SINGLE MODE OPTICAL FIBER OPTIMIZED TO OPERATE IN O AND E BAND, AND CORRESPONDING OPTICAL TRANSMISSION SYSTEM

TECHNICAL FIELD

The present disclosure relates to single-mode optical fibers used in optical transmission systems, and optical transmission systems comprising such single mode fibers. More specifically, the present invention relates to single-mode optical fibers, which are optimized to operate in O and E wavelength bands.

BACKGROUND

Telecommunication systems require optical fibers, which are capable of transmitting signals for a long distance without degradation. Such optical-fiber transmission systems often use single-mode optical fibers (SMFs), such as, for example, so-called “standard” single-mode fibers (SSMFs), which are used in terrestrial transmission systems. Indeed, a single-mode optical fiber (SMF) allows to obtain a lower attenuation of the optical signal in comparison with a multi-mode optical fiber (MMF), and therefore, is more suitable for long-distance transmissions. Furthermore, as indicated by its name, a multimode fiber presents a plurality of modes, each with different speeds, which induces a limited bandwidth, contrary to a single-mode optical fiber which theoretically presents an unlimited bandwidth, more suitable for long-distance transmissions.

Furthermore, to facilitate compatibility between optical systems from different manufacturers, the International Telecommunication Union (ITU) has defined several standards with which a standard optical transmission fiber should comply. Among these standards, the ITU-T G. 652 recommendation (Last revision of November 2016) describes the characteristics of single-mode fiber and cable-based networks, which can answer the growing demand for broadband services. The ITU-T G.652 recommendation (herein after “G.652”) has several attributes (i.e. A, B, C and D) defining the fiber attributes of a single mode optical fiber. The ITU-T G.657 (herein after “G.657”) recommendation focuses more precisely on bending-loss insensitive single-mode fibers. More particularly, the attributes of the G.657.A1 and G.657.A2 (Last revision of November 2016) are presented below.

Different optical wavelength communication bands can be used to transmit information through an optical fiber. These bands correspond to a wavelength region where optical fibers have smaller transmission losses. This low-loss wavelength region ranges from 1260 nm to 1625 nm, and is divided into five wavelength bands referred to as the O-, E-, S-, C- and L-bands.

Presently, most of the single mode optical fibers are operating at wavelength ranging from typically 1260 nm to 1625 nm, and more particularly in the O-band (1260-1360 nm) and the C&L-bands (1530-1625 nm), which is the case of G.652 and G.657 optical fibers.

More particularly, the optical performances of G.657 category A are: a Mode Field Diameter (MFD) for a 1310 nm wavelength comprised between 8.6 and 9.2 μm, a cable Cutoff below 1260 nm, and a Zero Dispersion Wavelength (ZDW) comprised between 1300 and 1324 nm (such ZDW is optimal for the use of fibers in the O-band), and a Zero Dispersion Slope (ZDS) lower or equal to 0.092 ps/(nm²·km).

The maximum accepted macrobend losses of G.657 fibers are:

TABLE 1

G.657.A1
G.657.A2

10 turns at radius of 15 mm, measured
0.25 dB
0.03 dB

at 1550 nm (R15BL at 1550)

10 turns at radius of 15 mm, measured
1.0 dB
0.1 dB

at 1625 nm (R15BL at 1625)

1 turn at radius of 10 mm, measured at
0.75 dB
0.1 dB

1550 nm (R15BL at 1550)

1 turn at radius of 10 mm, measured at
1.0 dB
0.2 dB

1625 nm (R15BL at 1625)

1 turn at radius of 7.5 mm, measured at

0.5 dB

1550 nm (R15BL at 1550)

1 turn at radius of 7.5 mm, measured at

1.0 dB

1625 nm (R15BL at 1625)

The international applications WO2015/092464 and WO2019/122943 disclose examples of optical fibers with Zero Dispersion wavelength between 1300 and 1324 nm as according to G.652 and G.657A.

However, with the long-term trend towards more and more expanding the transmission capacities, as data traffic keeps growing at a large rate, there is a need to optimize the use of the wavelengths at the top of the O-band used for optical fiber communications because the chromatic dispersion will be too high at these wavelengths for existing equipment. More particularly, Metro Wave Division Multiplexing (MWDM) systems with 25G transceivers, for example, are expected to operate in both O and E bands, from 1268 to 1375 nm, and need chromatic dispersion ranging from −9.5 to +3 ps/(nm²·km): this is not achieved with today G.652 and G657.A fibers because the zero-dispersion wavelength is ranging from 1300 to 1324 nm. Therefore, there is a need to find an optical fiber design able to answer this need.

SUMMARY OF THE INVENTION

These objectives are achieved by the invention, which concerns a single-mode optical fiber comprising:

- a core having a refractive index n, wherein the core comprises a region in which the value of n decreases from a value n₀at a radius r₀, to a value n₂at a radius r₁; and
- a cladding having a refractive index n′, said cladding comprising:
- a first layer of cladding wherein the refractive index n′ is equal to n₂; and
- a second layer of cladding wherein the refractive index n′ is equal to a value ng lower than n₂;
- a third layer of cladding wherein the refractive index n′ is equal to a value n₄higher than n₃;
  
  wherein the core radius r₁is comprised between 2.5 μm and 5.5 μm; and
  
  wherein a refractive-index difference Δn₀=n₀−n₄is higher than 5.8×10⁻³; and
  
  wherein a refractive-index difference Δn₂=n₂−n₄is between 1×10⁻³and 2.5×10⁻³; and
  
  wherein a refractive-index difference Δn₃=n₃−n₄is lower than 0
  
  wherein the refractive-index profile of the core and cladding is defined by the following profile parameters:

$K_{1} = V_{1 1} - 5.85 \times V_{0 1}$

$K_{2} = V_{0 2} + 0.65 \times V_{0 1}$

$K_{3} = V_{0 3} - 5 \times K_{2}$

where

V₀₁(μm) is a surface integral of the core;

V₁₁(μm²) is a volume integral of the core;

V₀₂(μm) is a surface integral of the first layer of cladding;

V₀₃(μm) is a surface integral of the second layer of cladding;

and wherein said parameters respect the following inequalities:

$- 5 9 < K_{1} < - 47$

$18 < K_{2} < 24$

$- 133 < K_{3} < - 1 1 8$

Thus, this invention allows to obtain optical fibers operating optimally in the O and E wavelength bands, thus with a Chromatic Dispersion (CD) slightly shifted in comparison to the G.652 and G.657 fibers but presenting the same optical performances. More particularly, the optical fiber according to the invention presents the same properties as the G.657.A fibers: a MFD-1310 at 9.0 μm, a cable Cutoff below 1260 nm and low bend losses; except for the ZDW which is comprised between 1340 and 1360 nm.

Therefore, the optical fiber according to the invention allow to maintain the chromatic dispersion between −9 and +3 ps/(nm·km) in the range from 1268 to 1375 nm.

Therefore, the invention is ideal for use in Metro Wave Division Multiplexing (MWDM) systems. These systems allow to double the number of wavelength channels under the same conditions as in the commonly used Coarse Wavelength Division Multiplexing (CWDM) systems, by reducing the wavelength spacing of CWDM from 20 nm to 10 nm.

