CN114236814A - Design method of high-efficiency focusing trapezoidal Kinoform lens - Google Patents
Design method of high-efficiency focusing trapezoidal Kinoform lens Download PDFInfo
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- CN114236814A CN114236814A CN202111484279.1A CN202111484279A CN114236814A CN 114236814 A CN114236814 A CN 114236814A CN 202111484279 A CN202111484279 A CN 202111484279A CN 114236814 A CN114236814 A CN 114236814A
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- 238000000034 method Methods 0.000 title claims abstract description 17
- 238000013461 design Methods 0.000 title claims abstract description 16
- 230000003287 optical effect Effects 0.000 claims abstract description 15
- 238000004364 calculation method Methods 0.000 claims description 9
- 230000010363 phase shift Effects 0.000 claims description 8
- 239000000463 material Substances 0.000 claims description 5
- 230000007704 transition Effects 0.000 claims description 5
- 238000010586 diagram Methods 0.000 claims description 4
- 238000005192 partition Methods 0.000 claims description 3
- 230000005540 biological transmission Effects 0.000 claims description 2
- 239000011541 reaction mixture Substances 0.000 claims description 2
- 238000003384 imaging method Methods 0.000 abstract description 4
- 238000002360 preparation method Methods 0.000 abstract description 4
- 238000004458 analytical method Methods 0.000 abstract description 2
- 239000010931 gold Substances 0.000 description 14
- 238000011161 development Methods 0.000 description 4
- 238000012545 processing Methods 0.000 description 3
- 238000005516 engineering process Methods 0.000 description 2
- PCHJSUWPFVWCPO-UHFFFAOYSA-N gold Chemical compound [Au] PCHJSUWPFVWCPO-UHFFFAOYSA-N 0.000 description 2
- 229910052737 gold Inorganic materials 0.000 description 2
- 238000004519 manufacturing process Methods 0.000 description 2
- 239000002184 metal Substances 0.000 description 2
- 229910052751 metal Inorganic materials 0.000 description 2
- 241001270131 Agaricus moelleri Species 0.000 description 1
- XUIMIQQOPSSXEZ-UHFFFAOYSA-N Silicon Chemical compound [Si] XUIMIQQOPSSXEZ-UHFFFAOYSA-N 0.000 description 1
- 238000010521 absorption reaction Methods 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000000877 morphologic effect Effects 0.000 description 1
- 238000005457 optimization Methods 0.000 description 1
- 230000000737 periodic effect Effects 0.000 description 1
- 238000012827 research and development Methods 0.000 description 1
- 229910052710 silicon Inorganic materials 0.000 description 1
- 239000010703 silicon Substances 0.000 description 1
- 230000005469 synchrotron radiation Effects 0.000 description 1
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- 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
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Abstract
The invention belongs to the technical field of optical element design, and particularly relates to a design method of a high-efficiency focusing trapezoidal Kinoform lens. The invention is based on a thin grating approximate Kirz formula of a geometric optics theory, unifies the design theory of a zone plate and a Kinoform lens, and provides the Kinoform lens with a trapezoidal shape. And performing theoretical analysis and modeling on the appearance of the lens, and calculating the theoretical focusing efficiency of the trapezoidal Kinoform lens. The method provided by the invention proves the advantages of the trapezoidal Kinoform lens combined with the phase type zone plate and the Kinoform lens, has the advantages of high focusing efficiency, easiness in preparation and light structure, and is verified by experiments. The lens designed by the invention breaks through the theoretical limit of the traditional flat lens on focusing and imaging efficiency, and provides effective guidance for developing a novel high-efficiency focusing lens in the future.
Description
Technical Field
The invention belongs to the technical field of optical lens design, and particularly relates to a design method of a trapezoidal Kinoform lens.
