HOLLOW-CORE FIBRE AND METHOD OF MANUFACTURING THEREOF

Abstract

A hollow-core fibre (100) of non-bandgap type comprises a hollow core region (10) axially extending along the hollow-core fibre (100) and having a smallest transverse core dimension (D), wherein the core region (10) is adapted for guiding a transverse fundamental core mode and transverse higher order core modes, and an inner cladding region (20) comprising an arrangement of anti-resonant elements (AREs) (21, 21A, 21B) surrounding the core region (10) along the hollow-core fibre (100), each having a smallest transverse ARE dimension (d.sub.i) and being adapted for guiding transverse ARE modes, wherein the core region (10) and the AREs (21, 21A, 21B) are configured to provide phase matching of the higher order core modes and the ARE modes and the ARE dimension (d.sub.i) and the core dimension (D) are selected such that a ratio of the ARE and core dimensions (d.sub.i/D) is approximated to a quotient of zeros of Bessel functions of first kind (u.sub.lm,ARE/u.sub.lm,core), multiplied with a fitting factor in a range of 0.9 to 1.5, with m being the m-th zero of the Bessel function of first kind of order l, said zeros of the Bessel functions describing the LP.sub.lm ARE modes and LP.sub.lm higher order core modes, respectively. Furthermore, an optical device (200) including the hollow-core fibre (100) and a method of manufacturing the hollow-core fibre are described.

Claims

1-27. (canceled)

28. A hollow-core fibre of non-bandgap type, comprising: a hollow core region axially extending along the hollow-core fibre and having a smallest transverse core dimension (D), wherein the core region is configured for guiding a transverse fundamental core mode and a plurality of transverse higher order core modes, and an inner cladding region including an arrangement of anti-resonant elements (AREs) surrounding the core region along the hollow-core fibre, each having a smallest transverse ARE dimension (d.sub.i) and being configured for guiding a plurality of transverse ARE modes, wherein the core region and the AREs are configured to provide phase matching of the higher order core modes and the ARE modes, and the ARE dimension (d.sub.i) and the core dimension (D) are selected such that a ratio of the ARE and core dimensions (d.sub.i/D) is approximated to a quotient of zeros of Bessel functions of first kind (u.sub.lm,ARE/u.sub.lm,core), multiplied with a fitting factor in a range from 0.9 to 1.5, with m being the m-th zero of the Bessel functions of first kind of order l, said zeros of the Bessel functions describing the LP.sub.lm ARE modes and LP.sub.lm higher order core modes, respectively.

29. The hollow-core fibre according to claim 28, wherein the AREs surrounding the core region are arranged in a non-touching manner.

30. The hollow-core fibre according to claim 28, wherein the AREs have a first smallest transverse ARE dimension (d.sub.1), and the ratio of the first ARE dimension and the core dimension (d.sub.1/D) is approximated to a quotient of zeros of Bessel functions of first kind (u.sub.01,ARE/u.sub.11core), multiplied with the fitting factor, said zeros (u.sub.01,ARE), (u.sub.11,core) describing the LP.sub.01 ARE modes and the LP.sub.11 core mode, respectively.

31. The hollow-core fibre according to claim 30, wherein the ratio of the first ARE dimension and the core dimension (d.sub.1/D) is selected in a range from 0.5 to 0.8.

32. The hollow-core fibre according to claim 31, wherein the ratio of the first ARE dimension and the core dimension (d.sub.1/D) is selected in a range from 0.62 to 0.74.

33. The hollow-core fibre according to claim 30, wherein each of the AREs has the first ARE dimension (d.sub.1).

34. The hollow-core fibre according to claim 30, wherein a first group of the AREs has the first ARE dimension (d.sub.1), and a second group of the AREs has a second smallest transverse ARE dimension (d.sub.2) smaller than the first ARE dimension (d.sub.1) of the first group of the AREs, and the ratio of the second ARE dimension and the core dimension (d.sub.2/D) is approximated to a quotient of zeros of Bessel functions of first kind (u.sub.01,ARE/u.sub.21,core), multiplied with the fitting factor, said Bessel functions (u.sub.01,ARE), (u.sub.21,core) describing the LP.sub.01 ARE modes and the LP.sub.21 core mode, respectively.