Ultimately, Metro Wave Division Multiplexing (MWDM) is proposed to meet the urgent needs of 5G commercialization. And, as it only makes parameter adjustments based on the mature CWDM technology, therefore, the industry can reuse the CWDM modules production process, and the industry chain can quickly meet market demand.

According to a particular embodiment, the third layer of cladding is composed of silica.

According to a particular aspect of the invention, the profile of the refractive index or the core is trapezoidal, with a ratio comprised between 0 and 1, and preferably between 0.05 and 0.95, wherein said ratio is equal to r₀/r₁.

According to another particular aspect of the invention, the profile of the refractive index or the core presents rounded edges.

According to a particular embodiment, the profile of the refractive index of the core presents an inner central depressed zone, from the center of the core to the radius r₀, wherein r₀is lower than r₁, and wherein the refractive index n of the core, presents a minimum value at the center of the core equal to n_0D, wherein n_0Dis lower than n₀.

According to a particular aspect of the invention, the region with decrease of refractive index is obtained by gradually changing a concentration of at least two dopants.

According to an embodiment of the invention, the at least two dopants are chosen among the following elements and/or molecules:

- germanium oxide (GeO₂);
- fluorine (F);
- phosphorus oxide (P_XO_Y);
- boron oxide (B_XO_Y);
- aluminum oxide (Al₂O₃).

According to a particular aspect of the invention, said optical fiber has a Chromatic Dispersion comprised between −9 and +3 ps/(nm·km) in the range of wavelength from 1268 to 1375 nm.

Therefore, the Chromatic Dispersion is slightly shifted in comparison with the G.562 and G.567 optical fibers, which allows to operate in both the O- and E-wavelength bands.

According to an embodiment of the invention, said optical fiber has a Mode Field Diameter (MFD) at a 1310 nm wavelength which is comprised between 8.6 and 9.2 μm and preferably at 9 μm.

According to a particular aspect of the invention, said optical fiber has a Cable cut-off wavelength comprised between 1170 nm and 1260 nm.

According to a particular aspect of the invention, the optical fiber has a Zero Dispersion Wavelength comprised between 1340 and 1360 nm.

The invention also relates to an optical fiber transmission system which comprises at least one single-mode optical fiber as described previously.

Therefore, the range of wavelength which can be used by this system is wider than the ones available for the optical communication system of the prior art. In fact, it can operate in the O- and E-wavelength bands (from 1268 to 1375 nm) using, for example, Metro Wave Division Multiplexing (MWDM) with a 25 Gb/s transceiver.

According to an embodiment of the invention, the optical fiber transmission system has a maximum Transmitter Dispersion Penalty of 1.5 dB.

BRIEF DESCRIPTION OF THE FIGURES

The present disclosure can be better understood with reference to the following description and drawings, given by way of example and not limiting the scope of protection, and in which:

FIG. 1 depicts an optical fiber according to the invention;

FIG. 2 depicts a diagrammatic representation of the evolution of the refractive index (a) of the core and cladding of an optical fiber according to FIG. 1, according to a first example of invention, together with a sectional view (b) of such optical fiber;

FIG. 3 depicts a diagrammatic representation of the evolution of the refractive index of the core and cladding of an optical fiber according to FIG. 3, according to a second example of the invention, the refractive index profile of the core comprising rounded edges;

FIG. 4 depicts a diagrammatic representation of the evolution of the refractive index of the core and cladding of an optical fiber according to FIG. 3, according to a third example of the invention, the refractive index profile of the core comprising a depressed central zone;

FIG. 5 depicts a diagrammatic representation of the evolution of the refractive index of the core and cladding of an optical fiber according to FIG. 3, according to a fourth example of the invention, the refractive index profile of the core comprising a depressed central zone, and rounded edges;

FIG. 6 depicts a diagrammatic representation of a transmission system comprising an optical fiber according to the invention.

The components in the figures are not necessarily to scale, emphasis instead being placed upon illustrating the principles of the invention.

DETAILED DESCRIPTION

The general principle of the invention relies on a single-mode optical fiber configured to be implemented in optical transmission systems operating in a range of wavelengths comprised between 1260 nm and 1625 nm. More particularly, the invention relies on a single-mode optical fiber optimized to be used in the highest wavelengths of the O-band and even in the E-band (for example, around 1375 nm). Indeed, the specific characteristics of the single-mode optical fiber according to the invention allow to obtain a Chromatic Dispersion (CD) slightly shifted in comparison to the G.652 and G.657 fibers but presenting the same optical performances. More particularly, the single-mode optical fiber according to the invention presents a ZDW comprised between 1340 and 1360 nm, allowing to maintain the Chromatic Dispersion (CD) between −9 and +3 ps/(nm·km) in the range from 1268 to 1375 nm. Such ZDW and all other optical parameters are obtained thanks to specific characteristics of the different elements composing the fiber. Furthermore, as for G.652 and G.657 fibers, the optical fiber according to the invention has a Mode Field Diameter (MFD) at a 1310 nm wavelength which is comprised between 8.6 and 9.2 μm and preferably at 9 μm. The optical fiber also has a Cable cut-off wavelength comprised between 1170 nm and 1260 nm. Thus, this optical fiber presents similar characteristics to the G.652 and G.657 fibers, but is further optimized for a use in the high O-band wavelengths.

As illustrated in [FIG. 1], the optical fiber 1 according to the invention comprises a core 10 which is the inner light-carrying member of the fiber, and a cladding 20 which serves to confine the light to the core. The cladding comprises three layers of cladding: a first layer of cladding 21 also referred to as an “intermediate cladding”, a second layer of cladding 22 also referred to as a “trench”, and a third layer of cladding 23 also referred to as “external cladding”.

The core 10 is defined by a radius r and a refractive index n varying with radius r, while the cladding is defined be a radius r′ and a refractive index n′ varying with radius r′. More particularly, [FIG. 2] represents the index profile of an optical fiber on the above graph (a) and a sectional view of this optical fiber in the part below (b), according to the invention. In the part (a) of this figure is represented the evolution of the refractive index (n, n′) of the core 10 and cladding 20 in function of the radius (r, r′) from the center of the core 10.

According to the invention, the core 10 is defined with an external radius r₁. The core 10 comprises a first region, from its center (r=0) to a radius r₀. In the embodiment illustrated in [FIG. 2], the first region of the core presents a constant refractive index equal to no. The optical core 10 further comprises a second region, from radius r₀to radius r₁, with a decreasing refractive index, and with a refractive index n₂at radius r₁. In the embodiment illustrated in [FIG. 2], the index of the core in the second region decreases from no to n₂. Furthermore, in the exemplary embodiment of [FIG. 2], the radiuses and indices of the core are defined as follow:

$0.1 80 µm \leq r_{0} \leq 3 µm$

$2.5 µm \leq r_{1} \leq 5.5 µm$

$r_{0} \leq r_{1}$

- Δn₀>0.0058 with Δn₀being the refractive index difference between the first region of the core and the third layer of cladding: Δn₀=n₀−n₄
- 1×10⁻³≤Δn₂≤2.5×10⁻³with Δn₂being the difference between the index at r₁(in the outer part of the second region of the core) and the index of the third layer of cladding: Δn₂=n₂−n₄

More particularly, according to a particular embodiment of the invention, Δn₀is comprised between 0.0058 and 0.0085.

