Hollow core optical fiber with a single nested capillary exhibiting improved confinement loss

Abstract

A hollow core optical fiber comprising 5 to 8 spaced cladding elements defining a hollow core region, each comprising (a) a first capillary and (b) a second capillary disposed within the first capillary. For each cladding element, (i) the second capillary is offset from the first capillary by an angle in the range of 20 to 120 degrees, and (ii) the ratio of the outer diameter of the second capillary to the outer diameter of the first capillary is in the range of 0.47 to 0.85. The hollow core optical fiber exhibits a confinement loss of less than 0.056 dB / km for electromagnetic radiation at 850 nm, less than 0.028 dB / km for electromagnetic radiation at 1310 nm, less than 0.204 dB / km for electromagnetic radiation at 1550 nm, and less than 0.016 dB / km for electromagnetic radiation at 2400 nm.

Description

Technical Field

[0001] This application claims the benefit of priority under 35 U.S.C. § 120 to U.S. Provisional Application No. 63 / 469,677, filed May 30, 2023, the content of which is relied upon herein and incorporated herein by reference in its entirety.

[0002] This disclosure relates to optical fibers, and more particularly, to optical fibers having an inner cladding of a nested hollow capillary to produce reduced confinement loss.

Background Art

[0003] An optical fiber is an optical waveguide that can transmit an optical signal over a long distance. "Light" in this background art section generally means electromagnetic radiation of a desired wavelength or wavelength range. Typically, data is encoded into an optical signal. An optical fiber includes a core and a cladding around the core. The optical signal is transmitted through the core and maintained within the core by different mechanisms. One such mechanism is based on internal reflection due to the refractive index difference between the core and the cladding. Another such mechanism is based on a photonic bandgap due to the periodic structure of the cladding. A further mechanism is an antiresonant mechanism based on an antiresonant effect in a thin glass layer of the cladding. Despite these mechanisms, the signal power of an optical signal decreases as the optical signal propagates along the optical fiber. The decrease in signal power is sometimes referred to as "signal loss" and is referred to as "attenuation" when quantified per unit distance. The greater the attenuation, the shorter the distance of data transmission, and thus, it may be necessary to incorporate signal amplifiers to overcome the attenuation and provide an optical signal at the output end that can decode the intended data. The causes of signal loss include absorption, scattering, mode leakage, and an imperfect cladding (referred to as confinement loss), as well as light leakage due to bending of the optical fiber (referred to as bending loss).

[0004] Various cladding design modifications have been seen as addressing the causes of signal loss, such as hollow-core optical fibers. Inducing light within a hollow-core optical fiber has many theoretical advantages, including lower losses due to absorption and scattering of the material. In the case of a hollow-core optical fiber, the core is filled with a gas (e.g., nitrogen or air) rather than a solid material like glass. Because it is a gas rather than a solid, the optical signal is subjected to less absorption and scattering. Therefore, signal loss should theoretically be reduced.

[0005] As an example of addressing confinement loss, hollow-core photonic bandgap optical fibers have been developed. These optical fibers incorporate a cladding of hollow capillaries arranged in a periodic structure around a hollow core. The geometry of the capillaries and the spacing between them are predetermined to form periodic fluctuations in refractive index. These periodic fluctuations in refractive index subsequently generate a photonic bandgap, which acts to prevent the transmission of light within a given wavelength range through the cladding. Thus, light within a given wavelength range is retained within the hollow core, and therefore, confinement loss is reduced.

[0006] As another example, an anti-resonant hollow core optical fiber incorporates a single ring of anti-resonant tubes. These tubes are typically made from thin glass and separated from each other by tiny gaps. The thickness and separation of the tubes are predetermined to produce an anti-resonant effect through canceling interference. The anti-resonant tubes reflect light back into the core.

[0007] To further reduce the confinement loss caused by hollow cores, hollow-core nested anti-resonant nodeless fibers (NANFs) are under development. Unlike the single, spaced-out tubes found in earlier anti-resonant hollow-core optical fibers, NANFs utilize larger tubes (e.g., larger capillaries) radially spaced around the core, with at least one smaller tube (e.g., smaller capillary) nested within each of the larger tubes. The tube spacing and geometry are predetermined to cause canceling interference between the light waves returning to the hollow core and their reflectivity. Recent efforts have advanced this idea further by placing even smaller tubes within each of the smaller tubes to create a double-nested tube structure.

[0008] However, hollow-core NANFs still produce a suboptimal amount of confinement loss, which causes suboptimal attenuation over long distances. While double-nested tube structures can reduce confinement loss, they present considerable manufacturing difficulties compared to hollow-core NANF structures. There is a need for hollow-core NANFs with improved confinement loss. [Overview of the project]

[0009] This disclosure addresses the need using a hollow-core optical fiber comprising 5 to 8 spaced-apart cladding elements. Each cladding element includes a first capillary and a second capillary nested with the first capillary. The first capillary of each cladding element is mounted on the inner surface of the substrate. The second capillary is mounted on the first capillary at an angle offset from the central longitudinal axis of the hollow-core optical fiber, the longitudinal axis of the first capillary, and a line extending through the region where the first capillary is bonded to the substrate. This angle is in the range of 20 to 120 degrees. The ratio of the outer diameter of the second capillary to the outer diameter of the first capillary is in the range of 0.47 to 0.85. Such a hollow-core optical fiber exhibits very low confinement loss to electromagnetic radiation having wavelengths in the near-infrared and infrared regions. The exhibited confinement loss is, in some examples, almost an order of magnitude lower than previously reported confinement losses.

[0010] According to a first aspect of this disclosure, the hollow core optical fiber comprises (1) a tubular substrate having an inner surface surrounding the central longitudinal axis of the hollow core optical fiber, and (2) a plurality of cladding elements spaced apart from each other and disposed within the substrate, wherein the plurality of cladding elements together define a hollow core region surrounding the central longitudinal axis of the hollow core optical fiber, and the plurality of cladding elements are radially arranged between the substrate and the hollow core region. The structure comprises a first capillary which is tubular and includes an outer surface having an outer diameter and contacting the inner surface of the substrate in a first contact area, and an inner surface defining a first cavity with the first longitudinal axis parallel to the central longitudinal axis, and (b) a tubular first capillary disposed within the first cavity defined by the first capillary. A second capillary comprising (i) an outer surface having an outer diameter and in contact with the inner surface of the first capillary in a second contact region, and (ii) an inner surface defining a second cavity, wherein (i) for each of the plurality of cladding elements, the first line extends orthogonally from the central longitudinal axis through the first longitudinal axis and the first contact region, and (ii) for each of the plurality of cladding elements, (iii) For each of the multiple cladding elements, the first and second lines are separated by an angle between 20 and 120 degrees, (iv) For each of the multiple cladding elements, the ratio of the outer diameter of the second capillary to the outer diameter of the first capillary is between 0.47 and 0.85, and (v) the number of multiple cladding elements is between 5 and 8 in total.

[0011] According to a second aspect of the second disclosure, a hollow core optical fiber of the first aspect is presented, wherein the inner surface of the substrate includes an inner diameter in the range of 30 μm to 140 μm.

[0012] According to a third aspect of this disclosure, a hollow core optical fiber described in the first or second aspect is presented, wherein the number of cladding elements totals six.

[0013] According to a fourth aspect of this disclosure, a hollow core optical fiber of any one of the first to third aspects is presented, wherein the hollow core region contains air or nitrogen.

[0014] According to a fifth aspect of this disclosure, a hollow core optical fiber is presented according to any one of the first to fourth aspects, wherein for each of the multiple cladding elements, the outer diameter of the first capillary is in the range of 8 μm to 52 μm.

