CN114236814B - Design method of trapezoid Kinoform lens with high-efficiency focusing - Google Patents

Abstract

The invention belongs to the technical field of optical element design, and particularly relates to a design method of a trapezoid Kinoform lens with high-efficiency focusing. The invention provides a Kinoform lens with a trapezoid shape 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. Theoretical analysis and modeling are carried out on the appearance of the lens, and the theoretical focusing efficiency of the trapezoidal Kinoform lens is calculated. The method proves that the trapezoidal Kinoform lens combines the advantages of 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-morphology high-efficiency focusing lens in the future.

Description

A design method for a high-efficiency focusing trapezoidal Kinoform lens

Technical Field

The invention belongs to the technical field of optical lens design, and in particular relates to a design method of a trapezoidal Kinoform lens.

Background technique

In extreme ultraviolet and X-ray imaging systems, focusing optical elements are crucial components. Among them, metal zone plates are common focusing optical elements. They use the principle of diffraction for focusing. Their main advantages are small size and relatively simple preparation process. However, the maximum theoretical focusing efficiency of phase-type zone plates is only 40%, and the efficiency obtained in practice is generally no 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 processing technology. Refractive Kinoform lenses have become a strong candidate for extreme ultraviolet and X-ray focusing due to their high focusing efficiency. The theoretical focusing efficiency can reach 100% without considering material absorption. However, it was not until recent years that Kinoform lenses were put into practical use. Further development is mainly due to the difficulty of preparation technology: (1) One-dimensional Kinoform lenses need to increase the lens aperture to more than 200 microns, requiring higher silicon sidewalls. Since the steepness and line width directly affect the focusing quality, it poses an increasingly severe challenge to nano-processing and greatly increases the manufacturing cost of the lens; (2) The triangular structure of two-dimensional Kinoform lenses has very high requirements for micro-nano process preparation. The above-mentioned limitations have hindered the further development and practical application of Kinoform lenses.

In order to break through the technical bottlenecks encountered in the development of the above-mentioned FZP and Kinoform lenses, it is urgently necessary to propose new design and processing solutions for key optical components in extreme ultraviolet and X-ray imaging systems in the future, so as to provide a new Kinoform lens design that is easy to prepare in practice, and open up a new development path for high-resolution and high-efficiency synchrotron radiation X-ray focusing and imaging.

Summary of the invention

The purpose of the present invention is to propose a design method for a trapezoidal Kinoform lens that is easy to prepare in practice and has high focusing efficiency, so as to solve the problems faced by other lenses mentioned in the above background technology.

The design method of the high-efficiency focusing trapezoidal Kinoform lens provided by the present invention is based on the thin grating approximation formula, and the specific steps are as follows:

(1) Set the incident light field and the parameters of the trapezoidal Kinoform lens; where:

The incident light field parameters include wavelength λ and amplitude C;

The calculation area of the trapezoidal morphology of each period in the lens is divided into three calculation areas: (I) light transmission area, (II) transition area, and (III) plane area;

The optical element (i.e. lens) parameters include: optical element structural parameters m and n, 0≤m, n≤0.5, preferably 0.1≤m, n≤0.5, respectively describing the proportion of the light-transmitting area and the plane area in a single period; thickness t; and the refractive index n ₀ = (1-δ)-iβ of the material used for the optical element; (1-δ) and β respectively represent the real part and the imaginary part of the refractive index; the optical element parameters are used to calculate the phase shift Φ in the lens;

A Φ-θ schematic diagram is drawn according to the partitions, where θ is the optical path length difference to the focal spot within one cycle; Φ ₀ =2πtδ/λ is the maximum phase shift of a lens with a thickness of t.

(2) Calculate the phase shift function Φ(θ) of each partition in a single period in the lens:

(I) Transparent region: Φ(θ)=0, 0<θ≤2mπ, (1)

(II) Transition zone: , 2mπ<θ≤2(1-n)π, (2)

(III) Plane region: Φ(θ)=Φ ₀ , 2(1-n)π<θ≤2π, (3)

(3) Calculate the sum of the amplitudes according to the thin grating approximation formula:

The first order amplitude sum _A1 is given by the following equation:

, (4)

(4) Computational efficiency:

, (5)

In formula (4), j represents an imaginary unit.

