Method of drawing hollow-core optical fibers

Abstract

A method includes heating a hollow-core preform comprising an outer tube and an inner tube. The outer tube includes an inner radius rocp and an outer radius Rocp. The inner tube includes an inner radius rcp and an outer radius Rcp. The method further includes drawing a hollow-core optical fiber from the hollow-core preform at a draw tension Tg in grams, thereby elongating the outer tube into an outer cladding of the hollow-core optical fiber and the inner tube to a capillary of the hollow-core optical fiber. The draw tension Tg and / or a differential capillary pressure Δpc are selected at least in part based on a non-dimensional parameter Formula (I), where T is the draw tension in dynes and T = 981×Tg, Δpc is in dynes / cm2, σc in dyne / cm is a surface energy of a glass material forming the inner tube, and -0.5 ≤ X1≤ 0.75.

Description

SP24-217 HOLLOW-CORE OPTICAL FIBERS AND METHODS FOR PRODUCING THE SAME

[0001] This application claims the benefit of priority under 35 U.S.C. § 119 of U.S.Provisional Application Serial No.63 / 683,586 filed on August 15, 2024, the content of which is relied upon and incorporated herein by reference in its entirety. FIELD

[0002] The present disclosure generally relates to methods for producing optical fibers, andmore specifically, to methods for producing hollow-core optical fibers. BACKGROUND

[0003] Hollow-core optical fibers are a new class of fibers that are attractive because of theiroptical properties of low loss, low attenuation, low latency, ultralow non-linearity, low flat dispersion, ultra broadband transmission, radiation hardness, and negligible Rayleighbackscattering. However, hollow-core optical fibers also suffer from the need for high precisionof fiber microstructures. A typical design of an anti-resonant hollow core optical fiber mayinclude an outer cladding along with two or more non-touching capillaries (or nested capillaries) attached on the inner surface of the outer cladding to define the hollow core through which thelight is propagated. The propagation characteristics of the hollow-core optical fibers, such asanti-resonant optical fibers, are strongly related to the microstructures and dimensions thereof for effective guiding by the waveguide.

[0004] Hollow-core optical fibers can be produced by drawing a hollow-core preform intofiber. During the manufacture of the anti-resonant hollow-core optical fiber, especially when thestarting preform sizes are increased for continuously drawing longer lengths of the fiber, therelative dimensions of the outer cladding and the capillaries may not be preserved from the preform to the fiber during the drawing of the fiber. Accordingly, it is important to understand the change in dimensions of the different components of the fiber during the draw process forscaling up and manufacturability.SP24-217 SUMMARY

[0005] Described herein are methods and processes addressing challenges in scaling up ofthe hollow-core optical fiber drawing process to large-volume manufacturing. The inventor hasrecognized that the degree of change in microstructure from the preform to the fiber may be impacted by the size of the preform and / or the size of the draw hot zone. The inventor further recognizes that the surface tension and / or pressure forces inside the outer cladding tube during the draw process may also affect the dimensions of the outer cladding and the capillaries of thefiber drawn. Accordingly, the inventor has developed methods and processes for achieving targefiber microstructure dimensions with high precision, including but not limited to determining the process conditions for attaining desired microstructures in the hollow-core optical fiber from hollow-core preform of different sizes during scaleup, which are all significant for scaleup and realizing low-cost large volume manufacturing of anti-resonant optical fibers.

[0006] In some embodiments, a method of producing a hollow-core optical fiber from ahollow-core preform, may include heating a hollow-core preform including an outer tube and an inner tube. The outer tube may include an inner surface defining an interior cavity and an inner radius rocpand an outer surface defining an outer radius Rocp. The inner tube may include an inner surface defining an interior cavity and an inner radius rcp and an outer surface defining an outer radius Rcp. The inner tube may be formed from a glass material. The method may further include drawing a hollow-core optical fiber from the hollow-core preform at a draw tension Tg in grams, thereby elongating the outer tube of the hollow-core preform into an outer cladding of the hollow-core optical fiber and elongating the inner tube of the hollow-core preform into a capillary of the hollow-core optical fiber. The draw tension Tgand a differential capillarypressure ^pc may be selected at least in part based on a non-dimensional parameter X1. Thedifferential capillary pressure ^pc is defined as a difference between a pressure inside the interiorcavity of the inner tube of the hollow-core preform and a pressure inside the interior cavity of theouter tube of the hollow-core preform. X3^^൫^^^2^^^^^−^^^2^^^^^൯^^^^^^൫∆^^^^^^^^^^−2^^^^൯ 1is defined as ^^1 = ^^^^ ^^^^−^^^^^^,4^^^^ ൫^^ ൯T is the draw tension in dynes, and T = 981×Tg, ^pc is in dynes / cm2, and ^c in dyne / cm is asurface energy of the glass material forming the inner tube. In some embodiments, X1may be greater than or equal to -0.5 and less than or equal to 0.75.SP24-217

[0007] Additional features and advantages are set forth in the Detailed Description thatfollows, and in part will be readily apparent to those skilled in the art from the description or recognized by practicing the embodiments as described in the written description and claims hereof, as well as the appended drawings. It is to be understood that both the foregoing general description and the following Detailed Description are merely exemplary, and are intended to provide an overview or framework to understand the nature and character of the claims. BRIEF DESCRIPTION OF THE DRAWINGS

[0008] The accompanying drawings are included to provide a further understanding, and areincorporated in and constitute a part of this specification. The drawings illustrate one or more embodiment(s), and together with the Detailed Description serve to explain principles and operation of the various embodiments. As such, the disclosure will become more fully understood from the following Detailed Description, taken in conjunction with the accompanying figured.

[0009] FIGS. 1A and 1B schematically depict cross-sectional views of exemplary hollow-core optical fibers.

[0010] FIG. 2A and 2B schematically depict cross-sectional views of exemplary hollow-corepreforms for drawing the hollow-core optical fibers of FIG.1A and FIG.1B, respectively.

[0011] FIG. 3 schematically depicts an exemplary drawing system.

[0012] FIG. 4 schematically illustrates an implementation of a finite-analytic solution ofevolution of preform outer tube inner and outer radii.

[0013] FIG. 5 is a plot showing inner diameters of capillaries drawn as a function ofdifferential capillary pressures during the drawing process for exemplary preform dimensions and operating conditions.

[0014] FIG. 6 is another plot showing inner diameters of capillaries drawn as a function ofdifferential capillary pressures during the drawing process for further exemplary preform dimensions and operating conditions.

[0015] FIG. 7 is another plot showing inner diameters of capillaries drawn as a function ofdifferential capillary pressures during the drawing process for further exemplary preform dimensions and operating conditions.SP24-217

[0016] FIG. 8 is another plot showing inner diameters of capillaries drawn as a function ofdifferential capillary pressures during the drawing process for further exemplary preform dimensions and operating conditions.

[0017] FIG. 9 is a plot showing the evolution of inner diameters of capillaries from innertubes of exemplary hollow-core preforms in the neck down region as a function of axial velocity in the neck down region, for different combinations of preform sizes, draw speeds, and differential capillary pressures. DETAILED DESCRIPTION

[0018] The present disclosure is provided as an enabling teaching and can be understoodmore readily by reference to the following description, drawings, examples, and claims. To this end, those skilled in the relevant art will recognize and appreciate that many changes can be made to the various aspects of the embodiments described herein, while still obtaining the beneficial results. It will also be apparent that some of the desired benefits of the present embodiments can be obtained by selecting some of the features without utilizing other features. Accordingly, those who work in the art will recognize that many modifications and adaptations are possible and can even be desirable in certain circumstances and are a part of the present disclosure. Therefore, it is to be understood that this disclosure is not limited to the specific compositions, articles, devices, and methods disclosed unless otherwise specified. It is also to be understood that the terminology used herein is for the purposes of describing particular aspects only and is not intended to be limiting.

[0019] In this specification and in the claims which follow, “greater than or equal to” and“≥” are used interchangeably, “less than or equal to” and “≤” are used interchangeably, “greater than” and “>” are used interchangeably, and “less than” and “<” are used interchangeably. When a parameter is described as greater than or equal to (or simply, ≥) a value, the parameter may be greater than (>) the referenced value or equal to (=) the referenced value. Similarly, when a parameter is described as less than or equal to (or simply, ≤) a value, the parameter may be less than (<) the referenced value or equal to (=) the referenced value.

[0020] Directional terms as used herein - for example up, down, right, left, front, back, top,bottom - are made only with reference to the figures as drawn and are not intended to imply absolute orientation.SP24-217

[0021] Various components described herein may be referred to as “directly connected” or“indirectly connected.” Components are directly connected when they are joined to one another with no intervening structure. Components may be joined by fusing, melting, welding, soldering, adhesives, or any other suitable attachment means. Components are “indirectly connected” when they are joined to one another with intervening structure. Examples of intervening structure include welding aids (e.g. frits, solders, fluxes), adhesives, and bonding materials. In some embodiments, components connected indirectly are connected only by a welding aid, adhesive, or bonding material. The term “connected” means “directly connected” or “indirectly connected.” Components “directly connected” to one another are said to be in direct contact with each other. Components “indirectly connected” to one another are said to be in indirect contact with each other. Components “connected” to one another are in direct or indirect contact with each other.

[0022] As used herein, the terms “upstream” and “downstream” refer to the relativepositioning of unit operations with respect to the direction of flow of the process streams. A first unit operation of a system may be considered “upstream” of a second unit operation if process streams flowing through the system encounter the first unit operation before encountering the second unit operation. Likewise, a second unit operation may be considered “downstream” of the first unit operation if the process streams flowing through the system encounter the first unit operation before encountering the second unit operation.

[0023] As used herein, the term “linear” refers to relative distances / lengths between points.A “linear” distance / length may refer to a distance between two points along a straight line.

[0024] As used herein, the singular forms “a,” “an” and “the” include plural referents inaddition to the single referent unless the context clearly dictates otherwise. Thus, for example, reference to “a” component includes aspects having one such component as well as two or more such components, unless the context clearly indicates otherwise.

[0025] Reference will now be made in detail to various embodiments. Whenever possible,the same reference numerals will be used throughout the drawings to refer to the same or like parts. Hollow-Core Optical Fiber

[0026] FIG. 1A schematically illustrates an example of a hollow-core optical fiber 100. Thehollow-core optical fiber 100 may include an outer cladding 110. The outer cladding 110 maySP24-217 include an inner surface 111 defining an interior cavity 115 and an inner radius rocf of the outer cladding 110, and an outer surface 112 defining an outer radius Rocf of the outer cladding 110.

[0027] The hollow-core optical fiber 100 may further include two or more (e.g., two, three,four, five, six, or more) cladding elements, such as capillaries 120, inside the interior cavity 115 of the outer cladding 110. The capillaries 120 may be in contact with and / or attached to the inner surface 111 of the outer cladding 110. The capillaries 120 may not be in contact with each other and may be evenly spaced along the inner surface 111 of the outer cladding 110. Each of the capillaries 120 may include an inner surface 121 defining an interior cavity 125 and an inner radius rcf of each of the capillaries 120, and an outer surface 122 defining an outer radius Rcf of each of the capillaries 120.