In addition, the radiuses parameters of the core 10 can further be defined as follows: 0≤r₀≤r₁with the ratio between the radius of the first region and the second region of the cladding being defined as follows: ratio=r₀/r₁, with 0≤ratio≤1, and preferably, 0.05≤ratio≤0.95.

Thus, the core 10 also presents a radius equivalent r_eqdefined as follows:

r
_eq
=r
₁×(1+ratio)/2, with 1.5 μm≤r_eq≤3.5 μm

Furthermore, the profile of the refractive index of the core 10 can be trapezoidal or rectangular, with edges which can be rounded or not.

The values of index and radius contribute to obtaining a single-mode optical fiber optimized for operating in the high wavelengths of the O-band. Indeed, the core radius of the single-mode optical fiber according to the invention is smaller than the prior art's ones, which allow to obtain a ZDW around 1350 nm.

The surface integral of the core 10 can be expressed by the following formula:

$V_{0 1} = \int_{0}^{r_{1}} Δ n (r) \cdot dr \approx \frac{r_{1}}{2} \cdot [Δ n_{0} \cdot (1 + ratio) + Δ n_{2} \cdot (1 - ratio)]$

In this formula, the index deltas (Δn₀, Δn₂) are multiplied by 1000, the unit of r₁is the μm, and therefore, the unit of V₀₁is the μm.

In a particular embodiment of the invention: 16 μm≤V₀₁≤25 μm.

And the volume integral of the core 10 can be expressed by the following formula:

$V_{1 1} = 2 \cdot \int_{0}^{r_{1}} Δ n (r) \cdot r \cdot dr \approx \frac{r_{1}^{2}}{3} \cdot [Δ n_{0} \cdot (1 + ratio + {ratio}^{2}) + Δ n_{2} \cdot (2 - ratio - {ratio}^{2})]$

In this formula, the index deltas (Δn₀, Δn₂) are multiplied by 1000, the unit of r₁is the μm, and therefore, the unit of V₁₁is the μm².

In a particular embodiment of the invention: 42 μm²≤V_11≤93μm².

The first layer of cladding 21 or “intermediate cladding” is defined with a radius r₂and a constant refractive index equal to n₂.

According to an embodiment of the invention, the radius of the first layer of cladding 21 is preferably defined as follows: 7.8 μm≤r₂≤9 μm.

The surface integral of the first layer of cladding 21 can be expressed by the following formula:

$V_{0 2} = \int_{r_{1}}^{r_{2}} Δ n (r) \cdot dr \approx (r_{2} - r_{1}) \cdot Δ n_{2}$

In this formula, the index delta Δn₂is multiplied by 1000, the unit of r₁and r₂is the μm, and therefore, the unit of V₀₂is the μm.

In a particular embodiment of the invention: 3 μm≤V₀₂≤12 μm.

The volume integral of the first layer of cladding 21 can be expressed by the following formula:

$V_{1 2} = 2 \cdot \int_{r_{1}}^{r_{2}} Δ n (r) \cdot r \cdot dr \approx (r_{2}^{2} - r_{1}^{2}) \cdot Δ n_{2}$

In this formula, the index delta Δn₂is multiplied by 1000, the unit of r₁and r₂is the μm, and therefore, the unit of V₁₂is the μm².

In a particular embodiment of the invention: 50 μm²≤V₁₂≤130 μm².

The second layer of cladding 22 or “trench” is defined with a radius r₃and a constant refractive index n₃, the index of the second layer of cladding being defined as follows: Δn_3≤0, with Δn₃being the refractive-index difference between the second layer of cladding 22 and the third layer of cladding 23: Δn₃=n₃−n₄Furthermore, according to a particular embodiment of the invention, the radius of the second layer of cladding 22 is preferably defined as follows: 10.8 μm≤r₃≤13.2 μm.

The surface integral of the second layer of cladding 22 can be expressed by the following formula:

$V_{0 3} = \int_{r_{2}}^{r_{3}} Δ n (r) \cdot dr \approx (r_{3} - r_{2}) \cdot Δ n_{3}$

In this formula, the index delta Δn₃is multiplied by 1000, the unit of r₂and r₃is the μm, and therefore, the unit of V₀₃is the μm.

In a particular embodiment of the invention: −30 μm≤V₀₃≤−14 μm.

The volume integral of the second layer of cladding 22 can be expressed by the following formula:

$V_{1 3} = 2 \cdot \int_{r_{2}}^{r_{3}} Δ n (r) \cdot r \cdot dr \approx (r_{3}^{2} - r_{2}^{2}) \cdot Δ n_{3}$

In this formula, the index delta Δn₃is multiplied by 1000, the unit of r₂and r₃is the μm, and therefore, the unit of V₁₃is the μm².

In a particular embodiment of the invention: −653 μm²≤V₁₃≤−272 μm².

Thus, the single-mode optical fiber 1 according to the invention requires a trench assisted design with a lower refractive index compared to the second layer of cladding, to reach the targeted performances, i.e. a ZDW comprised between 1340 and 1360 nm and a shifted CD and the same other parameters as G.652 and G.657 fibers.

Finally, the third layer of cladding 23 or “external cladding” is defined with a constant refractive index n₄which respects the following inequality: n₄≥n₃.

This third layer of cladding 23 participates in creating a trench in the second layer of cladding 22, and to protect the inner layers of cladding 20 and the core 10.

The third layer of cladding 23 is preferably composed of almost pure silica, and preferably pure silica.

Hereinafter are described specific embodiments of the invention. More particularly, the invention can present specific refractive-index profiles which are described in relation with [FIG. 2], [FIG. 3], [FIG. 4] and [FIG. 5], which are not limiting examples.

According to the invention, the refractive-index profile of the core 10 and the cladding 20 of the optical fiber 1 are described in relation with profile parameters (K₁, K₂, K₃), which are defined as follows:

$K_{1} = V_{1 1} - 5.85 \times V_{0 1}$

$K_{2} = V_{0 2} + 0.65 \times V_{0 1}$

$K_{3} = V_{0 3} - 5 \times K_{2}$

In these formulas, the unit of V₀₁, V₀₂and V₀₃is the μm, while the unit of V₁₁is the μm². Therefore, the formula of K₁can also be expressed: K₁=V₁₁−5.85 (μm)×V₀₁.

These profile parameters respect the following inequalities:

$- 5 9 < K_{1} < - 47$

$18 < K_{2} < 24$

$- 133 < K_{3} < - 1 1 8$

Thus, these profile parameters allow to better define the refractive-index profile of the optical fiber 1, and also allow to determine the limits of these profiles. Among the profiles defined by these profile parameters are angular profiles with a rectangular or trapezoidal shape, as illustrated by [FIG. 2], rounded profiles with a global rectangular or trapezoidal shape, as illustrated by [FIG. 3], and also profiles comprising a core with an inner central depressed zone 11 with either angular of rounded edges, as illustrated by [FIG. 4] and [FIG. 5].

Thus, as illustrated by [FIG. 3] the index profile of the core 10 can be rounded. In such a case, the first region of the core, with a radius r₀, ends exactly at the beginning of the refractive-index decrease, i.e. before the rounded part of the profile.

