Mode field adapter with ring core structure for low-loss coupling of single-mode and hollow-core optical fibers

Abstract

A mode field adapter and method for coupling single-mode optical fibers to hollow-core optical fibers. The mode field adapter includes a cladding (16), a high-contrast ring (14) surrounded by the cladding, and a low-contrast core (12) surrounded by the ring. The index of refraction of the ring is higher than that of the cladding, and the index of refraction of the core is lower than that of the ring. The mode field adapter further includes a solid-core matching end face, and a hollow- core matching end face operatively coupled by a tapered region. The tapered region has a length and a taper ratio that reduces the cross- sectional dimensions of the mode field adapter along the length such that each of the cladding diameter, the ring diameter, and the first core diameter at the solid-core matching end face is reduced by the taper ratio relative to their respective diameters at the hollow-core matching end face.

Description

Attorney Docket No.: HI25-008_PCT MODE FIELD ADAPTER WITH RING CORE STRUCTURE FOR LOW-LOSS COUPLING OF SINGLE-MODE AND HOLLOW-CORE OPTICAL FIBERSPriority Claim

[0001] This application claims the benefit of priority of U.S. Provisional Patent Application Serial No. 63 / 778,578 filed on March 27, 2025, the content of which is relied upon and incorporated herein by reference in its entirety.Technical Field

[0002] This disclosure relates generally to optical connectivity, and more particularly to an apparatus and method for connecting single-mode optical fibers to hollow-core optical fibers.Background

[0003] Optical fibers are useful in a wide variety of applications, including the telecommunications industry for voice, video, and data transmissions. Benefits of optical fibers include wide bandwidth and low noise operation. Traditional optical fibers include a solid core and a solid cladding that surrounds the core. The core and cladding are typically made of fused silica doped so that the core has a higher index of refraction than the cladding. The core and cladding of the optical fiber are thereby configured to define an optical waveguide that generally confines optical beams propagating through the optical fiber to a region of the optical fiber within and immediately adjacent to the core.

[0004] Hollow-core optical fibers are a relatively new type of optical fiber that guides light through a hollow air-filled core rather than through a solid silica core. The latest hollow-core optical fibers include anti-resonant structures that confine light over a broader range of wavelengths as compared to earlier photonic bandgap hollow-core optical fibers. One type of anti-resonant hollow-core optical fibers are known as nested anti-resonant nodeless fibers (NANF). The anti-resonant structures enable lower-loss transmission over a wider usable wavelength window than previously available from hollow-core optical fibers. Nested anti-resonant nodeless fiber designs have increased the performance of hollow-core optical fibersAttorney Docket No.: HI25-008_PCT to the point where they have become competitive with traditional solid-core optical fibers for long-haul transmission.

[0005] Hollow-core optical fibers operate based on a different physical mechanism than conventional solid-core silica fiber. This mechanism confines optical beams to a central “hollow” region filled with air rather than a doped silica region typical of single-mode optical fibers. Thus, hollow-core optical fiber has an effective index of refraction similar to that of air. As a result, light propagates through hollow-core optical fiber at essentially the same speed as light in vacuum (300,000 km / sec), which is about 50% faster than the speed at which light typically propagates through solid-core optical fiber (200,000 km / s). Thus, hollow-core optical fiber offers significantly reduced latency compared to solid-core optical fiber. Additional advantages of hollow-core optical fiber over solid-core optical fiber include low nonlinearities, reduced dispersion, and a broad transmission wavelength window. The reduced latency of hollow-core optical fibers has been identified as particularly advantageous for interconnecting regional hyperscale data centers over longer distances. Increasing data center demands combined with the low attenuation and low latency provided by hollow-core optical fiber has generated significant interest in using hollow-core optical fiber for building next generation optical networks.

[0006] One problem that continues to impede the use of hollow-core optical fiber is the difficulty in forming connections between hollow-core optical fiber and widely deployed single-mode optical fiber. One problem with coupling hollow-core and single-mode optical fibers is that the mode field diameter of the hollow-core optical fiber is typically much larger than that of single-mode optical fiber. By way of example, the mode field diameter of single-mode optical fiber is typically 8.5-10.5 pm, depending on the wavelength of the optical beam. In contrast, the mode field diameter of a hollow-core optical fiber is typically about 70% of the core diameter, which results in a mode field diameter of about 30 pm in some applications.

[0007] Attempts to match mode field diameters between single-mode optical fibers and anti-resonant hollow-core optical fibers have largely relied on using graded index multimode optical fibers to adjust the size of the mode field. However, mode field adapters made from graded-index multimode fibers tend to be sensitive to the lengthAttorney Docket No.: HI25-008_PCT of the adapter. Graded index lens mode field adapters also commonly fail to address issues that may arise due to mismatches between mode field profiles. The failure of current methods of mode field adaption to address mismatches between the shapes of mode field profiles can also undesirably excite higher order modes in nested anti-resonant nodeless fibers.

[0008] Thus, there is a need in the telecommunications industry for improved mode field adapters for optically coupling anti-resonant hollow-core optical fibers to singlemode optical fibers. More particularly, there is a need for apparatuses and methods of optically coupling anti-resonant hollow-core optical fibers to single-mode optical fibers that compensate for mismatches in both the size and mode field profiles of optical beams between the hollow-core and single-mode optical fibers.Summary

[0009] In one aspect of the disclosure, a mode field adapter for coupling a single-mode optical fiber to an anti-resonant hollow-core optical fiber is disclosed. The mode field adapter includes a cladding having a cladding diameter and a cladding index of refraction, a ring surrounded by the cladding and including a ring diameter and a ring index of refraction higher than the cladding index of refraction, a first core surrounded by the ring and including a first core diameter and first core index of refraction lower than the ring index of refraction, a solid-core matching end face, a hollow-core matching end face, and a tapered region operatively coupling the solid-core matching end face to the hollow-core matching end face. The tapered region includes a length and a taper ratio that reduces the cross-sectional dimensions of the mode field adapter along the length such that each of the cladding diameter, the ring diameter, and the first core diameter at the solid-core matching end face is reduced by the taper ratio relative to their respective diameters at the hollow-core matching end face.

[0010] In one embodiment of the mode field adapter, the first core index of refraction may be higher than the cladding index of refraction.

[0011] In another embodiment of the mode field adapter, the single-mode optical fiber may have a second core with a second core diameter, and the first coreAttorney Docket No.: HI25-008_PCT diameter at the solid-core matching end face may be less than the second core diameter.

[0012] In another embodiment of the mode field adapter, the ring diameter at the solid-core matching end face may be greater than the second core diameter.

[0013] In another embodiment of the mode field adapter, the mode field adapter may further include a length of single-mode optical fiber having a single-mode end face operatively coupled to the solid-core matching end face to define a first optical interface, and a length of anti-resonant hollow-core optical fiber having a hollow-core end face operatively coupled to the hollow-core matching end face to define a second optical interface.

[0014] In another embodiment of the mode field adapter, at least one of the first optical interface and the second optical interface may have a non-zero cleave angle.

[0015] In another embodiment of the mode field adapter, the non-zero cleave angle may be between two and three degrees.

[0016] In another embodiment of the mode field adapter, the anti-resonant hollowcore optical fiber may have an outer diameter, and the cladding diameter at the hollow-core matching end face may match the outer diameter of the anti-resonant hollow-core optical fiber.

[0017] In another embodiment of the mode field adapter, the single-mode optical fiber may have a single-mode cladding diameter, and the taper ratio may match a ratio of the outer diameter of the anti-resonant hollow core optical fiber to the singlemode cladding diameter.

