Hollow-core fibre and method of manufacturing thereof
A hollow-core fiber ( 100 ) of non-bandgap type comprises a hollow core region ( 10 ) axially extending along the hollow-core fiber ( 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, 21 A, 21 B) surrounding the core region ( 10 ) along the hollow-core fiber ( 100 ), each having a smallest transverse ARE dimension (d i ) and being adapted for guiding transverse ARE modes, wherein the core region ( 10 ) and the AREs ( 21, 21 A, 21 B) are configured to provide phase matching of the higher order core modes and the ARE modes and the ARE dimension (d i ) and the core dimension (D) are selected such that a ratio of the ARE and core dimensions (d i /D) is approximated to a quotient of zeros of Bessel functions of first kind (u lm,ARE /u 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 1 , said zeros of the Bessel functions describing the LP lm ARE modes and LP lm higher order core modes, respectively. Furthermore, an optical device ( 200 ) including the hollow-core fiber ( 100 ) and a method of manufacturing the hollow-core fiber are described.
1. 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 i ) and being configured for guiding a plurality of transverse ARE modes, wherein
the smallest transverse core dimension (D) is a smallest distance between AREs on diametrically opposite sides of the core region,
the smallest transverse ARE dimension (di) is a smallest inner cross-sectional dimension of the ARE,
the core region and the AREs are configured to provide phase matching of the higher order core modes and the ARE modes,
the ARE dimension (d i ) and the core dimension (D) are selected such that a ratio of the ARE and core dimensions (d i /D) is approximated to a quotient of zeros of Bessel functions of first kind (u lm,ARE /u 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 1, said zeros of the Bessel functions describing the LP lm , ARE modes and LP lm higher order core modes, respectively, and
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 covering wavelengths within a hollow-core fibre transparency window of the fundamental core mode.
2. The hollow-core fibre according to claim 1 , wherein
the AREs surrounding the core region are arranged in a non-touching manner.
3. The hollow-core fibre according to claim 1 , wherein
the AREs have a first smallest transverse ARE dimension (d 1 ), and
the ratio of the first ARE dimension and the core dimension (d 1 /D) is approximated to a quotient of zeros of Bessel functions of first kind (u 01,ARE /u 11core ), multiplied with the fitting factor, said zeros (u 01,ARE ), (u 11,core ) describing the LP 01 ARE modes and the LP 11 core mode, respectively.
4. The hollow-core fibre according to claim 3 , wherein
the ratio of the first ARE dimension and the core dimension (d 1 /D) is selected in a range from 0.5 to 0.8.
5. The hollow-core fibre according to claim 4 , wherein
the ratio of the first ARE dimension and the core dimension (d 1 /D) is selected in a range from 0.62 to 0.74.
6. The hollow-core fibre according to claim 3 , wherein
each of the AREs has the first ARE dimension (d 1 ).
7. The hollow-core fibre according to claim 3 , wherein
a first group of the AREs has the first ARE dimension (d 1 ), and
a second group of the AREs has a second smallest transverse ARE dimension (d 2 ) smaller than the first ARE dimension (d 1 ) of the first group of the AREs, and
the ratio of the second ARE dimension and the core dimension (d 2 /D) is approximated to a quotient of zeros of Bessel functions of first kind (u 01,ARE /u 21,core ), multiplied with the fitting factor, said Bessel functions (u 01,ARE ), (u 21,core ) describing the LP 01 ARE modes and the LP 21 core mode, respectively.
8. The hollow-core fibre according to claim 7 , wherein
the ratio of the second ARE dimension and the core dimension (d 2 /D) is selected in a range from 0.3 to 0.7.
9. The hollow-core fibre according to claim 7 , wherein
the ratio of the second ARE dimension and the core dimension (d 2 /D) is selected in a range from 0.45 to 0.54.
10. The hollow-core fibre according to claim 1 , wherein
the number of AREs is 3, 4, 5, 6 or 7.
11. The hollow-core fibre according to claim 1 , 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.
12. The hollow-core fibre according to claim 1 , 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.
13. The hollow-core fibre according to claim 1 , 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.
14. The hollow-core fibre according to claim 1 , 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.
15. The hollow-core fibre according to claim 1 , 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 shape, and
the AREs are evenly distributed in the curved shape.
16. The hollow-core fibre according to claim 1 , 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.
17. The hollow-core fibre according to claim 16 , 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.
18. The hollow-core fibre according to claim 16 , 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.
19. 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 i ) and being configured for guiding a plurality of transverse ARE modes, wherein
the smallest transverse core dimension (D) is a smallest distance between AREs on diametrically opposite sides of the core region,
the smallest transverse ARE dimension (d i ) is a smallest inner cross-sectional dimension of the ARE,
the core region and the AREs are configured to provide phase matching of the higher order core modes and the ARE modes,
the ARE dimension (d i ) and the core dimension (D) are selected such that a ratio of the ARE and core dimensions (d i /D) is approximated to a quotient of zeros of Bessel functions of first kind (u lm,ARE /u 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 1, said zeros of the Bessel functions describing the LP lm , ARE modes and LP lm higher order core modes, respectively, and
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 covering wavelengths within a hollow-core fibre transparency window of the fundamental core mode.
20. The optical device according to claim 19 , 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.
21. The optical device according to claim 20 , 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.
22. 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 i ) and being configured for guiding transverse ARE modes, wherein
the smallest transverse core dimension (D) is a smallest distance between AREs on diametrically opposite sides of the core region,
the smallest transverse ARE dimension (d i ) is a smallest inner cross-sectional dimension of the ARE,
the core region and the AREs are configured to provide phase matching of the higher order core modes and the ARE modes,
the ARE dimension (d i ) and the core dimension (D) are selected such that a ratio of the ARE and core dimensions (d i /D) is approximated to a quotient of zeros of Bessel functions of first kind (u lm,ARE /u 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 1, said zeros of the Bessel functions describing the LP lm ARE modes and LP lm higher order core modes, respectively, and
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 covering wavelength within a hollow-core fibre transparency window of the fundamental core mode.
23. The method according to claim 22 , 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 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 i ) and the core dimension (D) are selected such that a ratio of the ARE and core dimensions (d i /D) is approximated to a quotient of zeros of Bessel functions of first kind (u lm,ARE /u 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 1, said zeros of the Bessel functions describing the LP lm ARE modes and LP lm higher order core modes, respectively.
24. The method according to claim 22 , wherein
the ARE dimension (d 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 lm modes in the capillaries are approximated by
n
lm
=
1
-
(
u
lm
π
f
s
)
2
(
λ
d
i
)
2
wherein u lm is the m-th zero of the Bessel function J 1 , d i is the inner diameter of the capillary, and the parameter f s is a heuristic fit parameter.
25. The method according to claim 22 , 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.
26. The method according to claim 25 , 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.
27. The method according to claim 26 , 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.
28. The method according to claim 26 , 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.