Antiresonant hollow core fiber

Abstract

To provide an antiresonant hollow core fiber that can be manufactured accurately in a reproducible manner, and indicates low attenuation.SOLUTION: An antiresonant hollow core fiber 1000 comprises: a fiber cladding 2000 including an inner bore 2200; a fiber longitudinal axis 2300 and a fiber core radius R_Faser 2310; and some antiresonant units 3000. The antiresonant units each include an ARE element, an NE element, and a DNE element. The antiresonant units are arranged at desired positions inside the inner bore at an interval from each other so as not to be in contact with each other. In the antiresonant unit, the ARE element has a circular cross section, the NE element is arranged in a first inside of the ARE element, and the DNE element is arranged at least partially in a second inside of the NE element.SELECTED DRAWING: Figure 7

Description

Technical Field

[0001] The present invention relates to an anti-resonant hollow-core fiber.

Background Art

[0002] A hollow-core fiber has a core filled with a gas or a liquid and having a vacuum cavity. In a hollow-core fiber, the interaction between light and the core material is smaller than that in a solid-core fiber. Since the refractive index of the core is smaller than that of the surrounding fiber cladding, light transmission by total reflection is impossible. Hollow-core fibers are classified into "photonic bandgap fibers" and "anti-resonant hollow-core fibers" according to the physical mechanism of light transmission.

[0003] In an embodiment of a hollow-core fiber called an "anti-resonant hollow-core fiber" (ARHCF), the hollow-core region is surrounded by a fiber cladding, and therein is disposed something known as an "anti-resonance unit" (also known as an "anti-resonant element" or "ARE"). The walls of the anti-resonance units evenly distributed around the hollow core can act as Fabry-Perot cavities operating in anti-resonance, thereby reflecting incident light and thus enabling guided waves within the fiber core.

[0004] This technology promises a hollow-core fiber with low optical attenuation, a very wide transmission spectrum (even in the UV or IR wavelength ranges), and little latency during data transmission.

[0005] From International Publication No. WO 2019 / 053412 (A1), an anti-resonant hollow-core fiber is known in which a hollow core having anti-resonance units is surrounded by a fiber cladding. These anti-resonance units are three elements nested within each other, ● an outer ARE element, and ●An NE element arranged within the ARE element, ●A DNE element arranged within the NE element, and has.

[0006] However, this design has an unfavorable correlation between, ●On one hand, the waveguide loss in the fundamental mode, and ●On the other hand, the difference in the effective mode refractive index between the high-order core mode and the ARE mode with high loss, and is known to be disadvantageous.

[0007] Therefore, such an antiresonant hollow-core fiber is not suitable for applications in the field of telecommunications in particular.

Summary of the Invention

Problems to be Solved by the Invention

[0008] There is a need for an antiresonant hollow-core fiber having a low waveguide loss for industrial use. Furthermore, there is a need for an antiresonant hollow-core fiber that can be manufactured easily and on a large scale. This is the only way to keep the cost of the antiresonant hollow-core fiber within a reasonable range. It is important to note that an antiresonant hollow-core fiber that gives good results on a laboratory scale is not necessarily suitable for large-scale use.

[0009] An object of the present invention is to provide an antiresonant hollow-core fiber that overcomes the above-mentioned drawbacks.

[0010] An object of the present invention is to provide an antiresonant hollow-core fiber that can be manufactured accurately and reproducibly and that furthermore exhibits low attenuation.

[0011] In particular, an object of the present invention is to provide an antiresonant hollow-core fiber having a particularly low waveguide loss.

[0012] In particular, an object of the present invention is to provide an antiresonant hollow-core fiber that efficiently attenuates high-order modes within the fiber core.

[0013] In particular, an object of the present invention is to provide an anti-resonant hollow-core fiber having a favorable correlation between low waveguide loss in the fundamental mode on the one hand and efficient attenuation of higher-order modes in the core on the other hand.

Means for Solving the Problems

[0014] At least partial realization of at least one of the foregoing objects is made by the features of the independent claims. The dependent claims provide preferred embodiments contributing to at least partial realization of at least one of the objects.

[0015] The following embodiments of the anti-resonant hollow-core fiber contribute at least in part to realizing at least one of the foregoing objects. [1.] A first embodiment of an anti-resonant hollow-core fiber, a fiber cladding having an internal bore, a fiber longitudinal axis and a fiber core radius R_Faser, and a plurality of anti-resonant units, each anti-resonant unit comprising ● an ARE element, ● an NE element, ● a DNE element, and being provided with The anti-resonant units are spaced apart from each other and arranged at desired positions inside the internal bore so as not to contact each other, In the anti-resonant unit, ● the ARE element has a circular cross-section, ● the NE element is arranged inside the first of the ARE elements, ● the DNE element is at least partially arranged inside the second interior (3470) of the NE element. According to the present invention, in this embodiment, in at least one anti-resonant unit, ● the NE element has an arcuate cross-section and is connected to the DNE element along two connection seams, ● the DNE element has an oval cross-section, ● In a cross-section, the sum of the distances from two foci to any point on the DNE element wall is the same within a range of less than 15% of the sum of the distances for all points. [2.] A further embodiment of the anti-resonant hollow core fiber having the characteristics of the first embodiment is characterized in that, in a cross-section, the sum of the distances from two foci to any point on the DNE element wall is the same within a range of less than 10%, particularly less than 5% of the sum of the distances for all points. [3.] A further embodiment of the anti-resonant hollow core fiber having the characteristics of at least one of the two foregoing embodiments is characterized in that the DNE element has a longest cross-sectional axis AL and a shortest cross-sectional axis AK. [4.] A further embodiment of the anti-resonant hollow core fiber having the characteristics of the third embodiment is ● The longest cross-sectional axis AL extends substantially parallel to the inner bore and / or ● The shortest cross-sectional axis AK is substantially perpendicular to the inner bore and aligned with the fiber longitudinal axis, such that the DNE element is arranged. [5.] A further embodiment of the anti-resonant hollow core fiber having the characteristics of the third or fourth embodiment is characterized in that the following applies to the ratio of the longest cross-sectional axis AL to the shortest cross-sectional axis AK.

[0016]

Number

[0017] [Number] [8.] A further embodiment of the anti-resonant hollow core fiber having at least one feature of Embodiments 1 to 7 is characterized in that the following applies to the ratio obtained by multiplying the NE internal height H_NE by twice the NE circle radius NE_R and dividing by the fiber core surface area A_Faser. ● The ratio is 0.4 or more, particularly 0.50 or more, particularly 0.56 or more, ● The ratio is 0.65 or less, particularly 0.62 or less, particularly 0.6 or less. [9.] A further embodiment of the anti-resonant hollow core fiber having at least one feature of Embodiments 1 to 8 is characterized in that the following applies to the ratio obtained by dividing the ARE internal height H_ARE by the core radius R_Faser.

[0018] [Number] [10.] A further embodiment of the anti-resonant hollow core fiber having at least one feature of Embodiments 1 to 9 is characterized in that the following applies to the ratio obtained by dividing the ARE internal height H_ARE by the core radius R_Faser. ● The ratio is 0.9 or more, particularly 0.95 or more, particularly 1.0 or more, ● The ratio is 1.2 or less, particularly 1.15 or less, particularly 1.1 or less. [11.] A further embodiment of the anti-resonant hollow core fiber having at least one feature of Embodiments 1 to 10 is characterized in that the following applies to the ratio obtained by multiplying the ARE internal height H_ARE by twice the NE circle radius NE_R and dividing by the NE internal surface area A_NE.

