Anti-resonant hollow-core fiber and corresponding manufacturing method

Abstract

A novel design of hollow-core fiber is proposed comprising an outer cladding (1) having an inner surface and an inner cladding region (2) bounded by the inner surface, the inner cladding region comprising a plurality of anti-resonant modules distributed without touching each other around the longitudinal axis of the hollow-core fiber to define a hollow-core region (3). The anti-resonant modules comprise each at least two tubular elements (21, 22) embedded on two distinct levels, the lower-level tubular element being embedded inside the preceding upper-level tubular element and arranged in cross-section to be tangent at two points of the module in a tangential direction of the hollow-core fiber, only the first-level tubular element contacting the inner surface of the outer cladding.

Description

[0001] Anti-resonant hollow-core fiber and corresponding manufacturing method

[0002] Technical field

[0003] The invention relates to hollow-core optical fibers, in particular anti-resonant optical fibers. More particularly, the invention relates to a new design for hollow-core optical fiber, featuring enhanced optical properties.

[0004] The invention is especially, but not exclusively, suited to single-mode hollow-core optical fibers operating at telecom wavelengths.

[0005] Hollow-core fibers have many potential applications, such as long-distance data transmission, high-power beam guiding and delivery, gas-based non-linear optics, sensing and various laser applications.

[0006] Prior art

[0007] Hollow-core optical fibers are promising to guide light with very low optical attenuation and reduced latency because the light is guided in air or gas instead of in a solid material. Depending on the physical mechanism of light guidance, there are two main types of hollow-core fibers: "photonic bandgap fibers" and "anti-resonance fibers".

[0008] As indicated in Francesco Poletti's Publication "Nested antiresonant nodeless hollow core fiber" Optics Express Vol. 22, Issue 20, pp. 23807-23828 (2014), anti-resonant hollow-core fibers can achieve lower attenuation over a broader transmission spectrum than photonic bandgap fibers.

[0009] Traditionally, an anti-resonant hollow-core fiber comprises an outer cladding, which defines an inner cladding surface, and an inner cladding region bounded by the inner surface. The inner cladding region comprises multiple anti-resonant elements arranged, without touching, around the longitudinal axis of the fiber to define a hollow-core region. These anti-resonant elements extend along the longitudinal axis of the fiber, their walls contacting the inner cladding surface. Patent documents No EP3152607B1, No EP3766843A1 disclose well-known examples of configurations of nested anti-resonant tubular elements.

[0010] These anti-resonant elements (which are evenly distributed around the hollow-core region) act as a resonant cavity, reflecting the incident light and guiding it through the fiber core by making coupling of core and cladding modes anti-resonant. Such an inhibited coupling between core and cladding modes leads to low attenuation, broad transmission spectrum and low latency in data transmission. However, even with the use of anti-resonant structures, current fiber designs do not allow certain limits to be exceeded: two particular drawbacks of conventional anti-resonant hollow-core fibers are the leaky nature of the core modes, which makes very difficult the conception of low-loss single-mode, bend-insensitive anti-resonant hollow-core fiber and limitation in manufacturing thereof, in particular fabricating the anti- resonant elements at specific azimuthal locations in a sufficient stable and reproducible manner.

[0011] With the gradual development of telecommunications and the increasing requirements for high- capacity data transmission applications, there is therefore a real need to provide an enhanced hollowcore fiber structure, and in particular, a novel hollow-core fiber design that features an ultra-efficient single-mode operation and low sensitivity to bending over a wide range of bending radii in order to further improve optical transmission.

[0012] Goals of the invention

[0013] The invention, in at least one embodiment, is aimed especially at overcoming the drawbacks of the prior art. More specifically, at least one goal of at least one embodiment of the invention is to provide a hollow-core fiber that exhibits: a Fundamental Mode (FM) attenuation lower than ldB / km at telecom wavelengths, especially at wavelength of 1550 nm; a Fundamental Mode (FM) macro-bend loss lower than 0.1 dB for 100 turns at a bend radius of 30 mm at telecom wavelengths, especially at wavelength of 1550 nm; a Fundamental Mode (FM) macro-bend loss lower than 1 dB / turn at a bend radius of 10 mm at telecom wavelengths, especially at wavelength of 1550 nm; a Higher-Order Mode (HOM) extinction factor greater than 50, even greater than 100 at telecom wavelengths, especially at wavelength of 1550 nm.

[0014] Summary of the invention

[0015] According to a first aspect, the present invention relates to a hollow-core fiber comprising an outer cladding having an inner surface and an inner cladding region bounded by the inner surface, the inner cladding region comprising a plurality of anti-resonant modules distributed without touching each other around the longitudinal axis of the hollow-core fiber to define a hollow-core region. The hollowcore fiber is characterized by the fact that the anti-resonant modules comprise each at least two tubular elements embedded on at least two distinct levels, the lower-level tubular element being embedded inside the preceding upper-level tubular element and arranged in cross-section to be tangent at two points of said module in a tangential direction of said hollow-core fiber, only the first-level tubular element contacting the inner surface of the outer cladding. Thus, the invention proposes a hollow-core fiber design based on a novel configuration of tubular elements embedded on multiple levels and arranged around the central core region to enhancethe confinement of the fundamental mode of the core while decreasing the HOMs guidance. Contrary to prior art hollow-core fibers, the anti-resonant modules feature a multilevel settle configuration so that embedded elements touch only at two points of contact of the modules in a tangential direction of the fiber, so as to create a greater number of anti-resonant reflection surfaces oriented to allow to further reduce confinement losses. Indeed, contrary to prior art hollow-core fiber designs providing only one reflection surface per anti-resonant module (contact point at the inner surface of cladding), the embedding structure proposed by the present invention allows the fiber to exhibit at least two additional reflection surfaces per anti-resonant module without need for additional embedded elements, making inhibited coupling between core and cladding modes much more efficient.

[0016] According to a particular feature, at least one lower-level tubular element has a different cross- sectional geometry to that of the preceding upper-level tubular element, a preceding upper-level tubular element of said at least two embedded tubular elements having a circular cross-sectional geometry

[0017] According to a particular feature, the cross-sectional geometry belongs to the group comprising elliptical geometry, oval geometry and circular geometry. Thus, different cross-sectional shapes can be considered offering a wide range of design possibilities.

