Waveguide and method for manufacturing waveguide

Abstract

To provide a waveguide that guarantees an improvement in the uniformity on a cross section, especially, the sharpness of an image, an image guide, and a method for manufacturing the same.SOLUTION: Provided is a waveguide 1 for transmitting electromagnetic waves, especially image information, from a proximal end 2 of the waveguide to a distal end 4 of the waveguide, along a transmission direction 5 extending between the proximal end and the distal end, on a cross section extending in the lateral direction relative to the transmission direction. The waveguide includes a plurality of structure elements 10, which include at least two types of structure elements: the structure element of a first type 10a having a first refractive index and the structure element of a second type 10b having a second refractive index. The structure elements extend along the transmission direction and spread according to a ratio on the cross section of the waveguide. A plurality of cross-sectional areas 20 are defined on the cross section of the waveguide. The cross-sectional areas correspond to cross sections of individual structure elements. The structure elements, especially their cross-sectional areas are formed to be non-uniform but as determined clearly by predetermined rules.SELECTED DRAWING: Figure 2

Description

[Technical Field]

[0001] The present invention relates to a waveguide for transmitting electromagnetic waves, in particular for transmitting image information, and to a method for manufacturing a waveguide, in particular an image guide.

[0002] An image guide typically consists of multiple individual optical waveguides, each consisting of a core and a cladding surrounding the core. The optical waveguides are arranged in a bundle, and in cross section, the light entrance and exit surfaces are arranged one-to-one in a grid pattern to form multiple pixels. Essentially, each pixel is responsible for transmitting brightness and color information through the image guide.

[0003] In practice, it is often desirable to maximize the resolution of an image guide. In principle, this can be achieved by reducing the diameter of each individual optical waveguide. However, as the diameter of each individual optical waveguide becomes smaller, the electric field distribution of the transmission mode exceeds the dimensions of the optical waveguide, especially the cladding, to an increasing extent, resulting in increased crosstalk between adjacent optical waveguides and increased blurring. This makes it impossible to arbitrarily increase the resolution according to the laws of physics.

[0004] One approach to providing image guides with higher resolution is based on the wave phenomenon of transverse Anderson localization (TAL). This exploits the fact that the random distribution of refractive index in the cross section of the image guide, combined with the invariance of the refractive index along the length of the image guide, results in a cross-sectional restriction of the coupled light due to destructive interference. In practice, for example, multiple individual glass fibers with different refractive indices can be combined to form a random fiber bundle. When a light beam is coupled into such a waveguide, the light beam propagates along the length of the image guide with limited lateral extent in the cross section.

[0005] While image guides based on the Anderson localization principle in the lateral direction enable high resolution, they have the disadvantage that the image quality of the transmitted image information, especially the image sharpness, varies locally or is difficult to control due to the random distribution of refractive index. For example, the image sharpness of a certain part of the cross section may differ from the image sharpness of another part of the cross section.

[0006] These non-uniformities make it difficult to manufacture image guides to consistent quality standards in practice. Depending on the quality standards applied in manufacturing, a high degree of defects may occur. This problem becomes even more severe when the cross-sectional size of the image guide is increased. In particular, the side length and cross-sectional diameter of the faceplate can be several times the thickness of the faceplate.

[0007] A faceplate is typically a pair of spliced ​​optical fibers, often relatively short (a few mm), or an optical structural element (a few mm) whose axis is perpendicular to the plate surface. 2 or a few centimeters 2 ) whose central property is the ability to transmit images from one plate surface to the other in a strict discipline, i.e., 1:1, identical manner, or in a regularly varied, e.g., rotated, manner.

[0008] It is therefore an object of the present invention to provide a waveguide, in particular an image guide, and a method for producing the same, which ensures uniformity in the cross section of the waveguide, in particular an improvement in image sharpness. One aspect of the object of the present invention is to make the uniformity in the cross section better controllable, and particularly preferably even reproducible, in order to, for example, avoid defects in production and ensure that quality standards can be guaranteed.

[0009] One aspect of the problem of the present invention is to be able to provide a waveguide, in particular an image guide, which has a large cross-sectional area and at the same time complies with the above-mentioned conditions, in particular with a given uniformity. This relates in particular to waveguides formed as faceplates.

[0010] To solve this problem, the present invention discloses a waveguide for transmitting electromagnetic waves, particularly image information, from a proximal end of the waveguide to a distal end of the waveguide along a transmission direction extending between the proximal and distal ends, with a cross section extending transverse to the transmission direction, the waveguide comprising a plurality of structural elements.

[0011] At least two types of structural elements are included: a first type having a first refractive index and a second type having a second refractive index. Thus, the included plurality of structural elements can include at least one structural element of the first type and one or more structural elements of the second type, or conversely, one or more structural elements of the first type and one structural element of the second type, or both multiple structural elements of the first type and multiple structural elements of the second type. Of course, more than two types of structural elements, for example, three types, can also be included.

[0012] The structural elements each extend along the transmission direction and span the cross section of the waveguide proportionally, defining a number of cross-sectional areas in the cross section of the waveguide, each of which corresponds to the cross section of an individual structural element. The structural elements thus extend next to one another, in particular parallel to one another, along the transmission direction of the waveguide, and their cross sections each occupy a partial surface of the cross section of the waveguide and thus each define a cross-sectional area of ​​the cross section of the waveguide. The cross-sectional areas therefore correspond in particular to the surface areas formed by the structural elements when looking at the cross section of the waveguide, for example at the light entrance or light exit face.

[0013] According to the present invention, the structural elements, in particular their cross-sectional areas, are formed non-uniformly but in a clearly defined, predetermined order. The structural elements thus exhibit non-uniformity with respect to one another, i.e., are non-uniformly formed relative to one another, e.g., are non-uniformly arranged, have non-uniform shapes, and / or are non-uniformly configured. Here, the non-uniformity resides not in the individual structural elements themselves but in the aggregate of the structural elements, and thus, in particular, a physical disorder, i.e., a deviation from symmetry, is present. On the other hand, non-uniformly formed structural elements are formed in a defined, predetermined order, i.e., not randomly formed. The non-uniformity or disorder of the structural elements relative to one another is thus the opposite of regularity, in the sense that the non-uniformity or disorder is not random but follows a defined order. Thus, the non-uniformity or disorder is specifically predetermined or pre-given, or is or can be characterized by a rule.

[0014] Non-uniformity of a structural element, particularly of its cross-sectional area, can manifest itself in a variety of ways.

[0015] For example, the cross-sectional areas of the structural elements can have a non-uniform, in particular aperiodic, distribution that is clearly defined according to a predetermined rule, for example, the cross-sectional areas can be arranged differently from a periodic grid, but the cross-sectional areas can also be distributed non-uniformly on the periodic grid, for example.

[0016] Alternatively or additionally, the cross-sectional areas of the structural elements can have mutually non-uniform, in particular mutually different, geometric shapes, for example non-uniform diameters, that are clearly defined according to a predetermined rule, but the geometric shapes of the cross-sectional areas can also be formed in the same way, but rotated relative to one another, in particular in the case of cross-sectional areas with non-circular shapes.

[0017] Furthermore, the structural elements may alternatively or additionally have mutually non-uniform, in particular mutually different, refractive indices that are clearly defined in a predetermined manner.

[0018] In particular, due to the physical effect of transverse Anderson localization, the inhomogeneity of the structural elements can achieve, in particular, the amplitude restriction of the transmitted electromagnetic wave to a partial region of the cross section of the waveguide. Therefore, the structural elements, in particular their cross-sectional regions, are formed inhomogeneously, so that, in particular, the electromagnetic wave transmitted by the waveguide remains localized in a direction extending transversely to the direction of propagation, thereby providing, in particular, directed or restricted transmission of electromagnetic waves of an appropriately selected wavelength range, in particular visible light and / or infrared light and / or ultraviolet light, in particular image information. Here, due to the restricted propagation of light in the waveguide according to the present invention, image information can be transmitted with high sharpness, which can be improved compared to conventional optical fiber image guides.

[0019] On the other hand, the structural elements, in particular their cross-sectional areas, are formed in a manner determined by a predetermined rule, so that the waveguide has a reproducible structure, and in particular further waveguides can be produced with an identical structure to the waveguide, i.e., any non-uniformities or deviations from symmetry of the waveguide can only be produced according to the predetermined rule and reproduced for further waveguides. The predetermined rule therefore includes in particular detailed information for describing and / or constructing the waveguide in its structure formed by the structural elements, in particular their cross-sectional areas.

[0020] The structure of the waveguide, defined by the cross-sectional area of ​​the structural elements in the cross section, can be invariant along the direction of transmission or mathematically similar, in which case the waveguide can have a region along the direction of transmission whose cross section varies continuously, for example from the proximal end to the distal end or in at least one region therebetween, or varies continuously over at least one section of length L, in which case the length L is preferably at least as long as the maximum magnitude or difference of the cross-sectional variation, or at least corresponds to the maximum magnitude of the large input cross section.

[0021] If the waveguide is mathematically similar along the direction of transmission, this may or may not involve a change in cross-sectional shape. The corresponding positions of one or more structural elements at the end may also be changed so that they are rotated relative to one another, for example, by rotating or twisting the waveguide during manufacturing and / or by thermal post-treatment under the application of a rotational force or a corresponding directional force. A combination of cross-sectional change and rotation is also conceivable.

[0022] The rules that specifically define the location of the cross-sectional areas, the geometric shape of the cross-sectional areas and / or the refractive index of the structural elements may include the specification of characteristic values ​​of each structural element by deterministic prescriptions, in particular to define the location of the cross-sectional areas, the area of ​​the cross-sectional areas or the refractive index of each structural element.

[0023] In other words, the predetermined rule is preferably a deterministic rule that defines characteristic values ​​of structural elements in a clear and non-random manner in order to describe the structure of the waveguide by its structural elements.

[0024] The well-defined rules, in particular deterministic rules for specifying characteristic values, preferably include a mathematical sequence of set values. This sequence of values ​​may be formed as a non-uniformly distributed sequence and / or as a deterministic sequence, for example, as a Halton sequence, a Sobol sequence, a Niederreiter sequence, a Hammersley sequence, a Fowle sequence, or as a combination, concatenation, or merging of several sequences. For example, a portion of a first sequence for specifying characteristic values ​​and a portion of another sequence can be envisaged as being defined.