[0028] In some embodiments, the cladding elements of the hollow-core optical fiber 100may also include nested capillaries 130 with each disposed inside a capillary 120 and in contact with and / or attached to an inner surface of the capillary 120. Each of the nested capillaries 130 may include an inner surface 131 defining an interior cavity 135 and an inner radius rncfof each of the nested capillaries 130, and an outer surface 132 defining an outer radius Rncf of each of the nested capillaries 130. In some embodiments, the hollow-core optical fiber 100 may not include nested capillaries 130, such as shown in FIG.1B.

[0029] The cladding elements of the hollow-core optical fiber 100, e.g., the capillaries 120and / or the nested capillaries 130, may surround and define a hollow core 140 of the hollow-core optical fiber 100. The hollow core 140 may be the central portion of the interior cavity 115 and may correspond to the region of the hollow-core optical fiber 100 in which optical signals may be primarily confined and propagate. In some embodiments, the outer cladding 110, the capillaries 120, and / or the nested capillaries 130 may include silica glass and / or silica-based glass (i.e., silica glass comprising one or more dopants). Hollow-Core Preform

[0030] The hollow-core optical fiber 100 may be produced by drawing a hollow-corepreform into fiber. FIGS.2A and 2B schematically illustrate non-limiting examples of hollow- core preform 200 that may be utilized for producing the hollow-core optical fiber 100 shown in FIGS.1A and 1B, respectively. In some embodiments, the hollow-core preform 200 may include an outer tube 210. The outer tube 210 may be drawn into the outer cladding 110 of the hollow- core optical fiber 100. The outer tube 210 may include an inner surface 211 defining an interiorSP24-217 cavity 215 and an inner radius rocp of the outer tube 210, and an outer surface 212 defining an outer radius Rocp of the outer tube 210.

[0031] In some embodiments, the hollow-core preform 200 may further include two or more(e.g., two, three, four, five, six, or more) inner tubes 220 inside the interior cavity 215 of the outer tube 210. In some embodiments, the inner tubes 220 may be in contact with and / or attached to the inner surface 211 of the outer tube 210. In some embodiments, the inner tubes 220 may not be in contact with each other and may be evenly spaced along the inner surface 211 of the outer tube 210. Each of the inner tubes 220 may be drawn into a capillary 120 of the hollow-core optical fiber 100. Each of the inner tubes 220 may include an inner surface 221 defining an interior cavity 225 and an inner radius rcp of each of the inner tubes 220, and an outer surface 222 defining an outer radius Rcp of each of the inner tubes 220.

[0032] In some embodiments, such as shown in FIG. 2A, the hollow-core preform 200 mayalso include two or more nested tubes 230 with each disposed inside an inner tube 220 and in contact with and / or attached to an inner surface of the inner tube 220. Each of the nested tubes 230 may be drawn into a nested capillary 130 of the hollow-core optical fiber 100. Each of the nested tubes 230 may include an inner surface 231 defining an interior cavity 235 and an inner radius rncp of each of the nested tubes 230, and an outer surface 232 defining an outer radius Rncp of each of the nested tubes 230. In some embodiments, the hollow-core preform 200 may not include nested tubes 230, such as shown in FIG.2B.

[0033] The inner tubes 220 may surround and define a hollow section 240 that may be thecentral portion of the interior cavity 215 and correspond to the hollow core 140 of the hollow- core optical fiber 100 that may be drawn from the hollow-core preform 200. In some embodiments, the outer tube 210, the inner tubes 220, and / or the nested tubes 230 may include silica glass and / or silica-based glass (i.e., silica glass comprising one or more dopants). Fiber Drawing System

[0034] FIG. 3 schematically depicts an example of a drawing system 300 that may beutilized to produce the hollow-core optical fiber 100 from the hollow-core preform 200.

[0035] In some embodiments, the drawing system 300 may include a draw furnace 308configured for receiving and heating the hollow-core preform 200, thereby subjecting the hollow-core preform 200 to a draw temperature. After, and as, the hollow-core preform 200 is subjected to the draw temperature, the hollow-core preform 200 may be necked down, and theSP24-217 hollow-core optical fiber 100 may be drawn from the hollow-core preform 200. The draw furnace 308 may include a hot zone, which is defined as the axial span of the heating elements that are used to heat up the preform for drawing into fiber. An axial length of the hot zone may be greater than or equal to (i.e., ≥) 3 cm and less than or equal to (i.e., ≤) 50 cm – including all sub-ranges or values therebetween. For example, in some embodiments, the axial length of thehot zone may be ≥ 3 cm and ≤ 50 cm, ≥ 3 cm and ≤ 40 cm, ≥ 3 cm and ≤ 30 cm, ≥ 3 cm and ≤ 20cm, ≥ 3 cm and ≤ 10 cm, ≥ 10 cm and ≤ 50 cm, ≥ 10 cm and ≤ 40 cm, ≥ 10 cm and ≤ 30 cm, ≥ 10 cm and ≤ 20 cm, ≥ 20 cm and ≤ 50 cm, ≥ 20 cm and ≤ 40 cm, ≥ 20 cm and ≤ 30 cm, ≥ 30 cm and ≤ 50 cm, ≥ 30 cm and ≤ 40 cm, or ≥ 40 cm and ≤ 50 cm. In some embodiments, the axial length of the hot zone may be ≥ 3 cm, ≥ 5 cm, ≥ 10 cm, ≥ 15 cm, ≥ 20 cm, ≥ 25 cm, ≥ 30 cm, ≥ 35 cm, ≥ 40 cm, ≥ 45 cm, or greater. In some embodiments, the axial length of the hot zone may be ≤ 50 cm, ≤ 45 cm, ≤ 40 cm, ≤ 35 cm, ≤ 30 cm, ≤ 25 cm, ≤ 20 cm, ≤ 15 cm, ≤ 10 cm, ≤ 5 cm, or less.

[0036] In some embodiments, the drawing system 300 may further include a pressure controlsystem 310. The pressure control system 310 may be coupled to and configured for pressuring the interior cavities of the outer tube 210, the inner tubes 220, and / or the nested tubes 230 (if present) of the hollow-core preform 200. In some embodiments, the pressure control system 310 may include any or all of a pressure sensor, a vacuum system, a gas pressure source or gas supply, and / or a controller for monitoring the pressure(s) within the various cavities mentioned above and using vacuum and / or gas pressure to maintain the pressure(s) at a desired value(s). In some embodiments, the pressure control system 310 may include a manifold connected to the gas pressure source or gas supply for supplying gas to the hollow-core preform 200. The pressure(s) within the cavities mentioned above may at least in part determine the dimensions, such as radii, of the outer cladding 110, the capillaries 120, and / or the nested capillaries 130 of the hollow-core optical fiber 100, as will be discussed in more detail below.

[0037] In some embodiments, the drawing system 300 may further include a coolingchamber 312 to cool the hollow-core optical fiber 100. In some embodiments, the drawing system 300 may further include a non-contact sensor 314 for measuring the dimension, e.g., diameter of the outer surface 112 of the outer cladding 110. In some embodiments, the drawing system 300 may further include a coating apparatus 316 for applying and / or curing one or more coatings over the outer cladding 110.SP24-217

[0038] In some embodiments, the drawing system 300 may further include a tensionassembly 318, such as tractor, for applying a draw tension to draw the hollow-core optical fiber 100 from the hollow-core preform 200. The draw tension may be controlled via a control apparatus 320 to at least in part maintain the dimension of the hollow-core optical fiber 100 at a predetermined set point. In some embodiments, the drawing system 300 may further include a feedhead 322 for winding the hollow-core optical fiber 100 onto a storage spool 324. Evolution of Outer Tube to Outer Cladding (a) Finite Analytical Solution of Evolution of Preform Outer Tube Dimensions DuringDrawing

[0039] As discussed above, during the drawing of the hollow-core optical fiber, the hollow-core preform may be necked down, and the dimensions, e.g., the inner diameter / radius and outer diameter / radius, of the outer tube in the neckdown region evolve as they are subject to forces of surface tension, core pressure, and draw tension. The neckdown region refers to the region of the hollow-core preform between the axial location where the dimension(s) of the hollow-core preform, e.g., the outer diameter of the hollow-core preform, begins to reduce and the axial location where the final dimension(s), e.g., the outer diameter of the hollow-core optical fiber, is reached.

[0040] The evolution of the outer radius, Roc, and the inner radius, roc, of the outer tube in theneckdown region is given by the following relation:where z is the axial distance in the neckdown region, Vzis the axial velocity, Pcoreis the differential core pressure, σocis the surface energy of the glass material forming the outer tube(e.g., 300 dynes / cm for silica glass), and µ is the glass viscosity. The surface energy can bemeasured using the method described in Glass Engineering Handbook, 2nd Edition, by Shand, E. B.; Greene, C. H.; Grant, J. A.; Armistead, W. H., the content of which is incorporated by reference herein. The differential core pressure Pcore, which may also be referred to as the gauge pressure Pcore, is defined as the pressure difference between the pressure inside the interior cavity of the outer tube of the hollow-core preform and the atmospheric pressure around the exterior of the outer tube of the hollow-core preform.SP24-217

[0041] The draw tension under which the hollow-core optical fiber may be drawn from thehollow-core preform is given as:

[0042] Using a Corrocco type transformation and using Equation [2] to transform EquationEq. [1] with axial velocity as the independent variable, the following is obtained:

[0043] To capture the evolution of the outer radius Roc and the inner radius roc of the outertube of the hollow-core preform in the neckdown region, a finite-analytic solution, as shown in FIG.4, is implemented, where the analytic solution between the ith and the (i+1)the node is given as:which can be implemented with the mass balance equation as:(b) Exemplary Implementations of the Finite-Analytic Solution

[0044] The finite-analytic solution was implemented for different preform geometries thatresulted in the same inner diameter of the outer cladding of the hollow-core fiber (2×rocf) ofabout 79.7 µm, and the same outer diameter of the outer cladding of the hollow-core optical fiber(2×Rocf) of about 249 µm. However, it should be noted that the present disclosure is not limitedSP24-217to these specific fiber target dimensions (i.e., inner diameter of 79.7 µm and outer diameter of249 µm), which are used for non-limiting illustrative purposes. The present disclosure may beimplemented for achieving other target dimensions of the hollow-core optical fiber from different preform dimensions. For example, the solution described herein may be utilized for achieving any target inner diameter of the outer cladding of the hollow-core optical fiber thatmay be greater than or equal to (i.e., ≥) 45 µm and less than or equal to (i.e., ≤) 145 µm –including all sub-ranges or values therebetween. Similarly, the solution described herein may also be utilized for achieving any target outer diameter of the outer cladding of the hollow-coreoptical fiber that may be greater than or equal to (i.e., ≥) 150 µm and less than or equal to (i.e., ≤)300 µm – including all sub-ranges or values therebetween.