[0018] According to a first approach, the anti-resonant modules each consist of embedded first-level and second-level tubular elements, the second-level tubular element being embedded inside the first-level tubular element, which has an elliptical cross-sectional geometry or an oval cross-sectional geometry cross-sectional geometry. This first approach is thus based on a single embedded structure.

[0019] According to a second approach, the anti-resonant modules each consist of first-, second- and third-level embedded tubular elements, the third-level tubular element being embedded inside the second-level tubular element which is itself embedded inside the first-level tubular element, which has an elliptical cross-sectional geometry, or oval cross-sectional geometry. This second approach is thus based on a double embedded structure.

[0020] According to a first embodiment consistent with the first approach, said embedded first-level and second-level tubular elements are defined as follows: the first-level tubular element has an elliptical cross-sectional geometry defined by an ellipticity el, a major axis radius Rtubel arranged in radial direction of the hollow-core fiber and a minor axis radius Rtube2 arranged in tangential direction of the hollow-core fiber, such as:

[0021] Rtubel = (2 x sin(n / N) x Rcore - g) / (2 x (l - sin(n / N)))

[0022] Rtube2 = Rtubel x ^ / (l — el2) where: N is an integer, with N > 2, corresponding to the number of anti-resonant modules comprised in the inner cladding region,

[0023] Rcore is the hollow-core region radius defined as the smallest distance between the center of the hollowcore fiber and the outer edge of the first-level tubular elements, the second-level tubular element has a circular cross-sectional geometry defined by a first radius Rtube3 arranged in radial direction of the hollow-core fiber and a second radius Rtube4 arranged in tangential direction of the hollow-core fiber, such as:

[0024] Rtube3 = Rtube4 = Rtubel x ^ / (l — el2)

[0025] The structural parameters are chosen for optimized low-loss single-mode operation. The inventors determined that with such an anti-resonant element design, the hollow-core fiber obtained has significant reduced loss compared to known fiber designs.

[0026] According to a second embodiment consistent with the first approach, said embedded first-level and second-level tubular elements are defined as follows: the first-level tubular element has a circular cross-sectional geometry a first radius Rtubel' arranged in radial direction of the hollow-core fiber and a second radius Rtube2' arranged in tangential direction of the hollow-core fiber, such as:

[0027] Rtube2' = Rtubel' = (2 x sin(n / N') x Rcore' — g') / (2 x (1 — sin(n / N'))) the second-level tubular element has an elliptical cross-sectional geometry defined by an ellipticity e2, a major axis radius Rtube3' arranged in tangential direction of the hollow-core fiber and a minor axis radius Rtube4' arranged in radial direction of the hollow-core fiber, such as: where:

[0028] N' is an integer, with N' > 2, corresponding to the number of anti-resonant modules comprised in the inner cladding region,

[0029] Rcore' is the hollow-core region radius defined as the smallest distance between the center of the hollowcore fiber and the outer edge of the first-level tubular elements, g' is the azimuthal distance between two adjacent first-level tubular elements.

[0030] The structural parameters are chosen for optimized low-loss single-mode operation. This second embodiment is particularly advantageous in that it provides a contribution of the anti-resonant surface of the first-level tubular at efficiently reflecting back the fundamental mode of the core, which has a circular shape. This leads to an even more efficient anti-resonance effect compared to known fiber designs.

[0031] According to a third embodiment consistent with the second approach, said first-, second- and third-level embedded tubular elements are defined as follows: the first-level tubular element has an elliptical cross-sectional geometry defined by an ellipticity el", a first major axis radius Rtubel" arranged in the radial direction of the hollow-core fiber and a first minor axis radius Rtube2' arranged in said tangential direction of the hollow-core fiber, such as: where:

[0032] N" is an integer, with N > 2, corresponding to the number of tubular elements comprised in the inner cladding region,

[0033] Rcore" is the hollow-core region radius defined as the smallest distance between the center of the hollow-core fiber and the outer edge of the first-level tubular elements, g" is the azimuthal distance between two adjacent first-level tubular elements, the second-level tubular element has a circular cross-sectional geometry defined by a first radius Rtube3" arranged in the radial direction of the hollow-core fiber and a second radius Rtube4" arranged in said tangential direction of the hollow-core fiber, such as: the third-level tubular element has an elliptical cross-sectional geometry defined by an ellipticity e3, a second minor axis radius Rtube5 arranged in radial direction of the hollow-core fiber and a second major axis radius Rtube6 arranged in tangential direction of the hollow-core fiber, such as:

[0034] The structural parameters are chosen for optimized low-loss single-mode operation. The inventors determined that with such an anti-resonant element design, the hollow-core fiber obtained has significant reduced loss compared to known fiber designs.

[0035] According to a fourth embodiment consistent with the second approach, said first-, second- and third-level embedded tubular elements are defined as follows: the first-level tubular element has a circular cross-sectional geometry, a first radius Rtubel'" arranged in radial direction of the fiber and a second radius Rtube2"' arranged in tangential direction T of the fiber, such as:

[0036] Rtube2"' = Rtubel'" = (2 x sin(n / N'") x Rcore'" — g'") / (2 x (1 — sin(n / N'"))) the second-level tubular element has an elliptical cross-sectional geometry defined by an ellipticity e2'", a major axis radius Rtube3"' arranged in tangential direction T of the fiber and a minor axis radius Rtube4"' arranged in radial direction R of the hollow-core fiber, such as:

[0037] Rtube3'" = Rtubel'" = (2 x sin(n / N'") x Rcore'" — g'") / (2 x (1 — sin(n / N'"))) the third-level tubular element has an elliptical cross-sectional geometry defined by an ellipticity e3'", a major axis radius Rtube5"' arranged in tangential direction T of the fiber and a minor axis radius Rtube6"' arranged in radial direction R of the hollow-core fiber, such as: where:

[0038] N'" > 2,

[0039] Rcore'", the hollow-core region radius defined as the smallest distance between the center of the hollowcore fiber and the outer edge of the first-level tubular elements around the hollow-core region; g'", the smallest azimuthal distance between two adjacent first-level tubular elements.