[0018] In another embodiment of the mode field adapter, the mode field adapter may further include a first longitudinal coupling segment operatively coupling the solid-core matching end face to the tapered region, and a length of single-mode optical fiber having a second longitudinal coupling segment. In this embodiment, the first longitudinal coupling segment and the second longitudinal coupling segment may be configured so that the single-mode optical fiber is evanescently coupled to the mode field adapter by the first longitudinal coupling segment and the second longitudinal coupling segment.Attorney Docket No.: HI25-008_PCT

[0019] In another aspect of the disclosure, a method of coupling the single-mode optical fiber to the anti-resonant hollow-core optical fiber is disclosed. The method includes configuring an optical waveguide structure to have the cladding with the cladding diameter and the cladding index of refraction, the ring surrounded by the cladding and having the ring diameter and the ring index of refraction higher than the cladding index of refraction, and the first core surrounded by the ring and having the first core diameter and first core index of refraction lower than the ring index of refraction. The method further includes tapering the optical waveguide structure to define the tapered region including the length and the taper that reduces the cross-sectional dimensions of the optical waveguide structure along the length of the tapered region, and cleaving the optical waveguide structure to define the solid-core matching end face and the hollow-core matching end face operatively coupled to each other by the portion of the tapered region defining the taper ratio. Each of the cladding diameter, the ring diameter, and the first core diameter at the solid-core matching end face is reduced by the taper ratio relative to their respective diameters at the hollow-core matching end face.

[0020] In one embodiment of the method, configuring the optical waveguide structure may include configuring the first core index of refraction to be higher than the cladding index of refraction.

[0021] In another embodiment of the method, the single-mode optical fiber may have the second core with the second core diameter, and configuring the optical waveguide structure may include configuring the first core diameter at the solid-core matching end face to be less than the second core diameter.

[0022] In another embodiment of the method, configuring the optical waveguide structure may include configuring the ring diameter at the solid-core matching end face to be greater than the second core diameter.

[0023] In another embodiment of the method, the method may further include operatively coupling the single-mode end face of the length of single-mode optical fiber to the solid-core matching end face to define the first optical interface, and operatively coupling the hollow-core end face of the length of anti-resonant hollow-Attorney Docket No.: HI25-008_PCT core optical fiber to the hollow-core matching end face to define the second optical interface.

[0024] In another embodiment of the method, cleaving the optical waveguide structure to define the solid-core matching end face and the hollow-core matching end face may include cleaving at least one of the solid-core matching end face and the hollow-core matching end face to have the non-zero cleave angle.

[0025] In another embodiment of the method, the non-zero cleave angle may be between two and three degrees.

[0026] In another embodiment of the method, the anti-resonant hollow-core optical fiber may have an outer diameter, and configuring the optical waveguide structure may include configuring the cladding diameter at the hollow-core matching end face to match the outer diameter of the anti-resonant hollow-core optical fiber.

[0027] In another embodiment of the method, the single-mode optical fiber may have the single-mode cladding diameter, and configuring the optical waveguide structure may include configuring the taper ratio to match the ratio of the outer diameter of the anti-resonant hollow core optical fiber to the single-mode cladding diameter.

[0028] In another embodiment of the method, the method may further include operatively coupling the solid-core matching end face to the tapered region with the first longitudinal coupling segment, operatively coupling the second longitudinal coupling segment to the length of single-mode optical fiber, and evanescently coupling the first longitudinal coupling segment and the second longitudinal coupling segment so that the single-mode optical fiber is evanescently coupled to the optical waveguide structure by the first longitudinal coupling segment and the second longitudinal coupling segment.Brief Description of the Drawings

[0029] 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 description serve to explain principles and operation of the various embodiments. Features andAttorney Docket No.: HI25-008_PCT attributes associated with any of the embodiments shown or described may be applied to other embodiments shown, described, or appreciated based on this disclosure.

[0030] Fig. 1 is a diagrammatic cross-sectional view of a ring-core optical fiber having a low-contrast core, a high-contrast ring, and a cladding.

[0031] Fig. 2 is a graphical view of a mode field profile of the ring-core optical fiber of Fig. 1.

[0032] Fig. 3 is a diagrammatic cross-sectional view of an optical waveguide structure similar to the ring-core optical fiber of Fig. 1 only without the high-contrast ring.

[0033] Fig. 4 is a diagrammatic cross-sectional view of an optical waveguide structure similar to the ring-core optical fiber of Fig. 1 only without the low-contrast core.

[0034] Fig. 5 is a graphical view of the mode field profiles of the optical waveguide structures of Figs. 3 and 4.

[0035] Fig. 6 is a diagrammatic view of a mode field adapter coupling a single mode optical fiber to an anti-resonant hollow-core optical fiber using the optical fiber of Fig. 1 with a tapered region.

[0036] Fig. 7 is a diagrammatic view of the single-mode end face of the singlemode optical fiber of Fig. 6.

[0037] Fig. 8 is a diagrammatic view of a solid-core matching end face of the mode field adapter of Fig. 6.

[0038] Fig. 9 is a diagrammatic view of a hollow-core matching end face of the mode field adapter of Fig. 6.

[0039] Fig. 10 is a diagrammatic view of a hollow-core end face of the anti-resonant hollow-core optical fiber of Fig. 6.

[0040] Fig. 11 is a graphical view of a heat map depicting the fundamental modes for the mode field adapter and the anti-resonant hollow-core optical fiber of Fig. 6.

[0041] Fig. 12 is a graphical view of normalized electric field intensity versus radial distance of the fundamental modes for the mode field adapter and hollow-core optical fiber of Fig. 11.Attorney Docket No.: HI25-008_PCT

[0042] Fig. 13 is a graphical view of loss versus lateral offset for the mode field adapter and anti-resonant hollow-core optical fiber of Figs. 11 and 12.

[0043] Fig. 14 is a graphical view of a heat map depicting the fundamental mode for the mode field adapter and the LPn higher order mode of the anti-resonant hollowcore optical fiber of Fig. 6.

[0044] Fig. 15 is a graphical view of normalized electric field intensity versus radial distance of the fundamental and higher order modes of Fig. 14 showing the overlap between mode field diameters.

[0045] Fig. 16 is a graphical view of loss versus lateral offset for the mode field adapter and anti-resonant hollow-core optical fiber of Figs. 14 and 15.

[0046] Fig. 17 is a diagrammatic view of an alternative embodiment of the mode field adapter of Fig. 6 that uses evanescent coupling between the core regions of the mode field adapter and single-mode optical fiber.

[0047] Fig. 18 is a diagrammatic view of a length of expanded core optical fiber.

[0048] Fig. 19 is a diagrammatic view of a mode field adapter operatively coupling a single-mode optical fiber to an anti-resonant hollow-core optical fiber using the length of expanded core optical fiber of Fig. 18.

[0049] Fig. 20 is a diagrammatic view of a heat map illustrating the fundamental modes for the mode field adapter and the anti-resonant hollow-core optical fiber of Fig. 19.

[0050] Fig. 21 is a graphical view of mode field diameter verses longitudinal position along the expanded core optical fiber of Fig. 18.

[0051] Fig. 22 is a diagrammatic view of an exemplary thermal expansion system configured to fabricate an expanded core optical fiber such as depicted by Fig. 18.

[0052] Fig. 23 is a micrographic view of an optical fiber being processed by the thermal expansion system of Fig. 22.

[0053] Fig. 24 is a graphical view depicting an estimated back reflectance as a function of fiber cleave angle for light traveling across a glass-to-air interface.

[0054] Fig. 25 is a flowchart of an exemplary splicing process that may be used to operatively couple the expanded core optical fiber to the anti-resonant hollow-core optical fiber of Fig. 19.Attorney Docket No.: HI25-008_PCT

[0055] Fig. 26 is a schematic view of an exemplary laser cleaving system that may be used to cleave the optical fibers and couplers of Figs. 6 and 17-19 prior to splicing.Detailed Description

[0056] Various embodiments will be further clarified by examples in the description below. In general, the description relates to a mode field adapter including a tapered ring-core fiber having a relatively large mode field area at one end and a relatively narrow mode field area at the other end. The tapered ring-core structure enables both the size and profile of the mode field to be adapted, thereby improving optical coupling between single-mode and anti-resonant hollow-core optical fibers as compared to mode field adapters lacking this feature. Ring-core adapters use a unique fiber design to expand the mode field diameter of a single-mode optical fiber. The ring-core fiber on which the ring-core adapter is based includes a low-contrast core surrounded by a high-contrast ring, and a cladding that surrounds the high-contrast ring.

