Diffractive optical element, method for designing an efficiently achromatized diffraction structure, and method for manufacturing an efficiently achromatized diffraction element

Abstract

The present invention relates to a diffractive optical element (1) having a spatially varying refractive index. The spatially varying refractive index forms a series of adjacent sections (3A-3D) within which the refractive index varies. The series of adjacent sections forms a diffractive structure (3). The diffractive structure (3) has a diffraction efficiency of at least 0.95 averaged over the entire wavelength range in a spectral range extending at least 300 nm or more. The diffraction efficiency value of at least 0.95 averaged over the entire spectral range is achieved within each of the series of adjacent sections (3A-3D) by a single single-layer diffractive structure (3) having an optimal combination of at least two refractive indices and at least two Abbe numbers. The refractive index variation is achieved by doping, material blending, or structuring in the subwavelength range.

Description

[Technical field]

[0001] The project leading to this application has received funding from the European Union's Horizon 2020 research and innovation programme under Marie Skwodowska-Curie grant agreement No. 675745. The present invention relates to a diffractive optical element (DOE) having a diffractive structure with a spatial variation in refractive index, and further to a method for designing an efficiently achromatized diffractive structure and a method for manufacturing an efficiently achromatized diffractive element. [Background technology]

[0002] Diffractive optical elements are used, for example, for light splitting and light deflection. Such elements are based on the principle of diffraction of light waves and are designed to deflect light of a certain wavelength in a certain direction with the help of a diffractive structure, i.e. a diffraction grating. The diffraction efficiency of a diffractive optical element is an indicator of what proportion of the light reaching the grating structure is diffracted into a certain diffraction order, i.e. into a desired direction, and this diffraction efficiency depends on the grating profile within one period. The diffraction efficiency represents the ratio of the energy flux propagating in the desired diffraction order to the total propagating energy flux. In principle, for a certain wavelength of a diffractive optical element, the so-called design wavelength, it is possible to realize, ignoring shadowing effects, that all light of the design wavelength is diffracted in the same diffraction order and thereby deflected in the same direction, resulting in a diffraction efficiency of 1 (or 100%) for the design wavelength (so-called blazed or echelette grating). However, this is not the case for wavelengths that deviate from the design wavelength. Light of wavelengths that deviate from the design wavelength is deflected to different diffraction maxima and thus into different directions. In the case of diffraction of polychromatic light, this generates scattered light outside the diffraction orders, thereby reducing the resolution.

[0003] Therefore, diffractive optical elements have been developed that can achieve high diffraction efficiency in a specific diffraction order (mainly the first diffraction order) for all wavelengths in a specific wavelength range. Such diffractive optical elements are called efficiently achromatic diffractive optical elements. Therefore, an efficiently achromatic diffractive optical element is a diffractive optical element that can achieve high diffraction efficiency for all wavelengths in a specific wavelength range of a specific diffraction order. For example, C. Ribot et al., "Broadband and Efficient Diffraction" in Advanced Optical Materials 7 (2013), describes a metal lens that is efficiently achromatic in the infrared.

[0004] There are various approaches for the production of efficiently achromatic diffractive optical elements. For example, US 6,873,463, US 9,696,469, US 2001 / 013975 and US 5,487,877 propose the use of multi-layer diffractive optical elements to achieve efficient achromatism. From DE 102006007432, US 2011 / 026118, US 7,663,803, US 6,912,092, US 2013 / 057956, US 2004 / 051949 and US 5,847,887 it is also known to adjust the refractive index of one layer in a multi-layer diffractive optical element to cancel the dispersion of another layer. From US 2011 / 090566, US 9422414, US 7031078, US 7663803, US 7196132 and US 8773783 diffractive optical elements are known which use materials with anomalous dispersion to achieve efficient achromatism.

[0005] In a diffractive optical element, the period of which is very large compared to the wavelength of the diffracted light, the diffracted light has a predetermined design wavelength (λ 0A single-layer diffractive optical element can be designed so that the diffraction efficiency at the wavelength of interest is theoretically 100%. However, as the wavelength deviates from this design wavelength, the diffraction efficiency drops off rapidly with increasing deviation from the design wavelength. This causes unwanted scattering in optical imaging systems, and therefore such diffractive optical elements cannot be used in broadband optical systems. This problem can be solved by adding an additional diffractive layer made of a material with a different refractive index, as described, for example, in US Pat. No. 6,873,463, US Pat. No. 9,696,459, and US Patent Publication No. 2001 / 013975. The two layers can then have different profile heights, which can be adapted to maximize the average diffraction efficiency at the desired wavelength range. This is described, for example, in BH Kleemann et al. "Design-Concepts for broadband high-efficieny DOEs", Journal of the European Optical Society-Rapid publications 3 (2008). On the other hand, by appropriately selecting the second material, it is also possible to maximize the average diffraction efficiency in the desired wavelength range when the profile heights of the layers are the same. Diffractive optical elements with different profile heights are usually called multi-layer DOEs, whereas diffractive optical elements with the same profile heights of the layers are usually called "Common Depth DOEs". To realize a Common Depth DOE, it is necessary to choose a combination of materials whose dispersions are as complementary as possible. Common Depth DOEs are described, for example, in DE 102006007432, US 2011 / 0026118, US 7663803, US 6912092, US 2012 / 0597741, US 2004 / 051949 and US 5847877. Both approaches are already employed in commercially available photographic objectives.

[0006] Diffractive optical elements can be realized, for example, by tilted surfaces, as in the multi-layer DOEs and Common Depth DOEs mentioned above. An alternative approach to fabricating diffractive optical elements is to vary the refractive index periodically as a function of location within the element. This results in so-called gradient index DOEs (GRIN DOEs for short). However, the diffraction efficiency of gradient index DOEs is strongly wavelength dependent. This problem is also known for other single-layer diffractive optical elements and can be avoided by applying a second GRIN-DOE layer similar to the multi-layer DOE, as described, for example, in the above-cited publication by BH Kleemann. However, this also results in a two-layer diffractive optical element, which increases the overall height of the system. Summary of the Invention [Problem to be solved by the invention]

[0007] In view of such conventional techniques, a first object of the present invention is to provide an efficiently achromatized diffractive optical element that can be manufactured with a low profile height. A second object of the present invention is to provide a design method for an efficiently achromatized diffractive structure that enables the manufacture of an efficiently achromatized diffractive optical element having a low profile height, and a third object of the present invention is to provide a manufacturing method for an efficiently achromatized diffractive optical element having a low profile height. [Means for solving the problem]

[0008] The first problem is solved by a diffractive optical element according to claim 1, the second problem is solved by a method for designing an efficiently achromatized diffractive structure according to claim 16, and the third problem is solved by a method for producing a diffractive optical element according to claim 21. The dependent claims contain further advantageous embodiments of the invention.

[0009] The diffractive optical element (DOE) according to the invention comprises a single diffractive structure with a spatial variation of the refractive index. The spatial variation of the refractive index results in a series of adjacent sections in which the refractive index varies respectively, which series of adjacent sections form the diffractive structure. The diffractive optical element according to the invention is therefore a GRIN-DOE. The series of adjacent sections can form a periodic structure. Alternatively, instead of a periodic structure, a structure can be formed in which the lateral dimensions of the sections vary. This structure results in a defined and variable diffraction angle depending on the position on the diffractive structure, which can result in, for example, focusing effects, defocusing effects, aberration correction effects or other optical effects in addition to, for example, the deflection effect of the structure.

[0010] The diffractive structure has a diffraction efficiency of at least 0.95 averaged over a spectral range extending at least over 300 nm, preferably at least over 350 nm, which may be a part of the visible light range, in particular the entire visible light range, i.e. 400-800 nm or more narrowly 400-750 nm.

[0011] The diffractive optical element according to the invention has a diffraction efficiency value of at least 0.95, averaged over a spectral range of at least 300 nm, at least one optimized maximum refractive index n max , and one optimized minimum refractive index n min , and at least one optimized high Abbe number v max , and one optimized low Abbe number ν min in each section of the array of a series of adjacent sections is realized by a single monolayer diffractive structure having a combination of:

[0012] The diffractive optical element according to the invention can be manufactured with a low profile height due to the fact that a diffraction efficiency of at least 0.95 averaged over the spectral range is realized by a single monolayer diffractive structure. The lower the profile height of the diffractive structure, the lower the shadowing effect caused by the profile height. The lower the shadowing effect, the slower the decrease in diffraction efficiency when the angle of incidence of the light increases and / or when the lateral spread of the section of a series of adjacent sections decreases.