35. The hollow-core fibre according to claim 34, wherein the ratio of the second ARE dimension and the core dimension (d.sub.2/D) is selected in a range from 0.3 to 0.7.

36. The hollow-core fibre according to claim 34, wherein the ratio of the second ARE dimension and the core dimension (d.sub.2/D) is selected in a range from 0.45 to 0.54.

37. The hollow-core fibre according to claim 28, wherein the number of AREs is 3, 4, 5, 6 or 7.

38. The hollow-core fibre according to claim 28, wherein the arrangement of AREs has at least one of the features: the arrangement of AREs has three-fold symmetry, the arrangement of AREs has two-fold symmetry and causes optical birefringence, the AREs are arranged such that the cross-sections thereof are distributed on a single ring surrounding the core region, and the AREs are arranged such that the cross-sections thereof are distributed on multiple rings surrounding the core region.

39. The hollow-core fibre according to claim 28, wherein the AREs have at least one of the features: the AREs have a circular, elliptic or polygonal transverse cross-section, and the AREs are made of one of a glass, polymer, composite, metal and crystalline material.

40. The hollow-core fibre according to claim 28, wherein at least one of the core region and the AREs is evacuated or filled with at least one of a gas, a liquid, and a material having a non-linear optical response.

41. The hollow-core fibre according to claim 28, further comprising an outer cladding region surrounding the inner cladding region along the hollow-core fibre, wherein the outer cladding region has a transverse cross-section with a polygonal shape, and the AREs are located in corners of the polygonal shape.

42. The hollow-core fibre according to claim 28, further comprising an outer cladding region surrounding the inner cladding region along the hollow-core fibre, wherein the outer cladding region has a transverse cross-section with a curved, and the AREs are evenly distributed in the curved shape.

43. The hollow-core fibre according to claim 28, wherein the core region and the AREs are configured to provide the phase matching of the higher order core modes and the ARE modes in a broadband wavelength range.

44. The hollow-core fibre according to claim 43, wherein the core region and the AREs are configured to provide the phase matching of the higher order core modes and the ARE modes in a wavelength range covering up to all wavelengths within a hollow-core fibre transparency window of the fundamental core mode.

45. The hollow-core fibre according to claim 43, wherein the core region and the AREs are configured to provide the phase matching of the higher order core modes and the ARE modes in a wavelength range covering at least 10 THz.

46. An optical device, comprising at least one hollow-core fibre of non-bandgap type, the at least one hollow-core fibre including: a hollow core region axially extending along the hollow-core fibre and having a smallest transverse core dimension (D), wherein the core region is configured for guiding a transverse fundamental core mode and a plurality of transverse higher order core modes, and an inner cladding region including an arrangement of anti-resonant elements (AREs) surrounding the core region along the hollow-core fibre, each having a smallest transverse ARE dimension (d.sub.i) and being configured for guiding a plurality of transverse ARE modes, wherein the core region and the AREs are configured to provide phase matching of the higher order core modes and the ARE modes, and the ARE dimension (d.sub.i) and the core dimension (D) are selected such that a ratio of the ARE and core dimensions (d.sub.i/D) is approximated to a quotient of zeros of Bessel functions of first kind (u.sub.lm,ARE/u.sub.lm,core), multiplied with a fitting factor in a range from 0.9 to 1.5, with m being the m-th zero of the Bessel functions of first kind of order l, said zeros of the Bessel functions describing the LP.sub.lm ARE modes and LP.sub.lm higher order core modes, respectively.

47. The optical device according to claim 46, comprising at least one of a modal filtering device, a light source, an optical amplifier, a beam delivery system, a pulse shaper, a data communication system, and a frequency converter.

48. The optical device according to claim 47, including at least one of the features: the light source is a laser, the pulse shaper is configured for pulse compression, and the frequency converter is configured for supercontinuum generation.