[0015] According to a sixth aspect of this disclosure, a hollow core optical fiber is presented which is one of the first to fifth aspects, wherein for each of the multiple cladding elements, the outer diameter of the first capillary is in the range of 25 μm to 35 μm.

[0016] According to a seventh aspect of this disclosure, a hollow core optical fiber of any one of the first to sixth aspects is presented, wherein the first capillaries are spaced equally apart from one another.

[0017] According to the eighth aspect of this disclosure, a hollow core optical fiber is presented which is one of the first to seventh aspects, wherein the first capillaries of adjacent cladding elements among a plurality of cladding elements are separated by the shortest distance, which is in the range of 1.8 μm to 6.0 μm.

[0018] According to a ninth aspect of the present disclosure, a hollow core optical fiber of the eighth aspect is presented, wherein (i) each of a plurality of cladding elements has a first capillary thickness, and (ii) the ratio of the shortest distance to the thickness of the first capillary is in the range of 5 to 7.

[0019] According to a tenth aspect of the present disclosure, a hollow core optical fiber is presented according to any one of the first to eighth aspects, wherein for each of the multiple cladding elements, both the first and second capillaries have a thickness in the range of 0.20 μm to 2.0 μm.

[0020] According to an eleventh aspect of this disclosure, a hollow core optical fiber is presented which is one of the first to tenth aspects, wherein the hollow core region has an effective diameter in the range of 10 μm to 60 μm.

[0021] According to a twelfth aspect of the present disclosure, a hollow core optical fiber is presented which is one of the first to tenth aspects, wherein the hollow core region has an effective diameter in the range of 25 μm to 35 μm.

[0022] According to a thirteenth aspect of this disclosure, a hollow core optical fiber is presented according to any one of the first to twelfth aspects, wherein for each of the multiple cladding elements, the outer diameter of the second capillary is greater than 12 μm.

[0023] According to a fourteenth aspect of this disclosure, a hollow core optical fiber is presented according to any one of the first to thirteenth aspects, wherein for each of the multiple cladding elements, the outer diameter of the second capillary is in the range of 13 μm to 24 μm.

[0024] According to a 15th aspect of this disclosure, a hollow core optical fiber is presented according to any one of the 1st to 14th aspects, wherein for each of the multiple cladding elements, the ratio of the outer diameter of the second capillary to the inner diameter of the inner surface of the substrate is in the range of 0.14 to 0.25.

[0025] According to a sixteenth aspect of this disclosure, a hollow core optical fiber of the fifteenth aspect is presented, wherein the ratio of the outer diameter of the second capillary to the inner diameter of the inner surface of the substrate is in the range of 0.16 to 0.23.

[0026] According to a seventeenth aspect of the present disclosure, there is provided a hollow-core optical fiber according to any one of the first to sixteenth aspects, and for each of the plurality of cladding elements, the ratio of the outer diameter of the second capillary to the outer diameter of the first capillary is within a range of 0.60 to 0.72.

[0027] According to an eighteenth aspect of the present disclosure, there is provided a hollow-core optical fiber according to any one of the first to seventeenth aspects, and none of the plurality of cladding elements further includes another capillary disposed within a second cavity formed by the second capillary.

[0028] According to a nineteenth aspect of the present disclosure, there is provided a hollow-core optical fiber according to any one of the first to eighteenth aspects, and for each of the plurality of cladding elements, the first capillary and the second capillary include silica glass or doped silica glass.

[0029] According to a twentieth aspect of the present disclosure, there is provided a hollow-core optical fiber according to any one of the first to nineteenth aspects, and for each of the plurality of cladding elements, both the first capillary and the second capillary have a refractive index within a range of 1.4 to 2.8 with respect to electromagnetic radiation having a wavelength of 589.3 nm at room temperature.

[0030] According to a twenty-first aspect of the present disclosure, there is provided a hollow-core optical fiber according to any one of the first to twentieth aspects, and for each of the plurality of cladding elements, the angle separating the first line and the second line is within a range of 60 degrees to 110 degrees.

[0031] According to a twenty-second aspect of the present disclosure, there is provided a hollow-core optical fiber according to the twenty-first aspect, and the angle is within a range of 80 degrees to 100 degrees.

[0032] According to a twenty-third aspect of the present disclosure, there is provided a hollow-core optical fiber according to the twenty-second aspect, and the angle is within a range of 85 degrees to 95 degrees.

[0033] According to a 24th aspect of the present disclosure, a hollow core optical fiber is presented which is any one of the first to 23 aspects, wherein (i) the outer diameter of the first capillary of each of the plurality of cladding elements is substantially the same, (ii) the outer diameter of the second capillary of each of the plurality of cladding elements is substantially the same, and (iii) the angle separating the first and second lines of each of the plurality of cladding elements is substantially the same.

[0034] According to a 25th aspect of this disclosure, a hollow core optical fiber is presented in any one of the first to 21 aspects, wherein (i) for each of the plurality of cladding elements, the angle separating the first and second lines is in the range of 80 to 105 degrees, and (ii) for each of the plurality of cladding elements, the outer diameter of the second capillary is in the range of 17 μm to 19 μm.

[0035] According to the 26th aspect of this disclosure, a hollow-core optical fiber is presented which is any one of the first to 25 aspects, exhibiting a confinement loss of less than 1 dB / km for electromagnetic radiation having a wavelength of 1550 nm.

[0036] According to a 27th aspect of this disclosure, a hollow-core optical fiber of the 26th aspect is presented, which exhibits a confinement loss of less than 0.5 dB / km for electromagnetic radiation having a wavelength of 1550 nm.

[0037] According to a 28th aspect of this disclosure, a hollow-core optical fiber of the 27th aspect is presented, which exhibits a confinement loss of less than 0.1 dB / km for electromagnetic radiation having a wavelength of 1550 nm.

[0038] According to a 29th aspect of this disclosure, a hollow-core optical fiber of the 28th aspect is presented, which exhibits a confinement loss of less than 0.05 dB / km for electromagnetic radiation having a wavelength of 1550 nm.

[0039] According to a 30th aspect of the present disclosure, a hollow core optical fiber is presented in any one of the first to fourth aspects, wherein (a) the hollow core region has an effective diameter in the range of 17 μm to 21 μm, (b) for each of the multiple cladding elements, (i) the outer diameter of the first capillary is in the range of 13 μm to 17 μm, (ii) the outer diameter of the second capillary is in the range of 8.5 μm to 11.5 μm, (iii) both the first and second capillaries have a thickness in the range of 0.25 μm to 0.35 μm, and (iv) the angle separating the first and second lines is in the range of 40 degrees to 120 degrees.

[0040] According to a 31st aspect of this disclosure, a hollow-core optical fiber of the 30th aspect is presented, which exhibits a confinement loss of less than 0.16 dB / km for electromagnetic radiation having a wavelength of 1550 nm.

[0041] According to a 32nd aspect of the present disclosure, a hollow core optical fiber is presented in any one of the first to fourth aspects, wherein (a) the hollow core region has an effective diameter in the range of 26 μm to 32 μm, (b) for each of the multiple cladding elements, (i) the outer diameter of the first capillary is in the range of 20 μm to 26 μm, (ii) the outer diameter of the second capillary is in the range of 12 μm to 18 μm, (iii) both the first and second capillaries have a thickness in the range of 0.38 μm to 0.48 μm, and (iv) the angle separating the first and second lines is in the range of 20 degrees to 120 degrees.

[0042] According to a 33rd aspect of this disclosure, a hollow-core optical fiber of the 32nd aspect is presented, which exhibits a confinement loss of less than 0.16 dB / km for electromagnetic radiation having a wavelength of 1310 nm.

