Hollow core optical fiber

Abstract

A hollow core optical fiber (100) may include: a hollow core (110) extending along a central longitudinal axis of the optical fiber; a base material (130); a plurality of first cladding elements (122) spaced apart from each other and positioned between the hollow core and the substrate, each of the first cladding elements extending in a direction parallel to a central longitudinal axis (112) of the optical fiber, each of the first cladding elements (122) comprising a first capillary (310); and a plurality of second cladding elements (124) spaced apart from each other and positioned between the hollow core (112) and the substrate (130), each of the second cladding elements (112) extending in a direction parallel to the central longitudinal axis (112) of the optical fiber, each of the second cladding elements (124) comprising a second capillary (310). Each of the first cladding elements (122) directly contacts an inner surface of the substrate (310), and each of the second cladding elements (124) does not directly contact the inner surface of the substrate (310).

Description

[0001] This application claims the benefit of priority under 35 USC §120 to U.S. Provisional Application Serial No. 63 / 392,648, filed on July 27, 2022, the contents of which are hereby incorporated by reference in their entirety. background Technical Field

[0002] This specification relates generally to optical fibers and, more particularly, to hollow core optical fibers. Background Art

[0003] Hollow core optical fibers transmit light through a hollow core. Light loss from the hollow core along the length of the optical fiber may be an obstacle to the implementation of hollow core optical fibers in practical applications. Therefore, there is a need for hollow core optical fibers with a structure that confines light within the hollow core, thereby reducing light loss from the hollow core along the length of the optical fiber. Summary of the invention

[0004] According to a first aspect of the present disclosure, a hollow core extending along a central longitudinal axis of a hollow core optical fiber; a substrate including a tubular shape and an inner surface surrounding the central longitudinal axis of the hollow core optical fiber; a plurality of first cladding elements spaced apart from each other and positioned between the hollow core and the substrate, each of the plurality of first cladding elements extending in a direction parallel to the central longitudinal axis of the hollow core optical fiber, each of the plurality of first cladding elements including a first capillary including an inner surface defining a first cavity, the first cavity having a first diameter and being occupied only by a gas; and a plurality of second cladding elements spaced apart from each other and positioned between the hollow core optical fiber and the substrate, each of the second cladding elements extending in a direction parallel to the central longitudinal axis of the hollow core optical fiber, each of the second cladding elements including a second capillary including an inner surface defining a second cavity, the second cavity having a second diameter and being occupied only by a gas, the second diameter being different from the first diameter. Each of the plurality of first cladding elements directly contacts the inner surface of the substrate, and each of the second cladding elements does not directly contact the inner surface of the substrate.

[0005] A second aspect of the present disclosure may include the first aspect, wherein each first cladding element is spaced apart from adjacent first cladding elements in a circumferential direction.

[0006] A third aspect of the present disclosure may include the second aspect, wherein the first cladding elements are equally spaced apart in the circumferential direction.

[0007] A fourth aspect of the present disclosure may include any one of the first to third aspects, wherein each second capillary directly contacts at least one first capillary.

[0008] A fifth aspect of the present disclosure may include any one of the first to fourth aspects, wherein each second cladding element is spaced apart from an inner surface of the substrate in a radial direction.

[0009] A sixth aspect of the present disclosure may include any one of the first to fifth aspects, wherein each second cladding element is spaced apart from adjacent second cladding elements in a circumferential direction.

[0010] A seventh aspect of the present disclosure may include any one of the first to sixth aspects, wherein the second cladding elements are equally spaced apart in the circumferential direction.

[0011] An eighth aspect of the present disclosure may include any one of the first to seventh aspects, wherein the plurality of first cladding elements are symmetrically arranged about a central longitudinal axis of the hollow core optical fiber.

[0012] A ninth aspect of the present disclosure may include any one of the first to eighth aspects, wherein the plurality of second cladding elements are symmetrically arranged about a central longitudinal axis of the hollow core optical fiber.

[0013] A tenth aspect of the present disclosure may include any one of the first to ninth aspects, wherein each first capillary directly contacts two second capillaries.

[0014] An eleventh aspect of the present disclosure may include any one of the first to tenth aspects, wherein the plurality of first cladding elements includes 3 to 8 first capillaries.

[0015] A twelfth aspect of the present disclosure may include any one of the first to eleventh aspects, wherein the plurality of first cladding elements include 5 to 6 first capillaries.

[0016] A thirteenth aspect of the present disclosure may include any one of the first to twelfth aspects, wherein the plurality of second cladding elements include 3 to 12 second capillaries.

[0017] A fourteenth aspect of the present disclosure may include any one of the first to thirteenth aspects, wherein the plurality of second cladding elements include 5 to 6 second capillaries.

[0018] A fifteenth aspect of the present disclosure may include any one of the first to fourteenth aspects, wherein the number of the first cladding elements is equal to the number of the second cladding elements.

[0019] A sixteenth aspect of the present disclosure may include any one of the first to fifteenth aspects, wherein the number of the first capillaries is equal to the number of the second capillaries.

[0020] A seventeenth aspect of the present disclosure may include any one of the first to sixteenth aspects, wherein the second diameter is greater than the first diameter.

[0021] An eighteenth aspect of the present disclosure may include any one of the first to seventeenth aspects, wherein each first capillary comprises a first capillary central longitudinal axis parallel to a central longitudinal axis of the optical fiber.

[0022] A nineteenth aspect of the present disclosure may include any one of the first to eighteenth aspects, wherein each second capillary comprises a second capillary central longitudinal axis parallel to a central longitudinal axis of the optical fiber.

[0023] The twentieth aspect of the present disclosure may include any one of the first to nineteenth aspects, wherein each first capillary includes a first capillary central longitudinal axis parallel to the central longitudinal axis of the hollow core optical fiber, and the first capillary central longitudinal axis is at a first radial distance from the central longitudinal axis; each second capillary includes a second capillary central longitudinal axis parallel to the central longitudinal axis of the hollow core optical fiber, and the second capillary central longitudinal axis is at a second radial distance from the central longitudinal axis; and the first radial distance is greater than the second radial distance.

[0024] A twenty-first aspect of the present disclosure may include any one of the first to twentieth aspects, wherein each of the first capillaries includes silica-based glass.

[0025] A twenty-second aspect of the present disclosure may include any one of the first to twenty-first aspects, wherein each of the second capillaries includes silica-based glass.

[0026] A twenty-third aspect of the present disclosure may include any one of the first to twenty-second aspects, wherein the substrate includes silica-based glass.

[0027] A twenty-fourth aspect of the present disclosure may include any one of the first to twenty-third aspects, wherein the hollow core comprises one or more glasses.

[0028] A twenty-fifth aspect of the present disclosure may include any one of the first to twenty-fourth aspects, wherein the hollow core consists essentially of air.

[0029] A twenty-sixth aspect of the present disclosure may include any one of the first to twenty-fifth aspects, wherein each of the first capillaries has an inner diameter of 12 μm to 54 μm.

[0030] A twenty-seventh aspect of the present disclosure may include any one of the first to twenty-sixth aspects, wherein each of the first capillaries has a wall thickness of 0.1 μm to 4.0 μm.

[0031] A twenty-eighth aspect of the present disclosure may include any one of the first to twenty-seventh aspects, wherein each of the second capillaries has an inner diameter of 16 μm to 65 μm.

[0032] A twenty-ninth aspect of the present disclosure may include any one of the first to twenty-eighth aspects, wherein each second capillary has a wall thickness of 0.1 μm to 4.0 μm.

[0033] A thirtieth aspect of the present disclosure may include any one of aspects one to twenty-ninth, wherein a plurality of first cladding elements and a plurality of second cladding elements are configured to provide an anti-resonance effect operable to confine an optical signal having a wavelength of 350 nm to 8000 nm in a hollow core.

[0034] The thirty-first aspect of the present disclosure may include any one of the first to thirtieth aspects, wherein the hollow core optical fiber has a confinement loss that varies with wavelength, and the minimum confinement loss of the fundamental mode of an optical signal propagating in the hollow core optical fiber is less than or equal to 0.50 dB / km in the wavelength range of 350 nm to 8000 nm.

[0035] A thirty-second aspect of the present disclosure may include any one of aspects one to thirty-first, wherein the hollow core optical fiber further includes a plurality of third cladding elements spaced apart from one another and positioned between the plurality of second cladding elements and the hollow core optical fiber, each of the plurality of third cladding elements extending in a direction parallel to a central longitudinal axis of the hollow core optical fiber, wherein each of the plurality of third cladding elements includes a third capillary including an inner surface defining a third cavity having a third diameter and occupied only by gas.