[0025] The clearly defined rules, in particular deterministic rules for specifying characteristic values, preferably comprise referencing a specific value, in particular a determinable, clearly set value, of a deterministic sequence for specifying the characteristic value of a specific construction element, referencing a further value of a deterministic sequence for specifying the characteristic value of a further construction element, checking whether the value or characteristic value of the further construction element violates a predetermined condition, in particular taking into account the value or characteristic value of the specific construction element, and, if the predetermined condition is violated, discarding the further value, referencing a still further value of the deterministic sequence for specifying the characteristic value of the further construction element, or modifying the further value in a predetermined manner so that the predetermined condition is fulfilled or no longer violated. Here, the predetermined condition can be formed as a defined minimum difference in values ​​or characteristic values, in particular as a defined minimum distance between positions of the cross-sectional areas of the construction elements. In this connection, reference is made to the following exemplary description.

[0026] In a preferred embodiment of the waveguide, the distribution of the area of ​​the Voronoi regions of the cross-sectional area of ​​at least one type of structural element, in particular with respect to its position relative to the generating point, satisfies at least one of the following conditions, which may be formed as a uniformity criterion for the sharpness of the image in the image guide:

[0027] (i) Variance of the distribution V d is the variance V of the corresponding distribution for a random location in the cross-sectional area z Smaller, ratio V z / V d is preferably 1 to 10, in particular greater than 1, preferably greater than 2, most preferably greater than 2.5 and / or less than 8, preferably less than 7, most preferably less than 6.5. z / V d is particularly preferably in the range from 1 to 8, in particular in the range from 2 to 7, in particular in the range from 2.5 to 6.5. Dispersion in the sense of the present application means in particular the dispersion normalized to the cross-sectional area A of the waveguide, where V=σ / A 2 where σ denotes the variance of the distribution of the area of ​​the Voronoi region with respect to the position of the cross-sectional area of ​​the structuring element within area A.

[0028] (ii) Variance of the distribution V d is 0.38 / N 2.033 where N represents the number of structural elements of at least one type, and the variance here again in particular means the normalized variance.

[0029] (iii) Variance of the distribution V d is larger than the variance of the corresponding distribution for periodic positions in the cross-sectional area, and the variance V d / A 2 is preferably greater than 0, in particular 10 -10 Larger, preferably 10 -9 greater than 10, most preferably -8 Larger,variance here also means normalized variance.

[0030] (iv) Skewness of the distribution S d is the skewness S of the corresponding distribution for a random location in the cross-sectional area z Smaller, skewness S d is in the range of 0 to 1.5, in particular greater than 0.01, preferably greater than 0.05, most preferably greater than 0.1 and / or less than 1.4, preferably less than 1.2, most preferably less than 0.8. Alternatively or additionally, S z / S d The ratio may also be between 1 and 50, in particular greater than 1.1, preferably greater than 1.3, most preferably greater than 1.9, and / or less than 25, preferably less than 15, most preferably less than 10.

[0031] (v) Kurtosis of the distribution W d is the kurtosis W of the corresponding distribution for a random location in the cross-sectional area z Smaller, kurtosis W d is between 0 and 10, in particular greater than 0.5, preferably greater than 1, most preferably greater than 2 and / or less than 10, preferably less than 6, most preferably less than 5. Alternatively or additionally, the ratio W z / W dmay also be 1 to 5, in particular greater than 1.1, preferably greater than 1.5, most preferably greater than 2, and / or less than 4.5, preferably less than 4, most preferably less than 3.

[0032] The ratio of the total cross-sectional area of ​​the first type of structural elements to the total cross-sectional area of ​​the second type of structural elements is, for example, in the range of 1:9 to 9:1, preferably in the range of 3:7 to 7:3, particularly preferably in the range of 4:6 to 6:4, in particular also 5:5, which may also be understood as the degree of filling.

[0033] In particular, when a plurality of structural elements are envisaged in the form of filamentary channels, the ratio of the total area of ​​the cross-sectional areas of the first type of structural elements to the total area of ​​the cross-sectional areas of the second type of structural elements may also be in the range of 1:150 to 150:1, preferably in the range of 1:100 to 100:1, particularly preferably in the range of 1:50 to 50:1.

[0034] The total area of ​​the cross-sectional areas of each type of structural element is, for example, at least 1 / (10×T) of the cross-sectional area, preferably at least 1 / (5×T), particularly preferably at least 1 / (3×T), where T represents the number of types of structural elements.

[0035] The first refractive index of the first type of structural element and the second refractive index of the second type of structural element may be, for example, at least 10 -4 may differ by at least 10 -3 may differ by at least 10 -2 may differ by at least 10 -1 They may differ by at least one, particularly by at least two, particularly by at least three, particularly by at least four.

[0036] With regard to the lateral dimensions of the structural elements, it is possible to envisage that at least one cross-sectional area has a diameter of 100 nm to 50 μm, preferably 400 nm to 20 μm, particularly preferably 1 μm to 16 μm.

[0037] Furthermore, it is particularly preferable that at least one cross-sectional area has a diameter of 0.1 to 10 times the mean wavelength of the wavelength range of the electromagnetic wave to be transmitted, preferably 0.2 to 5 times the mean wavelength, and particularly preferably 0.5 to 2 times the mean wavelength.

[0038] With regard to the geometric shape of the construction elements, it is possible to envisage cross-sectional areas having non-circular or polygonal, for example pentagonal or hexagonal, geometric shapes.

[0039] As already mentioned, the waveguide comprises a plurality of structural elements, whereby structural elements of at least two types are included. Here, it is conceivable that in one embodiment of the waveguide, one structural element of a first type and a plurality of structural elements of a second type are included. Therefore, the plurality of structural elements in particular comprises exactly one structural element of the first type.

[0040] The first type of structural element is in particular formed as, for example, a monolithic substrate using or consisting of a first medium, the first medium having a first refractive index, and the second type of structural element may be formed as a cavity in the substrate, the cavity preferably forming a second refractive index, for example due to the refractive index of air or a gas that may be present as the medium in the cavity.

[0041] The cavities in the substrate may be formed as filamentary channels, i.e., channels having a significantly smaller area compared to the cross-sectional area of ​​the waveguide, which may be introduced into the substrate by a laser beam of an ultrashort pulse laser, and the filamentary channels in the substrate may be further post-treated, in particular by a chemical or physical etching process, for example, to smooth the contours of the filamentary channels.

[0042] In particular, if the waveguide is formed as a substrate with a cavity, but regardless of this, the waveguide may preferably have a larger dimension in cross section than along the direction of transmission. In particular, the waveguide may be formed as a faceplate.

[0043] It is conceivable that the waveguide has, in cross section, an area of ​​at least 4 square millimeters, preferably at least 2500 square millimeters, particularly preferably at least 10000 square millimeters.

[0044] The waveguide may have a cross-section that is at least twice as large as the dimension along the direction of transmission, preferably at least five times as large as the dimension along the direction of transmission, particularly preferably at least ten times as large as the dimension along the direction of transmission.

[0045] Substrates with cavities can be and have been produced in a variety of ways. On the one hand, the cavities in the substrate can be formed by additive manufacturing of the substrate, for example by 3D printing. Alternatively or additionally, the cavities can be introduced into the substrate by subtractive processes, in particular as bores, which are introduced into the substrate by material processing grinding processes, for example mechanical drilling. Depending on the method used, the bores are not limited to circular geometric shapes.

[0046] Preferably, the waveguide is manufactured in a multi-draw process, in particular such that the waveguide comprises in addition to the plurality of structural elements at least one second plurality of structural elements, and the waveguide has at least two surface areas in cross section, each of which comprises a cross-sectional area of ​​one of both plurality of structural elements, which have the same structure except for rotation and / or reflection.

[0047] With regard to the size of the waveguide along the transmission direction, it is conceivable that the waveguide has a dimension along the transmission direction of less than 10 millimeters, preferably less than 6 millimeters, particularly preferably less than 5 millimeters, especially when the waveguide is formed as a faceplate.

[0048] However, it is also possible to envisage that the waveguide has a dimension along the transmission direction of at least 10 millimetres, preferably at least 20 millimetres, particularly preferably at least 50 millimetres, and even more preferably at least 100 millimetres.

[0049] If the waveguide is formed as a substrate having a cavity, the cavity in the substrate, in particular the filamentary channels and / or bores, may be filled with a second medium, the second medium having a second refractive index.

[0050] With regard to the material, it is conceivable that at least one structural element, in particular a structural element of the first type, in particular a structural element formed as a substrate, comprises or consists of one or more of the following materials as medium: glass, quartz glass, polymer, crystalline, monocrystalline, polycrystalline material and / or glass ceramic.

[0051] Furthermore, at least one structural element, in particular a structural element of the first type, in particular a structural element formed as a substrate, can comprise or consist as a medium of an in particular infrared-transparent material, in particular a chalcogenide, in particular a material comprising at least one element from the group oxygen, sulfur, selenium and tellurium and at least one element from the group arsenic, germanium, phosphorus, antimony, lead, boron, aluminum, gallium, indium, titanium, sodium, which has an attenuation of less than 100 dB / m, in particular less than 50 dB / m, in particular less than 10 dB / m, in particular less than 1 dB / m in the wavelength range to be transmitted, in particular 2 μm to 20 μm.

[0052] Furthermore, optically active materials are conceivable, for example, as part of a medium or filler and / or as layers or coatings or other modifications on or on the surface of an array of structural elements formed as rods or tubes, by which, for example, a modification, in the sense of, for example, enhancement or transformation, of the guided electromagnetic waves can be achieved.

[0053] The further structural elements, in particular structural elements of the second type, preferably comprise or consist of another of the aforementioned materials. In other words, the structural elements, in particular structural elements of the second type, in particular the cavities in the substrate filled with the second medium, can likewise comprise or consist of one or more of the aforementioned materials, as the medium, and in particular can comprise or consist of a material not included in the aforementioned structural elements, in particular structural elements of the first type.

[0054] As already mentioned, the waveguide comprises a plurality of structural elements, where at least two types of structural elements are included, and as already mentioned, for example, one structural element of a first type and a plurality of structural elements of a second type.

[0055] In a further embodiment, it is contemplated that a plurality of structural elements of a first type and a plurality of structural elements of a second type are included.

[0056] In this case, the first type of structural element may be formed using or consisting of a first medium, in particular as a rod-shaped or tubular body, wherein the first medium has a first refractive index.