[0040] Advantageously, said at least two embedded tubular elements have a thickness in the range [0.3 pm - 1.2 pm], an azimuthal distance-to-thickness ratio in the range [2 - 13] and at least one of said at least two embedded tubular elements have an ellipticity in the range [0.30 - 0.95],

[0041] In accordance with the first embodiment, said at least two embedded tubular elements have a thickness in the range [0.3 pm - 0.8 pm], an azimuthal distance-to-thickness ratio in the range [2 - 5] and in which said first level tubular elements have an ellipticity in the range [0.6 - 0.8],

[0042] In accordance with the second embodiment, said at least two embedded tubular elements have a thickness in the range [0.3 pm - 0.8 pm], an azimuthal distance-to-thickness ratio in the range [6-13] and in which said second level tubular elements have an ellipticity in the range [0.8 - 0.9],

[0043] In accordance with the third embodiment, said at least three embedded tubular elements have a thickness in the range [0.3 pm - 0.8 pm], an azimuthal distance-to-thickness ratio in the range [2 - 5] and in which said first level tubular elements have an ellipticity in the range [0.6 - 0.95] and in which said third level tubular elements have an ellipticity in the range [0.5 - 0.8],

[0044] In accordance with the fourth embodiment, said at least three embedded tubular elements have a thickness in the range [0.3 pm - 0.8 pm], an azimuthal distance-to-thickness ratio in the range [6 - 13] and in which said second level tubular elements have an ellipticity in the range [0.8 - 0.9] and in which said third level tubular elements have an ellipticity in the range [0.5 - 0.7],

[0045] The geometric configuration retained according to any one of the above embodiments combined with these structural parameter ranges guaranties the hollow-core fiber an ultra-low-loss single-mode transmission operating. It should be noted that the second, third and fourth embodiments described above have the common feature that the anti-resonant modules each comprise a preceding upper-level tubular element having a circular cross-sectional geometry.

[0046] According to a second aspect, the invention relates to an optical transmission system comprising at least one hollow-core fiber as described her above according to the first aspect of the invention in any of its embodiments.

[0047] According to a third aspect, the invention relates to a method for manufacturing a hollow-core fiber as described her above according to the first aspect of the invention in any of its embodiments, the method comprising the following steps: providing a plurality of anti-resonant module tubes and a hollow cladding tube; attaching the anti-resonant module tubes to an inner surface of the cladding tube in a distributed manner; heating and drawing the set of tubes comprising the cladding tube and the anti-resonant module tubes until the outer cladding and the anti-resonant modules meet predefined dimensions.

[0048] Figures

[0049] Other features and advantages of the invention will become clearer on reading the following description, given merely as an illustrative and non-limiting example, and of the appended drawings, among which:

[0050] Fig 1 depicts a cross-sectional schematic view of a hollow-core optical fiber according to a first embodiment of the invention;

[0051] Fig 2 depicts a cross-sectional schematic view of a hollow-core optical fiber according to a second embodiment of the invention;

[0052] Fig 3 depicts a cross-sectional schematic view of a hollow-core optical fiber according to a third embodiment of the invention;

[0053] Fig 4 depicts a cross-sectional schematic view of a hollow-core optical fiber according to a fourth embodiment of the invention;

[0054] Fig 5 is a schematic diagram of an optical transmission system equipped with a hollow-core fiber according to the invention;

[0055] Fig 6 is a flowchart of a particular embodiment of the manufacturing method according to the invention; Fig 7 and Fig 8 graphically depicts confinement loss of fundamental mode (FM) and extinction factor of higher-optical modes (HOMs) of an exemplary hollow-core fiber consistent with the first embodiment as a function of wavelength; Fig 9 graphically depicts confinement loss of fundamental mode (FM) as a function of wavelength for different values of core radii of hollow-core fibers consistent with the first embodiment;

[0056] Fig 10 and Fig 11 graphically depicts confinement loss of fundamental mode (FM) and extinction factor of higher-optical modes (HOMs) of an exemplary hollow-core fiber consistent with the second embodiment as a function of wavelength;

[0057] Fig 12 graphically depicts confinement loss of fundamental mode (FM) as a function of bend radii of hollow-core fiber consistent with the second embodiment;

[0058] Fig 13 graphically depicts confinement loss of fundamental mode (FM) as a function of wavelength for different values of core radii of hollow-core fibers consistent with the second embodiment;

[0059] Fig 14 and Fig 15 graphically depicts confinement loss of fundamental mode (FM) and extinction factor of higher-optical modes (HOMs) of an exemplary hollow-core fiber consistent with the third embodiment as a function of wavelength.

[0060] Detailed description of the invention

[0061] On the figures in this document, identical elements are designated by a same numerical reference. The components in the figures are not necessarily to scale, emphasis instead being placed upon illustrating the principle of the invention. To make the figures easier to read, the various planes and axes are shown in dotted lines.

[0062] The general principle of the present invention relies on an enhanced structure for low-loss hollowcore fiber based on a re-thought embedding configuration of the anti-resonant cladding elements for improving capacity of single-mode optical transmission.

[0063] In the following, the principle of the invention is presented in three specific embodiments based on an elliptical-circular embedded hollow-core fiber particularly well suited to low-loss single-mode transmission: the first and second embodiments rely on single embedded element arrangements in relation to figures 1 and 2, while the third and fourth embodiments rely on a double embedded element arrangement in relation to figure 3 and figure 4.

[0064] Figure 1 depicts an anti-resonant hollow-core optical fiber HCF1 according to a first embodiment of the invention. The hollow-core fiber HCF1 has the general form of a waveguide extending along a longitudinal axis L, which corresponds to the axis of signal propagation. The hollow-core fiber HCF1 comprises an outer cladding 1 extending along a longitudinal axis and having a tubular inner surface defining an internal volume, a central hollow-core region 3 and an inner cladding region 2 arranged around the central hollow core region 3 and inside the internal volume and extending along the longitudinal axis L. The inner cladding region 2, which is bounded by the outer cladding inner surface comprises a set of six anti-resonant reflection modules lOa-lOf distributed without touching each other around longitudinal axis L of the hollow-core fiber to define the hollow-core region 3 of radius 'Rcore'. As shown in the figure, the anti-resonant modules lOa-lOf are regularly distributed around the hollow-core region 3 at azimuthal positions defined according to a uniform distance (called hereafter azimuthal distance 'g') so as to form a six-fold symmetry.