[0045] Table 1 below shows that different combinations of pressure, draw tension, andpreform geometries that result in substantially the same inner and outer diameters of the outer cladding of the hollow-core optical fiber. As shown in Table 1, the various outer diameters of the outer tube of the hollow-core preform (2×Rocp) between 17 mm and 50 mm and the various inner diameters of the outer tube of the hollow-core preform (2×rocp) between 5 mm and 9 mm result in substantially the same outer cladding dimensions of the hollow-core optical fiber, with the fiber draw speeds ranging between 1 m / s and 10 m / s. Table 1SP24-217(c) Approximate Solution of Preform Outer Tube Dimensions

[0046] Based on the example shown in Table 1, the following relations can be approximatedfor the differential core pressure Pcore as a function of draw tension Tg in grams:

[0047] Further, the following relations can be approximated for the inner radius rocp and theouter radius Rocpof the outer tube of the hollow-core preform:where rocf and Rocf are the inner and outer radii, respectively, of the outer cladding of the hollow- core optical fiber, Vp is the hollow-core preform feed rate,Vf is the hollow-core fiber draw rate, T is the draw tension in dynes and T = Tg*981, σoc is the surface energy of the glass material forming the outer tube (taken to be 300 dynes / cm), and r* and R* are given as:^^∗~5^^^^^^^^^^^^^^^^^[8b]

[0048] Based on the approximate solutions above, the inventor has found that when thedifferential core pressure Pcoresatisfies the following relation: 0.8 × ^^∗ < ^^ ∗^^^^^^^^ < 1.2 × ^^ [9]SP24-217where ^^∗ = 1.877 × 10−5 × ^^1.46^^ , consistent target inner radius rocf and consistent target outerradius Rocf of the outer cladding of the hollow-core optical fiber can be achieved with preforms having outer tuber inner radius rocp and outer tube outer radius Rocp that satisfy the following relations: 0.9 × ^^∗ ∗^^ < ^^^^^^^^ < 1.1 × ^^^^ [10a]0.95 × ^^∗ ∗^^ < ^^^^^^^^ < 1.05 × ^^^^ [10b]where:and ^^∗ = 5^^^^∗^^^^^^^^^ [12a]Evolution of Inner Tubes to Capillaries (a) Evolution of Preform Inner Tube Dimensions During Drawing

[0049] The evolution of the inner radius rc, and outer radius, Rc, of the inner tube in theneckdown region is described by the following relation:where z is the axial distance in the neckdown region, Vz is the axial velocity, ^pc is thedifferential capillary pressure in dynes / cm2, σc is the surface energy of the glass material formingthe inner tube (e.g., 300 dynes / cm for silica glass), and µ is the glass viscosity. The differentialcapillary pressure ^pc is defined as the difference between the pressure inside the interior cavityof each inner tube and the pressure outside the inner tubes, i.e., the pressure inside the interiorSP24-217 cavity of the outer tube of the hollow-core preform. Equation

[0013] for thin capillaries can be transformed with axial velocity in the neck down region, Vz, as the independent variables as:where T is the draw tension in dynes, and T = Tg*981.(i) Non-Dimensional Parameters X1and X2

[0050] For characterizing the evolution from the inner tubes of the hollow-core preform tothe capillaries of the hollow-core optical fiber during the drawing process, two non-dimensional parameters based on the structure in the starting hollow-core preform are defined as:where Rocp is the outer radius of the outer tube of the starting hollow-core preform, rocp is the inner radius of the outer tube of the starting hollow-core preform, Rcpis the outer radius of the inner tube of the starting hollow-core preform, and rcpis the inner radius of the inner tube of the starting hollow-core preform, Δpcis the differential capillary pressure in dynes / cm2, σcis the surface energy of the glass material forming the inner tube (e.g., 300 dynes / cm for silica glass), and T is the draw tension in dynes, and T = Tg*981.

[0051] The inventor has found that smaller values of the non-dimensional parameters X1 andX2may result in collapse of the capillaries. The inventor has also found that larger values of the non-dimensional parameters X1and X2may result in very large capillaries and process conditions the small changes of which, such as small change in pressure, can result in much more significant change in the capillary diameters as discussed in more detail below. The inventor has found that ranges of the non-dimensional parameters X1 and X2 may be selected (by, e.g.,SP24-217 choosing appropriate incoming preform dimensions, maintaining appropriate differential capillary pressure levels, applying appropriate draw tension values, etc.) such that relatively small changes in process conditions would not significantly alter the dimensions of the capillaries significantly, thereby achieving target capillary dimensions with precise during scale- up manufacturing.

[0052] In some embodiments, the non-dimensional parameter X1 may be greater than orequal to (i.e., ≥) -0.5 and less than or equal to (i.e., ≤) 0.75 – including all sub-ranges or values therebetween – for stable drawing of the capillaries of the hollow-core optical fibers. For example, in some embodiments, the non-dimensional parameter X1 may be ≥ 0 and ≤ 0.7 for stable drawing of the capillaries of the hollow-core optical fibers. In some embodiments, the non-dimensional parameter X1 may be ≥ 0.25 and ≤ 0.65 for stable drawing of the capillaries of the hollow-core optical fibers. In some embodiments, the non-dimensional parameter X1may be ≥ -0.5 and ≤ 0.75, ≥ -0.5 and ≤ 0.5, ≥ -0.5 and ≤ 0.25, ≥ -0.5 and ≤ 0, ≥ -0.5 and ≤ -0.25, ≥ -0.25 and ≤ 0.75, ≥ -0.25 and ≤ 0.5, ≥ -0.25 and ≤ 0.25, ≥ -0.25 and ≤ 0, ≥ 0 and ≤ 0.75, ≥ 0 and ≤ 0.5, ≥ 0 and ≤ 0.25, ≥ 0.25 and ≤ 0.75, ≥ 0.25 and ≤ 0.5, or ≥ 0.5 and ≤ 0.75. In some embodiments, the non-dimensional parameter X1 may be greater than or equal to (i.e., ≥) -0.5, ≥ -0.4, ≥ -0.3, ≥ - 0.2, ≥ -0.1, ≥ 0, ≥ 0.05, ≥ 0.1, ≥ 0.15, ≥ 0.2, ≥ 0.25, ≥ 0.3, ≥ 0.35, ≥ 0.4, ≥ 0.45, ≥ 0.5, ≥ 0.55, ≥ 0.6, ≥ 0.65, ≥ 0.7, or greater. In some embodiments, the non-dimensional parameter X1 may be less than or equal to (i.e., ≤) 0.75, ≤ 0.7, ≤ 0.65, ≤ 0.6, ≤ 0.55, ≤ 0.5, ≤ 0.45, ≤ 0.4, ≤ 0.35, ≤ 0.3, ≤ 0.25, ≤ 0.2, ≤ 0.15, ≤ 0.1, ≤ 0.05, ≤ 0, ≤ -0.1, ≤ -0.2, ≤ -0.3, ≤ -0.4, or less.

[0053] In some embodiments, the non-dimensional parameter X2 may be greater than orequal to (i.e., ≥) -0.35 and less than or equal to (i.e., ≤) 0.6 – including all sub-ranges or valuestherebetween – for stable drawing of the capillaries of the hollow-core optical fibers. In someembodiments, the non-dimensional parameter X2 may be ≥ 0 and ≤ 0.55 for stable drawing of thecapillaries of the hollow-core optical fibers. In some embodiments, the non-dimensionalparameter X2 may be ≥ 0.18 and ≤ 0.5 for stable drawing of the capillaries of the hollow-coreoptical fibers. In some embodiments, the non-dimensional parameter X2 may be ≥ 0.2 and ≤ 0.5for stable drawing of the capillaries of the hollow-core optical fibers. In some embodiments, thenon-dimensional parameter X2 may be ≥ -0.35 and ≤ 0.6, ≥ -0.35 and ≤ 0.4, ≥ -0.35 and ≤ 0.2, ≥ -0.35 and ≤ 0, ≥ -0.35 and ≤ -0.2, ≥ -0.2 and ≤ 0.6, ≥ -0.2 and ≤ 0.4, ≥ -0.2 and ≤ 0.2, ≥ -0.2 and ≤0, ≥ 0 and ≤ 0.6, ≥ 0 and ≤ 0.4, ≥ 0 and ≤ 0.2, ≥ 0.2 and ≤ 0.6, ≥ 0.2 and ≤ 0.4, or ≥ 0.4 and ≤ 0.6.SP24-217 In some embodiments, the non-dimensional parameter X2 may be greater than or equal to (i.e., ≥)-0.35, ≥ -0.3, ≥ -0.2, ≥ -0.1, ≥ 0, ≥ 0.05, ≥ 0.1, ≥ 0.15, ≥ 0.2, ≥ 0.25, ≥ 0.3, ≥ 0.35, ≥ 0.4, ≥ 0.45,≥ 0.5, ≥ 0.55, or greater. In some embodiments, the non-dimensional parameter X2 may be less than or equal to (i.e., ≤) 0.6, ≤ 0.55, ≤ 0.5, ≤ 0.45, ≤ 0.4, ≤ 0.35, ≤ 0.3, ≤ 0.25, ≤ 0.2, ≤ 0.15, ≤ 0.1, ≤ 0.05, ≤ 0, ≤ -0.1, ≤ -0.2, ≤ -0.3, or less. (ii) Non-Dimensional Parameters X3and X4

[0054] For characterizing the evolution from the nested tubes of the hollow-core preform tothe nested capillaries of the hollow-core optical fiber during the drawing process, two non- dimensional parameters based on the structure in the starting hollow-core preform are defined as:where Rocp is the outer radius of the outer tube of the starting hollow-core preform, rocp is the inner radius of the outer tube of the starting hollow-core preform, Rncpis the outer radius of the nested tube of the starting hollow-core preform, and rncpis the inner radius of the nested tube of the starting hollow-core preform, Δpncis the differential nested capillary pressure in dynes / cm2, which is defined as the difference between the pressure inside the interior cavity of each nested tube and the pressure outside the nested tubes, i.e., the pressure inside the interior cavity of the inner tubes of the hollow-core preform, σnc is the surface energy of the glass material forming the nested tube (taken to be 300 dynes / cm), and T is the draw tension in dynes, and T = Tg*981.