49. A method of manufacturing a hollow-core fibre of non-bandgap type, comprising: providing a hollow core region axially extending along the hollow-core fibre and having a smallest transverse core dimension (D), wherein the core region is configured for guiding a transverse fundamental core mode and transverse higher order core modes, and providing an inner cladding region comprising an arrangement of anti-resonant elements (AREs) surrounding the core region along the hollow-core fibre, each having a smallest transverse ARE dimension (d.sub.i) and being configured for guiding transverse ARE modes, wherein the core region and the AREs are configured to provide phase matching of the higher order core modes and the ARE modes, wherein the ARE dimension (d.sub.i) and the core dimension (D) are selected such that a ratio of the ARE and core dimensions (d.sub.i/D) is approximated to a quotient of zeros of Bessel functions of first kind (u.sub.lm,ARE/u.sub.lm,core), multiplied with a fitting factor in a range from 0.9 to 1.5, with m being the m-th zero of the Bessel functions of first kind of order l, said zeros of the Bessel functions describing the LP.sub.lm ARE modes and LP.sub.lm higher order core modes, respectively.

50. The method according to claim 49, wherein the hollow-core fibre is manufactured with the features of the hollow-core fibre of non-bandgap type, the hollow-core fibre including: a hollow core region axially extending along the hollow-core fibre and having a smallest transverse core dimension (D), wherein the core region is configured for guiding a transverse fundamental core mode and a plurality of transverse higher order core modes, and an inner cladding region including an arrangement of anti-resonant elements (AREs) surrounding the core region along the hollow-core fibre, each having a smallest transverse ARE dimension (d.sub.i) and being configured for guiding a plurality of transverse ARE modes, wherein the core region and the AREs are configured to provide phase matching of the higher order core modes and the ARE modes, and the ARE dimension (d.sub.i) and the core dimension (D) are selected such that a ratio of the ARE and core dimensions (d.sub.i/D) is approximated to a quotient of zeros of Bessel functions of first kind (u.sub.lm,ARE/u.sub.lm,core), multiplied with a fitting factor in a range from 0.9 to 1.5, with m being the m-th zero of the Bessel functions of first kind of order l, said zeros of the Bessel functions describing the LP.sub.lm ARE modes and LP.sub.lm higher order core modes, respectively.

51. The method according to claim 49, wherein the ARE dimension (d.sub.i) is selected by applying an analytical model in which the core and the AREs are treated as capillaries, wherein modal indices of the LP.sub.lm modes in the capillaries are approximated by $n_{\mathrm{lm}}=\sqrt{1-{\left(\frac{u_{\mathrm{lm}}}{.Math..Math.f_s}\right)}^2.Math.{\left(\frac{}{d_l}\right)}^2}$ wherein u.sub.lm is the m-th zero of the Bessel function J.sub.l, d.sub.i is the inner diameter of the capillary, and the parameter f.sub.s is a heuristic fit parameter.

52. The method according to 49, further comprising: (a) providing ARE preforms and a hollow jacket preform, (b) fixing the ARE preforms on an inner surface of the jacket preform in a distributed manner, and (c) heating and drawing the jacket preform including the ARE preforms until the ARE and core dimensions are set.

53. The method according to claim 52, wherein step (c) includes (c1) heating and drawing the jacket preform including the ARE preforms to a cane, and (c2) heating and drawing the cane until the ARE and core dimensions are set.

54. The method according to claim 53, wherein step (c) includes applying one of a vacuum and an increased pressure to at least one of the jacket preform, the ARE preforms, and hollow regions of the cane for setting the ARE and core dimensions.

55. The method according to claim 53, further comprising a post-processing step of filling at least one of the core region and the AREs with at least one of a gas, a liquid, and a material having a non-linear optical response.

Description

[0054] Further advantages and details of the invention are described in the following reference to the attached drawings, which show in:

[0055] FIG. 1: cross-sections of HC-AFs according to preferred embodiments of the invention;

[0056] FIG. 2: graphical illustrations of coupling HOMs of the core region with ARE modes and numerical simulations when varying d/D to find the optimum ratio between ARE dimension d and core dimension D;

[0057] FIG. 3: graphical illustrations of numerical simulations to illustrate the scalability of the inventive HC-AF;

[0058] FIG. 4: illustrations of applying the inventive model for designing a HC-AF;

[0059] FIG. 5: an optical device according to an exemplary embodiment of the invention;

[0060] FIG. 6: steps of a method of manufacturing an inventive HC-AF; and

[0061] FIG. 7: cross-sections of conventional solid or hollow core fibres (prior art).