[0057] Thermal expansion of the core may also be used to adjust the mode field diameter of standard single-mode optical fibers. Thermal expansion may be used to increase the size of the core and decrease the numerical aperture over a short section of a single-mode fiber. Thermal core expansion may be used to increase the mode field diameter of a single-mode optical fiber to match the mode field diameter of optical fibers having large mode areas, such as anti-resonant hollow-core optical fibers. However, the amount of mode field expansion that can be achieved with thermal core expansion may be limited by the need to maintain confinement of the optical beam.

[0058] Splice loss may be minimized by matching both the mode field diameter and mode field profile between the optical fibers being spliced. The term “mode field profile” refers to the spatial distribution of the electric field intensity of an optical beam propagating through a waveguide. The outer surface of an optical beam that determines the mode field diameter may be defined as the point at which the intensity I of the optical beam has dropped to a predetermined fraction of its on-axisAttorney Docket No.: HI25-008_PCT value, e.g., the radius rfrom the beam axis where lr= e2x / 0and Io is the on-axis intensity value.

[0059] The need to match mode field profiles arises when optically coupling singlemode and anti-resonant hollow-core optical fibers due to the non-Gaussian profile of the fundamental mode in the anti-resonant hollow-core optical fiber. Additional ways to improve mode field matching between the mode field adapter and anti-resonant hollow-core optical fiber may include improving the rotational symmetry of the anti-resonant hollow-core optical fiber or engineering the mode field profile generated by mode field adapters to better match the shape of the fundamental mode supported by the anti-resonant hollow-core optical fiber.

[0060] The ring-core optical fibers disclosed herein facilitate engineering the mode field emitted by the mode field adapter to provide low-loss coupling with anti-resonant hollow-core optical fibers. The additional design flexibility over conventional designs provided by the ring-core structure may enable both the diameter of the cladding and the diameter of mode field at the hollow-core end of the mode field adapter to be matched to the anti-resonant hollow-core optical fiber. Advantageously, matching cladding diameters may produce a mechanically stronger splice with the hollow-core optical fiber than would otherwise be possible. The lowest splice insertion loss between a ring-core optical fiber and anti-resonant hollow-core optical fiber (assuming no transverse offset) is estimated to be about 0.18 dB.

[0061] Embodiments of the ring-core optical fiber support a single guided mode at wavelengths near 1550 nm. This feature helps limit undesirable cross-coupling excitation into higher order modes in the anti-resonant hollow-core optical fiber at the splicing point. Accordingly, the cross-coupling into higher order modes is estimated to be below -100 dB. The ring-core optical fiber may also have a smaller core diameter as compared to mode field adapters made using graded-index optical fiber or thermally expanded core optical fiber. In particular, graded-index optical fibers (e.g., commercially available OM1, OM2, OM3, and OM4 optical fibers) support multiple higher order guided modes due to their large core diameters (e.g., 50.0-62.5 pm). These higher order modes are typically considered undesirable and mayAttorney Docket No.: HI25-008_PCT contribute to signal loss across splices between graded-index and hollow-core optical fibers.

[0062] Thermally expanded core-single-mode optical fiber-based mode field adapters may have certain advantages. One such advantage is that adapters may be made from a standard telecom fiber and do not rely on multimode fiber designs such as graded index optical fiber. Thermally expanded core-single-mode optical fibers also generally satisfy the single-mode cutoff condition (V < 2.405) after heat treatment. Accordingly, the mode field profile of the fundamental mode in optical fibers having thermally expanded cores is generally the same as in a standard single-mode optical fiber, and both optical fibers exhibit single-mode transmission of optical signals. Processes for fabricating thermally expanded core-single-mode optical fibers are also cost-effective and reliable.

[0063] Fig. 1 presents a cross-sectional view of an exemplary ring-core optical fiber 10 including a low-contrast core 12 having an index of refraction m and a core radius n, a high-contrast ring 14 surrounding the core 12 and having an index of refraction r>2 and ring radius r2, and a cladding 16 having an index of refraction m and a cladding radius <3. A graph 18 below the ring-core optical fiber 10 shows the relative indexes of refraction of the core 12, ring 14, and cladding 16. As can be seen, the ring 14 has a higher index of refraction than either the core 12 or cladding 16, and the cladding 16 has an index of refraction below that of both the core 12 and the ring 14. Accordingly, the core 12 has an index of refraction between those of the ring and cladding, such that:m > m > «3 Eqn. 1

[0064] Exemplary values of dimensions and indexes of refraction for the ring-core optical fiber 10 may be n = 5.7 pm, r2 = 10.5 pm, <3 = 130 pm, m = 1.4455, r2 = 1.4460, and m = 1.4450. However, it should be understood that embodiments of the ring-core optical fiber 10 may have different dimensions and indexes of refraction depending on the size and shape of the mode field profiles being matched.Accordingly, embodiments of the ring-core optical fiber 10 are not limited to the exemplary dimensions or indexes of refraction disclosed herein.Attorney Docket No.: HI25-008_PCT

[0065] Fig. 2 depicts a graph 20 and a heat map 22 of the mode field profile of ringcore optical fiber 10. The graph 20 includes a plot 24 of intensity versus radial distance for the fundamental mode of ring-core optical fiber 10. The heat map 22 provides a cross-sectional view of the mode field profile showing its intensity in two-dimensions. Each of the map 22 and plot 24 illustrate the electric field distribution of the fundamental mode for the ring-core optical fiber 10 of Fig. 1. The map 22 and plot 24 of Fig. 2, as well as the additional plots and maps described below, were generated using optical simulation software, e.g., COMSOL Multiphysics® software, which may be obtained from COMSOL, Inc. of Burlington Massachusetts, United States. According to the above numerical modeling, the effective index of refraction neff_oi for the fundamental mode (i.e. , LP01) of ring-core optical fiber 10 with the above characteristics is neff_oi = 1.4453. The next three higher order cladding modes (i.e., the LPn, LP21, and LP02 modes) were determined to have indexes of refraction of neff_n = 1.4449558, neff_2i = 1.4449556, and neff_02 = 1.4449222, respectively.

[0066] Fig. 3 and 4 present cross-sectional views of different optical waveguide structures 26, 28 and corresponding graphs 30, 32. The graphs 30, 32 show the relative indexes of refraction versus radial distance for the optical waveguide structures 26, 28. The radial dimensions n, r2, <3 in Figs. 3 and 4 used to model mode field profiles were assigned the same values as those disclosed above for modeling the exemplary ring-core optical fiber 10 of Fig. 1. The optical waveguide structure 26 of Fig. 3 includes a low-contrast core 12 surrounded by the cladding 16, but without the high-contrast ring 14. For the purpose of modeling optical waveguide structure 26, the index of refraction m of core 12 was set to m = 1.4453 (i.e., m = neff_oi for the ring-core optical fiber 10 of Fig. 1), and the index of refraction m of cladding 16 was set to m = 1.4448. The effective index of refraction neff_oi for the fundamental mode of the optical waveguide structure 26 with the above characteristics was determined to be neff_oi = 1.4447, i.e., slightly lower than for ringcore optical fiber 10. The resulting index delta 21 core — 0.035% of optical waveguide structure 26 is too low to support any core modes. The refractive index delta / Lore may be determined using the following equation,Attorney Docket No.: HI25-008_PCT^core 2 E(jn.2where the reference index of refraction m is provided by the cladding 16.

[0067] The optical waveguide structure 28 of Fig. 4 shows the case where the high-contrast ring 14 is present and has an index of refraction r2 = 1.4456, and the core 12 and cladding 16 have the same index of refraction, e.g., m = m = 1.4448. The effective index of refraction neff_oi for the fundamental mode of optical waveguide structure 28 with the above characteristics was determined to be neff_oi = 1 4451.

