Toward highly birefringent silica Large Mode Area optical fibers with anisotropic core

Damian Michalik; Damian Michalik; Alicja Anuszkiewicz; Alicja Anuszkiewicz; Ryszard Buczynski; Ryszard Buczynski; Rafał Kasztelanic; Rafał Kasztelanic

doi:10.1364/OE.428726

Optics Express
Vol. 29,
Issue 15,
pp. 22883-22899
(2021)
•https://doi.org/10.1364/OE.428726

Toward highly birefringent silica Large Mode Area optical fibers with anisotropic core

Damian Michalik, Alicja Anuszkiewicz, Ryszard Buczynski, and Rafał Kasztelanic

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Damian Michalik, Alicja Anuszkiewicz, Ryszard Buczynski, and Rafał Kasztelanic, "Toward highly birefringent silica Large Mode Area optical fibers with anisotropic core," Opt. Express 29, 22883-22899 (2021)

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Abstract

We test the development of a silica all-glass optical fiber with a highly birefringent large mode area (HB-LMA). In the fiber, the birefringence and single mode operation are independent of bending and results from the internal nanostructuring of the core, which makes the glass anisotropic. Taking into account technological limitations of the doped silica glasses, we optimized the HB-LMA fiber properties by appropriate selection of germanium and fluorine doping level of silica used in the fiber core and cladding. We demonstrated that the anisotropic glass can be successfully used as a core material in large core area fibres in C-band for polarization components of the fundamental mode. We obtained phase birefringence of 1.92 × 10⁻⁴ in the fiber with the core diameter of 30 µm and the effective mode area equal to 573 µm² and 804 µm², for x- and y-polarization, respectively. The same approach was applied to designing a single mode fiber with 40 µm core diameter and effective mode area over 1000 µm², which supports only single polarization.

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Data availability

Data underlying the results presented in this paper are based on numerical data obtained from the formulas presented in this paper therefore are not additionally published, but may be obtained from the authors upon reasonable request.

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Fig. 1. Scheme of an all-solid optical fiber with anisotropic core composed of interleaved subwavelength layers of high and low refractive indices.

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Fig. 2. Scheme of the three optical fiber structures considered in the paper.

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Fig. 3. Material dispersion of pure silica, Ge-doped and F-doped silica for selected molar fractions (a) and (b) refractive index difference for doped silica glasses in relation to pure silica glass.

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Fig. 4. Birefringence estimation for HB-LMA fiber based on the effective parameters. The first row (a)–(c) refers to F#1 structure. The second (d)–(f) and the third rows (g)–(i) refer to F#2 structure for different F-doping of the core, respectively for levels of 1 and 2 wt.%. The first column (a), (d), and (g) shows the refractive index contrast Δn in the core. The second column (b), (e), and (h) shows the map of the core refractive index n₁. The last column (c), (f), and (i) shows the phase birefringence as the function of Ge-doping level in the core layers for three selected core diameters indicated by the white dashed lines in the second column.

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Fig. 5. Effective mode area for fibers (a) structure F#1, (b) structure F#2 for 1 wt.% F-doping and (c) structure F#2 for 1 wt.% F-doping.

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Fig. 6. Birefringence estimation based on the ‘effective parameters’ for the HB-LMA fiber working in the SM regime. The first row (a) nd (b) refers to F#1 structure. The second (c) and (d) and the third rows (e) and (f) refer to F#2 structure for different F-doping of the core, respectively for the levels of 1 and 2 wt.%. The first column presents the cut-off wavelength maps (a), (c), and (e) for the selected range of core diameters. The second column presents phase birefringence (b), (d), and (f) as the function of Ge-doping level in the core layers for three selected core diameters indicated by the white dashed lines in the first column.

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Fig. 7. Birefringence estimation for the HB-LMA fiber with Ge-doped cladding (F#3 structure) working in the SM regime. The first column (a), (c), and (e) shows the required doping of both core and cladding to guarantee SM operation. The white dashed lines indicate 2 mol.% limit in cladding doping level. The second column (b), (d), and (f) presents the Ge-doping level in the core (red line) and phase birefringence (black line) as the function of core diameter based on the ‘effective parameters’. The rows present the cases for different F-doping in the core, respectively for levels of 0, 1 and 2 wt.%.

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Fig. 8. A comparison of the analyses based on the ‘effective parameters’ (first row) and the results of ‘numerical modelling’ (second row). The first column shows the optimal Ge-doping (red series) in the core of the HB-LMA fibers with assumed SM condition and the corresponding birefringence (black series) in a function of core diameter. Effective mode areas b) and d), calculated for fibers with parameters from a) and c), respectively. Insets show the normalized electric field amplitude for both polarization modes for the selected diameters of the cores indicated with the black dashed lines.

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Fig. 9. Influence of bending on (a) phase birefringence and (b) losses. Insets show modes for a bending radius of 10 mm. For better visibility, the modes views show the core area and not alternating layers.

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Tables (3)

Table 1. Properties of SM–LMA Fibers ^a

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Table 2. Sellmeier’s Coefficients for Pure Silica and Germanium Dioxide used in Eq. (1) and Coefficients for F-doped Silica Glass used in Interpolation Eq. (2).

