CN114236815A - Efficiency calculation method of waveband structure optical element - Google Patents
Efficiency calculation method of waveband structure optical element Download PDFInfo
- Publication number
- CN114236815A CN114236815A CN202111484301.2A CN202111484301A CN114236815A CN 114236815 A CN114236815 A CN 114236815A CN 202111484301 A CN202111484301 A CN 202111484301A CN 114236815 A CN114236815 A CN 114236815A
- Authority
- CN
- China
- Prior art keywords
- optical element
- efficiency
- waveband
- function
- morphology
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
- 230000003287 optical effect Effects 0.000 title claims abstract description 43
- 238000004364 calculation method Methods 0.000 title claims abstract description 27
- 238000000034 method Methods 0.000 claims abstract description 12
- 230000010363 phase shift Effects 0.000 claims description 19
- 239000000463 material Substances 0.000 claims description 7
- 230000004907 flux Effects 0.000 claims description 3
- 239000011541 reaction mixture Substances 0.000 claims 1
- 238000012876 topography Methods 0.000 abstract description 10
- 230000008569 process Effects 0.000 abstract description 7
- 238000004458 analytical method Methods 0.000 abstract description 3
- PCHJSUWPFVWCPO-UHFFFAOYSA-N gold Chemical compound [Au] PCHJSUWPFVWCPO-UHFFFAOYSA-N 0.000 description 8
- 239000010931 gold Substances 0.000 description 8
- 229910052737 gold Inorganic materials 0.000 description 8
- 238000002360 preparation method Methods 0.000 description 6
- 230000000694 effects Effects 0.000 description 4
- 230000006872 improvement Effects 0.000 description 3
- VYPSYNLAJGMNEJ-UHFFFAOYSA-N Silicium dioxide Chemical compound O=[Si]=O VYPSYNLAJGMNEJ-UHFFFAOYSA-N 0.000 description 2
- 238000010521 absorption reaction Methods 0.000 description 2
- 230000008859 change Effects 0.000 description 2
- 238000010586 diagram Methods 0.000 description 2
- 238000011156 evaluation Methods 0.000 description 2
- 239000002086 nanomaterial Substances 0.000 description 2
- 230000002411 adverse Effects 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 238000000609 electron-beam lithography Methods 0.000 description 1
- 238000003384 imaging method Methods 0.000 description 1
- 238000004519 manufacturing process Methods 0.000 description 1
- 238000001000 micrograph Methods 0.000 description 1
- 238000005457 optimization Methods 0.000 description 1
- 230000002093 peripheral effect Effects 0.000 description 1
- 229920002120 photoresistant polymer Polymers 0.000 description 1
- 230000008092 positive effect Effects 0.000 description 1
- 239000000377 silicon dioxide Substances 0.000 description 1
- 230000007847 structural defect Effects 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G02—OPTICS
- G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
- G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
- G02B27/0012—Optical design, e.g. procedures, algorithms, optimisation routines
Abstract
The invention belongs to the technical field of optical devices, and particularly relates to an efficiency calculation method of a waveband structured optical element. The invention popularizes a Kirz formula similar to a thin grating, and can be used for calculating the theoretical efficiency of the optical element with a waveband structure between the X-ray and the extreme ultraviolet waveband. The method is suitable for any zone morphology which can be expressed by functions, including rectangular zone plate morphology, triangular Kinoform morphology and the like. Meanwhile, the efficiency of a special waveband structure with a waveband topography function changing along with the period can be calculated, such as a non-rectangular waveband plate influenced by process factors. The calculation method provided by the invention is used for carrying out theoretical analysis and efficiency calculation on the appearance of the optical element, has the advantages of simple calculation, strong pertinence and wide applicable scene, and has an important guiding function on the design and performance analysis of the waveband structure optical element.
Description
Technical Field
The invention belongs to the technical field of optical devices, and particularly relates to an efficiency calculation method of a waveband structure optical element.