Background
In extreme ultraviolet and X-ray imaging systems, focusing optics are a critical component. The metal zone plate is a common focusing optical element, the metal zone plate focuses by utilizing the diffraction principle, the main advantages are small volume and relatively simple preparation process, but the maximum theoretical focusing efficiency of the phase type zone plate is only 40%, and the actually prepared efficiency is generally not more than 20%. In addition, the aspect ratio of the lens in the hard X-ray band is required to reach more than 20, which is a great challenge for the processing technology. Refractive Kinoform lenses are promising candidates for euv and X-ray focusing due to their high focusing efficiency, which can reach 100% without considering the theoretical focusing efficiency of material absorption, however, Kinoform lenses have not been practically used until recently. The further development is mainly due to the difficulty of the preparation technology: (1) the one-dimensional Kinoform lens needs to increase the aperture of the lens to more than 200 microns, requires a higher silicon side wall, and provides more and more serious challenges for nano processing because the steepness and the line width directly influence the focusing quality, and also greatly improves the manufacturing cost of the lens; (2) the triangular structure of the two-dimensional Kinoform lens has high requirements on micro-nano process preparation. The above limitations have hindered further development and practical use of Kinoform lenses.
In order to break through the technical bottleneck encountered by the development of the FZP and Kinoform lens, a new design and processing scheme is urgently needed to be provided for key optical components in extreme ultraviolet and X-ray imaging systems in the future, so that a design scheme of a novel Kinoform lens which is easy to actually prepare is provided, and a new development way is opened up for focusing and imaging of synchrotron radiation X-rays with high resolution and high efficiency.
Disclosure of Invention
The present invention is directed to a design method of a trapezoidal Kinoform lens with high focusing efficiency, which is easy to be practically manufactured, so as to solve the above-mentioned problems faced by other lenses in the background art.
The invention provides a design method of a high-efficiency focusing trapezoidal Kinoform lens, which is based on a thin grating approximation formula and comprises the following specific steps:
(1) setting an incident light field and parameters of a trapezoidal Kinoform lens; wherein:
the incident light field parameters comprise wavelength lambda and amplitude C;
dividing a calculation area of the trapezoidal morphology of each period in the lens into three calculation areas: a light transmission area, (II) a transition area, and (III) a plane area;
optical element (i.e., lens) parameters include: the structural parameters m and n of the optical element are more than or equal to 0 and less than or equal to 0.5, preferably more than or equal to 0.1 and less than or equal to 0.5, and the proportion of the light-transmitting area and the plane area in a single period is respectively described; the thickness t; and refractive index n of material for optical element0= (1- δ) -i β; (1- δ), β represent the real and imaginary parts of the refractive index, respectively; the optical element parameters are used for calculating the phase shift phi in the lens;
drawing a phi-theta schematic diagram according to the partitions, wherein theta is the optical path length difference from a focal spot in one period; phi0And =2 π t δ/λ is the maximum phase shift of a lens of thickness t.
(2) Calculating the phase shift function Φ (θ) for each zone of a single period in the lens:
(I) a light-transmitting region: phi (theta) =0, 0< theta ≦ 2m pi, (1)
(II) transition zone:
，2mπ<θ≤2(1-n)π，（2）
(III) planar area: phi (theta) = phi0，2(1-n)π<θ≤2π，（3）
(3) And (3) solving the sum of the amplitudes according to a thin grating approximation formula:
first order amplitude sum A1Given by the equation:
(4) calculating efficiency:
in the formula (4), the reaction mixture is,jrepresenting imaginary units.
(5) And repeating the above calculation according to different structural parameters m and n, drawing an efficiency graph of the structural parameters relative to the thickness, and finding out the parameters m and n corresponding to the trapezoid structure with higher efficiency.
In the present invention, the incident light is X-ray or ultraviolet.
In the invention, the trapezoidal shape of the section of each period of the lens is a right-angle trapezoidal shape and is quantitatively described by parameters.
In the invention, each trapezoidal period of the optical element is divided into 3 regions according to the morphological characteristics.
In the invention, the phase shift functions are calculated according to the partitions respectively.
In the present invention, the amplitude of each period is the sum of the amplitudes generated by the 3 structural regions.
In the invention, the optimization method comprises the steps of drawing an efficiency graph of different structure parameters relative to thickness or incident light energy, and finding out parameters m and n corresponding to a trapezoidal structure with higher efficiency
In the invention, the structural parameters m, n and the thickness t corresponding to the trapezoidal lens are between the zone plate and the Kinoform.