The cladding 20 of the optical fiber 1 can also present a profile with rounded edged. Such embodiment is not represented in the figures.

FIG. 4 represents another embodiment of the invention, in which the index profile of the core 10 comprises an inner central depressed zone 11, in the first region of the core. This figure represents an angular profile.

More particularly, as illustrated in [FIG. 4], this inner central depressed zone 11 extends from the center of the core (r=0) to a radius r₀, with r₀<r₀. In this inner central depressed zone 11, the refractive index n of the core, presents a minimum value at the center of the core equal to n_0D, with n_0D<n₀, or in other words, Δn_0D<Δn₀with Δn_0D=n_0D−n₄.

FIG. 5 represents another embodiment of the invention, in which the index profile of the core (10) is rounded and comprises an inner central depressed zone (11). Thus, all the profile of the core (10), with the inner central depressed zone (11), can present rounded edges. In this case, the inner central depressed zone (11), with a radius r_D, ends when the maximum value (n₀, or Δn₀) of the core refractive index (n) is reached. In the embodiment represented in [FIG. 5], r_D=r₀because the maximum value of n or Δn (which is n₀, or Δn₀) is only met at a unique point on the graph.

In an embodiment of the invention, the second region of the core from radius r₀to radius r₁, with decrease of refractive index can be obtained by gradually changing a concentration of at least two dopants, which can be chosen among the following elements and/or molecules:

- germanium oxide (GeO₂);
- fluorine (F);
- phosphorus oxide (P_XO_Y);
- boron oxide (B_XO_Y);
- aluminum oxide (Al₂O₃).

The modification of the refractive index of the other elements of the optical fiber 1 (other parts of the core 10, and the cladding 20) can also be obtained via a change in concentration of dopants in these different elements. More particularly, in an embodiment of the invention, the core 10 and the cladding 20 of the optical fiber 1 are both composed of silica, and the change in refractive index is obtained via the change in dopant concentration.

In a preferred embodiment, the impact of the inner central depressed zone 11 on V₁₁should not induce a V₁₁reduction of more than 1×10−3 μm², even more preferably 0.5×10−3 μm². [Table 2] below presents examples for an inner central depressed zone 11 presenting a fixed Δn_0D.

TABLE 2

r_D= 1 μm
n_0D− n₀≥ − 1 × 10⁻³,

and more preferably n_0D− n₀≥ − 0.5 × 10⁻³

r_D= 0.5 μm
n_0D− n₀≥ − 4 × 10⁻³,

and more preferably n_0D− n₀≥ − 2 × 10⁻³

r_D= 0.25 μm
n_0D− n₀≥ − 16 × 10⁻³,

and more preferably n_0D− n₀≥ − 8 × 10⁻³

The invention also relates to an optical fiber transmission system comprising an optical fiber 1 with the characteristics described previously. Preferentially, such system is a MDWDM system comprising a transmitter and a receiver, respectively comprising a multiplexer and a demultiplexer.

As an example, [FIG. 6] represents a MDWM system comprising an optical fiber 1, transmitters Tx, receivers

Rx, and optical multiplexers (OM) and demultiplexers (OD). The optical multiplexer and demultiplexer allow respectively to multiplex or concentrate several optical signals at one end of the system (λ₁, . . . λ_Nand λ₁, . . . λ_M) and to demultiplex or separate these signals at the other end of the system, in one direction of in the other. Thus, the signal propagated in the single-mode optical fiber 1 of the invention is a multiplexed signal (a combination of several signals).

Optionally, such system can comprise repeaters (100-1, . . . , 100-n) if the system transmits over long distances. The repeaters can comprise one or more filters, and/or one or more amplifiers 101, and/or one or more dispersion compensating fibers 102, etc.

By using the optical fiber of the invention, the range of wavelength which can be used by the optical fiber transmission system is wider than the ones available for the optical communication system of the prior art. In fact, it can operate in the O- and E-wavelength bands (from 1268 to 1375 nm) using, for example, Metro Wave Division Multiplexing (MWDM) with a 25 Gb/s transceiver.

Furthermore, the Transmitter Dispersion Penalty of such an optical fiber transmission system is lower than 1.5 dB, or even lower than 0.5 dB.

Theoretical examples of parameters, which can be used for obtaining a single-mode optical fiber 1 according to the invention, are presented in the tables hereinafter. [Table 3] to [Table 14] present 94 examples of sets of parameters (Ex1 to Ex94).

More particularly, [Table 3] lists 30 examples (Ex1 to Ex30), each comprising different parameters of ratios (r₀/r₁), radiuses (r₀, r₁, r₂, r₃), and refractive-index differences with the third layer of cladding (Δn₀, Δn₂, Δn₃).

TABLE 3

No
Ratio
r₀
r₁
r_eq
r₂
r₃
Δn₀
Δn₂
Δn₃

(Units)

(μm)
(μm)
(μm)
(μm)
(μm)
(×1000)
(×1000)
(×1000)