[0055] The inventor has found that smaller values of the non-dimensional parameters X3 andX4 may result in collapse of the nested capillaries. The inventor has also found that larger values of the non-dimensional parameters X3 and X4 may result in very large nested capillaries and process conditions the small changes of which, such as small change in pressure, can result in much more significant change in the capillary diameters as discussed in more detail below. The inventor has found that ranges of the non-dimensional parameters X3and X4may be selected (by, e.g., choosing appropriate incoming preform dimensions, maintaining appropriate differential nested capillary pressure levels, applying appropriate draw tension values, etc.) suchSP24-217 that relatively small changes in process conditions would not significantly alter the dimensions of the nested capillaries significantly, thereby achieving target capillary dimensions with precise during scale-up manufacturing.

[0056] In some embodiments, the non-dimensional parameter X3 may be greater than orequal to (i.e., ≥) -0.5 and less than or equal to (i.e., ≤) 0.75 – including all sub-ranges or values therebetween – for stable drawing of the nested capillaries of the hollow-core optical fibers. For example, in some embodiments, the non-dimensional parameter X3may be ≥ 0 and ≤ 0.7 for stable drawing of the nested capillaries of the hollow-core optical fibers. In some embodiments, the non-dimensional parameter X3 may be ≥ 0.25 and ≤ 0.65 for stable drawing of the nested capillaries of the hollow-core optical fibers. In some embodiments, the non-dimensionalparameter X3 may be ≥ -0.5 and ≤ 0.75, ≥ -0.5 and ≤ 0.5, ≥ -0.5 and ≤ 0.25, ≥ -0.5 and ≤ 0, ≥ -0.5and ≤ -0.25, ≥ -0.25 and ≤ 0.75, ≥ -0.25 and ≤ 0.5, ≥ -0.25 and ≤ 0.25, ≥ -0.25 and ≤ 0, ≥ 0 and ≤ 0.75, ≥ 0 and ≤ 0.5, ≥ 0 and ≤ 0.25, ≥ 0.25 and ≤ 0.75, ≥ 0.25 and ≤ 0.5, or ≥ 0.5 and ≤ 0.75. In some embodiments, the non-dimensional parameter X3may be greater than or equal to (i.e., ≥) - 0.5, ≥ -0.4, ≥ -0.3, ≥ -0.2, ≥ -0.1, ≥ 0, ≥ 0.05, ≥ 0.1, ≥ 0.15, ≥ 0.2, ≥ 0.25, ≥ 0.3, ≥ 0.35, ≥ 0.4, ≥ 0.45, ≥ 0.5, ≥ 0.55, ≥ 0.6, ≥ 0.65, ≥ 0.7, or greater. In some embodiments, the non-dimensional parameter X3 may be less than or equal to (i.e., ≤) 0.75, ≤ 0.7, ≤ 0.65, ≤ 0.6, ≤ 0.55, ≤ 0.5, ≤ 0.45, ≤ 0.4, ≤ 0.35, ≤ 0.3, ≤ 0.25, ≤ 0.2, ≤ 0.15, ≤ 0.1, ≤ 0.05, ≤ 0, ≤ -0.1, ≤ -0.2, ≤ -0.3, ≤ -0.4, or less.

[0057] In some embodiments, the non-dimensional parameter X4 may be greater than orequal to (i.e., ≥) -0.35 and less than or equal to (i.e., ≤) 0.6 – including all sub-ranges or valuestherebetween – for stable drawing of the nested capillaries of the hollow-core optical fibers. Insome embodiments, the non-dimensional parameter X4 may be ≥ 0 and ≤ 0.55 for stable drawingof the nested capillaries of the hollow-core optical fibers. In some embodiments, the non-dimensional parameter X4 may be ≥ 0.18 and ≤ 0.5 for stable drawing of the nested capillaries ofthe hollow-core optical fibers. In some embodiments, the non-dimensional parameter X4 may be≥ 0.2 and ≤ 0.5 for stable drawing of the nested capillaries of the hollow-core optical fibers. Insome embodiments, the non-dimensional parameter X4 may be ≥ -0.35 and ≤ 0.6, ≥ -0.35 and ≤0.4, ≥ -0.35 and ≤ 0.2, ≥ -0.35 and ≤ 0, ≥ -0.35 and ≤ -0.2, ≥ -0.2 and ≤ 0.6, ≥ -0.2 and ≤ 0.4, ≥ -0.2 and ≤ 0.2, ≥ -0.2 and ≤ 0, ≥ 0 and ≤ 0.6, ≥ 0 and ≤ 0.4, ≥ 0 and ≤ 0.2, ≥ 0.2 and ≤ 0.6, ≥ 0.2and ≤ 0.4, or ≥ 0.4 and ≤ 0.6. In some embodiments, the non-dimensional parameter X4 may begreater than or equal to (i.e., ≥) -0.35, ≥ -0.3, ≥ -0.2, ≥ -0.1, ≥ 0, ≥ 0.05, ≥ 0.1, ≥ 0.15, ≥ 0.2, ≥SP24-217 0.25, ≥ 0.3, ≥ 0.35, ≥ 0.4, ≥ 0.45, ≥ 0.5, ≥ 0.55, or greater. In some embodiments, the non- dimensional parameter X4 may be less than or equal to (i.e., ≤) 0.6, ≤ 0.55, ≤ 0.5, ≤ 0.45, ≤ 0.4, ≤ 0.35, ≤ 0.3, ≤ 0.25, ≤ 0.2, ≤ 0.15, ≤ 0.1, ≤ 0.05, ≤ 0, ≤ -0.1, ≤ -0.2, ≤ -0.3, or less.

[0058] The inventor has found that by selecting the appropriate preform dimensions (e.g.,inner and outer radii of the outer tube, inner tubes, and / or nested tubes) and / or the drawing conditions (e.g., draw tension, differential capillary pressures, differential nested capillary pressures, etc.), appropriate values of non-dimensional parameters X1, X2, X3, and X4with the various range described above may be obtained for achieving various target dimensions of the capillaries and / or nested capillaries. (b) Exemplary Implementations

[0059] The below examples are intended to be exemplary and are not intended to limit thescope of the disclosure. Tables 2-5 show the inner and outer diameters of the capillaries of the hollow-core optical fiber drawn as a function of differential capillary pressure for different draw tensions for preforms having outer tube outer diameter ranging between 17 mm and 50 mm and fiber draw speeds ranging between 1 m / s and 10 m / s. In Tables 2-5 below, the differential capillary pressure is shown as “Capillary dP” in dynes / cm2. Table 2-ATable 2-B1SP24-217Table 2-B2Table 2-B3SP24-217Table 2-B4Table 3-ATable 3-B1SP24-217Table 3-B2Table 3-B3SP24-217 Table 3-B4Table 4-ATable 4-B1Table 4-B2SP24-217Table 4-B3Table 4-B4SP24-217Table 5-ATable 5-B1Table 5-B2SP24-217

[0060] The plots of FIGS. 5-8 show the inner diameter of the capillaries drawn as a functionof the differential capillary pressure during the drawing process. The inventor has found that at relatively low differential capillary pressure, a small increase or decrease in the differential capillary pressure may not significantly affect the inner diameter of the capillaries drawn; at relatively high differential capillary pressure, even a small increase or decrease in the differential capillary pressure may result in drastic change in the inner diameter of the capillaries drawn.

[0061] FIG. 9 plots the evolution of the inner diameters of the capillaries from the innertubes of the hollow-core preform in the neck down region as a function of axial velocity in the neck down region, for the different combinations of preform sizes, draw speeds, and differential capillary pressures outlined in Tables 2-5. As shown, the inner diameter may initially gradually increase as the differential capillary pressure may be the dominant factor affecting the inner diameter. As the tubes are continuously drawn down, the effects of surface tension on the inner diameter may become prominent, in combination with the differential capillary pressure causing the inner diameter to gradually decrease. Thus, the evolution of the inner diameter of the capillaries from the inner diameter of the inner tubers of the hollow-core preform is a complex process. The non-dimensional parameters X1, X2, X3, and / or X4described herein provide simplified guidance for selecting the appropriate process condition ranges for drawing hollow- core optical fibers from preforms of different sizes to various desired target capillary dimensions. Operating Parameters

[0062] The various methods and relations described herein may be implemented with a widerange of operating parameters for scaling up the drawing of hollow-core optical fibers fromSP24-217 hollow-core preforms of various sizes while maintaining a tight control over target microstructure dimensions of the hollow-core optical fibers drawn. Draw Tension

[0063] In some embodiments, the draw tension under which the hollow-core optical fibermay be drawn from a hollow-core preform may be greater than or equal to (i.e., ≥) 50 g and less than or equal to (i.e., ≤) 600 g – including all sub-ranges or values therebetween. For example, insome embodiments, the draw tension may be ≥ 50 g and ≤ 600 g, ≥ 50 g and ≤ 550 g, ≥ 50 g and≤ 500 g, ≥ 50 g and ≤ 450 g, ≥ 50 g and ≤ 400 g, ≥ 50 g and ≤ 350 g, ≥ 50 g and ≤ 300 g, ≥ 50 gand ≤ 250 g, ≥ 50 g and ≤ 200 g, ≥ 50 g and ≤ 150 g, ≥ 50 g and ≤ 100 g, ≥ 100 g and ≤ 600 g, ≥100 g and ≤ 550 g, ≥ 100 g and ≤ 500 g, ≥ 100 g and ≤ 450 g, ≥ 100 g and ≤ 400 g, ≥ 100 g and≤ 350 g, ≥ 100 g and ≤ 300 g, ≥ 100 g and ≤ 250 g, ≥ 100 g and ≤ 200 g, ≥ 100 g and ≤ 150 g, ≥150 g and ≤ 600 g, ≥ 150 g and ≤ 550 g, ≥ 150 g and ≤ 500 g, ≥ 150 g and ≤ 450 g, ≥ 150 g and ≤400 g, ≥ 150 g and ≤ 350 g, ≥ 150 g and ≤ 300 g, ≥ 150 g and ≤ 250 g, ≥ 150 g and ≤ 200 g, ≥200 g and ≤ 600 g, ≥ 200 g and ≤ 550 g, ≥ 200 g and ≤ 500 g, ≥ 200 g and ≤ 450 g, ≥ 200 g and ≤400 g, ≥ 200 g and ≤ 350 g, ≥ 200 g and ≤ 300 g, ≥ 200 g and ≤ 250 g, ≥ 250 g and ≤ 600 g, ≥250 g and ≤ 550 g,≥ 250 g and ≤ 500 g, ≥ 250 g and ≤ 450 g, ≥ 250 g and ≤ 400 g, ≥ 250 g and ≤350 g, ≥ 250 g and ≤ 300 g, ≥ 300 g and ≤ 600 g, ≥ 300 g and ≤ 550 g, ≥ 300 g and ≤ 500 g, ≥300 g and ≤ 450 g, ≥ 300 g and ≤ 400 g, ≥ 300 g and ≤ 350 g, ≥ 350 g and ≤ 600 g, ≥ 350 g and ≤550 g,≥ 350 g and ≤ 500 g, ≥ 350 g and ≤ 450 g, ≥ 350 g and ≤ 400 g, ≥ 400 g and ≤ 600 g, ≥ 400g and ≤ 550 g, ≥ 400 g and ≤ 500 g, ≥ 400 g and ≤ 450 g, ≥ 450 g and ≤ 600 g, ≥ 450 g and ≤ 550g, ≥ 450 g and ≤ 500 g, ≥ 500 g and ≤ 600 g, ≥ 550 g and ≤ 600 g, or ≥ 550 g and ≤ 600 g.