[0019]

Number

[0020] Detailed Description of the Invention Some of the features described are associated with the term "substantially". The term "substantially" should be understood such that under actual conditions and manufacturing techniques, a mathematically exact interpretation of terms such as "elliptical", "vertical", "parallel", "diameter", or "oval" is not strictly carried out, but only within a specific manufacturing error tolerance. For example, "substantially parallel axes" include angles from -10 degrees to 10 degrees, particularly -5 degrees to 5 degrees, relative to each other. For example, a "device substantially made of fused silica" includes a fused silica content from 95 wt% to 100 wt%. Further, "substantially perpendicular" includes angles from 85 degrees to 95 degrees. Further explanations of the term "substantially" for some features are provided below.

[0021] The above object is achieved, at least in part, by an anti-resonant hollow-core fiber comprising a fiber cladding (also called a cladding) having an internal bore, a fiber longitudinal axis and a fiber core radius R_Faser, and a plurality of anti-resonant units, each of the anti-resonant units comprising ● an ARE element, ● a NE element, ● a DNE element, and the plurality of anti-resonant units are spaced apart from each other and arranged so as not to contact each other at desired positions inside the internal bore, and in the anti-resonant unit, ● the ARE element has a circular cross-section, ● the NE element is arranged inside a first interior of the ARE element, ● the DNE element is at least partially arranged inside a second interior of the NE element.

[0022] In this case, in at least one anti-resonant unit, ● the NE element has an arcuate cross-section and is connected to the DNE element along two connection seams, ● the DNE element has an oval cross-section, ● In a cross-section, the sum of the distances from two foci to any point on the DNE element wall is the same within a range of less than 15% of the sum of the distances at all points.

[0023] Surprisingly, it has been found that the elliptical shape of the DNE element combined with the arc-shaped cross-section of the NE element is advantageous for the waveguide loss in the fundamental mode.

[0024] The following modes are considered. ● Fundamental mode in the core. ○ Also called the core fundamental mode, it propagates within the fiber core. ● Higher-order mode in the core. ○ Also called the higher-order core mode (HOM). ● Mode in the ARE element. ○ Also called the ARE mode, it propagates within the first interior of the ARE element. ● Mode in the NE element. ○ Also called the NE mode, it propagates within the second interior of the NE element. ● Mode in the DNE element. ○ Also called the DNE mode, it propagates within the third interior of the DNE element.

[0025] The confinement loss (also known as waveguide loss or propagation loss) indicates the attenuation of each mode.

[0026] The effective mode refractive index n eff represents the phase velocity of each mode in the propagation direction along the fiber longitudinal axis through the relationship v phase = c / n eff where c represents the speed of light in a vacuum.

[0027] The mode refractive index difference Δn eff (ARE) represents the difference between the effective mode refractive index of the higher-order mode in the core and the effective mode refractive index of the ARE mode. Δn eff (ARE) = n eff,core-HOM - n eff,ARE mode

[0028] Equivalently, the mode refractive index difference Δn eff (NE) is the difference between the effective mode refractive index of the higher-order mode in the core and the effective mode refractive index of the NE mode. Δn eff (NE) = n eff,core-HOM - n eff,NE mode

[0029] When the mode refractive index difference Δn eff is close to 0, the two modes under consideration propagate at substantially the same phase propagation speed and can therefore couple coherently (phase-lock), resulting in effective energy coupling. In this case, the energy of the higher-order core mode couples to the ARE mode or NE mode with high loss. Therefore, the energy from the higher-order core mode moves to the mode of the antiresonant element, which leads to an improvement in the fundamental mode.

[0030] In the simulations described in more detail below, the effective mode refractive index n eff was extracted from the propagation constant β of each mode. The mode "j" is the solution of a physical system of equations. E j (x, y, z, t) = amplitude j (x, y) * exp(i * (β j * z - t)ω * t)) where ● E j (x, y, z, t) represents the electric field distribution in the three spatial dimensions x, y, z at time t, ● amplitude j (x, y) represents the transverse electric field distribution.

[0031] Therefore, the propagation constant β represents the phase characteristics of wave propagation along the fiber axis z. Based on the wavelength λ of light, the effective mode refractive index n eff of mode "j" is directly obtained from β. β j = 2 * pi / λ * neff,j

[0032] The propagation constant (β j ) of the j-th mode is generally a complex parameter as the solution of the simulation. The real part gives n_eff,j, while the waveguide loss can be derived from the imaginary part.

[0033] As will be described in more detail, the design of the DNE element results in an effective coupling between the higher-order modes in the core and the modes in the DNE element, such that only the fundamental mode propagates in the core after a short distance of travel. Preferably, the DNE element of the anti-resonant hollow-core fiber described has an elliptical cross-section. Here, a closed oval curve is called an ellipse, and the sum of the distances from two points, i.e., the foci, to an ellipse point is the same at all points. However, due to manufacturing tolerances, the cross-section of the DNE element of the disclosed anti-resonant hollow-core fiber will never be mathematically exactly elliptical. Rather, the cross-section of the DNE element optimally approximates an elliptical shape. Thus, the DNE element has an oval cross-section, and in the cross-section, the sum of the distances from two foci to any point on the DNE element wall is the same within a range of less than 15% of the sum of the distances at all points on the DNE element wall. This deviation from the optimal elliptical cross-section is, on the one hand, realistic from a manufacturing perspective and, on the other hand, continues to yield excellent results in guiding waves.

[0034] A further embodiment is characterized in that, in the cross-section, the sum of the distances from two foci on the DNE element wall to any point on the DNE element wall is the same within a range of less than 10%, particularly less than 5% of the sum of the distances at all points.

[0035] A further embodiment is characterized in that, in the cross-section, the DNE element has a longest cross-sectional axis AL and / or a shortest cross-sectional axis AK. The longest cross-sectional axis AL is the axis passing through two points on the DNE element wall that have the maximum distance from each other. The shortest cross-sectional axis AK is the axis passing through two points on the DNE element wall that have the minimum distance from each other. In particular, one or both of the cross-sectional axes are the axis of symmetry of the DNE element.

[0036] A further embodiment is characterized in that the focus is arranged on the longest cross-sectional axis AL. In this embodiment, the oval cross-section of the DNE element becomes closer to an elliptical shape, which has a favorable effect on waveguide loss.

[0037] A further embodiment is characterized in that, for at least one anti-resonance unit, the longest cross-sectional axis AL extends parallel to the circular tangent within an angular interval of [-10 degrees; 10 degrees], where the circular tangent is perpendicular to the inner radius of the cladding. In other words, the longest cross-sectional axis AL extends substantially parallel to the inner bore. In this embodiment, the oval cross-section of the DNE element becomes closer to an elliptical shape, which has a favorable effect on waveguide loss.

[0038] A further embodiment is that, for at least one anti-resonance unit, the shortest cross-sectional axis AK ● is parallel to the inner radius of the cladding within an angular interval of [-10 degrees; 10 degrees], and / or ● is within [-2 μm; 2 μm] of the fiber longitudinal axis and extends.

[0039] In other words, the shortest cross-sectional axis AK is substantially perpendicular to the inner bore.

[0040] A further embodiment is characterized in that the following applies to the ratio of the longest cross-sectional axis AL to the shortest cross-sectional axis AK.

[0041]

Number

[0042] This embodiment results in further optimization of waveguide loss.

[0043] A further embodiment is characterized in that the following applies to the ratio of the longest cross-sectional axis AL to the shortest cross-sectional axis AK. ● The ratio is 1.15 or more, particularly 1.20 or more, particularly 1.25 or more, particularly 1.50 or more, ● The ratio is 3.80 or less, particularly 3.60 or less, particularly 3.50 or less.

[0044] By using the DNE element having an elliptical cross-section with the ratio of the cross-sectional axis described above, the waveguide loss can be further reduced.

[0045] A further embodiment is characterized in that the following is applied to the ratio obtained by multiplying the NE internal height H_NE by twice the NE circle radius NE_R and dividing by the fiber core surface area A_Faser.