[0036] A thirty-third aspect of the present disclosure may include the thirty-second aspect, wherein each third capillary comprises a third capillary central longitudinal axis parallel to a central longitudinal axis of the optical fiber.

[0037] A thirty-fourth aspect of the present disclosure may include the thirty-second aspect or the thirty-third aspect, wherein each third capillary directly contacts at least one second capillary.

[0038] A thirty-fifth aspect of the present disclosure may include any one of the thirty-second to thirty-fourth aspects, wherein each second capillary directly contacts two third capillaries.

[0039] A thirty-sixth aspect of the present disclosure may include any one of the thirty-second to thirty-fifth aspects, wherein each third cladding element is spaced apart from adjacent third cladding elements in a circumferential direction.

[0040] A thirty-seventh aspect of the present disclosure may include the thirty-sixth aspect, wherein the second cladding elements are equally spaced apart in the circumferential direction.

[0041] A thirty-eighth aspect of the present disclosure may include any one of the thirty-second to thirty-seventh aspects, wherein the plurality of third cladding elements includes 3 to 8 third capillaries.

[0042] A thirty-ninth aspect of the present disclosure may include any one of the thirty-second to thirty-eighth aspects, wherein the plurality of third cladding elements includes 5 to 6 third capillaries.

[0043] A 40th aspect of the present disclosure may include any one of the 32nd to 39th aspects, wherein the number of first cladding elements is equal to the number of second cladding elements and the number of third cladding elements.

[0044] A forty-first aspect of the present disclosure may include any one of the thirty-second to fortieth aspects, wherein the third diameter is 15 μm to 66 μm.

[0045] A forty-second aspect of the present disclosure may include any one of the thirty-second to forty-first aspects, wherein each third capillary has a wall thickness of 0.1 μm to 4.0 μm.

[0046] A forty-third aspect of the present disclosure may include any one of aspects thirty-second to forty-second, wherein the third diameter is different from the first diameter and the second diameter.

[0047] According to the forty-fourth aspect of the present disclosure, a hollow-core optical fiber may include a hollow core extending along a central longitudinal axis of the hollow-core optical fiber; a substrate including a tubular shape and an inner surface surrounding the central longitudinal axis of the hollow-core optical fiber; a plurality of first cladding elements spaced apart from each other and positioned between the hollow core and the substrate, each of the plurality of first cladding elements extending in a direction parallel to the central longitudinal axis of the hollow-core optical fiber, each of the plurality of first cladding elements including a first capillary including an inner surface defining a first cavity, the first cavity having a first diameter, wherein each of the plurality of first cladding elements directly contacts the inner surface of the substrate; and a plurality of second cladding elements spaced apart from each other and positioned between the hollow-core optical fiber and the substrate, each of the second cladding elements extending in a direction parallel to the central longitudinal axis of the hollow-core optical fiber, each of the second cladding elements including a second capillary including an inner surface defining a second cavity, the second cavity having a second diameter, the second diameter being different from the first diameter, wherein each of the second cladding elements does not directly contact the inner surface of the substrate. Each first capillary includes nested capillaries, wherein each nested capillary directly contacts an inner surface of the first capillary; or each second capillary includes nested capillaries, wherein each nested capillary directly contacts an inner surface of the second capillary.

[0048] A forty-fifth aspect of the present disclosure may include the forty-fourth aspect, wherein each nested capillary has an inner diameter of 6 μm to 25 μm.

[0049] A forty-sixth aspect of the present disclosure may include any one of the forty-fourth to forty-fifth aspects, wherein each nested capillary has a wall thickness of 0.1 μm to 4.0 μm.

[0050] A forty-seventh aspect of the present disclosure may include any one of aspects forty-four to forty-six, wherein each nested capillary directly contacts an inner surface of a second capillary at a point proximate to the substrate.

[0051] A forty-eighth aspect of the present disclosure may include any one of aspects forty-four to forty-seven, wherein the hollow core optical fiber has a confinement loss that varies with wavelength, and the minimum confinement loss of the fundamental mode of an optical signal propagating in the hollow core optical fiber is less than or equal to 0.2 dB / km within a wavelength range of 350 nm to 8000 nm.

[0052] The following detailed description will describe additional features and advantages, and in part will be apparent to those skilled in the art from this description, or may be learned by practicing the embodiments described herein, including the following detailed description, claims, and accompanying drawings.

[0053] It should be understood that both the above general description and the following detailed description describe various embodiments, and that they are intended to provide an overview or framework for understanding the nature and character of the claimed subject matter. The accompanying drawings are included to provide a further understanding of the various embodiments, and are incorporated into and constitute a part of this specification. The accompanying drawings illustrate various embodiments described herein, and together with the description, serve to explain the principles and operation of the claimed subject matter. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 schematically depicts a cross-sectional view of a hollow core optical fiber according to one or more embodiments described herein;

[0055] Figure 2 schematically depicts a cross-sectional view of a hollow core optical fiber according to one or more embodiments described herein;

[0056] Figure 3 schematically depicts a cross-sectional view of a hollow core optical fiber according to one or more embodiments described herein;

[0057] Figure 4 schematically depicts a cross-sectional view of a hollow core optical fiber according to an embodiment of Example 1;

[0058] Figure 5 schematically depicts a cross-sectional view of a hollow core optical fiber according to an embodiment of Example 2;

[0059] Figure 6schematically depicts a cross-sectional view of a hollow core optical fiber according to an embodiment of Example 3;

[0060] Figure 7 graphically depicts the confinement loss of the hollow core optical fiber of Example 3 as a function of wavelength; and

[0061] Figure 8 A cross-sectional view of a hollow-core optical fiber of a comparative example is schematically depicted. DETAILED DESCRIPTION

[0062] Reference will now be made in detail to various embodiments of hollow core optical fibers. Wherever possible, the same reference numerals will be used throughout the drawings to indicate the same or similar components. In an embodiment, the hollow core optical fiber may include a hollow core, a substrate, and a cladding element positioned between the hollow core and the substrate. The hollow core optical fiber may include a plurality of first cladding elements and a plurality of second cladding elements, wherein the first cladding elements directly contact an inner surface of the substrate, and each of the plurality of second cladding elements does not directly contact an inner surface of the substrate. Embodiments of hollow core optical fibers will be described in further detail herein.

[0063] Ranges may be expressed herein as from "about" one particular value, and / or to "about" another particular value. When such a range is expressed, another embodiment includes from a particular value and / or to another particular value. Similarly, when a value is expressed as an approximation by using the antecedent "about," it will be understood that the particular value forms another embodiment. It will be further understood that the endpoints of each range are significant relative to the other endpoint and are independent of the other endpoint.

[0064] Directional terms (eg, up, down, right, left, front, back, top, bottom) as used herein are made solely with reference to the drawings as drawn and are not intended to imply an absolute orientation.

[0065] The various components described herein may be referred to as being "directly connected" or "indirectly connected". When components are connected to each other without intermediate structures, they are directly connected. Components may be connected by fusion, welding, adhesives, or any other suitable attachment means. When components are connected to each other with intermediate structures, they are "indirectly connected". Examples of intermediate structures include welding aids (e.g., frits, solder, flux), adhesives, and bonding materials. In an embodiment, indirectly connected components are connected only by welding aids, adhesives, or bonding materials. The term "connected" refers to "directly connected" or "indirectly connected". Components that are "directly connected" to each other are said to be in direct contact with each other. Components that are "indirectly connected" to each other are said to be in indirect contact with each other. Components that are "connected" to each other are in direct or indirect contact with each other.

[0066] As used herein, the singular forms "a", "an", and "the" include plural referents unless the context clearly dictates otherwise. Thus, for example, reference to "a" component includes aspects having two or more such components unless the context clearly dictates otherwise.

[0067] Without intending to be bound by theory, an optical signal (i.e., light) may pass through the hollow core of a hollow core optical fiber. As used herein, "attenuation" refers to a decrease in the intensity of an optical signal passing through a hollow core optical fiber. The attenuation of an optical signal guided through a hollow core optical fiber may be reduced by various effects, including but not limited to antiresonance effects and suppression coupling mechanisms. Each of these effects may reduce the leakage of light from the hollow core of the optical fiber to the cladding elements of the optical fiber, which in turn reduces the attenuation of the optical signal propagating in the hollow core. In other words, each of these effects may increase the constraint of the hollow core of the optical fiber on light, thereby reducing the attenuation of the optical signal propagating in the hollow core. Embodiments of the hollow core optical fiber described herein may include a structure that utilizes one or more of these effects to reduce the attenuation of an optical signal passing through a hollow core optical fiber.