[0068] Fig. 5 depicts a graph 34 including a plot 36 of the normalized electric field intensity of the mode of propagation for optical waveguide structure 26, and a plot 38 of the normalized electric field intensity of the mode of propagation for optical waveguide structure 28. As shown by plot 38, the high-contrast ring 14 of optical waveguide structure 28 provides a guided mode having a ring-like structure, e.g., a large mode field diameter with a notch centered on the optical axis. The low-contrast core 12 of optical waveguide structure 26 provides a quasi-Gaussian mode profile with a large mode field diameter. Combining these two fiber geometries produces the mode field profile shown in Fig. 2, which may be described as a flattened Gaussian shape. Thus, the combination of a low-contrast core 12 and high-contrast ring 14 may enable mode field profiles to be engineered with independent control over mode field diameter and shape. By way of example, an embodiment of the ring-core optical fiber 10 having a ring 14 with ring diameter dring = 21 pm (where c / ring = 2xr2) has been shown to support a fundamental mode having a quasiGaussian mode field profile and a mode field diameter of about 30 pm.

[0069] As described above, the mode field diameter of the fundamental mode (C / MF_OI) may be determined where lr= 1 / e2x / 0. Accordingly, using this definition, the intensity at the “edge” of the optical beam is about 13.5% of the beam’s peak intensity. Another way to calculate mode field diameter is to determine the effective area Aeff_oi and then derive an effective mode field diameter deff_oi from the effective area Aeff_oi as follows:(J / |£(x,y)|2dxdy)2eff~01^\E(x,y)\4dxdyqn'Attorney Docket No.: HI25-008_PCT 2 I - ^e / / _oi — Eqn.4

[0070] Numeric modeling of the fundamental mode in the ring-core optical fiber 10 in Fig. 1 predicts a mode field diameter deff_oi ~ 31 pm at 1550 nm. This is similar to the mode field diameter deff_oi ~ 32 pm of the fundamental mode in an anti-resonant hollow-core optical fiber having a core diameter dCOre = 40 pm.

[0071] Low-loss splicing between single-mode optical fibers and anti-resonant hollow-core optical fibers may benefit from meeting one or more of several conditions. These conditions may include matching the size and shape of the fundamental mode fields of the solid and hollow-core optical fibers at the splice, mitigating back-reflection induced loss, and lowering unwanted parasitic crosscoupling into higher order modes (e.g., LPn and LP02) of the anti-resonant hollowcore optical fiber. As described below in more detail, a ring-core fiber having a large mode area may be used as a mode field adapter for matching the mode field distribution of fundamental modes between a standard single-mode fiber and an anti-resonant hollow-core optical fiber.

[0072] Fig. 6 depicts an exemplary mode field adapter 40 for coupling asingle-mode optical fiber 42 to an anti-resonant hollow-core optical fiber 44, e.g., a nested anti-resonant nodeless hollow-core optical fiber. Figs. 7-10 depict cross-sectional views of the mode field adapter 40 (Figs. 8 and 9), the single-mode optical fiber 42 (Fig. 7), and the anti-resonant hollow-core optical fiber 44 (Fig. 10). Each of the mode field adapter 40, single-mode optical fiber 42, and anti-resonant hollowcore optical fiber 44 may include an optical axis 46 and one or more end faces 48a-48d. The mode field adapter 40 may include a tapered region 50 that operatively couples a solid-core matching end face 48a of mode field adapter 40 to a hollowcore matching end face 48b of mode field adapter 40. The tapered region 50 may have a length sufficient to ensure that the taper is adiabatic, i.e. , to ensure the taper is sufficiently gradual to allow the mode field profiles of optical beams propagating through the tapered region 50 to be modified adiabatically.

[0073] In operation, the solid-core matching end face 48a of mode field adapter 40 may be operatively coupled to the single-mode end face 48c of single-mode opticalAttorney Docket No.: HI25-008_PCT fiber 42 to define an optical interface 52 between the mode field adapter 40 and the single-mode optical fiber 42. The hollow-core matching end face 48b of mode field adapter 40 may be operatively coupled to the hollow-core end face 48d of anti-resonant hollow-core optical fiber 44 to define the optical interface 52 between the mode field adapter 40 and the anti-resonant hollow-core optical fiber 44. The optical axes 46 of the mode field adapter 40, single-mode optical fiber 42, and anti-resonant hollow-core optical fiber 44 may be generally aligned with one another at their respective optical interfaces 52. The respective end faces 48a-48d may be operatively coupled using one or more of fusion splicing, mechanical splicing, optical adhesives, butt-coupling, or any other suitable method that enables optical signals to pass through the resulting optical interface 52. Although the optical interface 52 is depicted as being formed using a zero-degree cleaving angle (i.e. , the end faces 48a-48d are normal to the optical axis 46), other cleave angles may be used to reduce back reflection insertion loss. Angle cleaving may be particularly beneficial between the hollow-core matching end face 48b of mode field adapter 40 and the hollow-core end face 48d of anti-resonant hollow-core optical fiber 44.

[0074] Fig. 7 presents a cross-sectional view of the exemplary single-mode optical fiber 42 of Fig. 6. The single-mode optical fiber 42 may include a core 54 that defines the single-mode optical fiber optical axis 46, and a cladding 56 that surrounds the core 54. The core 54 may have a core diameter dCOre_sMF (e.g., dcore_sMF = 9.0 pm) and an index of refraction nCOre_sMF (e.g., nCOre_sMF = 1.4493). The cladding 56 may have a single-mode cladding diameter dciad_sMF (e.g., dciad_sMF = 125 pm) and an index of refraction nciad_sMF such that nciad_sMF < nCOre_sMF (e.g., nciad_sMF = 1.4440). Using the index of refraction nciad_sMF of the cladding 56 as the reference index of refraction, the core 54 in the above example would have a refractive index deltaCore_sMF = 0.36%. The core 54 and cladding 56 may be made of fused silica with at least one of the core 54 and cladding 56 doped to adjust their respective indexes of refraction to achieve a desired refractive index delta. The core 54 and cladding 56 of single-mode optical fiber 42 may thereby work cooperatively to define an optical waveguide that generally confines optical signals propagating through the single-mode optical fiber 42 to a region of the single-mode optical fiberAttorney Docket No.: HI25-008_PCT 42 within and immediately adjacent to the core 54, e.g., having a mode field diameter of about 10.5 pm.

[0075] Fig. 10 presents a cross-sectional view of the anti-resonant hollow-core optical fiber 44 of Fig. 6. The anti-resonant hollow-core optical fiber 44 may include a cladding 60 and a plurality of anti-resonant structures 62, e.g., structural tubes. The cladding 60 may include an inner surface 64 on which the anti-resonant structures 62 are circumferentially arranged to define a hollow-core 66. The depicted embodiment includes six anti-resonant structures 62 each having a nested structure comprising an inner tube and an outer tube. However, it should be understood that the fiber optic coupling systems and methods disclosed herein may be used with anti-resonant hollow-core optical fibers 44 having other numbers of anti-resonant structures 62, as well as anti-resonant structures 62 that comprise a single tube (i.e. , unnested anti-resonant structures) or include more than two nested tubes (e.g., double-nested anti-resonant structures).

[0076] The cladding 60 and anti-resonant structures 62 of anti-resonant hollow-core optical fiber 44 may be formed, for example, of doped or undoped silica glass. The cladding 60 may have an inner diameter CIHCFJD and an outer diameter referred to as the hollow-core outer diameter CIHCF_OD, and the anti-resonant structures 62 may have an outer diameter CIARS- The hollow-core radius me may also be defined as the distance between the optical axis 46 of anti-resonant hollow-core optical fiber 44 and the surface of each anti-resonant structure 62 at the surface’s closest point to the optical axis 46. In the depicted embodiment in which each anti-resonant structure is opposite from another anti-resonant structure, the dimensions of the cladding 60 and anti-resonant structures 62 may be selected so that the hollow-core 66 has a diameter dne = dncFjD - 2 x dARs- The resulting hollow-core radius me may be half the hollow-core diameter dne. The dimensions of the cladding 60 and anti-resonant structures 62 may be selected so that adjacent anti-resonant structures 62 are separated by a gap that prevents adjacent anti-resonant structures 62 from contacting each other, thereby forming a node. Anti-resonant hollow-core optical fibers having anti-resonant structures that do not touch are commonly referred to as “nodeless” optical fibers.Attorney Docket No.: HI25-008_PCT

[0077] The dimensions and other characteristics of the cladding 60 and anti-resonant structures 62 (e.g., the refractive index or indexes) may be selected to define a waveguide that generally confines optical beams propagating through the anti-resonant hollow-core optical fiber 44 to the hollow-core 66 itself. The thicknesses of the walls of the anti-resonant structures 62 may be selected to provide an anti-resonant effect that reduces leakage of optical beams from the hollow-core 66 into the anti-resonant structures 62. This anti-resonant effect may be optimized by providing the anti-resonant structures 62 with a wall thickness that is an odd multiple of a quarter wavelength of the optical beam.