[0043] According to a 34th aspect of the present disclosure, a hollow core optical fiber is presented in any one of the first to fourth aspects, wherein (a) the hollow core region has an effective diameter in the range of 31 μm to 37 μm, (b) for each of the multiple cladding elements, (i) the outer diameter of the first capillary is in the range of 23 μm to 31 μm, (ii) the outer diameter of the second capillary is in the range of 15 μm to 21 μm, (iii) both the first and second capillaries have a thickness in the range of 0.4 μm to 0.6 μm, and (iv) the angle separating the first and second lines is in the range of 40 degrees to 110 degrees.

[0044] According to a 35th aspect of this disclosure, a hollow-core optical fiber of the 34th aspect is presented, which exhibits a confinement loss of less than 0.16 dB / km for electromagnetic radiation having a wavelength of 1550 nm.

[0045] According to the 36th aspect of the present disclosure, a hollow core optical fiber is presented in any one of the first to fourth aspects, wherein (a) the hollow core region has an effective diameter in the range of 50 μm to 56 μm, (b) for each of the multiple cladding elements, (i) the outer diameter of the first capillary is in the range of 39 μm to 45 μm, (ii) the outer diameter of the second capillary is in the range of 23 μm to 32 μm, (iii) both the first and second capillaries have a thickness in the range of 0.7 μm to 0.9 μm, and (iv) the angle separating the first and second lines is in the range of 35 degrees to 110 degrees.

[0046] According to the 37th aspect of this disclosure, a hollow-core optical fiber of the 36th aspect is presented, which exhibits a confinement loss of less than 0.16 dB / km for electromagnetic radiation having a wavelength of 2400 nm.

[0047] According to the 38th aspect of this disclosure, a hollow core optical fiber is presented in any one of the first to fourth aspects, wherein (a) the hollow core region has an effective diameter in the range of 22 μm to 28 μm, (b) for each of the multiple cladding elements, (i) the outer diameter of the first capillary is in the range of 17 μm to 23 μm, (ii) the outer diameter of the second capillary is in the range of 10 μm to 15 μm, (iii) both the first and second capillaries have a thickness in the range of 0.4 μm to 0.6 μm, and (iv) the angle separating the first and second lines is in the range of 40 degrees to 110 degrees.

[0048] According to the 39th aspect of this disclosure, a hollow-core optical fiber of the 38th aspect is presented, which exhibits a confinement loss of less than 0.26 dB / km for electromagnetic radiation having a wavelength of 1550 nm.

[0049] According to a forty-th aspect of the present disclosure, a hollow core optical fiber comprises (1) a tubular substrate having an inner surface surrounding the central longitudinal axis of the hollow core optical fiber, and (2) a plurality of cladding elements spaced apart from each other and disposed within the substrate, wherein the plurality of cladding elements together define a hollow core region surrounding the central longitudinal axis of the hollow core optical fiber, and the plurality of cladding elements are radially disposed between the substrate and the hollow core region. Each of the several cladding elements extends parallel to the central longitudinal axis, and each of the multiple cladding elements comprises (a) a tubular first capillary, (i) having an outer diameter and including an outer surface that contacts the inner surface of the substrate in a first contact region, and (ii) an inner surface that defines a first cavity, with the first longitudinal axis parallel to the central longitudinal axis, and (b) a tubular second capillary disposed within the first cavity defined by the first capillary, (i) (i) a second capillary having an outer diameter and an outer surface that contacts the inner surface of the first capillary in a second contact region, and (ii) an inner surface that defines a second cavity, wherein (i) for each of the plurality of cladding elements, the first line extends orthogonally from the central longitudinal axis through the first longitudinal axis and the first contact region, and (ii) for each of the plurality of cladding elements, the second line extends through the second longitudinal axis and the second contact region, (iii) for each of the multiple cladding elements, the first line and the second line are separated by an angle in the range of 20 to 120 degrees, (iv) the inner surface of the substrate has an inner diameter in the range of 26 μm to 164 μm, (v) for each of the multiple cladding elements, the ratio of the outer diameter of the second capillary to the inner diameter of the inner surface of the substrate is in the range of 0.14 to 0.25, and (vi) the number of multiple cladding elements is in the range of 5 to 8 in total.

[0050] According to the 41st aspect of this disclosure, the hollow core optical fiber comprises (1) a tubular substrate having an inner surface surrounding the central longitudinal axis of the hollow core optical fiber, and (2) a plurality of cladding elements spaced apart from each other and disposed within the substrate, wherein the plurality of cladding elements together define a hollow core region surrounding the central longitudinal axis of the hollow core optical fiber, and the plurality of cladding elements are radially disposed between the substrate and the hollow core region, and each of the plurality of cladding elements is Extending parallel to the central longitudinal axis, each of the multiple cladding elements comprises: (a) a tubular first capillary, (i) having an outer diameter and including an outer surface that contacts the inner surface of the substrate in a first contact region, and (ii) an inner surface defining a first cavity, with the first longitudinal axis parallel to the central longitudinal axis; and (b) a tubular second capillary disposed within the first cavity defined by the first capillary, (i) having an outer diameter and including an inner surface that contacts the first capillary in a second contact region. (i) an outer surface in contact with the inner surface, and (ii) a second capillary including an inner surface defining a second cavity, the second longitudinal axis being parallel to the central longitudinal axis, wherein (i) for each of the plurality of cladding elements, the first line extends orthogonally from the central longitudinal axis through the first longitudinal axis and the first contact region, (ii) for each of the plurality of cladding elements, the second line extends through the second longitudinal axis, the second contact region and the first longitudinal axis, and (iii) for each of the plurality of cladding elements (iv) The first and second lines are separated by an angle in the range of 20 to 120 degrees, (v) the hollow core region has an effective diameter in the range of 10 μm to 40 μm, (v) for each of the multiple cladding elements, the outer diameter of the first capillary is in the range of 8 μm to 52 μm, (vi) for each of the multiple cladding elements, both the first and second capillaries have a thickness in the range of 0.20 μm to 2.0 μm, and (vii) the number of multiple cladding elements is in the range of 5 to 8 in total. [Brief explanation of the drawing]

[0051] [Figure 1]This is an elevation view of a hollow core optical fiber, illustrating the central longitudinal axis of the hollow core optical fiber and a substrate extending longitudinally along the central longitudinal axis from the first end to the second end of the hollow core optical fiber. [Figure 2] Figure 1 is an elevation view of the cross-section of the hollow core optical fiber shown in Figure 1, taken through line II-II, illustrating that the hollow core optical fibers are spaced apart from each other and further include multiple cladding elements, each having a first capillary and a second capillary nested inside the first capillary. [Figure 3] This relates to Example 1, which is a map of the confinement loss in the cross-section of a hollow core optical fiber of the present disclosure, as calculated via a computer model. [Figure 4] The second embodiment relates to a graph plotting the confinement loss as determined by a computer model of the hollow core optical fiber of the present disclosure, as a function of (i) the angle at which the second capillary is offset within the first capillary, and (ii) the outer diameter of each of the second capillaries of the multiple cladding elements, illustrating that the confinement loss is smaller as the outer diameter increases. [Figure 5] The second example is a graph plotting the confinement loss as a function of the angle and outer diameter of the second capillary of each of the multiple cladding elements, illustrating that the modeled hollow core optical fiber exhibits the lowest confinement loss when the second outer diameter is approximately 15 μm or more and the angle is in the range of approximately 25 degrees to approximately 120 degrees. [Figure 6] The third embodiment is a graph plotting the confinement loss as determined by a computer model of the hollow core optical fiber of the present disclosure, as a function of the angle and outer diameter of the second capillary of each of the multiple cladding elements. [Figure 7] The fourth example is a graph plotting the confinement loss as determined by a computer model of the hollow core optical fiber of the present disclosure, as a function of the angle and outer diameter of the second capillary of each of the multiple cladding elements. [Figure 8A] The fifth example is a graph plotting the confinement loss as determined by a computer model of the hollow core optical fiber of the present disclosure, as a function of the angle and outer diameter of the second capillary of each of the multiple cladding elements. [Figure 8B] This relates to Example 5, and is a graph plotting the confinement loss as a function of the ratio of the outer diameter of the second (smaller) capillary to the outer diameter of the first (larger) capillary. [Figure 8C] This relates to Example 5, and is a graph plotting the confinement loss as a function of angle. [Figure 9] The sixth example is a graph plotting the confinement loss as determined by a computer model of the hollow core optical fiber of the present disclosure, as a function of the angle and outer diameter of the second capillary of each of the multiple cladding elements. [Figure 10] The present invention relates to Example 7, and is a graph plotting the confinement loss as determined by a computer model of the hollow core optical fiber in this disclosure, as a function of the angle and outer diameter of the second capillary of each of the multiple cladding elements. [Figure 11] The 8th example is a graph plotting the confinement loss as determined by a computer model of the hollow core optical fiber of the present disclosure, as a function of the angle and outer diameter of the second capillary of each of the multiple cladding elements. [Modes for carrying out the invention]