[0064] In some embodiments, the draw tension under which the hollow-core optical fibermay be drawn from a hollow-core preform may be greater than or equal to (i.e., ≥) 50 g, ≥ 70 g, ≥ 90 g, ≥ 110 g, ≥ 130 g, ≥ 150 g, ≥ 170 g, ≥ 190 g, ≥ 210 g, ≥ 230 g, ≥ 250 g, ≥ 270 g, ≥ 290 g,≥ 310 g, ≥ 330 g, ≥ 350 g, ≥ 370 g, ≥ 390 g, ≥ 410 g, ≥ 430 g, ≥ 450 g, ≥ 470 g, ≥ 490 g, ≥ 510 g,≥ 530 g, ≥ 550 g, ≥ 570 g, ≥ 590 g, or greater. In some embodiments, the draw tension underwhich the hollow-core optical fiber may be drawn from the hollow-core preform may be lessthan or equal to (i.e., ≤) 600 g, ≤ 580 g, ≤ 560 g, ≤ 540 g, ≤ 520 g, 500 g, ≤ 480 g, ≤ 460 g, ≤ 440g, ≤ 420 g, 400 g, ≤ 380 g, ≤ 360 g, ≤ 340 g, ≤ 320 g, ≤ 300 g, ≤ 280 g, ≤ 260 g, ≤ 240 g, ≤ 220 g,≤ 200 g, ≤ 180 g, ≤ 160 g, ≤ 140 g, ≤ 120 g, ≤ 100 g, ≤ 80 g, ≤ 60 g, or less.SP24-217 Draw Speed

[0065] In some embodiments, the hollow-core optical fiber may be drawn at a draw speed ofgreater than or equal to (i.e., ≥) 1 m / s and less than or equal to (i.e., ≤) 20 m / s – including all sub- ranges or values therebetween. For example, in some embodiments, the draw speed may be ≥ 1 m / s and ≤ 20 m / s, ≥ 1 m / s and ≤ 15 m / s, ≥ 1 m / s and ≤ 10 m / s, ≥ 1 m / s and ≤ 5 m / s, ≥ 5 m / s and ≤ 20 m / s, ≥ 5 m / s and ≤ 15 m / s, ≥ 5 m / s and ≤ 10 m / s, ≥ 10 m / s and ≤ 20 m / s, ≥ 10 m / s and ≤ 15 m / s, or ≥ 15 m / s and ≤ 20 m / s. In some embodiments, the hollow-core optical fiber may be drawn at a draw speed of greater than or equal to (i.e., ≥) 1 m / s, ≥ 3 m / s, ≥ 5 m / s, ≥ 7 m / s, ≥ 9 m / s, ≥ 11 m / s, ≥ 13 m / s, ≥ 15 m / s, ≥ 17 m / s, ≥ 19 m / s, or greater. Preform Feed Rate

[0066] In some embodiments, the hollow-core preform may be fed into the draw furnace at apreform feed rate Vp that may be greater than or equal to (i.e., ≥) 5 mm / min and less than orequal to (i.e., ≤) 100 mm / min – including all sub-ranges or values therebetween. For example, insome embodiments, the hollow-core preform may be fed into the draw furnace at a preform feedrate Vp that may be ≥ 5 mm / min and ≤ 100 mm / min, ≥ 5 mm / min and ≤ 75 mm / min, ≥ 5mm / min and ≤ 50 mm / min, ≥ 5 mm / min and ≤ 25 mm / min, ≥ 25 mm / min and ≤ 100 mm / min, ≥25 mm / min and ≤ 75 mm / min, ≥ 25 mm / min and ≤ 50 mm / min, ≥ 50 mm / min and ≤ 100mm / min, ≥ 50 mm / min and ≤ 75 mm / min, or ≥ 75 mm / min and ≤ 100 mm / min. In someembodiments, the hollow-core preform may be fed into the draw furnace at a preform feed rateVp that may be ≥ 5 mm / min, ≥ 10 mm / min, ≥ 15 mm / min, ≥ 20 mm / min, ≥ 25 mm / min, ≥ 30mm / min, ≥ 35 mm / min, ≥ 40 mm / min, ≥ 45 mm / min, ≥ 50 mm / min, ≥ 55 mm / min, ≥ 60mm / min, ≥ 65 mm / min, ≥ 70 mm / min, ≥ 75 mm / min, ≥ 80 mm / min, ≥ 85 mm / min, ≥ 90mm / min, ≥ 95 mm / min, or greater. In some embodiments, the hollow-core preform may be fedinto the draw furnace at a preform feed rate Vp that may be less than or equal to 100 mm / min, ≤95 mm / min, ≤ 90 mm / min, ≤ 85 mm / min, ≤ 80 mm / min, ≤ 75 mm / min, ≤ 70 mm / min, ≤ 65mm / min, ≤ 60 mm / min, ≤ 55 mm / min, ≤ 50 mm / min, ≤ 45 mm / min, ≤ 40 mm / min, ≤ 35mm / min, ≤ 30 mm / min, ≤ 25 mm / min, ≤ 20 mm / min, ≤ 15 mm / min, ≤ 10 mm / min, or less.Differential Core Pressure Pcore

[0067] In some embodiments, the differential core pressure Pcore may be greater than or equalto (i.e., ≥) 0.01 psig and less than or equal to (i.e., ≤) 2 psig – including all sub-ranges or values therebetween. For example, in some embodiments, the differential core pressure Pcoremay beSP24-217may be ≥ 0.01 psig and ≤ 2 psig, ≥ 0.01 psig and ≤ 1.5, ≥ 0.01 psig and ≤ 1, ≥ 0.01 psig and ≤0.5, ≥ 0.01 psig and ≤ 0.1 psig, ≥ 0.1 psig and ≤ 2 psig, ≥ 0.1 psig and ≤ 1.5, ≥ 0.1 psig and ≤ 1, ≥0.1 psig and ≤ 0.5, ≥ 0.5 psig and ≤ 2 psig, ≥ 0.5 psig and ≤ 1.5, ≥ 0.5 psig and ≤ 1, ≥ 1 psig and≤ 2 psig, ≥ 1 psig and ≤ 1.5, or ≥ 1.5 psig and ≤ 2 psig.

[0068] In some embodiments, the differential core pressure Pcore may be greater than or equalto (i.e., ≥) 0.01 psig, ≥ 0.05 psig, ≥ 0.1 psig, ≥ 0.2 psig, ≥ 0.3 psig, ≥ 0.4 psig, ≥ 0.5 psig, ≥ 0.6psig, ≥ 0.7 psig, ≥ 0.8 psig, ≥ 0.9 psig, ≥ 1 psig, ≥ 1.1 psig, ≥ 1.2 psig, ≥ 1.3 psig, ≥ 1.4 psig, ≥1.5 psig, ≥ 1.6 psig, ≥ 1.7 psig, ≥ 1.8 psig, ≥ 1.9 psig, or greater. In some embodiments, thedifferential core pressure Pcore may be less than or equal to (i.e., ≤) 2 psig, ≤ 1.9 psig, ≤ 1.8 psig,≤ 1.7 psig, ≤ 1.6 psig, ≤ 1.5 psig, ≤ 1.4 psig, ≤ 1.3 psig, ≤ 1.2 psig, ≤ 1.1 psig, ≤ 1 psig, ≤ 0.9psig, ≤ 0.8 psig, ≤ 0.7 psig, ≤ 0.6 psig, ≤ 0.5 psig, ≤ 0.4 psig, ≤ 0.3 psig, ≤ 0.2 psig, ≤ 0.1 psig, ≤0.05 psig, or less. Differential Capillary Pressure ΔPc

[0069] In some embodiments, the differential capillary pressure ΔPc may be greater than orequal to (i.e., ≥) 5,000 dynes / cm2 and less than or equal to (i.e., ≤) 100,000 dynes / cm2 –including all sub-ranges or values therebetween. For example, in some embodiments, thedifferential capillary pressure ΔPc may be ≥ 5,000 dynes / cm2 and ≤ 100,000 dynes / cm2, ≥ 5,000dynes / cm2 and ≤ 75,000 dynes / cm2, ≥ 5,000 dynes / cm2 and ≤ 50,000 dynes / cm2, ≥ 5,000dynes / cm2 and ≤ 25,000 dynes / cm2, ≥ 5,000 dynes / cm2 and ≤ 10,000 dynes / cm2, ≥ 10,000dynes / cm2 and ≤ 100,000 dynes / cm2, ≥ 10,000 dynes / cm2 and ≤ 75,000 dynes / cm2, ≥ 10,000dynes / cm2 and ≤ 50,000 dynes / cm2, ≥ 10,000 dynes / cm2 and ≤ 25,000 dynes / cm2, ≥ 25,000dynes / cm2 and ≤ 100,000 dynes / cm2, ≥ 25,000 dynes / cm2 and ≤ 75,000 dynes / cm2, ≥ 25,000dynes / cm2 and ≤ 50,000 dynes / cm2, ≥ 50,000 dynes / cm2 and ≤ 100,000 dynes / cm2, ≥ 50,000dynes / cm2 and ≤ 75,000 dynes / cm2, or ≥ 75,000 dynes / cm2 and ≤ 100,000 dynes / cm2.