[0057] In this case, the second type of structural element may be formed, in particular as a rod-shaped or tubular body, using or consisting of a second medium, wherein the second medium has a second refractive index and / or may be formed as a cavity in the first type of structural element, wherein the cavity preferably forms the second refractive index or is filled with the second medium having the second refractive index.

[0058] In particular, if the second type of structural element is present as a filled cavity within the first type of structural element, the structural element may be formed as a core-clad system, with the core corresponding to the filled cavity.

[0059] Here, rod-like or tubular objects do not necessarily mean objects having a circular cross-sectional geometric shape.

[0060] The present invention further relates to a waveguide for transmitting electromagnetic waves, in particular image information, from a proximal end of the waveguide to a distal end of the waveguide along a transmission direction extending between the proximal and distal ends, with a cross-section extending transverse to the transmission direction, in particular a waveguide having one or more of the aforementioned features, the waveguide comprising a plurality of structural elements, at least two types of structural elements, namely a first type having a first refractive index and a second type having a second refractive index, each of the structural elements extending along the transmission direction and spanning proportionally the cross-section of the waveguide, the cross-section of the waveguide defining a plurality of cross-sectional areas, each of the cross-sectional areas corresponding to a cross-section of an individual structural element, the waveguide having a larger dimension in the cross-section than along the transmission direction.

[0061] The present invention further provides a waveguide for transmitting electromagnetic waves, in particular image information, from a proximal end of the waveguide to a distal end of the waveguide along a transmission direction extending between the proximal and distal ends, in a cross section extending transversely to the transmission direction, in particular a waveguide having one or more of the aforementioned characteristics, the waveguide comprising a plurality of structural elements, at least two types of structural elements, namely a first type having a first refractive index and a second type having a second refractive index, each of the structural elements being , extending along the direction of transmission and spanning a proportionate cross-section of the waveguide, in which a plurality of cross-sectional areas are defined, each of which corresponds to the cross-section of an individual structural element, at least one structural element having an attenuation of less than or equal to 100 dB / m, in particular less than or equal to 50 dB / m, in particular less than or equal to 10 dB / m, in particular less than or equal to 1 dB / m in the wavelength range from 2 μm to 20 μm, and in particular comprising or consisting of an infrared-transparent material.

[0062] Also, depending on the dimensions of the waveguide in the direction of transmission, the following attenuations can be expected: For waveguides with a dimension of at least 5 millimeters in the direction of transmission, an attenuation of up to 100 dB / m can be expected; For waveguides with a dimension of at least 10 centimeters in the direction of transmission, an attenuation of up to 50 dB / m can be expected; For waveguides with a dimension of at least 1 meter in the direction of transmission, an attenuation of up to 30 dB / m can be expected.

[0063] The invention further relates to a method for manufacturing a waveguide, in particular a waveguide having one or more of the aforementioned characteristics, comprising the steps of providing one structural element of a first type with a first refractive index, in particular in the form of a monolithic substrate made of or consisting of a first medium, and introducing a plurality of structural elements of a second type with a second refractive index, for this purpose introducing cavities in the substrate and filling these cavities preferably with a second medium.

[0064] Now, a second type of structural element is introduced, such that each structural element spans a proportionate portion of the cross section of the waveguide, defining a plurality of cross-sectional areas in the cross section of the waveguide, each of which corresponds to the cross section of an individual structural element of the second type.

[0065] According to the invention, a second type of structural element is further introduced, so that the cross-sectional area of ​​the second type of structural element has a non-uniform, in particular aperiodic, but regularly defined arrangement and / or a non-uniform, but regularly defined geometric shape, for example a diameter.

[0066] In the method for manufacturing a waveguide, it is conceivable that the rules that specifically define the arrangement and / or the geometric shape of the cross-sectional area include the specification of characteristic values ​​of each structural element of the second type by deterministic prescription, in particular for determining the position and / or area of ​​the cross-sectional area of ​​each structural element.

[0067] The well-defined rules, in particular deterministic rules for specifying property values, may in particular involve the use of a mathematical sequence of set values, and reference is made to said sequence, and further to the steps of referencing the values, validating the values ​​and discarding / modifying the values ​​as necessary, as detailed above.

[0068] Preferably, the distribution of the areas of the Voronoi regions of the cross-sectional areas of at least one type of structuring element, in particular with respect to the position relative to the generating points, satisfies at least one of the above conditions, in particular (i), (ii), (iii), (iv) and (v).

[0069] In the method for manufacturing a waveguide, the cavities can be introduced into the substrate as filamentary channels, in particular by means of a laser beam, for example an ultrashort pulse laser. Furthermore, the filamentary channels in the substrate can be post-treated, in particular by chemical and / or physical etching processes, for example to smooth the contours of the filamentary channels, in particular before filling the filamentary channels with the second medium.

[0070] The cavities can be introduced into the substrate at intervals greater than the diameter of the cavities, preferably at intervals twice the diameter of the cavities, particularly preferably at intervals three times the diameter of the cavities.

[0071] Cavities can also be introduced into the substrate by additive manufacturing of the substrate and / or by subtractive processes, in particular by abrasive processes of material processing, such as mechanical drilling.

[0072] With regard to materials, it is conceivable that the substrate comprises or consists of one or more of the aforementioned materials as a medium. Furthermore, at least one structural element of the second type may comprise or consist of one or more of the materials mentioned for the substrate of the first type as a medium, in particular a material not included in the substrate.

[0073] The invention further relates to a method for manufacturing a waveguide, which method preferably can be referred to as a draw process or a multi-draw process, in particular comprising one or more of the method steps described above.

[0074] The method comprises forming a preform by arranging a waveguide having one or more of the aforementioned characteristics and one or more further waveguides, each also having one or more of the aforementioned characteristics, such that the transmission directions of the waveguides are parallel to one another.

[0075] The arrayed waveguides are then drawn together along the direction of transmission, with draw ratios of at least 1:2, preferably at least 1:10, particularly preferably at least 1:100 being considered here.

[0076] Preferably, the aligned and drawn waveguides can then be divided into sections transverse to the direction of transmission, and the sections can again be aligned with their directions of transmission parallel to one another to form a preform.

[0077] The aligned sections can then be reassembled and drawn along the direction of propagation, with draw ratios of at least 1:2, preferably at least 1:10, particularly preferably at least 1:100 being particularly contemplated here.

[0078] The waveguides and / or sections, respectively, may be arranged to form a preform, in particular according to the above detailed description, such that the arrangement of the arrangement is clearly defined by a predetermined rule.

[0079] The waveguides and / or sections, respectively, can further be arranged such that the structures formed by the cross-sectional areas of the second structural elements in the cross section are rotated relative to one another in a particular predetermined manner, in particular not rotated relative to one another, to form a preform. Furthermore, the waveguides and / or sections can be flipped lengthwise during arrangement, so that a mirror image of the cross section is generated.

[0080] In this case, it is also possible to arrange sections made from at least one further preform, which are arranged according to a common predetermined rule, preferably substantially identical, but which may also be arranged according to a different predetermined rule.

[0081] Furthermore, the waveguides and / or sections, respectively, can be arranged by automation, in particular by robotic assistance.

[0082] Additionally, the aligned and drawn waveguides and / or aligned and drawn sections can be fused together by application of heat and / or pressure, particularly under vacuum.

[0083] The invention further relates to a method for manufacturing a waveguide, in which two or more waveguides are similarly formed such that the cross-sectional areas of the second type of structural elements each have an identical, non-uniform, but regularly well-defined arrangement and / or an identical, non-uniform, but regularly well-defined geometric shape, e.g. diameter.

[0084] The method is particularly designed as a method for producing a plurality of identical waveguides, which are preferably produced independently of one another, so that further waveguides with identical structures can be produced in particular only on the basis of predetermined rules.

[0085] In addition to being able to produce identical waveguides by this method, the method is also suitable for producing waveguides that are identical with respect to at least certain properties, for example, the waveguides may satisfy certain uniformity criteria regarding image sharpness and / or may satisfy one or more of the above-mentioned conditions regarding the distribution of the area of ​​the Voronoi regions of the cross-sectional area of ​​at least one type of structural element, in particular with respect to its position relative to the generating point.

[0086] The invention further relates to a waveguide, in particular having one or more of the characteristics described above for the waveguide and produced or capable of being produced by a method comprising one or more of the method steps described above.

[0087] Finally, the invention also relates to a set comprising two or more waveguides, each of which has one or more of the characteristics described above for the waveguides and which has been or can be produced by a method comprising one or more of the method steps described above, in particular, and each of which comprises a plurality of structural elements, the structural elements, in particular their cross-sectional areas, being formed non-uniformly but in a clearly defined manner according to a predetermined rule, and the two or more waveguides being similarly formed so that the structural elements, in particular their cross-sectional areas, are similarly formed non-uniformly.

[0088] Preferred embodiments of the present invention will be described below with reference to the drawings. [Brief explanation of the drawings]