[0052] Referring to Figures 1-2, the hollow core optical fiber 10 includes a substrate 12 and a plurality of cladding elements 14. The substrate 12 is tubular, having an inner surface 16 that forms a cavity 18 and an outer surface 20. The inner surface 16 surrounds the central longitudinal axis 22 of the hollow core optical fiber 10. The outer surface 20 faces the external environment 24. The substrate 12 and the cavity 18 it forms extend longitudinally from a first end 26 to a second end 28. The inner surface 16 has an inner diameter 30. The outer surface 20 has an outer diameter 31. In this embodiment, the inner diameter 30 of the substrate 12 is in the range of 26 μm to 164 μm. In this embodiment, the inner diameter 30 is 26 μm, 30 μm, 35 μm, 40 μm, 45 μm, 50 μm, 55 μm, 60 μm, 65 μm, 70 μm, 75 μm, 80 μm, 85 μm, 90 μm, 95 μm, 100 μm, 105 μm, 110 μm, 115 μm, 120 μm, 125 μm, 130 μm, 135 μm, 140 μm, 145 μm, 150 μm, 155 μm, 160 μm, or 164 μm, or within any range bounded by any two of these values ​​(e.g., 55 μm to 130 μm, 90 μm to 135 μm, 30 μm to 140 μm, etc.). In this embodiment, the outer diameter 31 of the substrate 12 is within the range of 46 μm to 364 μm. In this embodiment, the outer diameter 31 is 46μm, 50μm, 60μm, 70μm, 80μm, 90μm, 100μm, 110μm, 120μm, 130μm, 140μm, 150μm, 160μm, 170μm, 180μm, 190μm, 200μm, 210μm, 220μm, 230μm, 240μm, 250μm, 260μm The thickness is 270 μm, 280 μm, 290 μm, 300 μm, 310 μm, 320 μm, 330 μm, 340 μm, 350 μm, 360 μm, or 364 μm, or any range bounded by any two of these values ​​(e.g., 110 μm to 240 μm, 60 μm to 320 μm, etc.). The substrate 12 has a thickness 33 between its inner surface 16 and outer surface 20. In this embodiment, the thickness 33 of the substrate 12 is in the range of 10 μm to 100 μm.In this embodiment, the thickness 33 is 10 μm, 20 μm, 30 μm, 40 μm, 50 μm, 60 μm, 70 μm, 80 μm, 90 μm, or 100 μm, or within any range bounded by any two of these values ​​(e.g., 20 μm to 90 μm, 30 μm to 70 μm, etc.).

[0053] Multiple cladding elements 14 are arranged within a cavity 18 of the substrate 12. The multiple cladding elements 14 extend longitudinally within the cavity 18 of the substrate 12, parallel to the central longitudinal axis 22 of the hollow core optical fiber 10. The multiple cladding elements 14 are spaced apart from each other and are radially positioned around the central longitudinal axis 22. For example, none of the multiple cladding elements 14 are in contact with any other of the multiple cladding elements 14. The number of multiple cladding elements 14 is in the range of 5 to 8 in total. In the embodiment, the hollow core optical fiber 10 includes 5, 6, 7, or 8 cladding elements 14.

[0054] Multiple cladding elements 14 together define a hollow core region 32. The hollow core region 32 radially surrounds the central longitudinal axis 22 and extends longitudinally parallel to the central longitudinal axis 22. The multiple cladding elements 14 are radially arranged between the substrate 12 and the hollow core region 32. The hollow core region 32 is not a physical component such as a tubular core, but rather a place where electromagnetic radiation is confined, mainly by the multiple cladding elements 14, and propagates longitudinally within the hollow core optical fiber 10. The multiple cladding elements 14 maintain the electromagnetic radiation mainly within the hollow core region 32 by anti-resonance. Cavities 18 in the substrate 12 that are not occupied by the multiple cladding elements 14, including the hollow core region 32, contain gas 34. In embodiments, the gas 34 is air or nitrogen.

[0055] Each of the multiple cladding elements 14 includes a first capillary 36 and a second capillary 38 nested with the first capillary 36. Both the first capillary 36 and the second capillary 38 are tubular and extend longitudinally parallel to the central longitudinal axis 22. The first capillary 36 includes an outer surface 40 and an inner surface 42. The outer surface 40 contacts the inner surface 16 of the substrate 12 and can be attached to the substrate 12 in a first contact area 44. The inner surface 42 defines a first cavity 46 having a first longitudinal axis 48 parallel to the central longitudinal axis 22 of the hollow core optical fiber 10.

[0056] The outer surface 40 of the first capillary 36 of each of the multiple clad elements 14 has an outer diameter 50. In the embodiment, the outer diameter 50 is in the range of 8 μm to 52 μm. In the embodiment, the outer diameter 50 is 8 μm, 10 μm, 12 μm, 15 μm, 20 μm, 25 μm, 30 μm, 35 μm, 40 μm, 45 μm, 46 μm, 50 μm, or 52 μm, or any range bounded by any two of these values ​​(e.g., 25 μm to 35 μm, 20 μm to 40 μm, 12 μm to 46 μm, etc.). The outer diameter 50 of each of the first capillaries 36 of the multiple cladding elements 14 are all approximately the same; that is, the hollow core optical fiber 10 is manufactured with the intention that all of the outer diameters 50 of the first capillaries 36 are identical, while acknowledging that there is some variation in the outer diameter 50 among the first capillaries 36 due to manufacturing inaccuracies. In the embodiment, all outer diameters 50 are within a tolerance of ±10% from the average of the outer diameters 50.

[0057] As already stated, none of the multiple cladding elements 14 are in contact with each other, and therefore none of the first capillaries 36 are in contact with each other. Each of the first capillaries 36 is separated from an adjacent first capillary 36 by the shortest distance 52 (from outer surface 40 to outer surface 40). In the embodiment, the shortest distance 52 is in the range of 1.8 μm to 6.0 μm. In the embodiment, the shortest distance 52 is 1.8 μm, 2.0 μm, 2.5 μm, 3.0 μm, 3.5 μm, 4.0 μm, 4.5 μm, 5.0 μm, 5.5 μm, or 6.0 μm, or any range bounded by any two of these values ​​(e.g., 2.0 μm to 4.5 μm, 2.5 μm to 5.5 μm, etc.). The shortest distances 52 separating adjacent first capillaries 36 are all approximately the same; that is, the hollow core optical fibers 10 are manufactured with the intention that the shortest distances 52 are all the same and the first capillaries 36 are evenly spaced apart, while acknowledging that there is some variation in the shortest distances 52 due to manufacturing inaccuracies. In the embodiment, all shortest distances 52 are within a tolerance of ±10% from the average of the shortest distances 52.