[0078] Figs. 8 and 9 present cross-sectional views of the exemplary mode field adapter 40 proximate to the solid-core matching end face 48a (Fig. 8) and hollowcore matching end face 48b (Fig. 9) thereof. The mode field adapter 40 may be fabricated from a length of ring-core optical fiber 10, such as depicted in Fig. 1.Fabrication may include configuring the ring-core optical fiber 10 to have a mode field profile that matches that of the hollow-core optical fiber 44 and tapering at least a portion of the length to define the tapered region 50 so that the mode field profile at the solid-core matching end face 48a has a mode field profile matching that of the single-mode optical fiber 42. In general, mode field profiles may be considered as matched when the characteristics of the mode field profiles being coupled are such that coupling losses are less than would be experienced without mode field adaption.

[0079] As shown by Fig. 9, the hollow-core matching end face 48b of mode field adapter 40 may include the low-contrast core 12 having the index of refraction m and a core radius n, the high-contrast ring 14 surrounding the core 12 having the index of refraction r2 and a ring radius r2, and the cladding 16 having the index of refraction n3 and a cladding radius <3. The diameter ch of the cladding 16 of mode field adapter 40 at the hollow-core matching end face 48b may be configured to be about the same as the hollow-core outer diameter CIHCF_OD. This similarity in outer diameters between the mode field adapter 40 and hollow-core optical fiber 44 may improve the strength of the splice between the two as compared to optical interfaces 52 between optical fibers having mismatched outer diameters. The dimensions and refractive indexes of the core 12, ring 14, and cladding 16 may be selected independently ofAttorney Docket No.: HI25-008_PCT the cladding diameter ds so that the mode field profile of the mode field adapter 40 at the hollow-core matching end face 48b matches the mode field profile of the hollowcore optical fiber 44.

[0080] Fig. 8 depicts the solid-core matching end face 48a of mode field adapter 40. At the solid-core matching end face 48a, the core 12 may have a core diameter d4, the ring 14 may have a ring diameter cfe, and the cladding 16 may have a cladding diameter ds. The tapered region 50 of mode field adapter 40 may reduce the cross-sectional dimensions of the core 12, ring 14, and cladding 16 at the solidcore matching end face 48a relative their dimensions at the hollow-core matching end face 48b by a taper ratio R. Specifically, the tapering process used to define the tapered region 50 may reduce the core diameter from di to d4, the ring diameter from d2 to ds, and the cladding diameter from ds to ds. In contrast, the refractive indexes of the core 12, ring 14, and cladding 16 may be essentially unchanged by the tapering process. The ratios between the above dimensions may be generally equal to each other and the taper ratio R such that:CZQ CI4 = C 5 = C g = * Eqn.S

[0081] The characteristics of the core 12 (e.g., core diameter d4 and refractive index m) ring 14 (e.g., ring diameter ds and refractive index ns , and cladding 16 (e.g., refractive index ns of mode field adapter 40 may be configured so that the mode field diameter of the mode field adapter 40 at the solid-core matching end face 48a matches (i.e. , is generally the same as) the mode field diameter of single-mode optical fiber 42. As with the hollow-core / mode field adapter interface 52, the cladding diameter ds at the solid-core matching end face 48a may match the singlemode cladding diameter dciad_sMF of single-mode optical fiber 42 (i.e., be generally the same as) to optimize the strength of the splice between the two as compared to optical interfaces 52 between optical fibers having mismatched diameters. Thus, in an embodiment of the mode field adapter 40, the taper ratio R may be set based on the ratio of the hollow-core outer diameter dncF_oD and single-mode cladding diameter dciad_sMF, e.g.Attorney Docket No.: HI25-008_PCT n d'clad SMF „ ,R = — - Eqn.6d-HCF_OD

[0082] Embodiments of the mode field adapter 40 may be fabricated, for example, by drawing a ring-core optical fiber 10 from a suitable preform so that the ring-core optical fiber 10 has dimensions which result in a mode field profile that matches the mode field profile of the hollow-core optical fiber 44. The ring-core optical fiber 10 may then be sectioned, and each section drawn to form a tapered region 50. The draw operation may be stopped while a length of undrawn ring-core optical fiber 10 is joined to the drawn length of the ring-core optical fiber 10 by a necked down region that defines the tapered region 50 of mode field adapter 40.

[0083] The final coupler preform may include the undrawn length of ring-core optical fiber 10 joined to the drawn length thereof by the tapered region 50. The end faces 48a, 48b of mode field adapter 40 may then be defined by cleaving each of the drawn and undrawn lengths of the final coupler preform at an appropriate position along the optical fiber 10. The parameters of each drawing operation may be adjusted to control the shapes and sizes of the core 12, ring 14, and cladding 16 at the solid-core matching end face 48a. Adjustable drawing parameters may include, but are not limited to, drawing speed and temperature.

[0084] The ideal splice loss between the mode field adapter 40 and anti-resonant hollow-core optical fiber 44 may be estimated using the overlap integral q between the two fundamental modes for the situation where there is no mismatch of effective indices of modes, no angular misalignment between optical axes 46, and no longitudinal or lateral offset between optical axes 46. The overlap integral may be determined using Equation 7 below,Iff x E*dA\2tf^dA x ^E^dAEqn’7where Ei and E2 represent the mode field profiles of the optical waveguides being coupled to one another. A non-zero lateral offset di_os, longitudinal gap D, or tilt angle 0 between the optical waveguides before splicing may introduce additional splicing loss. Another potential contributor to splice loss may be caused byAttorney Docket No.: HI25-008_PCT transmission loss due to Fresnel back-reflection between two material interfaces of air and glass at the splice interface.

[0085] Figs. 11-13 depict results of computer modeling showing the mode profile electric field distribution of the LP01 -I ike fundamental mode in mode field adapter 40 and the LPoi-like fundamental mode in anti-resonant hollow-core optical fiber 44. Fig. 11 depicts a bifurcated heat map 70 depicting the fundamental mode (LP01) for the mode field adapter 40 (left side 72) and the anti-resonant hollow-core optical fiber (right side 74). Fig. 12 depicts a graph 80 including plots 82, 84 of normalized electric field intensity versus radial distance of the fundamental modes (LP01) for the mode field adapter 40 (plot 82) and hollow-core optical fiber 44 (plot 84) showing the overlap of mode field diameter. Fig. 13 depicts a graph 90 including a plot 92 of loss versus lateral offset di_os along an x-axis for the mode field adapter 40 and anti-resonant hollow-core optical fiber 44 from Figs. 11 and 12, e.g., for a cartesian coordinate frame in which the optical axis 46 is aligned with the z-axis. The minimum splice loss was calculated to be ~0.18dB where each of the lateral offset di_os, longitudinal gap D, and tilt angle 0 are zero.

[0086] Loss due to Fresnel back- reflection may be estimated as about 0.15 dB using the effective indexes of refraction of the fundamental modes in the respective optical waveguides, which are neff_oi = 0.999 for the anti-resonant hollow-core optical fiber and neff_oi = 1.4452 for the ring-core optical fiber. The back reflection related loss may be mitigated by applying anti-reflection coating or using angle cleaving before splicing, for example. The estimated minimum loss of 0.18 dB may be attributed to mismatch of the mode field profile and mode field symmetry between the fundamental modes of the mode field adapter 40 and anti-resonant hollow-core optical fiber 44.