[0068] As used herein, "antiresonance" or "antiresonance effect" refers to the effect that occurs when the thickness of a material (e.g., a material used to form a cladding element) is proportional to the wavelength of light passing through a hollow core optical fiber, such that the light passing through the hollow core optical fiber is confined in the hollow core. Without intending to be bound by theory, the antiresonance effect occurs when the thickness of the material satisfies the quarter-wavelength condition (the phase accumulated over a single pass is one-quarter of 2π, and any odd multiple of a quarter wave). When this condition is applied to the thickness of the material, the light is confined in the hollow core and leakage to the cladding is minimized. In other words, this condition helps to suppress coupling between the core mode and the cladding mode, resulting in low transmission losses and increased confinement of the optical signal in the hollow core. In one embodiment, the antiresonance effect can be satisfied by a material having a thickness given by Equation 1: In equation 1, t AR is the thickness of the material that satisfies the anti-resonance effect, λ is the wavelength of the optical signal, m is an integer greater than or equal to 1, and n is the refractive index of the material. It should be noted that Equation 1 represents the ideal thickness of the material that will satisfy the anti-resonance effect and is not exactly equal to t AR The material thickness of t can also provide enhanced light confinement for the hollow core. For example, but not limited to, it is contemplated that a hollow core having a thickness of t AR Within 10% (from 90% t AR to 110%t AR ) materials can be operable to confine light within a hollow core.

[0069] As used herein, "inhibited coupling mechanism" refers to the effect that occurs when a cladding element having a negative curvature inhibits coupling between a core mode and a cladding mode to reduce light leakage from the hollow core. As used herein, "negative curvature" refers to a cladding element having a convex surface facing the central longitudinal axis of the hollow core optical fiber. Without intending to be bound by theory, the use of a cladding element having a convex surface facing the central longitudinal axis of the hollow core optical fiber can reduce the amount of light that contacts the cladding element, and can also reduce light leakage through the cladding element and the gaps between these cladding elements. In turn, this can reduce attenuation due to leakage of light signals through the cladding elements and their gaps, and can also reduce light scattering that may occur when light contacts the surface of the cladding element.

[0070] Reference now Figure 1 , the hollow core optical fiber 100 may include a hollow core 110 extending along a central longitudinal axis 112 of the optical fiber and a substrate 130. Generally, the hollow core 110 is a light guiding portion of the hollow core optical fiber 100. The hollow core 110 has a radius extending from the central longitudinal axis 112 to a closest point of contact with one of the cladding elements 120 in an orthogonal direction. The diameter of the hollow core 110 is twice the radius of the hollow core 110. The diameter of the hollow core 110 is greater than or equal to 15 microns, or greater than or equal to 20 microns, or greater than or equal to 25 microns, or less than or equal to 45 microns, or less than or equal to 40 microns, or less than or equal to 35 microns, or in a range of 15 microns to 45 microns, or in a range of 20 microns to 40 microns, or in a range of 25 microns to 35 microns.

[0071] The substrate 130 may be operable to support any cladding elements included in the hollow core optical fiber 100. In an embodiment, the substrate 130 may include a tubular shape including an inner surface 132 surrounding the central longitudinal axis 112 of the optical fiber. In an embodiment, the outer diameter of the substrate 130 may be 100 μm to 500 μm. For example, but not limited to, the outer diameter of the substrate 130 may be 100 μm to 500 μm, 200 μm to 500 μm, 300 μm to 500 μm, 400 μm to 500 μm, 100 μm to 400 μm, 100 μm to 300 μm, 100 μm to 200 μm, or any combination or subset of these ranges. In an embodiment, the outer diameter of the substrate may be 100 μm to 250 μm.

[0072] In an embodiment, the substrate 130 has a wall thickness of 1 μm to 100 μm. For example, but not limited to, the wall thickness of the substrate 130 can be 2 μm to 80 μm, 5 μm to 60 μm, 10 μm to 50 μm, 15 μm to 40 μm, 15 μm to 30 μm, 20 μm to 30 μm, or any combination or subset of these ranges. In an embodiment, the outer diameter of the substrate can be 100 μm to 250 μm.

[0073] In an embodiment, one or more protective coatings (not depicted) may be positioned on the outer surface of the substrate 130. These coatings may be, for example, organic materials such as plastics or polymers, and may protect the hollow core optical fiber 100 from the physical environment. The coatings may include a primary coating with a low Young's modulus (e.g., <1 MPa) surrounding and adjacent to the substrate 130 and a secondary coating with a high Young's modulus (e.g., >1000 MPa) surrounding and adjacent to the primary coating. Representative materials for the primary and secondary coatings include acrylate materials (e.g., urethane acrylates). In an embodiment, the coated optical fiber may have an outer diameter of 242 microns, 200 microns, or 190 microns. In an embodiment, in the radial direction, the thickness of the primary coating is greater than 10 microns, or greater than 15 microns, or greater than 20 microns, or less than 45 microns, or less than 40 microns, or less than 35 microns, or in the range of 10 microns to 45 microns, or in the range of 15 microns to 40 microns, or in the range of 20 microns to 35 microns. In an embodiment, in the radial direction, the thickness of the secondary coating is greater than 10 microns, or greater than 15 microns, or greater than 20 microns, or less than 45 microns, or less than 40 microns, or less than 35 microns, or in the range of 10 microns to 45 microns, or in the range of 15 microns to 40 microns, or in the range of 20 microns to 35 microns.

[0074] The hollow core optical fiber 100 includes a plurality of first cladding elements 122 and a plurality of second cladding elements 124. Each of the plurality of first cladding elements 122 may extend in a direction parallel to the central longitudinal axis 112 of the optical fiber. Each of the plurality of first cladding elements 122 may include a first capillary, the first capillary including an inner surface 152 defining a first cavity 162. In an embodiment, the first cavity 162 may have a first diameter and be occupied only by gas. Similarly, each of the plurality of second cladding elements 124 may extend in a direction parallel to the central longitudinal axis 112 of the optical fiber. Each of the plurality of second cladding elements 124 may include a second capillary, and each second capillary may include an inner surface 156 defining a second cavity 164. In an embodiment, the second cavity 164 may have a second diameter and be occupied only by gas. In an embodiment, the second diameter is different from the first diameter. For example, the second diameter may be greater than or less than the first diameter. In Figure 1 In the depicted embodiment, the second diameter is greater than the first diameter.

[0075] In an embodiment, each of the plurality of first cladding elements 122 may directly contact the inner surface 132 of the substrate 130, and each of the plurality of second cladding elements 124 may not directly contact the inner surface 132 of the substrate 130. In other words, the plurality of first cladding elements 122 may be positioned between the substrate 130 and the hollow core 110, and the plurality of second cladding elements 124 may be positioned between the plurality of first cladding elements 122 and the hollow core 110, such that the plurality of second cladding elements 124 are spaced apart from the substrate 130.

[0076] In an embodiment, the plurality of first cladding elements 122 may include 3 to 8 first capillaries. For example, but not limited to, the plurality of first cladding elements 122 may include 3, 4, 5, 6, 7, or 8 first capillaries. In an embodiment, the plurality of first cladding elements 122 may include 5 to 6 first capillaries. In an embodiment, the plurality of second cladding elements 124 may include 3 to 12 second capillaries. For example, but not limited to, the plurality of second cladding elements 124 may include 3, 4, 5, 6, 7, 8, 9, 10, 11, or 12 second capillaries. In an embodiment, the plurality of second cladding elements 124 may include 5 to 6 second capillaries. In an embodiment, the number of first cladding elements may be equal to the number of second cladding elements, such that the number of first capillaries is equal to the number of second capillaries. In an embodiment, the number of first cladding elements may be greater than or less than the number of second cladding elements, such that the number of first capillaries is greater than or less than the number of second capillaries.

[0077] As described herein, the capillary can have a closed cross-section including a wall having an inner surface and an outer surface. Therefore, it should be understood that the capillary can generally have a tubular shape. In an embodiment, the capillary can have a circular, elliptical, oval or any other suitable cross-sectional shape. Without intending to be bound by theory, when the capillary has a circular, elliptical, oval or similar cross-sectional shape, the convex surface of the capillary can face the hollow core of the hollow core optical fiber. Without intending to be bound by theory, the convex surface provides a negative curvature effect, which is conducive to suppressing the coupling mechanism to reduce the attenuation of the optical signal passing through the hollow core optical fiber.

[0078] In an embodiment, each first capillary in the plurality of first cladding elements 122 may be directly connected to the inner surface 132 of the substrate 130. For example, in Figure 1 In the depicted embodiment, the first capillary 140 directly connects to the inner surface 132 of the substrate 130 at a point 142. In an embodiment, the plurality of first cladding elements 122 are symmetrically disposed about the central longitudinal axis 112 of the hollow core optical fiber 100.