Ex1
0.05
0.185
3.7
1.9425
7.83
10.88
8.42
2.18
−4.77

Ex2
0.2
0.730
3.65
2.19
7.83
10.88
7.58
2.18
−4.77

Ex3
0.35
1.222
3.49
2.35575
7.83
10.88
7.04
2.2
−4.77

Ex4
0.5
1.635
3.27
2.4525
7.83
10.88
6.73
2.23
−4.77

Ex5
0.75
2.168
2.89
2.52875
7.83
10.88
6.49
2.25
−4.77

Ex6
0.95
2.480
2.61
2.54475
7.83
10.88
6.43
2.26
−4.77

Ex7
0.05
0.200
3.99
2.09475
8.27
10.88
8.18
1.94
−6.27

Ex8
0.2
0.784
3.92
2.352
8.27
10.88
7.35
1.95
−6.27

Ex9
0.35
1.309
3.74
2.5245
8.27
10.88
6.82
1.97
−6.27

Ex10
0.5
1.745
3.49
2.6175
8.27
10.88
6.51
2
−6.27

Ex11
0.75
2.303
3.07
2.68625
8.27
10.88
6.28
2.03
−6.27

Ex12
0.95
2.632
2.77
2.70075
8.27
10.88
6.23
2.03
−6.27

Ex13
0.05
0.212
4.24
2.226
8.7
10.88
8
1.72
−8.39

Ex14
0.2
0.832
4.16
2.496
8.7
10.88
7.17
1.74
−8.39

Ex15
0.35
1.383
3.95
2.66625
8.7
10.88
6.65
1.77
−8.39

Ex16
0.5
1.840
3.68
2.76
8.7
10.88
6.35
1.81
−8.39

Ex17
0.75
2.423
3.23
2.82625
8.7
10.88
6.13
1.83
−8.39

Ex18
0.95
2.765
2.91
2.83725
8.7
10.88
6.07
1.84
−8.39

Ex19
0.05
0.188
3.76
1.974
7.83
11.96
8.28
2.04
−4.35

Ex20
0.2
0.740
3.7
2.22
7.83
11.96
7.44
2.05
−4.35

Ex21
0.35
1.239
3.54
2.3895
7.83
11.96
6.91
2.07
−4.35

Ex22
0.5
1.655
3.31
2.4825
7.83
11.96
6.59
2.09
−4.35

Ex23
0.75
2.198
2.93
2.56375
7.83
11.96
6.34
2.11
−4.35

Ex24
0.95
2.508
2.64
2.574
7.83
11.96
6.29
2.11
−4.35

Ex25
0.05
0.201
4.01
2.10525
8.27
11.96
8.06
1.81
−5.74

Ex26
0.2
0.788
3.94
2.364
8.27
11.96
7.23
1.82
−5.74

Ex27
0.35
1.313
3.75
2.53125
8.27
11.96
6.7
1.85
−5.74

Ex28
0.5
1.755
3.51
2.6325
8.27
11.96
6.4
1.87
−5.74

Ex29
0.75
2.310
3.08
2.695
8.27
11.96
6.16
1.89
−5.74

Ex30
0.95
2.641
2.78
2.7105
8.27
11.96
6.11
1.9
−5.74

[Table 4] refers to the same 30 examples of [Table 3] and represents the subsequent surface integrals and volume integrals of the core and layers of cladding (V₀₁, V₁₁, V₀₂, V₁₂, V₀₃, V₁₃). The profile parameters K₁, K₂and K₃are also listed in this table.

TABLE 4

No
V₀₁
V₁₁
K₁
V₀₂
K₂
V₁₂
V₀₃
V₁₃
K₃

(Units)
(μm)
(μm²)
(μm²)
(μm)
(μm)
(μm²)
(μm)
(μm²)
(μm)

Ex1
20.2
59.8
−58.3
9.0
22.1
103.8
−14.5
−272.2
−125.2

Ex2
19.8
58.8
−57.0
9.1
22.0
104.6
−14.5
−272.2
−124.4

Ex3
19.1
55.7
−55.9
9.5
21.9
108.1
−14.5
−272.2
−124.3

Ex4
18.3
51.9
−55.3
10.2
22.1
112.9
−14.5
−272.2
−125.0

Ex5
17.2
46.1
−54.7
11.1
22.3
119.2
−14.5
−272.2
−126.1

Ex6
16.5
42.4
−54.2
11.8
22.5
123.2
−14.5
−272.2
−127.2

Ex7
20.8
65.7
−56.0
8.3
21.8
101.8
−16.4
−313.4
−125.5

Ex8
20.3
64.3
−54.8
8.5
21.7
103.4
−16.4
−313.4
−124.9

Ex9
19.6
60.9
−53.9
8.9
21.7
107.2
−16.4
−313.4
−124.7

Ex10
18.8
56.4
−53.5
9.6
21.8
112.4
−16.4
−313.4
−125.2

Ex11
17.6
50.0
−53.2
10.6
22.0
119.7
−16.4
−313.4
−126.5

Ex12
17.0
46.2
−53.0
11.2
22.2
123.3
−16.4
−313.4
−127.3

Ex13
21.3
70.5
−53.9
7.7
21.5
99.3
−18.3
−358.1
−125.8

Ex14
20.8
69.0
−52.7
7.9
21.4
101.6
−18.3
−358.1
−125.4

Ex15
20.0
65.0
−52.0
8.4
21.4
106.4
−18.3
−358.1
−125.3

Ex16
19.2
60.4
−51.9
9.1
21.6
112.5
−18.3
−358.1
−126.1

Ex17
18.1
53.7
−52.0
10.0
21.8
119.4
−18.3
−358.1
−127.0

Ex18
17.4
49.6
−51.9
10.7
21.9
123.7
−18.3
−358.1
−128.0

Ex19
20.0
59.8
−57.1
8.3
21.3
96.2
−18.0
−355.5
−124.4

Ex20
19.6
58.6
−55.8
8.5
21.2
97.6
−18.0
−355.5
−123.8

Ex21
18.9
55.7
−54.8
8.9
21.2
101.0
−18.0
−355.5
−123.8

Ex22
18.1
51.7
−54.2
9.4
21.2
105.2
−18.0
−355.5
−124.0

Ex23
17.0
46.1
−53.5
10.3
21.4
111.2
−18.0
−355.5
−125.0

Ex24
16.3
42.4
−53.1
11.0
21.6
114.7
−18.0
−355.5
−125.8

Ex25
20.4
64.4
−55.1
7.7
21.0
94.7
−21.2
−428.5
−126.1

Ex26
20.0
63.0
−53.8
7.9
20.9
96.2
−21.2
−428.5
−125.5

Ex27
19.2
59.5
−52.9
8.4
20.9
100.5
−21.2
−428.5
−125.4

Ex28
18.5
55.6
−52.6
8.9
20.9
104.9
−21.2
−428.5
−125.8

Ex29
17.3
49.2
−52.2
9.8
21.1
111.3
−21.2
−428.5
−126.5

Ex30
16.7
45.6
−52.0
10.4
21.3
115.3
−21.2
−428.5
−127.6

[Table 5] refers to the same 30 examples of [Table 3] and represents the corresponding Zero Dispersion Wavelength (ZDW), Zero Dispersion Shift (ZDS), Chromatic Dispersion (CD) at 1267.5 nm, at 1310 nm, and at 1374.5 nm, the Mode Filed Diameter (MFD) at 1310 nm and at 1550 nm, and the cable cutoff wavelength.

TABLE 5

CD
CD
CD
MFD
MFD
Cable

No
ZDW
ZDS
1267.5
1310
1374.5
1310
1550
Cutoff

(Units)
(nm)
(ps/(nm²· km))
(ps/(nm · km))
(ps/(nm · km))
(ps/(nm · km))
(μm)
(μm)
(nm)

