Anti-resonant hollow-core fiber

Abstract

An anti-resonant hollow-core fiber (1), comprising an outer protective tube (2) having an inner surface (21), and cladding elements located within the outer protective tube (2) and including a plurality of first cladding elements (31) circumferentially arranged along the inner surface (21). Any two adjacent first cladding elements (31) among the plurality of first cladding elements (31) are in contact with each other, and the plurality of first cladding elements (31) define a central air region (10) of the anti-resonant hollow-core fiber (1), wherein a fiber core fundamental mode field of the anti-resonant hollow-core fiber (1) is confined within the central air region (10); there is a contact point (C1, C2, C3, C4) closest to the center point (O) of the fiber core fundamental mode field between any two adjacent first cladding elements (31), and the ratio of the distance D1 from the closest contact point (C1, C2, C3, C4) to the closest boundary of the fiber core fundamental mode field to the distance D2 from the closest boundary to the center point (O) of the fiber core fundamental mode field satisfies the following relationship: D1 / D2 is greater than 0.46, wherein each first cladding element (31) further comprises at least one first main nested element (32).

Description

An anti-resonant hollow fiber

[0001] Related applications

[0002] This application claims priority to Chinese application No. 202411999077.4, filed on December 31, 2024, the entire contents of which are incorporated herein by reference. Technical Field

[0003] This disclosure relates to the field of hollow optical fibers, and more specifically to an anti-resonant hollow optical fiber. Background Technology

[0004] Depending on the optical guiding mechanism, hollow optical fibers can typically include hollow photonic bandgap fibers and anti-resonant hollow optical fibers.

[0005] Antiresonant hollow-core optical fiber is characterized by its simple structure, hollow-core light guiding, and wide transmission spectrum, making it suitable for important applications in fields such as light-filled material interactions, nonlinear optics, gas detection, gas laser generation, and optofluidics. Furthermore, its hollow-core light guiding properties, including ultra-low Rayleigh scattering, low nonlinear coefficient, and tunable dispersion, can provide a higher laser damage threshold, making it a potential candidate for high-power laser transmission, ultraviolet / mid-infrared light transmission, pulse compression, and optical soliton transmission.

[0006] Furthermore, the ultra-low loss, low dispersion, low nonlinearity, and near-light speed of propagation of anti-resonant hollow fiber enable the development of hollow fiber communication transmission and communication devices, laying the foundation for the construction and development of next-generation ultra-high capacity, low latency, and high-speed optical communication systems. Summary of the Invention

[0007] According to a first aspect of this disclosure, an anti-resonant hollow-core optical fiber is provided. The anti-resonant hollow-core optical fiber includes: an outer sheath having an inner surface; and cladding elements located within the outer sheath and including a plurality of first cladding elements arranged around the inner surface, wherein any two adjacent first cladding elements of the plurality of first cladding elements are in contact with each other and define an intermediate air region of the anti-resonant hollow-core optical fiber, wherein a core fundamental mode field of the anti-resonant hollow-core optical fiber is defined within the intermediate air region; wherein any two adjacent first cladding elements have a contact point closest to the center point of the core fundamental mode field, and the ratio between the distance D1 from the closest contact point to the nearest boundary of the core fundamental mode field and the distance D2 from the nearest boundary to the center point of the core fundamental mode field has the following relationship: D1 / D2 > 0.46; wherein the boundary of the core fundamental mode field is formed by an intensity of 1 / e of the intensity of the center point of the core fundamental mode field. 2The center point of the square of the fundamental mode electric field strength of the fiber core is defined as the peak point of the square of the fundamental mode electric field strength; wherein each of the first cladding elements also has at least one first main nested element.

[0008] It will be understood that, with the anti-resonant hollow fiber of this disclosure, since adjacent first cladding elements are in contact with each other, the requirements for drawing the hollow fiber can be reduced compared to existing non-contact structures, while the limitation of the range of D1 / D2 can ensure that the confinement loss of the anti-resonant hollow fiber is maintained at a satisfactory level.

[0009] In some embodiments, each of the first cladding elements is selected from a full tube, an arc, a straight wall, or a combination thereof.

[0010] In some embodiments, each of the first cladding elements is a first arcuate element with an opening facing the inner surface and having the same or similar dimensions to each other, and the number of the first cladding elements is 3, 4, or 5. In some embodiments, D1 / D2 is greater than 0.5, 0.6, 0.8, or 1. In these embodiments, the confinement loss of the antiresonant hollow fiber can be further optimized by further limiting the number of first cladding elements and the range of D1 / D2 values.

[0011] In some embodiments, the first primary nesting element is fully or partially nested within the first cladding element. In some embodiments, the first primary nesting element is selected from any of a full tube, a second arcuate element with its opening facing the inner surface, or a straight wall.

[0012] In some embodiments, when the first primary nested element is a full tube or the second arc-shaped element, each of the first primary nested elements also has at least one second primary nested element that is fully nested or partially nested therein.

[0013] In some embodiments, when the first primary nested element is a straight wall, each of the first primary nested elements further has at least one second primary nested element nested between the first primary nested element and the inner surface.

[0014] In some embodiments, the anti-resonant hollow fiber further includes a third main nesting element, which is nested within the second main nesting element or between the second main nesting element and the inner surface.

[0015] In some embodiments, the plurality of first cladding elements include a first cladding main element and a first cladding sub - element, wherein there is at least one corresponding first cladding sub - element between any two adjacent first cladding main elements, and at least some of the first cladding main elements are arranged to contact the largest virtual inscribed circle within the intermediate air region, while all the first cladding sub - elements do not contact the largest virtual inscribed circle at all.

[0016] In some embodiments, the at least one corresponding first cladding sub - element includes a corresponding one first cladding sub - element, and the corresponding one first cladding sub - element contacts two adjacent first cladding main elements respectively.

[0017] In some embodiments, the at least one corresponding first cladding sub - element includes two corresponding first cladding sub - elements contacting each other, and the two corresponding first cladding sub - elements also each contact a neighboring first cladding main element.

[0018] In some embodiments, there is a spacing d between any two adjacent first cladding main elements, the radius of the largest virtual inscribed circle is a, and the following relationship exists between the spacing d and a: 0.1 < d / a < 1.5. In these embodiments, the above numerical range of d / a can also be used to further optimize the preparation of the anti - resonant hollow - core fiber.

[0019] In some embodiments, the shape and size of each first cladding main element are the same or similar, and it is a full tube or nearly a full tube.

[0020] In some embodiments, the shape of each first cladding sub - element is the same or similar to the shape of the first cladding main element.

[0021] In some embodiments, the shape of each first cladding sub - element is different from the shape of the first cladding main element, and it is selected from either an arc - shaped element or a straight wall.

[0022] In some embodiments, the first cladding main element includes at least one main nested element, and the at least one main nested element is selected from either a full tube, an arc - shaped element or a straight wall.

[0023] In some embodiments, in the case where the first cladding sub - element is a full tube or an arc - shaped element with an opening facing the inner surface, the first cladding sub - element includes at least one first - level nested element.

[0024] In some embodiments, in the case where the first cladding sub - element is a straight wall, the first cladding sub - element is also configured with at least one first - level nested element located between the first cladding sub - element and the inner surface.

[0025] In some embodiments, the number of the first cladding master element and the first cladding layer element is the same, and is 3, 4, 5 or 6.

[0026] In some embodiments, all wall thicknesses of the first cladding element are substantially the same.

[0027] In some embodiments, the first cladding element includes different first cladding elements in orthogonal directions, the first cladding elements in the orthogonal directions having different wall thicknesses.

[0028] In some embodiments, the anti-resonant hollow fiber supports effective single-mode or multi-mode transmission.

[0029] In some embodiments, the loss ratio between the lowest-loss higher-order mode and the fundamental mode within the fiber core is at least one order of magnitude, or at least two orders of magnitude, or at least three orders of magnitude.

[0030] In some embodiments, the wall thickness t of the first cladding element and all nested elements satisfies the anti-resonance condition: m = 1, 2, 3, ... where

[0031] Where λ m λ is the resonant wavelength, m is the order of the anti-resonant layer, and n is the refractive index of the material of the component constituting the first cladding element.

[0032] In some embodiments, the ratio of the radius of the largest virtual inscribed circle of the fiber core to the wavelength of the light guided by the hollow fiber is between 3 and 40, or between 4.5 and 20.

[0033] According to a second aspect of the present disclosure, an anti-resonant hollow fiber is provided. The anti-resonant hollow fiber includes: an outer protective sleeve having an inner surface; and a cladding element located within the outer protective sleeve and including a plurality of first cladding elements arranged around the inner surface, any two adjacent first cladding elements of the plurality of first cladding elements contacting each other and defining an intermediate air region of the anti-resonant hollow fiber, wherein a core mode field of the anti-resonant hollow fiber is defined within the intermediate air region; wherein the plurality of first cladding elements includes a first cladding main element and a first cladding sub-element, wherein there is at least one corresponding first cladding sub-element between any two adjacent first cladding main elements, wherein at least some of the first cladding main elements are arranged to contact a maximum virtual inscribed circle within the intermediate air region, and all of the first cladding sub-elements do not contact the maximum virtual inscribed circle, wherein there is a spacing d between any two adjacent first cladding main elements, the radius of the maximum virtual inscribed circle is a, and there is the following relationship between the spacing d and a: 0.1 < d / a < 1.5; wherein there is the following relationship between the distance D3 from the contact point closest to the center point of the maximum virtual inscribed circle between the first cladding main element and the first cladding sub-element to the maximum virtual inscribed circle and the radius a of the maximum virtual inscribed circle: D3 / a > 0.6; wherein the first cladding main element includes at least one first main nested element.

[0034] It will be understood that in the anti-resonant hollow fiber of this second aspect, since adjacent first cladding elements contact each other, the requirements for drawing the hollow fiber can be reduced as compared with the existing non-contact structure. In addition, by defining the parameters of both d / a and D3 / a, the confinement loss of the anti-resonant hollow fiber can also be controlled at a satisfactory level.

[0035] In some embodiments, the first main nested element is selected from any one of a full tube, an arc-shaped element, and a straight wall, and the first main nested element is fully nested or partially nested within the first cladding main element.

[0036] In some embodiments, the at least one corresponding first cladding sub-element includes a corresponding one first cladding sub-element, and the corresponding one first cladding sub-element contacts two adjacent first cladding main elements respectively.

[0037] In some embodiments, the at least one corresponding first cladding sub-element includes two corresponding first cladding sub-elements contacting each other, and the two corresponding first cladding sub-elements also each contact a neighboring first cladding main element.

[0038] In some embodiments, the shape and size of each first cladding main element are the same, and it is a full tube or close to a full tube or an arc-shaped element.

[0039] In some embodiments, D3 / a > 0.8. In some embodiments, D3 / a > 1. In some embodiments, the following relationship exists between the spacing d and a: 0.15 < d / a < 1.3. In some embodiments, the following relationship exists between the spacing d and a: 0.15 < d / a < 1. In these embodiments, by further defining the numerical ranges of D3 / a and d / a, the loss level of the anti-resonant hollow-core fiber can be further optimized.

[0040] In some embodiments, the shape of each of the first cladding sub-elements is the same as the shape of the first cladding main element.

[0041] In some embodiments, the shape of each of the first cladding sub-elements is different from the shape of the first cladding main element and is selected from a full tube, an arc-shaped element, a straight wall, or a combination thereof.

[0042] In some embodiments, a second main nested element is further provided within each of the first main nested elements, and the second main nested element is completely or partially nested within the first main nested element.

[0043] In some embodiments, a third main nested element is further provided within each of the second main nested elements.

[0044] In some embodiments, in the case where the first cladding sub-element is a full tube or an arc-shaped element with an opening facing the inner surface, the first cladding sub-element includes at least one first nested element.

[0045] In some embodiments, in the case where the first cladding sub-element is a straight wall, the first cladding sub-element is further configured with at least one first nested element located between the first cladding sub-element and the inner surface. [[ID=२०]]

[0046] In some embodiments, each first cladding sub-element further contains a first nested element, and each first nested element further contains a second nested element.

[0047] In some embodiments, the number of the first cladding main elements and the first cladding sub-elements is the same and is 3, 4, 5, or 6.

[0048] In some embodiments, all the wall thicknesses of the first cladding main elements are substantially the same.