[0046]

Number

[0047] This embodiment is characterized in that the mode refractive index difference Δn eff (NE) is small, which means that the fundamental mode in the fiber is reached after a short distance of travel and the waveguide loss is also low.

[0048] A further embodiment is characterized in that the following is applied to the ratio obtained by multiplying the NE internal height H_NE by twice the NE circle radius NE_R and dividing by the fiber core surface area A_Faser. ● The ratio is 0.4 or more, particularly 0.50 or more, particularly 0.56 or more, ● The ratio is 0.65 or less, particularly 0.62 or less, particularly 0.6 or less.

[0049] The design of the anti-resonant hollow core fiber based on these parameters results in a further reduction of the mode refractive index difference Δn eff (NE). This leads to a further reduction in the travel distance required to achieve the fundamental mode.

[0050] A further embodiment is characterized in that the following is applied to the ratio of the ARE internal height H_ARE divided by the core radius R_Faser.

[0051]

Number

[0052] This embodiment is characterized in that the modal refractive index difference Δn eff (ARE) is small. As a result, the fundamental mode in the fiber is achieved after a short distance of movement.

[0053] A further embodiment is characterized in that the following applies to the ratio of the ARE internal height H_ARE divided by the core radius R_Faser. ● The ratio is 0.9 or more, particularly 0.95 or more, particularly 1.0 or more, ● The ratio is 1.2 or less, particularly 1.15 or less, particularly 1.1 or less.

[0054] The design of the anti-resonant hollow-core fiber based on these parameters results in a further reduction of the modal refractive index difference Δn eff (ARE). This leads to a further reduction in the movement distance required to achieve the fundamental mode.

[0055] A further embodiment is characterized in that the following applies to the ratio of the product of the ARE internal height H_ARE and twice the NE circle radius NE_R divided by the NE internal surface area A_NE.

[0056]

Number

[0057] This design of at least one anti-resonant unit results in an anti-resonant hollow-core fiber with low waveguide loss.

[0058] A further embodiment is characterized in that the following applies to the ratio of the product of the ARE internal height H_ARE and twice the NE circle radius NE_R divided by the NE internal surface area A_NE. ● The ratio is 0.25 or more, particularly 0.3 or more, ● The ratio is 0.95 or less, particularly 0.8 or less.

[0059] The parameters listed for the design of the anti-resonant hollow core fiber result in a further reduction of the waveguide loss.

[0060] A further embodiment is characterized in that the following applies to the ratio obtained by multiplying the NE internal height H_NE by twice the NE circle radius NE_R and dividing by the fiber core surface area A_Faser.

[0061]

Number

[0062]

Number

[0063] This embodiment ● The mode refractive index difference Δn between the fundamental mode and the NE mode eff (NE) is close to 0, ● The waveguide loss of the fundamental mode is minimized and is characterized by this.

[0064] A method for manufacturing a preform for stretching an anti-resonant hollow core fiber is as follows: ● Providing a fiber cladding preform; ● Preparing several anti-resonant unit preforms; ● Inserting the anti-resonant unit preforms into the internal bore of the fiber cladding preform; ● Processing a structure including the fiber cladding preform and several anti-resonant unit preforms by a hot forming process selected from at least one of stretching and shrinking. and may include.

[0065] The term "hot forming process" refers to a method step of raising the temperature of an element by heating. Known hot forming processes include flame-based hot processes based on the oxidation of exothermic reaction gases. The hot forming process creates a material bond between the internal bore of the anti-resonant unit preform and the fiber cladding preform. In the completed anti-resonant hollow core fiber, this is reflected in the material bond between the anti-resonant unit and the internal bore inside the cladding.

[0066] A further embodiment is characterized in that the anti-resonant hollow core fiber has three, four, five, six, seven, or eight anti-resonant units, and in particular, the anti-resonant hollow core fiber has an odd number of anti-resonant units. This embodiment makes it possible to further optimize the attenuation of the fundamental mode.

[0067] A further embodiment is characterized in that the anti-resonant units are asymmetrically arranged on the inner surface region of the cladding. As a result, the higher-order modes in the core are attenuated, and the hollow core fiber becomes the fundamental mode with a shorter travel distance.

[0068] A further embodiment is characterized in that at least one of the anti-resonant units has at least one of the following characteristics. ● The ARE element, NE element, and / or DNE element includes an amorphous solid, particularly glass, particularly silica glass. ● The ARE element, NE element, and / or DNE element consists of an amorphous solid, particularly glass, particularly silica glass. ● At least two of the ARE element, NE element, and DNE element are of the same material, and in particular, include or consist of glass having a refractive index of at least 1.4, particularly 1.4 to 3, particularly 1.4 to 2.8. ● The element walls of at least two of the ARE element, NE element, and DNE element are substantially the same.

[0069] These embodiments of the anti-resonant unit are optimized for low-loss transmission of signals at wavelengths of 0.3 μm to 3.0 μm, particularly 1.0 μm to 2.5 μm.

[0070] A further embodiment is characterized in that the anti-resonant hollow core fiber has at least one of the following features. ● For a transmission wavelength between 0.3 μm and 3.0 μm, particularly between 1.0 μm and 2.5 μm, a basic attenuation of less than 1.0 dB / km, particularly less than 0.25 dB / km, particularly less than 0.1 dB / km. ● A basic attenuation of less than 1 dB / km for a transmission wavelength up to 0.8 Μm.

[0071] This embodiment of the anti-resonant hollow core fiber is particularly suitable for use in data centers because of its low attenuation in the fundamental mode.

[0072] A further embodiment is characterized in that at least one anti-resonant unit has at least one of the following features. ● The wall thickness of the ARE element wall of the ARE element, the NE element wall of the NE element, and / or the DNE element wall of the DNE element is 0.1 μm to 2.5 μm, particularly 0.15 μm to 1.5 μm, particularly 0.25 μm to 0.75 μm, particularly 0.35 μm to 0.65 μm, particularly 0.5 μm. ● The wall thickness of the ARE element wall of the ARE element, the NE element wall of the NE element, and / or the DNE element wall of the DNE element is 0.35 μm to 0.65 μm, particularly 0.4 μm to 0.6 μm, particularly 0.5 μm at a signal wavelength of 1550 nm within the first transmission window. ● The wall thickness of the ARE element wall of the ARE element, the NE element wall of the NE element, and / or the DNE element wall of the DNE element is 0.75 μm to 1.25 μm, particularly 0.9 μm to 1.1 μm, particularly 1 μm at a signal wavelength of 1550 nm within the second transmission window.

[0073] In the case of an anti-resonant hollow core fiber particularly having one of specific wall thicknesses and particularly having a DNE element having a transmission wavelength of 0.3 μm to 3.0 μm, particularly 1.0 μm to 2.5 μm, a wide spectral range with low waveguide loss can be obtained.

[0074] A further embodiment is characterized in that the core radius \(R_{Faser}\) has at least one of the following features. ● The ratio is 26 μm or less, particularly 23 μm or less, particularly 20 μm or less. ● The ratio is 10 μm or more, particularly 12 μm or more, particularly 14 μm or more.

[0075] A further embodiment is characterized in that the ARE element has at least one of the following features. ● The first circular radius \(R_{ARE}\) is 30 μm or less, particularly 25 μm or less, particularly 22.5 μm or less, particularly 16 μm or less. ● The first circular radius \(R_{ARE}\) is 5 μm or more, particularly 7 μm or more, particularly 11.5 μm or more, particularly 12.25 μm or more, particularly 14.5 μm or more.

[0076] In the case of an anti-resonant hollow-core fiber having one of the first circular radii \(R_{ARE}\) listed above, a particularly effective interaction between the high-order modes in the core and the high-order modes in the ARE element can be observed. As a result, the difference in the effective mode refractive index \(\Delta n\) eff (ARE) becomes smaller. This is particularly true when the anti-resonant hollow-core fiber has one of the core radii \(R_{Faser}\) listed above.