[0058] Each of the first capillaries 36 has a thickness 54. The thickness 54 is the distance between the outer surface 40 and the inner surface 42. In embodiments, the thickness 54 is in the range of 0.20 μm to 2.00 μm. In embodiments, the thickness 54 is 0.20 μm, 0.50 μm, 0.75 μm, 1.00 μm, 1.25 μm, 1.50 μm, 1.75 μm, or 2.00 μm, or any range bounded by any two of these values ​​(e.g., 0.50 μm to 1.50 μm, 0.20 μm to 1.75 μm, etc.). The thicknesses 54 of the first capillaries 36 are all approximately the same; that is, the hollow core optical fibers 10 are manufactured with the intention that the thicknesses 54 are all the same, while acknowledging that there will be some variation in the thickness 54 due to manufacturing inaccuracies. In the embodiment, all thicknesses 54 are within a tolerance of ±10% from the average thickness 54. In the embodiment, (i) the shortest distance 52 separating adjacent first capillaries 36, and (ii) the ratio of the thickness 54 of the first capillary 36, are in the range of 5 to 7.

[0059] The hollow core region 32 has an effective diameter 56. The effective diameter 56 extends through the central longitudinal axis 22 and is bounded by the outer surfaces 40 of the first capillaries 36 of the multiple cladding elements 14. The effective diameter 56 is adjacent to but does not intersect with the outer surfaces 40. In the embodiment, the effective diameter 56 of the hollow core region 32 is in the range of 10 μm to 60 μm. In the embodiment, the effective diameter 56 is 10 μm, 15 μm, 20 μm, 25 μm, 30 μm, 35 μm, 40 μm, 45 μm, 50 μm, 55 μm, or 60 μm, or any range bounded by any two of these values ​​(e.g., 10 μm to 40 μm, 25 μm to 35 μm, 15 μm to 55 μm, etc.).

[0060] As already stated, each of the multiple clad elements 14 further includes a second capillary 38 nested with a first capillary 36. The second capillary 38 of any one of the multiple clad elements 14 is disposed within a first cavity 46 defined by the first capillary 36 of that clad element 14. Each of the first capillaries 36 has one of the second capillaries 38 disposed therein. Each second capillary 38 has an outer surface 58 and an inner surface 60. For each of the multiple clad elements 14, the outer surface 58 of the second capillary 38 is in contact with the inner surface 42 of the first capillary 36 in which the second capillary 38 is disposed in a second contact region 62. The second capillary 38 can be attached to the first capillary 36 in the second contact region 62. The inner surface 60 defines a second cavity 64 having a second longitudinal axis 66 parallel to the central longitudinal axis 22 of the hollow core optical fiber 10.

[0061] Each second capillary 38 has a thickness 68. The thickness 68 is the shortest distance between the outer surface 58 and the inner surface 60. In embodiments, the thickness 68 is in the range of 0.20 μm to 2.00 μm. In embodiments, the thickness 68 is 0.20 μm, 0.50 μm, 0.75 μm, 1.00 μm, 1.25 μm, 1.50 μm, 1.75 μm, or 2.00 μm, or any range bounded by any two of these values ​​(e.g., 0.50 μm to 1.50 μm, 0.20 μm to 1.75 μm, etc.). The thicknesses 68 of the second capillaries 38 are all approximately the same; that is, the hollow core optical fibers 10 are manufactured with the intention that the thicknesses 68 are all the same, while acknowledging that there is some variation in the thickness 68 due to manufacturing inaccuracies. In this embodiment, all thicknesses 68 are within a tolerance of ±10% from the average thickness 68.

[0062] Each of the multiple clad elements 14 has a second capillary 38 with an outer diameter 70 defined by its outer surface 58. The outer diameter 70 is smaller than the outer diameter 50 of the first capillary 36 on which the second capillary 38 is disposed. In the embodiment, the outer diameter 70 of each second capillary 38 is greater than 12 μm. In the embodiment, the outer diameter 70 of each second capillary 38 is 12 μm, 13 μm, 14 μm, 15 μm, 16 μm, 17 μm, 18 μm, 19 μm, 20 μm, 21 μm, 22 μm, 23 μm, or 24 μm, or within any range bounded by any two of these values ​​(e.g., 13 μm to 24 μm, 15 μm to 19 μm, etc.). The outer diameters 70 of the second capillaries 38 are all nearly the same; that is, the hollow core optical fibers 10 are manufactured with the intention that all have the same outer diameter, while acknowledging that there is some variation in the outer diameter 70 due to manufacturing inaccuracies. In the embodiment, all outer diameters 70 are within a tolerance of ±10% from the average outer diameter 70.

[0063] In the embodiment, the ratio of (i) the outer diameter 70 of each second capillary 38 to (ii) the inner diameter 30 of the inner surface 16 of the base material 12 is in the range of 0.14 to 0.25. In the embodiment, the ratio is 0.14, 0.15, 0.16, 0.17, 0.18, 0.19, 0.20, 0.21, 0.22, 0.23, 0.24, or 0.25, or any range bounded by any two of these values ​​(e.g., 0.16 to 0.23, 0.18 to 0.22, etc.).

[0064] In the embodiment, for each of the multiple clad elements 14, the ratio of (i) the outer diameter 70 of the second capillary 38 to (ii) the outer diameter 50 of the first capillary 36 is in the range of 0.47 to 0.85. In the embodiment, the range is 0.47, 0.48, 0.49, 0.50, 0.51, 0.52, 0.53, 0.54, 0.55, 0.56, 0.57, 0.58, 0.59, 0.60, 0.61, 0.62, 0.63, 0.64, 0.65, 0.66, 0.67, 0.68, 0.69, 0.70, 0.71, 0.72, 0.7 3, 0.74, 0.75, 0.76, 0.77, 0.78, 0.79, 0.80, 0.81, 0.82, 0.83, 0.84, or 0.85, or any range bounded by any two of these values ​​(e.g., 0.60 to 0.72, 0.62 to 0.69, 0.64 to 0.71, etc.).

[0065] In this embodiment, the hollow core optical fiber 10 is not a double-nested hollow core optical fiber 10. For example, none of the multiple cladding elements 14 further include another capillary disposed within the second cavity 64 formed by the second capillary 38. In other embodiments, each of the multiple cladding elements 14 further includes one or more capillaries (not shown separately) within the second cavity 64 formed by the second capillary 38.

[0066] In the embodiment, the first capillaries 36 and second capillaries 38 of each of the multiple clad elements 14 include (for example, are made from) glass such as silica glass, modified silica glass, or doped silica glass. In the embodiment, each of the first capillaries 36 and second capillaries 38 of the multiple clad elements 14 has a refractive index in the range of 1.4 to 2.8 for electromagnetic radiation having a wavelength of 589.3 nm at room temperature. Other compositions for the first capillaries 36 and second capillaries 38 are envisioned.

[0067] For each of the multiple cladding elements 14, the first line 72 extends orthogonally from the central longitudinal axis 22 through the first longitudinal axis 48 and the first contact region 44. Furthermore, for each of the multiple cladding elements 14, the second line 74 extends orthogonally through the second longitudinal axis 66 and intersects the first longitudinal axis 48 and the second contact region 62. The first line 72 and the second line 74 are conceptual references to illustrate the following, and are not structural components.