[0065] The anti-resonant modules lOa-lOf of fiber HCF1 comprises each two anti-resonant tubular elements embedded on two distinct levels: a second-level tubular element 12, which has a circular cross- sectional geometry, is embedded inside a first-level tubular element 11, which has an elliptical cross- sectional geometry, and arranged in cross-section to be tangent at two points of the module in a tangential direction T of fiber HCF1. These two points (or "nodes") are referred to Pl and P2 for the anti- resonant module 10a (shown here as an illustrative example). The first- and second-level tubular elements 11-12 have substantially equal and uniform wall thicknesses t and only the first-level tubular element 11 contacts the inner surface of the outer cladding 2. The first-level tubular element 11 is characterized by a major axis arranged along radial direction R of the fiber and by a minor axis arranged along tangential direction T of the fiber, both directions intersecting at the center O of the module 10a (which is also the center of tubular elements 11 and 12).

[0066] The hollow-core fiber shown in figure 1 contains six anti-resonant modules as an illustrative example, but the first embodiment is not restricted to that specific example and a larger or smaller number of anti-resonant modules can be provided without departing from the invention.

[0067] More generally, considering a number N of anti-resonant modules included in the inner cladding region, the structural parameters of an embedded structure according to the first embodiment are defined as follows (for a given anti-resonant module): the first-level tubular element has an elliptical cross-sectional geometry defined by an ellipticity el, a major axis radius Rtubel arranged in radial direction R of the fiber and a minor axis radius Rtube2 arranged in tangential direction T of the fiber, such as:

[0068] Rtubel = (2 x sin(n / N) x Rcore — g) / (2 x (1 — sin(n / N)))

[0069] Rtube2 = Rtubel x ^ / (l — el2) with:

[0070] N > 2;

[0071] Rcore, the hollow-core region radius defined as the smallest distance between the center of the hollowcore fiber and the outer edge of the first-level tubular elements around the hollow-core region; g, the smallest azimuthal distance between two adjacent first-level tubular elements. the second-level tubular element has a circular cross-sectional geometry defined by a first radius Rtube3 arranged in radial direction R and a second radius Rtube4 arranged in tangential direction T, such as:

[0072] Rtube3 = Rtube4 = Rtubel x ^ / (l — el2) the first- and second-level tubular elements are tangent at two points of the module in said tangential direction T of the fiber.

[0073] In other words, Rtubel is half the longest distance between the outer edges of the first-level tubular element in radial direction R of the fiber, Rtube2 is half the longest distance between the outer edges of the first-level tubular element in tangential direction T of the fiber, Rtube3 is half the longest distance between the outer edges of the second-level tubular element in radial direction R of the fiber, and Rtube4 is half the longest distance between the outer edges of the second-level tubular element in tangential direction T of the fiber.

[0074] Exemplary structure parameters of embedded element modules are presented hereafter: a value of wall thickness t of first- and second-level tubular elements comprised in the range 0.3 - 1.2 pm, and more particularly in the range 0.3 - 0.8 pm, and even more particularly in the range 0.4 - 0.5 pm; a value of azimuthal distance-to-thickness ratio g / t in the range 2 - 13, and more particularly in the range 2-5 , a value of ellipticity el in the range 0.30 - 0.95, and more particularly in the range 0.5 - 0.95, and even more particularly in the range 0.60 - 0.80, for the tubular element having an elliptical cross section.

[0075] The hollow-core fiber HCF1 has a value of Rcore comprised between 15 and 25 pm, and more particularly between 17 and 20 pm.

[0076] An exemplary hollow-core fiber consistent with the first embodiment and having the following structural features shows an efficient single-mode operation, exhibiting low confinement loss, especially at wavelength of 1550 nm: Rcore = 20 pm, N = 6, t = 0.47 pm, = 3, el = 0.635, e2 = 0, ncore= 1, nciaddin5= 1,45. Graphics of figures 7 and 8 depict FM confinement losses (expressed in dB / m) and HOM extinction factor exhibiting by such exemplary hollow-core fiber as a function of wavelength (expressed in pm). HOM extension factor is the ratio of HOM attenuation over FM attenuation. As shown on these graphs, this example of fiber HCF1 exhibits significant reduced confinement losses at 1550 nm, with a FM attenuation less than around 1 dB / km and HOM extension factor greater than 100.

[0077] Graphic of figure 9 depicts FM confinement loss (expressed in dB / m) as a function of wavelength (expressed in pm) for different values of core radii (curves referred A, B, C) of hollow-core fibers consistent with the first embodiment and having the following structural features: N = 3, el = 0.225, e2 = 0, ncore= 1, nciadding= 1,45. This graphic shows the impact of hollow-core region radius, delimited by the ring of anti-resonant modules, on FM confinement loss. Three core radii have been tested: 15 pm (curve A), 18 pm (curve B) and 20 pm (curve C). The inventors found that the fiber having a Rcore of 20 pm corresponds to the best compromise between the confinement loss and the HOM extinction factor at 1550 nm.

[0078] Figure 2 depicts an anti-resonant hollow-core optical fiber HCF2 according to a second embodiment of the invention. Hollow-core fiber HCF2 differs from hollow-core fiber HCF1 in that the inner cladding region 2 comprises a set of six anti-resonant reflection modules 20a-20f each consisting of two tubular elements embedded on two distinct levels: a second-level tubular element 22 of elliptical cross- sectional geometry which is embedded inside a first-level tubular element 21 of circular cross-sectional geometry. The first- and second-level tubular elements 21-22 are arranged in cross-section to be tangent at two points (nodes) Pl'-P2' of the anti-resonant module in tangential direction T of fiber HCF2. The firstand second-level tubular elements 21-22 have substantially equal and uniform wall thicknesses t' and only the first-level tubular element 21 contacts the inner surface of the outer cladding 2. The second-level tubular element 22 is characterized by a minor axis arranged along radial direction R of the fiber and by a major axis arranged along tangential direction T of the fiber, both directions intersecting at the center O of the module 20a.

[0079] Thus, as with fiber HCF1, fiber HCF2 comprises a set of six anti-resonant modules uniformly distributed without touching each other at the inner circumference of outer cladding according to sixfold symmetry, each consisting of two anti-resonant tubular elements embedded on two distinct levels (i.e. according to a single embedded-element configuration) but differs from fiber HCF1 in that, for each module, the elliptical tubular element 22 is embedded within the circular element 21.