[0049] In some embodiments, the first cladding main element includes different first cladding main elements in orthogonal directions, and the wall thicknesses of the different first cladding main elements are different.

[0050] In some embodiments, the anti-resonant hollow-core fiber supports effective single-mode or multi-mode transmission.

[0051] In some embodiments, the loss ratio between the lowest-loss higher-order mode and the fundamental mode within the fiber core is at least one order of magnitude, or at least two orders of magnitude, or at least three orders of magnitude.

[0052] In some embodiments, all wall thicknesses t of the first cladding main element satisfy the anti-resonance condition: m = 1, 2, 3, ... where

[0053] Where λ m λ is the resonant wavelength, m is the order of the anti-resonant layer, and n is the refractive index of the material of the component constituting the first cladding element.

[0054] In some embodiments, the ratio of the maximum inscribed circle radius of the fiber core to the wavelength of the light guided by the hollow fiber is between 3 and 40, or between 4.5 and 20.

[0055] It should also be understood that the description in the Summary of the Invention is not intended to limit the key or essential features of the embodiments of this disclosure, nor is it intended to restrict the scope of this disclosure. Other features of the embodiments of this disclosure will become readily apparent from the following description. Attached Figure Description

[0056] The above and other features, advantages, and aspects of the embodiments of this disclosure will become more apparent from the accompanying drawings and the following detailed description. In the drawings, the same or similar reference numerals denote the same or similar elements, wherein:

[0057] Figure 1 shows the conventional Kagome configuration of anti-resonant hollow fiber;

[0058] Figure 2 shows the conventional single-turn non-contact configuration of anti-resonant hollow fiber;

[0059] Figure 3 shows the conventional contact nesting configuration of anti-resonant hollow fiber;

[0060] Figure 4 shows the conventional non-contact nested configuration of anti-resonant hollow fiber;

[0061] Figure 5 shows a schematic illustration of drawing preforms into a non-contact nested configuration;

[0062] Figure 6a shows a typical structural schematic diagram of an anti-resonant hollow optical fiber according to a first exemplary embodiment of the present disclosure;

[0063] Figure 6b illustrates an example of altering the structure of an anti-resonant hollow fiber by adjusting the distance of the closest contact point relative to the inner surface of the outer sheath. From (a) to (c) in Figure 6b, the size of the core mode field remains constant, the distance D1 from the closest contact point to the nearest boundary of the core fundamental mode field and the distance D2 from the nearest boundary to the center point of the core fundamental mode field remain constant, the curvature of the first arc-shaped element also remains constant, while the distance of the closest contact point relative to the inner surface of the outer sheath gradually increases, and the sizes of both the nested tube and the outer sheath increase accordingly.

[0064] Figure 6c shows a simulation plot of the confinement loss of an anti-resonant hollow fiber with varying D1 / D2, taking a first cladding element with a different radius of curvature as an example, under the four-tube contact structure layout of Figure 6a.

[0065] Figure 6d shows a simulation plot of the limiting loss as a function of wavelength for a given D1 / D2;

[0066] Figure 6e shows a simulation plot of the limiting loss as the ratio of D1 / D2 varies, taking a given predetermined structural parameter as an example, under the four-tube contact structure layout of Figure 6a.

[0067] Figure 6f shows a simulation plot of the limiting loss as the ratio of D1 / D2 varies, taking another given predetermined structural parameters as an example, under the four-tube contact structure layout of Figure 6a.

[0068] Figure 6g shows a simulation plot of the effect of changing the ratio between the distance l from the nearest contact point to the outer sheath and the radius a of the largest virtual inscribed circle on limiting losses under the four-tube contact structure layout of Figure 6a, while keeping D1 / D2 constant.

[0069] Figures 6h (a) to (e) show examples of structural variations in the anti-resonant hollow fiber of Figure 6a, where the ratio k of the radius of the first main nested element within the first cladding element gradually increases to the radius of the inscribed circle of the fiber core.

[0070] Figure 6i shows a simulation plot of the limiting loss as the ratio k of the radius of the first main nested element to the radius of the inscribed circle of the fiber core varies under different D1 / D2 conditions;

[0071] Figure 6j shows a simulation plot of the limiting loss as a function of D1 / D2 under different size ratios k of the first main nested element relative to the radius of the inscribed circle of the fiber core;

[0072] Figure 6k shows a simulation plot of the limiting loss as a function of the size ratio k of the first main nested element relative to the radius of the inscribed circle of the fiber core at D1 / D2 = 0.93;

[0073] Figure 61 shows a simulation plot of the limiting loss as a function of the size ratio k of the first main nested element relative to the radius of the inscribed circle of the fiber core when D1 / D2 = 0.69;

[0074] Figure 7a shows a structural example of an anti-resonant hollow optical fiber of the present disclosure where there is a gap region between the closest contact point of two adjacent first cladding elements and the inner surface of the outer sheath.

[0075] Figure 7b shows a simulation plot of the effect of different filling materials (e.g., air and quartz) on the loss of anti-resonant hollow fiber in the gap region between the closest contact point of two adjacent first cladding elements and the inner surface of the outer sheath.

[0076] Figure 8 shows a simulation plot of the confinement loss of the four-tube contact structure as a function of wavelength under different bending radii BR.

[0077] Figure 9a shows a schematic diagram of a modified embodiment of the anti-resonant hollow fiber of Figure 6a;

[0078] Figure 9b shows an example simulation plot of the confinement loss as a function of wavelength under the structural layout of a variant embodiment of the anti-resonant hollow fiber of Figure 6a.

[0079] Figure 10a shows a schematic diagram of the structure of an anti-resonant hollow optical fiber according to a second exemplary embodiment of the present disclosure;

[0080] Figure 10b shows an example simulation plot of the limiting loss as a function of wavelength under the three-tube contact structure layout of Figure 10a;

[0081] Figure 10c shows a variation example of the three-tube contact structure of Figure 10a;

[0082] Figure 10d shows an example simulation plot of the confined loss of an anti-resonant hollow fiber as a function of D1 / D2, taking the first nested component of a given predetermined size as an example, under the three-tube contact structure layout of Figure 10a.

[0083] Figure 10e shows a simulation plot of the confined loss of an anti-resonant hollow fiber as a function of D1 / D2, taking a first nested component of a given additional predetermined size as an example, under the three-tube contact structure layout of Figure 10a.

[0084] Figure 10f shows a simulation plot of the confinement loss of an anti-resonant hollow fiber with varying D1 / D2, taking a first cladding element with a different radius of curvature as an example, under the three-tube contact structure layout of Figure 10a.

[0085] Figure 11 shows a simulation plot of the limiting loss of the anti-resonant hollow fiber under the three-tube contact structure layout of Figure 10a as the radius of the inscribed circle of the fiber core varies.

[0086] Figure 12 shows a simulation plot of the confinement loss of anti-resonant hollow fiber with different D1 / D2 ratios as a function of wavelength under the three-tube contact structure layout of Figure 10a.

[0087] Figure 13 shows a simulation plot of the surface scattering loss of the antiresonant hollow fiber as a function of wavelength under the three-tube contact structure layout of Figure 10a.

[0088] Figure 14 shows a simulation plot of the bending loss of the anti-resonant hollow fiber under different bending radii of curvature as a function of wavelength in the three-tube contact structure layout of Figure 10a.

[0089] Figure 15 shows a simulation plot of the coupling efficiency between the anti-resonant hollow fiber and a Gaussian beam under different core inscribed circle radii in the three-tube contact structure layout of Figure 10a.

[0090] Figure 16a shows a schematic diagram of the structure of an anti-resonant hollow optical fiber according to a third exemplary embodiment of the present disclosure;

[0091] Figure 16b shows a simulation plot of the limiting loss as a function of D1 / D2 under the five-tube contact structure layout of Figure 16a;

[0092] Figure 17a shows a typical structural schematic diagram of an anti-resonant hollow optical fiber according to a fourth exemplary embodiment of the present disclosure;

[0093] Figures 17b, 17c, 17d and 17e illustrate a variant embodiment of Figure 17a;

[0094] Figure 17f shows a schematic diagram of a structure with two corresponding first cladding layer elements between any two adjacent first cladding layer main elements;

[0095] Figure 17g shows a simulation plot of the limiting loss as the ratio of D1 / D2 changes under the contact structure layout of Figure 17a;

[0096] Figure 17h shows a simulation plot of the limitation loss as a function of wavelength under the contact structure layout of Figure 17a;

[0097] Figure 17i shows a simulation plot of the limiting loss as a function of wavelength under the contact structure layout of Figure 17g;

[0098] Figure 18a shows a schematic diagram of a variant of the typical structure of the fourth example embodiment of Figure 17a;

[0099] Figure 18b is a simulation drawing of the limiting loss as the ratio of D1 / D2 changes under the structural layout of Figure 18a.

[0100] Figure 19a shows a schematic diagram of the structure of an anti-resonant hollow fiber according to a fifth exemplary embodiment of the present disclosure, in which both the first cladding master element and the first cladding layer element have only one nested element (i.e., a single-layer nested structure).

[0101] Figure 19b shows a simulation plot of the confinement loss of the anti-resonant hollow fiber in Figure 19a as a function of wavelength;

[0102] Figure 20a shows a schematic diagram of the structure of an anti-resonant hollow fiber according to a fifth exemplary embodiment of the present disclosure, in which both the first cladding master element and the first cladding layer element have double-layer nested elements (i.e., double-layer nested structure) and the dimensions of the first cladding master element and the first cladding layer element are different from each other.

[0103] Figure 20b shows a simulation plot of the confinement loss of the anti-resonant hollow fiber in Figure 20a as a function of d / a;

[0104] Figure 20c shows a simulation plot of the confinement loss of the anti-resonant hollow fiber in Figure 20a as a function of D3 / a;

[0105] Figure 20d shows a schematic diagram of the confined loss of the anti-resonant hollow fiber in Figure 20a as a function of wavelength.

[0106] Figure 21a shows a schematic diagram of a structure in which both the first cladding master element and the first cladding layer element of an anti-resonant hollow optical fiber according to a fifth exemplary embodiment of the present disclosure have double-layer nested elements (i.e., double-layer nested structure) and the dimensions of the first cladding master element and the first cladding layer element are the same.

[0107] Figure 21b shows a simulation plot of the confinement loss of the anti-resonant hollow fiber in Figure 21a as a function of d / a;

[0108] Figure 21c shows a simulation plot of the confinement loss of the anti-resonant hollow fiber in Figure 21a as a function of D3 / a;

[0109] Figure 21d shows a schematic diagram of the confinement loss of the anti-resonant hollow fiber in Figure 21a as a function of wavelength under different spacing d.

[0110] Figure 22a shows a comparative simulation plot of the structure of the anti-resonant hollow fiber of Figure 20a (where the first cladding master element is the same size and different from the first cladding layer element) according to the fifth exemplary embodiment of the present disclosure, the structure of Figure 21a (where the first cladding master element and the first cladding layer element are the same size), and the confinement loss of the four-tube non-contact structure without the first cladding element of Figure 22b as a function of d / a.

[0111] Figure 22b shows a schematic diagram of a four-tube non-contact structure without a first cladding element for comparison.

[0112] Figure 22c shows a comparative simulation plot of the structure of the anti-resonant hollow fiber of Figure 20a (where the first cladding master element is the same size and different from the first cladding layer element) according to the fifth exemplary embodiment of the present disclosure, the structure of Figure 21a (where the first cladding master element and the first cladding layer element are the same size), and the confinement loss of the four-tube non-contact structure without the first cladding element of Figure 22b as a function of D3 / a.

[0113] Figures 23a and 23b show schematic diagrams of structures with strong and weak contact between two adjacent first cladding elements, respectively.

[0114] Figure 23c shows a comparative simulation plot of the confinement loss of the anti-resonant hollow fiber in the fifth exemplary embodiment of the present disclosure as a function of d / a under strong and weak contact conditions.

[0115] Figure 23d shows a comparative simulation plot of the confinement loss of the anti-resonant hollow fiber in the fifth exemplary embodiment of the present disclosure as a function of D3 / a under strong and weak contact conditions.

[0116] Figure 23e shows a comparative simulation plot of the confinement loss as a function of d / a for an anti-resonant hollow fiber with different core radii according to a fifth exemplary embodiment of the present disclosure.