[0079] Each first capillary in the plurality of first cladding elements 122 may include a first capillary central longitudinal axis 126 . In an embodiment, each first capillary central longitudinal axis 126 may be parallel to the central longitudinal axis 112 of the hollow core optical fiber 100. Each first capillary central longitudinal axis 126 may be parallel to each other. In an embodiment, each first capillary central longitudinal axis 126 may be positioned on the circumference of a circle perpendicular to the central longitudinal axis 112 of the hollow core optical fiber 100. For example, in an embodiment, each first capillary central longitudinal axis 126 may be positioned on the circumference of a circle perpendicular to and centered on the central longitudinal axis 112 of the hollow core optical fiber 100. In such embodiments, it should be understood that each first capillary central longitudinal axis 126 is equidistant from the central longitudinal axis 112 of the optical fiber.

[0080] In an embodiment, each first cladding element is spaced apart from adjacent first cladding elements in the circumferential direction 190. In other words, each first capillary in the plurality of first cladding elements 122 is spaced apart from adjacent first capillaries in the plurality of first cladding elements 122 in the circumferential direction 190. Each first capillary in the plurality of first cladding elements 122 may not be in direct contact with another first capillary in the plurality of first cladding elements 122. For example, according to Figure 1 In the embodiment depicted in FIG. 1 , both the first capillary 140 and the first capillary 144 are in the plurality of first cladding elements 122, and the first capillary 140 and the first capillary 144 are spaced apart in the circumferential direction 190 such that the first capillary 140 and the first capillary 144 are not in direct contact with each other. Each of the first capillaries 140 and each of the first capillaries 144 are in direct contact with the substrate 130. In an embodiment, the first cladding elements 122 are equally spaced apart in the circumferential direction 190. Without intending to be bound by theory, when the first capillaries in the plurality of first cladding elements 122 are in direct contact, local modes may be supported at points where the first capillaries are in direct contact, and the local modes may allow coupling between the core mode and the cladding mode, which may increase light leakage from the hollow core 110. Therefore, direct contact between the first capillaries may reduce confinement of light in the hollow core 110 of the hollow core optical fiber 100 at those points. This, in turn, may result in increased attenuation of the optical signal passing through the hollow core optical fiber 100 .

[0081] In an embodiment, each first capillary in the plurality of first cladding elements 122 may have an inner diameter of 12 μm to 54 μm. For example, but not limited to, each first capillary in the plurality of first cladding elements 122 may have an inner diameter of 12μm to 54μm, 16μm to 54μm, 20μm to 54μm, 24μm to 54μm, 28μm to 54μm, 32μm to 54μm, 36μm to 54μm, 40μm to 54μm, 44μm to 54μm, 48μm to 54μm, 52μm to 54μm, 12μm to 50μm, 12μm to 46μm, 12μm to 42μm, 12μm to 38μm, 12μm to 34μm, 12μm to 30μm, 12μm to 26μm, 12μm to 22μm, 12μm to 18μm, 12μm to 16μm, or any combination or subset of these ranges. In an embodiment, each first capillary in the plurality of first cladding elements 122 may have the same inner diameter.

[0082] In an embodiment, each first capillary in the plurality of first cladding elements 122 may have a wall thickness of 0.1 μm to 4.0 μm. As described herein, wall thickness refers to the distance between an outer surface 154 of each first capillary in the plurality of first cladding elements 122 and an inner surface 152 of each first capillary in the plurality of first cladding elements 122. For example, but not limited to, each first capillary in the plurality of first cladding elements 122 may have a wall thickness of 0.1 μm to 4.0 μm, 0.5 μm to 4.0 μm, 1 μm to 4.0 μm, 1.5 μm to 4.0 μm, 2.0 μm to 4.0 μm, 2.5 μm to 4.0 μm, 3 μm to 4.0 μm, 3.5 μm to 4.0 μm, 0.1 μm to 3.5 μm, 0.1 μm to 3.0 μm, 0.1 μm to 2.5 μm, 0.1 μm to 2.0 μm, 0.1 μm to 1.5 μm, 0.1 μm to 1.0 μm, 0.1 μm to 0.5 μm, or any combination or subset of these ranges. In an embodiment, each first capillary in the plurality of first cladding elements 122 may have the same wall thickness. In an embodiment, each first capillary may have a wall thickness that promotes confinement of the optical signal by the hollow core 110 through an anti-resonance effect, such as a wall thickness according to Equation 1. Without intending to be bound by theory, when each first capillary has a wall thickness that provides an anti-resonance effect, attenuation of the optical signal passing through the optical fiber may be reduced.

[0083] Each second capillary in the plurality of second cladding elements 124 may be in direct contact with at least one first capillary in the plurality of first cladding elements 122. In an embodiment, each capillary in the plurality of second cladding elements 124 may be directly connected to two or more first capillaries in the plurality of first cladding elements 122. For example, in Figure 1In the depicted embodiment, a second capillary 146 in the plurality of second cladding elements 124 may be directly connected to a first capillary 140 in the plurality of first cladding elements 122 at a point 147, and the second capillary 146 may be directly connected to a first capillary 144 in the plurality of first cladding elements 122 at a point 148. Without intending to be bound by theory, the direct connection between a capillary in the plurality of second cladding elements 124 and two capillaries in the plurality of first cladding elements 122 may increase the structural integrity of the plurality of second cladding elements 124. This may result in fewer defects in the plurality of second cladding elements 124 during the manufacture of the hollow core optical fiber 100.

[0084] The first capillaries in the plurality of first cladding elements 122 may be positioned in gaps between the second capillaries in the plurality of second cladding elements 124. For example, but not limited to, Figure 1 In the depicted embodiment, the first capillaries 144 in the plurality of first cladding elements 122 are positioned in the gaps between the second capillaries 146 and 149 in the plurality of second cladding elements 124. Without being bound by theory, positioning the first capillaries of the plurality of first cladding elements 122 in the gaps between the second capillaries of the plurality of second cladding elements 124 allows the plurality of first cladding elements 122 to support the plurality of second cladding elements 124. Additionally, positioning the first capillaries in the gaps between the second capillaries allows for further confinement of light in the hollow core 110 that might otherwise pass through the gaps between the second capillaries. This can result in reduced attenuation of light passing through the hollow core optical fiber 100.

[0085] In an embodiment, each second capillary in the plurality of second cladding elements 124 includes a second capillary central longitudinal axis 128. Each second capillary central longitudinal axis 128 may be parallel to the central longitudinal axis 112 of the hollow core optical fiber 100. In an embodiment, each second capillary central longitudinal axis 128 may be parallel to each other. In an embodiment, each second capillary central longitudinal axis 128 may be parallel to each first capillary central longitudinal axis. In an embodiment, the central longitudinal axis 112 of the hollow core optical fiber 100 may be parallel to both the first capillary central longitudinal axis 126 and the second capillary central longitudinal axis 128. In an embodiment, each second capillary central longitudinal axis 128 may be positioned on the circumference of a circle perpendicular to the central longitudinal axis 112 of the hollow core optical fiber 100. For example, in an embodiment, each second capillary central longitudinal axis 128 may be positioned on the circumference of a circle perpendicular to the central longitudinal axis 112 of the optical fiber and centered at the central longitudinal axis 112. In such embodiments, it should be understood that each second capillary central longitudinal axis 128 is equidistant from the central longitudinal axis 112 of the optical fiber. In an embodiment, the plurality of second cladding elements 122 are symmetrically disposed about the central longitudinal axis 112 of the hollow core optical fiber 100 .

[0086] In an embodiment, each first capillary central longitudinal axis 126 is a first radial distance from the central longitudinal axis 112 of the hollow core optical fiber 100. Likewise, each second capillary central longitudinal axis 128 is a second radial distance from the central longitudinal axis 112 of the hollow core optical fiber 100. In an embodiment, the first radial distance may be greater than the second radial distance.

[0087] Each second capillary in the plurality of second cladding elements 124 may be spaced apart from the inner surface 132 of the substrate 130 in the radial direction 192. That is, each capillary in the plurality of second cladding elements 124 may not be in direct contact with the inner surface 132 of the substrate 130. For example, according to Figure 1 In the embodiment depicted in FIG. 1 , the second capillaries 146 in the plurality of second cladding elements 124 are spaced apart from the inner surface 132 of the substrate 130 in the radial direction 192 , such that the second capillaries 146 are not in direct contact with the inner surface 132 of the substrate 130 .