[0080] This second embodiment is particularly advantageous because the configuration of anti-resonant elements 21-22 allows to provide increased negative curvature at the core region boundary as well as an anti-resonant multi-reflection configuration, all without compromising core size. This leads to further increased fundamental mode confinement while encouraging escape of higher-mode modes, as the core mode undergoes stronger inhibited coupling with the cladding modes residing in the inner cladding region.

[0081] Compared to the HCF1 fiber design, it has been observed an even more significant reduction of modal dispersion (PMD) and losses as the circular surface expels back better the light field inside the core. The hollow-core fiber shown in figure 2 contains six anti-resonant modules as an illustrative example, but the second embodiment is not restricted to that specific example and a larger or smaller number of anti-resonant modules can be provided without departing from the invention.

[0082] More generally, considering a number N' of anti-resonant modules included in the inner cladding region, the structural parameters of an embedded structure according to the second embodiment are defined as follows (for a given anti-resonant module): the first-level tubular element has a circular cross-sectional geometry, a first radius Rtubel' arranged in radial direction R of the fiber and a second radius Rtube2' arranged in tangential direction T of the fiber, such as:

[0083] Rtube2' = Rtubel' = (2 x sin(n / N') x Rcore' — g') / (2 x (1 — sin(n / N'))) the second-level tubular element has an elliptical cross-sectional geometry defined by an ellipticity e2', a major axis radius Rtube3 arranged in tangential direction T of the fiber and a minor axis radius Rtube4 arranged in radial direction R of the hollow-core fiber, such as: where:

[0084] N' > 2

[0085] Rcore', the hollow-core region radius defined as the smallest distance between the center of the hollowcore fiber and the outer edge of the first-level tubular elements around the hollow-core region; g', the smallest azimuthal distance between two adjacent first-level tubular elements.

[0086] In other words, for a given anti-resonant module, Rtubel' is half the longest distance between the outer edges of the first-level tubular element in radial direction R of the fiber, Rtube2' is half the longest distance between the outer edges of the first-level tubular element in tangential direction T of the fiber, Rtube3' is half the longest distance between the outer edges of the second-level tubular element in radial direction R of the fiber, Rtube4' is half the longest distance between the outer edges of the second-level tubular element in tangential direction T of the fiber.

[0087] Exemplary structure parameters of embedded element modules are presented hereafter: a value of wall thickness t' of first- and second-level tubular elements comprised in the range 0.3 - 1.2 pm, and more particularly in the range 0.3 - 0.8 pm, and even more particularly in the range 0.4 - 0.5 pm; a value of azimuthal distance-to-thickness ratio g' / t' in the range 2 - 13, and more particularly in the range 6 -13; a value of ellipticity e2' in the range 0.30 - 0.95, and more particularly in the range 0.8 - 0.90, , for the tubular element having an elliptical cross section. The hollow-core fiber HCF2 has a value of Rcore comprised between 15 and 25 pm, and more particularly between 17 and 20 pm.

[0088] An exemplary hollow-core fiber in accordance with the second embodiment and having the following structural features shows an efficient single-mode operation, exhibiting low confinement loss, especially at wavelength of 1550 nm: Rcore' = 17 pm, N' = 5, t = 0.47 pm, ® / , = 12, e2' = 0.87, el' = 0 / ncore=1 / nciadding = 1,45. Graphics of figures 10 and 11 depict FM confinement losses (expressed in dB / m) and HOM extinction factor exhibiting by such exemplary hollow-core fiber as a function of wavelength (expressed in pm). HOM extension factor is the ratio of HOM attenuation over FM attenuation. As shown on these graphs, this example of fiber exhibits significant reduced confinement losses at 1550 nm, with a FM attenuation between 0,1 and 1 dB / km and HOM extension factor greater than 100. Graphic of figure 12 depicts FM bend loss (in dB / turn) obtained for different bend radii of the exemplary hollow-core fiber at wavelength of 1550 nm. For a bend radius of 10 mm, FM macro-bend loss of 0.076 dB / turn is obtained for this fiber.

[0089] Graphic of figure 13 depicts FM confinement loss (expressed in dB / m) as a function of wavelength (expressed in pm) for different values of core radii (curves referred D, E, F) of hollow-core fibers consistent with the second embodiment and having the following structural features: N' = 5, t' = 0.47 pm, ® / , = 12, e2' = 0.87, el' = 0, ncore= 1, nciadding= 1,45. This graphic shows the impact of hollow-core region radius, delimited by the ring of anti-resonant modules, on FM confinement losses. Three core radii have been tested: 17 pm (curve D), 16 pm (curve E) and 15 pm (curve F). The inventors found that the fiber having a Rcore of 17 pm corresponds to the best compromise between the confinement loss and the HOM extinction factor at 1550 nm.

[0090] Figure 3 depicts an anti-resonant hollow-core optical fiber HCF3 according to a third embodiment of the invention. Hollow-core fiber HCF3 differs from fibers HCF1 and HCF2 in that the tubular elements of which the anti-resonant modules are made are arranged according to a double embedded-element configuration.

[0091] The inner cladding region 2 of fiber HCF3 comprises a set of six anti-resonant reflection modules 30a-30f each consisting of three tubular elements embedded at three distinct levels: the third-level tubular element 33, which has an elliptical cross-sectional geometry, is embedded inside the preceding second-level tubular element 32, which has a circular cross-sectional geometry, itself embedded inside the preceding first-level tubular element 31, which has an elliptical cross-sectional geometry. The first-, second-, third-level tubular elements 31-32-33 are arranged in cross-section to be tangent at two points (nodes) Pl"-P2" of the anti-resonant module in tangential direction T of fiber HCF3. The first-, second-, third-level tubular elements 31-32-33 have substantially equal and uniform wall thicknesses t". The first-tubular element 31 is characterized by a major axis arranged along radial direction R of the fiber and by a minor axis arranged along tangential direction ? of the fiber, both directions intersecting at the center O of the module 30a. While the third-tubular element 33 is characterized by a minor axis arranged along radial direction R of the fiber and by a major axis arranged along tangential direction T of the fiber.

[0092] Thus, as with fibers HCF1 and HCF2, the hollow-core fiber according to this third embodiment comprises a set of six anti-resonant modules uniformly distributed without touching each other at the inner cladding surface according to six-fold symmetry but differs in that each of the anti-resonant modules comprises three tubular elements embedded on three distinct levels.