Background
In various types of imaging systems, focusing optics are a critical component. The design and calculation of the optical lens are the first and critical steps for designing and developing the optical lens, and have important guiding effects on the design optimization, processing preparation and performance evaluation of the lens. In recent years, with the improvement of the resolution of the lens and the diversification of the preparation process, the influence of the micro-nano structure of the lens on the focusing efficiency cannot be ignored. The thin grating approximation formula (thin grating approximation) is a theoretical formula proposed by Kirz in 1974 for calculating the efficiency of the X-ray and extreme ultraviolet phase type zone plate, and can conveniently estimate the theoretical focusing efficiency of the phase type rectangular zone plate. It can only be used for theoretical efficiency calculations for phase zone plates, and there are still limitations for other types of zone structured lenses at present, such as Kinoform lenses. The phase type zone plate prepared under the actual process is not in an ideal rectangular shape generally, the side wall of the phase type zone plate is inclined due to the influence of process defects, the thickness of each period is not completely consistent, and the actually measured efficiency is greatly deviated from the theoretical value estimated by the Kirz formula. The efficiency calculation of these actually prepared lenses is a tedious and huge work, and the commonly used optical simulation software such as FDTD, Comsol and the like often has the problems of large calculation amount, low precision, long calculation time and the like when simulating extreme ultraviolet and X-ray lenses.
Therefore, a calculation method capable of quickly and effectively estimating the waveband structure optical element with a complex morphology needs to be established, and the influence of the micro-nano structure of the lens on the focusing efficiency can be considered, so that the prediction accuracy of the lens on the efficiency of the actual waveband structure optical element is improved.
Disclosure of Invention
The invention aims to provide an efficiency calculation method of a waveband structure optical element with a complex morphology, which is short in time consumption and high in precision.
The efficiency calculation method of the waveband structure optical element with the complex morphology is based on a thin grating approximation formula, and comprises the following specific steps:
(1) setting incident light field and optical element parameters; wherein:
the incident light field parameters comprise wavelength lambda and amplitude C;
the optical element parameters include: the number of wavebands N of the optical element, the refractive index N of the material used by the optical element is (1-delta) -i beta, and the refractive indexes 1-delta and beta respectively represent the real part and the imaginary part of the refractive index of the material; the morphology function of the ith wave band is ti(theta), theta is inThe optical path length difference to the focal spot within a period, the function describes the height t as a function of the optical path difference θ. The optical element parameters are used to calculate the phase shift and amplitude in the lens. 1, 2, …, N;
(2) calculating a phase shift function phi of the ith bandi(θ)：
According to the morphology function t of the ith wave bandi(θ), the corresponding phase shift function for the ith band may be expressed as:
(3) knowing the phase shift function, the amplitude A of the ith wave band is calculated according to a thin grating approximation formulai：
(4) Finding the efficiency of the ith band:
(5) repeating the above efficiency calculation according to the different morphology functions of 1 to N wave bands, wherein the initial luminous flux received by each wave band is the same, and the total efficiency of the final optical element is the average value of the efficiencies of all the wave bands:
j in the formula (2) represents an imaginary unit.
In the present invention, the optical element has a waveband structure.
In the invention, the wave band morphology of each period of the optical element is a function of the optical path difference and can be described by different functions respectively; the zone topography includes, but is not limited to, zone plates, Kinoform lenses, step lenses, fresnel lenses, and their non-ideal topography.
In the invention, the phase shift function can be calculated according to the morphology of each period.
In the present invention, the amplitude of each period is the integral of the phase shift function over that period.
In the present invention, the total efficiency of the optical element is an average of all band efficiencies.
In the present invention, the morphology function is tiAnd (theta) can be an analytical expression or a discrete numerical value, is used for describing the appearance characteristics, and is finally substituted into an efficiency formula for evaluation. The more complex the profile corresponds to the more complex the function, which needs to be determined how to model according to the objective. Example 1 shows a relatively complex morphology, which is described directly here by discrete numerical points as a function. The appearance of embodiment 2 is relatively simple and can be expressed analytically, so it is described by an analytical piecewise function.
Compared with the prior art, the method has the beneficial effects that:
firstly, the Kirz formula of the thin grating approximation is popularized, the Kirz formula can be used for calculating the theoretical efficiency of the optical element with the waveband structure, and the Kirz formula is suitable for any waveband morphology which can be expressed by functions, including rectangular waveband plate morphology and triangular Kinoform morphology;
second, the present invention considers the topography and materials of the actual lens and can calculate the efficiency of a particular zone structure where the zone topography function changes with period, such as a non-rectangular zone plate affected by process factors. The design freedom degree of the lens is greatly improved, the lens can be used for designing and researching novel lenses, and important theoretical guiding significance is achieved.