[0088] In an embodiment, each second capillary in the plurality of second cladding elements 124 is spaced apart from an adjacent second capillary in the plurality of second cladding elements 124 in the circumferential direction 190. Each second capillary in the plurality of second cladding elements 124 may not be in direct contact with another second capillary in the plurality of second cladding elements 124. For example, according to Figure 1In the embodiment depicted in FIG, both the second capillary 146 and the second capillary 149 are in the plurality of second cladding elements 124, and the second capillary 146 and the second capillary 149 are spaced apart in the circumferential direction 190 such that the second capillary 146 and the second capillary 149 are not in direct contact with each other. In an embodiment, the second cladding elements 124 are equally spaced apart in the circumferential direction 190. Without intending to be bound by theory, when the second capillaries in the plurality of second cladding elements 124 are in direct contact, local modes may be supported at the points where the second capillaries are in direct contact, and the local modes may allow coupling between the core mode and the cladding mode, which may increase light leakage from the hollow core 110. Therefore, the direct contact between the capillaries may reduce the confinement of light in the hollow core 110 of the hollow core optical fiber 100 at those points. In turn, this may result in increased attenuation of the optical signal passing through the hollow core optical fiber 100.

[0089] In an embodiment, each second capillary in the plurality of second cladding elements 124 has an inner diameter of 16 μm to 65 μm. For example, but not limited to, each second capillary in the plurality of second cladding elements 124 has an inner diameter of 16μm to 65μm, 20μm to 65μm, 25μm to 65μm, 30μm to 65μm, 35μm to 65μm, 40μm to 65μm, 45μm to 65μm, 50μm to 65μm, 55μm to 65μm, 60μm to 65μm, 16μm to 60μm, 16μm to 55μm, 16μm to 50μm, 16μm to 45μm, 16μm to 40μm, 16μm to 35μm, 16μm to 30μm, 16μm to 25μm, 16μm to 20μm, or any combination or subset of these ranges.

[0090] In an embodiment, each second capillary in the plurality of second cladding elements 124 has a wall thickness of 0.1 μm to 4.0 μm. As described herein, wall thickness refers to the distance between an outer surface 158 of each second capillary in the plurality of second cladding elements 124 and an inner surface 156 of each second capillary in the plurality of second cladding elements 124. For example, but not limited to, each second capillary in the plurality of second cladding elements 124 may have a wall thickness of 0.1 μm to 4.0 μm, 0.5 μm to 4.0 μm, 1 μm to 4.0 μm, 1.5 μm to 4.0 μm, 2.0 μm to 4.0 μm, 2.5 μm to 4.0 μm, 3 μm to 4.0 μm, 3.5 μm to 4.0 μm, 0.1 μm to 3.5 μm, 0.1 μm to 3.0 μm, 0.1 μm to 2.5 μm, 0.1 μm to 2.0 μm, 0.1 μm to 1.5 μm, 0.1 μm to 1.0 μm, 0.1 μm to 0.5 μm, or any combination or subset of these ranges. In an embodiment, each second capillary may have a wall thickness that facilitates confinement of the optical signal in the hollow core 110 through an anti-resonance effect, such as a wall thickness according to Equation 1. Without intending to be bound by theory, when each second capillary has a wall thickness that provides an anti-resonance effect, attenuation of the optical signal passing through the optical fiber may be reduced.

[0091] Reference now Figure 2 In an embodiment, the hollow core optical fiber 100 may further include a plurality of third cladding elements 210. The plurality of third cladding elements 210 may be spaced apart from each other and positioned between the plurality of second cladding elements 124 and the hollow core 110. Each of the plurality of third cladding elements 210 may extend in a direction parallel to the central longitudinal axis 112 of the hollow core optical fiber 100. Each third cladding element may include a third capillary. The third capillary includes an inner surface 252 defining a third cavity 262 having a third diameter. In an embodiment, the third cavity 262 is occupied only by gas.

[0092] In an embodiment, the plurality of third cladding elements 210 may include 3 to 8 third capillaries. For example, but not limited to, the plurality of third cladding elements 210 may include 3, 4, 5, 6, 7, or 8 third capillaries. In an embodiment, the plurality of third cladding elements 210 may include 5 to 6 third capillaries. In an embodiment, the plurality of first cladding elements 122, the plurality of second cladding elements 124, and the plurality of third cladding elements 210 may include the same number of capillaries. For example, according to Figure 2 In the embodiment depicted in FIG. 1 , each of the plurality of first cladding elements 122 , the plurality of second cladding elements 124 , and the plurality of third cladding elements 210 includes six capillaries.

[0093] Each third capillary in the plurality of third cladding elements 210 may be in direct contact with at least one second capillary in the plurality of second cladding elements 124. In an embodiment, each third capillary in the plurality of third cladding elements 210 may be directly connected to two or more second capillaries in the plurality of second cladding elements 124. For example, in Figure 2 In the depicted embodiment, the capillary 212 in the plurality of third cladding elements 210 can be directly connected to the capillary 223 in the plurality of second cladding elements 124 at point 214, and the capillary 212 can be directly connected to the capillary 223 in the plurality of second cladding elements 124 at point 215. In an embodiment, each second capillary can directly contact two third capillaries. Without intending to be bound by theory, the direct connection between the capillary in the plurality of third cladding elements 210 and the two capillaries in the plurality of second cladding elements 124 can increase the structural integrity of the plurality of third cladding elements 210. This can result in fewer defects in the plurality of third cladding elements 210 during the manufacture of the hollow core optical fiber 100.

[0094] In an embodiment, each third capillary in the plurality of third cladding elements 210 is spaced apart from an adjacent capillary in the plurality of third cladding elements 210 in the circumferential direction 190. Each third capillary in the plurality of third cladding elements 210 may not be in direct contact with another third capillary in the plurality of third cladding elements 210. For example, according to Figure 2 In the embodiment depicted in FIG. 1 , both the third capillary 212 and the third capillary 216 are cladding elements in the plurality of third cladding elements 210, and the third capillary 212 and the third capillary 216 are spaced apart in the circumferential direction 190 such that the third capillary 212 and the third capillary 216 are not in direct contact with each other. Without intending to be bound by theory, when the third capillaries in the plurality of third cladding elements 210 are in direct contact, local modes may be supported at the points where the capillaries are in direct contact, and the local modes may allow coupling between the core mode and the cladding mode, which may increase light leakage from the hollow core. Therefore, the direct contact between the capillaries may reduce the confinement of light in the hollow core 110 of the hollow core optical fiber 100 at those points. In turn, this may result in increased attenuation of the optical signal passing through the hollow core optical fiber 100.

[0095] Each third capillary in the plurality of third cladding elements 210 includes a third capillary central longitudinal axis 218. Each third capillary central longitudinal axis 218 may be parallel to the central longitudinal axis 112 of the hollow core optical fiber 100. In an embodiment, each third capillary central longitudinal axis 218 may be parallel to each other. In an embodiment, each third capillary central longitudinal axis 218 may be parallel to each first capillary central longitudinal axis 126. In an embodiment, each third capillary central longitudinal axis 218 may be parallel to each second capillary central longitudinal axis 128. In an embodiment, the central longitudinal axis 112 of the hollow core optical fiber 100 may be parallel to each first capillary central longitudinal axis 126, each second capillary central longitudinal axis 128, and each third capillary central longitudinal axis 218. In an embodiment, each third capillary central longitudinal axis 218 may be positioned on the circumference of a circle perpendicular to the central longitudinal axis 112 of the hollow core optical fiber 100. For example, in an embodiment, each third capillary central longitudinal axis 218 can be positioned on the circumference of a circle that is perpendicular to the central longitudinal axis 112 of the optical fiber and centered on the central longitudinal axis 112. In such embodiments, it should be understood that each third capillary central longitudinal axis 218 is equidistant from the central longitudinal axis 112 of the optical fiber.

[0096] In an embodiment, each third capillary in the plurality of third cladding elements 210 has an inner diameter of 15 μm to 66 μm. For example, but not limited to, each third capillary in the plurality of third cladding elements 210 has an inner diameter of 15μm to 66μm, 20μm to 66μm, 25μm to 66μm, 30μm to 66μm, 35μm to 66μm, 40μm to 66μm, 45μm to 66μm, 50μm to 66μm, 55μm to 66μm, 60μm to 66μm, 15μm to 60μm, 15μm to 55μm, 15μm to 50μm, 15μm to 45μm, 15μm to 40μm, 15μm to 35μm, 15μm to 30μm, 15μm to 25μm, 15μm to 20μm, or any combination or subset of these ranges.