[0117] Figure 23f shows a comparative simulation plot of the confinement loss of the anti-resonant hollow fiber according to the fifth exemplary embodiment of the present disclosure as a function of D3 / a at different core radii;

[0118] Figure 24a shows a schematic diagram of a variant embodiment of the anti-resonant hollow optical fiber according to the present disclosure;

[0119] Figure 24b shows a simulation plot of the confinement loss of the anti-resonant hollow fiber as a function of d / a, according to Figure 24a.

[0120] Figure 24c shows the confinement loss of the antiresonant hollow fiber as a function of D3 / a, based on the simulation plot of Figure 24a.

[0121] Figure 24d shows a schematic diagram of another variant embodiment of the anti-resonant hollow-core optical fiber according to the present disclosure;

[0122] Figure 24e shows a simulation plot of the confinement loss of the anti-resonant hollow fiber as a function of wavelength, according to Figure 24d.

[0123] Figures 25a(a), (b), and (c) show schematic diagrams of the structure of the first cladding main element and the first cladding layer element of the anti-resonant hollow fiber of this disclosure, respectively, which each have two nested elements.

[0124] Figure 25b shows a simulation comparison plot of the confinement loss of the core fundamental mode and higher-order modes of the anti-resonant hollow fiber in Figure 25a as the size ratio m of the first master nesting element relative to the first cladding master element changes;

[0125] Figure 25c shows a simulation plot of the high-order mode suppression ratio of the anti-resonant hollow fiber of Figure 25a as the size ratio m of the first master nesting element relative to the first cladding master element varies.

[0126] Figure 25d shows a simulation comparison plot of the effective refractive index of the core fundamental mode and higher-order modes and inter-tube cavity region mode of the anti-resonant hollow fiber of Figure 25a as a function of the size ratio m of the first main nested element relative to the first cladding main element.

[0127] Figures 26a, 26b and 26c show schematic diagrams of the structures of some other variant examples of the anti-resonant hollow fiber according to the present disclosure.

[0128] Figure 26d shows a schematic diagram of the structure of an existing anti-resonant hollow fiber consisting of cladding elements composed of four sets of circular tube units.

[0129] Figure 26e shows a comparative simulation plot of the confinement loss of anti-resonant hollow fiber as a function of d / a, according to Figures 26a to 26d.

[0130] Figure 26f shows a comparative simulation plot of the confinement loss of the antiresonant hollow fiber as a function of D3 / a, according to Figures 26a to 26c.

[0131] Figure 26g shows a simulation plot of the confinement loss of the anti-resonant hollow fiber as a function of wavelength at different d / a conditions, according to Figure 26a.

[0132] Figure 26h shows a simulation plot of the confinement loss of the anti-resonant hollow fiber as a function of wavelength under different D3 / a conditions, according to Figure 26a.

[0133] Figure 27a shows the possible deformation of the structure in Figure 25a during the actual drawing process;

[0134] Figure 27b shows a simulation plot of the effect of the aforementioned contact point thickening on the limiting loss in the case of the anti-resonant hollow fiber of Figure 27a.

[0135] Figure 27c shows a simulation plot of the limitation loss as a function of wavelength by changing the thickness of a portion of the tube wall (e.g., the thickness dimension of the first main nesting element relative to the first cladding main element) in the case of the anti-resonant hollow fiber of Figure 27a.

[0136] Figure 27d shows a simulation plot of the effect of changing the ratio m of the size of the first main nested element to the size of the first cladding main element on the confinement loss of the core fundamental mode and higher-order modes in the case of the anti-resonant hollow fiber of Figure 27a.

[0137] Figure 27e shows a simulation plot of the higher-order mode suppression ratio as a function of the ratio m of the size of the first master nested element to the size of the first cladding master element in the case of the anti-resonant hollow fiber of Figure 27a.

[0138] Figure 27f shows a simulation plot of the effect of changing the ratio m of the size of the first main nested element to the size of the first cladding main element on the effective refractive index of the core fundamental mode and higher-order modes in the case of the anti-resonant hollow fiber of Figure 27a.

[0139] Figure 28a shows a simulation plot of the effect of changing the size ratio n1 of the first nested element relative to the first cladding layer element on the core fundamental mode and higher-order modes in the case of the anti-resonant hollow fiber of Figure 27a.

[0140] Figure 28b shows a simulation plot of how the higher-order mode suppression ratio changes with the ratio n1 of the size of the first nested element to the size of the first cladding layer element in the case of the anti-resonant hollow fiber in Figure 27a.

[0141] Figure 28c shows a simulation plot of the effect of changing the size ratio n1 of the first nested element relative to the first cladding layer element on the effective refractive index of the core fundamental mode, higher-order modes and inter-tube cavity region modes in the case of the anti-resonant hollow fiber of Figure 27a.

[0142] Figure 29a shows a schematic diagram of the structure of the first cladding master element of the anti-resonant hollow fiber of this disclosure having different thicknesses in the orthogonal directions; and

[0143] Figure 29b shows a simulation diagram illustrating the phase birefringence of the structure in Figure 29a as a function of wavelength. Detailed Implementation

[0144] Embodiments of this disclosure will now be described in more detail with reference to the accompanying drawings. While some embodiments of this disclosure are shown in the drawings, it should be understood that this disclosure can be implemented in various forms and should not be construed as limited to the embodiments set forth herein. Rather, these embodiments are provided to provide a more thorough and complete understanding of this disclosure. It should be understood that the accompanying drawings and embodiments of this disclosure are for illustrative purposes only and are not intended to limit the scope of protection of this disclosure.

[0145] As mentioned earlier, antiresonant hollow-core optical fiber has significant application prospects in many fields, especially in optical fiber communication. A review of the development history of antiresonant hollow-core optical fiber reveals a progression from the Kagome configuration in Figure 1 to the single-turn non-contact configuration in Figure 2, then to the contact nested configuration in Figure 3, and finally to the non-contact nested configuration in Figure 4.

[0146] In the existing configurations described above, when there are contact points between tubes within the optical fiber, Fano oscillations occur at these contact points. These Fano oscillations couple with the fundamental mode field of the fiber core, resulting in oscillation peaks in the loss spectrum. The Kagome configuration described above is a contact structure, where the contact points are some distance from the fiber core to reduce loss, but the loss is still 40 dB / km, failing to achieve a loss below 1 dB / km. The single-turn non-contact configuration described above has too few anti-resonant layers, resulting in a loss of around 10 dB / km. In the contact nested configuration described above, the contact points are too close to the fiber core, resulting in more oscillation peaks and a loss greater than 1 dB / km. Only the non-contact nested configuration described above, where the ratio between the spacing between tube units and the fiber core radius is less than 0.4, can reduce the loss to below 0.1 dB / km.

[0147] However, in their research on the fluid dynamics of actual fiber drawing, the inventors discovered that mass production of non-contact structures with small inter-capillary gaps is quite challenging. This is due to the mid-draw contraction problem during the drawing process—that is, when entering the high-temperature furnace, the capillaries are small and wide, requiring expansion through gas pressure to form a non-contact structure with small gaps. Specifically, in the initial stage of the drawing process, gas pressure dominates, causing the capillary structure to expand. However, in the latter part of the drawing process, surface tension begins to dominate, leading to capillary contraction. If the capillaries have already made contact in the middle of the high-temperature furnace, they cannot separate as they move downwards. If they remain non-contact, the capillaries will shrink further as the temperature decreases, increasing the gap. Therefore, drawing non-contact structures requires very high tension, frequently resulting in fiber breakage. Furthermore, the larger the ratio of the preform to the fiber size (draw-down ratio), the larger the gap between the capillaries, and the draw-down ratio directly determines the yield. Due to limitations imposed by fiber breakage, preform size, and the requirement for small gaps, the current maximum actual production capacity is 15 kilometers. Some articles predict a maximum production capacity of 100 kilometers, but this is far from the production capacity of traditional optical fibers, which ranges from thousands to tens of thousands of kilometers. Figure 5 shows a schematic illustration of drawing the preform into a non-contact nested configuration.

[0148] To solve the above-mentioned problems in drawing and ensure that the anti-resonant hollow fiber has sufficiently low loss, the present disclosure proposes a novel anti-resonant hollow fiber, which includes: an outer protective sleeve having an inner surface; and a cladding element located within the outer protective sleeve and including a plurality of first cladding elements arranged around the inner surface, any two adjacent first cladding elements in the plurality of first cladding elements are in contact with each other, and define an intermediate air region of the anti-resonant hollow fiber, wherein the core fundamental mode field of the anti-resonant hollow fiber is defined within the intermediate air region; and one of the following applies: there is a contact point closest to the center point of the core fundamental mode field between any two adjacent first cladding elements, and the ratio between the distance D1 from the closest contact point to the nearest boundary of the core fundamental mode field and the distance D2 from the nearest boundary to the center point of the core fundamental mode field has the following relationship: D1 / D2 > 0.46, wherein the boundary of the core fundamental mode field is defined by 1 / e of the intensity of the center point of the core fundamental mode field 2 definition, and the center point of the square of the core fundamental mode field intensity is the peak point of the square of the fundamental mode electric field intensity; or the plurality of first cladding elements includes a first main cladding element and a first sub-cladding element, and there is at least one corresponding first sub-cladding element between any two adjacent first main cladding elements, wherein the first main cladding elements are arranged to be in contact with the largest virtual inscribed circle within the intermediate air region simultaneously, while the first sub-cladding elements are not in contact with the largest virtual inscribed circle, and there is a spacing d between any two adjacent first main cladding elements, the radius of the largest virtual inscribed circle is a, and the following relationship exists between the spacing d and a: 0.1 < d / a < 1.5, and the distance D3 from the contact point closest to the center point of the core mode field between the first main cladding element and the first sub-cladding element to the largest virtual inscribed circle and the radius a of the largest virtual inscribed circle have the following relationship: D3 / a > 0.6; at least one nested element is included in the first cladding element or the first main cladding element.

[0149] It will be understood that by making any two adjacent first cladding elements in the cladding elements defining the core contact each other, the drawing difficulty is greatly reduced. In addition, by defining the ratio between D1 and D2, the ratio between the spacing d and the radius a of the largest virtual inscribed circle, and / or the ratio between D3 and the radius a of the largest virtual inscribed circle, the anti-resonant hollow fiber can have sufficiently low loss.

[0150] Various exemplary embodiments of the anti-resonant hollow fiber according to the concept of the present disclosure will be described below with reference to the accompanying drawings.

[0151] First Exemplary Embodiment

[0152] Figure 6a shows a typical structural schematic diagram of an anti-resonant hollow optical fiber according to a first exemplary embodiment of the present disclosure.

[0153] As shown in Figure 6a, the anti-resonant hollow fiber 1 may include an outer sheath tube 2 and a cladding element located inside the outer sheath tube 2.

[0154] The outer sheath 2 has an inner surface 21, and the aforementioned cladding elements may include a plurality of first cladding elements 31 arranged around the inner surface 21.

[0155] According to the design of this disclosure, any two adjacent first cladding elements 31 are in contact with each other and define an intermediate air region 10 of the anti-resonant hollow fiber 1, wherein the core fundamental mode field (e.g., including the core fundamental mode and higher-order core modes) of the anti-resonant hollow fiber is confined within the intermediate air region 10. Each first cladding element 31 may also have at least one first main nested element 32.

[0156] According to some embodiments of this disclosure, the first cladding elements 31 are all first arc-shaped elements with openings facing the inner surface, and have the same or similar dimensions. In particular, the number of first cladding elements 31 can be 3, 4, or 5.

[0157] As an example only, Figure 6a shows four first cladding elements 31, all of which are first arc-shaped elements with openings facing the inner surface and are identical in size. Therefore, the first example embodiment of Figure 6a can also be referred to as a four-tube contact structure.

[0158] In a further embodiment of this disclosure, as an example, the first primary nesting element may be a full tube, a second arc-shaped element with its opening facing the inner surface, or a straight wall. In the example of FIG6a, the first primary nesting element 32 is a full tube, and each first cladding element 31 has two first primary nesting elements 32.