[0070] In some embodiments, the differential capillary pressure ΔPc may be greater than orequal to (i.e., ≥) 5,000 dynes / cm2, ≥ 10,000 dynes / cm2, ≥ 15,000 dynes / cm2, ≥ 20,000 dynes / cm2,≥ 25,000 dynes / cm2, ≥ 30,000 dynes / cm2, ≥ 35,000 dynes / cm2, ≥ 40,000 dynes / cm2, ≥ 45,000dynes / cm2, ≥ 50,000 dynes / cm2, ≥ 55,000 dynes / cm2, ≥ 60,000 dynes / cm2, ≥ 65,000 dynes / cm2,≥ 70,000 dynes / cm2, ≥ 75,000 dynes / cm2, ≥ 80,000 dynes / cm2, ≥ 85,000 dynes / cm2, ≥ 90,000dynes / cm2, ≥ 95,000 dynes / cm2, or greater.SP24-217

[0071] In some embodiments, the differential capillary pressure ΔPc may be less than orequal to (i.e., ≤) 100,000 dynes / cm2, ≤ 95,000 dynes / cm2, ≤ 90,000 dynes / cm2, ≤ 85,000dynes / cm2, ≤ 80,000 dynes / cm2, ≤ 75,000 dynes / cm2, ≤ 70,000 dynes / cm2, ≤ 65,000 dynes / cm2,≤ 60,000 dynes / cm2, ≤ 55,000 dynes / cm2, ≤ 50,000 dynes / cm2, ≤ 45,000 dynes / cm2, ≤ 40,000dynes / cm2, ≤ 35,000 dynes / cm2, ≤ 30,000 dynes / cm2, ≤ 25,000 dynes / cm2, ≤ 20,000 dynes / cm2,≤ 15,000 dynes / cm2, ≤ 10,000 dynes / cm2, or less.Differential Nested Capillary Pressure ΔPnc

[0072] In some embodiments, the differential nested capillary pressure ΔPnc may be greaterthan or equal to (i.e., ≥) 2,000 dynes / cm2 and less than or equal to (i.e., ≤) 50,000 dynes / cm2 –including all sub-ranges or values therebetween. For example, in some embodiments, thedifferential nested capillary pressure ΔPnc may be ≥ 2,000 dynes / cm2 and ≤ 50,000 dynes / cm2, ≥2,000 dynes / cm2 and ≤ 40,000 dynes / cm2, ≥ 2,000 dynes / cm2 and ≤ 30,000 dynes / cm2, ≥ 2,000dynes / cm2 and ≤ 20,000 dynes / cm2, ≥ 2,000 dynes / cm2 and ≤ 10,000 dynes / cm2, ≥ 10,000dynes / cm2 and ≤ 50,000 dynes / cm2, ≥ 10,000 dynes / cm2 and ≤ 40,000 dynes / cm2, ≥ 10,000dynes / cm2 and ≤ 30,000 dynes / cm2, ≥ 10,000 dynes / cm2 and ≤ 20,000 dynes / cm2, ≥ 20,000dynes / cm2 and ≤ 50,000 dynes / cm2, ≥ 20,000 dynes / cm2 and ≤ 40,000 dynes / cm2, ≥ 20,000dynes / cm2 and ≤ 30,000 dynes / cm2, ≥ 30,000 dynes / cm2 and ≤ 50,000 dynes / cm2, ≥ 30,000dynes / cm2 and ≤ 40,000 dynes / cm2, or ≥ 40,000 dynes / cm2 and ≤ 50,000 dynes / cm2.

[0073] In some embodiments, the differential nested capillary pressure ΔPnc may be greaterthan or equal to (i.e., ≥) 2,000 dynes / cm2, ≥ 5,000 dynes / cm2, ≥ 10,000 dynes / cm2, ≥ 15,000dynes / cm2, ≥ 20,000 dynes / cm2, ≥ 25,000 dynes / cm2, ≥ 30,000 dynes / cm2, ≥ 35,000 dynes / cm2,≥ 40,000 dynes / cm2, ≥ 45,000 dynes / cm2, or greater. In some embodiments, the differentialnested capillary pressure ΔPnc may be less than or equal to (i.e., ≤) 50,000 dynes / cm2, ≤ 45,000dynes / cm2, ≤ 40,000 dynes / cm2, ≤ 35,000 dynes / cm2, ≤ 30,000 dynes / cm2, ≤ 25,000 dynes / cm2,≤ 20,000 dynes / cm2, ≤ 15,000 dynes / cm2, ≤ 10,000 dynes / cm2, ≤ 5,000 dynes / cm2, or less.Preform Outer Tube Dimesions

[0074] In some embodiments, the inner diameter of the outer tube of the hollow-corepreform (2×rocp) may be greater than or equal to (i.e., ≥) 4 mm and less than or equal to (i.e., ≤) 20 mm – including all sub-ranges or values therebetween. For example, in some embodiments,the inner diameter of the outer tube of the hollow-core preform (2×rocp) may be ≥ 4 mm and ≤ 20mm, ≥ 4 mm and ≤ 16 mm, ≥ 4 mm and ≤ 12 mm, ≥ 4 mm and 8 mm, ≥ 8 mm and ≤ 20 mm, ≥ 8SP24-217mm and ≤ 16 mm, ≥ 8 mm and ≤ 12 mm, ≥ 12 mm and ≤ 20 mm, ≥ 12 mm and ≤ 16 mm, or ≥ 16mm and ≤ 20 mm. In some embodiments, the inner diameter of the outer tube of the hollow-corepreform (2×rocp) may be greater than or equal to (i.e., ≥) 4 mm, ≥ 5 mm, ≥ 6 mm, ≥ 7 mm, ≥ 8mm, ≥ 9 mm, ≥ 10 mm, ≥ 11 mm, ≥ 12 mm, ≥ 13 mm, ≥ 14 mm, ≥ 15 mm, ≥ 16 mm, ≥ 17 mm,≥ 18 mm, ≥ 19 mm, or greater. In some embodiments, the inner diameter of the outer tube of thehollow-core preform (2×rocp) may be less than or equal to (i.e., ≤) 20 mm, ≤ 19 mm, ≤ 18 mm, ≤17 mm, ≤ 16 mm, ≤ 15 mm, ≤ 14 mm, ≤ 13 mm, ≤ 12 mm, ≤ 11 mm, ≤ 10 mm, ≤ 9 mm, ≤ 8 mm,≤ 7 mm, ≤ 6 mm, ≤ 5 mm, or less.

[0075] In some embodiments, the outer diameter of the outer tube of the hollow-corepreform (2×Rocp) may be greater than or equal to (i.e., ≥) 15 mm and less than or equal to (i.e., ≤) to 100 mm – including all sub-ranges or values therebetween. For example, in someembodiments, the outer diameter of the outer tube of the hollow-core preform (2×Rocp) may be ≥15 mm and ≤ 100 mm, ≥ 15 mm and ≤ 75 mm, ≥ 15 mm and ≤ 50 mm, ≥ 15 mm and ≤ 25 mm, ≥25 mm and ≤ 100 mm, ≥ 25 mm and ≤ 75 mm, ≥ 25 mm and ≤ 50 mm, ≥ 50 mm and ≤ 100 mm,≥ 50 mm and ≤ 75 mm, or ≥ 75 mm and ≤ 100 mm. In some embodiments, the outer diameter ofthe outer tube of the hollow-core preform (2×Rocp) may be greater than or equal to (i.e., ≥) 15mm, ≥ 20 mm, ≥ 25 mm, ≥ 30 mm, ≥ 35 mm, ≥ 40 mm, ≥ 45 mm, ≥ 50 mm, ≥ 55 mm, ≥ 60 mm,≥ 65 mm, ≥ 70 mm, ≥ 75 mm, ≥ 80 mm, ≥ 85 mm, ≥ 90 mm, ≥ 95 mm, or greater. In someembodiments, the outer diameter of the outer tube of the hollow-core preform (2×Rocp) may beless than or equal to (i.e., ≤) 100 mm, ≤ 95 mm, ≤ 90 mm, ≤ 85 mm, ≤ 80 mm, ≤ 75 mm, ≤ 70mm, ≤ 65 mm, ≤ 60 mm, ≤ 55 mm, ≤ 50 mm, ≤ 45 mm, ≤ 40 mm, ≤ 35 mm, ≤ 30 mm, ≤ 25 mm,≤ 20 mm, or less.Preform Inner Tube Dimesions

[0076] In some embodiments, the inner diameter of the inner tube of the hollow-corepreform (2×rcp) may be greater than or equal to (i.e., ≥) 1 mm and less than or equal to (i.e., ≤) 8mm – including all sub-ranges or values therebetween. For example, in some embodiments, theinner diameter of the inner tube of the hollow-core preform (2×rcp) may be ≥ 1 mm and ≤ 8 mm,≥ 1 mm and ≤ 6 mm, ≥ 1 mm and ≤ 4 mm, ≥ 1 mm and ≤ 2 mm, ≥ 2 mm and ≤ 8 mm, ≥ 2 mmand ≤ 6 mm, ≥ 2 mm and ≤ 4 mm, ≥ 4 mm and ≤ 8 mm, ≥ 4 mm and ≤ 6 mm, or ≥ 6 mm and ≤ 8mm. In some embodiments, the inner diameter of the inner tube of the hollow-core preform(2×rcp) may be greater than or equal to (i.e., ≥) 1 mm, ≥ 1.5 mm, ≥ 2 mm, ≥ 2.5 mm, ≥ 3 mm, ≥SP24-2173.5 mm, ≥ 4 mm, ≥ 4.5 mm, ≥ 5 mm, ≥ 5.5 mm, ≥ 6 mm, ≥ 6.5 mm, ≥ 7 mm, ≥ 7.5 mm, orgreater. In some embodiments, the inner diameter of the inner tube of the hollow-core preform(2×rcp) may be less than or equal to (i.e., ≤) 8 mm, ≤ 7.5 mm, ≤ 7 mm, ≤ 6.5 mm, ≤ 6 mm, ≤ 5.5mm, ≤ 5 mm, ≤ 4.5 mm, ≤ 4 mm, ≤ 3.5 mm, ≤ 3 mm, ≤ 2.5 mm, ≤ 2 mm, ≤ 1.5 mm, or less.

[0077] In some embodiments, the outer diameter of the inner tube of the hollow-corepreform (2×Rcp) may be greater than or equal to (i.e., ≥) 1.4 mm and less than or equal to (i.e., ≤) 10 mm – including all sub-ranges or values therebetween. For example, in some embodiments, in some embodiments, the outer diameter of the inner tube of the hollow-core preform (2×Rcp) maybe ≥ 1.4 mm and ≤ 10 mm, ≥ 1.4 mm and ≤ 8 mm, ≥ 1.4 mm and ≤ 6 mm, ≥ 1.4 mm and ≤ 4mm, or ≥ 1.4 µm and ≤ 2 mm. In some embodiments, the outer diameter of the inner tube of thehollow-core preform (2×Rcp) may be greater than or equal to (i.e., ≥) 1.4 mm, ≥ 1.5 mm, ≥ 2 mm,≥ 2.5 mm, ≥ 3 mm, ≥ 3.5 mm, ≥ 4 mm, ≥ 4.5 mm, ≥ 5 mm, ≥ 5.5 mm, ≥ 6 mm, ≥ 6.5 mm, ≥ 7mm, ≥ 7.5 mm, ≥ 8 mm, ≥ 8.5 mm, ≥ 9 mm, ≥ 9.5 mm, or greater. In some embodiments, theouter diameter of the inner tube of the hollow-core preform (2×Rcp) may be less than or equal to(i.e., ≤) 10 mm, ≤ 9.5 mm, ≤ 9 mm, ≤ 8.5 mm, ≤ 8 mm, ≤ 7.5 mm, ≤ 7 mm, ≤ 6.5 mm, 6 mm, ≤ 5.5 mm, ≤ 5 mm, ≤ 4.5 mm, ≤ 4 mm, ≤ 3.5 mm, ≤ 3 mm, ≤ 2.5 mm, ≤ 2 mm, ≤ 1.5 mm, or less. Preform Nested Tube Dimesions