[0077] A further embodiment is characterized in that the NE element has at least one of the following features. ● The second circular radius \(R_{NE}\) is 25 μm or less, particularly 19 μm or less, particularly 17 μm or less. ● The second circular radius \(R_{NE}\) is 1.5 μm or more, particularly more than 2.5 μm, particularly 3.5 μm or more. ● The central point angle \(MW_{NE}\) is less than 340°, particularly less than 330°, particularly less than 320°. ● The central point angle \(MW_{NE}\) is greater than 180°, particularly greater than 200°, particularly greater than 230°.

[0078] In the case of an anti-resonant hollow-core fiber having one of the second circular radii R_ARE and / or the central point angles MW_NE listed above, a particularly effective interaction between the high-order modes in the core and the high-order modes in the NE element can be observed, and as a result, the difference in the effective mode refractive index Δn eff (NE) becomes smaller. This is particularly applicable when the anti-resonant hollow-core fiber has one of the core radii R_Faser listed above and / or one of the first circular radii R_ARE.

[0079] A further embodiment is characterized in that the DNE element has at least one of the following features. ● The longest cross-sectional axis AL is 20 μm or less, particularly 16.5 μm or less, particularly 14.6 μm or less. ● The longest cross-sectional axis AL is 4 μm or more, particularly 6.5 μm or more, particularly 8 μm or more. ● The shortest cross-sectional axis AK is 12 μm or less, particularly 9.5 μm or less, particularly 8 μm or less. ● The shortest cross-sectional axis AK is 1.5 μm or more, particularly 2.5 μm or more, particularly 4 μm or more.

[0080] In an anti-resonant hollow-core fiber having at least one anti-resonant unit provided with an ARE element having at least one of the listed features, a particularly effective interaction between the high-order modes in the core and the high-order modes in the ARE element can be observed, and as a result, the difference in the effective mode refractive index Δn eff (ARE) becomes smaller. This is particularly applicable when the anti-resonant hollow-core fiber has one of the core radii R_Faser listed above and / or one of the first circular radii R_ARE.

[0081] A further embodiment is characterized in that more than 70%, particularly all, of the anti-resonant units have a design according to one of the described embodiments. The anti-resonant units may all be designed uniformly or according to different embodiments. The characteristics and features of different embodiments can be combined separately or in any combination.

[0082] The characteristics and features disclosed in this specification may be essential for various embodiments of the present invention described in the claims, either separately or in combination with each other.

[0083] The present invention will be further described by the following examples with reference to the drawings. The present invention is not limited to the drawings.

Brief Description of the Drawings

[0084]

Figure 1

Figure 2

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Figure 11

DETAILED DESCRIPTION OF THE INVENTION

[0085] FIG. 1 shows a cross-section of the ARE element 3100. The ARE element 3100 is a tubular structure having a circular or circular cross-section. The ARE element 3100 extends along the first body longitudinal axis 3110. Thus, in FIG. 1, the ARE element 3100 extends in the plane of the drawing. The ARE element 3100 has a first circular radius R_ARE3200 due to its circular or circular cross-section.

[0086] The ARE element 3100 has an ARE element wall 3150. The ARE element wall 3150 surrounds the first interior 3170. The first interior 3170 has an ARE internal surface area 3180. The ARE internal surface area 3180 is proportional to the square of the first circular radius R_ARE3200.

[0087] Variations associated with the manufacture of the first circular radius R_ARE3200 are, based on the length of the first circular radius R_ARE3200, particularly 10% or less, preferably 5% or less, more preferably 3% or less.

[0088] FIG. 2 shows a cross-section of the NE element 3400. The NE element 3400 is a tubular structure having an arcuate cross-section. The NE element 3400 extends along the second body longitudinal axis 3410. Thus, in FIG. 2, the NE element 3400 extends in the plane of the drawing.

[0089] As shown in the cross-section illustrated in FIG. 2, the NE element 3400 has an arcuate cross-section. In the context of the present invention, the term "arc" refers to a part of a circular line. Two points on a circle divide the circular line into two arcs. In the context of the present invention, an element is described as "arcuate" if its outer shape follows the path of one of the two arcs. To illustrate this, a circle 2990 is drawn in FIG. 2. This circle 2990 is divided into two arcs by two intersecting lines H-H and I-I. The cross-section of the NE element 3400 follows one of the two arcs.

[0090] Furthermore, an intersecting line G-G passing through the two intersection points of the two intersecting lines H-H and I-I and the circle 2990 is drawn. The chord of the NE internal unit 3400 is on the intersecting line G-G and is the distance defined by the intersecting lines H-H and I-I. The chord length 3590 is the length of the chord.

[0091] The NE element 3400 has an NE element wall 3450. The NE element 3400 has a second circle radius R_NE3500. This second circle radius R_NE3500 represents the distance from the second body longitudinal axis 3410 to the NE element wall 3450.

[0092] Variations associated with the manufacture of the second circle radius R_NE3500 are, based on the length of the second circle radius R_ARE3500, particularly 10% or less, preferably 5% or less, more preferably 3% or less.

[0093] The NE element 3400 has a segment height SH_NE3580. This segment height SH_NE3580 is perpendicular to the chord and represents the length of a straight line extending to the apex of the NE element wall 3450.

[0094] The NE element 3400 has a center point angle MW_NE3550. This center point angle MW_NE3550 represents an angle whose vertex is at the center of the circle 2990 and whose sides intersect the boundary points of the arc (here, the intersection points of the circle 2990 and the intersection lines H-H and I-I). A complete circle has an angular value of 360°. Since the NE element 3400 is in an arc shape, the center point angle MW_NE3550 is less than 360°.

[0095] The NE element 3400 has a second interior 3470 defined by the NE element wall 3450 and the chord.

[0096] One embodiment is characterized in that the NE element 3400 has at least one of the following features. ● The second circle radius R_NE3500 is 25 μm or less, particularly 19 μm or less, particularly 17 μm or less. ● The second circle radius R_NE3500 is 1.5 μm or more, particularly more than 2.5 μm, particularly 3.5 μm or more. ● The center point angle MW_NE3550 is less than 340°, particularly less than 330°, particularly less than 320°. ● The center point angle MW_NE3550 is greater than 180°, particularly greater than 200°, particularly greater than 230°.

[0097] Figure 3 shows a cross-section of the DNE element 3900. The DNE element 3900 is a tubular structure having an oval cross-section. Thus, in Figure 2, the DNE element 3900 extends in the plane of the drawing.

[0098] The DNE element 3900 has a DNE element wall 3950. The DNE element wall 3950 surrounds a third interior 3970. The third interior 3970 has a DNE inner surface area 3980.

[0099] The DNE element 3900 has an oval cross-sectional shape. In the context of the present invention, the term "oval" is understood to mean a flat and rounded convex shape, including an ellipse as a special case. In contrast to an ellipse, any oval shape does not necessarily have an axis of symmetry.

[0100] The DNE element 3900 has a longest cross-sectional axis AL4010 and a shortest cross-sectional axis AK4020. Here, ● The longest cross-sectional axis AL4010 represents the longest straight-line extension between two points on the DNE element wall 3950, ● The shortest cross-sectional axis AK4020 represents the shortest straight-line extension between two points on the DNE element wall 3950.

[0101] In a further embodiment, the longest cross-sectional axis AL4010 and / or the shortest cross-sectional axis AK4020 is the axis of symmetry of the DNE element 3900.