[0159] Furthermore, when the first main nesting element 32 is a full tube (e.g., see FIG. 6a) or a second arc-shaped element, the first main nesting element 32 may also have at least one second main nesting element 33 nested therein; while when the first main nesting element 32 is a straight wall (e.g., see FIG. 9a later), the first main nesting element 32 may also have at least one second main nesting element 33 nested between the first main nesting element 32 and the inner surface 21. The aforementioned second main nesting element 33 can still be selected from a full tube, an arc-shaped element, or a straight wall. For example, in the example of FIG. 6a, the second main nesting element 33 is still a full tube, while in the example of FIG. 9a, which will be described later, the second main nesting element 33 can be a straight wall.

[0160] It should be understood that the nesting arrangement (including the number of layers and the shape of the nested elements) within the first cladding element 31 is selected according to the needs of the anti-resonance design. Therefore, those skilled in the art can select an appropriate nesting arrangement (including the number of layers, the shape and size of the nested elements) according to actual needs. For example, in some embodiments, the number of nested layers within the first cladding element 31 may be more or less than two layers.

[0161] Furthermore, since any two adjacent first cladding elements 31 are in contact with each other, any two adjacent first cladding elements 31 can have a contact point closest to the center point O of the core matrix field. For example, in the example of FIG6a, any two adjacent first cladding elements 31 of the four first cladding elements 31 are in contact with each other and have four contact points closest to the center point O of the core matrix field, such as C1, C2, C3, and C4.

[0162] According to the design of this disclosure, the ratio between the distance D1 from the nearest contact point (e.g., C1, C2, C3, C4) to the nearest boundary of the core matrix field and the distance D2 from the nearest boundary to the center point of the core matrix field can have the following relationship: D1 / D2 > 0.46, wherein the boundary of the core matrix field is formed by a strength equal to 1 / e of the strength of the center point of the core matrix field. 2 By definition, the center point of the square of the fundamental mode field strength of the fiber core is the peak point of the square of the fundamental mode electric field strength. Note: The nearest boundary of the aforementioned fundamental mode field can be seen more clearly, for example, from the common endpoints of D1 and D2 in (a) to (c) of Figure 6b below.

[0163] Simulation results show that the ratio of D1 / D2 > 0.46 can effectively limit the Fano oscillation caused by the contact between two adjacent first cladding elements to a sufficiently low level, thereby ensuring that the anti-resonant hollow fiber has a sufficiently low loss (e.g., a limit loss as low as 1 dB / km), while effectively utilizing the contact between any two adjacent first cladding elements to reduce the difficulty of drawing.

[0164] In some embodiments, the ratio of D1 / D2 and / or the limitation loss can be adjusted by adjusting the specific structural parameters of the anti-resonant hollow fiber (including but not limited to, the distance from the nearest contact point to the inner surface of the outer sheath, the diameter of the largest virtual inscribed circle in the intermediate air region, the wall thickness of each component in the cladding element, the curvature of the first arc-shaped element, the size of the first main nested element relative to the first cladding element, etc.) and the specific structural layout (including but not limited to, nesting arrangement, the number of anti-resonant layers, etc.).

[0165] Figure 6b illustrates an example of altering the structure of an anti-resonant hollow fiber by adjusting the distance of the closest contact point relative to the inner surface of the outer sheath. From (a) to (c) in Figure 6b, the size of the core mode field remains constant, as do the distances D1 from the closest contact point to the nearest boundary of the core fundamental mode field and D2 from the nearest boundary to the center point of the core fundamental mode field. The curvature of the first arc-shaped element also remains constant. Meanwhile, the distance of the closest contact point relative to the inner surface of the outer sheath gradually increases, and the dimensions of both the nested tube and the outer sheath increase accordingly.

[0166] In some embodiments, the ratio of D1 / D2 can be changed by simply adjusting the distance between the nearest contact point and the inner surface of the outer sheath, while keeping other structural parameters constant.

[0167] Figure 6c shows a simulation plot of the confinement loss as a function of the D1 / D2 ratio under the four-tube contact structure layout of Figure 6a. The D1 / D2 ratio is changed by altering the curvature of the first arc-shaped element to adjust the distance between the nearest contact point and the inner surface of the outer sheath. When D1 / D2 = 0.5, the confinement loss is less than 1 dB / km. Correspondingly, Figure 6d shows a simulation plot of the confinement loss as a function of wavelength when D1 / D2 = 0.63. As can be seen from Figure 6d, the antiresonant hollow-core fiber of this disclosure can maintain a low confinement loss level, for example, below 1 dB / km, within the desired wavelength range (e.g., 1350 nm to 1700 nm). Although the antiresonant hollow-core fiber of this disclosure forms fano resonance and oscillates, the amplitude is on the order of <0.1 dB / km.

[0168] In contrast, referring back to the Kagome configuration in Figure 1 and the contact nesting configuration in Figure 3, the measured D1 / D2 ratio in Figure 1 is approximately 0.32, while the D1 / D2 ratio in Figure 3 is approximately 0.37. Neither of them can effectively reduce the losses caused by Fano oscillations.

[0169] Although the above description of the effect of the D1 / D2 ratio on the confinement loss of antiresonant hollow fiber has been presented, it should be understood that, in addition to the aforementioned D1 / D2 ratio, individual adjustments to other structural parameters of the antiresonant hollow fiber (including but not limited to, the distance from the nearest contact point to the inner surface of the outer sheath, the diameter of the largest virtual inscribed circle in the intermediate air region, the wall thickness of each component in the cladding element, the size of the first main nesting element relative to the first cladding element, etc.) and specific structural layouts (including but not limited to, nesting arrangement, the number of antiresonant layers) will also affect the loss of the core fundamental mode field (e.g., core fundamental mode) in the antiresonant hollow fiber.

[0170] Figure 6e shows a simulation plot of the limited loss as a function of the D1 / D2 ratio, taking a given predetermined structural parameter as an example, under the four-tube contact structure layout of Figure 6a. The diameter of the largest virtual inscribed circle in the central air region of the antiresonant hollow fiber is 30 μm, and the wall thickness of each tube in the cladding element is 1.1 μm. The D1 / D2 ratio changes by moving the contact point towards the fiber core. In Figure 6e, when D1 / D2 = 0.62, the loss can be reduced to 1 dB / km, and the loss gradually decreases as D1 / D2 increases.

[0171] Figure 6f shows a simulation plot of the limited loss as a function of the D1 / D2 ratio, using a different set of predetermined structural parameters under the four-tube contact structure layout of Figure 6a. The diameter of the largest virtual inscribed circle in the central air region of the antiresonant hollow fiber is 30 μm, and the wall thickness of each component in the cladding element is 1.2 μm. The D1 / D2 ratio changes by moving the contact point towards the fiber core. In Figure 6f, at D1 / D2 = 0.62, the loss can be reduced to 1 dB / km, and the loss gradually decreases as D1 / D2 increases. At D1 / D2 = 0.73, the loss slightly rebounds above 1 dB / km.

[0172] Figure 6g shows a simulation plot illustrating the effect of changing the ratio between the distance *l* from the nearest contact point to the outer sheath and the radius *a* of the largest virtual inscribed circle on the confinement loss in the four-tube contact structure layout of Figure 6a, while keeping D1 / D2 constant. Here, *l / a* = 0 indicates that the distance *l* from the nearest contact point to the outer sheath is equal to 0, which is typically the case where the closest contact point between two adjacent first cladding elements contacts near the inner surface of the outer sheath; a larger value of *l / a* indicates a larger distance *l* from the nearest contact point to the outer sheath relative to the radius *a* of the largest virtual inscribed circle. As shown in Figure 6g, as the ratio of *l / a* increases, it initially decreases gradually and then gradually increases. In particular, while keeping D1 / D2 constant, the confinement loss of the antiresonant hollow fiber is at its lowest level when *l / a* is in the range of 0.2 to 1.6.

[0173] Figures 6h (a) to (e) show examples of structural variations in the anti-resonant hollow fiber of Figure 6a, where the ratio k of the size of the first master nested element within the first cladding element to the size of the first cladding element gradually increases.

[0174] Figure 6i shows a simulation plot of the limiting loss as a function of the size ratio k of the first main nested element to the first cladding element under different D1 / D2 conditions. Figure 6j shows a simulation plot of the limiting loss as a function of D1 / D2 under different size ratio k of the first main nested element to the first cladding element from another perspective.

[0175] As can be seen from Figures 6i and 6j, in embodiments where the D1 / D2 ratio is small (e.g., 0.46 < D1 / D2 < 0.59), the confinement loss gradually decreases as the size ratio k of the first main nested element relative to the first cladding element increases, and typically the confinement loss can be controlled to around 1 dB / km or less. That is, when D1 / D2 is small, the larger the first main nested element is relative to the first cladding element, the better. Furthermore, as can be seen from Figure 6j, by selecting an appropriate size ratio k of the first main nested element relative to the first cladding element, for example, k greater than 0.7, it is possible to ensure that the confinement loss is around 1 dB / km or less even when the D1 / D2 ratio is as low as close to 0.46.

[0176] Additionally, in embodiments where the D1 / D2 ratio is large (e.g., D1 / D2 > 0.6), selecting a size ratio k of the first primary nested element relative to the first cladding element that is in the middle (e.g., 0.55 < k < 0.68) may be preferable. Figure 6k shows a simulation plot of the confinement loss as a function of the size ratio k of the first primary nested element relative to the first cladding element when D1 / D2 = 0.93. As shown in Figure 6k, the confinement loss increases sharply as the size ratio k is greater than 0.68. Figure 6l shows a simulation plot of the confinement loss as a function of the size ratio k of the first primary nested element relative to the first cladding element when D1 / D2 = 0.69. As shown in Figure 6l, the confinement loss increases sharply when the size ratio k is less than 0.55.

[0177] Ideally, the closest contact point between two adjacent first cladding elements should be in close contact with the inner surface of the outer sheath, meaning there should be no air gap. However, in the actual drawing process, as shown in Figure 7a, the gap region 11 between the closest contact point of two adjacent first cladding elements and the inner surface of the outer sheath may be filled with air or a tube wall material such as quartz. Simulations show that the filling material of the aforementioned gap region 11 also affects the loss of the antiresonant hollow fiber.

[0178] Figure 7b shows a simulation plot of the effect of different filling materials (e.g., air and quartz) on the loss of antiresonant hollow fiber in the gap region between the closest contact point of two adjacent first cladding elements and the inner surface of the outer sheath. As shown in Figure 7b, in the wavelength range of 1300 nm to 1500 nm, the gap region filled with air can have lower loss compared to the gap region filled with, for example, quartz.

[0179] Furthermore, the study of the bending loss of the structure in Figure 6a reveals that there is no significant difference in loss under different bending radii (e.g., 6 cm, 8 cm, and 10 cm) in the anti-resonant hollow fiber, demonstrating the excellent bending loss stability of the example structure in Figure 6a. Figure 8 shows a simulation plot of the confinement loss versus wavelength under different bending radii BR.

[0180] Figure 9a shows a schematic diagram of a variant embodiment of the antiresonant hollow-core optical fiber of Figure 6a. The difference from Figure 6a is that the first main nesting element 32 has a straight wall. Furthermore, the second main nesting element 33 between the first main nesting element 32 and the inner surface 21 of the outer sheath 2 also has a straight wall. Figure 9b shows a schematic diagram of the confinement loss as a function of wavelength according to the exemplary structure of Figure 9a. As shown in Figure 9b, this structure can also maintain the confinement loss at around 1 dB / km or less within the desired wavelength range (e.g., 1350 nm to 1700 nm).

[0181] Second Example Implementation

[0182] Figure 10a shows a schematic diagram of the structure of an anti-resonant hollow optical fiber according to a second exemplary embodiment of the present disclosure.

[0183] The second example embodiment of Figure 10a is similar to the first example embodiment of Figure 6a, except that the cladding elements in Figure 10a consist only of three first cladding elements 31 arranged around the inner surface 21 of the outer sheath tube 2 (therefore, the second example embodiment of Figure 10a can also be referred to as a three-tube contact structure). It should be noted that, unless the context clearly contradicts itself, the description and effects of the first example embodiment of Figure 6a above can also be extrapolated to the second example embodiment of Figure 10a of this disclosure.