[0013] In an advantageous embodiment of the diffractive optical element according to the invention, a value of diffraction efficiency of at least 0.95, averaged over a spectral range of at least 300 nm, is optimized at a specific wavelength in a spectral range of at least 300 nm with one maximum refractive index n max , one minimum refractive index n optimized at a specific wavelength in a spectral range of at least 300 nm min , Optimized for high Abbe number ν max , and one optimized low Abbe number ν min , and, optionally, realized in each section of the series of adjacent sections by a single monolayer diffractive structure having at least one combination of an optimized first partial dispersion and an optimized second partial dispersion.

[0014] The refractive index is a wavelength-dependent quantity, and its wavelength dependence, especially in the visible light region, can be described, for example, by the Cauchy equation. Therefore, the optimized maximum refractive index n max and the optimized minimum refractive index n min In order to describe the wavelength dependence of , two Cauchy equations with different parameters are required. The wavelength dependence of the Cauchy equation can be determined with sufficient approximation by the value of the refractive index at a specific wavelength, the value of the Abbe number, and the value of the partial dispersion. Therefore, in this embodiment, the wavelength-dependent maximum refractive index n max , and the wavelength-dependent minimum refractive index n minwhere the six parameters are the maximum refractive index at a particular wavelength, n max , the minimum refractive index at a particular wavelength, n min , high Abbe number ν max , low Abbe number ν min , the first partial dispersion, and the second partial dispersion. Since the dependence of the Cauchy equation on the partial dispersion has little effect on the value of the diffraction efficiency averaged over a spectral range of at least 300 nm, the partial dispersions are kept at predetermined values ​​without changing the partial dispersions in the optimization.

[0015] The maximum refractive index, n, at a particular wavelength in the spectral range max , the minimum refractive index at a particular wavelength in the spectral range, n min , high Abbe number ν max , and low Abbe number ν min , and optionally, at the optimized values ​​of the first partial dispersion and the second partial dispersion, the difference Δn(λ)=n as a function of the wavelength λ in a spectral range of at least 300 nm. max (λ)-n max (λ) is approximately linear.

[0016] In the diffractive optical element according to the present invention, the optimized high Abbe number v max is preferably the optimized maximum refractive index n max and optimized for low Abbe number ν min is preferably the optimized minimum refractive index n min This can be achieved, for example, by using doped or mixed optical materials, which counter the tendency of optical materials to have lower Abbe numbers as their refractive index increases.

[0017] In the diffractive optical element according to the present invention, the greater the refractive index difference Δn, the lower the profile height of the diffractive structure can be kept. Therefore, the optimized maximum refractive index n max and the optimized minimum refractive index n minIt is advantageous if the refractive index difference Δn between has a value of at least 0.005, in particular a value of at least 0.01, preferably a value of at least 0.015, at least at a certain wavelength.

[0018] In the diffractive optical element according to the present invention, the optimized high Abbe number v max and optimized low Abbe number ν min It is advantageous if the Abbe number difference Δν between has a value of at least 8, in particular at least 15, preferably at least 30. The larger the Abbe number difference Δν, the larger the refractive index difference Δn, and the greater the average diffraction efficiency in the spectral range, which is at least 0.95 or more, which allows a lower profile height of the diffractive structure to be realized.

[0019] In the diffractive optical element according to the invention, at least two maxima of the spectral diffraction efficiency may be present in a spectral range that extends over at least 300 nm, preferably at least 350 nm. The diffraction efficiency averaged over a spectral range of at least 300 nm represents the value of the diffraction efficiency averaged over the spectral range, whereas the spectral diffraction efficiency represents the diffraction efficiency as a function of the wavelength of the diffracted light. If the spectral diffraction efficiency has at least two maxima, in particular in the case of two maxima of the spectral diffraction efficiency, the wavelengths at which the maxima are located differ from each other by at least 150 nm, preferably by at least 200 nm, a uniform progression of the spectral diffraction efficiency in the spectral range can be achieved for a specific value of the diffraction efficiency averaged over a spectral range of at least 300 nm. If there are more than two maxima, in particular in the case of the wavelengths at which the two outer maxima are located differ from each other by at least 150 nm, preferably by at least 200 nm.

[0020] The diffractive structure of the diffractive optical element according to the invention can be made of a doped material or a mixture of at least two materials with different refractive indices. The spatial variation of the refractive index is then based on a change in doping or a change in the mixture ratio. The diffractive structure can be manufactured relatively easily by introducing a spatially varying doping or by 3D printing with a time-varying mixture ratio of the supplied mixture. Also, when using a printer with multiple printing nozzles, instead of a time-varying mixture ratio, a nozzle-varying mixture ratio can also be used.

[0021] However, it is also possible to form the diffractive optical element according to the invention as a metasurface. A metasurface is made up of so-called meta-atoms, components in the nanometer range that are smaller than the wavelength but consist of several thousand atoms or molecules. By varying the properties of the meta-atoms, it is possible to vary the phase and amplitude of the incident wavefront as a function of location with subwavelength resolution. To avoid losses, designs are usually aimed at varying only the phase. Thereby, a diffractive optical element (DOE) can be realized. A diffractive optical element according to the invention, realized as a metasurface, has a diffractive structure in which first regions of a first material having a first refractive index are arranged alternately with second regions of a second material having a second refractive index higher than the first refractive index. The first and second regions are arranged alternately, respectively, within a series of adjacent sections, the width of the second regions increasing, respectively, from one end of the section to the other end, with respect to the width of the first regions in each section. The maximum width of the first and second regions is always smaller than the central wavelength of a spectral range that extends at least over 300 nm. Thereby, an effective refractive index can be provided that depends on the refractive index of the first region and the refractive index of the second region and the volume ratio of the first region to the second region in the volume. In particular, if the maximum width of the first region and the second region is smaller than 0.3 times the central wavelength of the spectral range extending at least 300 nm or more, the diffractive structure forms a metasurface that acts on the wavefront substantially as if it had an effective refractive index that increases continuously from one end of the respective section to the other. Alternatively, the maximum width of at least the second section can be at least 0.3 times the central wavelength of the spectral range extending at least 300 nm or more, and at most 1.0 times the central wavelength of the spectral range extending at least 300 nm or more. Thereby, the second region, at its maximum width, acts like a waveguide, which leads to a reduction in the shadowing effect according to P. Lalanne "Waveguiding in blazed-binary diffractive elements" in J.Opt.Soc.Am.16 (1999) compared to a diffractive element with a continuously increasing refractive index.A smooth transition between the metasurface with and without the waveguide effect occurs when the maximum width of at least the second region decreases, reaching a value of about 0.3 times the central wavelength of the spectral range that spans at least 300 nm or more, where the waveguide effect can still be present, particularly at small wavelengths in the wavelength range, but no longer at large wavelengths.

[0022] The present invention further provides a refractive or reflective optical element comprising a diffractive optical element according to the present invention. A diffractive optical element can add an additional degree of optical freedom to a refractive or reflective optical element. For example, lenses with multiple focal lengths can be realized by incorporating a Fresnel zone into a lens using a diffractive optical element, where one focal length is based on the refraction of light (refraction) and the other focal lengths are based on the diffraction of light (diffraction). In this way, for example, multifocal intraocular lenses can be produced. Such applications are also conceivable for mirrors, where one focal length is based on the reflection of light. Furthermore, based on the different wavelength dependence of the refractive focal length and the diffractive focal length, there is the possibility of correcting the color shift of the lens by a diffractive optical element incorporated in the lens.

[0023] A method for designing an efficiently achromatic diffractive structure made of a material having a spatial variation in refractive index according to the present invention, comprising forming a series of adjacent sections, each of which has a refractive index varying between a maximum refractive index and a minimum refractive index, the spatial variation being such that: - setting a spectral range that extends to at least 300 nm or more, preferably at least 350 nm or more, and a diffraction efficiency to be achieved averaged over a spectral range of at least 300 nm or more, preferably at least 350 nm or more, - at least the maximum refractive index n in the section max and the minimum refractive index n min , and the maximum refractive index n max High Abbe number ν related to max and the minimum refractive index n minLow Abbe number ν related to min is optimized to obtain at least the diffraction efficiency to be achieved, averaged over the entire spectral range.