In the invention, the proper structural parameter m corresponding to the trapezoidal lens is 0.1-0.25, and the n is 0-0.25, so that the focusing efficiency is higher, and the performance of the trapezoidal lens is superior to that of a zone plate and a Kinoform lens.
In the present invention, when the thickness t is between the zone plate and the Kinoform, there is a higher focusing efficiency, and the performance is better than the zone plate and the Kinoform lens.
Compared with the prior art, the method has the beneficial effects that:
first, the present invention breaks the boundary between the zone plate and the Kinoform lens through theoretical analysis, and proposes a new trapezoidal Kinoform lens from which the maximum focusing efficiency is higher than that of a Kinoform lens of the same parameters.
Second, the trapezoidal Kinoform lens proposed by the present invention has the advantages of both the zone plate and the Kinoform lens, has a flat-top structure and a smaller required thickness than the Kinoform lens in addition to high-efficiency focusing, and the manufacturing difficulty is greatly reduced.
Thirdly, the structural parameters of the trapezoid Kinoform lens provided by the invention have great freedom for adjustment, and more targeted lens research and development work can be carried out in extreme ultraviolet and X-ray wave bands by using the method.
Drawings
Fig. 1 is a schematic phase-division diagram of a single period of the Au trapezoidal Kinoform lens in example 1.
Fig. 2 is a comparison of the efficiency calculation results of the Au trapezoidal Kinoform lens in example 1 and the measured values of the focusing efficiency of the Au trapezoidal Kinoform lens and the Au zone plate lens actually prepared.
FIG. 3 is a SEM of a trapezoidal Kinoform lens made of Au as in example 1.
Fig. 4 is a graph of the efficiency of the Au trapezoidal Kinoform lens of example 2 as a function of the structural parameters and thickness.
FIG. 5 is a schematic diagram of a Kinoform trapezoidal lens and a general phase division.
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 a trapezoidal Kinoform lens (the thickness is 1.8 mu m, and m = n = 0.1) made of Au material under the energy of 5-15keV, and specifically comprising the following steps:
(1) the incident light field energy was set to 8keV, and plane waves of unit amplitude (C = 1) were normally incident. The trapezoidal Kinoform lens has a thickness of 2 μm, a refractive index set to gold, and a single periodic cross section and a division in the radial direction as shown in fig. 1.
(2) Calculating the phase shift function Φ (θ) for each zone of a single period in the lens:
(I) a light-transmitting region: phi (theta) =0, 0< theta is less than or equal to 2m pi;
(II) transition zone:
，2mπ<θ≤2(1-n)π；
(III) planar area: phi (theta) = phi0，2(1-n)π<θ≤2π；
Wherein m = n =0.1
(3) And (3) solving the sum of the amplitudes according to a thin grating approximation formula:
first order amplitude sum A1As given by the following equation,
(4) calculating the efficiency:
(5) the above steps are repeated to calculate the focusing efficiency of the trapezoidal Kinoform lens at energies of 5-15keV, resulting in a curve of efficiency versus energy, as shown in FIG. 2. The calculated result is compared with the actually prepared trapezoidal Kinoform lens made of Au (shown in figure 3) and the measured value of the focusing efficiency of the Au zone plate lens made of Au with the same parameters, so that the result can be well matched, the efficiency of the trapezoidal Kinoform lens made of Au is greatly improved, and the feasibility and the accuracy of the method are proved.
Example 2: searching structural parameters and thickness (assuming m = n) of the trapezoidal Kinoform lens made of Au material under the energy of 8keV under the highest efficiency, and specifically comprising the following steps:
(1) the energy of the incident light field was set to 8keV, and the incident light was vertically incident with a plane wave of unit amplitude. The thickness of the trapezoidal Kinoform lens is 2 μm, the refractive index is set to gold, and the cross section in the radial direction is shown in FIG. 1.
(2) Different structure parameters m and n are set, the same calculation in the embodiment 1 is repeated, and an efficiency graph of the structure parameters relative to the thickness is drawn, as shown in fig. 4.
(3) Finding parameters m and n corresponding to the trapezoid structure with higher efficiency: the focusing efficiency is highest up to 59% when m = n =0.15 and the lens thickness is 2.5 μm. The calculations indicate that the lens should have a structure factor m, n of 0.15 and a suitable thickness of 2.5 μm for maximum focusing efficiency at 8keV energy.