Thirdly, the calculation method provided by the invention is used for carrying out theoretical analysis and efficiency calculation on the appearance of the optical element, and has the advantages of simple calculation, strong pertinence and wide applicable scenes.
Drawings
Fig. 1 is a scanning electron microscope image of a gold Kinoform lens actually prepared in example 1.
Fig. 2 is a function of the topography of all wavebands for the gold Kinoform lens actually prepared in example 1.
FIG. 3 is a graph of the focusing efficiency of a gold Kinoform lens actually fabricated at 5-15 keV energy in example 1 as a function of energy.
FIG. 4 is a phase function diagram of the zone structured lens of the pinnacle topography of example 2.
FIG. 5 is a graph of the calculated results of the efficiency of the zone structured lens of the tip topography as a function of the structural parameters m and n at 500eV in example 2.
FIG. 6 is a schematic diagram of the calculation of the phase function of the zone structured optical element with any topography proposed by the present invention.
Detailed Description
The invention will be further described with reference to the drawings and examples, but the invention is not limited to the examples. All the simple changes of the calculation parameters in the embodiments are within the protection scope of the present invention.
Example 1: calculating the focusing efficiency of the actually prepared gold Kinoform lens under the energy of 5-15 keV (the resolution is 100nm, the diameter is 100 mu m, and the wave band number N is 125):
due to the influence of the proximity effect in the electron beam lithography, the Kinoform triangle shapes may shift to different degrees with the period, especially the shapes near the periphery may even become vertical due to the smaller dimension. This deviation will result in each band contributing differently to the efficiency. Here, we use the theoretical efficiency calculation formula provided by the present invention, and consider the influence of morphology and period on efficiency, and the specific steps are as follows:
(1) the incident light field energy was set to 10keV, and a plane wave with unit amplitude (C1) was perpendicularly incident. Setting the optical parameters of the lens: from the actually prepared gold Kinoform lens (see fig. 1), its topographic features were extracted and a topographic function t (θ) was established, where the topography is described by the actually collected data points for convenience, as shown in fig. 2, with the refractive index set to gold.
(2) Calculating a phase shift function phi of the 1 st band1(θ)：
Topographic function t according to 1 st wave band1(theta), corresponding to the 1 st wave bandThe phase shift function (numerical expression) can be expressed as
(3) Knowing the phase shift function, the amplitude A of the 1 st band is determined according to the approximation formula of the thin grating1：
(4) Finding the efficiency of the 1 st band:
(5) repeating the above efficiency calculation according to different morphology functions of 1-125 wave bands, wherein the initial luminous flux received by each wave band is the same, and the final total efficiency is the average value of the efficiencies of all the wave bands:
(6) and (4) repeating the efficiency calculation of the steps (1) to (5), and finally obtaining a curve of the focusing efficiency of the actually prepared golden Kinoform lens along with the energy change under the condition of 5-15 keV, as shown in a figure 3. It can be seen that the focusing efficiency of the gold Kinoform lens of the actual morphology is lower than the theoretical value, and the improvement of the process is needed in the actual preparation process to reduce the adverse effect of the structural defects on the efficiency.
Example 2: optimizing the structural parameters of the waveband structural lens of the pinnacle morphology under the energy of 500keV (the resolution is 100nm, the diameter is 100 mu m, the waveband number N is 125, and the maximum thickness is 700 nm):
in a soft X-ray wave band of 0-1 keV, the focusing efficiency of the traditional gold material is greatly limited due to strong absorption. In addition, the diffraction efficiency of the rectangular zone plate can not be further improved due to the morphology of the rectangular zone plate, and the Kinoform morphology has application limitation due to the difficulty of process preparation. In this embodiment, an HSQ photoresist material with low absorption rate is taken as an example, and a zone plate lens with a novel morphology is designed in a soft X-ray band, so that the zone plate lens is suitable for an actual preparation process and can realize high-efficiency and high-resolution focusing.
The method comprises the following specific steps:
(1) the energy of the incident light field was set to 500eV, and the incident light was made perpendicular to a plane wave of unit amplitude. The refractive index is set to silica and the topographic function is established in the radial direction as t (θ).