[0062] In the following, exemplary reference is made to choosing a proper geometry of the HC-AF, in particular the diameter of the core and AREs, like glass capillaries in the inner cladding region. Implementing the invention is not restricted to the indicated examples of geometric quantities, like the dimensions D, d and t, but rather possible with varied values providing the inventive design parameters. Features of HC-AFs, the manufacturing thereof and the application thereof are not described, as far as they are known from prior art.

Practical Examples of HC-AFs

[0063] FIGS. 1A to 1E show transverse cross-sections of practical examples of inventive HC-AFs 100 (perpendicular to the axial. extension thereof). The bright circles represent the solid material of the AREs or outer cladding region, like quartz glass or silica, while the dark portions are free of solid materials (evacuated or filled with gas or liquid). The geometric design of the HC-AFs 100 is selected as outlined in the model section below.

[0064] Each HC-AF 100 comprises a hollow core region 10 (represented in FIG. 1A by a dotted circle), an inner cladding region 20 with multiple AREs 21 and an outer cladding region 30. The hollow core region 10 is the empty space, between the AREs 21, extending along the longitudinal length of the HC-AF 100 and having a smallest transverse core dimension D. The AREs 21 of the inner cladding region 20 comprise capillaries having a wall thickness t and a smallest transverse ARE dimension d. The AREs 21 are fixed to the inner surface of the outer cladding region 30, e.g. as described below with reference to FIG. 6. The outer cladding region 30 comprises a larger capillary being made of e.g. glass and providing a closed cladding of the HC-AF 100.

[0065] HC-AF 100 of FIG. 1A illustrates an embodiment wherein the AREs 21 comprise a single-ring of six thin-wall capillaries with a circular transverse cross-section (inner diameter d=13.6 m and wall thickness t=0.2 m) arranged within the larger capillary of the outer cladding region 30 in six-fold symmetric pattern so as to create a central hollow core of diameter D (the shortest distance between diametrically opposite AREs 21), with D=20 m. The outer cladding region 30 has an outer diameter of 125 m and a cladding thickness of 38 m. Alternatively, the core dimension D can be selected in a range from 10 m to 1000 m, wherein the other geometrical parameters (like d, t) are scaled accordingly.

[0066] FIG. 1B shows a modified embodiment with multiple, in particular two coaxial rings of AREs 21 (d=13.6 m, t=0.2 m, and D=20 m arranged within the outer cladding region 30 with six-fold symmetry. For holding the inner and outer rings of AREs 21, a support tube 22 is included in the HC-AF 100. The support tube 22 is made of e.g. silica with a diameter of e.g. 48 m.

[0067] FIGS. 1C and 1D illustrate a three-fold symmetry and FIG. 1E shows a two-fold symmetry of the inventive HC-AF 100, advantageously offering enhanced eESM effects.

[0068] According to FIG. 1C, the AREs 21A, 21B comprise a first group of AREs 21A with a first, larger ARE dimension d.sub.i (e. g. 13.6 m) and a second group of AREs 21B with a second, smaller ARE dimension d.sub.2 (e. g. 10.2 m), both with a wall thickness of e.g. 0.2 m. On the inner surface of the outer cladding 30, longitudinal protrusions 31 are provided, which have an axial extension along the HC-AF 100. In the cross-sectional view of FIG. 1C, the protrusions 31 are shown as blobs. Preferably, the protrusions 31 are made of the same material like the AREs, e. g. glass. Each of the smaller AREs 21B is fixed to the top of one of the protrusions 31. The AREs 21A, 21B surround the core region 10 having a diameter D=20 m. The radial height of the protrusions 31 preferably is selected so as to yield the most circularly-symmetric guided mode in the central core region 10. Alternatively, the protrusions 31 could be omitted, yielding a simpler structure, as shown in FIG. 1D.