[0097] In an embodiment, each third capillary in the plurality of third cladding elements 210 has a wall thickness of 0.1 μm to 1.5 μm. As described herein, wall thickness refers to the distance between the outer surface 254 of each third capillary and the inner surface 252 of each third capillary. For example, but not limited to, each third capillary in the plurality of third cladding elements 210 may have a wall thickness of 0.1 μm to 1.5 μm, 0.3 μm to 1.5 μm, 0.5 μm to 1.5 μm, 0.7 μm to 1.5 μm, 0.9 μm to 1.5 μm, 1.1 μm to 1.5 μm, 1.3 μm to 1.5 μm, 0.1 μm to 1.3 μm, 0.1 μm to 1.1 μm, 0.1 μm to 0.9 μm, 0.1 μm to 0.7 μm, 0.1 μm to 0.5 μm, 0.1 μm to 0.3 μm, or any combination or subset of these ranges. In an embodiment, each third capillary may have a wall thickness that facilitates confinement of an optical signal in the hollow core 110 by an anti-resonance effect, such as a wall thickness according to Equation 1. Without intending to be bound by theory, when each third capillary has a wall thickness that provides an anti-resonance effect, attenuation of an optical signal passing through the optical fiber may be reduced.

[0098] In an embodiment, each first capillary in the plurality of first cladding elements 122 or each second capillary in the plurality of second cladding elements 124 may include a nested capillary 310. As used herein, "nested capillary" refers to a capillary positioned within another capillary such that an outer surface of the nested capillary is directly connected to an inner surface of the capillary. Figure 3 In the embodiment of the present invention, the outer surface 354 of each nested capillary 310 is directly connected to the inner surface 156 of the capillary in which it is positioned. Figure 3 In the embodiment depicted in FIG. 1 , the nested capillary 312 is in direct contact with the inner surface 322 of the second capillary 320. In an embodiment, each first capillary in the plurality of first cladding elements 122 may include a nested capillary (not shown). In an embodiment, each second capillary in the plurality of second cladding elements 124 may include a nested capillary 310, such as Figure 3 Note that while the nested capillaries may be occupied only by gas, the capillaries in which the nested capillaries are positioned are not. For example, according to Figure 3 In the embodiment depicted in FIG. 1 , the nested capillary tube 312 is occupied only by gas, but the second capillary tube 320 is necessarily partially occupied by the nested capillary tube 312 rather than being occupied only by gas.

[0099] Each nested capillary 310 may directly contact the inner surface of the first capillary or the inner surface of the second capillary at a point close to the substrate 130. As described herein, a point on the inner surface of a capillary is close to the substrate 130 when the point is assessed to be closest to the substrate 130 in the radial direction 192. For example, according to Figure 3In the embodiment depicted in , the nested capillary 312 is directly connected to the inner surface 322 of the second capillary 320 at a point 324 , which is close to the substrate 130 because the point 324 is the point on the inner surface 322 of the second capillary 320 closest to the substrate 130 when evaluated along the radial direction 192 .

[0100] Note that Figure 3 In the embodiment depicted in FIG. 1 , the capillaries including the nested capillaries are not in direct contact with the inner surface of the substrate 130. Instead, there is a gap. For example, the second capillary 320 includes the nested capillaries 312, and the second capillary 320 is spaced apart from the inner surface of the substrate 130. Without wishing to be bound by theory, it is believed that for some embodiments, the gap increases the confinement of the optical signal in the hollow core 110 (reduces confinement losses). In other embodiments, the capillaries including the nested capillaries are in direct contact with the inner surface of the substrate tube 130.

[0101] In an embodiment, each nested capillary 310 may have an inner diameter of 6 μm to 25 μm. For example, but not limited to, each nested capillary 310 may have an inner diameter of 6 μm to 25 μm, 9 μm to 25 μm, 12 μm to 25 μm, 15 μm to 25 μm, 18 μm to 25 μm, 21 μm to 25 μm, 6 μm to 22 μm, 6 μm to 19 μm, 6 μm to 16 μm, 6 μm to 13 μm, 6 μm to 10 μm, or any combination or subset of these ranges.

[0102] In an embodiment, each nested capillary 310 may have a wall thickness of 0.1 μm to 1.5 μm. Wall thickness refers to the distance between the outer surface 354 of the nested capillary 310 and the inner surface 352 of the nested capillary 310. For example, but not limited to, each nested capillary 310 may have a wall thickness of 0.1 μm to 1.5 μm, 0.3 μm to 1.5 μm, 0.5 μm to 1.5 μm, 0.7 μm to 1.5 μm, 0.9 μm to 1.5 μm, 1.1 μm to 1.5 μm, 1.3 μm to 1.5 μm, 0.1 μm to 1.3 μm, 0.1 μm to 1.1 μm, 0.1 μm to 0.9 μm, 0.1 μm to 0.7 μm, 0.1 μm to 0.5 μm, 0.1 μm to 0.3 μm, or any combination or subset of these ranges. In an embodiment, each nested capillary may have a wall thickness to provide an anti-resonance effect, such as a wall thickness according to Equation 1. Without intending to be bound by theory, when each nested capillary has a wall thickness that provides an anti-resonance effect, attenuation of an optical signal passing through an optical fiber may be reduced.

[0103] In an embodiment, each capillary may include a silica-based glass. The silica-based glass may include pure silica or silica doped with one or more dopants to change the refractive index of the silica. Each of the first capillaries in the plurality of first cladding elements 122 may include a silica-based glass. Each of the second capillaries in the plurality of second cladding elements 124 may include a silica-based glass. In an embodiment, each of the first capillaries, each of the second capillaries, or both may consist essentially of or consist of silica-based glass. In an embodiment, each of the third capillaries in the plurality of third cladding elements 210 may include a silica-based glass. Each of the third capillaries in the plurality of third cladding elements 210 may consist essentially of or consist of silica-based glass. In an embodiment, each nested capillary 310 may include a silica-based glass. Each nested capillary may consist essentially of or consist of silica-based glass. In an embodiment, the substrate 130 may include a silica-based glass. In an embodiment, substrate 130 may consist essentially of or consist of silica-based glass.

[0104] The hollow core 110 may include one or more gases. In an embodiment, the hollow core 110 may include one or more inert gases. In an embodiment, the hollow core 110 may include, consist essentially of, or consist of air.

[0105] In embodiments described herein, the cladding element may be configured to confine a fundamental mode of an optical signal (i.e., light) propagating in the hollow core 110 of the hollow core optical fiber 100 in the hollow core 110 by one or more of an anti-resonance effect and an inhibited coupling mechanism. In embodiments, the confinement occurs without the effect of a periodic photonic bandgap structure. In embodiments, the fundamental mode of the optical signal may have a wavelength from 350 nm to 8000 nm. For example, but not limited to, the fundamental mode of the optical signal may have a wavelength of 350 nm to 8000 nm, 500 nm to 8000 nm, 1000 nm to 8000 nm, 1500 nm to 8000 nm, 2000 nm to 8000 nm, 2500 nm to 8000 nm, 3000 nm to 8000 nm, 3500 nm to 8000 nm, 4000 nm to 8000 nm, 4500 nm to 8000 nm, 5000 nm to 8000 nm, 5500 nm to 8000 nm, 6000 nm to 8000 nm, 6500 nm to 8000 nm, 7000 nm to 8000 nm. , 7500nm to 8000nm, 350nm to 7500nm, 350nm to 7000nm, 350nm to 6500nm, 350nm to 6000nm, 350nm to 5500nm, 350nm to 5000nm, 350nm to 4500nm, 350nm to 4000nm, 350nm to 3500nm, 350nm to 3000nm, 350nm to 2500nm, 350nm to 2000nm, 350nm to 1500nm, 350nm to 1000nm, 350nm to 500nm, or a wavelength of any combination or subset of these ranges. In an embodiment, the plurality of first cladding elements and the plurality of second cladding elements may be configured to provide an antiresonance effect at wavelengths from 350 nm to 8000 nm, the antiresonance effect being operable to confine an optical signal propagating in the hollow core optical fiber at wavelengths from 350 nm to 8000 nm within the hollow core 110 .

[0106] Without intending to be bound by theory, confinement loss may be the dominant attenuation factor in the hollow core optical fibers described herein. Confinement loss may occur when light leaks from the hollow core 110 to the cladding 130. Confinement loss may be calculated using Equation 2 and Equation 3. n eff =n r +i·n im Equation 2 In Equation 2 and Equation 3, n eff is the effective refractive index of the mode propagating in the hollow core fiber, where the real part is n r , the imaginary part is n imThe real part of the effective refractive index is related to the propagation velocity of the mode, and the imaginary part is related to the confinement loss of the mode. For an antiresonant hollow core fiber with a given core and cladding structure, fiber modeling tools such as COMSOL ) to determine the effective refractive index. The confinement loss is calculated using Equation 3.