[0087] One challenge with optically coupling the single-mode optical fiber 42 to the anti-resonant hollow-core optical fiber 44 is mitigating parasitic cross-coupling (i.e., excitation) of higher order modes in the anti-resonant hollow-core optical fiber 44. In theory, the anti-resonant hollow-core optical fibers can be designed to have a very large loss differential between the LP01 fundamental mode (e.g., a loss of less than 0.1 dB / km) and LPn higher order mode (e.g., a loss of greater than 10 dB / km), e.g.,Attorney Docket No.: HI25-008_PCT with optical signal to noise ratios of about 20 to 30 dB, or greater. In practice, the anti-resonant hollow-core optical fiber 44 may not always have a high optical signal to noise ratio. Moreover, even with an optical signal to noise ratio of 20 dB, there may still be power fluctuations of + / - 2.5% beyond the optical interface 52 due to multipath interference between the LP01 and LPn modes in the anti-resonant hollowcore optical fiber 44.

[0088] Figs. 14-16 depict estimated parasitic cross-coupling using the overlap integral between the fundamental mode (LP01) of the mode field adapter 40 and higher order mode (LPn) of the anti-resonant hollow-core optical fiber 44. Fig. 14 depicts a bifurcated heat map 100 depicting the fundamental mode (LP01) for the mode field adapter 40 (left side 102) and a higher order mode (LPn) of the anti-resonant hollow-core optical fiber (right side 104). Fig. 15 depicts a graph 110 including plots 112, 114 of normalized electric field intensity versus radial distance of the fundamental mode (LP01) for the mode field adapter 40 (plot 112) and a higher order mode (LPn) for the hollow-core optical fiber 44 (plot 114) showing the overlap of mode field diameters. Fig. 16 depicts a graph 120 including a plot 122 of loss versus lateral offset di_os for the mode field adapter 40 and anti-resonant hollow-core optical fiber 44 from Figs. 14 and 15 along the x-axis. As can be seen from plot 122, the parasitic cross-coupling into the LPn mode of anti-resonant hollow-core optical fiber 44 may be maintained below -30 dB for transverse offsets below 0.5 pm, e.g., di_os 0.5 pm. This result is comparable with mode field adapters that use a graded index optical fiber to adapt the mode fields between single-mode optical fiber 42 and anti-resonant hollow-core optical fiber 44.

[0089] Fig. 17 depicts an alternative embodiment of the mode field adapter 40 in which the optical interface 52 between the mode field adapter 40 and the singlemode optical fiber 42 uses evanescent coupling between the core regions of the mode field adapter 40 and single-mode optical fiber 42. In this embodiment, each of the mode field adapter 40 and single-mode optical fiber 42 may include a respective longitudinal coupling segment 124, 126. The longitudinal coupling segment 124 of mode field adapter 40 may extend from the solid-core end face 48a to the tapered region 50 of mode field adapter 40. The longitudinal coupling segment 126 of singleAttorney Docket No.: HI25-008_PCT mode optical fiber 42 may extend from the single-mode end face 48c to a main portion of single-mode optical fiber 42. Each of the longitudinal coupling segments 124, 126 may be defined by tapering the mode field adapter 40 or single-mode optical fiber 42, respectively, to define a longitudinal segment 124, 126 having desired cross-sectional dimensions. The cross-sectional dimensions of the longitudinal coupling segment 124, 126 may be selected so that the segments can be placed relative to each other in such a manner that their respective core regions run parallel along a predetermined coupling length lc and at a predetermined radial distance dR.

[0090] Optical beams propagating through the mode field adapter 40 and singlemode optical fiber 42 may be coupled across the optical interface 52 due to evanescent field coupling when the radial distance dR is within a minimum distance and the coupling length lc is sufficient to achieve full coupling at the radial distance dp. To reduce the radial distance dR, portions of the cladding 16, 56 of one or both of the mode field adapter 40 and single-mode optical fiber 42 may be removed, or the taper ratios used to define the longitudinal coupling segments 124, 126 may be adjusted. When the radial distance dR is small enough to allow evanescent coupling between the core regions of mode field adapter 40 and single-mode optical fiber 42, energy may be transferred therebetween due to interaction of evanescent optical fields of the mode field adapter 40 and single-mode optical fiber 42. Typical radial distances may be in the range of dR = 2-20 pm, and corresponding coupling lengths may be in the range of lc = 2-12 mm. The longitudinal coupling coefficient may depend on both the radial distance dR and coupling length lc- Radial distances and coupling lengths that provide desired coupling coefficients may be determined using numerical techniques and computer modeling.

[0091] Longitudinal surface optical fiber coupling may reduce the sensitivity of coupling efficiency to alignment errors between the optical fibers and can thus provide relatively high tolerance to misalignment. Alignment error tolerance in a coupled mode system may be larger than in a butt-coupled system because the electromagnetic energy oscillates from one core region to another longitudinally along the coupling length. The length of this oscillation may increase as the radialAttorney Docket No.: HI25-008_PCT distance dp between the two core regions increases. If the radial distance dp between the core regions is large enough, optical energy may oscillate slowly along the coupling region. Accordingly, the coupling coefficient for evanescent coupling may be relatively insensitive to alignment imperfections.

[0092] Another type of optical fiber that may be used to adapt mode fields is known as thermally expanded core-single-mode optical fiber, referred to herein as simply “expanded core optical fiber”. Expanded core optical fiber may be used, for example, to increase the mode field diameter of an optical beam, e.g., from nominal value of about 9.2 pm up to as much as 40 pm. To thermally expand a germanium doped core of a single-mode optical fiber, the optical fiber may be heated so that the germanium atoms of a GeC dopant in the SiC>2 core are diffused out into the cladding. This diffusion may produce an expanded core cross section as well as alter the core’s index of refraction due to the dopant being distributed into a larger volume. Accordingly, the refractive index delta 21 of the optical fiber may decrease as the diameter of the core is increased.

[0093] The above relationship between core size and refractive index delta of thermally expanded core-single-mode optical fiber may result in the normalized frequency V (also called the V number) remaining unchanged. The normalized frequency 1 / for a step-index optical fiber may be determined by,2naV = ——NA Eqn.8Awhere a is the fiber core radius, A is the free space wavelength of the optical beam, and NA is the numerical aperture of the optical fiber. The numerical aperture may be determined by,NA = Jn^ore- nc2ladEqn.9where nCOre is the refractive index along the optical axis.

[0094] The single-mode condition may be maintained through the thermal expansion process because the normalized frequency 1 / of the expanded core-single-mode optical typically remains less than 2.405 during heat treatment. Thus, the optical mode field distribution in the expanded core optical fiber at the expanded-Attorney Docket No.: HI25-008_PCT core end may be the same as the fundamental mode of the single-mode optical fiber at the unexpanded-core end, e.g., d / MF_oi = 10.4 pm at A = 1550 nm.

[0095] Fig. 18 depicts a length of expanded core optical fiber 130 including a core 54 and a cladding 56 surrounding the core 54. The expanded core optical fiber 130 may include an unexpanded end face 48e operatively coupled to an expanded end face 48f by a tapered region 132. The core 54 may be thermally expanded sufficiently, for example, to provide a mode field diameter at the expanded end face 48f that matches the mode field diameter of the anti-resonant hollow-core optical fiber 44. As can be seen from the graphs 134, 136 showing the index of refraction of the core region versus radial distance from the optical axis 46 at respective end faces 48e, 48f, the expanded core optical fiber 130 may have a step-index like refractive index profile at the unexpanded end face 48e, and a more parabolic shape at the expanded end face 48f. This change in the refractive index profile may be due to the thermal treatment causing core dopants to diffuse out of the core 54 and into the cladding 56, thereby depleting dopants in the outer portions of the core 54.