[0024] Using the method for designing an efficient achromatic diffractive structure according to the present invention, an efficient achromatic diffractive structure can be realized that has only a single diffractive layer.Therefore, the profile height of the diffractive structure can be kept low.For the diffraction efficiency to be achieved averaged in a spectral range of at least 300 nm, preferably at least 350 nm, in order to achieve the best possible efficient achromatism in the diffractive structure, a value of at least 0.95 can be set in particular.

[0025] In an advantageous embodiment of the method according to the invention, the maximum refractive index n max , minimum refractive index n min , high Abbe number ν max , and low Abbe number ν min In addition, the maximum refractive index n max The first partial dispersion associated with the minimum refractive index n min is optimized such that a set diffraction efficiency is achieved, averaged over a spectral range of at least 300 nm, preferably at least 350 nm.

[0026] As mentioned above, the wavelength dependence of the Cauchy equation can be determined with a sufficient approximation by the value of the refractive index at a particular wavelength, the value of the Abbe number and the value of the partial dispersion. Therefore, in the above-mentioned advantageous embodiment of the method, up to six parameters are determined, namely the maximum refractive index n max , the minimum refractive index at a particular wavelength, n min , high Abbe number ν max and low Abbe number ν min , and optionally, the optimization can be based on the optimization of the first partial dispersion and the second partial dispersion. These six values ​​fully determine the parameters of the Cauchy equation, thereby determining the maximum refractive index n maxWavelength dependence of and minimum refractive index n min The wavelength dependence of the maximum refractive index n at a particular wavelength in the spectral range is well determined. max , the minimum refractive index at a particular wavelength in the spectral range, n min , high Abbe number ν max , and low Abbe number ν min , and optionally, at the optimized values ​​of the first partial dispersion and the second partial dispersion, the difference Δn(λ)=n as a function of wavelength λ in a spectral range of at least 300 nm. max (λ)-n max (λ) is approximately linear.

[0027] Within the scope of the method according to the invention for designing an efficiently achromatic diffractive structure, the maximum refractive index n max , minimum refractive index n min , high Abbe number ν max and low Abbe number ν min , and, if necessary, the first partial dispersion and the second partial dispersion can be optimized so that the profile height h of the diffractive structure is minimized or at least does not exceed a certain maximum value, thereby minimizing shadowing effects, which lead to a slower decrease in the diffraction efficiency averaged over a spectral range of at least 300 nm, preferably at least 350 nm, with increasing angles of incidence and / or with decreasing lateral dimensions of the sections of the diffractive structure.

[0028] In particular, in the method according to the invention for designing an efficiently achromatic diffractive structure, the maximum refractive index n max , minimum refractive index n min , high Abbe number ν max , and low Abbe number ν min, and, if necessary, the first partial dispersion and the second partial dispersion are optimized in such a way that at least two maxima of the spectral diffraction efficiency are present in the spectral range. This allows a uniform progression of the spectral diffraction efficiency to be achieved over a wide part of the set spectral range. In particular, it is achieved that the spectral diffraction efficiency between the maxima is not below 0.95, preferably 0.97, in particular 0.98. As a result, a high spectral diffraction efficiency is obtained over a large part of the set spectral range. The wavelengths at which the maxima are located, if there are two maxima, advantageously differ from one another by at least 150 nm, preferably by at least 200 nm, in order to obtain a wavelength range in which this high diffraction efficiency is obtained as wide as possible. In the case of two or more maxima, the wavelengths at which the two outer maxima are present differ from one another by at least 150 nm, preferably by at least 200 nm.

[0029] In the method for designing an efficient achromatic diffractive structure of the present invention, a series of adjacent sections may form a particularly periodic structure. However, a series of sections with different widths may also be formed in order to provide the diffractive structure with further optical properties. For example, the diffractive structure may be a focusing or defocusing structure with a series of sections with different widths, and thus function as a diffractive lens. However, other forms of the diffractive structure using a series of sections with different widths are also possible, for example, the diffractive structure may be an aberration correction structure using sections with different widths.

[0030] The method according to the invention allows the design of an efficiently achromatized diffractive structure for the manufacture of an efficiently achromatized diffractive optical element according to the invention.

[0031] The present invention further provides a method for manufacturing a diffractive optical element, in which a diffractive structure designed according to the method of the present invention is provided for designing an efficiently achromatic diffractive structure, which is produced by using a doped material and a change in its doping or by using a mixed material and a change in its mixing ratio, the doping or the mixing ratio determining at least the refractive index and the Abbe number of the doped material or the mixed material, the change in the doping or the change in the mixing ratio being performed such that at least the change in the refractive index and the Abbe number resulting from the optimization is realized by the change in the doping or the change in the mixing ratio.

[0032] Thereby, by utilizing doping or material mixing, for example, by printing the diffractive structure using 3D printing and using doped or mixed printing materials with varying doping or mixing ratios during printing, an optical element with the designed diffractive structure can be manufactured. Alternatively, the manufacture of a diffractive optical element can include introducing spatially varying doping into a body of a substrate.

[0033] Further features, properties and advantages of the present invention will become apparent from the following detailed description of the embodiments, taken in conjunction with the accompanying drawings. [Brief description of the drawings]

[0034] [Figure 1] FIG. 2 shows a first exemplary embodiment of a diffractive optical element. [Diagram 2] This is a graph in which the maximum refractive index is 1.7 and the maximum Abbe number is 50, and this can show an appropriate combination of the minimum refractive index and the minimum Abbe number. [Diagram 3] FIG. 2 illustrates the spectral diffraction efficiency as a function of wavelength for various diffractive optical elements. [Figure 4] 4 is a diagram showing combinations of the maximum refractive index, the minimum refractive index, the high Abbe number, and the low Abbe number of the diffractive optical element of FIG. 3. [Diagram 5] FIG. 2 illustrates a second exemplary embodiment of a diffractive optical element. [Figure 6] 1 is a schematic diagram of a lens incorporating a diffractive optical element. [Figure 7] 1 is a flowchart of a manufacturing process of a diffractive optical element. [Figure 8] FIG. 4 illustrates a third exemplary embodiment of a diffractive optical element. [Figure 9] FIG. 1 is a diagram showing the diameter dependence of the refractive index of a cylindrical waveguide. [Figure 10] FIG. 10 is a diagram showing the dependence of the refractive index of the waveguide of FIG. 9 on the surrounding medium. [Figure 11] FIG. 10 illustrates the dependence of the Abbe number of the waveguide of FIG. 9 on the surrounding medium. [Figure 12] FIG. 10 illustrates the dependence of the partial dispersion of the waveguide of FIG. 9 on the surrounding medium. [Figure 13] FIG. 2 shows the polychromatic integral diffraction efficiency of a diffractive structure with a refractive index of TiO2 selected at nmax(λ0) as a function of nd and νd in the visible wavelength range. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0035] A first embodiment of a diffractive optical element according to the invention will now be described with reference to Figs. 1 to 4. Fig. 1 shows a cross section of a diffractive optical element 1 having a diffractive structure 3 consisting of a series of adjacent sections 3A to 3D. The diffractive structure 3 (and thus the optical element 1) has a profile height h of 100 μm or less, in particular 50 μm or less, preferably 20 μm or less. In a direction perpendicular to the profile height, the diffractive structure has a spatial variation of the refractive index, which defines the sections 3A to 3D. In each section 3A to 3D, the refractive index increases continuously from a region 5 indicated by a low dot density to a region 7 indicated by a high dot density. Here, the regions 5 are arranged such that the refractive index is proportional to a specific wavelength λ of the diffractive structure. 0 The minimum refractive index n min (λ 0 ), and region 7 represents a region having a specific wavelength λ 0 Maximum refractive index nmax (λ 0 ) This type of diffraction structure is called a Gradient Index DOE (abbreviated as GRIN-DOE). Such a diffraction grating is a diffraction grating that is used to des (so-called design wavelength), the spectral diffraction efficiency η(λ) can be designed to be theoretically 1 or 100%. des is a specific wavelength λ 0 However, if one wishes to achieve high diffraction efficiency over the entire visible light range and at the same time reduce the profile height of the diffractive structure, then a specific wavelength λ 0 and the design wavelength λ des The agreement between these two makes it easier to design the diffractive structure.