[0078] In some embodiments, the inner diameter of the nested tube of the hollow-corepreform (2×rncp) may be greater than or equal to (i.e., ≥) 0.5 mm and less than or equal to (i.e., ≤) 1.3 mm – including all sub-ranges or values therebetween. For example, in some embodiments, the inner diameter of the nested tube of the hollow-core preform (2×rncp) may be ≥ 0.5 mm and ≤1.3 mm, ≥ 0.5 mm and ≤ 1.1 mm, ≥ 0.5 mm and ≤ 0.9 mm, ≥ 0.5 mm and ≤ 0.7 mm, ≥ 0.7 mmand ≤ 1.3 mm, ≥ 0.7 mm and ≤ 1.1 mm, ≥ 0.7 mm and ≤ 0.9 mm,≥ 0.9 mm and ≤ 1.3 mm, ≥ 0.9mm and ≤ 1.1 mm, or ≥ 1.1 mm and ≤ 1.3 mm. In some embodiments, the inner diameter of thenested tube of the hollow-core preform (2×rncp) may be greater than or equal to (i.e., ≥) 0.5 mm,≥ 0.6 mm, ≥ 0.7 mm, ≥ 0.8 mm, ≥ 0.9 mm, ≥ 1 mm, ≥ 1.1 mm, ≥ 1.2 mm, or greater. In someembodiments, the inner diameter of the nested tube of the hollow-core preform (2×rncp) may beless than or equal to (i.e., ≤) 1.3 mm, ≤ 1.2 mm, ≤ 1.1 mm, ≤ 1 mm, ≤ 0.9 mm, ≤ 0.8 mm, ≤ 0.7mm, ≤ 0.6 mm, or less.

[0079] In some embodiments, the outer diameter of the nested tube of the hollow-corepreform (2×Rncp) may be greater than or equal to (i.e., ≥) 0.6 mm and less than or equal to (i.e.,SP24-217 ≤) to 1.5 mm – including all sub-ranges or values therebetween. For example, in some embodiments, the outer diameter of the nested tube of the hollow-core preform (2×Rncp) may be≥ 0.6 mm and ≤ 1.5 mm, ≥ 0.6 mm and ≤ 1.3 mm, ≥ 0.6 mm and ≤ 1.1 mm, ≥ 0.6 mm and ≤ 0.9mm, ≥ 0.6 mm and ≤ 0.7 mm, ≥ 0.8 mm and ≤ 1.5 mm, ≥ 0.8 mm and ≤ 1.3 mm, ≥ 0.8 mm and ≤1.1 mm, ≥ 0.8 mm and ≤ 0.9 mm, ≥ 1 mm and ≤ 1.5 mm, ≥ 1 mm and ≤ 1.3 mm, ≥ 1 mm and ≤1.1 mm, ≥ 1.2 mm and ≤ 1.5 mm, ≥ 1.2 mm and ≤ 1.3 mm, or ≥ 1.4 mm and ≤ 1.5 mm. In someembodiments, the outer diameter of the nested tube of the hollow-core preform (2×Rncp) may begreater than or equal to (i.e., ≥) 0.6 mm, ≥ 0.7 mm, ≥ 0.8 mm, ≥ 0.9 mm, ≥ 1 mm, ≥ 1.1 mm, ≥1.2 mm, ≥ 1.3 mm, ≥ 1.4 mm, or greater. In some embodiments, the outer diameter of the nestedtube of the hollow-core preform (2×Rncp) may be less than or equal to (i.e., ≤) 1.5 mm, ≤ 1.4 mm,≤ 1.3 mm, ≤ 1.2 mm, ≤ 1.1 mm, ≤ 1 mm, ≤ 0.9 mm, ≤ 0.8 mm, ≤ 0.7 mm, or less.Fiber Outer Cladding Dimensions

[0080] In some embodiments, the inner diameter of the outer cladding of the hollow-coreoptical fiber (2×rocf) may be greater than or equal to (i.e., ≥) 45 µm and less than or equal to (i.e., ≤) 135 µm – including all sub-ranges or values therebetween. For example, in some embodiments, the inner diameter of the outer cladding of the hollow-core optical fiber (2×rocf)may be ≥ 45 µm and ≤ 135 µm, ≥ 45 µm and ≤ 115 µm, ≥ 45 µm and ≤ 95 µm, ≥ 45 µm and ≤75 µm, ≥ 45 µm and ≤ 55 µm, ≥ 55 µm and ≤ 135 µm, ≥ 55 µm and ≤ 115 µm, ≥ 55 µm and ≤ 95µm, ≥ 55 µm and ≤ 75 µm, ≥ 75 µm and ≤ 135 µm, ≥ 75 µm and ≤ 115 µm, ≥ 75 µm and ≤ 95µm, ≥ 95 µm and ≤ 135 µm, ≥ 95 µm and ≤ 115 µm, or ≥ 115 µm and ≤ 135 µm. In someembodiments, the inner diameter of the outer cladding of the hollow-core optical fiber (2×rocf)may be greater than or equal to (i.e., ≥) 45 µm, ≥ 50 mm, ≥ 55 mm, ≥ 60 mm, ≥ 65 mm, ≥ 70mm, ≥ 75 mm, ≥ 80 mm, ≥ 85 mm, ≥ 90 mm, ≥ 95 mm, ≥ 100 mm, ≥ 105 mm, ≥ 110 mm, ≥ 115mm, ≥ 120 mm, ≥ 125 mm, ≥ 130 µm, or greater. In some embodiments, the inner diameter ofthe outer cladding of the hollow-core optical fiber (2×rocf) may be less than or equal to (i.e., ≤)135 µm, ≤ 130 µm, ≤ 125 µm, ≤ 120 µm, ≤ 115 µm, ≤ 110 µm, ≤ 105 µm, ≤ 100 µm, ≤ 95 µm, ≤ 90 µm, ≤ 85 µm, ≤ 80 µm, ≤ 75 µm, ≤ 70 µm, ≤ 65 µm, ≤ 60 µm, ≤ 55 µm, ≤ 50 µm, or less.

[0081] In some embodiments, the outer diameter of the outer cladding of the hollow-coreoptical fiber (2×Rocf) may be greater than or equal to (i.e., ≥) 150 µm and less than or equal to (i.e., ≤) 300 µm – including all sub-ranges or values therebetween. For example, in some embodiments, the outer diameter of the outer cladding of the hollow-core optical fiber (2×Rocf)SP24-217may be ≥ 150 µm and ≤ 300 µm, ≥ 150 µm and ≤ 250 µm, ≥ 150 µm and ≤ 200 µm, ≥ 200 µmand ≤ 300 µm, ≥ 200 µm and ≤ 250 µm, or ≥ 250 µm and ≤ 300 µm. In some embodiments, theouter diameter of the outer cladding of the hollow-core optical fiber (2×Rocf) may be greater thanor equal to (i.e., ≥) 150 µm, ≥ 160 µm, ≥ 170 µm, ≥ 180 µm, ≥ 190 µm, ≥ 200 µm, ≥ 210 µm, ≥220 µm, ≥ 230 µm, ≥ 240 µm, ≥ 250 µm, ≥ 260 µm, ≥ 270 µm, ≥ 280 µm, ≥ 290 µm, or greater.In some embodiments, the outer diameter of the outer cladding of the hollow-core optical fiber(2×Rocf) may be less than or equal to (i.e., ≤) 300 µm, ≤ 290 µm, ≤ 280 µm, ≤ 270 µm, ≤ 260µm, ≤ 250 µm, ≤ 240 µm, ≤ 230 µm, ≤ 220 µm, ≤ 210 µm, ≤ 200 µm, ≤ 190 µm, ≤ 180 µm, ≤170 µm, ≤ 160 µm, or less.Fiber Capillary Dimensions

[0082] In some embodiments, the inner diameter of the capillaries of the hollow-core opticalfiber (2×rcf) may be greater than or equal to (i.e., ≥) 10 µm and less than or equal to (i.e., ≤) 40µm – including all sub-ranges or values therebetween. For example, in some embodiments, theinner diameter of the capillaries of the hollow-core optical fiber (2×rcf) may be ≥ 10 µm and ≤40 µm, ≥ 10 µm and ≤ 30 µm, ≥ 10 µm and ≤ 20 µm, ≥ 20 µm and ≤ 40 µm, ≥ 20 and ≤ 30 µm,or ≥ 30 µm and ≤ 40 µm. In some embodiments, the inner diameter of the capillaries of thehollow-core optical fiber (2×rcf) may be greater than or equal to (i.e., ≥) 10 µm, ≥ 12.5 µm, ≥ 15µm, ≥ 17.5 µm, ≥ 20 µm, ≥ 22.5 µm, ≥ 25 µm, ≥ 27.5 µm, ≥ 30 µm, ≥ 32.5 µm, ≥ 35 µm, ≥ 37.5µm, or greater. In some embodiments, the inner diameter of the capillaries of the hollow-coreoptical fiber (2×rcf) may be less than or equal to (i.e., ≤) 40 µm, ≤ 37.5 µm, ≤ 35 µm, ≤ 32.5 µm,≤ 30 µm, ≤ 27.5 µm, ≤ 25 µm, ≤ 22.5 µm, ≤ 20 µm, ≤ 17.5 µm, ≤ 15 µm, ≤ 12.5 µm, or less.

[0083] In some embodiments, the outer diameter of the capillaries of the hollow-core opticalfiber (2×Rcf) may be greater than or equal to (i.e., ≥) 14 um and less than or equal to (i.e., ≤) 50 µm – including all sub-ranges or values therebetween. For example, in some embodiments, theouter diameter of the capillaries of the hollow-core optical fiber (2×Rcf) may be ≥ 14 µm and ≤50 µm, ≥ 14 µm and ≤ 40 µm, ≥ 14 µm and ≤ 30 µm, ≥ 14 µm and ≤ 20 µm, ≥ 20 µm and ≤ 50µm, ≥ 20 µm and ≤ 40 µm, ≥ 20 µm and ≤ 30 µm, ≥ 30 µm and ≤ 50 µm, ≥ 30 µm and ≤ 40 µm,or ≥ 40 µm and ≤ 50 µm. In some embodiments, the outer diameter of the capillaries of thehollow-core optical fiber (2×Rcf) may be greater than or equal to (i.e., ≥) 14 µm, ≥ 15 µm, ≥17.5 µm, ≥ 20 µm, ≥ 22.5 µm, ≥ 25 µm, ≥ 27.5 µm, ≥ 30 µm, ≥ 32.5 µm, ≥ 35 µm, ≥ 37.5 µm, ≥40 µm, ≥ 42.5 µm, ≥ 45 µm, ≥ 47.5 µm, or greater. In some embodiments, the outer diameter ofSP24-217 the capillaries of the hollow-core optical fiber (2×Rcf) may be less than or equal to (i.e., ≤) 50µm, ≤ 47.5 µm, ≤ 45 µm, ≤ 42.5 µm, ≤ 40 µm, ≤ 37.5 µm, ≤ 35 µm, ≤ 32.5 µm, ≤ 30 µm, ≤ 27.5µm, ≤ 25 µm, ≤ 22.5 µm, ≤ 20 µm, ≤ 17.5 µm, ≤ 15 µm, or less.Fiber Nested Capillary Dimesions

[0084] In some embodiments, the inner diameter of the nested capillaries of the hollow-coreoptical fiber (2×rncf) may be greater than or equal to (i.e., ≥) 10 µm and less than or equal to (i.e.,≤) 28 µm – including all sub-ranges or values therebetween. For example, in some embodiments,the inner diameter of the nested capillaries of the hollow-core optical fiber (2×rncf) may be ≥ 10µm and ≤ 28 µm, ≥ 10 µm and ≤ 24 µm, ≥ 10 µm and ≤ 20 µm, ≥ 10 µm and ≤ 16 µm, ≥ 10 µmand ≤ 12 µm, ≥ 14 µm and ≤ 28 µm, ≥ 14 µm and ≤ 24 µm, ≥ 14 µm and ≤ 20 µm, ≥ 14 µm and≤ 16 µm, ≥ 18 µm and ≤ 28 µm, ≥ 18 µm and ≤ 24 µm, ≥ 18 µm and ≤ 20 µm, ≥ 22 µm and ≤ 28µm, ≥ 22 µm and ≤ 24 µm, or ≥ 26 µm and ≤ 28 µm. In some embodiments, the inner diameterof the nested capillaries of the hollow-core optical fiber (2×rncf) may be greater than or equal to(i.e., ≥) 10 µm, ≥ 11 µm, ≥ 12 µm, ≥ 13 µm, ≥ 14 µm, ≥ 15 µm, ≥ 16 µm, ≥ 17 µm, ≥ 18 µm, ≥19 µm, ≥ 20 µm, ≥ 21 µm, ≥ 22 µm, ≥ 23 µm, ≥ 24 µm, ≥ 25 µm, ≥ 26 µm, ≥ 27 µm, or greater.In some embodiments, the inner diameter of the nested capillaries of the hollow-core opticalfiber (2×rncf) may be less than or equal to (i.e., ≤) 28 µm, ≤ 27 µm, ≤ 26 µm, ≤ 25 µm, ≤ 24 µm,≤ 23 µm, ≤ 22 µm, ≤ 21 µm, ≤ 20 µm, ≤ 19 µm, ≤ 18 µm, ≤ 17 µm, ≤ 16 µm, ≤ 15 µm, ≤ 14 µm, ≤ 13 µm, ≤ 12 µm, ≤ 11 µm, or less.

[0085] In some embodiments, the outer diameter of the nested capillaries of the hollow-coreoptical fiber (2×Rncf) may be greater than or equal to (i.e., ≥) 11 µm and less than or equal to(i.e., ≤) 30 µm – including all sub-ranges or values therebetween. For example, in someembodiments, the outer diameter of the nested capillaries of the hollow-core optical fiber(2×Rncf) may be ≥ 11 µm and ≤ 30 µm, ≥ 11 µm and ≤ 25 µm, ≥ 11 µm and ≤ 20 µm, ≥ 11 µmand ≤ 15 µm, ≥ 15 µm and ≤ 30 µm, ≥ 15 µm and ≤ 25 µm, ≥ 15 µm and ≤ 20 µm, ≥ 20 µm and≤ 30 µm, ≥ 20 µm and ≤ 25 µm, or ≥ 25 µm and ≤ 30 µm. In some embodiments, the outerdiameter of the nested capillaries of the hollow-core optical fiber (2×Rncf) may be greater than orequal to (i.e., ≥) 11 µm, ≥ 12 µm, ≥ 13 µm, ≥ 14 µm, ≥ 15 µm, ≥ 16 µm, ≥ 17 µm, ≥ 18 µm, ≥ 19µm, ≥ 20 µm, ≥ 21 µm, ≥ 22 µm, ≥ 23 µm, ≥ 24 µm, ≥ 25 µm, ≥ 26 µm, ≥ 27 µm, ≥ 28 µm, ≥ 29 µm, or greater. In some embodiments, the outer diameter of the nested capillaries of the hollow-core optical fiber (2×Rncf) may be less than or equal to (i.e., ≤) 30 µm, ≤ 29 µm, ≤ 28 µm, ≤ 27SP24-217µm, ≤ 26 µm, ≤ 25 µm, ≤ 24 µm, ≤ 23 µm, ≤ 22 µm, ≤ 21 µm, ≤ 20 µm, ≤ 19 µm, ≤ 18 µm, ≤ 17µm, ≤ 16 µm, ≤ 15 µm, ≤ 14 µm, ≤ 13 µm, ≤ 12 µm, or less.

[0086] It will be apparent to those skilled in the art that various modifications to the preferredembodiments of the disclosure as described herein can be made without departing from the spirit or scope of the disclosure as defined in the appended claims. Thus, the disclosure covers the modifications and variations provided they come within the scope of the appended claims and the equivalents thereto.

Claims

SP24-217 CLAIMSWhat is claimed is:

1. A method of producing a hollow-core optical fiber from a hollow-core preform, themethod comprising: heating a hollow-core preform comprising an outer tube and an inner tube, wherein the outer tube comprises an inner surface defining an interior cavity and an inner radius rocp and an outer surface defining an outer radius Rocp, wherein the inner tube comprises an inner surface defining an interior cavity and an inner radius rcp and an outer surface defining an outer radius Rcp, wherein the inner tube is formed from a glass material; and drawing a hollow-core optical fiber from the hollow-core preform at a draw tension Tgin grams, thereby elongating the outer tube of the hollow-core preform into an outer cladding of the hollow-core optical fiber and elongating the inner tube of the hollow-core preform into a capillary of the hollow-core optical fiber, wherein the draw tension Tg and a differential capillary pressure ^pc are selected at least in part based on a non-dimensional parameter X1, wherein the differentialcapillary pressure ^pc is defined as a difference between a pressure inside the interior cavity of theinner tube of the hollow-core preform and a pressure inside the interior cavity of the outer tube ofthe hollow-core preform, wherein X1 is defined as:where: T is the draw tension in dynes, and T = 981×Tg; ^pc is in dynes / cm2; andin dyne / cm is a surface energy of the glass material forming the inner tube; and wherein X1 is greater than or equal to -0.5 and less than or equal to 0.75.

2. The method of claim 1, wherein the draw tension Tg and the differential capillarypressure ^pc are selected at least in part further based on a non-dimensional parameter X2,wherein X2 is defined as:SP24-217 wherein X2 is greater than or equal to -0.35 and less than or equal to 0.6.

3. The method of any of claims 1 to 2, wherein the non-dimensional parameter X1 is greaterthan or equal to 0 and less than or equal to 0.7.

4. The method of any of claims 1 to 3, wherein the non-dimensional parameter X1 is greaterthan or equal to 0.25 and less than or equal to 0.65.

5. The method of any of claims 1 to 4, wherein the non-dimensional parameter X2 is greaterthan or equal to 0 and less than or equal to 0.55.

6. The method of any of claims 1 to 5, wherein the non-dimensional parameter X2 is greaterthan or equal to 0.18 and less than or equal to 0.5.

7. The method of any of claims 1 to 6, wherein the hollow-core preform further comprises anested tube in contact with an inner surface of the inner tube of the hollow-core preform, and wherein the nested tube comprises an inner surface defining an interior cavity and an inner radius rncp and an outer surface defining an outer radius Rncp.

8. The method of claim 7, wherein the drawing further elongates the nested tube of thehollow-core preform to a nested capillary of the hollow-core optical fiber.

9. The method of any of claims 7 to 8, wherein the draw tension Tg and a differentialcapillary pressure ^pnc are selected at least in part based on a non-dimensional parameter X3,wherein the differential nested capillary pressure ^pnc is defined as a difference between apressure inside the interior cavity of the nested tube of the hollow-core preform and a pressure inside the interior cavity of the outer tube of the hollow-core preform, wherein X3 is defined as:where ^nc is the surface energy of a glass material forming the nested tube;wherein X3 is greater than or equal to -0.5 and less than or equal to 0.75.SP24-21710. The method of any of claims 7 to 9, wherein the draw tension Tg and the differentialcapillary pressure ^pnc are selected at least in part further based on a non-dimensional parameterX4, wherein X4is defined as:wherein X4 is greater than or equal to -0.35 and less than or equal to 0.6.

11. The method of any of claims 9 to 10, wherein the non-dimensional parameter X3 isgreater than or equal to 0 and less than or equal to 0.7.

12. The method of any of claims 9 to 11, wherein the non-dimensional parameter X3 isgreater than or equal to 0.25 and less than or equal to 0.65.

13. The method of any of claims 9 to 12, wherein the non-dimensional parameter X4 isgreater than or equal to 0 and less than or equal to 0.55.

14. The method of any of claims 9 to 13, wherein the non-dimensional parameter X4 isgreater than or equal to 0.18 and less than or equal to 0.5.

15. The method of any of claims 7 to 14, wherein the differential nested capillary pressure∆pnc is greater than or equal to 2,000 dynes / cm2and less than or equal to 50,000 dynes / cm2.

16. The method of any of claims 1 to 15, wherein a fiber draw speed is greater than or equalto 1 m / s and less than or equal to 20 m / s.

17. The method of any of claims 1 to 16, wherein a preform feed rate is greater than or equalto 5 mm / min and less than or equal to 100 mm / min.

18. The method of any of claims 1 to 17, wherein the outer radius Rocp of the outer tube ofthe hollow-core preform is greater than or equal to 7.5 mm and less than or equal to 50 mm.

19. The method of any of claims 1 to 18, wherein the inner radius rocp of the outer tube of thehollow-core preform is greater than or equal to 2 mm and less than or equal to 10 mm.SP24-21720. The method of any of claims 1 to 19, wherein the outer radius Rc of the inner tube of thehollow-core preform is greater than or equal to 0.7 mm and less than or equal to 5 mm.

21. The method of any of claims 1 to 20, wherein the inner radius rc of the inner tube of thehollow-core preform is greater than or equal to 0.5 mm and less than or equal to 4 mm.

22. The method of any of claims 1 to 21, wherein the draw tension under which the opticalfiber is drawn is between 50 g and 600 g.

23. The method of any of claims 1 to 22, wherein a differential core pressure is between 0.01and 2 psig.

24. The method of any of claims 1 to 23, wherein the differential capillary pressure ∆pc isgreater than or equal to 5,000 dynes / cm2and less than or equal to 100,000 dynes / cm2.

25. The method of any of claims 1 to 24, wherein the hollow-core optical fiber is drawn in adraw furnace having hot zone ranging between 3 cm and 50 cm.

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