical range in adjacent rounds, an upper limit can be set for the weight correction coefficient, and the position and minimum reflectivity of the insufficient reflection interval in the previous round can be retained. The spectral changes of the corresponding interval after the current round of correction can be compared.

[0075] When no underreflection region is found in the recalculated reflectivity spectrum, the update of the center reflection wavelength distribution weight sequence ends, and the current film structure parameter set is used as the final output. When the number of updates reaches the preset maximum correction count, even if underreflection regions still exist, the current update process ends, and the current film structure parameter set and the remaining underreflection regions are output simultaneously. S100 can be restarted subsequently by adjusting the number of effective layer pairs, material combination, target reflection band, or reflectivity threshold, without indefinitely increasing local weights in the current round.

[0076] The final output set of polymer multilayer reflective film structural parameters corresponds to the target reflection band, number of effective layer pairs, material refractive index dispersion data, and center reflection wavelength distribution weight sequence of this design task. This set of structural parameters can be directly provided to film system simulation programs, polymer multilayer film process design programs, or film parameter output programs. When the material dispersion data, target reflection band, number of effective layer pairs, or target polarization direction changes, the dispersion design parameter set is re-established from S100, and S200, S300, and S400 are executed sequentially.

Claims

1. A method for designing a polymer reflective film with localized reflection bandwidth weighting, characterized in that, include: S100: Acquire target reflection band, number of effective layer pairs, and refractive index dispersion data of high and low refractive index polymer materials; A set of dispersion design parameters is generated by associating the refractive indices of the two polymer materials with the target wavelength. S200. Based on the dispersion design parameter set, calculate the local normalized reflection bandwidth at each target wavelength; take the product of the target wavelength and the local normalized reflection bandwidth as the local absolute reflection bandwidth, and take the reciprocal of the local absolute reflection bandwidth to generate the center reflection wavelength distribution weight sequence. S300. Accumulate the distribution weight of the center reflection wavelength from the shortwave boundary of the target reflection band to generate an accumulated weight sequence; divide the total accumulated weight according to the number of effective layer pairs with equal weight, and interpolate and inversely solve the center reflection wavelength corresponding to each equal weight position in the accumulated weight sequence to generate a nonlinear center reflection wavelength sequence. S400. Based on the nonlinear central reflection wavelength sequence, read the high and low refractive indices at each central reflection wavelength from the refractive index dispersion data; calculate the physical thickness of the corresponding high and low refractive index polymer layers according to the quarter-wave optical thickness condition; alternately arrange the high and low refractive index polymer layers according to the nonlinear central reflection wavelength sequence to generate a polymer multilayer reflective film structure parameter set.

2. The method according to claim 1, characterized in that, The set of generated dispersion design parameters includes: Verify that the target reflection band is within the effective band of the refractive index dispersion data; Establish a common wavelength grid within the target reflection band; The refractive index dispersion data of the two polymer materials are fitted using the Cauchy formula or the Sellmeier formula, respectively, or piecewise interpolation is used to obtain the high and low refractive indices corresponding to each target wavelength in the common wavelength grid.

3. The method according to claim 1, characterized in that, The local normalized reflection bandwidth and the local absolute reflection bandwidth are calculated according to the following formula: in, For target wavelength Local refractive index contrast factor at that location For the high refractive index polymer material at the target wavelength The refractive index at that point, For the low refractive index polymer material at the target wavelength The refractive index at that point, The local normalized reflection bandwidth, The local absolute reflection bandwidth is given.

4. The method according to claim 1, characterized in that, The weight of the central reflection wavelength distribution is calculated according to the following formula: in, For target wavelength Weighting of the center reflection wavelength distribution at the location; When the weight of the center reflection wavelength distribution is greater than the preset weight limit, the preset weight limit shall be used as the weight of the center reflection wavelength distribution at the corresponding target wavelength. The center reflection wavelength distribution weight sequence is updated by dividing the center reflection wavelength distribution weight at each target wavelength by the sum of the center reflection wavelength distribution weights at all target wavelengths.

5. The method according to claim 4, characterized in that, The target wavelengths in the common wavelength grid are sequentially denoted as follows: The corresponding center reflection wavelength distribution weights are denoted as follows: ; The cumulative weight sequence is calculated according to the following formula: in, , For target wavelength The corresponding cumulative weight, This represents the total cumulative weight.

6. The method according to claim 5, characterized in that, The number of effective layer pairs is denoted as , No. The cumulative target weight corresponding to each equally weighted position is calculated according to the following formula: in, ; Searching for the condition in the cumulative weight sequence Adjacent cumulative weights and And solve the inverse solution according to the following formula. One center reflection wavelength: in, For the first One center reflection wavelength.

7. The method according to claim 1, characterized in that, The high-refractive-index polymer material and the low-refractive-index polymer material are anisotropic polymer materials; The refractive index dispersion data includes the principal axis refractive indices of the two polymer materials along multiple principal axis directions; The principal axis refractive index is selected according to the target polarization direction, and the principal axis refractive index corresponding to the same target polarization direction is used when calculating the local normalized reflection bandwidth and the physical thickness.

8. The method according to claim 1, characterized in that, The polymer multilayer reflective film structure parameter set includes multiple layer pair records. Each layer pair record includes the layer pair number, central reflection wavelength, high refractive index, low refractive index, physical thickness of the high refractive index polymer layer, physical thickness of the low refractive index polymer layer, and arrangement order. Multiple layer pairs are recorded in ascending or descending order of the central reflection wavelength, and the high refractive index polymer layer and the low refractive index polymer layer are alternately arranged in the order of arrangement.

9. The method according to claim 1, characterized in that, Also includes: Based on the set of structural parameters of the polymer multilayer reflective film, the reflectivity spectrum in the target reflection band is calculated using the transfer matrix method. The continuous wavelength range with reflectivity below a preset reflectivity threshold is marked as the insufficient reflectivity range; The weight of the center reflection wavelength distribution within the insufficient reflection range is multiplied by a weight correction factor to update the center reflection wavelength distribution weight sequence. Based on the updated center reflection wavelength distribution weight sequence, the cumulative weight sequence is regenerated, the nonlinear center reflection wavelength sequence is solved, and the physical thickness of the corresponding high and low refractive index polymer layers is calculated.

10. The method according to claim 9, characterized in that, The weight correction coefficient is calculated based on the difference between the preset reflectivity threshold and the reflectivity within the insufficient reflectivity range; Each time the set of structural parameters of the polymer multilayer reflective film is updated, the reflectance spectrum is recalculated. When the insufficient reflection region is not present in the reflectivity spectrum, or when the number of updates reaches the preset maximum correction number, the update of the center reflection wavelength distribution weight sequence ends.

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