[0184] It will also be understood that, compared to the four-tube contact structure of Figure 6a, the three-tube contact structure of Figure 10a is highly advantageous for limiting the Fano oscillations at the contact points of Figure 10a, since the core fundamental mode field and the nearest contact point can be designed to be relatively farther apart. In some embodiments, the limiting loss of the three-tube contact structure of Figure 10a can even be adjusted to below 0.1 dB / km. Furthermore, the curvature and angle of the first cladding element in the three-tube contact structure of Figure 10a have little effect on the loss. Therefore, compared to the four-tube contact structure of Figure 6a, the three-tube contact structure of Figure 10a has greater design and drawing redundancy.

[0185] As an example, Figure 10b shows an example simulation plot of the confinement loss as a function of wavelength under the three-tube contact structure layout of Figure 10a. As can be seen from Figure 10b, a confinement loss of less than 0.1 dB / km can be achieved in the range of 1300 nm to 1550 nm.

[0186] Figure 10c shows a variation of the three-tube contact structure of Figure 10a, in which the curvature of the tube wall of the first cladding element defining the intermediate air region or core is reduced compared to Figure 10a, and the closest contact point between two adjacent first cladding elements 31 is designed to be closer to the center point O of the core fundamental mode field. Assuming other conditions remain unchanged, this means a reduced D1 / D2 ratio. As an example, the D1 / D2 ratio in Figure 10c could be, for example, 0.7.

[0187] It should be understood that, similar to the four-tube contact structure described above, the limiting loss of the three-tube contact structure can be related not only to the ratio of D1 / D2, but also to other structural parameters of the anti-resonant hollow fiber (including, but not limited to, the distance from the closest contact point to the inner surface of the outer sheath, the diameter of the largest virtual inscribed circle in the intermediate air region, the wall thickness of each component in the cladding element, the curvature of the first arc-shaped element, the size and shape of the first main nested element relative to the first cladding element, etc.) and the specific structural layout (including, but not limited to, the nesting arrangement, the number of anti-resonant layers, etc.). Therefore, the limiting loss of the three-tube contact structure can be optimized, for example, by adjusting the specific structural parameters and / or the specific structural layout of the anti-resonant hollow fiber.

[0188] Figure 10d shows an example simulation plot of the confined loss as a function of D1 / D2 for an antiresonant hollow fiber with a given predetermined size, exemplified by a first nested component of a given size, under the three-tube contact structure layout of Figure 10a. The first main nested element 32 is relatively small relative to the size within the first cladding element 31, and the change in D1 / D2 is caused by altering the radius of curvature of the first cladding element. As can be seen from Figure 10d, the confined loss can be maintained below 1 dB / km. Figure 10e shows a simulation plot of the confined loss as a function of D1 / D2 for an antiresonant hollow fiber with a given additional predetermined size, exemplified by a first nested component of a given size under the three-tube contact structure layout of Figure 10a. The first main nested element 32 is designed to be relatively large relative to the size within the first cladding element 31, and the change in the radius of curvature of the first cladding element alters the structural intersection points between the first cladding elements, resulting in changes in the contact points and thus changes in D1 / D2. Analysis of the data in Figure 10e reveals that a smaller radius of curvature of the first cladding element and a greater contact point distance result in lower loss.

[0189] A comparison of Figures 10d and 10e shows that by increasing the size of the first main nested element 32 relative to the first cladding element 31, the confinement loss of the anti-resonant hollow fiber can be significantly reduced. For example, the confinement loss can be reduced to 0.1 dB / km.

[0190] Figure 10f shows a simulation plot of the confinement loss of an antiresonant hollow fiber with varying D1 / D2, using first cladding elements with different radii of curvature as examples, under the three-tube contact structure layout of Figure 10a. As can be seen from Figure 10f, the antiresonant hollow fiber exhibits different confinement losses for different radii of curvature R. Specifically, as the radius of curvature of the first cladding element increases (i.e., the first cladding element, as the first arc-shaped element, becomes flatter), the confinement loss can be relatively reduced. Furthermore, considering the actual contact point thickness, even without changing the curvature, as long as the contact point position is within the specified range, a low-loss standard can still be achieved. For structures with larger radii of curvature, the lower limit of the specified range can be even lower.

[0191] Figure 11 shows a simulation plot of the confinement loss of the antiresonant hollow-core fiber under the three-tube contact structure layout of Figure 10a, as the radius of the circumscribed circle of the fiber core varies. As can be seen from Figure 11, given that other conditions remain constant, the confinement loss can be effectively reduced as the radius of the virtual circumscribed circle of the fiber core gradually increases. Therefore, in practice, the confinement loss can be effectively reduced by selecting the size of the radius of the circumscribed circle of the fiber core.

[0192] Figure 12 shows a simulation plot of the confinement loss of antiresonant hollow-core optical fibers with different D1 / D2 ratios as a function of wavelength under the three-tube contact structure layout of Figure 10a. As can be seen from Figure 12, the antiresonant hollow-core optical fiber exhibits low confinement loss across the entire wavelength range of 1300 to 1700 nm under different D1 / D2 ratios.

[0193] Figure 13 shows a simulation plot of the surface scattering loss of the antiresonant hollow fiber as a function of wavelength under the three-tube contact structure layout of Figure 10a. The simulation results in Figure 13 show that the Fano oscillations introduced by the contact points do not affect the surface scattering loss of the antiresonant hollow fiber.

[0194] Figure 14 shows a simulation plot of the bending loss of the anti-resonant hollow fiber under different bending radii in the tube contact structure layout of Figure 10a as a function of wavelength. The simulation results in Figure 14 show that, at the same bending radius, the bending loss of the three-tube contact structure is greater than that of the four-tube contact structure in Figure 6a, but it is still within a relatively low loss level.

[0195] Figure 15 shows a simulation plot of the coupling efficiency between the antiresonant hollow fiber and a Gaussian beam under different core inscribed circle radii in the tube-contact structure layout of Figure 10a. The simulation results in Figure 15 show that the antiresonant hollow fiber in the three-tube-contact structure layout of Figure 10a can achieve an optical coupling efficiency of over 90% with a Gaussian beam.

[0196] Third Example Implementation

[0197] Figure 16a shows a schematic diagram of the structure of an anti-resonant hollow optical fiber according to a third exemplary embodiment of the present disclosure.

[0198] The third example embodiment of Figure 16a is similar to the first example embodiment of Figure 6a, except that the cladding elements of Figure 16a include five first cladding elements 31 arranged around the inner surface 21 of the outer sheath tube 2 (therefore, the third example embodiment of Figure 16a can also be referred to as a five-tube contact structure). It should be noted that, unless the context clearly contradicts itself, the description and effects of the first example embodiment of Figure 6a above can also be extrapolated to the third example embodiment of Figure 16 of this disclosure.

[0199] Similar to the four-tube contact structure described above, the limiting loss of the five-tube contact structure is related not only to the D1 / D2 ratio but also to the specific structural parameters of the anti-resonant hollow fiber (including but not limited to, the distance from the closest contact point to the inner surface of the outer sheath, the diameter of the largest virtual inscribed circle in the intermediate air region, the wall thickness of each component in the cladding element, the curvature of the first arc-shaped element, and the size and shape of the first main nested element relative to the first cladding element) and the specific structural layout (including but not limited to, the nesting arrangement and the number of anti-resonant layers). Therefore, the limiting loss of the five-tube contact structure can be optimized, for example, by adjusting the specific structural parameters and / or the specific structural layout of the anti-resonant hollow fiber.

[0200] As an example, Figure 16b shows a simulation plot of the confinement loss as a function of D1 / D2 under the five-tube contact structure layout of Figure 16a, where the change in D1 / D2 is caused by filling the contact points with quartz, thus moving the closest contact point toward the fiber core. As can be seen from Figure 16b, in this example, when D1 / D2 > 0.54, the confinement loss can be kept below 1 dB / km.

[0201] Fourth Example Implementation

[0202] Figure 17a shows a typical structural schematic diagram of an anti-resonant hollow optical fiber according to a fourth exemplary embodiment of the present disclosure.

[0203] The fourth exemplary embodiment of this disclosure has a slightly different concept from the first, second, and third exemplary embodiments described above. Similar to the first, second, and third exemplary embodiments described above, as shown in FIG17a, the anti-resonant hollow fiber 1 also includes an outer sheath 2 and cladding elements located within the outer sheath 2, wherein the outer sheath 2 has an inner surface 21, and the cladding elements may include a plurality of first cladding elements 31 arranged around the inner surface 21.

[0204] However, unlike the concepts of the first, second, and third example embodiments above, the plurality of first cladding elements 31 in the fourth example embodiment can be divided into first cladding main elements 31-1 and first cladding layer elements 31-2. According to the design of this disclosure, at least one corresponding first cladding layer element 31-2 is present between any two adjacent first cladding main elements 31-1 and first cladding layer elements 31-2, wherein at least some of the first cladding main elements 31-1 are in contact with the largest virtual inscribed circle within the intermediate air region 10, while all the first cladding layer elements are not in contact with the largest virtual inscribed circle.

[0205] For example, when the fiber core is roughly circular, all the first cladding main elements 31-1 will simultaneously contact the largest virtual inscribed circle within the intermediate air region 10. However, when the fiber core is slightly elliptical, only some of the first cladding main elements 31-1 may contact the largest virtual inscribed circle within the intermediate air region 10.

[0206] In the above arrangement, any two adjacent first cladding master elements will have a spacing d, where the spacing d is defined by the shortest distance between the two adjacent first cladding master elements. Typically, the first cladding element 31-2 between two adjacent first cladding master elements 31-1 is further away from the center point of the core matrix field relative to the first cladding master element 31-1.

[0207] In some embodiments, each first cladding main element 31-1 has the same or similar shape and size, and is a full tube or near-full tube. Furthermore, each first cladding main element 31-1 may also include at least one main nested element 34-1, and each main nested element 34-1 may be selected from any of full tubes, arc-shaped elements, and straight walls.

[0208] Each first-layer element 31-2 may also be a full tube or a near-full tube. Furthermore, each first-layer element 31-2 may include at least one first-nested element 34-2, which may be selected from any of a full tube, an arc-shaped element, and a straight wall.

[0209] In some embodiments, the shape of each first layer element may differ from the shape of the first layer main element and is selected from either an arcuate element or a straight wall. Specifically, in the case where the first layer element is an arcuate element or a straight wall with an opening facing the inner surface, the first layer element may include at least one secondary nested element 34-2, which is located between the first layer element 31-2 and the inner surface 21. In some embodiments, each primary nested element may also contain at least one secondary nested element.

[0210] In some embodiments, any two adjacent first cladding main elements 31-1 may have only one corresponding first cladding layer element 31-2, thereby the first cladding main elements 31-1 and the first cladding layer elements 31-2 alternate with each other and are the same in number. Typically, the number of first cladding main elements 31-1 and first cladding layer elements 31-2 may both be 3, 4, 5 or 6.

[0211] As an example, Figure 17a shows four first cladding main elements 31-1 and four first cladding layer elements 31-2, all of which are full tubes. Furthermore, the size of each first cladding layer element 31-2 is much smaller than that of the first cladding main element 31-1. Figures 17b, 17c, 17d, and 17e show variant embodiments of Figure 17a, wherein the size of the four first cladding layer elements 31-2 in Figures 17b, 17c, 17d, and 17e is increased compared to Figure 17a. Additionally, the outer contours of the cladding elements in Figure 17d form a square arrangement within the outer sheath, while the outer contours of the cladding elements in Figure 17e form a circular arrangement.

[0212] In some embodiments, any two adjacent first cladding main elements 31-1 may have a plurality of corresponding first cladding layer elements 31-2, and these plurality of corresponding first cladding layer elements 31-2 may be in contact with each other. As an example, FIG17f shows a schematic diagram of a structure in which any two adjacent first cladding main elements 31-1 have two corresponding first cladding layer elements 31-2, wherein the two corresponding first cladding layer elements 31-2 are in contact with each other and each is also in contact with a neighboring first cladding main element.

[0213] Furthermore, according to the design of this disclosure, the first cladding main element 31-1 and / or the first cladding layer element 31-2 can be arranged to contact or not contact the inner surface of the outer sheath, which can be a regular shape (e.g., circular or square) or an irregular shape. For example, the inner surface of the outer sheath in Figures 17a, 17b, and 17c is irregular, the inner surface of the outer sheath in Figure 17d is square, and the inner surface of the outer sheath in Figures 17e and 17f is circular. Additionally, the first cladding main element in Figure 17f is arranged not to contact the inner surface of the outer sheath.