Ex1
1350
0.097
−8.9
−4.1
2.4
9.00
10.33
1212

Ex2
1350
0.096
−8.9
−4.1
2.4
9.00
10.33
1211

Ex3
1350
0.096
−8.8
−4.1
2.3
9.00
10.33
1211

Ex4
1350
0.096
−8.8
−4.1
2.4
9.00
10.34
1212

Ex5
1350
0.096
−8.8
−4.1
2.3
9.00
10.33
1214

Ex6
1350
0.096
−8.7
−4.1
2.4
9.00
10.34
1214

Ex7
1350
0.096
−8.8
−4.1
2.4
9.00
10.34
1209

Ex8
1350
0.096
−8.8
−4.1
2.3
9.00
10.34
1209

Ex9
1350
0.096
−8.8
−4.1
2.3
9.00
10.34
1209

Ex10
1350
0.095
−8.7
−4.1
2.3
9.00
10.35
1210

Ex11
1350
0.095
−8.7
−4
2.3
9.01
10.35
1210

Ex12
1350
0.095
−8.7
−4.1
2.3
9.00
10.35
1210

Ex13
1350
0.095
−8.7
−4.1
2.3
9.00
10.34
1209

Ex14
1350
0.095
−8.7
−4.1
2.3
9.00
10.34
1209

Ex15
1350
0.095
−8.7
−4
2.3
9.00
10.34
1209

Ex16
1350
0.095
−8.6
−4
2.3
9.01
10.35
1209

Ex17
1350
0.094
−8.6
−4
2.3
8.99
10.34
1209

Ex18
1350
0.094
−8.6
−4
2.3
9.00
10.35
1209

Ex19
1350
0.097
−8.9
−4.1
2.4
9.00
10.33
1210

Ex20
1350
0.097
−8.8
−4.1
2.4
9.00
10.34
1210

Ex21
1350
0.096
−8.8
−4.1
2.3
8.99
10.33
1210

Ex22
1350
0.096
−8.8
−4.1
2.4
9.00
10.34
1210

Ex23
1350
0.096
−8.7
−4
2.4
9.00
10.34
1208

Ex24
1350
0.096
−8.8
−4.1
2.3
9.00
10.34
1209

Ex25
1350
0.097
−8.8
−4.1
2.4
9.00
10.34
1213

Ex26
1350
0.096
−8.8
−4.1
2.4
9.00
10.34
1212

Ex27
1350
0.096
−8.8
−4.1
2.4
9.01
10.34
1213

Ex28
1350
0.096
−8.7
−4.1
2.3
9.00
10.33
1213

Ex29
1350
0.096
−8.7
−4.1
2.3
9.00
10.34
1212

Ex30
1350
0.095
−8.7
−4.1
2.3
9.00
10.34
1212

[Table 6] refers to the same 30 examples of [Table 3] and represents the corresponding bend losses (R7.5BL, R10BL and R15BL) for either 1 or 10 turns, measured at different wavelengths (1550 μm and 1625 μm), and for different radiuses (7.5 mm, 10 mm, and 15 mm).

TABLE 6

R15BL
R10BL
R7.5BL
R15BL
R10BL
R7.5BL

No
at 1550
at 1550
at 1550
at 1625
at 1625
at 1625

(Units)
(dB/10turn)
(dB/turn)
(dB/turn)
(dB/10turn)
(dB/turn)
(dB/turn)
BL Type

Ex1
0.034
0.16
0.92
0.184
0.47
1.94
A1

Ex2
0.035
0.16
0.93
0.189
0.48
1.96
A1

Ex3
0.035
0.17
0.94
0.191
0.48
1.97
A1

Ex4
0.036
0.17
0.95
0.194
0.49
1.99
A1

Ex5
0.035
0.17
0.95
0.192
0.48
1.99
A1

Ex6
0.036
0.17
0.95
0.193
0.49
2
A1

Ex7
0.035
0.16
0.84
0.189
0.45
1.75
A1

Ex8
0.036
0.16
0.85
0.191
0.45
1.76
A1

Ex9
0.037
0.16
0.86
0.196
0.46
1.79
A1

Ex10
0.037
0.16
0.87
0.198
0.46
1.81
A1

Ex11
0.039
0.17
0.9
0.207
0.48
1.85
A1

Ex12
0.04
0.17
0.9
0.21
0.48
1.86
A1

Ex13
0.035
0.14
0.75
0.184
0.41
1.56
A1

Ex14
0.036
0.15
0.76
0.188
0.42
1.57
A1

Ex15
0.037
0.15
0.78
0.192
0.42
1.6
A1

Ex16
0.038
0.15
0.8
0.199
0.43
1.63
A1

Ex17
0.041
0.16
0.83
0.213
0.45
1.69
A1

Ex18
0.042
0.16
0.84
0.217
0.46
1.71
A1

Ex19
0.043
0.15
0.7
0.218
0.41
1.42
A1

Ex20
0.042
0.15
0.7
0.217
0.41
1.42
A1

Ex21
0.043
0.15
0.7
0.219
0.41
1.43
A1

Ex22
0.045
0.15
0.72
0.228
0.42
1.46
A1

Ex23
0.048
0.16
0.75
0.244
0.44
1.52
A1

Ex24
0.048
0.16
0.75
0.245
0.44
1.51
A1

Ex25
0.043
0.13
0.57
0.213
0.35
1.15
A1

Ex26
0.043
0.13
0.58
0.217
0.36
1.16
A1

Ex27
0.043
0.13
0.58
0.217
0.36
1.17
A1

Ex28
0.045
0.13
0.59
0.223
0.37
1.19
A1

Ex29
0.049
0.14
0.62
0.241
0.38
1.24
A1

Ex30
0.05
0.14
0.63
0.247
0.39
1.25
A1

[Table 7], [Table 8] and [Table 9] represent 30 more examples (Ex31 to Ex60), listing the same parameters as respectively [Table 3], [Table 4], [Table 5] and [Table 6].

TABLE 7

No

r₀
r₁
r_eq
r₂
r₃
Δn₀
Δn₂
Δn₃

(Units)
Ratio
(μm)
(μm)
(μm)
(μm)
(μm)
(×1000)
(×1000)
(×1000)

Ex31
0.05
0.212
4.24
2.226
8.7
11.96
7.89
1.59
−7.58

Ex32
0.2
0.832
4.16
2.496
8.7
11.96
7.05
1.6
−7.58

Ex33
0.35
1.383
3.95
2.66625
8.7
11.96
6.54
1.65
−7.58

Ex34
0.5
1.840
3.68
2.76
8.7
11.96
6.24
1.68
−7.58

Ex35
0.75
2.423
3.23
2.82625
8.7
11.96
6
1.7
−7.58

Ex36
0.95
2.765
2.91
2.83725
8.7
11.96
5.95
1.7
−7.58

Ex37
0.05
0.194
3.87
2.03175
7.83
13.05
8.11
1.9
−3.95

Ex38
0.2
0.762
3.81
2.286
7.83
13.05
7.27
1.9
−3.95

Ex39
0.35
1.274
3.64
2.457
7.83
13.05
6.76
1.94
−3.95

Ex40
0.5
1.700
3.4
2.55
7.83
13.05
6.45
1.97
−3.95

Ex41
0.75
2.250
3
2.625
7.83
13.05
6.21
1.98
−3.95

Ex42
0.95
2.575
2.71
2.64225
7.83
13.05
6.15
1.99
−3.95

Ex43
0.05
0.204
4.08
2.142
8.27
13.05
7.95
1.7
−5.25

Ex44
0.2
0.804
4.02
2.412
8.27
13.05
7.12
1.71
−5.25

Ex45
0.35
1.337
3.82
2.5785
8.27
13.05
6.6
1.74
−5.25

Ex46
0.5
1.780
3.56
2.67
8.27
13.05
6.29
1.77
−5.25

Ex47
0.75
2.348
3.13
2.73875
8.27
13.05
6.06
1.79
−5.25

Ex48
0.95
2.689
2.83
2.75925
8.27
13.05
6
1.79
−5.25

Ex49
0.05
0.215
4.3
2.2575
8.7
13.05
7.78
1.48
−6.9

Ex50
0.2
0.844
4.22
2.532
8.7
13.05
6.95
1.5
−6.9

Ex51
0.35
1.400
4
2.7
8.7
13.05
6.44
1.54
−6.9

Ex52
0.5
1.860
3.72
2.79
8.7
13.05
6.14
1.57
−6.9

Ex53
0.75
2.445
3.26
2.8525
8.7
13.05
5.91
1.6
−6.9

Ex54
0.95
2.793
2.94
2.8665
8.7
13.05
5.86
1.61
−6.9

Ex55
0.45
1.481
3.29
2.38525
8.27
13.05
6.54
1.95
−5.25

Ex56
0.25
0.908
3.63
2.26875
8.27
13.05
7.18
1.86
−5.25

Ex57
0.4
1.352
3.38
2.366
7.83
13.05
6.54
1.93
−3.95

Ex58
0.7
2.072
2.96
2.516
7.83
11.96
6.55
2.28
−4.35

Ex59
0.15
0.593
3.95
2.27125
8.27
10.88
7.73
2.05
−6.27

Ex60
0.1
0.390
3.9
2.145
7.83
10.88
7.92
2.19
−4.77

TABLE 8

No
V₀₁
V₁₁
K₁
V₀₂
K₂
V₁₂
V₀₃
V₁₃
K₃

(Units)
(μm)
(μm²)
(μm²)
(μm)
(μm)
(μm²)
(μm)
(μm²)
(μm)