[0068] For each of the multiple cladding elements 14, the first line 72 and the second line 74 are separated by an angle 76. The angle 76 is in the range of 20 to 120 degrees. In embodiments, the angle 76 is 20, 30, 40, 50, 60, 70, 80, 90, 100, or 110 degrees, or any range bounded by any two of these values ​​(e.g., 60 to 110 degrees, 80 to 100 degrees, 85 to 95 degrees, etc.). For each of the multiple cladding elements 14, the angle 76 separating the first line 72 and the second line 74 is approximately the same; that is, the hollow core optical fiber 10 is manufactured with the intention that the angle 76 is always the same, while acknowledging that there will be some variation in the angle 76 due to manufacturing inaccuracies. In the embodiment, all angles 76 are within a tolerance of ±10% from the average of the angles 76. In the embodiment, for each clad element 14, (i) the angle 76 separating the first line 72 and the second line 74 is in the range of 80 to 105 degrees, and (ii) the outer diameter 70 of the second capillary 38 is in the range of 17 μm to 19 μm.

[0069] The hollow core optical fiber 10 described herein exhibits particularly low confinement loss for electromagnetic radiation having wavelengths in the range of approximately 850 nm to approximately 2400 nm or more. In one embodiment, the hollow core optical fiber 10 exhibits a confinement loss of less than 1 dB / km for electromagnetic radiation having a wavelength of 1550 nm. In another embodiment, the hollow core optical fiber 10 exhibits a confinement loss of less than 0.5 dB / km for electromagnetic radiation having a wavelength of 1550 nm. In yet another embodiment, the hollow core optical fiber 10 exhibits a confinement loss of less than 0.1 dB / km for electromagnetic radiation having a wavelength of 1550 nm. In yet another embodiment, the hollow core optical fiber 10 exhibits a confinement loss of less than 0.05 dB / km for electromagnetic radiation having a wavelength of 1550 nm. The physical confinement loss of a hollow core optical fiber can be estimated by taking a cross-section of the hollow core optical fiber, measuring its components (using a scanning electron microscope, for example), and inputting the measurements into a mode solver software program such as COMSOL® Multiphysics equipped with a wave optics module. The software program employs the finite difference method to solve the wave equation governing optical propagation and determine the mth optical mode (n eff,m It is possible to generate an effective refractive index of (n eff,m ) can be expressed as a complex number having a real part and an imaginary part via the following equation (1). n eff,m =n re,m +i·n im,m (1) The confinement loss can be calculated from the imaginary part using the following equation (2), where λ is the wavelength in meters.

number

[0070] As another example, the effective diameter 56 of the hollow core region 32 is in the range of 17 μm to 21 μm, and for each of the multiple cladding elements 14, (i) the outer diameter 50 of the first capillary 36 is in the range of 13 μm to 17 μm, (ii) the outer diameter 70 of the second capillary 38 is in the range of 8.5 μm to 11.5 μm, (iii) the thicknesses 54 and 68 of the first capillary 36 and the second capillary 38 are both in the range of 0.25 μm to 0.35 μm, and (iv) the angle 76 separating the first line 72 and the second line 74 is in the range of 40 degrees to 120 degrees. The hollow core optical fiber 10 as described can exhibit a confinement loss of less than 0.16 dB / km for electromagnetic radiation having a wavelength of 1550 nm.

[0071] As another example, the effective diameter 56 of the hollow core region 32 is in the range of 26 μm to 32 μm, and for each of the multiple cladding elements 14, (i) the outer diameter 50 of the first capillary 36 is in the range of 20 μm to 26 μm, (ii) the outer diameter 70 of the second capillary 38 is in the range of 12 μm to 18 μm, (iii) the thicknesses 54 and 68 of the first capillary 36 and the second capillary 38 are both in the range of 0.38 μm to 0.48 μm, and (iv) the angle 76 separating the first line 72 and the second line 74 is in the range of 20 degrees to 120 degrees. The hollow core optical fiber 10 as described can exhibit a confinement loss of less than 0.16 dB / km for electromagnetic radiation having a wavelength of 1310 nm.

[0072] As another example, the effective diameter 56 of the hollow core region 32 is in the range of 31 μm to 37 μm, and for each of the multiple cladding elements 14, (i) the outer diameter 50 of the first capillary 36 is in the range of 23 μm to 31 μm, (ii) the outer diameter 70 of the second capillary 38 is in the range of 15 μm to 21 μm, (iii) the thicknesses 54 and 68 of the first capillary 36 and the second capillary 38 are both in the range of 0.40 μm to 0.60 μm, and (iv) the angle 76 separating the first line 72 and the second line 74 is in the range of 40 degrees to 110 degrees. The hollow core optical fiber 10 as described can exhibit a confinement loss of less than 0.16 dB / km for electromagnetic radiation having a wavelength of 1550 nm.

[0073] As another example, the effective diameter 56 of the hollow core region 32 is in the range of 50 μm to 56 μm, and for each of the multiple cladding elements 14, (i) the outer diameter 50 of the first capillary 36 is in the range of 39 μm to 45 μm, (ii) the outer diameter 70 of the second capillary 38 is in the range of 23 μm to 32 μm, (iii) the thicknesses 54 and 68 of the first capillary 36 and the second capillary 38 are both in the range of 0.70 μm to 0.90 μm, and (iv) the angle 76 separating the first line 72 and the second line 74 is in the range of 35 degrees to 110 degrees. The hollow core optical fiber 10 as described can exhibit a confinement loss of less than 0.16 dB / km for electromagnetic radiation having a wavelength of 2400 nm.

[0074] As another example, the effective diameter 56 of the hollow core region 32 is in the range of 22 μm to 28 μm, and for each of the multiple cladding elements 14, (i) the outer diameter 50 of the first capillary 36 is in the range of 17 μm to 23 μm, (ii) the outer diameter 70 of the second capillary 38 is in the range of 10 μm to 15 μm, (iii) the thicknesses 54 and 68 of the first capillary 36 and the second capillary 38 are both in the range of 0.40 μm to 0.60 μm, and (iv) the angle 76 separating the first line 72 and the second line 74 is in the range of 40 degrees to 110 degrees. The hollow core optical fiber 10 as described can exhibit a confinement loss of less than 0.26 dB / km for electromagnetic radiation having a wavelength of 1550 nm.

[0075] The hollow-core optical fiber 10 of the present disclosure addresses the aforementioned need by exhibiting very low confinement loss. Very low confinement loss includes low confinement loss in the fundamental mode. The multiple cladding elements 14 in which the second capillary 38 contacts the first capillary 36 in a second contact region 62 that is angled 76 degrees from the first contact region 44, effectively confine electromagnetic radiation of a desired wavelength within the hollow core region 32, in particular, when the ratio of the outer diameter 70 of the second capillary 38 to the outer diameter 50 of the first capillary 36 is within the range highlighted above. The embodiments presented below support the high level of confinement provided by the hollow-core optical fiber 10 of the present disclosure based on optical modeling. Although not bound by theory, it is believed that the hollow-core optical fiber 10 effectively confines electromagnetic radiation within the hollow core region 32 through anti-resonance and negative curvature effects from the multiple first capillaries 36 facing the hollow core region 32. The extremely low confinement loss exhibited by the hollow core optical fiber 10, while utilizing multiple cladding elements 14 nested within the first capillary 36 by only the second capillary 38, eliminates the need to incorporate any further capillaries nested with the second capillary 38, thus avoiding the manufacturing difficulties caused by incorporating such further capillaries.