[0036] In this embodiment, a specific wavelength λ 0 Refractive index n(λ 0 ) is a specific wavelength λ present in region 5. 0 The minimum refractive index n min (λ 0 ) from the specific wavelength λ present in region 7 0 Maximum refractive index n max (λ 0 ) at a specific wavelength λ of the diffractive structure 3. 0 The minimum refractive index n min (λ 0 ) and maximum refractive index n max (λ 0 ) is the design wavelength λ des The light with a maximum refractive index of n max (λ 0 ) area, the minimum refractive index is n min (λ 0 ), j is chosen to exhibit a phase shift of j×2π (j representing the diffraction order) compared to transmission through a region of 0.5 mm. In this exemplary embodiment, j=1 is chosen so that the light is deflected into the first diffraction order. However, it is also possible to choose j>1, i.e., a high diffraction order, or j<0, i.e., a negative diffraction order. For negative diffraction orders, the maximum refractive index n max (λ 0) in region 5, with the minimum refractive index n min (λ 0 ) will be in region 7.

[0037] Specific wavelength λ 0 The minimum refractive index n min (λ 0 ) and maximum refractive index n max (λ 0 ) is the maximum refractive index at a particular wavelength, n max (λ 0 ) is the minimum refractive index at a particular wavelength, n min (λ 0 ) by at least 0.005, in particular by at least 0.01, and preferably by at least 0.015. 0 At the same time, the design wavelength λ of the diffractive structure des If , the refractive index difference between the maximum and minimum refractive indices Δn(λ des )=n max (λ des )-n min (λ des ) determines the profile height h of the diffractive structure (in the first diffraction order) by: h=λ des / Δn(λ des ) For the jth diffraction order, the profile height h is, correspondingly, h=jλ des / Δn(λ des ) is given by: Specific wavelength λ 0 is the design wavelength λ of the diffractive structure des To calculate the profile height of a diffractive structure, first determine the refractive index at a given wavelength, n max (λ 0 ) and n min (λ 0 ) at the design wavelength λ des Refractive index n max (λ des ) and n min (λ des ) needs to be converted.

[0038] The particular wavelength λ in this exemplary embodiment 0 is the design wavelength λ of the diffractive structure des and has a value of 587.56 nm, which corresponds to the d line of helium. However, in principle, any given wavelength λ within the wavelength range in which the efficiency achromatization of the diffractive structure occurs can be used. 0 Any wavelength other than λ can be used, for example, the wavelength of the E line of mercury (546.07 nm). In this embodiment, this wavelength range is the visible wavelength range, that is, the wavelength range of 400 to 800 nm, or in a somewhat narrower sense, the wavelength range of 400 to 750 nm. Therefore, the specific wavelength λ 0 The wavelength of 587.56 nm is more or less in the center of the visible wavelength range.

[0039] To achieve efficient achromatism of the diffractive structure 3 in the visible light range, the material has a maximum refractive index n of 1.700 in this exemplary embodiment. max (λ 0 ), and a minimum refractive index n of 1.695 min (λ 0 ), thereby achieving a refractive index difference Δn(λ) of 0.005. 0 )=n max (λ 0 )-n min (λ 0 ) exists. Furthermore, the maximum refractive index n max (λ 0 ) in region 7, the Abbe number ν max is 50, and the low refractive index n min (λ 0 ) in region 5, the Abbe number ν min is 42, so there is an Abbe number difference Δν of value 8. This value is obtained by dividing the combination of values ​​(n max (λ 0 )=1.7000, ν max = 50) is fixed, and n min (λ 0 ) and ν min The value of the refractive index difference Δn(λ 0 ) and the Abbe number difference Δν are optimized to obtain high average diffraction efficiency in the visible light range. max (λ 0 ) and νmax Instead of the value of n min (λ 0 ) and ν min It is also possible to fix the value of the maximum refractive index n max (λ 0 ), minimum refractive index n min (λ 0 ), Abbe number ν max , and Abbe number ν min It is also possible to optimize the values ​​of and not fix any of these values.

[0040] A quantity that may find use to give the height of the diffraction efficiency averaged over a certain spectral range (i.e., a quantity that indicates the degree of efficiency achromatism of a diffractive structure) is the polychromatic integrated diffraction efficiency η PIDE (PIDE:Polychromatic Integral Diffraction Efficiency) PIDE is the spectral diffraction efficiency η(λ) averaged over a particular spectral range (in this embodiment, the visible light range) and is calculated according to the following formula:

number

number

[0041] The wavelength dependence of the refractive index n(λ) can be very well approximated, especially in the visible light region, by the following Cauchy equation using the Abbe number and partial dispersion:

number

number

number

number

[0042] The Abbe number is a dimensionless quantity that represents the dispersion characteristic of an optical material. In this embodiment, the Abbe number is defined as follows:

number

[0043] Partial dispersion refers to the difference in refractive index between two specific wavelengths relative to a reference wavelength interval, and indicates the strength of dispersion in the spectral range between these two wavelengths. The two wavelengths in this embodiment are the wavelength of the G line of mercury (435.83 nm) and the wavelength of the F line of hydrogen (486.13 nm), so the partial dispersion P g,F is given as follows:

number

[0044] The refractive index n of helium at the d-line wavelength is included directly in the coefficients of the Cauchy equation as long as the other wavelengths are within the spectral range for efficient achromatization. d can be replaced by the refractive index at that other wavelength, but the equations for the coefficients a, b, and c must be adapted to the refractive index at that other wavelength.

[0045] Thereby, the above optimization results in the polychromatic integrated diffraction efficiency η PIDEor the polychromatic integrated diffraction efficiency η PIDE In this case, the polychromatic integrated diffraction efficiency η PIDE Partial variance P g,F It has been shown that the effect of the partial dispersion P g,F Polychromatic integrated diffraction efficiency η for a wide range of values ​​of PIDE is Δn(λ 0 ) and Δν optimization, or n max (λ 0 ), n min (λ 0 ), ν max , and v min By optimizing n, it is possible to obtain values ​​of 0.95 or higher. However, in principle, max (λ 0 ), n min (λ 0 ), ν max , and v min The optimal value of Δn(λ 0 ) and νΔ, n max (λ 0 ), n min (λ 0 ), ν max , v min , P g,F,1 , and P g,F,2 It is also possible to determine the optimal value of P g,F,1 n max (λ 0 ) and ν max , is assigned, and P g,F,2 n min (λ 0 ) and ν min Simply, n max (λ 0 ), n min (λ 0 ), ν max and v min , or Δn(λ 0 When P ) and Δν are optimized, the spectral diffraction efficiency η(λ) has two maxima. g,F,1 and P g,F,2 If you optimize both, Pg,F,1 and P g,F,2 As long as the difference between g,F,1 is large enough, P g,F,2 As long as is sufficiently small, three maxima can be obtained for the spectral diffraction efficiency η(λ).

[0046] Figure 2 shows the 0 = the desired maximum refractive index at 587.56 nm, n max (λ 0 ) is 1.700, the maximum Abbe number ν max Polychromatic integrated diffraction efficiency η when is 50 PIDE The minimum refractive index n min (λ 0 ) and the minimum Abbe number ν min The plots in Figure 2 are plotted in grayscale depending on the partial variance P g,F,1 and P g,F,2 was kept constant. The polychromatic integrated diffraction efficiency η PIDE is the curve n min (ν min ) along the line θ = 1. This curve is shown by the dashed line in Fig. 2. Surprisingly, the polychromatic integrated diffraction efficiency η PIDE The maximum value of is close to 1, and furthermore reaches a value of 0.95 or more in the range centered on this curve. min ,n min ) deviates from the curve, the polychromatic integrated diffraction efficiency η PIDE The above value n max (λ 0 )=1.700, n min (λ 0 )=1.695, ν max = 50, ν min At = 42, as can be seen from the plot in Fig. 2, the polychromatic integrated diffraction efficiency η PIDE achieves at least 0.95.