Ex31
20.8
68.3
−53.2
7.1
20.6
91.8
−24.7
−510.5
−127.7

Ex32
20.3
66.7
−51.8
7.3
20.4
93.4
−24.7
−510.5
−126.9

Ex33
19.6
63.2
−51.2
7.8
20.5
99.1
−24.7
−510.5
−127.5

Ex34
18.8
58.8
−51.0
8.4
20.6
104.4
−24.7
−510.5
−127.9

Ex35
17.6
52.3
−50.9
9.3
20.8
110.9
−24.7
−510.5
−128.5

Ex36
17.0
48.6
−50.9
9.8
20.9
114.3
−24.7
−510.5
−129.2

Ex37
20.0
61.1
−55.7
7.5
20.5
88.0
−20.6
−430.5
−123.1

Ex38
19.5
59.8
−54.4
7.6
20.3
88.9
−20.6
−430.5
−122.2

Ex39
18.9
57.1
−53.5
8.1
20.4
93.2
−20.6
−430.5
−122.7

Ex40
18.1
53.0
−53.0
8.7
20.5
98.0
−20.6
−430.5
−123.2

Ex41
17.0
47.2
−52.5
9.6
20.6
103.6
−20.6
−430.5
−123.8

Ex42
16.4
43.7
−52.2
10.2
20.8
107.4
−20.6
−430.5
−124.8

Ex43
20.3
64.8
−54.1
7.1
20.3
88.0
−25.1
−535.0
−126.8

Ex44
19.9
63.8
−52.8
7.3
20.2
89.3
−25.1
−535.0
−126.2

Ex45
19.2
60.2
−52.0
7.7
20.2
93.6
−25.1
−535.0
−126.1

Ex46
18.4
55.8
−51.6
8.3
20.3
98.6
−25.1
−535.0
−126.5

Ex47
17.3
49.8
−51.4
9.2
20.4
104.9
−25.1
−535.0
−127.3

Ex48
16.7
46.4
−51.2
9.7
20.6
108.1
−25.1
−535.0
−128.0

Ex49
20.6
68.2
−52.2
6.5
19.9
84.7
−30.0
−652.8
−129.5

Ex50
20.1
66.8
−50.9
6.7
19.8
86.8
−30.0
−652.8
−129.0

Ex51
19.4
63.1
−50.3
7.2
19.8
91.9
−30.0
−652.8
−129.2

Ex52
18.6
58.6
−50.1
7.8
19.9
97.1
−30.0
−652.8
−129.5

Ex53
17.5
52.3
−50.1
8.7
20.1
104.1
−30.0
−652.8
−130.4

Ex54
16.9
48.8
−50.1
9.3
20.3
107.9
−30.0
−652.8
−131.4

Ex55
17.4
48.5
−53.1
9.7
21.0
112.3
−25.1
−535.0
−130.1

Ex56
18.8
55.2
−54.9
8.6
20.9
102.7
−25.1
−535.0
−129.4

Ex57
17.4
49.4
−52.5
8.6
19.9
96.3
−20.6
−430.5
−120.2

Ex58
17.5
47.3
−55.0
11.1
22.5
119.8
−18.0
−355.5
−130.3

Ex59
21.0
66.6
−56.2
8.9
22.5
108.2
−16.4
−313.4
−128.9

Ex60
20.8
65.6
−56.3
8.6
22.1
101.0
−14.5
−272.2
−125.3

TABLE 9

CD
CD
CD
MFD
MFD
Cable

No
ZDW
ZDS
1267.5
1310
1374.5
1310
1550
Cutoff

(Units)
(nm)
(ps/(nm²· km))
(ps/(nm · km))
(ps/(nm · km))
(ps/(nm · km))
(μm)
(μm)
(nm)