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Table 3. Optimized Single Mode HB-LMA Fibers: Composition, Birefringence and Effective Mode Area

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Equations (13)

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n_{G e O_{2}}^{2} (λ) - 1 = \sum_{i = 1}^{3} \frac{[S A_{i} + X (G A_{i} - S A_{i})] λ^{2}}{λ^{2} - {[S I_{i} + X (G I_{i} - S I_{i})]}^{2}}

\frac{{n_{F}}^{2} (λ) - 1}{{n_{F}}^{2} (λ) + 2} = \sum_{i = 1}^{3} \frac{[A_{s i} + B_{i} f] λ^{2}}{λ^{2} - {z_{s i}}^{2}}

Δ n = n_{1 G e O_{2}} - n_{1 F},

n_{1} = \sqrt{f_{1 F} n_{1 F}^{2} + f_{1 G e O_{2}} n_{1 G e O_{2}}^{2}} = \sqrt{(n_{1 F}^{2} + n_{1 G e O_{2}}^{2}) / 2}

n_{X}^{2} = n_{1}^{2} + \frac{1}{3} {(\frac{Λ π}{4 λ} (n_{1 G e O_{2}}^{2} - n_{1 F}^{2}))}^{2}

n_{Y}^{2} = n_{Y, 0}^{2} + \frac{1}{3} {(\frac{Λ π}{4 λ} (\frac{1}{n_{1 F}^{2}} - \frac{1}{n_{1 G e O_{2}}^{2}}) n_{1} n_{Y, 0}^{3})}^{2} .

n_{Y, 0}^{2} = 2 \frac{n_{1 F}^{2} n_{1 G e O_{2}}^{2}}{n_{1 F}^{2} + n_{1 G e O_{2}}^{2}}

n_{X, Y}^{e f f} = n_{2} + b (n_{X, Y} - n_{2})

b \approx (1.1428 - 0.996 / V)^{2}

V = \frac{π Φ}{λ} \sqrt{n_{X, Y}^{2} - n_{2}^{2}} .

B = | n_{X}^{e f f} - n_{Y}^{e f f} | .

λ_{0} = \frac{π Φ}{V} \sqrt{n_{1}^{2} - n_{2}^{2}}

c n_{2}^{2} = c n_{1}^{2} - 1

Author	MFA (µm²)	Core Diameter (µm)	Cladding Diameter (µm)	Core NA	OW (nm)	SM	PM	B@OW (× 10⁻⁴)	Type	Ref.
Belardi et al.	216	19.1	194	n/a	1550	yes^d	AHC	0.12	PCF	[9]
Aleshkina et al.	870	80	175	n/a	1064	yes	SP-bend	1	all-solid	[7]
Vanvincq et al.	510	35	n/a	n/a	1000	y-pol.	SAPs	0.8	PBF	[8]
Schreiber et al.	700^b	35	n/a	0.03	1040	yes	SAPs	0.4	PCF	[10]
Nufern	219^c	20	395	0.065	1015–1115	no	SAPs	4	PANDA	[13]
NKT	760	40	540	0.03	1064	x-pol.	SAPs	≥1	PCF	[16]
This work	x-573 y-804	30	125	0.02	1550	yes	AC	1.92	all-solid	[–]

Material	A ₁	A ₂	A ₃	I ₁	I ₂	I ₃
SiO₂ (S)	0.6961	0.0684	0.4079	0.1162	0.8975	9.8962
GeO₂ (G)	0.8069	0.0690	0.7182	0.1540	0.8542	11.8419
Material	A _s1	A _s2	A _s3	z _s1	z _s2	z _s3	B ₁	B ₂	B ₃
F	0.2045	0.0645	0.1312	0.0613	0.1109	8.9644	−0.0541	−0.1789	−0.0745

Core Diameter (µm)	Core Dopants Concentration (mol.%)		Cladding Dopant Concertation (mol.%)	Phase Birefringence (× 10⁻⁴)	Effective Mode Area (µm²)
Core Diameter (µm)	GeO₂	F	GeO₂	Phase Birefringence (× 10⁻⁴)	LP₀₁^x	LP₀₁^y
10	14.0	6.1	2	2.54	115	133
15	12.5	6.1	2	2.33	181	206
20	11.4	6.1	2	2.16	282	345
25	10.6	6.1	2	2.03	410	541
30	10.1	6.1	2	1.92	573	804
35	9.9	6.1	2	—	766	—
40	9.8	6.1	2	—	1022	—

Author	MFA (µm²)	Core Diameter (µm)	Cladding Diameter (µm)	Core NA	OW (nm)	SM	PM	B@OW (× 10⁻⁴)	Type	Ref.
Belardi et al.	216	19.1	194	n/a	1550	yes^d	AHC	0.12	PCF	[9]
Aleshkina et al.	870	80	175	n/a	1064	yes	SP-bend	1	all-solid	[7]
Vanvincq et al.	510	35	n/a	n/a	1000	y-pol.	SAPs	0.8	PBF	[8]
Schreiber et al.	700^b	35	n/a	0.03	1040	yes	SAPs	0.4	PCF	[10]
Nufern	219^c	20	395	0.065	1015–1115	no	SAPs	4	PANDA	[13]
NKT	760	40	540	0.03	1064	x-pol.	SAPs	≥1	PCF	[16]
This work	x-573 y-804	30	125	0.02	1550	yes	AC	1.92	all-solid	[–]

Material	A ₁	A ₂	A ₃	I ₁	I ₂	I ₃
SiO₂ (S)	0.6961	0.0684	0.4079	0.1162	0.8975	9.8962
GeO₂ (G)	0.8069	0.0690	0.7182	0.1540	0.8542	11.8419
Material	A _s1	A _s2	A _s3	z _s1	z _s2	z _s3	B ₁	B ₂	B ₃
F	0.2045	0.0645	0.1312	0.0613	0.1109	8.9644	−0.0541	−0.1789	−0.0745

Damian Michalik	https://orcid.org/0000-0002-9983-3242
Alicja Anuszkiewicz	https://orcid.org/0000-0001-6395-5902
Ryszard Buczynski	https://orcid.org/0000-0003-2863-725X
Rafał Kasztelanic	https://orcid.org/0000-0002-6901-4641

Abstract

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