[0093] The hollow-core fiber shown in figure 3 contains six anti-resonant modules as an illustrative example, but the third embodiment is not restricted to that specific example and a larger or smaller number of anti-resonant modules can be provided without departing from the invention, it being understood that the overall anti-resonant structure must be symmetrical to allow uniform guiding of light along the fiber axis.

[0094] More generally, considering a number N" of anti-resonant modules included in the inner cladding region, the structural parameters of an embedded structure according to the third embodiment are defined as follows (for a given anti-resonant module): the first-level tubular element has an elliptical cross-sectional geometry defined by an ellipticity el", a first major axis radius Rtubel" arranged in the radial direction of the hollow-core fiber and a first minor axis radius Rtube2' arranged in said tangential direction of the hollow-core fiber, such as: with: N" > 2,

[0095] Rcore", the hollow-core region radius defined as the smallest distance between the center of the hollowcore fiber and the outer edge of the first-level tubular elements around the hollow-core region; g", the smallest azimuthal distance between two adjacent first-level tubular elements. the second-level tubular element has a circular cross-sectional geometry defined by a first radius Rtube3" arranged in the radial direction of the hollow-core fiber and a second radius Rtube4" arranged in said tangential direction of the hollow-core fiber, such as: the third-level tubular element has an elliptical cross-sectional geometry defined by an ellipticity e3, a second minor axis radius Rtube5 arranged in the radial direction of the hollow-core fiber and a second major axis radius Rtube6 arranged in said tangential direction of the hollow-core fiber, such as:

[0096] In other words, for a given anti-resonant module, Rtubel" is half the longest distance between the outer edges of the first-level tubular element in radial direction R of the fiber; Rtube2" is half the longest distance between the outer edges of the first-level tubular element in tangential direction T of the fiber; Rtube3" is half the longest distance between the outer edges of the second-level tubular element in radial direction R of the fiber; Rtube4" is half the longest distance between the outer edges of the second-level tubular element in tangential direction T of the fiber; Rtube5 is half the longest distance between the outer edges of the third-level tubular element in radial direction R of the fiber; Rtube6 is half the longest distance between the outer edges of the third-level tubular element in tangential direction T of the hollow core fiber.

[0097] Exemplary structure parameters of embedded element modules are presented hereafter: a value of wall thickness t" of first-, second- and third-level tubular elements comprised in the range 0.3 - 1.2 pm, and more particularly in the range 0.3 - 0.8 pm, and even more particularly in the range 0.4 - 0.5 pm; a value of azimuthal distance-to-thickness ratio g" / t" in the range 2 - 13, and more particularly in the range 2-5, a value of ellipticity e in the range 0.30 - 0.95 for the tubular elements having an elliptical cross section, and more particularly a value of ellipticity el"in the range 0.6 - 0.95 for the first-level tubular elements and a value of ellipticity e3 in the range 0.5 - 0.80 for the third-level tubular elements.

[0098] The hollow-core fiber HCF3 has a value of Rcore comprised between 15 and 25 pm, and more particularly between 15 and 20 pm.

[0099] An exemplary hollow-core fiber in accordance with the third embodiment and having the following structural features shows an efficient single-mode operation, exhibiting low confinement loss, especially at wavelength of 1550 nm: Rcore = 20 pm, N = 6, t = 0.47 pm, = 3, el" = 0.635, e2" = 0, e3 = 0.800 ncore= 1, nciadding= 1,45. Graphics of figures 14 and 15 depict FM confinement losses (expressed in dB / m) and HOM extinction factor exhibiting by such exemplary hollow-core fiber as a function of wavelength (expressed in pm). HOM extension factor is the ratio of HOM attenuation over FM attenuation. As shown on these graphs, this example of fiber exhibits significant reduced confinement losses at 1550 nm, with a FM attenuation next to 0,1 dB / km and HOM extension factor greater than 100. Figure 4 depicts an anti-resonant hollow-core optical fiber HCF4 according to a fourth embodiment of the invention. As for fiber HCF3, this hollow-core fiber HCF4 has tubular elements arranged according to a double embedded-element configuration.

[0100] The inner cladding region 2 of fiber HCF4 comprises a set of six anti-resonant reflection modules 40a-40f each consisting of three tubular elements embedded at three distinct levels: the third-level tubular element 43, which has an elliptical cross-sectional geometry, is embedded inside the preceding second-level tubular element 42, which has an elliptical cross-sectional geometry, itself embedded inside the preceding first-level tubular element 41, which has a circular cross-sectional geometry. The first-, second-, third-level tubular elements 41-42-43 are arranged in cross-section to be tangent at two points (nodes) P1"'-P2"' of the anti-resonant module in tangential direction T of fiber HCF4. The first-, second-, third-level tubular elements 41-42-43 have substantially equal and uniform wall thicknesses t'".

[0101] The second- and third-tubular element 42-43 are both characterized by a major axis arranged along tangential direction T of the fiber and by a minor axis arranged along radial direction R of the fiber, both directions intersecting at the center O of the module 40a. As for fibers HCF1 and HCF2, this hollowcore fiber HCF4 comprises a set of six anti-resonant modules uniformly distributed without touching each other at the inner cladding surface according to six-fold symmetry but differs in that each of the anti- resonant modules comprises three tubular elements embedded on three distinct levels.

[0102] The hollow-core fiber shown in figure 4 contains six anti-resonant modules as an illustrative example, but the fourth embodiment is not restricted to that specific example and a larger or smaller number of anti-resonant modules can be provided without departing from the invention.

[0103] More generally, considering a number N'" of anti-resonant modules included in the inner cladding region, the structural parameters of an embedded structure according to the fourth embodiment are defined as follows (for a given anti-resonant module): the first-level tubular element has a circular cross-sectional geometry, a first radius Rtubel'" arranged in radial direction R of the fiber and a second radius Rtube2"' arranged in tangential direction T of the fiber, such as:

[0104] Rtube2"' = Rtubel'" = (2 x sin(n / N'") x Rcore'" — g'") / (2 x (1 — sin(n / N'"))) the second-level tubular element has an elliptical cross-sectional geometry defined by an ellipticity e2'", a major axis radius Rtube3"' arranged in tangential direction T of the fiber and a minor axis radius Rtube4"' arranged in radial direction R of the hollow-core fiber, such as: the third-level tubular element has an elliptical cross-sectional geometry defined by an ellipticity e3'", a major axis radius Rtube5"' arranged in tangential direction T of the fiber and a minor axis radius Rtube6"' arranged in radial direction R of the hollow-core fiber, such as: with:

[0105] N'" > 2,

[0106] Rcore'", the hollow-core region radius defined as the smallest distance between the center of the hollowcore fiber and the outer edge of the first-level tubular elements around the hollow-core region; g'", the smallest azimuthal distance between two adjacent first-level tubular elements.