[0102] FIG. 4 serves to provide a clearer understanding of the term "oval" and shows a cross-section of the DNE element 3900 shown in FIG. 3. The oval cross-section of the DNE element 3900 is defined such that, in the cross-section, the sum of the distances 4001, 4001' from two foci 4000, 4000' to any point on the DNE element wall 3950 is the same within a range of less than 15% of the sum of the distances 4001, 4001' at all points. The foci 4000, 4000' are separated and not identical. Therefore, an elliptical cross-section is desirable for the DNE element 3900, but due to manufacturing reasons, this is achieved only within certain variations. The embodiment of the DNE element 3900 shown in FIG. 4 is characterized in that the foci 4000, 4000' are on the longest cross-sectional axis AL4010.

[0103] A further embodiment of the DNE element 3900 is characterized in that, in the cross-section, especially on the longest cross-sectional axis AL4010, the sum of the distances 4001, 4001' from two foci 4000, 4000' to any point on the DNE element wall 3950 is the same within a range of less than 10%, especially less than 5%, of the sum of the distances 4001, 4001' at all points.

[0104] Surprisingly, it has been found that the DNE element 3900 having an oval cross-section has a favorable effect on the transmission characteristics of the anti-resonant hollow-core fiber 1000. One embodiment of the DNE element 3900 is The following applies to the ratio of the longest cross-sectional axis AL4010 to the shortest cross-sectional axis AK. AL / AK = [1.1; 4.0]

[0105] This embodiment results in the optimization of waveguide loss.

[0106] A further embodiment is characterized in that the following applies to the ratio of the longest cross-sectional axis AL4010 to the shortest cross-sectional axis AK4020. ● The ratio is 1.15 or more, particularly 1.20 or more, particularly 1.25 or more, particularly 1.50 or more, ● The ratio is 3.80 or less, particularly 3.60 or less, particularly 3.50 or less.

[0107] By using the DNE element 3900 having an elliptical cross-section with the above-described ratio, the waveguide loss can be further reduced.

[0108] A further embodiment is characterized in that the DNE element 3900 has at least one of the following features. ● The longest cross-sectional axis AL4010 is 20 μm or less, particularly 16.5 μm or less, particularly 14.6 μm or less. ● The longest cross-sectional axis AL4010 is 4 μm or more, particularly 6.5 μm or more, particularly 8 μm or more. ● The shortest cross-sectional axis AK4020 is 12 μm or less, particularly 9.5 μm or less, particularly 8 μm or less. ● The shortest cross-sectional axis AK4020 is 1.5 μm or more, particularly 2.5 μm or more, particularly 4 μm or more.

[0109] FIG. 5a shows a cross-section of the antiresonant unit 3000 including the ARE element 3100, the NE element 3400, and the DNE element 3900. The NE element 3400 and the DNE element 3900 are arranged within the first interior 3170 of the ARE element 3100. The DNE element 3900 having an elliptical shape protrudes at least partially into the second interior 3470 of the arc-shaped NE element 3400. This means that, in the cross-section, the DNE element 3900 extends at least partially over the chord of the NE element 3400.

[0110] The NE element 3400 has an NE internal surface area A_NE3480. This NE internal surface area A_NE is defined by the NE element wall 3450 and the DNE element wall 3950. As a result, the NE internal surface area A_NE3480 and the second interior 3470 do not exactly coincide.

[0111] The arc-shaped NE element 3400 and the oval-shaped DNE element 3900 are connected to each other along two connection joints 3700, 3700' arranged substantially parallel to the first body longitudinal axis 3110. In particular, this joining can be achieved by a hot process.

[0112] To explain this, the region around the connection joint 3700 is shown enlarged in FIG. 5b. As a result, ● The connection joint 3700 is formed as a joint between the first end point of the NE element wall 3450 and the first point on the DNE element wall 3950. ● The connection joint 3700' is formed as a joint between the second end point of the NE element wall 3450 and the second point on the DNE element wall 3950.

[0113] Similar to FIG. 5b, FIG. 5c shows a part of the arc-shaped NE element 3400 and the oval-shaped DNE element 3900 defined by the intersection lines C and D.

[0114] Three exemplary positions A1, A2, A3 of the first end point of the NE element wall 3450 on the DNE element wall 3950 are shown respectively.

[0115] Each of the three positions A1, A2, A3 has a connection height 3705, 3705', 3705''. The connection heights 3705, 3705', 3705'' are obtained from the distances from the upper edge of the DNE element 3900 to the respective circles 2990, 2990', 2990''.

[0116] For clarity, connection height 3705'' is described in more detail with respect to position A3. Connection height 3705'' is obtained from the distance between the following two elements. ● Upper edge of DNE element 3900: The upper edge can be the intersection of the shortest cross-sectional axis AK4020 and the DNE element wall 3950 (see also Figure 3). ● Corresponding circle 2990'' of NE element 3400: Circle 2990 is depicted in Figure 2 to show the arcuate cross-section of NE element 3400. This circle 2990 is divided into two arcs by two intersection lines H-H and I-I. The cross-section of NE element 3400 follows one of the two arcs.

[0117] Therefore, the connection height 3705'' at position A3 does not correspond to the distance between the plane spanning connection joints 3700, 3700' and the upper edge of DNE element 3900. Rather, the connection height 3705'' is greater than the distance to the plane spanning connection joints 3700, 3700'.

[0118] If connection heights 3705, 3705', 3705'' are 0, NE element 3400 and DNE element 3900 contact at only one point and the NE element forms substantially a circle. Therefore, to ensure the arcuate cross-section of NE element 3400, the connection heights 3705, 3705', 3705'' of hollow core fiber 1000 are greater than 0. In one embodiment, the connection heights 3705, 3705', 3705'' can be from 1.25 μm to 5.75 μm.

[0119] Since Figures 5a, 5b, 5c each show a cross-section of anti-resonance unit 3000, in the three-dimensional view of hollow core fiber 1000, the two connection joints 3700, 3700' extend in the plane of the drawing.

[0120] Figures 1 to 5a, 5b, and 5c show the antiresonance unit 3000, the ARE element 3100, the NE element 3400, and the DNE element 3900, respectively, in cross-sectional views, i.e., axial views. Therefore, in three-dimensional views, the antiresonance unit 3000, the ARE element 3100, the NE element 3400, and the DNE element 3900 each represent an elongated and / or tubular structure.

[0121] The ARE element 3100, the NE element 3400, and / or the DNE element 3900 can include and / or can consist of an amorphous solid, particularly glass, particularly quartz glass. The antiresonance unit 3000 shown in FIG. 5 can have at least one of the following features. ● The wall thickness of the ARE element wall 3150 of the ARE element 3100, the NE element wall 3450 of the NE element 3400, and / or the DNE element wall 3950 of the DNE element 3900 is 0.1 μm to 2.5 μm, particularly 0.15 μm to 1.5 μm, particularly 0.25 μm to 0.75 μm, particularly 0.35 μm to 0.65 μm, particularly 0.5 μm. ● The wall thickness of the ARE element wall 3150 of the ARE element 3100, and / or the NE element wall 3450 of the NE element 3400, and / or the DNE element wall 3950 of the DNE element 3900 is 0.35 μm to 0.65 μm, particularly 0.4 μm to 0.6 μm, particularly 0.5 μm at the signal wavelength of 1550 nm within the first transmission window. ● The wall thickness of the ARE element wall 3150 of the ARE element 3100, the NE element wall 3450 of the NE element 3400, and / or the DNE element wall 3950 of the DNE element 3900 is 0.75 μm to 1.25 μm, particularly 0.9 μm to 1.1 μm, particularly 1 μm at the signal wavelength of 1550 nm within the second transmission window.