[0089] [Figure 1] (a), (b), and (c) are schematic cross-sections of waveguides with two types of structural elements, and (d) and (e) are schematic cross-sections of waveguides with three types of structural elements, where the cross-sectional area of ​​each structural element is non-uniformly distributed. [Figure 2] Schematic perspective view of two waveguides with (a) two types of structural elements arranged such that their cross-sectional areas are non-uniformly distributed on a lattice, and (b) multiple structural elements with non-uniform refractive index (multiple types) and / or non-uniform geometric shapes (diameters). [Figure 3] FIG. 1 is a schematic cross-sectional view of a waveguide having two types of structural elements arranged such that their cross-sectional areas are non-uniformly distributed on a hexagonal lattice. [Figure 4] 1 is a schematic cross-sectional view of a waveguide having two types of structural elements, where the type / refractive index of each structural element is or is determined by a deterministic prescription. [Figure 5] 1 is a schematic cross-sectional view of a waveguide formed, for example as a faceplate, with a single structural element of a first type as a substrate and multiple structural elements of a second type as cavities within the substrate, where the position of the second type of structural element within the substrate is or is determined by a deterministic prescription. [Figure 6] 10A and 10B are graphs showing the variance of the distribution of the area of ​​Voronoi regions relative to the position of the cross-sectional area of ​​a second type of structural element placed within a first type of structural element, plotted against the number of second type of structural elements, in (a) logarithmic and (b) double logarithmic representations. [Figure 7] A figure showing (a) an example of a Voronoi region for the position of the cross-sectional area of ​​a second type of structural element using a Halton sequence placed within a first type of structural element having a circular cross-section, (b) a positional relationship using a Sobol sequence, (c) a random positional relationship, and (d) a periodic positional relationship as a further comparative example. [Figure 8]A figure showing (a) an example of a Voronoi region for the position of the cross-sectional area of ​​a second type of structural element placed within a first type of structural element having a square cross-section, (b) a positional relationship according to a Sobol sequence, (c) a random positional relationship, and (d) a periodic positional relationship as a further comparative example. [Figure 9] (a) Waveguides are arranged to form a preform, which is then drawn; (b) and (c) waveguides are again arranged from the preform to form a preform, which is then drawn; (d) this is again arranged; and (e) the waveguides are fused under pressure. [Figure 10] 10A and 10B are schematic cross-sectional views of the preforms formed by rearranging the waveguides in FIG. 9, where (a) and (b) are preform sections each consisting of one drawn waveguide, and (c) and (d) are preform sections each consisting of two drawn waveguides, with the waveguides (a) and (c) not rotated relative to each other, and the waveguides (b) and (d) rotated relative to each other in a predetermined manner. [Figure 11] 1A-1C are schematic diagrams showing various possibilities for waveguides in which the structural elements or their cross-sectional areas are formed non-uniformly but in a well-defined manner according to certain rules; [Figure 12] 1 is a schematic diagram showing various aspects of the variation of a structural element or its cross-sectional area, and possible combinations of these aspects. [Figure 13] Schematic diagrams showing various further possibilities for waveguides in which the structural elements or their cross-sectional areas are formed non-uniformly but in a clearly defined manner, each waveguide comprising one structural element of a first type and multiple structural elements of a second type. [Figure 14] Schematic diagrams showing various further possibilities for waveguides in which the structural elements or their cross-sectional areas are formed non-uniformly but in a clearly defined manner, each waveguide comprising a plurality of structural elements of a first type and a plurality of structural elements of a second type and optionally further types. [Figure 15]1 is a photograph of an end face of a waveguide fabricated with a first type of structural element formed within which a plurality of a second type of structural element are formed as filamentary channels. [Figure 16] 1A-1C are photographs (and various enlarged cross-sectional views) of a waveguide fabricated having a plurality of structural elements of a first type and a plurality of structural elements of a second type. [Figure 17] 17 is a photograph showing the waveguide of FIG. 16 applied as an image guide.

[0090] FIG. 1 shows various principle examples of waveguides 1 that can be used, in particular, as image guides. Each of the waveguides 1, shown in cross section, includes a number of structural elements 10, each extending along the waveguide's transmission direction, which here extends perpendicular to the plane of the drawing, and proportionally spanning the cross section. Each structural element 10 thus defines a cross-sectional area 20, i.e., a partial surface of the waveguide's cross section. Each of the illustrated examples of waveguides 1 has at least two structural elements with different refractive indices. These principle illustrations are intended to illustrate variations in the non-uniformity, and in particular, possible deviations from the deterministic positional relationship of the structural elements defined by the present invention.

[0091] The waveguide shown in cross section in FIG. 1(a) has a first type of structural element 10a formed as a substrate, which houses a plurality of second type of structural elements 10b. Here, the second type of structural elements 10b may be formed, for example, as cavities or hollow channels extending along the transmission direction within the first type of structural element 10a. Here, the first type of structural element 10a formed as a substrate includes a first material having a first refractive index, and the second type of structural element 10b formed, for example, as a cavity, forms a second refractive index, for example, due to the presence of air or other gas therein. In this case, the cross-sectional area 20 of the first type of structural element 10a corresponds to the cross-sectional area of ​​the waveguide minus the holes defined by the cavities within this area, while the cross-sectional area 20 of the second type of structural element 10b corresponds to the cross-sectional area of ​​each cavity. However, cavities in the substrate may be filled with a second material, such that the second type of structural elements 10b represent filled cavities. As shown schematically in the figure, the cross-sectional area 20 of the second type of structural elements 10b is non-uniform in that their positions are non-uniformly distributed across the cross section and, in particular, do not lie on a periodic grid. At the same time, however, the positions of the structural elements are clearly defined according to a predetermined rule, as will be explained in more detail below.

[0092] The waveguide shown in FIG. 1(b) similarly has two types of structural elements 10a, 10b: again, just one structural element 10a formed as a substrate with a first refractive index, and multiple structural elements 10b with a second refractive index different from the first. In the example shown, the cross-sectional areas 20 of the second type of structural elements 10b are not only non-uniformly arranged, but also have non-uniform geometric shapes, in this case non-uniform diameters, of which there are a limited number, i.e., two different diameters. In this case, the non-uniformity of the arrangement and / or the non-uniformity of the geometric shapes are clearly defined by predetermined rules.

[0093] 1(c) also has two types of structural elements 10a, 10b, with the cross-sectional area of ​​the second type of structural elements 10b being arranged within the first type of structural elements 10a, in particular as a core-clad system. Thus, in this case, a plurality of first type of structural elements 10a and a plurality of second type of structural elements 10b are envisaged. The structural elements or their cross-sectional areas are non-uniform in that the first type of structural elements 10a (which house the second type of structural elements 10b) are arranged non-uniformly, in particular aperiodically, in the cross-section of the waveguide, with this arrangement being determined by a predetermined rule.

[0094] The waveguides shown in cross section in Figures 1(d) and (e) are similar in some respects to the waveguides shown in Figures 1(a) or 1(b), but have three structural elements 10a, 10b, and 10c with different refractive indices. In particular, the cavities in structural element 10a, which is formed as a substrate, may be filled with different media. Therefore, structural elements 10b and 10c in particular exhibit inhomogeneity in that their refractive indices differ from one another, and the determination of which of the structural elements formed as cavities will have which refractive index preferably follows a predetermined rule.

[0095] 2 shows two further examples of waveguides 1 that can be used in particular as image guides. The waveguide 1 again comprises a number of structural elements 10, each of which extends along the direction of transmission 5 from the proximal end 2 to the distal end 4 of the waveguide 1 and is formed, for example, in the shape of a rod.

[0096] The waveguide shown in Figure 2(a) has a plurality of structural elements of a first type 10a and a plurality of structural elements of a second type 10b. In this example, the cross-sectional areas of the structural elements are arranged on a periodic lattice. However, the structural elements have a non-uniform arrangement in that the first type structural elements 10a and the second type structural elements 10b, and thus the refractive indexes, are non-uniformly arranged and / or distributed, which arrangement or distribution is again clearly defined by a predetermined rule.

[0097] The waveguide shown in FIG. 2(b) again has a plurality of structural elements 10 arranged on a periodic lattice, in this case the cross-sectional areas of the structural elements having a non-uniform geometric shape. This geometric shape may differ in particular in that the diameters of the structural elements or their cross-sectional areas differ from one another. Preferably, the form of this non-uniformity is also clearly defined according to a predetermined rule. Furthermore, the structural elements 10 may have a particular predetermined non-uniformity in that the refractive indices of the structural elements differ from one another. In this case, a discrete number of refractive indices, for example two, three, or four, may be envisaged, although in principle a continuous variation of the refractive index may also be envisaged.

[0098] Figure 3 is a further cross-sectional view of a waveguide similar in some respects to the waveguide shown in Figure 2(a). The waveguide shown in Figure 3 has a plurality of, in particular rod-shaped, structural elements 10, namely a plurality of structural elements 10a of a first type and a plurality of structural elements 10b of a second type, which are arranged in cross section on a periodic lattice, in this example corresponding to a hexagonal lattice. It is therefore envisaged that at least one of the structural elements 10, or its cross-sectional area 20, is equidistant from and preferably adjacent to six of its nearest neighboring structural elements 10 or their cross-sectional areas 20.

[0099] 4 and 5, an example in which structural elements may be formed non-uniformly but in a manner clearly defined by a predetermined rule is given below. In this regard, rules for clearly defining parameters, such as position, type, refractive index, or even geometric shape, may be envisaged, and these rules preferably include a deterministic sequence (e.g., Halton sequence). This sequence forms part of the deterministic definition for specifying the parameters of the structural elements, which will be described in detail below. For the sake of clarity, this definition is explained in individual steps, with particular importance being placed on the overall structure of the waveguide, which can be defined before the waveguide is manufactured, so that the overall structure of the waveguide is clearly defined in advance.

[0100] For a waveguide according to the invention, the structural elements are filled in the available area, for example the cross-sectional area of ​​the waveguide according to a deterministic rule, in positions that can be determined in this way, for example according to predetermined parameters, which generally include information about the dimensions, in particular the shape and size, of the structural elements and their position and spacing, as well as data about the filling factor, which indicates the percentage of the area that should be filled with one or more types of structural elements.

[0101] For example, for a circular waveguide 1 (see FIG. 3), and in particular for example also for its preform (see FIG. 10), structural elements 10b are selected, which are occupied by a medium having, for example, a second refractive index, in a predetermined arrangement and number of structural elements (here, in the example, identical diameter, hexagonal close-packed), with a predetermined filling factor, according to a deterministic algorithm (including, for example, a Halton sequence).

[0102] For this purpose, in a square 100 surrounding the circle of the waveguide 1, points 102 are generated according to, for example, a two-dimensional Halton sequence, whose values ​​lie in the range [0,1) x [0,1) and are scaled according to the dimensioning of a given area of ​​the waveguide.

[0103] Halton sequences are multidimensional extensions of one-dimensional van der Korps sequences in different bases. Here, the van der Korps sequence x in base b is n =φ b (n) is defined by reversing the base b notation of the number n. For example, all natural numbers n ≥ 0 can be expressed as a sum over base b ≥ 2,

number

number

[0104] Since the structural elements 10 are localized at predetermined positions and the sequence covers the complete range [0,1) x [0,1), the following assignment is made: the sequence elements are looked at in order. The assignment to a structural element, in particular to a second type 10b, is made by the smallest Euclidean distance. In this way, sequence elements that have already been assigned to a selected structural element or that are outside the constellation are ignored, and the sequence continues with the next sequence element. This continues until the number of structural elements, in particular of the second type 10b, that corresponds to the desired filling factor has been selected.

[0105] To clarify this, two example embodiments will be described.

[0106] The first example embodiment shows a circular waveguide or preform for a waveguide 1 (FIG. 4), which is formed from at least two similarly circular structural elements with two different predefined refractive indices in a hexagonal packing or arrangement.