[0076] Embodiments of the hollow core optical fiber 10 can be fabricated by the following method. Cladding elements 14 can be sleeved within a substrate 12 in a desired arrangement. The cladding elements 14 can be joined to the substrate 12 to form a preform assembly. The cladding elements 14 and the substrate 12 can be joined by any suitable method, but not limited to welding, baffling, and bonding. Welding techniques include laser welding, flame welding, and plasma welding. The preform assembly can be re-stretched into a fiber preform using conventional fiber re-stretching techniques. The fiber preform can then be stretched into a hollow core optical fiber 10 using conventional fiber stretching techniques. [Examples]

[0077] Example 1 - In Example 1, related to Figure 3, a computer model was used to determine the confinement loss and map the degree of confinement of the fundamental modes of electromagnetic radiation after making several assumptions about variables. The modeled hollow core optical fiber contained six cladding elements. For each of the six cladding elements, it was assumed that the first and second lines were separated by an angle of 90 degrees. The hollow core region was assumed to have an effective diameter of 34.5 μm. The cavity in the substrate surrounding the six cladding elements was assumed to be filled with air. Each of the first capillaries was assumed to have an outer diameter of 27.5 μm. Each of the second capillaries was assumed to have an outer diameter of 18 μm. All of the first capillaries were assumed to have a thickness of 0.50 μm. All of the second capillaries were assumed to have a thickness of 0.50 μm. Adjacent first capillaries were evenly spaced apart. The inner diameter of the inner surface of the substrate was assumed to be 89.5 μm. The computer model predicted a confinement loss of approximately 0.022 dB / km for electromagnetic radiation with a wavelength of 1550 nm. The computer model generated contour plots (reproduced in Figure 3) showing the normalized power of the electric field on a logarithmic axis (-6 to 0). The contour plots indicate good confinement of electromagnetic radiation within the hollow core region, with low losses through the cladding elements and the space between adjacent cladding elements. In addition, the contour plots indicate that the electric field does not reach the substrate, which indicates low radiation loss.

[0078] Example 2 – In Example 2, related to Figures 4 and 5, a computer model was again used to determine the confinement loss of various hollow-core optical fibers having six evenly spaced cladding elements. Specifically, the confinement loss for electromagnetic radiation with a wavelength of 1550 nm was determined as a function of the outer diameter of the second capillary of each cladding element, and the angle separating the first and second lines of each cladding element. All parameters are otherwise the same as in Example 1.

[0079] Figure 4 reproduces a graph plotting the confinement loss calculated as a function of the angle and outer diameter of the second capillary. In addition, a triaxial graph (reproduced in Figure 5) was generated to plot the confinement loss calculated as a function of the angle and outer diameter of the second capillary. Some associated contour plots of the modeled hollow core fibers are also reproduced in Figure 5. The graphs reveal that the confinement loss can increase as a function of the increasing angle when the outer diameter of each second capillary in the cladding element is too small (6 μm and 12 μm in this example), but decreases significantly as a function of the increasing angle (up to at least about 110 degrees) when the outer diameter of each second capillary in the cladding element is sufficiently large (18 μm in this example). Even with a large outer diameter of 18 μm, the confinement loss increases when the angle exceeds 110 degrees. While not bound by theory, the arrangement of the increased confinement loss between the second capillaries in such an example is thought to be too close to the hollow core region to provide an anti-resonance effect.

[0080] Example 3 - In Example 3, related to Figure 6, the computer model was again used to determine the confinement loss of various hollow-core optical fibers having six evenly spaced cladding elements. Specifically, the confinement loss for electromagnetic radiation with a wavelength of 1550 nm was determined as a function of the outer diameter of the second capillary of each cladding element, and the angle separating the first and second lines of each cladding element. The model assumed that the hollow core region had an effective diameter of 34.5 μm and the outer diameter of the first capillary of each cladding element was 27.5 μm. A triaxial graph was generated (and reproduced in Figure 6) and the confinement loss was plotted again as a function of the angle and outer diameter of the second capillary. This graph showed that the modeled hollow-core optical fiber with an outer diameter of approximately 18 μm of the second capillary and an angle of approximately 90 degrees had a confinement loss of less than 0.025 dB / km (e.g., logarithmic). 10 It becomes clear that this produces the lowest confinement loss (less than -1.6 at scale).

[0081] Example 4 – In Example 4, and relating to Figure 7, the computer model assumed that the hollow core region had an effective diameter of 19 μm, the outer diameter of the first capillary of each cladding element was 15 μm, the thickness of the first and second capillaries of each cladding element was 0.30 μm, the number of cladding elements was 6, and the wavelength of the electromagnetic radiation propagating through the modeled hollow core optical fiber was 850 nm. The confinement loss was then calculated as a function of the outer diameter of the second capillary of each cladding element, and the angle separating the first and second lines of each cladding element. The results are reproduced in the graph of Figure 7. These results reveal that an outer diameter of approximately 10 μm for the second capillary and an angle of approximately 105 degrees provided the lowest confinement loss of less than 0.058 dB / km. The ratio of the outer diameter of the second capillary (10 μm) to the outer diameter of the first capillary (15 μm) is 0.67.

[0082] Example 5 – In Example 5, and relating to Figures 8A and 8B, the computer model assumed that the hollow core region had an effective diameter of 29 μm, the outer diameter of the first capillary of each cladding element was 23 μm, the thickness of the first and second capillaries of each cladding element was 0.43 μm, the number of cladding elements was 6, and the wavelength of the electromagnetic radiation propagating through the modeled hollow core optical fiber was 1310 nm. The confinement loss was then calculated as a function of the outer diameter of the second capillary of each cladding element, and the angle separating the first and second lines of each cladding element. The results are reproduced in the graph of Figure 8A. These results reveal that an outer diameter of approximately 15 μm for the second capillary and an angle of approximately 120 degrees provided the lowest confinement loss of less than 0.028 dB / km. The ratio of the outer diameter of the second capillary (10 μm) to the outer diameter of the first capillary (15 μm) is 0.65.

[0083] In addition, the confinement loss was then plotted as a function of the ratio of the outer diameter of the second capillary to the outer diameter of the first capillary, with respect to a 90-degree angle. The results are reproduced in Figure 8B. These results show that the modeled hollow-core optical fibers with ratios in the range of 0.52 to 0.83 produced confinement losses of less than 0.2 dB / km.

[0084] Furthermore, the confinement loss was plotted as a function of angle, assuming that the outer diameter of the second capillary was set to 15 μm. The results are reproduced in Figure 8C. These results show that the modeled hollow-core optical fibers with angles in the range of approximately 40 to 120 degrees produced a confinement loss of less than 0.1 dB / km.

[0085] Example 6 – In Example 6, and relating to Figure 9, the computer model assumed that the hollow core region had an effective diameter of 34.5 μm, the outer diameter of the first capillary of each cladding element was 27.5 μm, the thickness of the first and second capillaries of each cladding element was 0.50 μm, the number of cladding elements was 6, and the wavelength of the electromagnetic radiation propagating through the modeled hollow core optical fiber was 1550 nm. The confinement loss was then calculated as a function of the outer diameter of the second capillary of each cladding element, and the angle separating the first and second lines of each cladding element. The results are reproduced in the graph of Figure 9. These results reveal that an outer diameter of approximately 18 μm for the second capillary and an angle of approximately 90 degrees provided the lowest confinement loss of less than 0.022 dB / km. The ratio of the outer diameter of the second capillary (18 μm) to the outer diameter of the first capillary (27.5 μm) is 0.65.

[0086] Example 7 – In Example 7, and relating to Figure 10, the computer model assumed that the hollow core region had an effective diameter of 53 μm, the outer diameter of the first capillary of each cladding element was 42 μm, the thickness of the first and second capillaries of each cladding element was 0.79 μm, the number of cladding elements was 6, and the wavelength of the electromagnetic radiation propagating through the modeled hollow core optical fiber was 2400 nm. The confinement loss was then calculated as a function of the outer diameter of the second capillary of each cladding element, and the angle separating the first and second lines of each cladding element. The results are reproduced in the graph of Figure 10. These results reveal that an outer diameter of approximately 27 μm for the second capillary and an angle of approximately 90 degrees provided the lowest confinement loss of less than 0.016 dB / km. The ratio of the second diameter of the second capillary (27 μm) to the outer diameter of the first capillary (42 μm) is 0.64.