[0047] Refractive index difference Δn(λ 0 When the refractive index difference Δn(λ) is 0.005, the profile height h is 117.5 μm, as in the above embodiment. 0The larger the value of ) the lower the profile height can be achieved. 0 In addition to the combination of Δν and Abbe number difference, polychromatic integrated diffraction efficiency η of 0.95 or more can be achieved. PIDE The refractive index difference Δn(λ 0 ) and the Abbe number difference Δν. For example, the minimum refractive index n min (λ 0 ) is 1.650 instead of 1.695, and the refractive index difference Δn(λ 0 If the value of ) is 0.05 instead of 0.005, the profile height h can be 11.75 μm. In this case, the polychromatic integrated diffraction efficiency η PIDE In order to make the Abbe number ν min should be in the range of about 18 to about 30. The best polychromatic integrated diffraction efficiency η PIDE is the Abbe number ν min At about 25, n min (λ 0 ) = 1.650, i.e., when the Abbe number difference Δν is about 25. Within the above optimization range, a maximum profile height h can be set as a boundary condition to avoid the optimization resulting in undesirably large profile heights. However, Δn(λ 0 ) and Δν optimization, or n max (λ 0 ), n min (λ 0 ), ν max , v min Optimization of, or,n max (λ 0 ), n min (λ 0 ), ν max , v min , P g,F,1 , and P g,F,2 The optimization of the polychromatic integrated diffraction efficiency η PIDE It is also possible to maximize the diffraction efficiency η and minimize the profile height h. PIDE and / or instead of or in addition to the optimization with respect to maximization of the profile height h, the polychromatic integrated diffraction efficiency η PIDEIt is also possible to optimize for reaching a predetermined minimum value and / or for the profile height h to be below a predetermined maximum value.

[0048] An example of the spectral diffraction efficiency η(λ) of an optimized diffractive structure in the visible light range is shown below with the refractive index difference Δn(λ 0 ) and the Abbe number difference Δν are shown in Figs. 3 and 4. 0 In both cases, λ is the wavelength of the helium d line. 0 =587.56 nm.

[0049] Figure 3 shows the spectral diffraction efficiency η(λ) of four types of diffractive optical elements with different diffractive structures. The diffractive optical element labeled DOE1 is a single-layer comparison element that has not been optimized according to the present invention. The diffractive optical elements labeled DOE2 to DOE4 represent examples of diffractive optical elements optimized according to the present invention.

[0050] In the diffractive optical element labeled DOE1 in FIG. 3, the profile height h is 7.70 μm and the design wavelength λ 0 is 553 nm, the refractive index difference Δn(λ 0 ) is 0.08. As can be seen from FIG. 4, the low refractive index is about 1.5, and the high refractive index is just under 1.6. In this case, the Abbe number for the low refractive index is about 60, which is about 10 higher than the Abbe number for the high refractive index (about 50). The spectral diffraction efficiency η(λ) drops off already at small deviations from the design wavelength, and in the visible light range, the polychromatic integrated diffraction efficiency η PIDE It can be seen that it is not possible to make it greater than 0.95.

[0051] In the diffractive optical element DOE2 according to the present invention, the profile height is 4.0 μm, the design wavelength is 503 nm, and the refractive index difference Δn(λ 0 ) is about 0.15, and the minimum refractive index n min (λ 0 ) is just below 1.6, and the maximum refractive index n min (λ 0) is slightly above 1.7. As can be seen from FIG. 4, the Abbe number of the diffractive optical element DOE2 has a value of about 60 in the high refractive index region of the diffractive structure 3, while it has a value of about 10 in the low refractive index region of the diffractive structure 3, so that the Abbe number difference Δν has a value of about 50. As a result, a very high spectral diffraction efficiency η(λ) of almost 1 over the entire visible wavelength range is achieved with a very low profile height of only 4.0 μm, as shown in the progression in FIG. 3. In the spectral diffraction efficiency η(λ) curve shown in FIG. 3, the polychromatic integrated diffraction efficiency η PIDE can also be achieved.

[0052] Similarly, the diffractive optical element DOE3 designed according to the present invention has a profile height of 18.1 μm, a design wavelength of 445 nm, and a refractive index difference of about 0.03, with a maximum refractive index of just over 1.6 and a minimum refractive index of just under 1.6. In the high refractive index regions of the diffractive structure 3, the diffractive optical element DOE3 has an Abbe number of about 50, and in the low refractive index regions of the diffractive structure 3, the Abbe number has a value of about 25. The Abbe number difference Δν of the diffractive optical element DOE3 is therefore about 25. The diffractive structure 3 of the diffractive optical element DOE3 has a refractive index difference Δn(λ 0 ) and the Abbe number difference Δν, the diffractive optical element DOE3 does not exhibit a spectral diffraction efficiency η(λ) as uniform as that of the diffractive optical element DOE2. However, the spectral diffraction efficiency η(λ) is still 0.97 or more over almost the entire visible light range. Therefore, the diffractive optical element DOE3 has a high polychromatic integrated diffraction efficiency η of 0.95 or more. PIDE has.

[0053] The fourth diffractive optical element DOE4 shown in FIG. 3 has a profile height of 32.6 μm, a design wavelength of 437 nm, and a refractive index difference Δn(λ 0) is about 0.015, with the low refractive index being around 1.56 and the high refractive index being around 1.58. The Abbe number of the high refractive index region 7 of the diffractive structure 3 has a value of about 55, and the Abbe number of the low refractive index region 5 of the diffractive structure 3 has a value of about 35, so that the Abbe number difference of the diffractive optical element DOE4 has a value of about 20. The spectral diffraction efficiency η(λ) of the diffractive optical element DOE4 shows a more irregular progression than that of the diffractive optical element DOE3, but this diffractive optical element also has a spectral diffraction efficiency η(λ) of 0.97 or more in most of the visible light range. Therefore, the diffractive optical element DOE3 also has a high polychromatic integrated diffraction efficiency η of 0.95 or more. PIDE has.

[0054] A comparison of the spectral diffraction efficiency η(λ) of the conventional diffractive optical element DOE1 with the spectral diffraction efficiency η(λ) of the diffractive optical elements DOE2 to DOE4 according to the present invention shows that the optimization of the diffractive optical element according to the present invention can increase the spectral diffraction efficiency η(λ) over the entire visible light range and can also make it very uniform compared to the diffractive optical element DOE1. This is realized in the example of DOE2 to DOE4 by having multiple maximum values ​​of the spectral diffraction efficiency η(λ) compared to the conventional diffractive optical element DOE1. The diffractive optical element DOE2 has three maximum values ​​of the spectral diffraction efficiency η(λ), located at about 725 nm and about 400 nm in addition to 486.13 nm. The diffractive optical element DOE3 has two maximum values ​​of the spectral diffraction efficiency η(λ), located at 656.27 nm and about 445 nm. The diffractive optical element DOE4 also has two maximum values ​​of the spectral diffraction efficiency η(λ), located at 643.45 nm and about 437 nm. Between the minima, the spectral diffraction efficiency η(λ) decreases, the decrease being smaller the larger the refractive index difference, which leads to a smaller profile height h of the diffractive structures 3 of the diffractive optical element.

[0055] As can be seen from the examples of DOE2 to DOE4, the larger the refractive index difference, the larger the Abbe number difference should be selected. A large refractive index difference Δn(λ0 The combination of the refractive index difference and Abbe number difference of the diffractive optical elements DOE2 to DOE4 is advantageous in that it has a polychromatic integrated diffraction efficiency η PIDE is in a narrow range centered on the line where it is maximum.

[0056] A second exemplary embodiment of a diffractive optical element 10 according to the invention is shown in Fig. 5. Whereas in the diffractive optical element 1 of Fig. 1 a periodic diffractive structure 3 with a constant width in its cross sections 3A-3D is realized by a change in refractive index, the diffractive structure 13 in the diffractive optical element 10 of the second exemplary embodiment has a change such that two horizontally mirrored diffractive structures 13, 13' adjoin at the centre of the diffractive structure 13. As the distance from the centre of the diffractive structure 13 increases the refractive index approaches a minimum refractive index n min (λ 0 ) to the maximum refractive index n max (λ 0 ) the lateral dimensions of the sections 13A-13D and 13A'-13D', respectively, which vary from 0.1 to 0.1 mm, are reduced. This makes it possible for the diffractive optical element 10 to be formed, for example, as a diffractive lens. The way in which the lateral dimensions decrease with increasing distance from the centre of the diffractive structure 13 then depends in particular on which focal position is to be realised.

[0057] As in the first exemplary embodiment, the design wavelength λ of the diffractive structure 13 des The minimum refractive index n min (λ 0 ) and maximum refractive index n max (λ 0 ) is selected as follows: des The light with a maximum refractive index of n max (λ 0 ) when transmitted through a region with a minimum refractive index n min (λ 0 ) is selected to produce a phase shift of j×2π (j represents the diffraction order) relative to the time when the light is transmitted through a region having a maximum refractive index n max (λ 0) from areas 7D and 7D' to the minimum refractive index n min (λ 0 This means that the refractive index transition up to areas 5D, 5D' must be steeper than, for example, the wider sections 13B, 13B'.