[0107] In an embodiment, the hollow core optical fiber 100 has a confinement loss that varies with wavelength, and the hollow core optical fiber has a minimum confinement loss of a fundamental mode of an optical signal propagating in the hollow core 110 that is less than or equal to 0.50 dB / km in a wavelength range of 350 nm to 8000 nm. For example, but not limited to, the hollow core optical fiber 100 can have a wavelength between 350nm and 8000nm, 500nm and 8000nm, 1000nm and 8000nm, 1500nm and 8000nm, 2000nm and 8000nm, 2500nm and 8000nm, 3000nm and 8000nm, 3500nm and 8000nm, 4000nm and 8000nm, 4500nm and 8000nm, 5000nm and 8000nm, 5500nm and 8000nm, 6000nm and 8000nm, 6500nm and 8000nm, 7000nm and 8000nm, 7500nm and 8000nm, 350nm and 7500nm m, 350nm to 7000nm, 350nm to 6500nm, 350nm to 6000nm, 350nm to 5500nm, 350nm to 5000nm, 350nm to 4500nm, 350nm to 4000nm, 350nm to 3500nm, 350nm to 3000nm, 350nm to 2500nm, 350nm to 2000nm, 350nm to 1500nm, 350nm to 1000nm, 350nm to 500nm, or a minimum restrained loss of less than or equal to 0.5dB / km, 0.4dB / km, 0.3dB / km, 0.2dB / km, 0.1dB / km, or 0.5dB / km over a wavelength range of 350nm to 7000nm, 350nm to 6500nm, 350nm to 6000nm, 350nm to 5500nm, 350nm to 5000nm, 350nm to

[0108] In embodiments where the hollow core optical fiber includes a cladding element including nested capillaries, the hollow core optical fiber can have a confinement loss that varies with wavelength, and the hollow core optical fiber can have a minimum confinement loss of a fundamental mode of an optical signal propagating in the hollow core optical fiber that is less than or equal to 0.2 dB / km in a wavelength range of 350 nm to 8000 nm. For example, but not limited to, the hollow core optical fiber 100 may have a wavelength in the range of 350 nm to 8000 nm, 500 nm to 8000 nm, 1000 nm to 8000 nm, 1500 nm to 8000 nm, 2000 nm to 8000 nm, 2500 nm to 8000 nm, 3000 nm to 8000 nm, 3500 nm to 8000 nm, 4000 nm to 8000 nm, 4500 nm to 8000 nm, 5000 nm to 8000 nm, 5500 nm to 8000 nm, 6000 nm to 8000 nm, 6500 nm to 8000 nm, 7000 nm to 8000 nm, 7500 nm to 8000 nm, 350 nm to 7000 nm, 350 nm to 6500 nm, The invention relates to a minimum restrained loss of less than or equal to 0.2 dB / km, 0.15 dB / km, 0.1 dB / km, 0.06 dB / km, 0.05 dB / km, 0.04 dB / km, 0.03 dB / km, 0.02 dB / km, or 0.01 dB / km over a wavelength range of 350 nm to 6000 nm, 350 nm to 5500 nm, 350 nm to 5000 nm, 350 nm to 4500 nm, 350 nm to 4000 nm, 350 nm to 3500 nm, 350 nm to 3000 nm, 350 nm to 2500 nm, 350 nm to 2000 nm, 350 nm to 1500 nm, 350 nm to 1000 nm, 350 nm to 500 nm, or any combination or subset of these ranges.

[0109] Embodiments of hollow core optical fibers may be manufactured by the following method. Cladding elements, such as a plurality of first cladding elements 122 and a plurality of second cladding elements 124, may be sleeved into a substrate 130 in a desired arrangement. The cladding elements may be bonded to the substrate and to each other as desired to form a preform assembly. The cladding elements and the substrate may be bonded by any suitable means, such as, but not limited to, fusion, welding, and adhesives. Welding techniques include laser welding, flame welding, and plasma welding. The preform assembly may be redrawn into an optical fiber preform using conventional optical fiber redrawing techniques. The optical fiber preform may then be drawn into an optical fiber using conventional optical fiber drawing techniques. Example

[0110] The embodiments described herein will be further illustrated by the following examples. Example 1 - Modeling the Constraint Losses of Hollow Core Fibers

[0111] A hollow core optical fiber 100 having a plurality of first cladding elements 122 and a plurality of second cladding elements 124 is modeled to determine the confinement loss of the optical fiber. Figure 4 , a cross section of the hollow core fiber modeled in Example 1 is depicted in FIG. The plurality of first cladding elements 122 include six capillaries. Each capillary in the plurality of first cladding elements 122 has an inner diameter of 30 μm and a wall thickness of 560 nm. The plurality of first cladding elements 122 are symmetrically arranged around the central longitudinal axis of the hollow core 110. The plurality of second cladding elements 124 include six capillaries. Each capillary in the plurality of second cladding elements 124 has an inner diameter of 27 μm and a wall thickness of 560 nm. The plurality of second cladding elements 124 are symmetrically arranged around the central longitudinal axis of the hollow core 110. The inner diameter of the substrate 130 is 132 μm, and the wall thickness of the substrate 130 is 2 μm. The diameter of the hollow core 110 is approximately 34.5 μm. The diameter of the hollow core 100 is defined as the diameter of a circle that contacts each of the plurality of second cladding elements 124 at a point closest to the central longitudinal axis of the hollow core 110. The substrate 130, the plurality of first cladding elements 122, and the plurality of second cladding elements 124 comprise pure silicon dioxide. Figure 4 As shown, the structure of the hollow core optical fiber is 60° rotationally symmetrical or 6-fold repeated symmetry.

[0112] Using COMSOL The modeling software models the confinement of the optical signal within the hollow core 110 of the hollow core optical fiber of Example 1. According to the model, the hollow core optical fiber of Example 1 effectively confines the optical signal within the hollow core of the optical fiber. In particular, for the fundamental mode of the optical signal having a wavelength of 1550 nm, the confinement loss of the optical fiber is 0.46 dB / km. Example 2 - Modeling the Constrained Losses of a Hollow Core Fiber Containing Nested Capillaries

[0113] A hollow core optical fiber 100 having a plurality of first cladding elements 122 and a plurality of second cladding elements 124 is modeled to determine the confinement loss of the optical fiber. Figure 5A cross section of the hollow core optical fiber 100 modeled in Example 2 is depicted in FIG. The plurality of first cladding elements 122 includes six capillaries. Each capillary in the plurality of first cladding elements has an inner diameter of 20 μm and a thickness of 570 nm. The plurality of first cladding elements 122 are symmetrically arranged around the central longitudinal axis of the hollow core 110. The plurality of second cladding elements 124 includes six capillaries, each capillary having a nested capillary 310. Each capillary in the plurality of second cladding elements 124 has an inner diameter of 27.5 μm and a thickness of 520 nm. The plurality of second cladding elements 124 are symmetrically arranged around the central longitudinal axis of the hollow core 110. Each nested capillary 310 has an inner diameter of 12.8 μm and a thickness of 520 nm. The plurality of nested cladding elements are symmetrically arranged around the central longitudinal axis of the hollow core 110. The inner diameter of the substrate 130 is 110 μm, and the wall thickness of the substrate 130 is 2 μm. The diameter of the hollow core 110 is about 34.5 μm. The substrate 130, the plurality of first cladding elements 122, and the plurality of second cladding elements 124 comprise pure silica. Figure 5 As shown, the structure of the hollow core optical fiber 100 is 60° rotationally symmetric or 6-fold repeated symmetric.