[0069] By arranging the AREs 21A, 21B so as to form a two-fold symmetric structure (FIG. 1E), a birefringent polarization-maintaining HC-AF is obtained, displaying eESM behaviour.

[0070] The examples of inventive HC-AFs 100 as shown in FIG. 1 can be modified, in particular with regard to the shape of the AREs 21, 21A, 21B, which can have e. g. an elliptic or polygonal cross-section; the inner shape of the outer cladding 30, which can have e. g. a polygonal cross-section (see FIG. 6); the solid materials of the AREs 21, 21A, 21B, which may comprise e. g. plastic material, like PMMA, glass, like silica, or soft-glass, like ZBLAN; the dimensions of the AREs 21, 21A, 21B; the number of rings of AREs, e. g. three or more; the number of AREs, e. g. 4 or 5 or 7 or more; and the symmetry of the ARE arrangement.

[0071] Model for HC-AF Design

[0072] The ARE dimension (d.sub.i) and the core dimension (D) of the inventive HC-AFs 100 are selected such that a ratio of the ARE and core dimensions (d.sub.i/D) is approximated to a quotient of zeros of Bessel functions of first kind (u.sub.lm,ARE/u.sub.lm,core), multiplied with the fitting factor, as defined above. If all AREs have the same ARE dimension (d.sub.1), the ratio of the ARE dimension and the core dimension (d.sub.1/D) preferably is approximated to a quotient of zeros of Bessel functions of first kind (u.sub.01,ARE/u.sub.11core), multiplied with the fitting factor, wherein the zeros (u.sub.01,ARE), (u.sub.11,core) describe the LP.sub.01 ARE modes and the LP.sub.11 core mode, respectively. If further AREs have a second, smaller ARE dimension, the ratio of the second ARE dimension and the core dimension (d.sub.2/D) preferably is approximated to a quotient of zeros of Bessel functions of first kind (u.sub.01,ARE/u.sub.21,core), multiplied with the fitting factor, wherein the Bessel functions (u.sub.01,ARE), (u.sub.21,core) describe the LP.sub.01 ARE modes and the LP.sub.21 core mode, respectively.

[0073] These design conditions are found on the basis of the theoretical considerations and numerical simulations illustrated in the following with reference to FIGS. 2 to 4. These theoretical considerations and numerical simulations can be correspondingly extended to the coupling of core modes higher than the LP.sub.21 core mode to the ARE modes.

[0074] The central core region 10 of the HC-AF 100 supports several transverse core modes each with a characteristic modal refractive index and leakage loss. The inventive structure is provided in such a way that the LP.sub.01 mode (with the highest effective index) has a loss that is much lower than any of the core HOMs. This is achieved by designing the AREs 21, 21A, 21B and the gaps between them so that they support a band of leaky modes (or states) that phase-match to HOMs in the core region 10, making them highly leaky. This strong loss discrimination can be made broadband enough for obtaining eESM behaviour.

[0075] FIG. 2A shows the HC-AF 100 of FIG. 1A (left) illustrating the fundamental LP.sub.01 core mode (centre) and the LP.sub.11 core mode (right) as well as the leaky ARE modes (right), to which the LP.sub.11 core mode and higher core modes are resonantly coupled. FIG. 2B shows curves of the finite-element (FE) modelling computed effective refractive index in dependency on the parameter d/D, and FIG. 2C shows curves of leakage loss for changing ARE dimension d but constant core dimension D. The central curve in FIG. 2C shows the corresponding HOM suppression. The dashed lines show the fully vectorial computed values for the LP.sub.01 mode of a free standing tube with diameter d and thickness t. Exemplary structure parameters are t/D=0.01 and D/=20, n.sub.glass=1.45 and n.sub.core=1.

[0076] The structure shown in FIG. 2A supports several leaky transverse core modes formed by anti-resonant reflection at the walls of the AREs 21 with negative curvature. The AREs 21 support a cladding photonic bandstructure provided by the inner cladding region 20, and they can be approximated by quasi free-standing, thin-walled. tubes. The thick surrounding glass wall of the outer cladding region 30 does not appreciably influence the modal properties, but is provided to physically support the AREs 21.