[0107] This arrangement is then occupied by two refractive indices according to a deterministic sequence prescription until a predetermined filling level is reached, so that some occupied structural elements are given one refractive index and other occupied structural elements are given the other refractive index.

[0108] This is done under the following condition: if the column point 102 is inside the circle and the position or the structural element belonging to it has not yet been occupied (for example, assigned to type 10b), then the structural element closest to column point 102 is occupied (for example, assigned to type 10b). In this case, the column point is discarded and the next column point is looked at. Thus, the first point in the deterministic column is determined, scaled and placed on the shape (black point), the above condition is verified, and in this first case the structural element highlighted in gray is occupied. The following points are processed in the same way.

[0109] Furthermore, if any column points 102 fall outside or overlap the shape, here a circle, then these column points 102 are discarded and the next column point 102 is continued until a predetermined fill level is reached.

[0110] The figure shows the results for discarded points 102v (not discarded here), which are points outside the circular shape or overlapping points, and for a fill level of 50%.

[0111] A further example embodiment (FIG. 5) illustrates the occupation of a predetermined area. The objective here is to position structural elements, such as holes with a certain diameter, on a square plate 110 with a side length D according to the Halton sequence, for example, for a laser filamentation process or a drilling process. Here, the sequence points 112 are scaled from the range [0, 1) to the predetermined area dimension range [-D / 2, D / 2). This is done until a predetermined filling level is reached, which is determined from the area ratio of the sum of the holes to the substrate area. Holes can be placed according to the sequence points (FIG. 5a). Alternatively, the sequence points can be finished to the diameter of the holes (FIG. 5b). If overlapping holes (overlapping hole pairs 114) are undesirable, such sequence points should be discarded. The double placement (FIG. 5b) is discarded accordingly, and the sequence is continued. Similarly, further restrictions may be placed here, for example, defining a minimum distance between structural elements.

[0112] It will be appreciated that the method basically described above and in more detail in the two examples can be applied, without limitation to further possible variations, to structural elements having two or more refractive indices and / or different or variable geometric shapes, dimensions, e.g., two or more diameters and / or shapes or combinations thereof, over any, if necessary, predetermined area, and whose structures can be explicitly predetermined, and the conditions for occupancy or occupancy possibility of the available area can be adapted or extended as appropriate in each case to achieve the desired or required occupancy.

[0113] With reference to FIG. 6, the waveguide according to the invention meets certain uniformity criteria, in particular with regard to the non-uniformity of the structural elements and preferably with regard to the sharpness of the image of the waveguide formed as an image guide.

[0114] For example, the distribution of areas that correspond to or can be clearly assigned to the cross-sectional areas of the structural elements can satisfy certain conditions. For the location of the cross-sectional areas of at least one type of structural element, an exemplary variance of the distribution of the area of ​​the Voronoi region with respect to the square of the total area of ​​the cross-section to be occupied, A (normalized variance V = σ / A 2 ) versus the number N of at least one type of structural element is shown in logarithmic (FIG. 6a) and log-log (FIG. 6b) representations.

[0115] A waveguide according to the present invention can be characterized by a deterministic sequence as described above. Thus, dispersion curve 200 is based on the location of the cross-sectional area defined by the Halton sequence, and dispersion curve 202 is based on the location of the cross-sectional area defined by the Sobol sequence. For comparison, dispersion curve 204 based on the location of the cross-sectional area defined randomly and the fitting curve 206 corresponding to dispersion curve 204 are shown (dispersion = 0.38 A). 2 / N 2.033 ) It can be seen that the variance of the distribution (for each N) of the waveguide according to the invention is smaller than that of the waveguide with random disorder.

[0116] Note that the curves shown are based on a distribution spanning the range [0,1).

[0117] 7 and 8 show exemplary Voronoi regions 210 relative to the position 212 of the cross-sectional area of ​​the structural elements for waveguides with a circular cross-section ( FIG. 7 ) and a square cross-section ( FIG. 8 , which is based on FIG. 6 ). FIGS. 7a and 8a show the position 212 and Voronoi region 210 based on the Halton sequence, while FIGS. 7b and 8b show those based on the Sobol sequence, which correspond to the non-uniformity of the waveguide according to the present invention. For comparison, FIGS. 7c and 8c show the position 212 and Voronoi region 210 based on a random arrangement, while FIGS. 7d ​​and 8d show those based on a periodic arrangement. It is clear that the waveguide according to the present invention is characterized by the structural elements, particularly their cross-sectional areas, being formed non-uniformly, but with a higher uniformity than a random arrangement.

[0118] Figure 9 shows steps in a method for manufacturing a waveguide by a multi-draw process, in which a number of waveguides 1 are arranged in a preform 30 and drawn (Figure 9a), where the waveguides 1 may be, for example, an arrangement of structural elements 10, 20 or 10a, 10b, for example according to Figure 3, or other configurations, for example according to Figures 1(a) to 1(e), which are preferably already drawn in a known manner.

[0119] The aligned and drawn waveguides ("multi-fiber") are then sectioned and realigned to form preform 40 (Figure 9b, "multi-multi assembly"). Preform 40 can then be redrawn (Figure 9c) and, if necessary, re-aligned (Figure 9d). Finally, the resulting array can be fused together by application of heat and / or pressure, particularly under vacuum (Figure 9e).

[0120] 10, when the aligned and drawn waveguides ("multi-fibers," herein designated "M1") are arranged to form a further preform, they can be arranged without rotation relative to each other (FIG. 10a), or in particular rotated relative to each other in a predetermined manner (FIG. 10b). Furthermore, when arranging, sections made up of at least two different aligned and drawn waveguides ("M1," "M2") can be arranged without rotation (FIG. 10c), or in particular rotated relative to each other in a predetermined manner (FIG. 10d). Similar to the arrangements shown in FIGS. 10a and 10b, the waveguides can be arranged or positioned without rotation, or in particular rotated relative to each other in a predetermined manner, during the arranging of the first preform. When a preform is arranged from sections of at least two different waveguides ("M1," "M2"), the arrangement of these different waveguides can be carried out according to the arrangement of the different types of structural elements described above (e.g., FIG. 3) and therefore, in this case too, can be clearly defined by a predetermined rule.

[0121] Various embodiments of the non-uniformity of the structural elements according to the invention will now be described, again by way of example, with reference to Figures 11 to 14. As mentioned above, the structural elements, and in particular their cross-sectional areas, are characterized on the one hand by their non-uniformity with respect to one another, and on the other hand by a regularity in that the non-uniformity of the structural elements is clearly predetermined, in particular deterministic and / or reproducible and not of random origin.

[0122] For example, the structural elements or their cross-sectional areas may have a regularly defined non-uniform arrangement, may have regularly defined non-uniform geometric shapes relative to one another, and / or may have regularly defined non-uniform refractive indices relative to one another.

[0123] FIG. 11 shows various possibilities for realizing a regularly defined non-uniform arrangement by means of a tree diagram. In FIG. 11a, a structural element 10a is shown as a starting point, which may be formed, for example, as a matrix material (it is also possible for the structural element 10a to be formed as air or not present at all). FIG. 11b shows a further starting point derived from this, with a structural element 10a and a number of periodic positions P of occupation by the structural elements, which in this case have a periodic positional relationship. FIG. 11d shows a further starting point derived from FIG. 11a, with a structural element 10a and a number of aperiodic positions P of occupation by the structural elements to achieve a non-periodic positional relationship. Starting from the starting points shown in FIGS. 11b and 11d, a waveguide according to the present invention is obtained by occupying the positions P of the structural elements as will be explained in detail below.

[0124] Starting from Fig. 11b, Fig. 11c shows a waveguide 1 having structural elements 10b, 10c whose cross-sectional areas have a periodic relationship and / or are periodically positioned. The waveguide shown in Fig. 11c has three types of structural elements 10a, 10b, 10c, each of which may have a different refractive index. For example, structural element 10a may be formed as a matrix material, and structural elements 10b and 10c may be cavities formed by filling the matrix material with materials having different refractive indices.

[0125] However, it is equally conceivable that one of the materials of the structural elements 10b and 10c also corresponds in this case to the matrix material of the structural element 10a, and that there are no (filled) cavities in the matrix material corresponding to these structural elements (see in this regard the following Fig. 13a).It is also equally possible that the structural element 10a is formed as air or does not exist, and that the structural elements 10b and 10c adjoin one another (see in this regard the following Fig. 14a).

[0126] The waveguide 1 shown in FIG. 11c has structural elements 10b, 10c that are periodically positioned. However, the structural elements 10b, 10c are of different types, and the occupancy of the different types on the regular lattice is non-uniform but regular. In particular, the variation of the structural elements 10b, 10c relative to one another is thus non-uniform but regular. The structural elements 10b, 10c can be described as exhibiting a particularly deterministic disorder. Thus, FIG. 11c illustrates the case of a waveguide 1 having a non-uniform arrangement of the structural elements or their cross-sectional areas that is clearly defined and regular. The term "arrangement" here should be understood to mean that the selection or occupancy of the different types of structural elements 10b, 10c at their respective periodic positions is non-uniform but regular, i.e., not random.

[0127] Furthermore, it is also possible that the structural elements 10b, 10c do not differ with respect to their refractive index, i.e., have the same refractive index or are made of the same material, but differ with respect to other aspects (see in this regard FIG. 12 below).It is also possible that the structural elements 10b, 10c differ not only with respect to their refractive index but also with respect to other aspects.

[0128] Starting from FIG. 11d, FIG. 11e shows a waveguide 1 having two types of structural elements: a structural element 10a, which may be formed, for example, as a matrix material, and a plurality of structural elements 10b, which may be formed, for example, as filled cavities in the matrix material. The cross-sectional areas of the structural elements 10b are arranged aperiodically in this case. In this case, the relative positions of the structural elements 10b can exhibit regular, non-uniformity. In particular, the second type of structural elements 10b can have a non-uniform, but regularly-defined position. Thus, FIG. 11e shows the case of a waveguide 1 in which the structural elements or their cross-sectional areas have a regularly-defined, non-uniform arrangement. Here, the term "arrangement" should be understood to mean that the structural elements or their cross-sectional areas, or parts thereof, are arranged aperiodically and their positions are regularly-defined, i.e., not random. In particular in the case of Figure 11e, it is assumed that the second type of structural elements 10b have a uniform refractive index, a uniform geometric shape and / or are uniformly formed, in particular identically formed, with respect to further aspects, which can be said to be a uniform occupation of the aperiodic positions.