[0122] FIG. 6 shows a partial cross-sectional view of the anti-resonant hollow core fiber 1000. A cross-section of the anti-resonant hollow core fiber 1000 between two intersecting lines A-A and B-B is shown. The anti-resonant hollow core fiber 1000 has a fiber cladding 2000 (also called a cladding). The fiber cladding 2000 can be integrally formed from an elongated cladding material or from an elongated jacket tube combined with an elongated cladding material. The fiber cladding 2000 has a cladding inner radius 2170, which is obtained from the distance from the fiber longitudinal axis 2300 of the anti-resonant hollow core fiber 1000 to the inside 2150 of the cladding 2000. An anti-resonant unit 3000 is disposed on the inside 2150. The anti-resonant unit 3000 is materially connected to the fiber cladding 2000. The anti-resonant unit 3000 corresponds to the anti-resonant unit 3000 particularly shown in FIG. 5a.

[0123] The ARE element 3100 is circular in shape. Deviations of the ARE element wall 3150 and / or the first circular radius R_ARE 3200 from the ideal circular shape are based particularly on variations associated with manufacturing. In particular, the first circular radius R_ARE 3200 cannot deviate by more than 15%, particularly by more than 10%, particularly by more than 3% from the average first circular radius R_ARE 3200 of the ARE element 3100, and in particular cannot deviate azimuthally over the circle and at different positions in the axial direction of the anti-resonant hollow core fiber 1000 such that an oval path is generated.

[0124] The NE element 3400 is arcuate in shape. Deviations of the NE element wall 3450 and / or the second circular radius R_ARE 3500 from the ideal arcuate shape are based particularly on variations associated with manufacturing. In particular, the second circular radius R_ARE 3500 cannot deviate by more than 15%, particularly by more than 10%, particularly by more than 3% from the average second circular radius R_ARE 3500, and in particular cannot deviate azimuthally over the arc and at different positions in the axial direction of the anti-resonant hollow core fiber 1000 such that an oval path is generated.

[0125] The anti-resonance unit 3000 includes an ARE element 3100, a NE element 3400, and a DNE element 3900. The amount of the inner radius of the cladding 2170 corresponds to the following total. ● The core radius R_Faser2310 obtained from the shortest distance between the fiber longitudinal axis 2300 and the anti-resonance unit 3000. ● The ARE internal height H_ARE3190 obtained from the distance between the ARE element wall 3150 and the NE element wall 3450 on the line to the fiber longitudinal axis 2300. ● The NE internal height H_NE3490 obtained from the distance between the NE element wall 3450 and the DNE element wall 3950 on the line to the fiber longitudinal axis 2300. ● The length of the shortest cross-sectional axis AK4090. ● The total wall thickness of the ARE element wall 3150, the NE element wall 3450, and the DNE element wall 3950.

[0126] FIG. 7 shows a cross-sectional view of the anti-resonance hollow-core fiber 1000. The anti-resonance hollow-core fiber 1000 has a hollow core through which electromagnetic waves can propagate. The hollow core has a core radius 2310 and a fiber core surface area A_Faser2320. The fiber cladding 2000 has an arc-shaped cross-section and a tubular shape. In this regard, the fiber cladding 2000 surrounds the inner bore 2200 in which the anti-resonance unit 3000 is disposed.

[0127] One embodiment is characterized in that the core radius R_Faser2310 has at least one of the following features. ● The core radius R_Faser2310 is 26 μm or less, particularly 23 μm or less, particularly 20 μm or less. ● The core radius R_Faser2310 is 10 μm or more, particularly 12 μm or more, particularly 14 μm or more.

[0128] FIG. 7 shows the arrangement of a plurality of anti-resonance units 3000 on the inner side 2150. In one embodiment, the anti-resonance hollow core fiber 1000 can have three, four, five, six, seven, or eight anti-resonance units 3000. In FIG. 7, the anti-resonance hollow core fiber 1000 has five anti-resonance units 3000. In this embodiment, the anti-resonance units 3000 are asymmetrically arranged on the inner side 2150 of the cladding 2000.

[0129] FIGS. 8 to 11 show the results of the simulation of the anti-resonance hollow core fiber 1000. For the numerical calculation, the finite element method mode solver of the COMSOL Multiphysics program was used. A perfectly matched layer (PML) with a thickness of 10 μm was implemented on the outer interface of the optical fiber to investigate the radiation characteristics of the waveguide structure by absorbing the energy radiated in the radial direction.

[0130] The starting point of the simulation was the anti-resonance hollow core fiber 1000. This anti-resonance hollow core fiber 1000 includes a fiber longitudinal axis 2300, a fiber core radius R_Faser 2310, and a fiber cladding 2000 having an internal bore 2200. Further, the anti-resonance hollow core fiber 1000 includes five anti-resonance units 3000, each of which ● an ARE element 3100, ● a NE element 3400, ● a DNE element 3900, and in this case, the anti-resonance units 3000 are spaced apart from each other and arranged so as not to contact each other at desired positions on the inner side 2150 of the internal bore 2200.

[0131] Here, in each anti-resonance unit 3000 ● the ARE element 3100 has a circular cross-section, ● the NE element 3400 is arranged within a first interior 3170 of the ARE element 3100, ● the DNE element 3900 is at least partially arranged within a second interior 3470 of the NE element 3400.

[0132] The anti-resonance unit 3000 within the anti-resonance hollow core fiber 1000 is such that ● the DNE element 3900 has an oval cross-section, ● the NE element 3400 has an arcuate cross-section and is connected to the DNE element 3400 along two connection joints 3700, 3700', ● in cross-section, the sum of the distances from two foci 4000, 4000' to any point on the DNE element wall 3950 is the same within a range of less than 15% of the sum of the distances for all points, which is characterized by.

[0133] The simulated anti-resonance hollow core fiber 1000 had the following characteristics. ● A wall thickness of 500 nm, particularly corresponding to a wide transmission range (first transmission band) near a signal wavelength of 1550 nm. ● Five anti-resonance units 3000 in each case. ● The DNE element had an ideal elliptical contour.

[0134] Table 1 shows further parameters of seven different designs of the simulated anti-resonance hollow core fiber 1000.

[0135]

Table 1

[0136] For each of a total of seven designs, multiple calculations were performed. The following parameters were varied. 1. The second circle radius R_NE 3500, and 2. The connection heights 3705, 3705', 3705'', i.e., the position of the NE element on the DNE element.

[0137] Regarding 1: For the other fixed designs, the second circle radius R_NE 3500 was varied in 500 nm increments (except for design 5). For example, the intervals listed for design 1 [3.5;11.0] shows that during the simulation, the second circle radius \(R_{NE3500}\) was changed in steps of \(0.5\ \mu m\) at intervals \([3.5\ \mu m; 11.0\ \mu m]\).

[0138] Regarding 2: For other fixed designs, the position of the NE element on the DNE element was changed (see Fig. 5c). For example, for the intervals listed for Design 1 [1.25; 5.75] in steps of 0.50 shows that the connection heights \(3705, 3705', 3705''\) were changed in steps of \(0.5\ \mu m\) from \(1.25\ \mu m\) to \(5.75\ \mu m\) during the simulation.

[0139] Further parameters are defined as follows. ● Value "oval diameter" calculated from the arithmetic mean of the longest cross-sectional axis \(AL\) and the shortest cross-sectional axis \(AK\): \(((AL_{4010}+AK_{4020}) / 2)\). ● The value of "ovalness" is calculated from the ratio of the longest cross-sectional axis \(AL\) to the shortest cross-sectional axis \(AK\) (\(AL_{4010} / AK_{4020}\)). ● The penetration depth of the ARE element into the cladding indicates that the ARE element penetrates \(1\ \mu m\) into the cladding during the hot process. ● The penetration depth of the DNE element into the cladding indicates that the DNE element penetrates \(0.25\ \mu m\) into the cladding during the hot process.