[0077] FIG. 2B shows the effective index distribution of the two highest-index core modes LP.sub.01 and LP.sub.11 when varying the ARE diameter (for fixed D), effectively changing the cladding photonic bandstructure. The index of the LP.sub.01 core mode is high enough to avoid resonant coupling to the fundamental ARE modes, and remains almost independent of d/D, whereas the LP.sub.11 core mode undergoes a strong anti-crossing with the fundamental ARE mode at d/D0.68. As one moves away from this anti-crossing, the even and odd eigenmodes evolve asymptotically into uncoupled LP.sub.11 core and fundamental ARE modes. Core modes of even higher order (not shown in FIG. 2B) have lower indices and couple to highly leaky modes of the ARE ring, some of which are concentrated in the gaps between the AREs 21.

[0078] FIG. 2C plots the calculated leakage loss of the LP.sub.01 mode and the two hybrid LP.sub.11/ARE.sub.01 modes. Over the range shown the LP.sub.01 core mode has a relatively constant loss with a minimum value of 0.17 dB/m at d/D 0.65. For smaller ARE 21 diameters the loss increases, closely matching the value for an isolated thick-walled dielectric capillary in the limit d/D.fwdarw.0 (not shown in FIG. 2C). This limit was used to cross-check the FE calculations with analytical results [16], in particular the accuracy of the perfectly matched layers (PMLs). At the anti-crossing point the loss of the two hybrid LP.sub.11/ARE.sub.01 modes strongly increases, almost reaching the value for an isolated capillary in vacuum (dashed brown line), which was calculated by solving Maxwell's equations in full vectorial form. This provides further confirmation that the PMLs were set up correctly.

[0079] The HOM suppression increases strongly at the anti-crossing, peaking at a value of about 1200. Far from the anti-crossing it drops to less than 5, which is similar to values typically achieved in kagom-PCF [15]. For a comprehensive analysis, the HOM suppression of all the higher-order core modes must be calculated. FE modelling reveals that the HOM with the next-lowest loss after the LP.sub.11 core mode is the four-lobed LP.sub.21 core mode, with a HOM suppression of 70 at d/D0.68 and an anti-crossing with the fundamental ARE mode at d/D0.51. In experiments, however, this particular core mode is less likely to be excited by end-fire illumination or by stress- and bend-induced scattering from the LP.sub.01 core mode (the index difference is some two times larger than for the LP.sub.11 core mode). FE modeling shows that LP.sub.lm core modes of even higher order do not affect the overall HOM suppression because they phase-match to modes of the ARE ring (some of which are concentrated in the gaps between the AREs 21), resulting in strong leakage loss.

[0080] FIG. 3A plots, versus D/ (: wavelength), the difference n.sub.lm between the refractive indices of the LP.sub.lm core modes and the fundamental ARE mode at constant d/D=0.68 and t/D=0.01. n.sub.01 decreases with increasing D/ but overall remains positive. As a consequence, the LP.sub.01 core mode is anti-resonant with the fundamental ARE mode and remains confined to the core (see also left panel of the inset in FIG. 3A). In contrast, n.sub.11 is much smaller, reaching values as small as 10.sup.6 at D/66.

[0081] At certain values of D/, anti-crossings appear between the LP.sub.01 mode and the q-th order transverse mode in the glass walls of the AREs 21, following the simple relationship:

[00001]$\begin{array}{cc}{\left(\frac{D}{}\right)}_q\frac{q}{2.Math.\left(t.Math.\text{/}.Math.D\right).Math.\sqrt{n_g^2-1}}& \left(1\right)\end{array}$

[0082] The vertical dotted lines in FIG. 3 are centred at the first two of these resonances, for t/D=0.01. In the vicinity of these points the LP.sub.01 core mode leaks rapidly through the resonant AREs 21 into the solid glass jacket 30, yielding loss values that are close to those of an isolated thick-walled dielectric capillary [16]; the result is a strong reduction in the HOM suppression (see FIG. 3B). Away from these narrow regions, however, the HOM suppression remains relatively higha consequence of the fact that the indices of the LP.sub.11 core and fundamental ARE modes remain close to each other. The result is very strong LP.sub.11 core mode suppression over all the ranges of LP.sub.01 mode transmission.