[0129] In contrast, Fig. 11f shows, starting from Fig. 11d, a waveguide 1 in which a non-periodic arrangement of structural elements is assumed, with structural elements 10b, 10c of different types at the same time. In this case, the irregularity, clearly defined by a predetermined rule, can be present in the non-periodic arrangement of the structural elements 10b, 10c, or in the occupation state, i.e., in the variation of the structural elements 10b, 10c with respect to one another, or in both the arrangement and the occupation state.

[0130] 12 shows various possible variations of the structural elements (middle row) and possible combinations of these variations (bottom row), which should be understood as exemplary and not exhaustive. The variations shown refer in particular to the occupation of positions by structural elements that are formed non-uniformly but are clearly defined by a predetermined rule. Structural elements whose cross-sectional areas are, for example, localized in periodic or even aperiodic positions within a matrix material can differ from one another, for example, in terms of their shape, their type or refractive index, their substructure, and / or their rotation (and / or local position).

[0131] For example, variations in the geometry of the structural element, in particular its cross-sectional area, can be realized as variations in shape (number of vertices, diameter). Variations in geometry can also be realized as variations in the substructure. The substructure can in particular be such that the structural element, in particular its cross-sectional area, has at least two different regions with different refractive indices, in particular a core and a surrounding cladding (core-clad system).

[0132] In combination, for example, a first type of structural element can have a polygonal cladding and / or a polygonal core, and a second type of structural element can have a circular cladding and a polygonal core (bottom row, first column), in which case the two types of structural elements can be used to occupy, for example, periodic or even aperiodic positions.

[0133] Further, for example, a first type of structural element may have a first refractive index and a first diameter, and a second type of structural element may have a second refractive index and a second diameter (bottom row, second column); a first type of structural element may have a core-clad system with a core having a first diameter, and a second type of structural element may have a core-clad system with a core having a second diameter (bottom row, third column); a first type of structural element may have a core-clad system with a core having a first refractive index, and a second type of structural element may have a core-clad system with a core having a second refractive index. It is also possible for the structural elements to have a clad system (bottom row, fourth column); a first type of structural element to have a first diameter and rotate around a fulcrum external to the structural element, and a second type of structural element to have a second diameter and rotate around a fulcrum external to the structural element (bottom row, fifth column); a first type of structural element to have a core-clad system with a central core, and a second type of structural element to have a core-clad system with a core that rotates around a fulcrum external to the core (bottom row, sixth column), etc.

[0134] FIG. 13a shows a waveguide 1 similar in some respects to the waveguide of FIG. 11c. The waveguide has a first structural element 10a, which may be formed, for example, as a matrix material. Furthermore, the waveguide includes a plurality of structural elements 10b, which may be formed, for example, as filamentary cavities in the matrix material. The structural elements 10b are periodically arranged, but not all of the periodic positions are occupied by structural elements. Thus, FIG. 13a shows the case of a waveguide 1 in which the structural elements or their cross-sectional areas have a non-uniform arrangement that is clearly defined by a predetermined rule. The term "arrangement" here is understood to mean that the structural elements or their cross-sectional areas, or portions thereof, are periodically arranged, some of the periodic positions are occupied, some of the periodic positions are unoccupied, and the occupation is clearly defined by a predetermined rule, i.e., not random.

[0135] FIG. 13b shows a waveguide 1 similar in some respects to the waveguide of FIG. 11f. The waveguide has a first structural element 10a, which may be formed, for example, as a matrix material. Furthermore, the waveguide has a plurality of structural elements 10b having a first diameter and a plurality of structural elements 10c having a second diameter. In this example, the structural elements are arranged aperiodically, and the aperiodic positional relationship may be formed non-uniformly but in a clearly defined manner. Thus, FIG. 13b shows the case of a waveguide 1 in which the structural elements or their cross-sectional areas have a non-uniform, clearly defined arrangement. Here, the term "arrangement" is understood to mean that the structural elements or their cross-sectional areas or parts thereof are arranged aperiodically, and the aperiodic position is defined in a defined manner, i.e., not random, and / or the structural elements have a non-uniform, but clearly defined, variation, such as in the form of two types of structural elements with different diameters.

[0136] FIG. 14 shows several waveguides 1, each having a plurality of structural elements of a first type and a plurality of structural elements of a second type (and possibly further types in FIG. 14d). The waveguides 1 shown here notably lack a matrix material (i.e., are not formed as faceplates), and the structural elements are adjacent to one another. The waveguides 1 shown in FIG. 14 have in common that the various types of structural elements, particularly their cross-sectional areas, are periodically arranged, but the occupation of the periodic positions by the structural elements of each type is nonuniform but in a clearly defined, predetermined order. Thus, the waveguides 1 shown in FIG. 14 are characterized by a regularly defined, nonuniform arrangement of the structural elements or their cross-sectional areas, where the term arrangement is understood to mean that the selection or occupation of the various types of structural elements at the periodic positions is nonuniform but in a clearly defined, predetermined order, i.e., not random.

[0137] FIG. 14a shows, for example, a waveguide 1 having a plurality of structural elements 10a and a plurality of structural elements 10b with different refractive indices.

[0138] 14b shows a waveguide 1 having multiple structural elements 10d and multiple structural elements 10e with different refractive indices and different substructures, where the substructures are defined by substructures 10a and 10b (with refractive indices a and b) or 10a and 10c (with refractive indices a and c), where the substructures are such that structural elements 10d and 10e are formed as a core-clad system with different cores.

[0139] 14c similarly shows a waveguide 1 having multiple structural elements 10d and multiple structural elements 10e with different refractive indices and different substructures, the substructures being defined by substructures 10a and 10b (with refractive indices a and b) or 10c and 10b (with refractive indices c and b), where the substructures have structural elements 10d and 10e formed as a core-clad system with different claddings.

[0140] 14d similarly shows a waveguide 1 having multiple structural elements 10e, multiple structural elements 10f, multiple structural elements 10g, and multiple structural elements 10h with different refractive indices and different substructures, where the substructures are defined by substructures 10a and 10b (with refractive indices a and b), or 10a and 10c (with refractive indices a and c), or 10b and 10d (with refractive indices b and d), or 10c and 10d (with refractive indices c and d), where in the substructures, structural elements 10e, 10f, 10g, and 10h are formed as a core-clad system, with both the cladding and the core being different.

[0141] Figure 14e shows a waveguide 1 having multiple structural elements 10c and multiple structural elements 10d with different geometries and different substructures, where the substructure of structural element 10c is defined by substructure elements 10a and 10b (having refractive indices a and b and a first core diameter), and the substructure of structural element 10d is defined by substructure elements 10a and 10b (having refractive indices a and b and a second core diameter).

[0142] Figure 14f shows a waveguide 1 having multiple structural elements 10c and multiple structural elements 10d with different geometries and different substructures, where the substructure of structural element 10c is defined by substructural elements 10a and 10b (having refractive indices a and b and a centrally located core), and the substructure of structural element 10d is defined by substructural elements 10a and 10b (having refractive indices a and b and an eccentrically located core).

[0143] 15a and 15b show photographs of an example of an actual waveguide 1 in which a plurality of filamentary channels as second-type structural elements 10b are introduced by laser filamentation into a monolithic substrate as a first-type structural element 10a, and these channels have a non-periodic positional relationship, with the non-periodic positions being uneven but clearly defined by a predetermined rule. However, it is also conceivable that, in laser filamentation, a laser may scan the substrate line by line to create a periodicity or a grating. In particular, in such a case, the second-type structural elements 10b formed as filamentary channels may be arranged at periodic positions, with some of the periodic positions being occupied and some of the periodic positions being unoccupied, and the occupation being clearly defined by a predetermined rule.

[0144] FIG. 16a shows a photograph of an example of a waveguide 1 having a first type of structural element 10a with a plurality of fibers having a first refractive index and a second type of structural element 10b with a plurality of fibers having a second refractive index, and FIG. 16b shows an enlarged and simplified view of the same. In this case, the fibers of the structural elements 10a and 10b are adjacent to each other and arranged according to a periodic lattice, with the positions occupied by the types 10a and 10b being unevenly but clearly defined by a predetermined rule. The first type of structural element 10a and the second type of structural element 10b may be surrounded by a third type of structural element 10c formed as a jacket tube. Preferably, the jacket tube has a refractive index lower than both the refractive index of the first type of structural element 10a and the refractive index of the second type of structural element 10b.

[0145] Figure 17 is a photograph showing the state in which the waveguide 1 of Figure 16a is used as an image guide to transmit an image showing the number 5. Here, the non-uniform arrangement of structural elements realizes high-resolution image transmission based on the lateral Anderson localization phenomenon. At the same time, the arrangement according to a predetermined rule realizes locally controllable image sharpness and uniformity.

[0146] In summary, for example, the structural elements, in particular their cross-sectional areas, have a non-uniform arrangement that is clearly defined according to a predetermined rule, and the non-uniform arrangement that is clearly defined according to a predetermined rule (a) The structural elements are formed as a periodic relationship between the structural elements, particularly their cross-sectional areas, and the periodically arranged structural elements have variations formed in a non-uniform but clearly defined manner according to a predetermined rule; The variations between the periodically arranged structural elements are preferably formed as variations in the type of structural element, the refractive index of the structural elements and / or the geometry of the structural elements (e.g., shape, diameter and / or substructure); (b) It is formed as a non-periodic positional relationship of structural elements, especially their cross-sectional areas, and the non-periodic positioning of the structural elements is formed unevenly but in accordance with a clearly defined predetermined rule; Optionally, the structural elements may further have variations that are non-uniform but are formed as clearly defined by predetermined rules. and / or (c) structural elements at periodic positions, in particular formed as a relationship of their cross-sectional areas, some of the periodic positions being occupied and some of the periodic positions being unoccupied, the occupation being formed as clearly defined by predetermined rules; Optionally, the structural elements may further have variations that are non-uniform but are formed as clearly defined by predetermined rules. A waveguide 1 can be envisaged.

[0147] As mentioned above, the structural elements may differ from one another in their shape or geometry. In particular, when the waveguide is formed as a fiber rod by a fiber drawing process of the preform, which may be repeated multiple times if necessary, the initial shape or geometry can be retained, but thermal and possibly mechanical influences may also lead to deformations in the waveguide. In particular, at least some of the structural elements may take the form of hexagons and / or hyperbolic polygons, in particular triangles or hexagons. The introduction of structural elements by laser processing may also involve variations in such geometry, for example by appropriately directing the laser beam or laser radiation and / or optically adjusting its beam profile.