[0096] Fig. 19 depicts an embodiment of the mode field adapter 40 comprising the length of expanded core optical fiber 130 of Fig. 18. The unexpanded end face 48e may be spliced (e.g., fusion spliced) to the end face 48c of single-mode optical fiber 42, and the expanded end face 48f may be spliced (e.g., fusion spliced) to the end face 48d of anti-resonant hollow-core optical fiber 44. Each of the splices may define a respective optical interface 52. Although not shown in Fig. 19, angle cleaving may be used to reduce back reflection insertion loss at one or more of the interfaces 52.

[0097] Fig. 20 depicts a bifurcated heat map 140 generated by computer modeling of the mode field adapter 40 of Fig. 19. The map 140 illustrates the fundamental mode (LP01) for the mode field adapter 40 (left side 142) and the anti-resonant hollow-core optical fiber 44 (right side 144). The mode field diameter of the mode field adapter 40 may be configured to match the mode field diameter of the anti-resonant hollow-core optical fiber 44, which may be about 30 pm.

[0098] The mode profiles of the fundamental modes in the expanded core optical fiber 130 and anti-resonant hollow-core optical fiber 44 having a hollow-coreAttorney Docket No.: HI25-008_PCT diameter dnc = 40 m were numerically modeled using optical simulation software. Fig. 21 depicts a graph 150 depicting experimental results for core expansion of standard single-mode optical fiber having a mode field diameter of 10.4 pm at a wavelength of = 1550 nm. The graph 150 is a scatter plot of mode field diameter verses longitudinal position, where the horizontal axis denotes distance from the untreated portion of the optical fiber. The simulation results indicate the expanded core optical fiber 130 can be made with a mode field diameter that matches the mode field diameter of the anti-resonant hollow-core optical fiber 44. The expanded core optical fiber 130 may need to be cleaved at a specific position, as indicated by the dashed line 151, in order to match the mode field diameter. Thus, the amount of mode field diameter expansion may be adjusted by changing the position of the cleave.

[0099] Fabrication of the expanded core optical fiber 130 may involve heating a portion of an optical fiber having a relatively small core diameter (e.g., a standard single-mode optical fiber having a core diameter dCOre = 8.2 pm) to a temperature sufficient to cause the core dopants to diffuse into the cladding. Heat treatment may be provided using an arc discharge or CO2 laser based fusion fiber splicer, or using a gas burner fused biconic taper setup.

[0100] Fig. 22 depicts an exemplary thermal expansion system 152 including one or more gas burners 153 (e.g., two H2-O2 burners), and left and right stages 154 each including a respective chuck 156 configured to hold an optical fiber, e.g., a single-mode optical fiber 42. Gas flow rates in the burners 153 may be adjusted to transfer a sufficient amount of heat to radially diffuse dopants from the core 54 to the cladding 56 of optical fiber 42. This diffusion of dopants may enlarge the core 54 without altering the external diameter of the optical fiber 42. The amount of diffusion may be controlled by adjusting one or more of the amount of time heat is applied, the oscillation velocity of the burners 153, and the temperature of the flame.

[0101] Fig. 23 presents an image of a single-mode optical fiber 42 undergoing a thermal expansion process in which the optical fiber 42 is heated from above and below by gas burners 153. The gas burners may be positioned at a radial distance dR_HEAT from the optical fiber 42 (e.g., dR_HEATa1.000 ± 0.016 mm) and configured toAttorney Docket No.: HI25-008_PCT heat the fiber along a longitudinal distance di__HEAT (e.g., di__HEAT ~ 3.175 mm).During the thermal expansion process, the optical fiber 42 may be kept straight over the length of the expanded core region to avoid any bend associated losses. As indicated by graph 150 of Fig. 21, the expanded core region may have a length of 1.0-1.5 mm.

[0102] Fig. 24 depicts a graph of estimated back reflectance as a function of fiber cleave angle for light propagating across a glass-to-air interface. A high level of back reflection can cause unwanted feedback to the source, resulting in increased noise and reduced performance, e.g., degraded bit error rates. Back reflection from a standard single-mode optical fiber 42 may be reduced by introducing an angled cleave to the end face 48c. A typical cleave angle is about eight degrees, which reduces the back reflection into the optical fiber from an air interface to about -60 dB. However, cleave angles other than zero degrees may cause the mode field to exit the end face 48c of a single-mode optical fiber 42 at an angle to the optical axis.

[0103] When a single-mode optical fiber 42 is operatively coupled to an anti-resonant hollow-core optical fiber 44, cleave angles may introduce coupling loss due to this angle. Thus, there may be an optimum cleave angle for the expanded core optical fiber 130 that balances losses due to reflection with losses due to the tilt angle introduced by the cleave angle. In practice, it may be advantageous to have a non-zero cleave angle at the optical interface 52 between the anti-resonant hollowcore optical fiber 44 and expanded core optical fiber 130 to reduce back-reflections. The optimum cleave angle may be determined as the angle that provides an optimal combination of back-reflection reduction and minimum degradation of splice loss. It has been determined that a cleave angle of 2-3 degrees between a solid core fiber and a hollow-core fiber optimizes these competing requirements.

[0104] As shown by the graph of Fig. 24, a cleave angle of two degrees provides a back reflection of about -55 dB at 1550 nm for the thermally expanded core-single-mode optical fiber 130 described above. For a mode field diameter of 30 pm, the amount of back reflection was calculated using the overlap integral between forward propagating mode and the back reflected mode as a result of the Fresnel reflection at a fiber-air interface. A step index profile was used for this calculation. BecauseAttorney Docket No.: HI25-008_PCT thermally expanding the core typically changes the core doping profile from a stepindex to a graded index, actual back reflection performance is expected to be better than predicted.

[0105] Fig. 25 depicts an exemplary splicing process 160 for operatively coupling an expanded core optical fiber 130 to an anti-resonant hollow-core optical fiber 44. In block 162, the process 160 may remove the coatings from a length of single-mode optical fiber. The process may then proceed to block 164 and thermally expand the core of the single-mode optical fiber, e.g., by exposing a portion of the optical fiber to heat. In block 166, the process 160 may cleave the expanded-core optical fiber at a position where the mode field diameter thereof is about the same as that of the anti-resonant hollow-core optical fiber to which it is being mated. The cleaving process may be configured to produce an end face with an angle, e.g., a two degree cleave angle. The process 160 may then proceed to block 168 and insert the cleaved end of the expanded-core optical fiber into an alignment tube. The alignment tube may have a length and inner diameter configured to prevent twisting of the expanded core optical fiber.

[0106] In block 170, the process 160 may remove the coating from theanti-resonant hollow-core optical fiber. Once the coating has been removed, the process 160 may proceed to block 172 and cleave the anti-resonant hollow-core optical fiber. The cleaving process may be configured to define an end face with the same cleave angle as the expanded core optical fiber, e.g., a flat (i.e. , zero degree) or two degree cleave angle. The process 170 may then insert the cleaved end face of the anti-resonant hollow-core optical fiber into the other side of the alignment tube. The placement (i.e., position and orientation) of each of the expanded-core optical fiber and the anti-resonant hollow-core optical fiber inside the alignment tube may be controlled using stages to minimize coupling loss and reduce the effect of back reflection. The optical fibers may be placed within the alignment tube so that they are essentially butt coupled. In response to the optical fibers being properly placed within the alignment tube, the process 160 may proceed to block 176, and seal the ends of the alignment tube, e.g., using LIV curable optical epoxy. In an embodiment of the process 160, the alignment tube may include funnel-shaped openings at eachAttorney Docket No.: HI25-008_PCT end thereof to receive a coated portion of each optical fiber. Advantageously, the funnel-shaped openings may contribute to a robust splice.

[0107] In an alternative embodiment of the splicing process 160, after cleaving the expanded core optical fiber in block 166, the cleaved end face of the expanded core optical fiber may be spliced to anti-resonant hollow-core optical fiber using a fusion splicer. In this embodiment, a suitable splice protector may be used.

[0108] Optical fibers may be cleaved by scoring the outer surface of the optical fiber surface with a fiber cleaving tool, e.g., a diamond cutter. This scoring may introduce a crack in the surface that, in response to application of a tensile force, results in a clean break in the optical fiber. Typically, this produces a flat, perpendicular end face on the optical fiber having a zero degree cleave angle, i.e. , an end face normal to the optical axis of the optical fiber.