[0083] To explain why maximum HOM suppression occurs at d/D=0.68 for all wavelengths (except in the vicinity of ARE wall resonances, see Eq. 1), the inventors have applied an analytical model in which the real structure with the core 10 and the AREs 21 are treated as thick-walled capillaries (see FIG. 4A). The modal indices of the LP.sub.1m modes in a thick-walled capillary can be approximated by the modified Marcatili-Schmeltzer expression [16]:

[00002]$\begin{array}{cc}{n}_{\mathrm{lm}}=\sqrt{1-{\left(\frac{u_{\mathrm{lm}}}{.Math..Math.f_s}\right)}^2.Math.{\left(\frac{}{d_l}\right)}^2}& \left(2\right)\end{array}$

where u.sub.lm is the m-th zero of the Bessel function J.sub.l and d.sub.i is the inner diameter of the capillary. The parameter f.sub.s (which has a value close to 1, s=co represents the core 10 and s=ARE the AREs 21) is used to heuristically fit the analytical values from the model equation to the results of FE simulations. It corrects for the non-circular core and the finite wall thicknesses of core 10 and AREs 21.

[0084] FIG. 4B plots the effective index of the two LP.sub.11/ARE.sub.01 hybrid modes together with the fitted values for the LP.sub.11 mode (zero line) computed using Eq. (2) with fit parameters f.sub.co=1.077 for the core 10 and f.sub.ARE=0.990 for the ARE 21. The convenient analytical form of Eq. (2) allows one to derive a simple expression for the d/D value at which the LP.sub.11 core and ARE.sub.01 modes couple optimally:

[00003]$\begin{array}{cc}\frac{d}{D}=\frac{u_{01}}{u_{11}}.Math.\frac{f_{\mathrm{co}}}{f_{\mathrm{ARE}}}=0.68& \left(3\right)\end{array}$

[0085] Eq. (3) provides a convenient rule-of-thumb for designing robustly single-mode eESM PCFs. To a first approximation it depends neither on the refractive indices nor on the absolute physical dimensions of the fibre, making the design scalable. This means that, provided the ratio d/D is maintained, it becomes possible to design large-core eESM PCFs and to deliver losses of some dB/km in multiple transmission windows, the broadest of which spans more than one octave.

[0086] By using Eq. (2) one can also easily find structural parameters where higher order core modes (e.g. the LP.sub.21 core mode) are effectively suppressed. Also by adjusting the physical dimensions, the resonance bands can be blue/red shifted (for smaller/thicker wall thickness t) and the minimum transmission loss of the LP.sub.01 core mode can be adjusted (for changing core diameter).

[0087] Eq. (2) can be also used to find appropriate geometrical parameters for designing a HC-AF with an enhanced eESM effect, i.e., a fibre where the first two HOMs of the core couple to resonances in the AREs. This yields the conditions:

[00004]$\begin{array}{cc}\frac{d_1}{D}=\frac{u_{01}}{u_{11}}.Math.\frac{f_{\mathrm{co}}}{f_{\mathrm{ARE}}}=0.68.Math..Math.\mathrm{and}.Math..Math.\frac{d_2}{D}=\frac{u_{01}}{u_{21}}.Math.\frac{f_{\mathrm{co}}}{f_{\mathrm{ARE}}}=0.51& \left(4\right)\end{array}$

[0088] A fibre structure with such an enhanced eESM effect is depicted in FIGS. 1C to 1E consisting of one or several of single rings of AREs with different inner diameters d.sub.1 and d.sub.2.

[0089] Embodiments of Optical Device

[0090] The inventive HC-AF 100 has multiple applications for light guiding, e.g. for beam delivery, data transmission or frequency conversion purposes. Accordingly, an optical device, which represents a further subject of the invention, comprises at least one inventive HC-AF 100 and further optical components, monitoring components, detector components and/or control components, which are selected in dependency on the particular application of the optical device.