Claims

1. 1. A waveguide (1) for transmitting electromagnetic waves, in particular image information, from a proximal end (2) of the waveguide to a distal end (4) of the waveguide along a transmission direction (5) extending between the proximal and distal ends, in a cross section extending transversely to the transmission direction, the waveguide (1) comprising: The optical element includes a plurality of structural elements (10), including at least two types of structural elements, namely, a first type (10a) having a first refractive index and a second type (10b) having a second refractive index; a waveguide (1) in which each of the structural elements (10) extends along the transmission direction (5) and proportionately spans the cross section of the waveguide (1), defining a plurality of cross-sectional areas (20) in the cross section of the waveguide (1), each of the cross-sectional areas (20) corresponding to the cross section of an individual structural element (10); A waveguide (1), characterized in that the structural element (10), in particular its cross-sectional area (20), is formed non-uniformly but in a well-defined manner according to a predetermined rule.

2. the structural elements, in particular the cross-sectional areas, have a predetermined, non-uniform, in particular aperiodic, arrangement that is clearly defined according to a predetermined rule; and / or the structural elements, in particular their cross-sectional areas, have regularly defined, non-uniform, in particular mutually different, geometric shapes, for example non-uniform diameters, and / or 2. The waveguide according to claim 1, wherein the structural elements have non-uniform, in particular mutually different, refractive indices that are clearly defined according to a predetermined rule.

3. the structural element, in particular its cross-sectional area, is non-uniformly shaped, so that the electromagnetic waves transmitted by the waveguide remain localized in a direction extending transversely to the direction of transmission, thereby transmitting in particular image information; and / or the structural elements, in particular their cross-sectional areas, are formed in a prescribed manner, so that the waveguide has a reproducible structure, in particular so that further waveguides can be produced which have an identical structure to the waveguide; and / or 3. A waveguide according to claim 1 or 2, wherein the structure of the waveguide defined by the cross-sectional areas of the structural elements in the cross section is similar in a mathematical sense, in particular invariant, along the direction of propagation.

4. The rules, which in particular define the arrangement of the cross-sectional areas, the geometric shape of the cross-sectional areas and / or the refractive index of the structural elements, are:

4. A waveguide according to claim 1, comprising the specification of characteristic values ​​of each structural element by deterministic definition, in particular for defining the position of the cross-sectional area, the area of ​​the cross-sectional area or the refractive index of each structural element.

5. said well-defined rules, in particular deterministic rules for specifying characteristic values, comprise in particular a mathematical sequence of set values; the sequence of values ​​is preferably formed as a non-uniformly distributed sequence, and / or 5. The waveguide according to claim 1, wherein the sequence of values ​​is preferably formed as a deterministic sequence, for example as a Halton sequence, a Sobol sequence, a Niederreiter sequence, a Hammersley sequence, a Fowle sequence, or a combination of several sequences.

6. The well-defined rules, in particular the deterministic rules for specifying the property values, are: Referencing a particular value of a deterministic sequence to specify a property value of a particular structural element; referencing further values ​​of said deterministic sequence to specify property values ​​of further structural elements; checking whether the value or the characteristic value of the further structural element violates a predetermined condition, taking into account in particular the value or the characteristic value of the specific structural element, and if so, discarding said further value and referring to a still further value of said deterministic sequence for specifying said characteristic value of said further structural element, or modifying said further value in a predetermined manner so that said predetermined condition is met or is no longer violated.

6. A waveguide according to any one of claims 1 to 5, comprising:

7. 7. A waveguide according to claim 6, wherein the predetermined condition is formed as a defined minimum difference in the value or characteristic value, in particular as a defined minimum distance between positions of the cross-sectional areas of the structural elements.

8. The distribution of the area of ​​the Voronoi regions of the cross-sectional areas of at least one type of structuring element, in particular with respect to the positions relative to the generating points, satisfies at least one of the following conditions: (1) The variance V of the distribution ｄ is the variance V of the corresponding distribution for a random position of the cross-sectional area ｚ Smaller, ratio V ｚ / V ｄ is preferably 0 to 10, in particular greater than 1, preferably greater than 2, most preferably greater than 2.5, and / or less than 8, preferably less than 7, most preferably less than 6.5, and / or (2) The variance V of the distribution ｄ is 0.38 / N ２．０３３ where N represents the number of structural elements of at least one type; and / or (3) The variance V of the distribution ｄ is greater than the variance of the corresponding distribution for the periodic positions of the cross-sectional area, and the variance V ｄ is preferably greater than 0, in particular 10 －１０ greater than 10, preferably 10 －９ greater than 10, most preferably －８ Greater than 8. The waveguide according to claim 1, wherein:

9. the ratio of the total area of ​​the cross-sectional areas of the first type of structural elements to the total area of ​​the cross-sectional areas of the second type of structural elements is in the range of 1:9 to 9:1, preferably in the range of 3:7 to 7:3, particularly preferably in the range of 4:6 to 6:4; and / or the total area of ​​the cross-sectional areas of the structural elements of each type is at least 1 / (10 x T), preferably at least 1 / (5 x T), particularly preferably at least 1 / (3 x T) of the cross-sectional area, where T represents the number of types; and / or The first refractive index of the structural elements of the first type and the second refractive index of the structural elements of the second type are at least 10 －４ differ by at least 10 －３ differ by at least 10 －２ differ by at least 10 －１ 9. A waveguide according to claim 1, wherein the radii differ by at least one, in particular by at least two, in particular by at least three, in particular by at least four.

10. At least one cross-sectional area has a diameter of 100 nm to 50 μm, preferably 400 nm to 20 μm, particularly preferably 1 μm to 16 μm, and / or At least one cross-sectional area has a diameter of 0.1 to 10 times the mean wavelength, preferably 0.2 to 5 times the mean wavelength, particularly preferably 0.5 to 2 times the mean wavelength, and / or 10. A waveguide according to any one of claims 1 to 9, wherein at least one cross-sectional area has a polygonal, e.g. pentagonal or hexagonal, geometric shape.

11. a structural element of the first type and a plurality of structural elements of the second type; the structural elements of the first type are in particular formed as a monolithic body using or made of a first medium, the first medium having the first refractive index, 11. A waveguide according to any one of claims 1 to 10, wherein the structural elements of the second type are formed as cavities in the substrate, the cavities preferably forming the second refractive index.

12. the cavities in the substrate are formed as filamentary channels, which are introduced into the substrate by a laser beam, in particular an ultrashort pulse laser; the filamentary channels in the substrate have been post-treated, preferably chemically, in particular by etching, to smooth the contours of the channels; 12. A waveguide according to any one of claims 1 to 11, wherein the waveguide preferably has a larger dimension in the cross section than along the direction of transmission, the waveguide preferably being formed as a faceplate.

13. the waveguide has an area in the cross section of at least 4 square millimeters, preferably at least 2500 square millimeters, particularly preferably at least 10000 square millimeters; and / or 13. The waveguide according to claim 1, wherein the waveguide has a dimension in the cross section that is at least twice the dimension along the transmission direction, preferably at least five times the dimension along the transmission direction, particularly preferably at least ten times the dimension along the transmission direction.

14. the cavity in the substrate is formed by additive manufacturing of the substrate and / or is introduced into the substrate by a subtractive process, in particular as a bore, the bore being introduced into the substrate in particular by mechanical drilling, 14. The waveguide according to claim 1, wherein the waveguide is preferably manufactured in a multi-draw process, in particular such that the waveguide comprises at least one second plurality of structural elements in addition to the plurality of structural elements, and the waveguide has at least two surface areas in the cross section, each of the surface areas comprising a cross-sectional area of ​​one of both plurality of structural elements and having the same structure except for rotation.

15. the waveguide has a dimension along the transmission direction of less than 10 millimeters, preferably less than 6 millimeters, particularly preferably less than 5 millimeters, in particular when the waveguide is formed as a faceplate, or 15. The waveguide according to claim 1, wherein the waveguide has a dimension along the transmission direction that is greater than the cross-sectional dimension, in particular of at least 10 millimeters, preferably at least 20 millimeters, particularly preferably at least 50 millimeters, and even more preferably at least 100 millimeters.

16. 16. A waveguide according to claim 15, wherein the cavities in the substrate, in particular the filamentary channels and / or the bores, are filled with a second medium, the second medium having the second refractive index.

17. at least one structural element, in particular a structural element of the first type, in particular a structural element formed as a substrate, comprises or consists of one or more of the following materials as a medium: glass, quartz glass, polymer, crystalline, monocrystalline, polycrystalline material and / or glass ceramic; and / or 17. The waveguide according to claim 1, wherein at least one structural element, in particular a structural element of the first type, in particular a structural element formed as a substrate, comprises or consists of a material, in particular an infrared-transparent material, in particular a chalcogenide, in particular a material comprising at least one element from the group oxygen, sulfur, selenium and tellurium and at least one element from the group arsenic, germanium, phosphorus, antimony, lead, boron, aluminum, gallium, indium, titanium, sodium, as a medium, which has an attenuation of less than or equal to 50 dB / m, in particular less than or equal to 10 dB / m, in particular less than or equal to 1 dB / m in the wavelength range from 2 μm to 20 μm.

18. 18. A waveguide according to any one of claims 1 to 17, wherein at least one structural element, in particular a structural element of the second type, in particular a cavity in the substrate filled with a second medium, comprises or consists as medium of one or more of the materials listed in any one of claims 1 to 17 for the structural elements of the first type, in particular a material not included in the structural elements of the first type.

19. a plurality of structural elements of the first type and a plurality of structural elements of the second type; the structural elements of the first type are formed using or made of a first medium, in particular as rod-shaped or tubular bodies, the first medium having the first refractive index, the structural elements of the second type are formed using or made of a second medium, in particular as rod-shaped or tubular bodies, the second medium having the second refractive index, or 19. A waveguide according to any one of claims 1 to 18, wherein the structural elements of the second type are formed as cavities within the structural elements of the first type, the cavities preferably forming the second refractive index.

20. A waveguide for transmitting electromagnetic waves, in particular image information, from a proximal end of the waveguide to a distal end of the waveguide along a transmission direction extending between the proximal and distal ends, in a cross section extending transversely to the transmission direction, in particular a waveguide according to any one of claims 1 to 19, wherein the waveguide comprises: a plurality of structural elements, including at least two types of structural elements, a first type having a first refractive index and a second type having a second refractive index; each of the structural elements extends along the propagation direction and spans the cross section of the waveguide proportionally, the cross section of the waveguide defining a plurality of cross-sectional areas, each of the cross-sectional areas corresponding to the cross section of an individual structural element; The waveguide has a larger dimension in the cross section than along the direction of transmission.