(2) Calculating a phase shift function phi of the 1 st band1(θ): fig. 4 shows the phase shift function of a steeple zone plate. m and n describe the relative positions of the gap and the tip in the waveband (0)<m<n<1). The sidewalls are arranged to be non-vertical in consideration of the influence of proximity effect in actual manufacturing. In order to calculate its theoretical efficiency, each cycle is represented by a piecewise function.
Topographic function t according to 1 st wave band1(θ), the corresponding phase shift function for the 1 st band may be expressed as:
wherein phi0Is the maximum phase shift value of the lens, the segment intervals of the phase shift function correspond to the 3 regions marked in fig. 4, respectively.
(3) Knowing the phase shift function, the amplitude A of the 1 st band is determined according to the approximation formula of the thin grating1：
(4) Finding the efficiency of the 1 st band:
(5) since the profile will be discussed further in step 6, the profile is set here to not change with period. The overall efficiency is therefore:
FE＝FE1＝FE2＝…＝FEN，
(6) different structural parameters m and n are set, the efficiency calculation of the steps (1) to (5) is repeated, and a graph of the efficiency varying with the structural parameters at 500eV is drawn, as shown in FIG. 5. The highest efficiency of the lens is achieved when n is 1 and m is 0.2, the peripheral side walls of each period are perfectly vertical and 20% of the gap remains. The calculation result shows that the gaps have positive effects on the efficiency improvement of the waveband structure lens, and meanwhile, the difficulty in process preparation is reduced; in addition, to achieve higher efficiency focusing, each period of the lens needs to have a strict vertical edge.
Claims (2)
1. A method for calculating the efficiency of a waveband structure optical element is characterized by comprising the following specific steps:
(1) setting incident light field and optical element parameters; wherein:
the incident light field parameters comprise wavelength lambda and amplitude C;
the optical element parameters include: the number N of wave bands of the optical element, the refractive index N = (1-delta) -i beta of the material used for the optical element, and the refractive indexes 1-delta and beta respectively represent the real part and the imaginary part of the refractive index of the material; the morphology function of the ith wave band is ti(θ), θ is the optical path length difference to the focal spot over a period, and the function describes the height t as a function of the optical path difference θ;
the optical element parameters are used for calculating phase shift and amplitude in the lens; i =1, 2, …, N;
(2) calculating a phase shift function phi of the ith bandi(θ)：
According to the morphology function t of the ith wave bandi(θ), the corresponding phase shift function for the ith band may be expressed as:
(3) knowing the phase shift function, the amplitude A of the ith wave band is calculated according to a thin grating approximation formulai：
(4) Finding the efficiency of the ith band:
(5) repeating the above efficiency calculation according to different morphology functions of 1-N wave bands, wherein the initial luminous flux received by each wave band is the same, and the total efficiency of the final optical element is the average value of the efficiencies of all the wave bands:
in the formula (2), the reaction mixture is,jrepresenting imaginary units.