(5) Repeat the above calculations for different structural parameters m and n, draw an efficiency graph of the structural parameters with respect to thickness, and find the parameters m and n corresponding to the trapezoidal structure with higher efficiency.

In the present invention, the incident light is X-ray or ultraviolet light.

In the present invention, the cross-sectional trapezoidal morphology of each period of the lens is a right-angled trapezoidal morphology, which is quantitatively described by parameters.

In the present invention, each trapezoidal period of the optical element is divided into three regions according to morphological characteristics.

In the present invention, the phase shift function is calculated respectively according to the partitions.

In the present invention, the amplitude of each cycle is the sum of the amplitudes generated by the three structural regions.

In the present invention, the optimization method is to draw an efficiency diagram of different structural parameters with respect to thickness or incident light energy, and find the parameters m and n corresponding to the trapezoidal structure with higher efficiency.

In the present invention, the structural parameters m, n and thickness t of the trapezoidal lens are between those of the zone plate and the Kinoform.

In the present invention, the trapezoidal lens has a suitable structural parameter m between 0.1 and 0.25, and n between 0 and 0.25, which results in a higher focusing efficiency, and its performance is better than that of the zone plate and the 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 its performance is better than that of the zone plate and the Kinoform lens.

Compared with the prior art, the method of the present invention has the following beneficial effects:

First, the present invention breaks the boundary between the zone plate and the Kinoform lens through theoretical analysis, and proposes a new type of trapezoidal Kinoform lens, whose maximum focusing efficiency is higher than that of the Kinoform lens with the same parameters.

Second, the trapezoidal Kinoform lens proposed in the present invention has the advantages of both the zone plate and the Kinoform lens. In addition to high-efficiency focusing, it has a flat-top structure and the required thickness is smaller than that of the Kinoform lens, which greatly reduces the difficulty of preparation.

Third, the structural parameters of the trapezoidal Kinoform lens proposed in the present invention have a large degree of freedom for adjustment, and this method can be used to do more targeted lens research and development work in the extreme ultraviolet and X-ray bands.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of phase partitioning of a single period of a trapezoidal Kinoform lens made of Au material in Example 1. FIG.

FIG2 is a comparison of the efficiency calculation results of the Au trapezoidal Kinoform lens in Example 1 and the focusing efficiency measurement values of the actually prepared Au trapezoidal Kinoform lens and Au zone plate lens.

FIG. 3 is a scanning electron microscope image of the Au-made trapezoidal Kinoform lens in Example 1.

FIG. 4 is a graph showing the efficiency of the Au trapezoidal Kinoform lens in Example 2 as a function of structural parameters and thickness.

FIG. 5 is a schematic diagram of the Kinoform trapezoidal lens and a general phase partition proposed by the present invention.

Detailed ways

The present invention is further described below in conjunction with the accompanying drawings and embodiments, but the present invention is not limited to the embodiments. Any simple changes to the calculation parameters in the embodiments fall within the protection scope of the present invention.

Example 1: Calculate the focusing efficiency of a trapezoidal Kinoform lens (thickness 1.8 μm, m=n=0.1) made of Au at 5-15 keV energy. The specific steps are as follows:

(1) The incident light field energy is set to 8 keV, and the plane wave with unit amplitude (C=1) is incident vertically. The thickness of the trapezoidal Kinoform lens is 2 μm, and the refractive index is set to gold. The single periodic cross section and partition along the radial direction are shown in Figure 1.