[0058] A diffractive optical element 10 as shown in FIG. 5 can be incorporated, for example, into a lens 15 as shown diagrammatically in FIG. 6, thereby creating a focus based on diffraction by the diffractive optical element 10 in addition to the focus based on refraction by the lens 15. This is interesting, for example, in the case of intraocular lenses, since such lenses allow intraocular lenses with multiple foci to be created, allowing the wearer of the intraocular lens to see clearly at different distances with the same lens. Furthermore, refraction and diffraction have different wavelength dependencies. Therefore, a diffractive optical element can be made such that its wavelength dependency complements the refraction wavelength dependency of the lens, thereby correcting the color shift of the lens.

[0059] A third exemplary embodiment of a diffractive optical element 100 according to the present invention is shown in Figure 8. Unlike the diffractive optical elements of the first and second exemplary embodiments, the refractive index in sections 103A, 103B, 103C, 103D of the diffractive structure 113 is des At the minimum refractive index n min (λ 0 ) to the maximum refractive index n max (λ 0 Instead, each of the sections 103A, 103B, 103C, and 103D has a first refractive index n a (λ 0 ) and a plurality of first regions 115 of a first material A having a second refractive index n b (λ 0 ) and a plurality of second regions 117 of a second material B, the first regions 115 being interchangeable with the second regions 117 within the section. b (λ 0 ) is the first refractive index n a (λ 0) The maximum width of the individual regions 115, 117 of the diffractive structure, of which the sections 103A, 103B, 103C, 103D follow one another, at least in the extension direction, is smaller than the central wavelength of the wavelength range in which the diffractive structure is efficiently achromatized. Such structures form so-called metasurfaces.

[0060] In this exemplary embodiment, the wavelength range in which the efficient achromatization of the diffractive structure is performed is the visible wavelength range, i.e., the wavelength range from 400 to 800 nm, or more narrowly, the wavelength range from 400 to 750 nm, and the maximum width B max is 100 nm. Therefore, the maximum width B max is smaller than 0.3 times the central wavelength of the visible wavelength range and smaller than 0.3 times the minimum wavelength of the visible wavelength range. max is realized for the regions 115 of the ends 105A, 105B, 105C, and 105D of the sections 103A, 103B, 103C, and 103D, respectively. On the other hand, the maximum width B max is realized for the regions 117 of the ends 107A, 107B, 107C, 107D of the sections 103A, 103B, 103C, 103D, respectively. max is smaller than the central wavelength, the volume element having an edge length corresponding to the wavelength (an edge length of 400 to 800 nm in this embodiment) in the sections 103A, 103B, 103C, and 103D has an effective refractive index n eff (λ 0 ), with an effective refractive index n eff (λ 0 ) is the refractive index n of the first region 115 a (λ 0 ) and the refractive index n b (λ 0 ) and the volume ratio of the first and second regions 115, 117 within such a volume element. Then, the effective refractive index n eff (λ 0) can be used to provide the phase shift required for diffraction. eff (λ 0 The variation of the minimum effective refractive index n at ends 105A, 105B, 105C, 105D can be achieved by varying the width of first region 115 and / or second region 117 as a function of position within sections 103A-103D, and thereby varying the volume fraction of first material A and second material B. eff,min (λ 0 ) and the maximum effective refractive index n eff,max (λ 0 ) between the effective refractive index n eff (λ 0 ) can be varied as a function of position within each section 103A, 103B, 103C, 103D. For efficient achromatism, the minimum effective refractive index n eff,min (λ 0 ) and the maximum effective refractive index n eff,max (λ 0 ) is optimized based on the minimum refractive index n min (λ 0 ) and maximum refractive index n max (λ 0 ) The realization of a defined refractive index can be achieved in the metasurface by appropriate selection of the first material A and the second material B and / or by appropriate dimensions of the first region 115 and the second region 117.

[0061] In a variation of the third exemplary embodiment, the maximum width Bmax of the regions 115, 117 is equal to or greater than 0.3 times the central wavelength of the wavelength range between 400 nm and 800 nm. Instead, the maximum width Bmax of the high refractive index region is at least max , i.e., in this exemplary embodiment, the refractive index n b The maximum width of the second region 117 having a maximum width B is between 0.3 and 1.0 times the central wavelength of the wavelength range in which the diffractive structure is efficiently achromatized.max The second region 117 functions like a waveguide when the refractive index reaches n , which can reduce the shadowing effect compared to a gradient index DOE. This is particularly effective when the angle of incidence is large or the cross-sectional width is small, as described, for example, in P. Lalanne, "Waveguiding in brazed-binary diffractive elements," in J. Opt. Soc. Am. A16 (1999). The refractive index n of the second region 117 forming the waveguide b depends on both the geometry of the region 117 having the higher refractive index and the refractive index of the surrounding medium, and in this exemplary embodiment, therefore, the refractive index n a The same applies to the Abbe number and the partial dispersion.

[0062] Figure 9 shows the structure of titanium oxide (TiO 2 The wavelength dependence of the refractive index of a large host consisting of titanium dioxide (TiO) with diameters ranging from 100 nm to 1000 nm was investigated. 2 The figure shows that as the waveguide diameter decreases, the wavelength-dependent refractive index deviates more and more from that of a larger host of titanium dioxide. wav It is evident from the figure that the refractive index, Abbe number and partial dispersion in 0.1000 nm are clearly dependent on the surrounding material.

[0063] Figures 10, 11, and 12 show the results of the measurements of titanium dioxide (TiO 2 The dependence of the refractive index (Fig. 10), Abbe number (Fig. 11), and partial dispersion (Fig. 12) of the fundamental mode of a cylindrical waveguide consisting of a waveguide with a diameter D wav The material surrounding the waveguide is shown as a function of . The material surrounding the waveguide is selectively air, water (with a refractive index n d :1.33, Abbe number ν d :55.8, partial variance P g,F:0.51), and glass material N-SF11 (refractive index n d :1.78, Abbe number ν d :25.8, partial variance P g,F For comparison, the figure also shows the surface area of ​​titanium dioxide (TiO 2 The refractive index of the large matrix consisting of .

[0064] Figure 13 shows TiO 2 The refractive index of n max (λ 0 Polychromatic integrated diffraction efficiency η of the selected diffractive structure PIDE , n d and ν d The solid line in Fig. 13 shows the TiO 2 In a cylindrical waveguide of diameter D wav n resulting from the change between 0 and 2500 nm d and ν d The figure shows a combination of TiO surrounded by air. 2 In the cylindrical waveguide, the polychromatic integrated diffraction efficiency η PIDE This shows that it is not possible to make the eigenvalue greater than 0.95.

[0065] The dotted line represents TiO surrounded by water. 2 In a cylindrical waveguide consisting of wav n resulting from the change between 0 and 2500 nm d and ν d The combination of n d = 1.5, ν d In the range of η = 1.5, the polychromatic integrated diffraction efficiency is very high. PIDE It can be recognized that n d =1.5 and ν d The value of =1.5 is based on the diameter D of the cylindrical waveguide, as can be seen in Figs. 10 and 11. wavcan be achieved at about 80 nm. This diameter corresponds to about 0.13 times 600 nm (0.13 times the central wavelength of the visible wavelength range) and about 0.2 times 400 nm (0.2 times the minimum wavelength of the visible wavelength range). In the case of a combination of titanium dioxide and water, n d and ν d By optimizing the effective minimum refractive index n eff,min (λ 0 ) is obtained, but the waveguide effect does not occur.

[0066] The dashed line indicates TiO surrounded by N-SF11. 2 In a cylindrical waveguide consisting of wav n resulting from the change between 0 and 2500 nm d and ν d The combination of n d = 2, ν d Very high polychromatic integrated diffraction efficiency in the range of η = 4.2 PIDE As can be seen from Figs. 10 and 11, n d =2 and ν d The value of =4.2 is the diameter D of the cylindrical waveguide. wav can be achieved at about 280 nm, which corresponds to about 0.7 times 400 nm, about 0.46 times 600 nm, and about 0.35 times 800 nm, which is about 0.7 times the minimum wavelength, about 0.46 times the mid-wavelength, and about 0.35 times the maximum wavelength in the visible wavelength range. This case corresponds to the modified third exemplary embodiment, i.e., a metasurface with a waveguide effect.