2. The method of claim 1, wherein the zone profile of each period of the optical element is a function of optical path difference, described by a different function, and the zone profile of the optical element comprises zone plates, Kinoform lenses, step lenses, fresnel lenses, and non-ideal profiles thereof.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202111484301.2A CN114236815A (en) | 2021-12-07 | 2021-12-07 | Efficiency calculation method of waveband structure optical element |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202111484301.2A CN114236815A (en) | 2021-12-07 | 2021-12-07 | Efficiency calculation method of waveband structure optical element |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN114236815A true CN114236815A (en) | 2022-03-25 |
Family
ID=80753673
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202111484301.2A Pending CN114236815A (en) | 2021-12-07 | 2021-12-07 | Efficiency calculation method of waveband structure optical element |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN114236815A (en) |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| IL115295A0 (en) * | 1995-09-14 | 1996-12-05 | Yeda Res & Dev | Multilevel diffractive optical element |
| WO2013132024A2 (en) * | 2012-03-08 | 2013-09-12 | MAX-PLANCK-Gesellschaft zur Förderung der Wissenschaften e.V. | Method of producing a fresnel zone plate for applications in high energy radiation |
| CN112885499A (en) * | 2021-01-17 | 2021-06-01 | 复旦大学 | Kinoform medium lens for synchrotron radiation soft X-ray focusing imaging and preparation method thereof |
| CN113281900A (en) * | 2021-05-26 | 2021-08-20 | 复旦大学 | Optical modeling and calculating method based on Hankel transformation and beam propagation method |
-
2021
- 2021-12-07 CN CN202111484301.2A patent/CN114236815A/en active Pending
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| IL115295A0 (en) * | 1995-09-14 | 1996-12-05 | Yeda Res & Dev | Multilevel diffractive optical element |
| WO2013132024A2 (en) * | 2012-03-08 | 2013-09-12 | MAX-PLANCK-Gesellschaft zur Förderung der Wissenschaften e.V. | Method of producing a fresnel zone plate for applications in high energy radiation |
| CN112885499A (en) * | 2021-01-17 | 2021-06-01 | 复旦大学 | Kinoform medium lens for synchrotron radiation soft X-ray focusing imaging and preparation method thereof |
| CN113281900A (en) * | 2021-05-26 | 2021-08-20 | 复旦大学 | Optical modeling and calculating method based on Hankel transformation and beam propagation method |
Non-Patent Citations (3)
| Title |
|---|
| XUJIE TONG，YIFANG CHEN等: "high-efficiency focusing and imaging by dielectric kinoform zone plate lenses with soft X-rays", JOURNAL OF SYNCHROTRON RADIATION, vol. 30, 31 March 2023 (2023-03-31), pages 319 - 326 * |
| 李海亮等: "大高宽比硬 Ｘ 射线波带片制作及聚焦测试", 光学 精密工程, vol. 25, no. 11, 15 November 2017 (2017-11-15), pages 2803 - 2809 * |
| 肖凯等: "软 X 射线相位型聚焦波带片的研制", 光学学报, vol. 25, no. 12, 17 December 2005 (2005-12-17), pages 1722 - 1723 * |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| US5982545A (en) | Structure and method for manufacturing surface relief diffractive optical elements | |
| US7001697B2 (en) | Photomask having a transparency-adjusting layer, method of manufacturing the photomask, and exposure method using the photomask | |
| JP2006258930A (en) | Method for manufacturing microlens and method for manufacturing die for microlens | |
| WO2012157697A1 (en) | Diffraction grating manufacturing method, spectrophotometer, and semiconductor device manufacturing method | |
| JP2002189112A (en) | Method for manufacturing diffraction optical element, and die for manufacture of diffraction optical element and diffraction optical element manufactured by the method for manufacturing diffraction optical element, and optical system, optical appliance and aligner having the diffraction optical element, method for manufacturing device, and device | |
| WO1999001787A1 (en) | Phase mask for machining optical fibers and method of manufacturing the same | |
| WO2021031111A1 (en) | Method for manufacturing surface relief grating structure | |
| JP4629473B2 (en) | Manufacturing method of solid-state imaging device | |
| KR100413175B1 (en) | Lens having diffractive elements attached thereto | |
| JP2000249818A (en) | Diffraction lend and method for designing the same | |
| US10416568B2 (en) | Light intensity modulation method | |
| CN114236815A (en) | Efficiency calculation method of waveband structure optical element | |
| CN105676587B (en) | A kind of method of determining OPC model focal plane | |
| JP2018136529A5 (en) | ||
| US20200363569A1 (en) | Diffuser | |
| JP2004077957A (en) | Diffraction optical element | |
| US9103981B2 (en) | Method for designing and method for manufacturing diffraction-grating lens | |
| JP2006162822A (en) | Diffraction optical element | |
| US20140240840A1 (en) | Optical member | |
| JP2001296649A (en) | Distributed density mask, method for manufacturing the same, and method for forming surface shape | |
| Chalony et al. | Optical and manufacturing design aware flow for metalenses | |
| CN111624689A (en) | Diaphragm and preparation method thereof | |
| CN114815229B (en) | Design method of wide-band light splitting micro-nano diffraction grating | |
| CN113640330B (en) | Offline characterization method of multilayer film Laue lens | |
| CN110209011A (en) | The optical parameter optimization method of the non-key layer pattern of large scale is directed in OPC model establishment process |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination |