HOLLOW-CORE OPTICAL FIBERS AND METHODS FOR PRODUCING THE SAME

Abstract

A method may include: feeding a hollow-core preform into a draw furnace at a preform feed rate V.sub.p; heating the hollow-core preform comprising an outer tube having an inner radius/diameter r.sub.p/ID.sub.preform and an outer radius/diameter R.sub.p/OD.sub.preform; and drawing a hollow-core optical fiber from the hollow-core preform at a fiber draw rate V.sub.f and a draw tension , thereby elongating the outer tube of the hollow-core preform to an outer cladding of the hollow-core optical fiber having an inner radius/diameter r.sub.f/ID.sub.fiber and an outer radius/diameter R.sub.f/OD.sub.fiber; wherein: the interior cavity of the outer tube is under a differential core pressure P.sub.core, the differential core pressure P.sub.core, the inner and outer radii r.sub.p and R.sub.p of the outer tube are selected such that a tight control over target inner and outer radii r.sub.f and R.sub.f and a fiber dimension sensitivity ID.sub.fiber of the outer cladding can be achieved.

Claims

1. A method of producing a hollow-core optical fiber from a hollow-core preform, the method comprising: feeding a hollow-core preform into a draw furnace at a preform feed rate V.sub.p in mm/min; heating the hollow-core preform comprising an outer tube, wherein the outer tube comprises an inner surface defining an interior cavity and an inner radius r.sub.p in mm of the outer tube of the hollow-core preform and an outer surface defining an outer radius R.sub.p in mm of the outer tube of the hollow-core preform; and drawing a hollow-core optical fiber from the hollow-core preform at a fiber draw rate V.sub.f in mm/min and a draw tension in grams, thereby elongating the outer tube of the hollow-core preform to an outer cladding of the hollow-core optical fiber, wherein the outer cladding comprises an inner surface defining an inner radius r.sub.f in m of the outer cladding of the hollow-core fiber and an outer surface defining an outer radius R.sub.f in m of the outer cladding of the hollow-core optical fiber; wherein: the interior cavity of the outer tube of the hollow-core preform is under a differential core pressure P.sub.core in psig that satisfies the following relation: $0\text{.8}P*<P_{\mathrm{core}}<1\text{.2}P*,$ $\mathrm{where}:$ $P*=1.87710^{-5}{}^{1.46},$ the inner radius r.sub.p of the outer tube of the hollow-core preform and the outer radius R.sub.p of the outer tube of the hollow-core preform satisfy the following relations: $0.9r_p^{*}<r_p<1.1r_p^{*},$ $0.95R_p^{*}<R_p<1.05R_p^{*},$ $\mathrm{where}:$ $r_p^{*}=\frac{r_f}{{\left(V_f/V_p\right)}^{-\left(T+3R_{*}-3P_{\mathrm{core}}{R}_{*}^2\right)/2T}},$ $R_p^{*}=\frac{R_f}{{\left(V_f/V_p\right)}^{-\left(T+3r_{*}-3P_{\mathrm{core}}{r}_{*}^2\right)/2T}},$ where: T is the draw tension in dynes, and T=981, is a surface energy of a material forming the outer tube; $r_{*}=5\sqrt{r_p^{*}{r}_f};\mathrm{and}$ $R_{*}=5\sqrt{R_p^{*}{R}_f}.$

2. The method of claim 1, wherein the draw tension in gram under which the hollow-core optical fiber is drawn is greater than or equal to 50 g and less than or equal to 600 g.

3. The method of claim 1, wherein the differential core pressure P.sub.core in the interior cavity of the outer tube of the hollow-core preform is greater than or equal to 0.01 psig and less than or equal to 2 psig.

4. The method of claim 1, wherein a fiber draw speed (V.sub.f divided by 60,000) is greater than or equal to 1 m/s and less than or equal to 20 m/s.

5. The method of claim 1, wherein the preform feed rate V.sub.p is greater than or equal to 5 mm/min and less than or equal to 100 mm/min.

6. The method of claim 1, wherein the outer diameter of the outer tube of the hollow-core preform (OD.sub.preform=2R.sub.p) is greater than or equal to 15 mm and less than or equal to 100 mm.

7. The method of claim 1, wherein the inner diameter of the outer tube of the hollow-core preform (ID.sub.Preform=2r.sub.p) is greater than or equal to 4 mm and less than or equal to 20 mm.

8. The method of claim 1, wherein the outer diameter of the outer cladding of the hollow-core optical fiber (OD.sub.fiber=2R.sub.f) is greater than or equal to 150 m and less than or equal to 300 m.

9. The method of claim 1, wherein the inner diameter of the outer cladding of the hollow-core optical fiber (ID.sub.fiber=2r.sub.f) is greater than or equal to 45 m and less than or equal to 135 m.

10. The method of claim 1, wherein the draw furnace comprises a hot zone having an axial length greater than or equal to 3 cm and less than or equal to 50 cm.

11. The method of claim 1, wherein the hollow-core preform further comprises an inner tube in contact with the inner surface of the outer tube of the hollow-core preform, wherein the drawing further elongates the inner tube of the hollow-core preform to a capillary of the hollow-core optical fiber in contact with the inner surface of the outer cladding of the hollow-core optical fiber.

12. The method of claim 1, wherein the hollow-core preform further comprises a nested tube in contact with an inner surface of the inner tube of the hollow-core preform, wherein the drawing further elongates the nested tube of the hollow-core preform to a nested capillary of the hollow-core optical fiber in contact with an inner surface of the inner tube of the hollow-core optical fiber.

13. A method of producing a hollow-core optical fiber from a hollow-core preform, the method comprising: feeding a hollow-core preform into a draw furnace at a preform feed rate V.sub.p (in mm/min); heating the hollow-core preform comprising an outer tube, wherein the outer tube comprises an inner surface defining an interior cavity and an inner diameter ID.sub.preform (in mm) of the outer tube of the hollow-core preform and an outer surface defining an outer diameter OD.sub.preform (in mm) of the outer tube of the hollow-core preform; and drawing a hollow-core optical fiber from the hollow-core preform at a fiber draw rate V.sub.f (in mm/min) and a draw tension , thereby elongating the outer tube of the hollow-core preform to an outer cladding of the hollow-core optical fiber, wherein the outer cladding comprises an inner surface defining an inner diameter ID.sub.fiber (in m) of the outer cladding of the hollow-core fiber and an outer surface defining an outer diameter OD.sub.fiber (in m) of the outer cladding of the hollow-core optical fiber; wherein a fiber dimension sensitivity ID.sub.fiber (in m), as defined as a variation in the inner diameter ID.sub.fiber of the outer cladding of the hollow-core optical fiber when a differential core pressure P.sub.core undergoes a fluctuation of 0.01 psig, satisfies the following: $I{D}_{\mathrm{fiber}}=M$ where: M is a proportionality constant and M=2277.778ID.sub.fiber+(1.19710.sup.5), is a grouping parameter and $=A{x}^{-1.18}{T}_{\mathrm{fiber}}^{-2},$ where: A is a scaling factor and $A=\frac{O{D}_{\mathrm{preform}}^2-I{D}_{\mathrm{preform}}^2}{136},$ x is the operating draw stress (in MPa) and $x=\frac{4}{}\frac{}{\left(O{D}_{\mathrm{fiber}}^2-I{D}_{\mathrm{fiber}}^2\right)},$ and T.sub.fiber (in m) is the thickness of the outer cladding of the hollow-core optical fiber and $T_{\mathrm{fiber}}=\frac{1}{2}O{D}_{\mathrm{fiber}}-\frac{1}{2}I{D}_{\mathrm{fiber}}.$

14. The method of claim 13, wherein: the interior cavity of the outer tube of the hollow-core preform is under a differential core pressure P.sub.core in psig that satisfies the following relation: $0.8P*<P_{\mathrm{core}}<1\text{.2}P*,$ $\mathrm{where}:$ $P*=1.87710^{-5}{}^{1.46},$ the inner radius r.sub.p of the outer tube of the hollow-core preform and the outer radius R.sub.p of the outer tube of the hollow-core preform satisfy the following relations: $0.9r_p^{*}<r_p<1.1r_p^{*},$ $0.95R_p^{*}<R_p<1.05R_p^{*},$ $\mathrm{where}:$ $r_p^{*}=\frac{r_f}{{\left(V_f/V_p\right)}^{-\left(T+3R_{*}-3P_{\mathrm{core}}{R}_{*}^2\right)/2T}},$ $R_p^{*}=\frac{R_f}{{\left(V_f/V_p\right)}^{-\left(T+3r_{*}-3P_{\mathrm{core}}{r}_{*}^2\right)/2T}},$ where: T is the draw tension in dynes, and T=981, is a surface energy of a material forming the outer tube of the hollow-core preform, $r_{*}=5\sqrt{r_p^{*}{r}_f};\mathrm{and}$ $R_{*}=5\sqrt{R_p^{*}{R}_f}.$

15. The method of claim 13, wherein the inner diameter ID.sub.fiber of the outer cladding of the hollow-core optical fiber is greater than or equal to 45 m and less than or equal to 135 m.

16. The method of claim 13, wherein the fiber dimension sensitivity ID.sub.fiber satisfies at least one of: $I{D}_{\mathrm{fiber}}<5.m;\mathrm{or}$ $I{D}_{\mathrm{fiber}}<2.m.$

17. The method of claim 13, wherein the grouping parameter satisfies at least one of: $0<<2.210^{-5};$ $0<<1.510^{-5};$ $0<<1.210^{-5};$ $0<<0.910^{-5};$ $0<<0.710^{-5};\mathrm{or}$ $0<<0.510^{-5}.$

18. The method of claim 13, wherein the proportionality constant M satisfies at least one of: $M2.010^5;$ $M4.510^5;\mathrm{or}$ $2.24210^{5}M4.29210^5.$

19. The method of claim 13, wherein the differential core pressure P.sub.core is greater than or equal to 0.01 psig and less than or equal to 2 psig.

20. The method of claim 13, wherein the draw tension is greater than or equal to 50 g and less than or equal to 600 g.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0010] The accompanying drawings are included to provide a further understanding, and are incorporated 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.

[0011] FIGS. 1A and 1B schematically depict cross-sectional views of exemplary hollow-core optical fibers.

[0012] FIGS. 2A and 2B schematically depict cross-sectional views of exemplary hollow-core preforms for drawing the hollow-core optical fibers of FIG. 1A and FIG. 1B, respectively.

[0013] FIG. 3 schematically depicts an exemplary drawing system.

[0014] FIG. 4 schematically illustrates an implementation of a finite-analytic solution of evolution of preform outer tube inner and outer radii.

[0015] FIGS. 5A and 5B show the evolution of perform outer and inner diameters as a function of axial draw velocity in the neckdown region with different draw parameters.

[0016] FIG. 6 is a plot of fiber dimension sensitivity as a function of preform outer tube outer diameter.

[0017] FIG. 7 is a plot of fiber dimension sensitivity multiplied by the square of fiber outer cladding thickness as a function of draw stress.

[0018] FIG. 8 is a plot of fiber dimension sensitivity as a function of a grouping parameter .

[0019] FIG. 9 is a plot of draw tension needed for maintaining fiber dimension sensitivity as a function of fiber outer cladding outer diameter.

[0020] FIG. 10 is a plot of draw tension needed for maintaining fiber dimension sensitivity as a function of fiber yield.

DETAILED DESCRIPTION

[0021] The present disclosure is provided as an enabling teaching and can be understood more 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.

[0022] 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.

[0023] Directional terms as used hereinfor example up, down, right, left, front, back, top, bottomare made only with reference to the figures as drawn and are not intended to imply absolute orientation.

[0024] 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.

[0025] As used herein, the terms upstream and downstream refer to the relative positioning 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.

[0026] 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.

[0027] As used herein, the singular forms a, an and the include plural referents in addition 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.

[0028] 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

[0029] FIG. 1A schematically illustrates an example of a hollow-core optical fiber 100. The hollow-core optical fiber 100 may include an outer cladding 110. The outer cladding 110 may include an inner surface 111 defining an interior cavity 115 and an inner radius r.sub.f of the outer cladding 110, and an outer surface 112 defining an outer radius R.sub.f of the outer cladding 110. 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. In some embodiments, the cladding elements of the hollow-core optical fiber 100 may 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. In some embodiments, the hollow-core optical fiber 100 may not include nested capillaries 130, such as shown in FIG. 1B. The cladding elements of the hollow-core optical fiber 100, e.g., the capillaries 120 and/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-core preform 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 include an inner surface 211 defining an interior cavity 215 and an inner radius r.sub.p of the outer tube 210, and an outer surface 212 defining an outer radius R.sub.p of the outer tube 210. 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. In some embodiments, such as shown in FIG. 2A, the hollow-core preform 200 may also 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. In some embodiments, the hollow-core preform 200 may not include nested tubes 230, such as shown in FIG. 2B. The inner tubes 220 may surround and define a hollow section 240 that may be the central 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

[0031] FIG. 3 schematically depicts an example of a drawing system 300 that may be utilized to produce the hollow-core optical fiber 100 from the hollow-core preform 200.

[0032] In some embodiments, the drawing system 300 may include a draw furnace 308 configured 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 the 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 cmincluding all sub-ranges or values therebetween. For example, in some embodiments, the axial length of the hot zone may be 3 cm and 50 cm, 3 cm and 40 cm, 3 cm and 30 cm, 3 cm and 20 cm, 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.

[0033] In some embodiments, the drawing system 300 may further include a pressure control system 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.

[0034] In some embodiments, the drawing system 300 may further include a cooling chamber 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.

[0035] In some embodiments, the drawing system 300 may further include a tension assembly 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.

Processing Preforms of Various Sizes

(a) Finite Analytical Solution of Evolution of Preform Dimensions During Drawing

[0036] 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.

[0037] The evolution of the outer radius, R, and the inner radius, r, of the outer tube in the neckdown region is given by the following relation:

[00015]$\begin{array}{cc}\frac{d}{\mathrm{dz}}\left(r^2{V}_z\right)=\frac{d}{\mathrm{dz}}\left(R^2{V}_z\right)=\frac{P_{\mathrm{core}}{r}^2{R}^2-\mathrm{rR}\left(r+R\right)}{\left(R^2-r^2\right)}& \left[1\right]\end{array}$

where z is the axial distance in the neckdown region, V.sub.z is the axial velocity, P.sub.core is the differential core pressure, is the surface energy of the glass material forming the outer tube (e.g., 300 dynes/cm for silica glass), and is the glass viscosity. The surface energy can be measured 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 P.sub.core, which may also be referred to as the gauge pressure P.sub.core, 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.

[0038] The draw tension under which the hollow-core optical fiber may be drawn from the hollow-core preform is given as:

[00016]$\begin{array}{cc}T=3\frac{d\left(V_Z\right)}{\mathrm{dz}}\left(R^2-r^2\right)& \left[2\right]\end{array}$

[0039] Using a Corrocco type transformation and using Equation [2] to transform Equation Eq. [1] with axial velocity as the independent variable, the following is obtained:

[00017]$\begin{array}{cc}\frac{d}{{\mathrm{dV}}_z}\left(r\right)=\frac{3\left(P_{\mathrm{core}}{\mathrm{rR}}^2-R\left(R+r\right)\right)}{2{\mathrm{TV}}_z}-\frac{r}{2V_z}& \left[3a\right]\end{array}$$\begin{array}{cc}\frac{d}{{\mathrm{dV}}_z}\left(R\right)=\frac{3\left(P_{\mathrm{core}}{\mathrm{Rr}}^2-r\left(R+r\right)\right)}{2{\mathrm{TV}}_z}-\frac{R}{2V_z}& \left[3b\right]\end{array}$

[0040] To capture the evolution of the outer radius R and the inner radius r of the outer tube 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:

[00018]$\begin{array}{cc}{r}_{j+1}=\left(\frac{3R_j^2}{T+3R_j-3P_{\mathrm{core}}{R}_j^2}\right)+\left(r_j-\frac{3R_j^2}{T+3R_j-3P_{\mathrm{core}}{R}_j^2}\right){\left(\frac{V_{z,j+1}}{V_{z,j}}\right)}^{-\left(+3R_j-3P_{\mathrm{core}}{R}_j^2\right)/2T}& \left[4a\right]\end{array}$$\begin{array}{cc}{R}_{j+1}=\left(\frac{3r_j^2}{T+3r_j-3P_{\mathrm{core}}{r}_j^2}\right)+\left(R_j-\frac{3r_j^2}{T+3r_j-3P_{\mathrm{core}}{r}_j^2}\right){\left(\frac{V_{z,j+1}}{V_{z,j}}\right)}^{-\left(+3r_j-3P_{\mathrm{core}}{r}_j^2\right)/2T}& \left[4b\right]\end{array}$

which can be implemented with the mass balance equation as:

[00019]$\begin{array}{cc}{V}_{z,j+1}\left(R_{j+1}^2-r_{j+1}^2\right)=V_{z,j}\left(R_j^2-r_j^2\right)& \left[5\right]\end{array}$

(i) Exemplary Implementations of the Finite-Analytic Solution

[0041] The finite-analytic solution was implemented for different preform geometries that resulted in the same microstructure for the hollow-core optical fiber, such as the same inner diameter of the outer cladding of the hollow-core fiber (ID.sub.Fiber=2r.sub.f) of about 79.7 m, and the same outer diameter of the outer cladding of the hollow-core optical fiber (OD.sub.fiber=2R.sub.f) of about 249 m. However, it should be noted that the present disclosure is not limited to these specific fiber target dimensions (i.e., inner diameter of 79.7 m and outer diameter of 249 m), which are used for non-limiting illustrative purposes. The present disclosure may be implemented 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 that may be greater than or equal to (i.e., ) 45 m and less than or equal to (i.e., ) 145 mincluding 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-core optical fiber that may be greater than or equal to (i.e., ) 150 m and less than or equal to (i.e., ) 300 mincluding all sub-ranges or values therebetween.

[0042] Table 1 below shows that different combinations of pressure, draw tension, and preform 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 (OD.sub.preform=2R.sub.p) between 17 mm and 50 mm and the various inner diameters of the outer tube of the hollow-core preform (ID.sub.Preform=2r.sub.p) between 5 mm and 9 mm result in substantially the same microstructures of the hollow-core optical fiber, with the fiber draw speeds ranging between 1 m/s and 10 m/s.

TABLE-US-00001 TABLE 1 Fiber Preform Preform Fiber Fiber Differential Preform Fiber Draw OD, ID, OD, ID, Draw Core Feed Draw Speed, 2 R.sub.p 2 r.sub.p 2 R.sub.f 2 r.sub.f Tension, Pressure, Rate, V.sub.p Rate, V.sub.f V.sub.f/60000 Ex (mm) (mm) (um) (um) (g) P.sub.core (psig) (mm/min) (mm/min) (m/sec) 1 17.25 5 248.5 79.72 100 0.014 12.5 60000 1.00 2 17.25 5 249.4 79.67 150 0.032 12.5 60000 1.00 3 17.25 5 249.85 79.64 200 0.05 12.5 60000 1.00 4 17.25 5 250.12 79.71 250 0.069 12.5 60000 1.00 5 17.25 5 250.32 79.69 300 0.087 12.5 60000 1.00 6 25.875 7 246.96 79.73 100 0.013 12.5 136858.2 2.28 7 25.875 7 248.625 79.625 150 0.027 12.5 136857.4 2.28 8 25.875 7 248.99 79.81 200 0.04 12.5 136857 2.28 9 25.875 7 249.3775 79.74 250 0.056 12.5 136856.8 2.28 10 25.875 7 249.63 79.69 300 0.07 12.5 136856.6 2.28 11 34.6 8 246.99 79.72 100 0.018 12.5 247134.8 4.12 12 34.6 8 248.719 79.72 150 0.0335 12.5 247132.8 4.12 13 34.6 8 249.6 79.89 200 0.049 12.5 247131.8 4.12 14 34.6 8 250.08 79.77 250 0.064 12.5 247130.2 4.12 15 34.6 8 250.04 79.688 300 0.079 12.5 247130.8 4.12 16 49.6 9 246.42 79.63 100 0.0157 12.5 512464.3 8.54 17 49.6 9 248.74 79.82 150 0.0287 12.5 512458.3 8.54 18 49.6 9 249.88 79.78 200 0.0415 12.5 512455.3 8.54 19 49.6 9 250.58 79.77 250 0.0543 12.5 512453.4 8.54 20 49.6 9 251.03 79.706 300 0.067 12.5 512452.2 8.54

[0043] FIGS. 5A and 5B show the evolution of the outer diameter (OD) and the inner diameter (ID) of the outer tube of the hollow-core preform as a function of the axial draw velocity in the neckdown region during the drawing. The outer tubes of the hollow-core preforms in FIGS. 5A and 5B have different outer and inner diameters (OD/ID) ((A) 17.25 mm/5 mm and (B) 49.6 mm/9 mm), but yield identical outer cladding dimensions (OD/ID) of the hollow-core optical fibers drawn (250 m/79.6 m). Both hollow-core optical fibers are drawn with the same draw tension of 200 g. The hollow-core preforms are fed at the same preform feed rate of 12.5 mm/min, and the hollow-core optical fibers are drawn at different fiber draw rates of (A) 60,000 mm/min and (B) 512,455 mm/min.

[0044] Table 2 below shows the sensitivity of the ratio of the inner radius of the outer cladding of the hollow-core optical fiber to the inner radius of the outer tube of the hollow-core preform (r.sub.f/r.sub.p) to the ratio of the preform feed rate and the fiber draw rate (V.sub.f/V.sub.p), as well as the sensitivity of the ratio of the outer radius of the outer cladding of the hollow-core optical fiber to the outer radius of the outer tube of the hollow-core preform (R.sub.f/R.sub.p) to the ratio of the preform feed rate and the fiber draw rate (V.sub.f/V.sub.p).

TABLE-US-00002 TABLE 2 Ex V.sub.f/V.sub.p r.sub.f/r.sub.p R.sub.f/R.sub.p ln(V.sub.f/V.sub.p) ln(r.sub.f/r.sub.p) ln(R.sub.f/R.sub.p) m = ln(r.sub.f/r.sub.p)/ln(V.sub.f/V.sub.p) n = ln(R.sub.f/R.sub.p)/ln(V.sub.f/V.sub.p) 1 4800.0 0.0159 0.0144 8.476 4.139 4.240 0.488 0.500 2 4800.0 0.0159 0.0145 8.476 4.139 4.237 0.488 0.500 3 4800.0 0.0159 0.0145 8.476 4.140 4.235 0.488 0.500 4 4800.0 0.0159 0.0145 8.476 4.139 4.234 0.488 0.499 5 4800.0 0.0159 0.0145 8.476 4.139 4.233 0.488 0.499 6 10948.7 0.0114 0.0095 9.301 4.475 4.652 0.481 0.500 7 10948.6 0.0114 0.0096 9.301 4.476 4.645 0.481 0.499 8 10948.6 0.0114 0.0096 9.301 4.474 4.644 0.481 0.499 9 10948.5 0.0114 0.0096 9.301 4.475 4.642 0.481 0.499 10 10948.5 0.0114 0.0096 9.301 4.476 4.641 0.481 0.499 11 19770.8 0.0100 0.0071 9.892 4.609 4.942 0.466 0.500 12 19770.6 0.0100 0.0072 9.892 4.609 4.935 0.466 0.499 13 19770.5 0.0100 0.0072 9.892 4.607 4.932 0.466 0.499 14 19770.4 0.0100 0.0072 9.892 4.608 4.930 0.466 0.498 15 19770.5 0.0100 0.0072 9.892 4.609 4.930 0.466 0.498 16 40997.1 0.0088 0.0050 10.621 4.728 5.305 0.445 0.499 17 40996.7 0.0089 0.0050 10.621 4.725 5.295 0.445 0.499 18 40996.4 0.0089 0.0050 10.621 4.726 5.291 0.445 0.498 19 40996.3 0.0089 0.0051 10.621 4.726 5.288 0.445 0.498 20 40996.2 0.0089 0.0051 10.621 4.727 5.286 0.445 0.498

[0045] The inventors have recognized that the inner radius of the outer cladding of the hollow-core optical fiber drawn, r.sub.f, can be more sensitive to select drawing parameters, e.g., the preform dimensions (e.g., increased preform inner radius r.sub.p and/or outer radius R.sub.p) and/or the fiber draw rate V.sub.f, than the outer radius of the outer cladding of the hollow-core optical fiber drawn, R.sub.f, as suggested by the greater variation in value m=ln(r.sub.f/r.sub.p)/ln(V.sub.f/V.sub.p) than in value n=ln(R.sub.f/R.sub.p)/ln(V.sub.f/V.sub.p) from example 1 to example 20. Accordingly, when preform size and/or fiber draw rate may be increased to scale up production, the present disclosure provides the drawing parameters, such as the preform dimensions (e.g., preform inner and outer radii r.sub.p and R.sub.p), fiber draw rate/speed, draw tension, core pressure, etc., and solutions (e.g., finite analytical solution, as well as approximate solution discussed below) for selecting these drawing parameters so that target microstructure dimensions of the fiber (e.g., fiber inner and outer radii r.sub.f and R.sub.f, especially the inner radius r.sub.f) can be achieved consistently, as shown by examples 1-20.

(b) Approximate Solution of Preform Outer Tube Dimensions

[0046] Based on the example shown in Table 1, the following relations can be approximated for the differential core pressure P.sub.core as a function of draw tension in grams:

[00020]$\begin{array}{cc}{P}_{\mathrm{core}}\left(\mathrm{psig}\right)1.87710^{-5}{}^{1.46}& \left[6\right]\end{array}$

[0047] Further, the following relations can be approximated for the inner radius r.sub.p and the outer radius R.sub.p of the outer tube of the hollow-core preform:

[00021]$\begin{array}{cc}{r}_p\frac{r_f}{{\left(V_f/V_p\right)}^{-\left(T+3R_{*}-3P_{\mathrm{core}}{R}_{*}^2\right)/2T}}& \left[7a\right]\end{array}$$\begin{array}{cc}{R}_p\frac{R_f}{{\left(V_f/V_p\right)}^{-\left(T+3r_{*}-3P_{\mathrm{core}}{r}_{*}^2\right)/2T}}& \left[7b\right]\end{array}$

where r.sub.f and R.sub.f are the inner and outer radii, respectively, of the outer cladding of the hollow-core optical fiber, V.sub.p is the hollow-core preform feed rate, V.sub.f is the hollow-core fiber draw rate, T is the draw tension in dynes and T=*981, is the surface energy of the glass material forming the outer tube of the hollow-core preform (e.g., 300 dynes/cm for silica glass), and r* and R* are given as:

[00022]$\begin{array}{cc}{r}_{*}5\sqrt{r_p{r}_f}& \left[8a\right]\end{array}$$\begin{array}{cc}{R}_{*}5\sqrt{R_p{R}_f}& \left[8b\right]\end{array}$

[0048] Based on the approximate solutions above, the inventors have found that when the differential core pressure P.sub.core satisfies the following relation:

[00023]$\begin{array}{cc}0\text{.8}P*<P_{\mathrm{core}}<1\text{.2}P*& \left[9\right]\end{array}$

where P*=1.87710.sup.5.sup.1.46, consistent target inner radius r.sub.f and consistent target outer radius R.sub.f of the outer cladding of the hollow-core optical fiber can be achieved with preforms having outer tuber inner radius r.sub.p and outer tube outer radius R.sub.p that satisfy the following relations:

[00024]$\begin{array}{cc}0.9r_p^{*}<r_p<1.1r_p^{*}& \left[10a\right]\end{array}$$\begin{array}{cc}0.95R_p^{*}<R_p<1.05R_p^{*}& \left[10b\right]\end{array}$$\begin{array}{cc}{r}_p^{*}=\frac{r_f}{{\left(V_f/V_p\right)}^{-\left(T+3R_{*}-3P_{\mathrm{core}}{R}_{*}^2\right)/2T}}& \left[11a\right]\end{array}$$\begin{array}{cc}{R}_p^{*}=\frac{R_f}{{\left(V_f/V_p\right)}^{-\left(T+3r_{*}-3P_{\mathrm{core}}{r}_{*}^2\right)/2T}}& \left[11b\right]\end{array}$$\mathrm{and}$$\begin{array}{cc}{r}_{*}=5\sqrt{r_p^{*}{r}_f}& \left[12a\right]\end{array}$$\begin{array}{cc}{R}_{*}=5\sqrt{R_p^{*}{R}_f}& \left[12b\right]\end{array}$

Improving Process Stability

[0049] As discussed above, scale-up manufacturing of the hollow-core optical fiber may be achieved by, for example, increasing the size of the hollow-core preform while still achieving the same or similar target microstructures of the hollow-core optical fiber. To further limiting any variation in the dimensions of the hollow-core optical fiber that may be affected due to change in process conditions, the process parameters may be selected such that variations in fiber dimensions due to process induced perturbations, e.g., inherent fluctuations in the differential core pressure P.sub.core, may be limited such that longer length fibers with target dimensions may be achieved. In some embodiments, tight control in target fiber dimensions may be achieved through selecting appropriate dimensions of the incoming preform to be used for drawing, selecting appropriate dimensions of the fiber to be drawn, and/or selecting appropriate drawing conditions, such as draw tension, draw stress, preform feed rate, fiber draw rate, etc.

[0050] For a given incoming preform, the law of conservation of mass of glass fed through the draw furnace dictates the following:

[00025]$\begin{array}{cc}\left[O{D}_{\mathrm{preform}}^2-I{D}_{\mathrm{preform}}^2\right]V_p=\left[O{D}_{\mathrm{fiber}}^2-I{D}_{\mathrm{fiber}}^2\right]V_f& \left[13\right]\end{array}$

where OD.sub.preform=2R.sub.p is the outer diameter of the outer tube of the hollow-core preform, ID.sub.preform=2r.sub.p is the inner diameter of the outer tube of the hollow-core preform, V.sub.p is the preform feed rate, OD.sub.fiber=2R.sub.f is the outer diameter of the outer cladding of the hollow-core optical fiber, ID.sub.fiber=2r.sub.f is the inner diameter of the outer cladding of the hollow-core optical fiber, and V.sub.f is the fiber draw rate.

[0051] The inventors have also derived the following relation:

[00026]$\begin{array}{cc}I{D}_{\mathrm{fiber}}=\mathrm{sqrt}\left[\frac{\left(O{D}_{\mathrm{preform}}^2-I{D}_{\mathrm{preform}}^2\right)\left(V_p/V_f\right)}{\exp \left\{\ln \frac{O{D}_{\mathrm{preform}}^2}{I{D}_{\mathrm{preform}}^2}-\frac{3}{4}{P}_{\mathrm{core}}\frac{3}{4}{P}_{\mathrm{core}}\left(O{D}_{\mathrm{preform}}^2-I{D}_{\mathrm{preform}}^2\right)\left(1-\frac{V_p}{V_f}\right)\frac{1}{}\right\}-1}\right]& \left[14\right]\end{array}$

where P.sub.core is the differential core pressure, which also correspond to the centerline pressure applied to the interior cavity of the outer tube of the hollow-core preform, and is the draw tension.
(a) Process Scale-Up with Constant Draw Ratio to Draw Fibers with Same ID.sub.fiber and Same OD.sub.fiber from Varying ID.sub.preform and Varying OD.sub.preform

[0052] Through processing modeling, fiber dimension sensitivity to exemplary process parameters is examined and results are shown in Tables 3A and 3B below. In each modeled process/run, same dimensions of the outer cladding of the hollow-core optical fiber are targeted, i.e., same inner diameter of the outer cladding of the hollow-core optical fiber, ID.sub.fiber=90.0 m, and same outer diameter of the outer cladding of the hollow-core optical fiber, OD.sub.fiber=175.4 m. Hollow-core preforms of different sizes are modeled for different yields. For each preform, two different draw tensions, i.e., 150 g and 250 g, are considered, which correspond to two different draw stress levels, i.e., draw stress of 82.66 MPa and draw stress of 137.77 MPa, respectively, which are calculated based on the following:

[00027]$\begin{array}{cc}\mathrm{Draw}\mathrm{Stress},x=\frac{4}{}\frac{}{\left(O{D}_{\mathrm{fiber}}^2-I{D}_{\mathrm{fiber}}^2\right)}& \left[15\right]\end{array}$

where is the draw tension applied to the fiber, OD.sub.fiber is the outer diameter of the outer cladding of the hollow-core optical fiber drawn, and ID.sub.fiber is the inner diameter of the outer cladding of the hollow-core optical fiber drawn. The data associated with the draw tension of 150 g are shown Table 3A, and the data associated with the draw tension of 250 g are shown in Table 3B.

[0053] The preform feed rate V.sub.p is varied at multiples of 5 mm/min, and the fiber draw rate V.sub.f is varied at multiples of 30,000 mm/min; however, the draw ratio, i.e., the ratio of the preform feed rate V.sub.p to the fiber draw rate V.sub.f (V.sub.p:V.sub.f), is kept constant at 1:6,000. It is noted that other process conditions, e.g., differential core pressure P.sub.core, are varied such that the same target fiber dimensions ID.sub.fiber and OD.sub.fiber are achieved from the various incoming preforms.

TABLE-US-00003 TABLE 3A Label Preform 1 Preform 2 Preform 3 Fiber OD.sub.preform (mm) 12.5 17.5 25.0 / ID.sub.preform (mm) 4.5 5.0 5.0 / OD.sub.fiber (m) / / / 175.4 ID.sub.fiber (m) / / / 90.0 Yield (in km per m) 6.00 12.41 26.47 / Draw Tension (g) / / / 150 Draw Stress (MPa) / / / 82.66 Differential core pressure 0.47 0.19 0.09 / P.sub.core (psig) ID.sub.fiber Sensitivity, 0.931 1.923 3.985 / ID.sub.fiber (m)

TABLE-US-00004 TABLE 3B Label Preform 1 Preform 2 Preform 3 Fiber OD.sub.preform (mm) 12.5 17.5 25.0 / ID.sub.preform (mm) 4.5 5.0 5.0 / OD.sub.fiber (m) / / / 175.4 ID.sub.fiber (m) / / / 90.0 Yield (in km per m) 6.00 12.41 26.47 / Draw Tension (g) / / / 250 Draw Stress (MPa) / / / 137.77 Differential core pressure 0.79 0.32 0.16 / P.sub.core (psig) ID.sub.fiber Sensitivity, 0.557 1.147 2.365 / ID.sub.fiber (m)

[0054] The fiber dimension sensitivity is evaluated in terms of the change in the inner diameter of the outer cladding of the hollow-core optical fiber (from 90.0 m), ID.sub.fiber, as the differential core pressure P.sub.core undergoes a 0.01 psig fluctuation, more specifically, an increase of 0.01 psig, using equation [14] provided above. It is noted that by maintaining the same feed to draw ratio (V.sub.p:V.sub.f), for a given preform, the same fiber dimension sensitivity ID.sub.fiber results.

[0055] As shown in Tables 3A and 3B, respectively, when the same draw tension is applied, the fiber dimension sensitivity increases as the preform size increases for higher yields. Comparing the results in Tables 3A and 3B, for the same preform, fiber dimension sensitivity may be reduced by increasing the draw tension. Thus, as the preform size decreases and/or the draw stress increases such as when greater draw tension is applied, a lesser degree of variation in the inner diameter of the outer cladding of the hollow-core optical fiber (or fiber dimension sensitivity ID.sub.fiber) may be achieved as the differential core pressure P.sub.core undergoes the same fluctuation.

(b) Process Scale-Up with Varied Draw Ratios to Draw Fibers with Same ID.sub.fiber and Varying OD.sub.fiber from Same ID.sub.preform and Varying OD.sub.preform

[0056] Additional exemplary fiber draw processes/runs are modeled, where the same inner diameter of the outer cladding of the hollow-core optical fiber, i.e., ID.sub.fiber=90.0 m, is targeted while the outer diameter of the outer cladding of the hollow-core optical fiber OD.sub.fiber is varied. The inner diameter of the outer tube of the hollow-core preform ID.sub.preform is kept at about 5.0 mm while the outer diameter of the outer tube of the hollow-core preform OD.sub.preform is varied. The differential core pressure P.sub.core needed to achieve the ID.sub.fiber of 90.0 m from different preform sizes is obtained based on equation [14] above and also shown in Table 4 below. The following process conditions are maintained for different runs: preform feed speed V.sub.p=5 mm/min, fiber draw speed V.sub.f=30000 mm/min, and operating draw tension of 150 g.

TABLE-US-00005 TABLE 4 PREFORM OD PREFORM ID Differential Core [mm] [mm] Pressure P.sub.core [psig] 12.5 4.5 0.36 17.5 5.0 0.19 25.0 5.0 0.09 50.0 5.0 0.02 75.0 5.0 0.01 100.0 5.0 0.01

[0057] Fiber dimension sensitivity, more specifically, deviation in the inner diameter of the outer cladding of the hollow-core optical fiber (from 90.0 m), ID.sub.fiber, is modeled when the core pressure is increased by 0.01 psig, i.e., P.sub.core=0.01 psig. FIG. 6 is a plot of the sensitivity of the inner diameter of the outer cladding of the hollow-core optical fiber (Fiber ID sensitivity, [m]) as a function of the outer diameter of the outer tube of the preform (Preform OD, [mm]).

[0058] As shown in FIG. 6, the fiber dimension sensitivity, ID.sub.fiber, increases as the outer diameter OD.sub.preform of the outer tube of the hollow-core preform increases. As shown in Table 4, with increasing thickness of the outer tube of the hollow-core preform, the differential core pressure P.sub.core needed to achieve the same target inner diameter of the outer cladding of the hollow-core optical fiber ID.sub.fiber of 90.0 m is decreased. Thus, the effects of the fluctuation in core pressure (P.sub.core=0.01 psig) becomes more significant such that it can induce much greater change in the inner diameter of the outer cladding of the hollow-core optical fiber, ID.sub.fiber, as highlighted in FIG. 6.

(c) Dependence of Fiber Dimension SensitivityThickness Squared on Draw Stress

[0059] Additional exemplary fiber draw processes/runs are modeled to analyze the relationship between the fiber dimension sensitivity and the draw stress. The following are implemented for these draw processes/runs: the same inner diameter of the outer cladding of the hollow-core optical fiber, i.e., ID.sub.fiber=90.0 m, is targeted while the outer diameter of the outer cladding of the hollow-core optical fiber is varied; preforms of three different sizes are considered (OD.sub.preform and ID.sub.preform of 12.5 mm and 4.5 mm, 17.5 mm and 5.0 mm, and 25.0 and 5 mm, respectively); the fiber draw rate V.sub.f is varied from 30,000 mm/min to 600,000 mm/min while the preform feed rate V.sub.p is kept constant (V.sub.p=5 mm/min); various draw tension levels (150 g, 250 g, and 350 g) are considered so that a wide range of draw stress levels are examined. The differential core pressure P.sub.core needed to achieve the target ID.sub.fiber of 90.0 m is calculated based on equation above. The modeling analysis of these draw processes/runs is reflected in FIG. 7, which plots the fiber dimension sensitivity ID.sub.fiber (i.e., variation in the inner diameter of the outer cladding of the hollow-core fiber due to differential core pressure fluctuation P.sub.core of 0.1 psig) multiplied by the square of the thickness of the outer cladding of the hollow-core optical fiber (i.e., (OD.sub.fiberID.sub.fiber).sup.2) (Fiber ID sensitivityThickness.sup.2, [m.sup.3]) as a function of draw stress (Draw Stress, [MPa]).

[0060] Based on the modeling analysis shown in FIG. 7, a relation between the fiber dimensional term (Fiber ID sensitivityFiber Thickness.sup.2) and the operating draw stress can be derived as follows for drawing a hollow-core optical fiber of which the inner diameter of the outer cladding is 90.0 m:

[00028]$\begin{array}{cc}y=A\left(3.20810^5\right)x^{-1.18}& \left[16\right]\end{array}$

where x is the operating draw stress that is estimated using equation [15], y is the fiber dimensional term Fiber ID sensitivityFiber Thickness.sup.2, i.e.,

[00029]$\begin{array}{cc}y=I{D}_{\mathrm{fiber}}\mathrm{Fiber}{\mathrm{Thickness}}^2& \left[17\right]\end{array}$

where Fiber Thickness refers to the thickness of the outer cladding of the hollow-core optical fiber as defined by the difference between the outer radius R.sub.f= OD.sub.fiber and the inner radius r.sub.f= ID.sub.fiber of the outer cladding, and thus, Fiber Thickness=R.sub.fr.sub.f= OD.sub.fiber ID.sub.fiber, and A is a scaling factor that correlates with the cross-sectional area of incoming preform scaled by the cross-sectional area of an outer tube having an outer diameter OD.sub.preform of 12.5 mm and an inner diameter ID.sub.preform of 4.5 mm, and thus,

[00030]$\begin{array}{cc}A=\frac{O{D}_{\mathrm{preform}}^2-I{D}_{\mathrm{preform}}^2}{12.5^2-4.5^2}=\frac{O{D}_{\mathrm{preform}}^2-I{D}_{\mathrm{preform}}^2}{136}& \left[18\right]\end{array}$

[0061] Table 5 below provides the scaling factor A for various preform sizes.

TABLE-US-00006 TABLE 5 OD.sub.preform [mm] ID.sub.preform [mm] SCALING FACTOR, A 12.5 4.5 1.000 17.5 5.0 2.068 25.0 5.0 4.412 50.0 5.0 18.199 75.0 5.0 41.176 100.0 5.0 73.346

[0062] Combining equations [16], [17], and [18], the following is obtained:

[00031]$\begin{array}{cc}I{D}_{\mathrm{fiber}}=\frac{O{D}_{\mathrm{preform}}^2-I{D}_{\mathrm{preform}}^2}{34{\left(O{D}_{\mathrm{fiber}}-I{D}_{\mathrm{fiber}}\right)}^2}\left(3.20810^5\right)x^{-1.18}& \left[19\right]\end{array}$

[0063] Using equations [16]-[19], the fiber dimension sensitivity, more specifically, ID.sub.fiber, to the core pressure fluctuation of P.sub.core=0.01 psig can be obtained for any operating draw stress when using various preforms for drawing a hollow-core optical fiber where the targeted inner diameter of the outer cladding of the hollow-core optical fiber is 90.0 m.

[0064] Referring back to the modeling analysis shown in FIG. 7, when different fibers are drawn from the same hollow-core preform, it is observed that for the same operating draw stress, a thicker outer cladding of the hollow-core optical fiber may lead to a lower fiber dimension sensitivity ID.sub.fiber as compared to a thinner outer cladding. Thus, it may be desirable to draw fibers having thicker outer claddings to reduce fiber dimension sensitivity ID.sub.fiber. However, drawing fibers with thicker outer claddings may require greater draw tension, which may pose other challenges during the drawing process when the draw tension becomes too high. Thus, appropriate draw tension, e.g., greater than or equal to (i.e., ) 50 g and less than or equal to (i.e., ) 600 g, may be selected for optimal drawing conditions to minimize the fiber dimension sensitivity ID.sub.fiber.

[0065] Additionally, as also shown in FIG. 7, when different preforms are used for scaling up, fiber dimension sensitivity ID.sub.fiber may increase as the thickness of the outer tube of the preform increases, especially at relatively small draw stress levels. Therefore, when drawing from a preform having a relatively thick outer tube for longer fiber production, relatively high draw stress levels may be implemented to maintain a tight control on the target fiber dimensions, such as the target inner diameter ID.sub.fiber of the outer cladding of the hollow-core optical fiber drawn. When drawing from a preform having a thinner outer tube, smaller draw stress levels may be implemented while still maintaining a tight control over the target fiber dimensions.

(d) Dependence of Fiber Dimension Sensitivity on Grouping Parameter

[0066] Further exemplary fiber draw processes/runs are modeled to analyze the fiber dimension sensitivity. The following are implemented for these draw processes/runs: three different inner diameters of the outer cladding of the hollow-core optical fiber, i.e., ID.sub.fiber=45.0 m, ID.sub.fiber=90.0 m, and ID.sub.fiber=135.0 m, are targeted while the outer diameter of the outer cladding of the hollow-core optical fiber OD.sub.fiber is varied; substantially the same inner diameter of the outer tube of the hollow-core preform ID.sub.preform of about 5.0 mm is considered while the outer diameter of the outer tube of the hollow-core preform OD.sub.preform is varied; the fiber draw rate V.sub.f is varied while a constant preform feed rate V.sub.p of 5 mm/min is utilized; and the draw tension is varied so that a wide range of draw stress levels are examined; the differential core pressure P.sub.core and draw stress are calculated using equation and equation [15], respectively.

[0067] The modeling analysis of these draw processes/runs is reflected in FIG. 8, which plots the fiber dimension sensitivity ID.sub.fiber, more specifically, variation in the inner diameter of the outer cladding of the hollow-core optical fiber in m, as a function of a grouping parameter in MPa.sup.1 um.sup.2, which is defined as:

[00032]$\begin{array}{cc}=A{x}^{-1.18}\mathrm{Fiber}{\mathrm{Thickness}}^{-2}& \left[20\right]\end{array}$

where x is the draw stress as determined based on equation [15] above, and Fiber Thickness refers to the thickness of the outer cladding of the hollow-core optical fiber as defined by the difference between the outer radius R.sub.f= OD.sub.fiber and the inner radius r.sub.f= ID.sub.fiber of the outer cladding, and thus, Fiber Thickness=R.sub.fr.sub.f= OD.sub.fiber ID.sub.fiber, and A is the scaling factor as given in equation [18] above. Combining equations [15], [18], and [20], the following is obtained:

[00033]$\begin{array}{cc}=\frac{O{D}_{\mathrm{preform}}^2-I{D}_{\mathrm{preform}}^2}{136}{\left(\frac{4}{}\frac{}{\left(O{D}_{\mathrm{fiber}}^2-I{D}_{\mathrm{fiber}}^2\right)}\right)}^{-1.18}{\left(\frac{1}{2}O{D}_{\mathrm{fiber}}-\frac{1}{2}I{D}_{\mathrm{fiber}}\right)}^{-2}& \left[21\right]\end{array}$

[0068] Based on the modeling analysis shown in FIG. 8, for the same target fiber dimension, more specifically, the same target inner diameter ID.sub.fiber of the outer cladding of the hollow-core optical fiber, the fiber dimension sensitivity ID.sub.fiber may be linearly related to the grouping parameter . Further, a relation between the fiber dimension sensitivity ID.sub.fiber and the grouping parameter can be derived as follows for drawing hollow-core optical fibers where the inner diameter ID.sub.fiber of the outer cladding may be in the range of 45 m to 135 m:

[00034]$\begin{array}{cc}I{D}_{\mathrm{fiber}}=M& \left[22\right]\end{array}$

where M is a proportionality constant (in MPa um.sup.3) dependent on the target inner diameter ID.sub.fiber of the outer cladding of the hollow-core optical fiber drawn, and is given by the following:

[00035]$\begin{array}{cc}M=2277.778I{D}_{\mathrm{fiber}}+\left(1.19710^5\right)& \left[23\right]\end{array}$

[0069] Table 6 below provides the values of the proportionality constant M for select target inner diameters ID.sub.fiber of the outer cladding of the hollow-core optical fiber drawn. For drawing hollow-core optical fibers where the inner diameter ID.sub.fiber of the outer cladding may range from 45 m to 135 m, the proportionality constant M may be greater than or equal to (i.e., ) 2.010.sup.5 and less than or equal to (i.e., ) 4.510.sup.5including all sub-ranges or values therebetween. For example, in some embodiments, the proportionality constant M may be 2.24210.sup.5 and less than or equal to (i.e., ) 4.29210.sup.5. For example, in some embodiments, the proportionality constant M may be 2.010.sup.5 and 4.510.sup.5, 2.010.sup.5 and 4.010.sup.5, 2.010.sup.5 and 3.510.sup.5, 2.010.sup.5 and 3.010.sup.5, 2.010.sup.5 and 2.510.sup.5, 2.510.sup.5 and 4.510.sup.5, 2.510.sup.5 and 4.010.sup.5, 2.510.sup.5 and 3.510.sup.5, 2.510.sup.5 and 3.010.sup.5, 3.010.sup.5 and 4.510.sup.5, 3.010.sup.5 and 4.010.sup.5, 3.010.sup.5 and 3.510.sup.5, 3.510.sup.5 and 4.510.sup.5, 3.510.sup.5 and 4.010.sup.5, or 4.010.sup.5 and 4.510.sup.5. In some embodiments, the proportionality constant M may be greater than or equal to (i.e., ) 2.0, 2.2, 2.4, 2.6, 2.8, 3.0, 3.2, 3.4, 3.6, 3.8, 4.0, 4.2, 4.4, or greater. In some embodiments, the proportionality constant M may be less than or equal to (i.e., ) 4.5, 4.3, 4.1, 3.9, 3.7, 3.5, 3.3, 3.1, 2.9, 2.7, 2.5, 2.3, 2.1, or less.

TABLE-US-00007 TABLE 6 Target Fiber ID.sub.fiber [um] Proportionality Constant, M [MPa um.sup.3] 45.0 2.242 10.sup.5 90.0 3.208 10.sup.5 135.0 4.292 10.sup.5

[0070] Further, using the grouping parameter Q, the desired range of the fiber dimension sensitivity ID.sub.fiber may be quantitatively tracked. For example, for drawing hollow-core optical fibers with a target outer cladding inner diameter ID.sub.fiber of greater than or equal to (i.e., ) 45 m and less than or equal to (i.e., ) 135 m, to achieve a fiber dimension sensitivity ID.sub.fiber of less than or equal to (i.e., ) 5.0 m, the grouping parameter may be less than or equal to (i.e., ) 2.210.sup.5, 1.510.sup.5, 1.210.sup.5, or less, and to achieve a fiber dimension sensitivity ID.sub.fiber of less than or equal to (i.e., ) 2.0 m, the grouping parameter may be less than or equal to (i.e., ) 0.910.sup.5, 0.710.sup.5, 0.510.sup.5, or less. Table 7 below provides exemplary grouping parameter ranges for achieving desired levels of fiber dimension sensitivity ID.sub.fiber for select target inner diameter of the outer cladding of the hollow-core optical fiber that may be drawn using the processes described herein.

TABLE-US-00008 TABLE 7 Grouping parameter Grouping parameter Target Fiber range for achieving range for achieving ID.sub.fiber [um] ID.sub.fiber < 2 m 2 m < ID.sub.fiber < 5 m 45.0 0 < < 0.9 10.sup.5 0.9 10.sup.5 < < 2.2 10.sup.5 90.0 0 < < 0.7 10.sup.5 0.7 10.sup.5 < < 1.5 10.sup.5 135.0 0 < < 0.5 10.sup.5 0.5 10.sup.5 < < 1.2 10.sup.5

(e) Draw Tension for Maintaining Fiber Dimension Sensitivity ID.SUB.fiber

[0071] Further exemplary fiber draw processes/runs are modeled to analyze the draw tension needed for maintaining the same fiber dimension sensitivity ID.sub.fiber. The following are implemented for these draw processes/runs: the same inner diameter ID.sub.fiber of 10.sup.5 m of the outer cladding of the hollow-core optical fiber and the same fiber dimension sensitivity ID.sub.fiber of 5 m are targeted; different outer diameters OD.sub.fiber of the outer cladding of the hollow-core optical fiber, more specifically, OD.sub.fiber of 125 m, 140 m, 160 m, 180 m, 200 m, 225 m, and 260 m, are considered for different thicknesses of the outer cladding of the hollow-core optical fiber; the following outer diameter OD.sub.preforminner diameter ID.sub.preform combinations for the outer tube of the hollow-core preform are considered for different fiber yields: 12.5 mm4.5 mm, 17.5 mm5.0 mm, 25.0 mm5.0 mm, and 50.0 mm5.0 mm; the preform feed rate is kept at V.sub.p of 5 mm/min while the fiber draw rate V.sub.f is varied from 30,000 mm/min to 600,000 mm/min.

[0072] Using equations [21]-[23] above and ID.sub.fiber of 5 m and the various ID.sub.fiber, OD.sub.fiber, ID.sub.preform, and OD.sub.preform values as the input, the draw tension needed for maintaining the fiber dimension sensitivity ID.sub.fiber of 5 m can be calculated, and the results are plotted in FIGS. 9 and 10. Specifically, FIG. 9 plots the draw tension needed for maintaining the fiber dimension sensitivity ID.sub.fiber of 5 m as a function of the outer diameter OD.sub.fiber of the outer cladding of the hollow-core optical fiber drawn, and FIG. 10 plots the draw tension needed for maintaining the fiber dimension sensitivity ID.sub.fiber of 5 m as a function of the fiber yield from different preforms.