[0067] n eff,min (λ 0 ) and n eff,max (λ 0 ) can be achieved through different approaches. First, the material surrounding each waveguide can be adjusted. Second, the material of the waveguide itself can be adjusted. Finally, the shape of the waveguide can also be optimized, however this requires the use of shapes more complex than a cylinder.

[0068] The manufacture of an efficiently achromated diffractive optical element according to the invention will now be described with reference to FIG. 7. The figure shows a flow chart of the manufacturing process, which in this embodiment includes a method for designing the diffractive structures of the diffractive optical element by steps S1 and S2. Among the steps of the method for manufacturing an efficiently achromated diffractive optical element according to the invention, the steps related to the design of the diffractive structures are enclosed by dashed lines in FIG. 7. Thus, in this exemplary embodiment, the actual manufacture of the diffractive optical element is preceded by the method for designing the diffractive structures. However, it is also possible to separate the manufacture of the diffractive optical element from the design of the diffractive structures, for example, if a catalog of diffractive structures is designed in advance and diffractive structures are selected from it for the manufacture of the diffractive optical element.

[0069] In this embodiment, the manufacturing process of the diffractive optical element starts with the first step S1 of designing a diffractive optical structure. In step S1, the polychromatic integrated diffraction efficiency η to be achieved for all wavelengths in a spectral range of at least 300 nm or more, preferably 350 nm or more, is calculated. PIDE_Ziel The polychromatic integrated diffraction efficiency η PIDE_Ziel Typically has a value of at least 0.95. Optionally, the maximum profile height h max can also be set in step S1.

[0070] The value of polychromatic integrated diffraction efficiency η to be achieved in step S1 PIDE_Ziel After being set, in step S2 of the exemplary embodiment, the polychromatic integrated diffraction efficiency η PIDE To optimize n max (λ 0 ), n min (λ 0 ), ν max , v min , P g,F,1 , and P g,F,2 The value of the error function Δη PIDE = η PIDE_Ziel -η PIDE changes until the termination condition is satisfied. PIDE is the integral of

number

[0071] n max (λ 0 ), n min (λ 0 ), ν max , v min , P g,F,1 , and P g,F,2 The value of n enters, in the optimization framework, into the refractive index n(λ) via the Cauchy equation, and thereby into the spectral diffraction efficiency η(λ) integrated via the Cauchy equation. max (λ 0 ), n min (λ 0 ), ν max , v min , P g,F,1 , and P g,F,2 Constraints on the value of θ are given by the available materials. These constraints can optionally be included in the optimization as boundary conditions.

[0072] n max (λ 0 ), n min (λ 0 ), ν max , v min , P g,F,1 , and P g,F,2Instead of optimizing P, it is also possible to give fixed values ​​to one or two of these quantities and optimize only the remaining free quantities. g,F,1 and P g,F,2 can be given a fixed value because ηP IDE is n max (λ 0 ), n min (λ 0 ), ν max , and v min Compared to P g,F,1 and P g,F,2 This is because there is less reliance on g,F,1 >P g,F,2 However, it is advantageous when P g,F,1 =P g,F,2 In the case of P g,F,1 <P g,F,2 In the latter case, P g,F,1 and P g,F,2 The present invention can be realized so long as the difference between them is not too large.

[0073] Furthermore, the highest possible diffraction efficiency η averaged over the spectral range PIDE The optimization can be performed not only with respect to the error function Δη but also with respect to the lowest possible profile height h. PIDE =1-η PIDE or the error function Δη PIDE = η PIDE_Ziel -η PIDE In addition to minimizing the profile height h, the profile height h is also minimized. Also, instead of minimizing the profile height h, in step S1, the maximum value of the profile height h max Also, set h≦h max It is also possible to perform optimization under the boundary condition that the following equation is satisfied.

[0074] After the design of the diffractive structure is completed in step S2, in step S3, a predetermined wavelength λ determined in the optimization is 0 Maximum refractive index n max (λ 0 ) and the Abbe number ν determined during optimization maxand a first material having a predetermined wavelength λ determined in the optimization. 0 The minimum refractive index n min (λ 0 ) and the Abbe number ν determined by optimization min and P, which is fixed or determined during optimization. g,F,1 and P g,F,2 and a second material is selected having a value of n max (λ 0 ), ν max , and P g,F,1 The corresponding values ​​of min (λ 0 ), ν min , and P g,F,2 Materials with corresponding values ​​of θ can be provided, for example, as composites of materials with embedded nanoparticles. As materials with embedded nanoparticles, in particular polymers come into consideration, such as polymethylmethacrylate (abbreviated PMMA) or polycarbonate (abbreviated PC). The nanoparticles can be, for example, indium tin oxide (ITO), zirconium dioxide (ZrO 2 ), titanium dioxide (TiO 2 ) or from diamond.

[0075] In step S4, a diffractive optical element having the designed diffractive structure is manufactured by 3D printing. The selected materials are fed into the 3D printer in a mixture ratio that changes with time. At that time, the time change in the mixture ratio is a maximum refractive index n max (λ 0 ), Abbe number ν max , partial variance P g,F,1 (see Fig. 1 and Fig. 5) The area 7 of the diffractive structure is printed only with the first material and has a minimum refractive index n min (λ 0 ), Abbe number ν min and partial variance P g,F,2The region 5 of the diffractive structure which should have a first material is printed only with the second material. The region of a series of adjacent sections 3A-3D lying between these regions 5,7 is printed such that the mixture ratio of the first material to the second material varies continuously from 100% first material to 100% second material. When using a printer with several printing nozzles, the mixture ratio which changes over time can be replaced by supplying different mixture ratios to different printing nozzles.

[0076] Alternatively, it is also possible to manufacture the diffractive structure 2 of the diffractive optical element 1 using a single material fed to the printer instead of a varying mixture of materials, which is doped with nanoparticles during printing. The doping of this material then leads to a maximum refractive index n max (λ 0 ), Abbe number ν max , and the partial partial variance P g,F,1 (see FIGS. 1 and 5), those regions 7 of the diffractive structure have a first doping and a minimum refractive index n min (λ 0 ), Abbe number ν min and partial partial variance P g,F,2 The doping of the substrate is then performed such that within each section 3Ab-3D of the diffractive structure 3 the doping changes continuously from the first doping value to the second doping value. The first doping and the second doping can represent a maximum doping and a minimum doping with the same doping material, or two dopings with different doping materials.

[0077] As a further alternative, a substrate body can first be provided, for example by means of 3D printing, and then the substrate can be provided with a spatially varying doping, such that within each section 3Ab-3D of the diffractive structure 3 the spatial variation of the doping is formed such that the doping changes continuously from a first doping value to a second doping value.

[0078] The present invention has been described in detail with reference to exemplary embodiments for illustrative purposes. However, those skilled in the art will recognize that deviations from the exemplary embodiments may be made within the scope of the present invention to realize further embodiments. For example, the polychromatic integrated diffraction efficiency used in the exemplary embodiments can be replaced by another diffraction efficiency averaged over a spectral range, as long as the diffraction efficiency averaged over a spectral range is a suitable measure of the degree of efficiency achromatism achieved. Furthermore, other polymeric or nanoparticle materials than those mentioned in the exemplary embodiments are in principle conceivable as materials in which nanoparticles are embedded. The present invention is therefore not intended to be limited by the described exemplary embodiments, but only by the appended claims.

Claims

1. A diffractive optical element (1;10;100) made of a material having a spatial variation in refractive index, the spatial variation of the refractive index forms a series of adjacent sections (3A-3D; 13A-13D, 13'A-13';, 103A-103D) within which the refractive index varies respectively, the series of adjacent sections forming a diffractive structure (3; 13; 113), A diffractive optical element, wherein the diffractive structure (3; 13; 113) has a polychromatic integrated diffraction efficiency of at least 0.95 in a spectral range extending at least over 300 nm, A diffraction efficiency value of at least 0.95, averaged over a spectral range of at least 300 nm, is present at at least one maximum refractive index n ｍａｘ and one minimum refractive index n ｍｉｎ , and at least one high Abbe number v ｍａｘ and one low Abbe number ν ｍｉｎ in each section (3A-3D; 13A-13D, 13'A-13'D; 103A-103D) of the series of adjacent sections, by a single single-layer diffractive structure (3; 13; 113) having a combination of The high Abbe number ν max is in the region having the maximum refractive index n max (7A to 7D, 107A to 107D), and the low Abbe number ν min is in the region having the minimum refractive index n min (5A to 5D, 105A to 105D), The maximum refractive index n ｍａｘ and the minimum refractive index n ｍｉｎ The refractive index difference Δn between is in the range of 0.005 to 0.15, The high Abbe number ν ｍａｘ and the low Abbe number ν ｍｉｎ and the Abbe number difference Δν between them is in the range of 8 to 50 (1; 10; 100).