[0107] Exemplary structure parameters of embedded element modules are presented hereafter: a value of wall thickness t" of first-, second and third-level tubular elements comprised in the range 0.3 - 1.2 pm, and more particularly in the range 0.3 - 0.8 pm, and even more particularly in the range 0.4 - 0.5 pm; a value of azimuthal distance-to-thickness ratio g" / t" in the range 2 - 13, and more particularly in the range 6 -13 a value of ellipticity e in the range 0.30 - 0.95 for the tubular elements having an elliptical cross section, and more particularly a value of ellipticity e2'" in the range 0.8 - 0.90 for the second level tubular elements and a value of ellipticity e3'" in the range 0.5 - 0.8 for for the third level tubular elements.

[0108] The hollow-core fiber HCF4 has a value of Rcore comprised between 15 and 25 pm, and more particularly between 15 and 20 pm.

[0109] The anti-resonant elements discussed above (in any one of embodiments described here) refer to any hollow wave-guiding elements extending along the length of the hollow-core fiber and circumferentially arranged around longitudinal axis of the fiber to reflect the incident light and guide it by anti-resonant reflection through the hollow-core region. The anti-resonance elements are uniformly distributed tubes with substantially equal and uniform wall thicknesses so as to create the desired antiresonance effects. They can have a polygonal cross-section among elliptical, oval or circular geometry, provided that the lower-level tubular element is arranged in cross-section to be tangent at two points of the considered module in tangential direction of the fiber. The anti-resonant elements are preferably made of glass, in particular silica, but can be made of a plastic material (polymer or composite or a crystalline material suitable for anti-resonant guiding. The anti-resonant elements are empty (air) or filled like gas or liquid, e. g. like the hollow-core region. An even number of anti-resonant elements, e. g. 4 or 6, or an odd number of anti-resonant elements, e. g. 3 or 5, can be provided, which is arranged with an even or odd-numbered symmetry delimiting the hollow-core region.

[0110] Figure 5 schematically illustrates an example of an optical transmission system equipped with an anti-resonant hollow-core fiber according to the invention. In that example, the optical transmission system comprises a data transmitter Tx, a data receiver Rx and at least one hollow-core optical fiber OF according to one of the previously described embodiments, which is connected between the transmitter Tx and receiver Rx and adapted for high-capacity data transmission, e.g. in a Passive Optical Network. Such a transmission system can also comprise other equipment necessary for system operation (not shown on the figure), such as multiplexer / multiplexer, optical modulator, connector, photodetector, etc.

[0111] Figure 6 schematically illustrates the main steps of manufacturing a hollow-core fiber according to a particular embodiment of the invention.

[0112] In step SI ("STR"), a plurality of glass anti-resonant module tubes and a glass hollow cladding tube are provided. To that end, a glass large hollow-core tube is stretched to form so called capillaries (e.g. capillaries have a diameter of approximately 1 to few mm and a length of approximately 1 m or more). These capillaries will form the antiresonance elements of the fibers.

[0113] In step S2 ("ATT"), the anti-resonant module tubes are attached to an inner surface of the cladding tube in a distributed manner. To that end, the glass capillaries are inserted into a first hollow cladding tube, which is larger than glass capillaries, then they are welded, for example, one by one on the inner surface of the cladding tube, in order to form a large scale of the fiber structure. The term "distributed" refers to a contactless arrangement of glass capillaries around longitudinal axis of the structure.

[0114] In step S3 ("DRW"), the cladding tube and the anti-resonant module tubes are drawn until the outer cladding and the anti-resonant modules meet predefined dimensions. To that end, the structure is heated and drawn until to form a micro-structured cane. This case is then inserted into a second glass hollow tube. The new tubular structure thus obtained is called preform and is then drawn in presence of gases. Gases are injected into the preformed tubes and capillaries of the tubular structure with precisely controlled pressure and temperature to maintain the air holes not collapsed and adjust dimensions of the cavities being formed. The thermal forming process and associated parameters are not detailed here, as far they can be derived from prior art methods.

Claims

1. CLAIMS1. Hollow-core fiber comprising an outer cladding (1) having an inner surface and an inner cladding region (2) bounded by the inner surface, the inner cladding region comprising a plurality of anti-resonant modules distributed without touching each other around the longitudinal axis of the hollow-core fiber to define a hollow-core region (3), characterized in that the anti-resonant modules comprise each at least two tubular elements embedded on at least two distinct levels, the lower-level tubular element being embedded inside the preceding upper-level tubular element and arranged in cross-section to be tangent at two points of said module in a tangential direction of said hollow-core fiber, only the first-level tubular element contacting the inner surface of the outer cladding.

2. Hollow-core fiber according to claim 1, wherein at least one lower-level tubular element has a different cross-sectional geometry to that of the preceding upper-level tubular element, a preceding upper-level tubular element of said at least two embedded tubular elements having a circular cross- sectional geometry.

3. Hollow-core fiber according to claim 2, wherein the cross-sectional geometry belongs to the group comprising elliptical geometry, oval geometry and circular geometry.

4. Hollow-core fiber according to claim 3, in which the anti-resonant modules (lOa-lOf ; 2Oa-2Of) each consist of embedded first-level and second-level tubular elements (11, 12 ; 21, 22), the second-level tubular element embedded inside the first-level tubular element, which has an elliptical cross-sectional geometry, or an oval cross-sectional geometry cross-sectional geometry.

5. Hollow-core fiber according to claim 3, in which the anti-resonant modules (30a-30f) each consist of first-, second- and third-level embedded tubular elements (31, 32, 33), the third-level tubular element being embedded inside the second-level tubular element which is itself embedded inside the first-level tubular element, which has an elliptical cross-sectional geometry, or oval cross-sectional geometry.