[0214] In some embodiments, when the first cladding main element 31-1 and / or the first cladding layer element 31-2 can be arranged to not contact the inner surface of the outer sheath, they can be supported or attached to the inner surface of the outer sheath by, for example, a support 35 (e.g., a straight wall or arcuate element or a columnar element).

[0215] Similar to the first, second, and third exemplary embodiments described above, in this fourth exemplary embodiment, adjacent first cladding elements 31 (here, between adjacent first cladding main elements 31-1 and first cladding layer elements 31-2) will also have the closest contact points, such as C1, C2, C3, C4, C5, C6, C7, and C8 in Figure 17a. Similarly, the confinement loss of the anti-resonant hollow fiber will vary with D1 / D2.

[0216] Figure 17g shows a simulation plot of the limiting loss as a function of the D1 / D2 ratio under the contact structure layout of Figure 17a. As shown in Figure 17g, the loss can be reduced as the D1 / D2 value increases. Figure 17h shows a simulation plot of the limiting loss as a function of wavelength under the contact structure layout of Figure 17a, showing that the limiting loss can be limited to below 1 dB / km, or even below 0.1 dB / km, in the range of 1200 nm to 1750 nm. Figure 17i shows a simulation plot of the limiting loss as a function of wavelength under the contact structure layout of Figure 17g. As can be seen from Figure 17i, the contact structure of Figure 17g can also limit the loss to below 0.1 dB / km.

[0217] Similar to the first, second, and third example embodiments described above, the confinement loss of antiresonant hollow fiber is related not only to the D1 / D2 ratio but also to other structural parameters of the antiresonant hollow fiber (including but not limited to, the distance from the nearest contact point to the inner surface of the outer sheath, the diameter of the largest virtual inscribed circle in the intermediate air region, the wall thickness of each component in the cladding elements, the size of the first cladding layer element relative to the first cladding master element, the size and shape of the first main nested element relative to the first cladding master element, and the size and shape of the first nested element relative to the first cladding layer element, etc.) and the specific structural layout (including but not limited to, nesting arrangement, the number of antiresonant layers, etc.). Therefore, the confinement loss of antiresonant hollow fiber can be optimized by adjusting the aforementioned specific structural parameters and / or specific structural layout of the antiresonant hollow fiber.

[0218] Figure 18a shows a schematic diagram of a variant of the typical structure of the fourth example embodiment of Figure 17a. The variant structure of Figure 18a differs from that of Figure 17a in that the first cladding element 31-2 is formed as a straight wall, thus having a completely different shape from the first cladding main element 31-1. Figure 18b shows a simulation drawing of the limiting loss as the D1 / D2 ratio changes under the contact structure layout of Figure 18a. As shown in Figure 18b, in this example, as the D1 / D2 ratio increases, the loss decreases, thus exhibiting characteristics similar to those in Figure 17g.

[0219] Fifth Example Implementation

[0220] Although the above mainly refers to D1 / D2 to study the confinement loss of the anti-resonant hollow-core fiber. However, for the fourth exemplary embodiment above, it is also found that: the confinement loss of the anti-resonant hollow-core fiber can also be characterized by the ratio d / a between the spacing d between any two adjacent first cladding main elements and the radius a of the largest virtual inscribed circle in the core, and / or the ratio D3 / a between the distance D3 from the contact point closest to the center point of the core fundamental mode field between the adjacent first cladding main element and the first cladding sub-element to the largest virtual inscribed circle and the radius a of the largest virtual inscribed circle. In particular, it is particularly advantageous that the following relationships hold between the spacing d and a and between the distance D3 and a: 0.15 < d / a < 1 and / or D3 / a > 0.6.

[0221] FIG. 19a shows a schematic structural diagram of an anti-resonant hollow-core fiber having only one layer of nested elements (i.e., a single-layer nested structure) both in the first cladding main element and the first cladding sub-element according to a fifth exemplary embodiment of the present disclosure. In the structure shown in FIG. 19a, the structure of the cladding element is approximately square, and the sizes of the first cladding main element and the first cladding sub-element are the same. FIG. 19b shows a simulation plot of the confinement loss of the anti-resonant hollow-core fiber of FIG. 19a as a function of wavelength. As can be seen from FIG. 19b, the overall loss of the single-layer nested structure is relatively high.

[0222] FIG. 20a shows a schematic structural diagram of an anti-resonant hollow-core fiber having two layers of nested elements (i.e., a double-layer nested structure) both in the first cladding main element and the first cladding sub-element according to a fifth exemplary embodiment of the present disclosure. Similar to the structure shown in FIG. 19a, the structure of the cladding element is also approximately square, where the size of the first cladding main element can vary according to the spacing d between the first cladding main elements, while the size of the first cladding sub-element can be smaller than, equal to, or larger than the size of the first cladding main element.

[0223] Figure 20b shows a simulation plot of the confinement loss of the antiresonant hollow fiber in Figure 20a as a function of d / a. Simulation results show that when the ratio of spacing d to a is between 0.15 and 0.87, the confinement loss can be limited to within 1 dB / km, and even below 0.1 dB / km. Figure 20c shows a simulation plot of the confinement loss of the antiresonant hollow fiber in Figure 20a as a function of D3 / a. Simulation results show that when the ratio of D3 to a is greater than 1.2 and less than 3.5, the confinement loss can be controlled at a relatively low level, even below 0.1 dB / km or 0.01 dB / km. Furthermore, Figure 20d shows a schematic diagram of the confinement loss of the antiresonant hollow fiber in Figure 20a as a function of wavelength at D3 / a = 2.21227. As can be seen from Figure 20d, the confinement loss can be controlled below 0.1 dB / km in the wavelength range from 1300 nm to 1700 nm.

[0224] Figure 21a shows a schematic diagram of a variant structure in which both the first cladding master element and the first cladding layer element of the antiresonant hollow fiber according to a fifth exemplary embodiment of the present disclosure have double-layer nested elements (i.e., a double-layer nested structure). Unlike the exemplary structure of Figure 20a, the inner surface of the outer sheath of the antiresonant hollow fiber in Figure 21a is irregular, wherein the size of the first cladding master element can vary according to the spacing d between the first cladding master elements, while the size of the first cladding layer element is the same as the size of the first cladding master element.

[0225] Figure 21b shows a simulation plot of the confinement loss of the antiresonant hollow fiber in Figure 21a as a function of d / a. Simulation results show that when the ratio of spacing d to a is in the range of 0.15 to 0.87, the confinement loss can be essentially limited to within 1 dB / km, and even below 0.1 dB / km. Figure 21c shows a simulation plot of the confinement loss of the antiresonant hollow fiber in Figure 21a as a function of D3 / a. Simulation results show that when the ratio of D3 to a is greater than 1.2 and less than 3.5, the confinement loss can be essentially controlled at a low level, even below 0.1 dB / km or 0.01 dB / km. Furthermore, Figure 21d shows a schematic diagram of the confinement loss of the antiresonant hollow fiber in Figure 21a as a function of wavelength for different spacings d, where spacings d are 10 μm and 9 μm, respectively. The simulation in Figure 21d shows that a slight increase in spacing d does not have a substantial impact on the confinement loss. In particular, when there are only three first cladding main elements in the anti-resonant hollow fiber, the ratio requirement can be further relaxed when the fiber core is increased. For example, it can reach d / a<1, or even d / a<1.3, or even d / a<1.5.

[0226] It should be understood that the presence of the first cladding layer elements in Figures 19a to 21d above can widen the spacing d between two adjacent first cladding layer main elements, thereby increasing the redundancy of the spacing d between two adjacent first cladding layer main elements. This reduces the requirements for drawing the anti-resonant hollow fiber of this disclosure.

[0227] For comparison, Figure 22a shows a comparative simulation plot of the confinement loss as a function of d / a for the structure of the anti-resonant hollow-core optical fiber of Figure 20a (where the first cladding main element has the same size and is different from the size of the first cladding layer element), the structure of Figure 21a (where the first cladding main element and the first cladding layer element have the same size), and the four-tube non-contact structure without the first cladding element of Figure 22b, according to the fifth exemplary embodiment of the present disclosure; Figure 22c shows a comparative simulation plot of the confinement loss as a function of d / a for the structure of the anti-resonant hollow-core optical fiber of Figure 20a (where the first cladding main element has the same size and is different from the size of the first cladding layer element), the structure of Figure 21a (where the first cladding main element and the first cladding layer element have the same size), and the four-tube non-contact structure without the first cladding element of Figure 22b, according to the fifth exemplary embodiment of the present disclosure. It should be noted that Figure 22b shows a schematic diagram of a four-tube non-contact structure without a first cladding element for comparison. Similar to the structures in Figures 20a and 21a, the structure in Figure 22b has four first cladding main elements, each with a double-layer nested structure, but this four-tube non-contact structure does not have a first cladding element. Furthermore, multiple solid quartz rods are present between adjacent first cladding main elements. As can be seen from Figures 22a and 22c, compared to the confinement loss of the anti-resonant hollow-core fiber in the four-tube non-contact structure of Figure 22b, the confinement loss of the anti-resonant hollow-core fiber in the fifth exemplary embodiment of this disclosure can be substantially maintained below 1 dB / km. In contrast, the confinement loss of the anti-resonant hollow-core fiber in the non-contact structure of Figure 2 increases significantly after d / a is greater than 0.6 or D3 / a is less than 2.

[0228] Figures 23a and 23b show schematic diagrams of structures with strong and weak contact between two adjacent first cladding elements, respectively. The term "weak contact" is defined as the two adjacent first cladding elements just making contact; while the term "strong contact" is relative to "weak contact" and is defined as the two adjacent first cladding elements having a relatively large contact area.

[0229] Figure 23c shows a comparative simulation plot of the confinement loss of the antiresonant hollow fiber according to the fifth exemplary embodiment of the present disclosure as a function of d / a under strong and weak contact conditions; Figure 23d shows a comparative simulation plot of the confinement loss of the antiresonant hollow fiber according to the fifth exemplary embodiment of the present disclosure as a function of D3 / a under strong and weak contact conditions. The simulation results in Figures 23c and 23d show that strong and weak contact have no significant impact on the confinement loss of the antiresonant hollow fiber of the present disclosure. This is highly advantageous for the actual drawing process, as it relaxes the requirements for the drawing process.

[0230] Furthermore, as an example of studying the influence of different core radii on confinement loss, Figure 23e shows a comparative simulation plot of the confinement loss of the antiresonant hollow-core optical fiber according to the fifth exemplary embodiment of this disclosure as a function of d / a under different core radii; and Figure 23f shows a comparative simulation plot of the confinement loss of the antiresonant hollow-core optical fiber according to the fifth exemplary embodiment of this disclosure as a function of D3 / a under different core radii. As can be seen from Figures 23e and 23f, different core radii (e.g., core radii a shown in the figures are 23 μm, 19 μm, and 15 μm, respectively) can also have a corresponding effect on confinement loss, with larger core radii resulting in better confinement effect. Therefore, in some cases, the confinement loss of the optical fiber can be adjusted by increasing the core radius of the antiresonant hollow-core optical fiber of this disclosure.

[0231] Other example embodiments

[0232] Figure 24a shows a schematic diagram of a variant embodiment of the antiresonant hollow-core optical fiber according to this disclosure, wherein the cladding elements in the antiresonant hollow-core optical fiber include three first cladding main elements 31-1 and three first cladding layer elements 31-2, wherein the size of the first cladding main elements is much smaller than that of the first cladding layer elements. Figure 24b shows a simulation plot of the confinement loss of the antiresonant hollow-core optical fiber according to Figure 24a as a function of d / a; Figure 24c shows a simulation plot of the confinement loss of the antiresonant hollow-core optical fiber according to Figure 24a as a function of D3 / a, wherein the core radius is chosen to be 20 μm. Simulation results show that by selecting appropriate antiresonant hollow-core optical fiber structures and related parameters, such as 1 < d / a < 1.4, and / or 1.25 < D3 / a < 3, the confinement loss can be controlled at a suitable level, for example, below 1 dB / km.