[0109] Obtaining a non-zero cleave angle may require a more specialized cleaving process. For example, a precision laser cleaver may be used to control the cleave angle by controlling the interaction of a laser beam with the optical fiber. Laser cleaving may offer a number of advantages over mechanical cleaving. The use of a focused laser beam may enable higher precision and accuracy than mechanical cleaving. The high precision and accuracy may enable more precise cleaving angles and less chance of damage to the optical fiber. Laser cleaving may also contribute to reduced material waste due to its precision, making it a more economical choice than mechanical cleaving. Moreover, the laser cleaving process may be more readily automated than mechanical cleaving, offering high repeatability and flexibility, which may be beneficial for mass production.

[0110] Fig. 26 depicts an exemplary laser cleaving system 180 including a laser 182, an optical system 184, a staging and imaging system 186, and a controller 188. The laser 182 may include a CO2 laser system for cleaving and polishing optical fibers. To create a controlled heat-affected zone, a circular laser beam 190 generated by the laser 182 may be converted into a laser beam 192 having a different shape by the optical system 184. To this end, the optical system 184 may include one or more lenses or a lens system 194. The staging and imaging system 186 may include a stage 196 that positions an optical fiber 198 being cleaved, andAttorney Docket No.: HI25-008_PCT an imager 200 that provides magnified images of the end face of the optical fiber 198. The controller 188 may be in communication with the laser(s) 182, stage 196, and imager 200, and the controller 188 may be configured to control the cleaving process. During the cleaving process, heat from the laser beam 192 may be localized within the optical fiber 198. This localized heating may prevent the laser beam 192 from altering the physical and optical properties of the optical fiber 198 as it is cleaved.

[0111] While the present disclosure has been illustrated by the description of specific embodiments thereof, and while the embodiments have been described in considerable detail, it is not intended to restrict or in any way limit the scope of the appended claims to such detail. The various features discussed herein may be used alone or in any combination within and between the various embodiments.Additional advantages and modifications will readily appear to those skilled in the art. The present disclosure in its broader aspects is therefore not limited to the specific details, representative apparatus and methods and illustrative examples shown and described. Accordingly, departures may be made from such details without departing from the scope of the present disclosure.

Claims

Attorney Docket No.: HI25-008_PCT What is claimed is:

1. A mode field adapter for coupling a single-mode optical fiber to an anti-resonant hollow-core optical fiber, comprising:a cladding including a cladding diameter and a cladding index of refraction; a ring surrounded by the cladding and including a ring diameter and a ring index of refraction higher than the cladding index of refraction;a first core surrounded by the ring and including a first core diameter and first core index of refraction lower than the ring index of refraction;a solid-core matching end face;a hollow-core matching end face; anda tapered region operatively coupling the solid-core matching end face to the hollow-core matching end face,wherein the tapered region includes a length and a taper ratio that reduces cross-sectional dimensions of the mode field adapter along the length such that each of the cladding diameter, the ring diameter, and the first core diameter at the solidcore matching end face is reduced by the taper ratio relative to their respective diameters at the hollow-core matching end face.

2. The mode field adapter of claim 1 , wherein the first core index of refraction is higher than the cladding index of refraction.

3. The mode field adapter of claim 1 or 2, wherein the single-mode optical fiber has a second core with a second core diameter, and the first core diameter at the solid-core matching end face is less than the second core diameter.

4. The mode field adapter of claim 3, wherein the ring diameter at the solid-core matching end face is greater than the second core diameter.Attorney Docket No.: HI25-008_PCT 5. The mode field adapter of any of claims 1-4, further comprising:a length of single-mode optical fiber having a single-mode end face operatively coupled to the solid-core matching end face to define a first optical interface, anda length of anti-resonant hollow-core optical fiber having a hollow-core end face operatively coupled to the hollow-core matching end face to define a second optical interface.

6. The mode field adapter of claim 5, wherein at least one of the first optical interface and the second optical interface has a non-zero cleave angle.

7. The mode field adapter of claim 6, wherein the non-zero cleave angle is between two and three degrees.

8. The mode field adapter of any of claims 1-7, wherein the anti-resonant hollowcore optical fiber has an outer diameter, and the cladding diameter at the hollow-core matching end face matches the outer diameter of the anti-resonant hollow-core optical fiber.

9. The mode field adapter of claim 8, wherein the single-mode optical fiber has a single-mode cladding diameter, and the taper ratio matches a ratio of the outer diameter of the anti-resonant hollow-core optical fiber to the single-mode cladding diameter.

10. The mode field adapter of any of claims 1-9, further comprising:a first longitudinal coupling segment operatively coupling the solid-core matching end face to the tapered region; anda length of single-mode optical fiber having a second longitudinal coupling segment,wherein the first longitudinal coupling segment and the second longitudinal coupling segment are configured so that the single-mode optical fiber isAttorney Docket No.: HI25-008_PCT evanescently coupled to the mode field adapter by the first longitudinal coupling segment and the second longitudinal coupling segment.

11. A method of coupling a single-mode optical fiber to an anti-resonant hollowcore optical fiber, comprising:configuring an optical waveguide structure to include a cladding having a cladding diameter and a cladding index of refraction, a ring surrounded by the cladding and including a ring diameter and a ring index of refraction higher than the cladding index of refraction, and a first core surrounded by the ring and including a first core diameter and first core index of refraction lower than the ring index of refraction;tapering the optical waveguide structure to define a tapered region including a length and a taper that reduces cross-sectional dimensions of the optical waveguide structure along the length of the tapered region; andcleaving the optical waveguide structure to define a solid-core matching end face and a hollow-core matching end face operatively coupled to each other by at least a portion of the tapered region defining a taper ratio,wherein each of the cladding diameter, the ring diameter, and the first core diameter at the solid-core matching end face is reduced by the taper ratio relative to their respective diameters at the hollow-core matching end face.

12. The method of claim 11 , wherein configuring the optical waveguide structure includes configuring the first core index of refraction to be higher than the cladding index of refraction.

13. The method of claim 11 or 12, wherein the single-mode optical fiber has a second core with a second core diameter, and configuring the optical waveguide structure includes configuring the first core diameter at the solid-core matching end face to be less than the second core diameter.Attorney Docket No.: HI25-008_PCT 14. The method of claim 13, wherein configuring the optical waveguide structure includes configuring the ring diameter at the solid-core matching end face to be greater than the second core diameter.

15. The method of any of claims 11-14, further comprising:operatively coupling a single-mode end face of a length of single-mode optical fiber to the solid-core matching end face to define a first optical interface; and operatively coupling a hollow-core end face of a length of anti-resonant hollow-core optical fiber to the hollow-core matching end face to define a second optical interface.

16. The method of claim 15, wherein cleaving the optical waveguide structure to define the solid-core matching end face and the hollow-core matching end face includes cleaving at least one of the solid-core matching end face and the hollowcore matching end face to have a non-zero cleave angle.

17. The method of claim 16, wherein the non-zero cleave angle is between two and three degrees.

18. The method of any of claims 11-17, wherein the anti-resonant hollow-core optical fiber has an outer diameter, and configuring the optical waveguide structure includes configuring the cladding diameter at the hollow-core matching end face to match the outer diameter of the anti-resonant hollow-core optical fiber.

19. The method of claim 18, wherein the single-mode optical fiber has a singlemode cladding diameter, and configuring the optical waveguide structure includes configuring the taper ratio to match a ratio of the outer diameter of the anti-resonant hollow core optical fiber to the single-mode cladding diameter.Attorney Docket No.: HI25-008_PCT 20. The method of any of claims 11-19, further comprising:operatively coupling the solid-core matching end face to the tapered region with a first longitudinal coupling segment;operatively coupling a second longitudinal coupling segment to a length of single-mode optical fiber; andevanescently coupling the first longitudinal coupling segment and the second longitudinal coupling segment so that the single-mode optical fiber is evanescently coupled to the optical waveguide structure by the first longitudinal coupling segment and the second longitudinal coupling segment.

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