21. a structural element of the first type and a plurality of structural elements of the second type; the structural elements of the first type are in particular formed as a monolithic body using or made of a first medium, the first medium having the first refractive index, the structural elements of the second type are formed as cavities in the substrate, the cavities preferably forming the second refractive index; the cavities in the substrate are formed as filamentary channels, which are introduced into the substrate by a laser beam, in particular an ultrashort pulse laser; the filamentary channels in the substrate have been post-treated, preferably chemically, in particular by etching, to smooth the contours of the channels; 21. A waveguide according to claim 20, wherein cavities in the substrate formed as said filamentary channels are preferably filled with a second medium, said second medium having said second refractive index.

22. the waveguide has an area in the cross section of at least 4 square millimeters, preferably at least 2500 square millimeters, particularly preferably at least 10000 square millimeters; and / or the waveguide has a dimension in the cross section that is at least twice its dimension along the transmission direction, preferably at least five times its dimension along the transmission direction, particularly preferably at least ten times its dimension along the transmission direction; and / or 22. The waveguide according to claim 20 or 21, wherein the waveguide has a dimension along the direction of transmission of less than 10 mm, preferably less than 6 mm, particularly preferably less than 5 mm.

23. A waveguide for transmitting electromagnetic waves, in particular image information, from a proximal end of the waveguide to a distal end of the waveguide along a transmission direction extending between the proximal and distal ends, in a cross section extending transversely to the transmission direction, in particular a waveguide according to any one of claims 1 to 19, wherein the waveguide comprises: a plurality of structural elements, including at least two types of structural elements, a first type having a first refractive index and a second type having a second refractive index; each of the structural elements extends along the propagation direction and spans the cross section of the waveguide proportionally, the cross section of the waveguide defining a plurality of cross-sectional areas, each of the cross-sectional areas corresponding to the cross section of an individual structural element; 23. A waveguide, in particular according to any one of claims 1 to 22, wherein at least one of the structural elements has an attenuation in the wavelength range from 2 μm to 20 μm of less than or equal to 50 dB / m, in particular less than or equal to 10 dB / m, in particular less than or equal to 1 dB / m, and in particular comprises or consists of an infrared-transparent material.

24. 24. A waveguide according to claim 23, wherein at least one structural element, in particular a structural element formed as a substrate, comprises or consists of a chalcogenide, said chalcogenide in particular comprising at least one element from the group of oxygen, sulfur, selenium and tellurium, and at least one element from the group of arsenic, germanium, phosphorus, antimony, lead, boron, aluminum, gallium, indium, titanium, sodium.

25. A method for manufacturing a waveguide (1), in particular according to any one of claims 1 to 24, said method comprising the steps of: providing one structural element (10a) of a first type, in particular in the form of a monolithic substrate made of or consisting of a first medium, and having a first refractive index; introducing a plurality of structural elements (10b) of a second type having a second refractive index, for this purpose introducing cavities in said substrate and filling said cavities preferably with a second medium, introducing said second type of structural elements (10b) so that each of said structural elements (10b) proportionately spans a cross section of said waveguide (1) and defines a plurality of cross-sectional areas (20) in said cross section of said waveguide (1), each of said cross-sectional areas (20) corresponding to said cross section of an individual structural element (10b) of said second type, introducing said second type of structural elements (10b), so that said cross-sectional areas (20) of said second type of structural elements (10b) have a non-uniform, in particular aperiodic, but regularly well-defined arrangement and / or a non-uniform, but regularly well-defined geometric shape, for example a diameter.

26. In particular, the rules defining the arrangement of the cross-sectional areas and / or the geometric shapes are:

26. A method for manufacturing a waveguide according to claim 25, comprising specifying characteristic values ​​of each structural element of said second type by means of a deterministic prescription, in particular for defining the position and / or the area of ​​said cross-sectional area of ​​each structural element.

27. said well-defined rules, in particular deterministic rules for specifying characteristic values, comprise in particular a mathematical sequence of set values; the sequence of values ​​is preferably formed as a non-uniformly distributed sequence, and / or 27. A method for producing a waveguide according to claim 25 or 26, wherein the sequence of values ​​is preferably formed as a deterministic sequence, for example as a Halton sequence, as a Sobol sequence, as a Niederreiter sequence, as a Hammersley sequence, as a Fowle sequence or as a combination of several sequences.

28. The well-defined rules, in particular the deterministic rules for specifying the property values, are: Referencing a particular value of a deterministic sequence to specify a property value of a particular structural element; referencing further values ​​of said deterministic sequence to specify property values ​​of further structural elements; checking whether the value or the characteristic value of the further structural element violates a predetermined condition, taking into account in particular the value or the characteristic value of the specific structural element, and if so, discarding said further value and referring to a still further value of said deterministic sequence for specifying said characteristic value of said further structural element, or modifying said further value in a predetermined manner so that said predetermined condition is met or is no longer violated. A method for manufacturing a waveguide according to any one of claims 25 to 27, comprising:

29. 29. The method for manufacturing a waveguide according to claim 25, wherein the predetermined condition is formed as a defined minimum difference in the value or characteristic value, in particular as a defined minimum distance between the positions of the cross-sectional areas of the structural elements.

30. The distribution of the area of ​​the Voronoi regions of the cross-sectional areas of at least one type of structuring element, in particular with respect to the positions relative to the generating points, satisfies at least one of the following conditions: (1) The variance V of the distribution ｄ is the variance V of the corresponding distribution for a random position of the cross-sectional area ｚ Smaller, ratio V ｚ / V ｄ is preferably 0 to 10, in particular greater than 1, preferably greater than 2, most preferably greater than 2.5, and / or less than 8, preferably less than 7, most preferably less than 6.5, and / or (2) The variance V of the distribution ｄ is 0.38 / N ２．０３３ where N represents the number of structural elements of at least one type; and / or (3) The variance V of the distribution ｄ is the variance V of the corresponding distribution for the periodic positions of the cross-sectional area ｐ The variance V ｄ is preferably greater than 0, in particular 10 －１０ greater than 10, preferably 10 －９ greater than 10, most preferably －８ Greater than 30. The method for manufacturing a waveguide according to claim 25, wherein the above formula (1) is satisfied.

31. said cavities being introduced as filamentary channels in said substrate by means of a laser beam, in particular an ultrashort pulse laser, 31. A method for producing a waveguide according to any one of claims 25 to 30, in particular before filling the filamentary channels with a second medium, wherein the filamentary channels in the substrate are post-treated, preferably chemically, in particular by etching, in order to smooth the contours of the channels.

32. 32. A method for producing a waveguide according to claim 25, wherein the cavities are introduced into the substrate at intervals greater than the diameter of the cavities, preferably at intervals twice the diameter of the cavities, particularly preferably at intervals three times the diameter of the cavities.

33. 33. A method for manufacturing a waveguide according to any one of claims 25 to 32, wherein the cavity in the substrate is produced by additive manufacturing of the substrate and / or is introduced into the substrate by a subtractive process, in particular by mechanical drilling.

34. said substrate comprises or consists of one or more of the following materials as a medium: glass, quartz glass, polymer, crystalline, monocrystalline, polycrystalline material and / or glass ceramic; and / or the substrate comprises or consists as a medium of an in particular infrared-transparent material, in particular a chalcogenide, in particular a material comprising at least one element from the group oxygen, sulfur, selenium and tellurium, and at least one element from the group arsenic, germanium, phosphorus, antimony, lead, boron, aluminum, gallium, indium, titanium, sodium, which has an attenuation of less than or equal to 50 dB / m, in particular less than or equal to 10 dB / m, in particular less than or equal to 1 dB / m in the wavelength range from 2 μm to 20 μm; and / or 34. A method for manufacturing a waveguide according to any one of claims 25 to 33, wherein at least one structural element of the second type comprises or consists, as a medium, of one or more of the materials listed above for the substrate of the first type, in particular a material not included in the structural elements of the first type.

35. A waveguide (1) according to any one of claims 1 to 24 and one or more further waveguides (1) according to any one of claims 1 to 24 are arranged in parallel transmission directions to form a preform (30), A method for manufacturing a waveguide, particularly according to any one of claims 25 to 34, wherein the array of waveguides is drawn together along the transmission direction.

36. dividing the aligned and drawn waveguide into sections transverse to the direction of transmission; the sections are again arranged with their directions of transmission parallel to one another to form a preform (40); 36. The method of claim 35, further comprising regrouping the aligned sections and drawing them along the direction of transmission.

37. arranging the waveguides and / or the sections, respectively, such that the arrangement of the arrangement is clearly defined by a predetermined rule, in particular according to any one of claims 2 to 9; and / or Arranging the waveguides and / or the sections, respectively, so that the structures formed by the cross-sectional areas of the second structural elements in the cross-section are rotated relative to one another in a particular predetermined manner, in particular not rotated relative to one another, to form a preform; and / or 37. Method for manufacturing a waveguide according to any one of claims 25 to 36, wherein the waveguides and / or the sections, respectively, are arranged in an automated manner, in particular with robotic assistance.

38. 38. A method for producing a waveguide according to any one of claims 25 to 37, wherein the aligned and drawn waveguides and / or the aligned and drawn sections are fused together by application of heat and / or pressure, in particular under vacuum.

39. 39. A method for manufacturing a waveguide according to any one of claims 25 to 38, comprising producing two or more similarly formed waveguides in which the cross-sectional areas of the second type of structural elements each have an identical, non-uniform, but regularly defined arrangement and / or an identical, non-uniform, but regularly defined geometric shape, e.g. diameter.

40. A waveguide, in particular according to any one of claims 1 to 24, produced or producible by a method according to any one of claims 25 to 39.

41. A set comprising two or more waveguides, each of which has been produced or is producible by a method, in particular according to one of claims 25 to 39, in particular according to one of claims 1 to 24, each of said waveguides comprises a plurality of structural elements, said structural elements, in particular their cross-sectional areas, being formed non-uniformly but in a well-defined manner according to a predetermined rule; The two or more waveguides are similarly formed such that the structural elements, particularly their cross-sectional areas, are similarly non-uniformly formed.

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