[0114] Using COMSOL The modeling software models the confinement of the optical signal within the hollow core of the hollow core optical fiber of Example 2. According to the model, the hollow core optical fiber of Example 2 provides excellent confinement of the optical signal by the hollow core of the optical fiber. In particular, for the fundamental mode of the optical signal having a wavelength of 1550 nm, the confinement loss of the optical fiber is 0.035-0.055 dB / km, depending on the polarization of the light. Example 3 - Modeling the confinement loss of a hollow core optical fiber as a function of wavelength

[0115] One hollow core fiber (Fiber 1) having multiple first cladding elements and multiple second cladding elements and four hollow core fibers (Fibers 2-5) having multiple first cladding elements, multiple second cladding elements, and multiple third cladding elements were modeled to analyze the confinement loss of the hollow core fibers as a function of wavelength. Figure 6 The general structure of each of four hollow core optical fibers (optical fibers 2-5 in Table 1) including a plurality of first, second, and third cladding elements is depicted in FIG. Figure 4 The general structure of optical fiber 1 is depicted in Table 1. In each of these optical fibers, the plurality of first cladding elements 122 have six capillaries, the plurality of second cladding elements 124 have six capillaries, and the plurality of third cladding elements 210 have six capillaries. Each of the capillaries 122, 124, and 210 are symmetrically arranged around the central longitudinal axis of the hollow core 110. The cladding elements and substrates of optical fibers 1-5 include pure silica. The dimensions of each of the five optical fibers are included in Table 1. Table 1. Hollow core fiber dimensions. <![CDATA[D 芯 (μm)]]> <![CDATA[d1(μm)]]> <![CDATA[t1(nm)]]> <![CDATA[d2(μm)]]> <![CDATA[t2(nm)]]> <![CDATA[d3(μm)]]> <![CDATA[t3(nm)]]> Fiber 1 34.5 30 560 27.5 560 NA NA Fiber 2 34.5 33 560 32 560 27.5 560 Fiber 3 34.5 33 580 32 580 27.5 580 Fiber 4 34.5 33 600 32 600 27.5 600 Fiber 5 34.5 33 620 32 620 27.5 620

[0116] The confinement loss of each fiber was calculated at wavelengths from 1300 nm to 1700 nm. The results are shown in Figure 7 In addition, Figure 7 Including as Figure 8 800. The comparative hollow core fiber 800 includes six capillaries 822 with a single nested capillary 850 positioned in each capillary 822. The single nested capillary 850 is attached to the capillary 822 at a point proximate to the substrate 830. Each capillary 822 has a diameter of 27.5 μm and a thickness of 0.5 μm, and each nested capillary 850 has a diameter of 13 μm and a thickness of 0.53 μm. The hollow core 810 has a diameter of approximately 34.5 μm. The substrate 830 has an inner diameter of approximately 165 μm and a wall thickness of 2 μm. The substrate 830, the capillaries 822, and the nested capillaries 850 include pure silica such as Figure 8 As shown, the structure of the comparative hollow core optical fiber 800 is 60° rotationally symmetrical or 6 times repeated symmetrical. Figure 7 , Figure 7 It is shown that the confinement loss of hollow-core fibers, including the wavelength at which minimum confinement loss occurs, can be tuned by adjusting the thickness of the capillary and by adjusting the number of multiple cladding elements.

[0117] The present disclosure relates to various embodiments of hollow core optical fibers. In an embodiment, the hollow core optical fiber includes a hollow core extending along a central longitudinal axis of the optical fiber; a substrate; a plurality of first cladding elements spaced apart from each other and positioned between the hollow core and the substrate; and a plurality of second cladding elements spaced apart from each other and positioned between the hollow core and the plurality of first cladding elements. The hollow core optical fiber may be operable to transmit an optical signal, and the cladding elements may reduce attenuation of the optical signal by one or more of an anti-resonance effect and a negative curvature effect.

[0118] It is obvious to those skilled in the art that various modifications and changes can be made to the embodiments described herein without departing from the spirit and scope of the subject matter claimed. Therefore, it is intended that the specification covers various modifications and changes of the embodiments described herein, as long as these modifications and changes fall within the scope of the attached claims and their equivalents.

Claims

1. A hollow core optical fiber, comprising: a hollow core extending along a central longitudinal axis of the hollow core optical fiber; a substrate comprising a tubular shape and an inner surface surrounding the central longitudinal axis of the hollow core optical fiber; a plurality of first cladding elements spaced apart from one another and positioned between the hollow core and the substrate, each of the plurality of first cladding elements extending in a direction parallel to the central longitudinal axis of the hollow core optical fiber, each of the plurality of first cladding elements comprising a first capillary including an inner surface defining a first cavity having a first diameter and being occupied only by a gas; as well as a plurality of second cladding elements spaced apart from one another and positioned between the hollow core and the substrate, each of the plurality of second cladding elements extending in a direction parallel to the central longitudinal axis of the hollow core optical fiber, each of the plurality of second cladding elements comprising a second capillary tube, the second capillary tube comprising an inner surface defining a second cavity, the second cavity having a second diameter and being occupied only by a gas, the second diameter being different from the first diameter, wherein: Each of the plurality of first cladding elements directly contacts the inner surface of the substrate; and Each of the second cladding elements does not directly contact the inner surface of the substrate.

2. The hollow core optical fiber of claim 1, wherein each first cladding element is spaced apart from adjacent first cladding elements in a circumferential direction.

3. The hollow core optical fiber of claim 1 or 2, wherein each second capillary is in direct contact with at least one first capillary.

4. The hollow core optical fiber of any one of claims 1 to 3, wherein each second cladding element is spaced apart from the inner surface of the substrate in a radial direction.

5. The hollow core optical fiber of any one of claims 1 to 4, wherein each second cladding element is spaced apart from an adjacent second cladding element in a circumferential direction.

6. The hollow core optical fiber of any one of claims 1 to 5, wherein each first capillary is directly connected to two second capillaries.

7. The hollow core optical fiber of any one of claims 1 to 6, wherein the second diameter is greater than the first diameter.

8. The hollow core optical fiber according to any one of claims 1 to 7, wherein: Each first capillary comprises a first capillary central longitudinal axis parallel to the central longitudinal axis of the hollow core optical fiber and the first capillary central longitudinal axis is a first radial distance from the central longitudinal axis; Each second capillary comprises a second capillary central longitudinal axis parallel to the central longitudinal axis of the hollow core optical fiber and the second capillary central longitudinal axis is a second radial distance from the central longitudinal axis; The first radial distance is greater than the second radial distance.

9. The hollow core optical fiber of any one of claims 1 to 8, wherein each first capillary has an inner diameter of 12 μm to 54 μm.

10. The hollow core optical fiber of any one of claims 1 to 9, wherein each first capillary has a wall thickness of 0.1 μm to 4.0 μm.

11. The hollow core optical fiber of any one of claims 1 to 10, wherein each second capillary has an inner diameter of 16 μm to 65 μm.

12. The hollow core optical fiber of any one of claims 1 to 11, wherein each second capillary has a wall thickness of 0.1 μm to 4.0 μm.

13. The hollow core optical fiber of any one of claims 1-12, wherein the plurality of first cladding elements and the plurality of second cladding elements are configured to provide an anti-resonance effect operable to confine an optical signal having a wavelength of 350 nm to 8000 nm in the hollow core.

14. The hollow core optical fiber according to any one of claims 1 to 13, wherein the hollow core optical fiber has a confinement loss that varies with wavelength, and the minimum confinement loss of a fundamental mode of an optical signal propagating in the hollow core optical fiber is less than or equal to 0.50 dB / km in a wavelength range of 350 nm to 8000 nm.

15. The hollow core optical fiber according to any one of claims 1 to 14, further comprising: a plurality of third cladding elements spaced apart from one another and positioned between the plurality of second cladding elements and the hollow core, each of the plurality of third cladding elements extending in a direction parallel to the central longitudinal axis of the hollow core optical fiber, wherein each of the plurality of third cladding elements comprises a third capillary including an inner surface defining a third cavity having a third diameter and occupied only by the gas.

16. The hollow core optical fiber of claim 15, wherein each third capillary directly contacts at least one second capillary.

17. The hollow core optical fiber of claim 15 or 16, wherein the third diameter is different from the first diameter and the second diameter.

18. A hollow core optical fiber, comprising: a hollow core extending along a central longitudinal axis of the hollow core optical fiber; a substrate comprising a tubular shape and an inner surface surrounding the central longitudinal axis of the hollow core optical fiber; a plurality of first cladding elements spaced apart from one another and positioned between the hollow core and the substrate, each of the plurality of first cladding elements extending in a direction parallel to the central longitudinal axis of the hollow core optical fiber, each of the plurality of first cladding elements comprising a first capillary including an inner surface defining a first cavity, the first cavity having a first diameter, wherein each of the plurality of first cladding elements directly contacts the inner surface of the substrate; as well as a plurality of second cladding elements spaced apart from one another and positioned between the hollow core and the substrate, each of the plurality of second cladding elements extending in a direction parallel to the central longitudinal axis of the hollow core optical fiber, each of the plurality of second cladding elements comprising a second capillary including an inner surface defining a second cavity, the second cavity having a second diameter, the second diameter being different from the first diameter, wherein each of the second cladding elements does not directly contact the inner surface of the substrate; as well as The second capillary tube comprises nested capillaries, wherein each nested capillary tube directly contacts the inner surface of the second capillary tube.

19. The hollow core optical fiber of claim 18, wherein each nested capillary has an inner diameter of 6 μm to 25 μm.

20. The hollow core optical fiber of claim 18 or 19, wherein each nested capillary has a wall thickness of 0.1 μm to 4.0 μm.

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