Claims (5)
1. A design method of a high-efficiency focusing trapezoidal Kinoform lens is characterized by comprising the following specific steps:
(1) setting an incident light field and parameters of a trapezoidal Kinoform lens; wherein:
the incident light field parameters comprise wavelength lambda and amplitude C;
the trapezoidal profile of each period in a trapezoidal Kinoform lens is divided into three calculation regions: a light transmission area, (II) a transition area, and (III) a plane area;
the optical element parameters include: the structural parameters m and n of the optical element, wherein m is more than or equal to 0, and n is more than or equal to 0.5, and the proportion of the light-transmitting area and the planar area in a single period is respectively described; the thickness t; refractive index n of material for optical element0= (1- δ) -i β; (1- δ), β represent the real and imaginary parts of the refractive index, respectively; the optical element parameters are used for calculating the phase shift phi in the lens;
drawing a phi-theta diagram according to the partitions, wherein theta is the optical path length difference from a focal spot in one period; phi0=2 π t δ/λ is the maximum phase shift of a lens of thickness t;
(2) calculating the phase shift function Φ (θ) for each zone of a single period in the lens:
(I) a light-transmitting region: phi (theta) =0, 0< theta ≦ 2m pi, (1)
(II) transition zone:
，2mπ<θ≤2(1-n)π，（2）
(III) planar area: phi (theta) = phi0，2(1-n)π<θ≤2π， （3）
(3) And (3) solving the sum of the amplitudes according to a thin grating approximation formula:
first order amplitude sum A1Given by the equation:
(4) calculating efficiency:
in the formula (4), the reaction mixture is,jrepresents an imaginary unit;
(5) and repeating the above calculation according to different structural parameters m and n, drawing an efficiency graph of the structural parameters relative to the thickness, and finding out the parameters m and n corresponding to the trapezoid structure with higher efficiency.
2. The design method of claim 1, wherein said incident light is X-rays or ultraviolet rays.
3. The design method of claim 1, wherein the cross-sectional trapezoidal profile of each period of the lens is a right-angled trapezoidal profile, quantitatively described by a parameter.
4. The design method of claim 1, wherein the trapezoidal lens has a corresponding structure parameter m, n and a thickness t between the zone plate and the Kinoform.
5. The design method according to claim 4, wherein the structural parameters of the trapezoidal lens are: m is between 0.1 and 0.25, n is between 0 and 0.25, and higher focusing efficiency exists.
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| US20140293422A1 (en) * | 2011-11-09 | 2014-10-02 | Institute Of Physics, Chinese Academy Of Sciences | Diffractive optical element, design method thereof and application thereof to solar cell |
| CN104132305A (en) * | 2014-07-04 | 2014-11-05 | 佛山市中山大学研究院 | Condensing lens |
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| US20190187416A1 (en) * | 2017-12-15 | 2019-06-20 | Samsung Display Co., Ltd. | F-theta lens having diffractive optical element and optical system including the f-theta lens |
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Patent Citations (8)
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|---|---|---|---|---|
| KR20030001071A (en) * | 2001-06-28 | 2003-01-06 | 주식회사 하이닉스반도체 | Image sensor |
| US6992824B1 (en) * | 2003-12-27 | 2006-01-31 | Motamedi Manouchehr E | Efficient wave propagation for terahertz imaging and sensing |
| US20140293422A1 (en) * | 2011-11-09 | 2014-10-02 | Institute Of Physics, Chinese Academy Of Sciences | Diffractive optical element, design method thereof and application thereof to solar cell |
| CN104132305A (en) * | 2014-07-04 | 2014-11-05 | 佛山市中山大学研究院 | Condensing lens |
| US20190187416A1 (en) * | 2017-12-15 | 2019-06-20 | Samsung Display Co., Ltd. | F-theta lens having diffractive optical element and optical system including the f-theta lens |
| JP2019133002A (en) * | 2018-01-31 | 2019-08-08 | 日本電信電話株式会社 | Diffraction element |
| CN109283685A (en) * | 2018-09-27 | 2019-01-29 | 中山大学 | A kind of design method of super structure lens nano unit and super structure lens |
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