[0233] Figure 24d shows a schematic diagram of another variant embodiment of the antiresonant hollow-core optical fiber according to this disclosure, wherein the cladding elements in the antiresonant hollow-core optical fiber include five first cladding main elements 31-1 and five first cladding layer elements 31-2, wherein the first cladding main elements and the first cladding layer elements are identical in shape and size. Figure 24e shows a simulation plot of the confinement loss of the antiresonant hollow-core optical fiber according to Figure 24d as a function of wavelength. As can be seen from Figure 24e, the confinement loss can be controlled at an optimal level of 0.1 dB / km in the wavelength range of 1250 nm to 1600 nm.

[0234] Figures 25a(a), (b), and (c) show schematic diagrams of the structure of the first cladding main element and the first cladding layer element of the anti-resonant hollow fiber of this disclosure, respectively, in which the ratio m of the size of the first main nested element to the size of the first cladding main element varies, in (a) m = 0.5, in (b) m = 0.7, and in (c) m = 0.9.

[0235] FIG. 25b shows a simulation comparison plot of the confinement losses of the core fundamental mode and higher-order modes of the anti-resonant hollow-core fiber of FIG. 25a varying with the size ratio m of the first main nested element relative to the first cladding main element; FIG. 25c shows a simulation plot of the higher-order mode suppression ratio of the anti-resonant hollow-core fiber of FIG. 25a varying with the size ratio m of the first main nested element relative to the first cladding main element; FIG. 25d shows a simulation comparison plot of the effective refractive indices of the core fundamental mode, higher-order modes, and the mode in the inter-tube cavity region of the anti-resonant hollow-core fiber of FIG. 25a varying with the size ratio m of the first main nested element relative to the first cladding main element. As can be seen from FIGS. 25b and 25c, the confinement losses and higher-order mode suppression ratio of the higher-order modes of the anti-resonant hollow-core fiber of FIG. 25a can be adjusted to an appropriate range by changing the ratio of the size of the first main nested element relative to the first cladding element; as can be seen from FIG. 25d, changing the size ratio m of the first main nested element relative to the first cladding main element has a greater impact on the effective refractive index of the cavity region between the nested tubes of the anti-resonant hollow-core fiber, while having little impact on the effective refractive indices of the fundamental mode LP_{01} and higher-order mode LP_{11} of the anti-resonant hollow-core fiber. In particular, as m changes, for example, when 0.5 < m < 0.65, the gradual decrease in the cavity area between the first main nested element and the second main nested element nested within the first cladding main element causes the effective refractive index of the fundamental mode at this cavity to gradually approach the effective refractive index of the higher-order mode LP_{11}. At the intersection point where m = 0.58, the higher-order mode LP_{11} is phase-matched with the fundamental mode at the cavity, causing LP_{11} to leak from the cavity, resulting in an increase in loss and thus an increase in the higher-order mode suppression ratio; when 0.7 < m < 0.9, the cavity area between the second main nested element and the third main nested element nested within the first cladding main element gradually increases, and the effective refractive index gradually increases, approaching LP_{11}. At the intersection point where m = 0.82, the higher-order mode P_{11} is phase-matched with the fundamental mode at the cavity, causing LP_{11} to leak from the cavity, resulting in an increase in loss and thus an increase in the higher-order mode suppression ratio.

[0236] FIGS. 26a, 26b, and 26c show schematic structural diagrams of some other variant examples of the anti-resonant hollow-core fiber according to the present disclosure. Among them, the cladding element in FIG. 26a includes four first cladding main elements that are substantially circular tubes and four first cladding sub-elements each consisting of only a straight wall. The difference between FIG. 26b and FIG. 26a is that there is a nested element in the form of a straight wall between the first cladding sub-element in the form of a straight wall and the outer protective tube in FIG. 26b. The difference between FIG. 26c and FIG. 26b is that the cladding element in FIG. 26c only includes three first cladding main elements that are substantially circular tubes. For comparison, FIG. 26d shows a schematic structural diagram of an existing anti-resonant hollow-core fiber including a cladding element composed of 4 groups of circular tube units.

[0237] Figure 26e shows a comparative simulation plot of the confinement loss of the antiresonant hollow fiber as a function of d / a according to Figures 26a to 26d; Figure 26f shows a comparative simulation plot of the confinement loss of the antiresonant hollow fiber as a function of D3 / a according to Figures 26a to 26c. Figure 26g shows a simulation plot of the confinement loss of the antiresonant hollow fiber as a function of wavelength under different d / a conditions according to Figure 26a; Figure 26h shows a simulation plot of the confinement loss of the antiresonant hollow fiber as a function of wavelength under different D3 / a conditions according to Figure 26a. As can be seen from Figure 26e, although there are contact points between adjacent first cladding elements in Figures 26a to 26c, by optimizing the ratio between d / a, the confinement loss of the antiresonant hollow fiber can still be limited to a good range, such as 1 dB / km, or even within the range of 0.1 dB / km. As can be seen from Figures 26g and 26h, by selecting an appropriate ratio of d / a and D3 / a for the anti-resonant hollow fiber in Figure 26a, the confinement loss of the anti-resonant hollow fiber can be limited to a low loss level.

[0238] It should be noted that the various structures of the antiresonant hollow fiber disclosed herein, as illustrated above, are ideal structures. In the actual drawing process, the structure of the antiresonant hollow fiber may deform under pressure.

[0239] As an example, Figure 27a shows a possible deformation of the structure of Figure 25a during the actual drawing process. The first cladding main element 31-1 and the first cladding layer element 31-2, which are essentially full-tube shapes, may become irregularly circular because the tube walls between the contact points of adjacent first cladding elements 31 will straighten during drawing. Furthermore, since supports 35 (e.g., quartz pillars) may be arranged between the inner surfaces of the first cladding main element and the outer sheath, the four supports 35 may be tangent to the inner surfaces 21 of the corresponding first cladding main element and the outer sheath. In this case, the tube walls between the contact points and the supports may also straighten during drawing. Simultaneously, the contact points between adjacent first cladding elements may also thicken due to compression during drawing.

[0240] Figure 27b shows a simulation plot of the effect of the thickened contact point on the confinement loss in the case of the anti-resonant hollow fiber of Figure 27a. The simulation results show that the thickened contact point has no substantial effect on the confinement loss.

[0241] During the drawing process, the thickness of the tube wall may vary locally. Figure 27c shows a simulation plot of the limitation loss versus wavelength for the anti-resonant hollow fiber of Figure 27a, where the thickness of a portion of the tube wall is changed (e.g., the thickness of the first main nested element relative to the first cladding main element). Plot: Although the actual structure differs from the ideal structure, it can still exhibit good fundamental mode loss performance.

[0242] Figure 27d shows a simulation plot of the effect of changing the ratio *m* of the size of the first main nesting element to the size of the first cladding main element on the fundamental and higher-order modes in the case of the anti-resonant hollow fiber of Figure 27a. Figure 27e shows a simulation plot of the higher-order mode suppression ratio as a function of the ratio *m* of the size of the first main nesting element to the size of the first cladding main element in the case of the anti-resonant hollow fiber of Figure 27a. As can be seen from Figure 27d, changing the aforementioned ratio *m* has a significant impact on the fundamental mode loss; when 0.65 < *m* < 0.75, the loss is ≤ 0.01 dB / km. However, in some embodiments, simply changing the value of *m* may not effectively filter out higher-order modes; for example, when 0.65 < *m* < 0.75, the higher-order mode suppression ratio is ≤ 100, meaning the filtering effect on higher-order modes is poor. Figure 27f shows a simulation plot of the effect of changing the size ratio *m* of the first master nesting element relative to the first cladding master element on the effective refractive index of the core fundamental mode, higher-order modes, and inter-tube cavity region modes in the case of the anti-resonant hollow fiber of Figure 27a. Furthermore, the simulation plot of the effective refractive index in Figure 27f shows that the effective refractive index of the cavity within the first cladding master element is significantly different from the effective refractive index of the higher-order modes in the core.

[0243] In some embodiments, the aforementioned higher-order mode suppression ratio can be suppressed by adjusting the size of the first nested element relative to the first cladding layer element. Figure 28a shows a simulation plot of the effect of changing the size ratio n1 of the first nested element relative to the first cladding layer element on the limiting loss of the core fundamental mode and higher-order modes in the case of the anti-resonant hollow fiber of Figure 27a; Figure 28b shows a simulation plot of the higher-order mode suppression ratio as the size ratio n1 of the first nested element relative to the first cladding layer element changes in the case of the anti-resonant hollow fiber of Figure 27a; Figure 28c shows a simulation plot of the effect of changing the size ratio n1 of the first nested element relative to the first cladding layer element on the effective refractive index of the core fundamental mode, higher-order modes, and inter-tube cavity region modes in the case of the anti-resonant hollow fiber of Figure 27a.

[0244] As can be seen from Figures 28a and 28b, changing the size ratio n1 of the first nested tube relative to the first layered element has a relatively small impact on the fundamental mode loss; for example, the fundamental mode loss can be less than 0.01 dB / km. However, changing this ratio can effectively match the effective refractive index of the higher-order modes in the fiber core with the effective refractive index of the cavity within the first layered element, thereby changing the higher-order mode loss and achieving a higher higher-order mode suppression ratio. For example, Figure 28b shows that at n = 0.53, the higher-order mode suppression ratio can reach 2093. Furthermore, from the simulation plot of the effective refractive index in Figure 28c, the effective refractive index of the cavity between the first layered element and the first nested element is also close to the effective refractive index of the higher-order modes in the fiber core, for example, Δn eff ≈0.00001.

[0245] Therefore, higher-order modes within the fiber core can be suppressed by alternating arrangements of multiple first cladding master elements and multiple first cladding layer elements, especially by nested arrangements within the first cladding layer elements.

[0246] Various embodiments of the antiresonant hollow fiber of this disclosure have been described above. It should be understood that, since adjacent first cladding elements in the antiresonant hollow fiber of this disclosure are in contact with each other, the requirements for drawing are reduced compared to existing non-contact structures. At the same time, by optimizing the specific structural parameters (especially the ratios of D1 / D2, d / a, and / or D3 / a) and / or the specific layout of the antiresonant hollow fiber of this disclosure, the confinement loss of the antiresonant hollow fiber can be maintained at a satisfactory level.

[0247] Typically, all wall thicknesses t of the first cladding element of this disclosure can satisfy the anti-resonance condition: m = 1, 2, 3, ... where m = 1, 2, 3, ...

[0248] Where λm is the resonant wavelength, m is the order of the anti-resonant layer, and n is the refractive index of the material of the component constituting the first cladding element.

[0249] Specifically, in some embodiments, all wall thicknesses of the first cladding element can be substantially the same. In still other embodiments, the first cladding element may include different first cladding elements (or first cladding master elements) in orthogonal directions, and the wall thicknesses of these different first cladding elements (or first cladding master elements) in orthogonal directions may be different from each other. As an example, FIG29a shows a schematic diagram of the structure of the first cladding master element of the antiresonant hollow fiber of this disclosure having different thicknesses in orthogonal directions. For example, as shown in FIG29a, the first cladding master element has a thickness of 1.3 μm in the first direction and only 1.1 μm in the second direction orthogonal to the first direction. In the case of inconsistent wall thicknesses in the above-mentioned orthogonal directions, the antiresonant hollow fiber can make the effective refractive index of the mode field in the orthogonal directions within the fiber core different, thereby generating birefringence and achieving the technical effect of polarization preservation. FIG29b shows a simulation schematic diagram of the phase birefringence of the structure of FIG29a as a function of wavelength.

[0250] In some other embodiments, the ratio of the radius of the largest virtual inscribed circle of the fiber core to the wavelength of the light guided by the hollow fiber is between 3 and 40, or between 4.5 and 20. Furthermore, the antiresonant hollow fiber of this disclosure can support effective single-mode or multimode transmission, wherein the loss ratio between the lowest-loss higher-order mode and the fundamental mode within the fiber core can be at least one order of magnitude, or at least two orders of magnitude, or at least three orders of magnitude.

[0251] Furthermore, it should be understood that, without contradiction, the features of the above embodiments can be combined with each other, and the description of the above embodiments can be applied to other embodiments.

[0252] While the invention has been detailed and described in the accompanying drawings and foregoing description, these descriptions and descriptions should be considered illustrative or exemplary rather than restrictive; the invention is not limited to the disclosed embodiments. Other variations of the disclosed embodiments will be understood and practiced by those skilled in the art in practicing the claimed invention through study of the drawings, disclosure, and appended claims.