6. Hollow-core fiber according to claim 1, in which said embedded first-level and second-level tubular elements are defined as follows: the first-level tubular element has an elliptical cross-sectional geometry defined by an ellipticity el, a major axis radius Rtubel arranged in radial direction of the hollow-core fiber and a minor axis radius Rtube2 arranged in tangential direction of the hollow-core fiber, such as:Rtubel = (2 x sin(n / N) x Rcore — g) / (2 x (1 — sin(n / N)))Rtube2 = Rtubel x ^ / (l — el2) where:N is an integer, with N > 2, corresponding to the number of anti-resonant modules comprised in the inner cladding region,Rcore is the hollow-core region radius defined as the smallest distance between the center of the hollowcore fiber and the outer edge of the first-level tubular elements, g is the azimuthal distance between two adjacent first-level tubular elements, the second-level tubular element has a circular cross-sectional geometry defined by a first radius Rtube3 arranged in radial direction of the hollow-core fiber and a second radius Rtube4 arranged in tangential direction of the hollow-core fiber, such as:Rtube3 = Rtube4 = Rtubel x ^ / (l — el2)7. Hollow-core fiber according to claim 4, in which said embedded first-level and second-level tubular elements are defined as follows: the first-level tubular element has a circular cross-sectional geometry a first radius Rtubel' arranged in radial direction of the hollow-core fiber and a second radius Rtube2' arranged in tangential direction of the hollow-core fiber, such as:Rtube2' = Rtubel' = (2 x sin(n / N') x Rcore' — g') / (2 x (1 — sin(n / N'))) the second-level tubular element has an elliptical cross-sectional geometry defined by an ellipticity e2, a major axis radius Rtube3' arranged in tangential direction of the hollow-core fiber and a minor axis radius Rtube4' arranged in radial direction of the hollow-core fiber, such as:where:N' is an integer, with N' > 2, corresponding to the number of anti-resonant modules comprised in the inner cladding region,Rcore' is the hollow-core region radius defined as the smallest distance between the center of the hollowcore fiber and the outer edge of the first-level tubular elements, g' is the azimuthal distance between two adjacent first-level tubular elements.

8. Hollow-core fiber according to claim 5, in which said first-, second- and third-level embedded tubular elements are defined as follows: the first-level tubular element has an elliptical cross-sectional geometry defined by an ellipticity el", a first major axis radius Rtubel" arranged in radial direction of the hollow-core fiber and a first minor axis radius arranged in tangential direction of the hollow-core fiber, such as:where:N" is an integer, with N > 2, corresponding to the number of tubular elements comprised in the inner cladding region,Rcore" is the hollow-core region radius defined as the smallest distance between the center of the hollow-core fiber and the outer edge of the first-level tubular elements, g" is the azimuthal distance between two adjacent first-level tubular elements, the second-level tubular element has a circular cross-sectional geometry defined by a first radius Rtube3" arranged in radial direction of the hollow-core fiber and a second radius Rtube4" arranged in tangential direction of the hollow-core fiber, such as:the third-level tubular element has an elliptical cross-sectional geometry defined by an ellipticity e3, a second minor axis radius Rtube5 arranged in radial direction of the hollow-core fiber and a second major axis radius Rtube6 arranged in tangential direction of the hollow-core fiber, such as:

9. Hollow-core fiber according to claim 5, in which said first-, second- and third-level embedded tubular elements are defined as follows: the first-level tubular element has a circular cross-sectional geometry, a first radius Rtubel'" arranged in radial direction of the fiber and a second radius Rtube2"' arranged in tangential direction T of the fiber, such as:Rtube2"' = Rtubel'" = (2 x sin(n / N'") x Rcore'" — g'") / (2 x (1 — sin(n / N'"))) the second-level tubular element has an elliptical cross-sectional geometry defined by an ellipticity e2'", a major axis radius Rtube3"' arranged in tangential direction T of the fiber and a minor axis radius Rtube4"' arranged in radial direction R of the hollow-core fiber, such as:the third-level tubular element has an elliptical cross-sectional geometry defined by an ellipticity e3'", a major axis radius Rtube5"' arranged in tangential direction T of the fiber and a minor axis radius Rtube6"' arranged in radial direction R of the hollow-core fiber, such as:where:N'" > 2,Rcore'", the hollow-core region radius defined as the smallest distance between the center of the hollowcore fiber and the outer edge of the first-level tubular elements around the hollow-core region; g'" , the smallest azimuthal distance between two adjacent first-level tubular elements.

10. Hollow-core fiber according to any one of claims 2 to 9, in which said at least two embedded tubular elements have a thickness in the range [0.3 pm - 1.2 pm], an azimuthal distance-to-thickness ratio in the range [2 - 13] and in which at least one of said at least two embedded tubular elements have an ellipticity in the range [0.30 - 0.95],11. Hollow-core fiber according to claim 6, in which said at least two embedded tubular elements have a thickness in the range [0.3 pm - 0.8 pm], an azimuthal distance-to-thickness ratio in the range [2 - 5] and in which said first level tubular elements have an ellipticity in the range [0.6 - 0.8],12. Hollow-core fiber according to claim 7, in which said at least two embedded tubular elements have a thickness in the range [0.3 pm - 0.8 pm], an azimuthal distance-to-thickness ratio in the range [6- 13] and in which said second level tubular elements have an ellipticity in the range [0.8 - 0.9],13. Hollow-core fiber according to claim 8, in which said at least three embedded tubular elements have a thickness in the range [0.3 pm - 0.8 pm], an azimuthal distance-to-thickness ratio in the range [2 - 5] and in which said first level tubular elements have an ellipticity in the range [0.6 - 0.95] and in which said third level tubular elements have an ellipticity in the range [0.5 - 0.8],14. Hollow-core fiber according to claim 9, in which said at least three embedded tubular elements have a thickness in the range [0.3 pm - 0.8 pm], an azimuthal distance-to-thickness ratio in the range [6 - 13] and in which said second level tubular elements have an ellipticity in the range [0.8 - 0.9] and in which said third level tubular elements have an ellipticity in the range [0.5 - 0.7],15. Optical transmission system characterized in that it comprises at least one hollow-core fiber according to any one of claims 1 to 14.

Images