[0091] FIG. 5 schematically illustrates an optical device 200 according to an embodiment of the invention, which is adapted for a high power beam delivery, e.g. for surface processing purposes. The optical device 200 comprises a light source 210, like a laser source, and the HC-AF 100. The output of the light source 210 is optically coupled with an input side of the HC-AF 100, while an output side thereof is directed to a location of beam delivery (see arrow).

[0092] With alternative applications of the invention, the light source 210 comprises a laser source for driving a frequency conversion process, in particular a supercontinuum generation process or pulse compression, inside the HC-AF 100. According to yet further applications, the light source 210 may comprise an optical transmitter of a data communication system, which is coupled via the HC-AF 100 with an optical receiver (not shown).

[0093] It is noted that FIG. 5 represents a schematic drawing only. Details of an optical device including at least one inventive HC-AF 100 can be implemented as it is known from conventional optical devices.

[0094] Method of Manufacturing HC-AFs

[0095] FIG. 6 schematically illustrates the main steps of manufacturing an inventive HC-AF 100. FIG. 6 is a schematic illustration only, which presents the main steps of providing ARE preforms 23 and a hollow jacket preform 32 (FIG. 6A), fixing the ARE preforms 23 on an inner surface of the jacket preform 32 (FIG. 6B) and heating and drawing the preform jacket 32 including the ARE preforms 23 for obtaining the HC-AF 100 (FIG. 6C). Optionally, the heating and drawing step may include a first step of heating and drawing the jacket preform 32 with the ARE preforms 23 to a cane, and a second step of heating and drawing the cane until the ARE and core dimensions are set. Details of the steps in FIGS. 6A, 6B and 6C can be implemented as far as they are known from conventional fibre manufacturing methods.

[0096] According to FIG. 6A, the jacket preform 32 is a hollow tubular form, made of glass, which has an inner transverse cross-sectional regular hexagonal shape. The outer diameter of the preform jacket 32 is e.g. 28 mm, while the inner transverse dimension is about 22 mm. The longitudinal length of the preform jackets 32 and the ARE preforms 23 is about 120 cm.

[0097] With the fixing step of FIG. 6B, the ARE preforms 23 are fixed to the corners of the inner hexagonal shape of the jacket preform 32. This is obtained by applying heat resulting in a physical connection between ARE preforms and jacket preform. Subsequently, the composite of the jacket preform 32 and the ARE preforms 23 is drawn during the application of heat until the ARE and core transverse dimensions are obtained. The ARE and core transverse dimensions can be influenced by applying a vacuum or an increased pressure to the jacket preform 32 and/or the ARE preforms 23 during the heating and drawing steps.

[0098] Applying a vacuum or an increased pressure during the heating and drawing steps is schematically illustrated in FIG. 6B. The hollow inner space of the jacket preform 32 is connected with a first external reservoir 41, like a source of pressurized nitrogen. Furthermore, the ARE preforms 23 are connected with at least one second external reservoir 42, like e.g. an external source of pressurized nitrogen. If all AREs are to be produced with the same inner transverse dimension, all AREs can be connected with a common external reservoir. Otherwise, e.g. two groups of AREs are connected to two different external reservoirs for creating different inner transverse dimensions, as shown e.g. in FIG. 1E. The final heating and drawing step is conducted e.g. in a furnace selected in dependency of the material of the jacket preform 32 and the ARE preforms 23 (e.g. around 2000 C. for silica components).

[0099] After obtaining the final HC-AF 100, it can be filled with a gas, like air or a noble gas or hydrogen, or a liquid, like water, and the input and output sides of the HC-AF 100 are enclosed by a cell withstanding high fluidic pressure and which is partially transmissive, e.g. by including a glass plate, for optical radiation, e.g. from a laser source.

[0100] The features of the invention disclosed in the above description, the drawings and the claims can be of significance individually, in combination or sub-combination for the implementation of the invention in its different embodiments.