2. A value of diffraction efficiency of at least 0.95 averaged over a spectral range of at least 300 nm is at least one maximum refractive index n at a specific wavelength in the spectral range of at least 300 nm ｍａｘ and one minimum refractive index n at a specific wavelength in the spectral range of at least 300 nm ｍｉｎ and one high Abbe number ν ｍａｘ and one low Abbe number ν ｍｉｎ and is realized within each section (3A to 3D; 13A to 13D, 13'A to 13'D; 103A to 103D) of the series of adjacent sections by a single monolayer diffraction structure (3; 13; 113) having a combination consisting of, the diffractive optical element (1; 10; 100) according to claim 1, characterized in that.

3. At least one maximum refractive index n at a particular wavelength in a spectral range of at least 300 nm ｍａｘ and the minimum refractive index n ｍｉｎ and the high Abbe number v ｍａｘ and the low Abbe number v ｍｉｎ 3. A diffractive optical element (1; 10; 100) according to claim 2, characterized in that in addition to the combination of:

4. 4. A diffractive optical element (1) according to any one of claims 1 to 3, characterized in that the series of adjacent sections (13A to 13D, 13'A to 13'D) form a diffractive structure (13) varying in lateral dimensions of the sections (13A to 13D, 13'A to 13'D), which diffractive structure provides a defined and varying diffraction angle depending on the position on the diffractive structure (13).

5. 5. A diffractive optical element (1; 10) according to claim 1 , characterized in that the diffractive structure (3; 13) consists of a doped material and the spatial variation of the refractive index is due to a variation of the doped material.

6. 5. A diffractive optical element (1; 10) according to claim 1 , characterized in that the diffractive structure (3; 13) consists of a mixture of at least two materials having different refractive indices, the spatial variation of the refractive index resulting from a change in the mixture ratio of the materials in which the mixture is mixed.

7. said diffractive structure (113) is constituted by alternating first regions (115) of a first material (A) having a first refractive index and second regions (117) of a second material (B) having a second refractive index higher than the first refractive index, - said first and second regions (115, 117) are alternately arranged within a section (103A-103D) of said series of adjacent sections (103A-103D), respectively, and the width of said second regions (117) increases relative to the width of the first regions (115) within said section from one end of the section to the other end of the section, respectively; A diffractive optical element (100) according to any one of claims 1 to 4, characterized in that the maximum width of the first regions (115) and the second regions (117) is always smaller than the central wavelength of a spectral range extending at least over 300 nm.

8. 8. A diffractive optical element (100) according to claim 7, characterized in that the maximum width of the first region (115) and the second region (117) is always smaller than 0.3 times the central wavelength of a spectral range extending at least over 300 nm.

9. 8. The diffractive optical element (100) of claim 7, characterized in that the maximum width of at least the second region (117) is at least 0.3 times the central wavelength of the spectral range spanning at least 300 nm and at most 1.0 times the central wavelength of the spectral range spanning at least 300 nm.

10. 10. A diffractive optical element (1; 10) according to any one of the preceding claims, characterized in that in the spectral range extending at least over 300 nm there are at least two maxima of the spectral diffraction efficiency.

11. 11. A diffractive optical element (1; 10) according to claim 10, characterized in that if there are at least two maxima, the wavelengths at which the two outermost maxima are present differ from each other by at least 150 nm.

12. 12. A refractive or reflective optical element (15) comprising a diffractive optical element (10) according to any one of claims 1 to 11.

13. A method for designing an efficiently achromatic diffractive structure (3; 13) having a spatial variation of the refractive index, the spatial variation of the refractive index forming a series of adjacent sections (3A to 3D; 13A to 13D, 13'A to 13'D), the refractive indexes in the sections (3A to 3D; 13A to 13D, 13'A to 13'D) each having a maximum refractive index n ｍａｘ and the minimum refractive index n ｍｉｎ and - defining a spectral range that extends over at least 300 nm and a diffraction efficiency that is to be achieved on average over said spectral range of at least 300 nm, at least said maximum refractive index n ｍａｘ and the minimum refractive index n ｍｉｎ , and the maximum refractive index n ｍａｘ The high Abbe number ν ｍａｘ and the minimum refractive index n ｍｉｎ Low Abbe number v ｍｉｎ so as to obtain the diffraction efficiency to be achieved on average in the set spectral range of at least 300 nm; the refractive index difference Δn between the maximum refractive index n max and the minimum refractive index n min is in the range of 0.005 to 0.15; A method according to claim 1, wherein the Abbe number difference Δν between said high Abbe number v max and said low Abbe number v min is in the range of 8 to 50.

14. The maximum refractive index n ｍａｘ , the minimum refractive index n ｍｉｎ , the high Abbe number ν ｍａｘ and the low Abbe number v ｍｉｎ In addition, the maximum refractive index n ｍａｘ and the first partial dispersion associated with the minimum refractive index n ｍｉｎ and a second partial dispersion associated with said first partial dispersion, said first partial dispersion associated with said second ... and said second partial dispersion associated with said second partial dispersion, associated with said first partial dispersion, are optimized so as to achieve said set diffraction efficiency, averaged over a spectral range of at least 300 nm.

15. The maximum refractive index n ｍａｘ , the minimum refractive index n ｍｉｎ , the high Abbe number ν ｍａｘ and the low Abbe number v ｍｉｎ 15. The method according to claim 13 or 14, characterized in that the optimization of the profile height h is performed in such a way that the profile height h is minimized or at least does not exceed a predefined maximum value.

16. The maximum refractive index n ｍａｘ , the minimum refractive index n ｍｉｎ , the high Abbe number ν ｍａｘ and the low Abbe number v ｍｉｎ and the optimization of the first partial dispersion and the second partial dispersion is performed such that the profile height h is minimized or at least does not exceed a predetermined maximum value.

17. The maximum refractive index n ｍａｘ , the minimum refractive index n ｍｉｎ , the high Abbe number ν ｍａｘ and the low Abbe number v ｍｉｎ 17. A method according to claim 13, characterized in that the optimization of is performed such that there are at least two maxima of the spectral diffraction efficiency.

18. The maximum refractive index n ｍａｘ , the minimum refractive index n ｍｉｎ , the high Abbe number ν ｍａｘ and the low Abbe number v ｍｉｎ 15. The method according to claim 14, characterized in that the optimization of the first partial dispersion and the second partial dispersion is performed such that there are at least two maxima of the spectral diffraction efficiency.

19. The maximum refractive index n ｍａｘ , the minimum refractive index n ｍｉｎ , the high Abbe number ν ｍａｘ and the low Abbe number v ｍｉｎ 19. The method according to claim 17 or 18, characterized in that the optimization of (a) is performed such that the at least two maxima are at least 150 nm apart from each other.

20. The maximum refractive index n ｍａｘ , the minimum refractive index n ｍｉｎ , the high Abbe number ν ｍａｘ and the low Abbe number v ｍｉｎ and optimizing the first partial distribution P １ 15. The method according to claim 14, characterized in that the optimization of the second partial dispersion is performed such that the at least two maxima are at least 150 nm apart from each other.

21. A method for producing an efficiently achromatized diffractive optical element (1;10), comprising the steps of: Providing a diffractive structure (3; 13) designed according to any one of claims 13 to 20, said diffractive structure (3; 13) being produced by the use of doped materials and varying said doped materials or by the use of mixed materials and varying their mixing ratios, the doping or the mixture ratio determines at least the refractive index and the Abbe number of the doped or mixed material, 4. A method according to claim 3, characterized in that the change in doping or the change in the mixing ratio is carried out in such a way that at least the change in the refractive index and the Abbe number resulting from the optimization is realized by the change in doping or the change in the mixing ratio.

22. 22. The method according to claim 21, characterized in that the manufacturing of the diffractive optical element (1; 10) comprises printing the diffractive structure (3; 13) using 3D printing and using doped or mixed printing materials, the doping or mixing ratio of which is changed during printing.

23. 22. The method according to claim 21, characterized in that the manufacturing of the diffractive optical element (1; 10) comprises manufacturing the diffractive structure (3; 13) by introducing a spatially varying doping into a body of a substrate.

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