[0073] As shown, a greater draw tension may be needed to maintain the same level of fiber dimension sensitivity ID.sub.fiber for drawing a thinner outer cladding (or smaller outer diameter OD.sub.fiber of the outer cladding) of the hollow-core optical fiber. However, there may be an inherent upper limit to the draw tension that may be applied during the drawing process before the fiber may break. Thus, when drawing larger preforms to increase fiber yield, the draw tension range that may be implemented for maintaining the same fiber dimension sensitivity ID.sub.fiber may become narrower.

Operating Parameters

[0074] The various methods and relations described herein may be implemented with a wide range of operating parameters for scaling up the drawing of hollow-core optical fibers from hollow-core preforms of various sizes while maintaining a tight control over target microstructure dimensions of the hollow-core optical fibers drawn.

Draw Tension

[0075] In some embodiments, the draw tension under which the hollow-core optical fiber may 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, in some 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 g and 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, 400 g and 550 g, 400 g and 500 g, 400 g and 450 g, 450 g and 600 g, 450 g and 550 g, 450 g and 500 g, 500 g and 600 g, 500 g and 550 g, 550 g and 600 g, or 550 g and 600 g.

[0076] In some embodiments, the draw tension under which the hollow-core optical fiber may 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 under which the hollow-core optical fiber may be drawn from the hollow-core preform may be less than or equal to (i.e., ) 600 g, 580 g, 560 g, 540 g, 520 g, 500 g, 480 g, 460 g, 440 g, 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.

Draw Speed

[0077] 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 and less than or equal to (i.e., ) 20 m/sincluding 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

[0078] In some embodiments, the hollow-core preform may be fed into the draw furnace at a preform feed rate V.sub.p that may be greater than or equal to (i.e., ) 5 mm/min and less than or equal to (i.e., ) 100 mm/min-including all sub-ranges or values therebetween. For example, in some embodiments, the hollow-core preform may be fed into the draw furnace at a preform feed rate V.sub.p that may be 5 mm/min and 100 mm/min, 5 mm/min and 75 mm/min, 5 mm/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 100 mm/min, 50 mm/min and 75 mm/min, or 75 mm/min and 100 mm/min. In some embodiments, the hollow-core preform may be fed into the draw furnace at a preform feed rate V.sub.p that may be 5 mm/min, 10 mm/min, 15 mm/min, 20 mm/min, 25 mm/min, 30 mm/min, 35 mm/min, 40 mm/min, 45 mm/min, 50 mm/min, 55 mm/min, 60 mm/min, 65 mm/min, 70 mm/min, 75 mm/min, 80 mm/min, 85 mm/min, 90 mm/min, 95 mm/min, or greater. In some embodiments, the hollow-core preform may be fed into the draw furnace at a preform feed rate V.sub.p 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, 65 mm/min, <60 mm/min, 55 mm/min, 50 mm/min, 45 mm/min, 40 mm/min, 35 mm/min, 30 mm/min, 25 mm/min, 20 mm/min, 15 mm/min, 10 mm/min, or less.

Differential Core Pressure P.SUB.core

[0079] In some embodiments, the differential core pressure P.sub.core may be greater than or equal to (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 P.sub.core may be may 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.

[0080] In some embodiments, the differential core pressure P.sub.core may be greater than or equal to (i.e., ) 0.01 psig, 0.05 psig, 0.1 psig, 0.2 psig, 0.3 psig, 0.4 psig, 0.5 psig, 0.6 psig, 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, the differential core pressure P.sub.core 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, 0.9 psig, 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.

Preform Outer Tube Dimensions

[0081] In some embodiments, the inner diameter of the outer tube of the hollow-core preform (ID.sub.Preform=2r.sub.p) 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 (ID.sub.Preform=2r.sub.p) may be 4 mm and 20 mm, 4 mm and 16 mm, 4 mm and 12 mm, 4 mm and 8 mm, 8 mm and 20 mm, 8 mm and 16 mm, 8 mm and 12 mm, 12 mm and 20 mm, 12 mm and 16 mm, or 16 mm and 20 mm. In some embodiments, the inner diameter of the outer tube of the hollow-core preform (ID.sub.Preform=2r.sub.p) may be greater than or equal to (i.e., ) 4 mm, 5 mm, 6 mm, 7 mm, 8 mm, 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 the hollow-core preform (ID.sub.Preform=2r.sub.p) 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.

[0082] In some embodiments, the outer diameter of the outer tube of the hollow-core preform (OD.sub.preform=2R.sub.p) 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 some embodiments, the outer diameter of the outer tube of the hollow-core preform (OD.sub.preform=2R.sub.p) 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 of the outer tube of the hollow-core preform (OD.sub.preform=2R.sub.p) may be greater than or equal to (i.e., ) 15 mm, 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 some embodiments, the outer diameter of the outer tube of the hollow-core preform (OD.sub.preform=2R.sub.p) may be less than or equal to (i.e., ) 100 mm, 95 mm, 90 mm, 85 mm, 80 mm, 75 mm, 70 mm, 65 mm, 60 mm, 55 mm, 50 mm, 45 mm, 40 mm, 35 mm, 30 mm, 25 mm, 20 mm, or less.

Fiber Outer Cladding Dimensions

[0083] In some embodiments, the inner diameter of the outer cladding of the hollow-core optical fiber (ID.sub.fiber=2r.sub.f) may be greater than or equal to (i.e., ) 45 m and less than or equal to (i.e., ) 135 m-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 (ID.sub.fiber=2r.sub.f) may be 45 m and 135 m, 45 m and 115 m, 45 m and 95 m, 45 m and 75 m, 45 m and 55 m, 55 m and 135 m, 55 m and 115 m, 55 m and 95 m, 55 m and 75 m, 75 m and 135 m, 75 m and 115 m, 75 m and 95 m, 95 m and 135 m, 95 m and 115 m, or 115 m and 135 m. In some embodiments, the inner diameter of the outer cladding of the hollow-core optical fiber (ID.sub.fiber=2r.sub.f) may be greater than or equal to (i.e., ) 45 m, 50 mm, 55 mm, 60 mm, 65 mm, 70 mm, 75 mm, 80 mm, 85 mm, 90 mm, 95 mm, 100 mm, 105 mm, 110 mm, 115 mm, 120 mm, 125 mm, 130 m, or greater. In some embodiments, the inner diameter of the outer cladding of the hollow-core optical fiber (ID.sub.fiber=2r.sub.f) may be less than or equal to (i.e., ) 135 m, 130 m, 125 m, 120 m, 115 m, 110 m, 105 m, 100 m, 95 m, 90 m, 85 m, 80 m, 75 m, 70 m, 65 m, 60 m, 55 m, 50 m, or less.

[0084] In some embodiments, the outer diameter of the outer cladding of the hollow-core optical fiber (2R.sub.ocf) may be greater than or equal to (i.e., ) 150 m and less than or equal to (i.e., ) 300 m-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 (2R.sub.ocf) may be 150 m and 300 m, 150 m and 250 m, 150 m and 200 m, 200 m and 300 m, 200 m and 250 m, or 250 m and 300 m. In some embodiments, the outer diameter of the outer cladding of the hollow-core optical fiber (2R.sub.ocf) may be greater than or equal to (i.e., ) 150 m, 160 m, 170 m, 180 m, 190 m, 200 m, 210 m, 220 m, 230 m, 240 m, 250 m, 260 m, 270 m, 280 m, 290 m, or greater. In some embodiments, the outer diameter of the outer cladding of the hollow-core optical fiber (2R.sub.ocf) may be less than or equal to (i.e., ) 300 m, 290 m, 280 m, 270 m, 260 m, 250 m, 240 m, 230 m, 220 m, 210 m, 200 m, 190 m, 180 m, 170 m, 160 m, or less.

[0085] It will be apparent to those skilled in the art that various modifications to the preferred embodiments 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.