[0140] In Figs. 8 - 11, the results of the simulation are plotted as follows. ● Results based on Design 1 are marked with dots. ● Results based on Design 2 are marked with crosses. ● Results based on Design 3 are marked with x's. ● Results based on Design 4 are marked with circles. ● Results based on Design 5 are marked with asterisks. ● Results based on Design 6 are marked with triangles. ● Results based on Design 7 are marked with rectangles.

[0141] In addition to the above definitions, the following modes were considered in the simulation. ● Higher-order modes in the core. ● In the simulation, only the second-order mode (i.e., one mode above the fundamental mode) was considered. This is because modes of the third order and higher typically have higher waveguide losses and are thus less relevant to the consideration of the fundamental mode, which is mainly determined by the power and waveguide losses in the second-order mode. ● Modes in the ARE element. ● Only the fundamental mode in the ARE element was considered in the simulation. ● Modes in the NE element. ● Only the fundamental mode in the NE element was considered in the simulation.

[0142] In the simulation, the effective mode refractive index n eff was extracted from the propagation constant β of each mode. The mode "j" is the solution of the physical simultaneous equations. E j (x, y, z, t) = amplitude j (x, y) * exp(i * (β j * z - t)ω * t)) Here, ● E j (x, y, z, t) represents the electric field distribution in the three spatial dimensions x, y, z at time t, ● amplitude j (x, y) represents the transverse electric field distribution.

[0143] Therefore, the propagation constant β represents the phase characteristics of wave propagation along the fiber axis z. Based on the wavelength λ of light, n of the mode "j" eff is directly obtained from β. β j = 2 * pi / λ * n eff,j

[0144] The propagation constant (β j ) of the j-th mode is generally a complex parameter as the solution of the simulation. The real part gives n_eff,j, while the waveguide loss determined for the core mode can be derived from the imaginary part. Thus, the parameter β j includes all the characteristics important here.

[0145] The above-mentioned drawbacks of the known anti-resonant hollow-core fiber are overcome, especially when a high-speed fundamental mode is achieved. This means that the higher-order modes are attenuated within the core, and the anti-resonant hollow-core fiber acts as effectively as the fundamental mode after a shorter propagation distance. The shorter this propagation distance, the higher the fundamental mode. The physical background is that the energy of the higher-order modes within the core couples to the more lossy ARE modes and / or DNE modes. This means that the higher-order modes no longer have an adverse effect on the optical signal transmission within the core. The simulation of the anti-resonant hollow-core fiber 1000 surprisingly showed that the elliptical shape of the DNE element 3900 affects the fundamental mode.

[0146] In FIG. 8, the difference in the effective mode refractive index Δn eff (NE) of the simulated design is plotted against the ratio obtained by multiplying the NE internal height H_NE3490 by twice the NE circle radius NE_R3500 and dividing by the fiber core surface area A_Faser2320.

[0147] The desired coupling between the fundamental mode and the NE mode, and thus a good fundamental mode, is achieved when the magnitude of the mode refractive index Δn eff (NE) is small, especially when it is 0. It has been proven to be advantageous when the following applies to the ratio obtained by multiplying the NE internal height H_NE3490 by twice the NE circle radius NE_R3500 and dividing by the fiber core surface area A_Faser2320.

[0148]

Equation

[0149] When the following is applied to the ratio obtained by multiplying the internal height H_NE3490 of NE by twice the NE circle radius NE_R3500 and dividing by the fiber core surface area A_Faser2320, a further favorable influence on the fundamental mode can be achieved. ● The ratio is 0.4 or more, particularly 0.50 or more, particularly 0.56 or more, ● The ratio is 0.65 or less, particularly 0.62 or less, particularly 0.6 or less.

[0150] In FIG. 9, the waveguide loss for the simulation design of the antiresonant hollow core fiber 1000 is plotted against the ratio obtained by multiplying the internal height H_NE3490 of NE by twice the NE circle radius NE_R3500 and dividing by the fiber core surface area A_Faser2320, which is also plotted in FIG. 8. The aim is to achieve the lowest possible waveguide loss. This is achieved for the simulated design when the following is applied.

[0151]

Number

[0152] This interval corresponds to the optimal interval of the fundamental mode.

[0153] FIGS. 8 and 9 show the special features of the antiresonant hollow core fiber 1000 described. The following,

[0154]

Number

[0155] In FIG. 10, the difference in the effective mode refractive index Δn eff is plotted against the ratio of the ARE internal height H_ARE3190 divided by the core radius R_Faser2310. It has been found to be advantageous when the following applies to the ratio of the ARE internal height H_ARE3190 divided by the core radius R_Faser2310.

[0156] [Number]

[0157] As a result of this geometric design of the antiresonant hollow-core fiber 1000, the difference in the effective mode refractive index Δn eff (ΔRE) approaches or equals zero.

[0158] When the following applies to the ratio of the ARE internal height H_ARE3190 divided by the core radius R_Faser2310, a further favorable influence on the fundamental mode can be achieved. ● The ratio is 0.9 or more, particularly 0.95 or more, particularly 1.0 or more, ● The ratio is 1.2 or less, particularly 1.15 or less, particularly 1.1 or less.

[0159] In FIG. 11, the waveguide loss regarding the design of the anti-resonance hollow core fiber 1000 is plotted against the ratio obtained by multiplying the ARE internal height H_ARE3190 by twice the NE circle radius NE_R3500 and dividing by the NE internal area A_NE3480. It has been proven to be advantageous when the following is applied to the ratio obtained by multiplying the ARE internal height H_ARE3190 by twice the NE circle radius NE_R3500 and dividing by the NE internal surface area A_NE3480.

[0160]

Number

[0161] When the following is applied to the ratio obtained by multiplying the ARE internal height H_ARE3190 by twice the NE circle radius NE_R3500 and dividing by the NE internal surface area A_NE3480, a further favorable influence on the waveguide loss can be achieved. ● The ratio is 0.25 or more, particularly 0.3 or more, ● The ratio is 0.95 or less, particularly 0.8 or less.

[0162] 1. A further favorable influence on the coupling between the higher-order mode in the core and the mode in the anti-resonance unit 3000, 2. A further favorable influence on the waveguide loss of the fundamental mode is, It can be achieved when at least two of the following are applied to the anti-resonance hollow core fiber 1000. ● The ratio of the longest cross-sectional axis AL4010 to the shortest cross-sectional axis AK is as follows.

[0163]

Number

[0164]

Number

[0165]

Number

[0166]

Number

Explanation of Symbols

[0167] 1000 Anti-resonant hollow core fiber 2000 Clad or fiber clad 2150 Inside of the clad 2170 Inner radius of the clad 2300 Fiber longitudinal axis 2310 Core radius R_Faser 2320 Fiber core surface area A_Faser 2990 Circle 3000 Anti-resonant unit, i.e., ARE unit 3100 ARE element 3110 First body longitudinal axis 3150 ARE element wall 3170 First inside of the ARE element 3180 ARE internal surface area 3190 ARE internal height H_ARE 3200 First circle radius R_ARE 3400 NE element 3410 Second body longitudinal axis 3450 NE element wall 3470 Second inside of the NE element 3480 NE internal surface area A_NE 3490 NE internal height H_NE 3500 Second circle radius R_NE 3550 Center point angle MW_NE 3580 Segment height SH_NE 3590 Chord length 3700, 3700' Connection joint 3705, 3705', 3705'' Connection height 3900 DNE element of anti-resonant hollow core fiber 3950 DNE element wall 3970 Third interior of DNE element 3980 DNE internal surface area A_DNE 4000, 4000' Two foci 4010 Longest cross-sectional axis AL 4020 Shortest cross-sectional axis AK 4080 Length of the longest cross-sectional axis AL 4090 Length of the shortest cross-sectional axis AK

Claims

1. a fiber cladding (2000) having an internal bore (2200); the fiber longitudinal axis (2300) and the fiber core radius R_Faser (2310); A number of anti-resonant units (3000); An anti-resonant hollow-core fiber (1000), wherein each of the anti-resonant units (3000) comprises: ● ARE element (3100), ●NE elements (3400), A DNE element (3900); Equipped with the anti-resonant units (3000) are spaced apart from one another and arranged at desired positions inside (2150) of the internal bore (2200) so as not to contact one another; In the anti-resonance unit (3000), said ARE element (3100) has a circular cross-section; said NE element (3400) is disposed in a first interior portion (3170) of said ARE element (3100); the DNE element (3900) is at least partially disposed within a second interior (3470) of the NE element (3400); In an anti-resonant hollow-core fiber (1000), In at least one anti-resonant unit (3000), the NE element (3400) has an arc-shaped cross section and is connected to the DNE element (3400) along two connection seams (3700, 3700′); said DNE element (3900) having an oval cross-section; In cross section, the sum of the distances from the two foci (4000, 4000') to any point on the DNE element wall (3950) is the same at all points to within less than 15% of said sum of said distances; 1. An anti-resonant hollow-core fiber (1000).