[0087] Example 8 – In Example 8, and relating to Figure 11, the computer model assumed that the hollow core region had an effective diameter of 25 μm, the outer diameter of the first capillary of each cladding element was 20 μm, the thickness of the first and second capillaries of each cladding element was 0.50 μm, the number of cladding elements was 6, and the wavelength of the electromagnetic radiation propagating through the modeled hollow core optical fiber was 1550 nm. The confinement loss was then calculated as a function of the outer diameter of the second capillary of each cladding element, and the angle separating the first and second lines of each cladding element. The results are reproduced in the graph of Figure 11. These results reveal that an outer diameter of approximately 13 μm for the second capillary and an angle of approximately 105 degrees provided the lowest confinement loss of less than 0.204 dB / km. The ratio of the outer diameter of the first capillary (13 μm) to the outer diameter of the second capillary (20 μm) is 0.65.

Claims

1. It is a hollow core optical fiber, A tubular substrate having an inner surface surrounding the central longitudinal axis of the hollow core optical fiber, A plurality of cladding elements are provided spaced apart from each other and disposed within the substrate, wherein the plurality of cladding elements together define a hollow core region surrounding the central longitudinal axis of the hollow core optical fiber, and the plurality of cladding elements are radially disposed between the substrate and the hollow core region, wherein each of the plurality of cladding elements extends parallel to the central longitudinal axis, and each of the plurality of cladding elements A first capillary that is tubular, comprising (i) an outer surface having an outer diameter and in contact with the inner surface of the substrate in a first contact region, and (ii) an inner surface defining a first cavity, the first capillary having a first longitudinal axis parallel to the central longitudinal axis, A tubular second capillary disposed within the first cavity defined by the first capillary, comprising: (i) an outer surface having an outer diameter and in contact with the inner surface of the first capillary in a second contact region; and (ii) an inner surface defining a second cavity, the second longitudinal axis of which is parallel to the central longitudinal axis. For each of the plurality of cladding elements, the first line extends orthogonally from the central longitudinal axis through the first longitudinal axis and the first contact region. For each of the plurality of cladding elements, the second line extends through the second longitudinal axis, the second contact region, and the first longitudinal axis. For each of the plurality of cladding elements, the first line and the second line are separated by an angle within the range of 20 degrees to 120 degrees. For each of the plurality of cladding elements, the ratio of the outer diameter of the second capillary to the outer diameter of the first capillary is in the range of 0.47 to 0.

85. A hollow core optical fiber having a total of 5 to 8 cladding elements.

2. The hollow core optical fiber according to claim 1, wherein the inner surface of the substrate has an inner diameter in the range of 30 μm to 140 μm.

3. The hollow core optical fiber according to claim 1 or 2, wherein for each of the plurality of cladding elements, the outer diameter of the first capillary is in the range of 8 μm to 52 μm.

4. The hollow core optical fiber according to any one of claims 1 to 3, wherein the first capillaries of adjacent cladding elements among the plurality of cladding elements are separated by the shortest distance in the range of 1.8 μm to 6.0 μm.

5. The hollow core optical fiber according to claim 4, wherein, for each of the plurality of cladding elements, the first capillary has a thickness, and the ratio of the shortest distance to the thickness of the first capillary is in the range of 5 to 7.

6. The hollow core optical fiber according to any one of claims 1 to 5, wherein for each of the plurality of cladding elements, both the first capillary and the second capillary have a thickness in the range of 0.20 μm to 2.0 μm.

7. The hollow core optical fiber according to any one of claims 1 to 6, wherein the hollow core region has an effective diameter in the range of 10 μm to 60 μm.

8. The hollow core optical fiber according to any one of claims 1 to 7, wherein, for each of the plurality of cladding elements, the outer diameter of the second capillary is in the range of 13 μm to 24 μm.

9. The hollow core optical fiber according to any one of claims 1 to 8, wherein for each of the plurality of cladding elements, the ratio of the outer diameter of the second capillary to the inner diameter of the inner surface of the substrate is in the range of 0.14 to 0.

25.

10. The hollow core optical fiber according to any one of claims 1 to 9, wherein for each of the plurality of cladding elements, the ratio of the outer diameter of the second capillary to the outer diameter of the first capillary is in the range of 0.60 to 0.

72.

11. The hollow core optical fiber according to any one of claims 1 to 10, wherein none of the plurality of cladding elements further include another capillary disposed within the second cavity formed by the second capillary.

12. The hollow core optical fiber according to any one of claims 1 to 11, wherein, for each of the plurality of cladding elements, the angle separating the first line and the second line is in the range of 60 degrees to 110 degrees.

13. The outer diameter of the first capillary of each of the plurality of cladding elements is approximately the same. The outer diameter of the second capillary of each of the plurality of cladding elements is approximately the same. The hollow core optical fiber according to any one of claims 1 to 12, wherein the angles separating the first line and the second line of each of the plurality of cladding elements are substantially the same.

14. For each of the plurality of cladding elements, the angle separating the first line and the second line is in the range of 80 degrees to 105 degrees. The hollow core optical fiber according to any one of claims 1 to 13, wherein, for each of the plurality of cladding elements, the outer diameter of the second capillary is in the range of 17 μm to 19 μm.

15. The hollow core optical fiber according to claim 14, wherein the hollow core optical fiber exhibits a confinement loss of less than 0.1 dB / km with respect to electromagnetic radiation having a wavelength of 1550 nm.

16. The hollow core region has an effective diameter in the range of 17 μm to 21 μm. For each of the aforementioned multiple cladding elements, The outer diameter of the first capillary is in the range of 13 μm to 17 μm. The outer diameter of the second capillary is in the range of 8.5 μm to 11.5 μm. Both the first capillary and the second capillary have a thickness in the range of 0.25 μm to 0.35 μm. The hollow core optical fiber according to claim 1 or 2, wherein the angle separating the first line and the second line is in the range of 40 degrees to 120 degrees.

17. The hollow core region has an effective diameter in the range of 26 μm to 32 μm. For each of the aforementioned multiple cladding elements, The outer diameter of the first capillary is in the range of 20 μm to 26 μm. The outer diameter of the second capillary is in the range of 12 μm to 18 μm. Both the first capillary and the second capillary have a thickness in the range of 0.38 μm to 0.48 μm. The hollow core optical fiber according to claim 1 or 2, wherein the angle separating the first line and the second line is in the range of 20 degrees to 120 degrees.

18. The hollow core region has an effective diameter in the range of 31 μm to 37 μm. For each of the aforementioned multiple cladding elements, The outer diameter of the first capillary is in the range of 23 μm to 31 μm. The outer diameter of the second capillary is in the range of 15 μm to 21 μm. Both the first capillary and the second capillary have a thickness in the range of 0.4 μm to 0.6 μm. The hollow core optical fiber according to claim 1 or 2, wherein the angle separating the first line and the second line is in the range of 40 degrees to 110 degrees.

19. The hollow core region has an effective diameter in the range of 50 μm to 56 μm. For each of the aforementioned multiple cladding elements, The outer diameter of the first capillary is in the range of 39 μm to 45 μm. The outer diameter of the second capillary is in the range of 23 μm to 32 μm. Both the first capillary and the second capillary have a thickness in the range of 0.7 μm to 0.9 μm. The hollow core optical fiber according to claim 1 or 2, wherein the angle separating the first line and the second line is in the range of 35 degrees to 110 degrees.

20. The hollow core region has an effective diameter in the range of 22 μm to 28 μm. For each of the aforementioned multiple cladding elements, The outer diameter of the first capillary is in the range of 17 μm to 23 μm. The outer diameter of the second capillary is in the range of 10 μm to 15 μm. Both the first capillary and the second capillary have a thickness in the range of 0.4 μm to 0.6 μm. The hollow core optical fiber according to claim 1 or 2, wherein the angle separating the first line and the second line is in the range of 40 degrees to 110 degrees.

Images