(2) Calculate the phase shift function Φ(θ) of each partition in a single period in the lens:

(I) Transparent region: Φ(θ)=0, 0<θ≤2mπ;

(II) Transition zone: , 2mπ<θ≤2(1-n)π;

(III) Plane region: Φ(θ)=Φ ₀ , 2(1-n)π<θ≤2π;

Where m=n=0.1

(3) Calculate the sum of the amplitudes according to the thin grating approximation formula:

The first order amplitude sum _A1 is given by the following equation,

(4) Calculate efficiency:

(5) Repeat the above steps to calculate the focusing efficiency of the trapezoidal Kinoform lens at 5-15 keV energy, and the obtained efficiency curve with respect to energy is shown in Figure 2. The figure compares the calculated results with the focusing efficiency measurement values of the actually prepared Au material trapezoidal Kinoform lens (as shown in Figure 3) and the Au material zone plate lens with the same parameters. It can be seen that the results are well consistent, and the efficiency of the Au material trapezoidal Kinoform lens is greatly improved, which proves the feasibility and accuracy of the method of the present invention.

Example 2: Find the structural parameters and thickness of the Au trapezoidal Kinoform lens with the highest efficiency at 8 keV energy (assuming m=n). The specific steps are:

(1) The incident light field energy is set to 8 keV, and the plane wave with unit amplitude is incident vertically. The thickness of the trapezoidal Kinoform lens is 2 μm, and the refractive index is set to gold. The cross section along the radial direction is shown in Figure 1.

(2) Setting different structural parameters m and n, repeating the calculation in Example 1, and drawing an efficiency diagram of the structural parameters with respect to thickness, as shown in FIG4 .

(3) Find the parameters m and n corresponding to the trapezoidal structure with higher efficiency: When m=n=0.15 and the lens thickness is 2.5μm, the focusing efficiency is the highest, reaching 59%. The calculation results show that at 8 keV energy, in order to achieve the maximum focusing efficiency, the structure factors m and n of the lens should be 0.15, and the appropriate thickness should be 2.5μm.

Claims (5)

1. A design method for a high-efficiency focusing trapezoidal Kinoform lens, characterized in that the specific steps are as follows: (1) Set the incident light field and the parameters of the trapezoidal Kinoform lens; where: The incident light field parameters include wavelength λ and amplitude C; The trapezoidal morphology of each period in the trapezoidal Kinoform lens is divided into three calculation regions: (Ⅰ) light transmission region, (Ⅱ) transition region, and (Ⅲ) plane region; The optical element parameters include: optical element structural parameters m and n, 0≤m, n≤0.5, respectively describing the proportion of the light-transmitting area and the plane area in a single period; thickness t; refractive index n ₀ =(1-δ)-iβ of the material used for the optical element; (1-δ) and β respectively represent the real part and imaginary part of the refractive index; the optical element parameters are used to calculate the phase shift Φ in the lens; Draw a Φ-θ diagram based on the partitions, where θ is the optical path length difference to the focal spot within one cycle; Φ ₀ = 2πtδ/λ is the maximum phase shift of a lens with a thickness of t; (2) Calculate the phase shift function Φ(θ) of each partition in a single period in the lens: (I) Transparent region: Φ(θ) = 0, 0 < θ ≤ 2 mπ, (1) (II) Transition zone: (III) Planar region: Φ(θ)＝Φ ₀ , 2(1-n)π<θ≤2π, (3) (3) Calculate the sum of the amplitudes according to the thin grating approximation formula: The first order amplitude sum _A1 is given by the following equation: (4) Computational efficiency: In formula (4), j represents the imaginary unit; (5) Repeat the calculations in steps (2) to (4) according to different structural parameters m and n, draw an efficiency diagram of the structural parameters with respect to thickness, and find the parameters m and n corresponding to the trapezoidal structure with higher efficiency. 2. The design method according to claim 1, characterized in that the incident light is X-rays or ultraviolet rays. 3. The design method according to claim 1 is characterized in that the cross-sectional trapezoidal morphology of each period of the lens is a right-angled trapezoidal morphology, which is quantitatively described by parameters. 4. The design method according to claim 1 is characterized in that the structural parameters m, n and thickness t corresponding to the trapezoidal Kinoform lens are between those of the zone plate and the Kinoform. 5. The design method according to claim 4 is characterized in that the structural parameters of the trapezoidal Kinoform lens are: m is between 0.1 and 0.25, n is between 0 and 0.25, and has a higher focusing efficiency.