2. The anti-resonant hollow core fiber (1000) of claim 1, characterized in that in a cross section, the sum of the distances from two foci (4000, 4000') to any point on the DNE element wall (3950) is the same at all points within a range of less than 10%, in particular less than 5%, of the sum of the distances.

3. The DNE element (3900) has a longest cross-sectional axis AL (4010) and a shortest cross-sectional axis AK (4020), and the ratio of the longest cross-sectional axis AL (4010) to the shortest cross-sectional axis AK is as follows: [0010] The anti-resonant hollow-core fiber (1000) according to claim 1 or 2, characterized in that:

4. The ratio of the longest cross-sectional axis AL (4010) to the shortest cross-sectional axis AK (4020) is as follows: said ratio is greater than or equal to 1.15, in particular greater than or equal to 1.20, in particular greater than or equal to 1.25, in particular greater than or equal to 1.50; said ratio is less than or equal to 3.80, in particular less than or equal to 3.60, in particular less than or equal to 3.50; 4. The anti-resonant hollow-core fiber (1000) according to claim 3, characterized in that:

5. The ratio of the NE inner height H_NE (3490) multiplied by twice the NE circle radius NE_R (3500) divided by the fiber core surface area A_Faser (2320) is as follows: [0025] The anti-resonant hollow-core fibre (1000) according to any one of claims 1 to 4, characterized in that:

6. The ratio obtained by multiplying the NE inner height H_NE (3490) by twice the NE circle radius NE_R (3500) and dividing it by the fiber core surface area A_Faser (2320) is as follows: said ratio is greater than or equal to 0.4, in particular greater than or equal to 0.50, in particular greater than or equal to 0.56; said ratio is less than or equal to 0.65, in particular less than or equal to 0.62, in particular less than or equal to 0.6; 6. The anti-resonant hollow-core fiber (1000) according to claim 5, characterized in that:

7. For the ratio of the ARE inner height H_ARE (3190) divided by the core radius R_Faser (2310), [0030] The anti-resonant hollow-core fibre (1000) according to any one of claims 1 to 6, characterized in that:

8. For the ratio of the ARE inner height H_ARE (3190) divided by the core radius R_Faser (2310), said ratio is greater than or equal to 0.9, in particular greater than or equal to 0.95, in particular greater than or equal to 1.0; said ratio is less than or equal to 1.2, in particular less than or equal to 1.15, in particular less than or equal to 1.1; 8. The anti-resonant hollow-core fiber (1000) according to claim 7, characterized in that:

9. The ratio obtained by multiplying the ARE internal height H_ARE (3190) by twice the NE circle radius NE_R (3500) and dividing the result by the NE internal surface area A_NE (3480) is as follows: [0045] The anti-resonant hollow-core fibre (1000) according to any one of claims 1 to 8, characterized in that:

10. The ratio obtained by multiplying the ARE internal height H_ARE (3190) by twice the NE circle radius NE_R (3500) and dividing the result by the NE internal surface area A_NE (3480) is as follows: said ratio is greater than or equal to 0.25, in particular greater than or equal to 0.3; said ratio is less than or equal to 0.95, in particular less than or equal to 0.8; 10. The anti-resonant hollow-core fiber (1000) according to claim 9, characterized in that:

11. The at least one anti-resonant unit (3000) has the following: the wall thickness of the ARE element wall (3150) of said ARE element (3100), the NE element wall (3450) of said NE element (3400) and / or the DNE element wall (3950) of said DNE element (3900) is between 0.1 μm and 2.5 μm, in particular between 0.15 μm and 1.5 μm, in particular between 0.25 μm and 0.75 μm, in particular between 0.35 μm and 0.65 μm, in particular 0.5 μm; the wall thickness of the ARE element wall (3150) of said ARE element (3100), the NE element wall (3450) of said NE element (3400) and / or the DNE element wall (3950) of said DNE element (3900) is between 0.35 μm and 0.65 μm, in particular between 0.4 μm and 0.6 μm, in particular 0.5 μm, at a signal wavelength of 1550 nm within the first transmission window; the wall thickness of the ARE element wall (3150) of said ARE element (3100), the NE element wall (3450) of said NE element (3400) and / or the DNE element wall (3950) of said DNE element (3900) is between 0.75 μm and 1.25 μm, in particular between 0.9 μm and 1.1 μm, in particular 1 μm, at a signal wavelength of 1550 nm within the second transmission window; The anti-resonant hollow-core fiber (1000) according to any one of claims 1 to 10, characterized in that it has at least one of the following features:

12. The core radius R_Faser (2310) is as follows: the core radius R_Faser(2310) is equal to or less than 26 μm, in particular equal to or less than 23 μm, in particular equal to or less than 20 μm; The core radius R_Faser(2310) is 10 μm or more, in particular 12 μm or more, in particular 14 μm or more; The anti-resonant hollow-core fiber (1000) according to any one of claims 1 to 11, characterized in that it has at least one of the following features:

13. The ARE element (3100) is as follows: The first circle radius R_ARE(3200) is equal to or less than 30 μm, in particular equal to or less than 25 μm, in particular equal to or less than 22.5 μm, in particular equal to or less than 16 μm; the first circle radius R_ARE(3200) is 5 μm or more, in particular 7 μm or more, in particular 11.5 μm or more, in particular 12.25 μm or more, in particular 14.5 μm or more; An anti-resonant hollow-core fiber (1000) according to any one of claims 1 to 12, characterized in that it has at least one of the following features:

14. The NE element (3400) is as follows: The second circle radius R_NE(3500) is equal to or less than 25 μm, in particular equal to or less than 19 μm, in particular equal to or less than 17 μm; The second circle radius R_NE(3500) is 1.5 μm or more, in particular more than 2.5 μm, in particular 3.5 μm or more; The center point angle MW_NE (3550) is less than 340°, in particular less than 330°, in particular less than 320°; the center point angle MW_NE (3550) is greater than 180°, in particular greater than 200°, in particular greater than 220°; The anti-resonant hollow-core fiber (1000) according to any one of claims 1 to 13, characterized in that it has at least one of the following features:

15. The DNE element (3900) is as follows: the longest cross-sectional axis AL(4010) is equal to or less than 20 μm, in particular equal to or less than 16.5 μm, in particular equal to or less than 14.6 μm; The longest cross-sectional axis AL (4010) is 4 μm or more, in particular 6.5 μm or more, in particular 8 μm or more; The shortest cross-sectional axis AK (4020) is 12 μm or less, in particular 9.5 μm or less, in particular 8 μm or less; The shortest cross-sectional axis AK (4020) is 1.5 μm or more, in particular 2.5 μm or more, in particular 4 μm or more; An anti-resonant hollow-core fiber (1000) according to any one of claims 3 to 14, characterized in that it has at least one of the following features:

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