[0253] In the claims, the word "comprising" does not exclude other elements, and the indefinite articles "a" or "an" do not exclude a plurality. A single element or other component may fulfill the function of multiple items set forth in the claims. The mere fact that certain features are recited only in dissimilar embodiments or dependent claims does not imply that combinations of these features cannot be advantageously used. Without departing from the spirit and scope of this application, the scope of protection of this application covers any possible combination of the various features recited in the various embodiments or dependent claims.

[0254] Furthermore, any reference numerals in the claims should not be construed as limiting the scope of the invention.

Claims

1. An anti-resonant hollow-core optical fiber, comprising: Outer sheath with an inner surface; as well as A cladding element, located within the outer sheath and comprising a plurality of first cladding elements arranged around the inner surface, wherein any two adjacent first cladding elements are in contact with each other and define an intermediate air region of the anti-resonant hollow fiber, wherein the core fundamental mode field of the anti-resonant hollow fiber is confined within the intermediate air region. Between any two adjacent first cladding elements, there is a contact point closest to the center point of the core matrix field. The ratio between the distance D1 from the closest contact point to the nearest boundary of the core matrix field and the distance D2 from the nearest boundary to the center point of the core matrix field has the following relationship: D1 / D2 > 0.

46. The boundary of the core matrix mode field is defined by a strength equal to 1 / e of the strength at the center point of the core matrix mode field. 2 By definition, the center point of the square of the fundamental mode electric field strength of the fiber core is the peak point of the square of the fundamental mode electric field strength; Each of the first cladding elements further includes at least one first main nested element.

2. The anti-resonant hollow optical fiber according to claim 1, wherein each of the first cladding elements is selected from a full tube, a circular arc, a straight wall, or a combination thereof.

3. The anti-resonant hollow optical fiber according to claim 1, wherein each of the first cladding elements is a first arc-shaped element with an opening facing the inner surface and having the same or similar dimensions to each other, and the number of the first cladding elements is 3, 4 or 5.

4. The anti-resonant hollow fiber according to claim 1, wherein D1 / D2 is greater than 0.5, 0.6, 0.8 or 1.

5. The anti-resonant hollow fiber according to claim 1, wherein the first main nesting element is fully or partially nested in the first cladding element.

6. The anti-resonant hollow optical fiber according to claim 1, wherein the first main nesting element is selected from any one of a full tube, a second arc-shaped element with its opening facing the inner surface, or a straight wall.

7. The anti-resonant hollow fiber according to claim 6, wherein when the first main nesting element is a full tube or the second arc-shaped element, each of the first main nesting elements further comprises at least one second main nesting element that is fully or partially nested therein.

8. The anti-resonant hollow fiber according to claim 6, wherein when the first main nesting element is a straight wall, each of the first main nesting elements further comprises at least one second main nesting element nested between the first main nesting element and the inner surface.

9. The anti-resonant hollow optical fiber according to claim 7 or 8 further includes a third main nesting element, the third main nesting element being nested within the second main nesting element or between the second main nesting element and the inner surface.

10. The anti-resonant hollow fiber according to claim 1, wherein the plurality of first cladding elements comprises first cladding master elements and first cladding layer elements, wherein at least one corresponding first cladding layer element is present between any two adjacent first cladding master elements, wherein at least some of the first cladding master elements are arranged to contact the largest virtual inscribed circle in the intermediate air region, while all the first cladding layer elements are not in contact with the largest virtual inscribed circle at all.

11. The anti-resonant hollow-core optical fiber according to claim 10, wherein the corresponding at least one first cladding layer element includes a corresponding first cladding layer element, and the corresponding first cladding layer element is in contact with two adjacent first cladding main elements respectively.

12. The anti-resonant hollow fiber according to claim 10, wherein the corresponding at least one first cladding layer element comprises two corresponding first cladding layer elements in contact with each other, and each of the two corresponding first cladding layer elements is in contact with an adjacent first cladding main element.

13. The anti-resonant hollow-core optical fiber according to claim 10, wherein any two adjacent first cladding principal elements are spaced by a distance d, the radius of the largest virtual inscribed circle is a, and the distance d and a have the following relationship: 0.1 <d / a<1.5。 14. The anti-resonant hollow fiber according to claim 10, wherein each of the first cladding master elements has the same or similar shape and size, and is a full tube or nearly a full tube.

15. The anti-resonant hollow fiber according to claim 10, wherein the shape of each of the first cladding layer elements is the same as or similar to the shape of the first cladding main element.

16. The anti-resonant hollow fiber according to any one of claims 10 to 15, wherein the shape of each of the first cladding layer elements is different from the shape of the first cladding master element, and is selected from either arc-shaped elements and straight walls.

17. The anti-resonant hollow-core optical fiber according to any one of claims 10 to 15, wherein the first cladding master element comprises at least one master nested element, the at least one master nested element being selected from any one of a full tube, an arc-shaped element, and a straight wall.

18. The anti-resonant hollow fiber according to any one of claims 10 to 15, wherein in the case where the first cladding layer element is a full tube or an arc-shaped element with an opening facing the inner surface, the first cladding layer element includes at least one sub-nested element.

19. The anti-resonant hollow fiber according to any one of claims 10 to 15, wherein, in the case where the first cladding layer element is a straight wall, the first cladding layer element is further configured with at least one sub-nested element located between the first cladding layer element and the inner surface.

20. The anti-resonant hollow fiber according to any one of claims 10 to 15, wherein the number of the first cladding main element and the number of the first cladding layer elements are the same, and are 3, 4, 5 or 6.

21. The anti-resonant hollow fiber according to any one of claims 1-8 and 10-15, wherein all wall thicknesses of the first cladding element are substantially the same.

22. The anti-resonant hollow fiber according to any one of claims 1-8 and 10-15, wherein the first cladding element comprises different first cladding elements in orthogonal directions, the first cladding elements in the orthogonal directions having different wall thicknesses.

23. The anti-resonant hollow fiber according to any one of claims 1-8 and 10-15, wherein the anti-resonant hollow fiber supports effective single-mode or multimode transmission.

24. The anti-resonant hollow-core optical fiber according to any one of claims 1-8 and 10-15, wherein the loss ratio between the lowest loss higher-order mode in the core and the fundamental mode in the core is at least one order of magnitude, or at least two orders of magnitude, or at least three orders of magnitude.

25. The anti-resonant hollow-core optical fiber according to any one of claims 1-8 and 10-15, wherein all wall thicknesses t of the first cladding element and all nested elements satisfy the anti-resonance condition: in Where λ m λ is the resonant wavelength, m is the order of the anti-resonant layer, and n is the refractive index of the material of the component constituting the first cladding element.

26. The anti-resonant hollow-core optical fiber according to any one of claims 1-8 and 10-15, wherein the ratio of the radius of the largest virtual inscribed circle of the fiber core to the wavelength of the light guided by the hollow-core optical fiber is between 3 and 40, or between 4.5 and 20.

27. An anti-resonant hollow optical fiber, comprising: Outer sheath with an inner surface; as well as A cladding element, located within the outer sheath and comprising a plurality of first cladding elements arranged around the inner surface, wherein any two adjacent first cladding elements are in contact with each other and define an intermediate air region of the anti-resonant hollow fiber, wherein the core mode field of the anti-resonant hollow fiber is confined within the intermediate air region. The plurality of first cladding elements includes first cladding main elements and first cladding layer elements, wherein at least one corresponding first cladding layer element is present between any two adjacent first cladding main elements, wherein at least some of the first cladding main elements are arranged to contact the largest virtual inscribed circle in the intermediate air region, while none of the first cladding layer elements are in contact with the largest virtual inscribed circle. The first cladding master element is spaced d apart from any two adjacent elements, and the radius of the largest virtual inscribed circle is a. The spaced d and a are related as follows: 0.1 <d / a<1.5; The distance D3 between the contact point closest to the center of the largest virtual inscribed circle and the first cladding main element and the first cladding layer element, and the radius a of the largest virtual inscribed circle, has the following relationship: D3 / a>0.6; The first cladding master element includes at least one first master nested element.

28. The anti-resonant hollow optical fiber according to claim 27, wherein the first main nesting element is selected from any one of a full tube, an arc-shaped element, and a straight wall, and the first main nesting element is fully nested or partially nested within the first cladding main element.

29. The anti-resonant hollow-core optical fiber according to claim 27, wherein the corresponding at least one first cladding layer element includes a corresponding first cladding layer element, and the corresponding first cladding layer element is in contact with two adjacent first cladding main elements respectively.

30. The anti-resonant hollow fiber according to claim 27, wherein the corresponding at least one first cladding layer element comprises two corresponding first cladding layer elements in contact with each other, and each of the two corresponding first cladding layer elements is in contact with an adjacent first cladding main element.

31. The anti-resonant hollow fiber according to claim 27, wherein each first cladding master element has the same shape and size, and is a full tube or near-full tube or arc-shaped element.

32. The anti-resonant hollow optical fiber according to claim 27, wherein D3 / a > 0.

8.

33. The anti-resonant hollow optical fiber according to claim 27, wherein D3 / a>1.

34. The anti-resonant hollow-core optical fiber according to claim 27, wherein the spacing d and a have the following relationship: 0.15 <d / a<1.3。 35. The anti-resonant hollow fiber according to claim 27, wherein the spacing d and a have the following relationship: 0.15 <d / a<1。 36. The anti-resonant hollow fiber according to any one of claims 27 to 35, wherein the shape of each of the first cladding layer elements is the same as the shape of the first cladding master element.

37. The anti-resonant hollow fiber according to any one of claims 27 to 35, wherein the shape of each of the first cladding layer elements is different from the shape of the first cladding master element, and is selected from full tube, arc-shaped element, straight wall or combination thereof.

38. The anti-resonant hollow fiber according to any one of claims 27 to 35, wherein each of the first main nesting elements is further provided with a second main nesting element, the second main nesting element being wholly or partially nested within the first main nesting element.

39. The anti-resonant hollow optical fiber according to claim 38, wherein each of the second main nested elements further comprises a third main nested element.

40. The anti-resonant hollow fiber according to any one of claims 27 to 35, wherein each first cladding layer element further comprises a first nested element.

41. The anti-resonant hollow fiber according to any one of claims 27 to 35, wherein each first nested element further comprises a second nested element.

42. The anti-resonant hollow fiber according to any one of claims 27 to 35, wherein in the case where the first cladding element is a full tube or an arcuate element with its opening facing the inner surface, the first cladding element includes at least one first nesting element.

43. The anti-resonant hollow fiber according to any one of claims 27 to 35, wherein, in the case where the first cladding layer element is a straight wall, the first cladding layer element is further configured with at least one first nested element located between the first cladding layer element and the inner surface.

44. The anti-resonant hollow fiber according to any one of claims 27 to 35, wherein the number of the first cladding main element and the number of the first cladding layer elements are the same, and are 3, 4, 5 or 6.

45. The anti-resonant hollow fiber according to any one of claims 27 to 35, wherein all wall thicknesses of the first cladding master element are substantially the same.

46. ​​The anti-resonant hollow-core optical fiber according to any one of claims 27 to 35, wherein the first cladding master element comprises different first cladding master elements in orthogonal directions, and the different first cladding master elements have different wall thicknesses.

47. The anti-resonant hollow fiber according to any one of claims 27 to 35, wherein the anti-resonant hollow fiber supports effective single-mode or multimode transmission.

48. The anti-resonant hollow-core optical fiber according to any one of claims 27 to 35, wherein the loss ratio between the lowest loss higher-order mode in the core and the fundamental mode in the core is at least one order of magnitude, or at least two orders of magnitude, or at least three orders of magnitude.

49. The anti-resonant hollow-core optical fiber according to any one of claims 27 to 35, wherein all wall thicknesses t of the first cladding principal element satisfy the anti-resonance condition: in Where λ m λ is the resonant wavelength, m is the order of the anti-resonant layer, and n is the refractive index of the material of the component constituting the first cladding element.

50. The anti-resonant hollow optical fiber according to any one of claims 27 to 35, wherein the ratio of the maximum inscribed circle radius of the fiber core to the wavelength of the light guided by the hollow optical fiber is between 3 and 40, or between 4.5 and 20.

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