Ex31
1350
0.096
−8.8
−4.1
2.3
8.99
10.33
1216

Ex32
1350
0.096
−8.7
−4.1
2.3
9.00
10.33
1215

Ex33
1350
0.096
−8.7
−4
2.3
9.00
10.34
1219

Ex34
1350
0.095
−8.6
−4
2.3
9.00
10.34
1218

Ex35
1350
0.095
−8.6
−4
2.3
9.00
10.35
1215

Ex36
1350
0.095
−8.6
−4
2.3
9.00
10.34
1215

Ex37
1350
0.096
−8.8
−4.1
2.4
9.00
10.34
1214

Ex38
1350
0.096
−8.8
−4.1
2.4
9.00
10.34
1213

Ex39
1350
0.096
−8.8
−4.1
2.3
9.00
10.34
1218

Ex40
1350
0.096
−8.7
−4
2.4
9.00
10.35
1219

Ex41
1350
0.095
−8.7
−4
2.3
9.00
10.34
1217

Ex42
1350
0.095
−8.7
−4
2.4
9.00
10.35
1216

Ex43
1350
0.096
−8.8
−4.1
2.3
9.00
10.34
1214

Ex44
1350
0.096
−8.8
−4.1
2.3
9.00
10.34
1215

Ex45
1350
0.096
−8.7
−4.1
2.3
9.00
10.34
1218

Ex46
1350
0.095
−8.7
−4
2.3
9.01
10.35
1213

Ex47
1350
0.095
−8.7
−4
2.3
9.00
10.35
1214

Ex48
1350
0.095
−8.6
−4
2.3
9.00
10.34
1214

Ex49
1350
0.096
−8.7
−4.1
2.3
9.00
10.34
1205

Ex50
1350
0.096
−8.7
−4
2.3
9.00
10.34
1205

Ex51
1350
0.095
−8.7
−4
2.3
9.00
10.34
1207

Ex52
1350
0.095
−8.6
−4
2.3
9.00
10.34
1206

Ex53
1350
0.095
−8.6
−4
2.3
9.00
10.35
1206

Ex54
1350
0.095
−8.6
−4
2.3
9.00
10.35
1206

Ex55
1352
0.098
−9.3
−4.4
2.2
9.18
10.58
1221

Ex56
1356
0.097
−9.5
−4.7
1.8
9.03
10.43
1215

Ex57
1350
0.097
−8.8
−4.1
2.4
9.15
10.52
1186

Ex58
1350
0.096
−8.8
−4.1
2.4
9.01
10.35
1245

Ex59
1351
0.096
−8.9
−4.2
2.3
8.98
10.31
1237

Ex60
1345
0.096
−8.3
−3.6
2.8
9.04
10.33
1229

TABLE 10

R15BL
R10BL
R7.5BL
R15BL
R10BL
R7.5BL

No
at 1550
at 1550
at 1550
at 1625
at 1625
at 1625

(Units)
(dB/10turn)
(dB/turn)
(dB/turn)
(dB/10turn)
(dB/turn)
(dB/turn)
BL Type

Ex31
0.04
0.11
0.46
0.197
0.29
0.91
A1

Ex32
0.041
0.11
0.46
0.203
0.3
0.93
A1

Ex33
0.039
0.11
0.46
0.194
0.29
0.92
A1

Ex34
0.043
0.11
0.48
0.21
0.31
0.95
A1

Ex35
0.048
0.12
0.5
0.232
0.33
1
A1

Ex36
0.049
0.12
0.51
0.236
0.33
1.01
A1

Ex37
0.046
0.12
0.51
0.224
0.33
1.02
A1

Ex38
0.047
0.12
0.51
0.229
0.33
1.03
A1

Ex39
0.043
0.12
0.5
0.213
0.32
1.01
A1

Ex40
0.044
0.12
0.51
0.219
0.33
1.02
A1

Ex41
0.048
0.13
0.52
0.236
0.34
1.05
A1

Ex42
0.049
0.13
0.53
0.241
0.35
1.07
A1

Ex43
0.036
0.09
0.34
0.177
0.24
0.69
A1

Ex44
0.036
0.09
0.34
0.177
0.24
0.69
A1

Ex45
0.037
0.09
0.35
0.18
0.24
0.7
A1

Ex46
0.04
0.09
0.36
0.192
0.25
0.72
A1

Ex47
0.042
0.1
0.37
0.202
0.26
0.74
A1

Ex48
0.043
0.1
0.37
0.206
0.26
0.74
A1

Ex49
0.031
0.07
0.24
0.151
0.18
0.48
A1

Ex50
0.031
0.07
0.24
0.151
0.18
0.48
A1

Ex51
0.032
0.07
0.24
0.152
0.18
0.49
A1

Ex52
0.034
0.07
0.25
0.163
0.19
0.51
A1

Ex53
0.037
0.07
0.26
0.173
0.19
0.52
A1

Ex54
0.037
0.07
0.26
0.176
0.19
0.52
A1

Ex55
0.071
0.13
0.48
0.310
0.34
0.92
A1

Ex56
0.052
0.11
0.42
0.241
0.29
0.82
A1

Ex57
0.150
0.24
0.83
0.636
0.59
1.57
A1

Ex58
0.018
0.09
0.51
0.101
0.27
1.09
A1

Ex59
0.015
0.09
0.60
0.089
0.28
1.31
A1

Ex60
0.018
0.11
0.71
0.106
0.33
1.55
A1

Finally, [Table 11], [Table 12], [Table 13] and [Table 14] represent 34 more examples (Ex61 to Ex94), listing the same parameters as respectively [Table 3], [Table 4], [Table 5] and [Table 6].

TABLE 11

No

r₀
r₁
r_eq
r₂
r₃
Δn₀
Δn₂
Δn₃

(Units)
Ratio
(μm)
(μm)
(μm)
(μm)
(μm)
(×1000)
(×1000)
(×1000)

Ex61
0.5
1.610
3.22
2.415
7.83
10.88
7.04
2.38
−4.77

Ex62
0.3
1.062
3.54
2.301
8.27
11.96
7.04
2.09
−5.74

Ex63
0.6
1.938
3.23
2.584
7.83
10.88
6.47
1.99
−4.77

Ex64
0.3
1.236
4.12
2.678
8.27
10.88
6.9
1.76
−6.27

Ex65
0.25
0.785
3.14
1.9625
7.83
10.88
7.66
2.33
−4.77

Ex66
0.1
0.407
4.07
2.2385
7.83
10.88
7.72
2.05
−4.77

Ex67
0.25
0.928
3.71
2.31875
7.83
10.88
7.25
2.39
−4.77

Ex68
0.95
2.584
2.72
2.652
7.83
10.88
6.18
2.28
−4.77

Ex69
0.7
2.289
3.27
2.7795
8.7
10.88
6.27
1.98
−8.39

Ex70
0.7
2.156
3.08
2.618
7.83
13.05
6.58
2.16
−3.95

Ex71
0.1
0.506
5.06
2.783
8.27
13.05
7.74
1.18
−5.25

Ex72
0.2
0.828
4.14
2.484
7.83
11.96
7.43
1.94
−4.35

Ex73
0.3
1.332
4.44
2.886
8.27
13.05
6.39
1.43
−5.25

Ex74
0.1
0.441
4.41
2.4255
8.7
13.05
7.39
1.6
−6.9

Ex75
0.4
1.652
4.13
2.891
8.7
13.05
6.48
1.21
−6.9

Ex76
0.5
1.720
3.44
2.58
7.83
13.05
6.39
2.17
−3.95

Ex77
0.1
0.480
4.8
2.64
8.27
10.88
7.86
1.66
−6.27

Ex78
0.6
2.292
3.82
3.056
7.83
11.96
6.54
1.87
−4.35

Ex79
0.9
2.763
3.07
2.9165
8.27
10.88
6.21
2.13
−6.27

Ex80
0.4
1.612
4.03
2.821
8.27
11.96
6.44
1.82
−5.74

Ex81
0.45
1.899
4.22
3.0595
8.27
13.05
6.17
1.4
−5.25

Ex82
0.4
1.664
4.16
2.912
8.27
13.05
6.55
1.34
−5.25

Ex83
0.3
1.305
4.35
2.8275
8.7
11.96
6.54
1.65
−7.58

Ex84
0.6
2.394
3.99
3.192
8.7
11.96
6.15
1.44
−7.58

Ex85
0.7
2.345
3.35
2.8475
8.7
11.96
6.42
1.6
−7.58

Ex86
0.1
0.434
4.34
2.387
7.83
13.05
8.16
1.76
−3.95

Ex87
0.85
2.992
3.52
3.256
8.7
13.05
5.99
1.23
−6.9

Ex88
0.1
0.448
4.48
2.464
8.7
10.88
7.93
1.74
−8.39

Ex89
0.25
1.150
4.6
2.875
8.27
10.88
7.11
1.74
−6.27

Ex90
0.2
0.894
4.47
2.682
7.83
11.96
7.15
1.74
−4.35

Ex91
0.45
1.733
3.85
2.79125
8.7
11.96
6.75
1.57
−7.58

Ex92
0.9
2.790
3.1
2.945
8.27
13.05
6.09
1.69
−5.25

Ex93
0.75
2.790
3.72
3.255
8.7
11.96
6.26
1.44
−7.58

Ex94
0.25
1.070
4.28
2.675
7.83
10.88
7.53
2.04
−4′.77

TABLE 12

No
V₀₁
V₁₁
K₁
V₀₂
K₂
V₁₂
V₀₃
V₁₃
K₃

(Units)
(μm)
(μm²)
(μm²)
(μm)
(μm)
(μm²)
(μm)
(μm²)
(μm)

Ex61
18.9
52.9
−57.8
11.0
23.3
121.2
−14.5
−272.2
−130.9

Ex62
18.8
54.9
−55.0
9.9
22.1
116.8
−21.2
−428.5
−131.7

Ex63
18.0
51.3
−54.0
9.2
20.9
101.2
−14.5
−272.2
−118.8

Ex64
21.0
70.3
−52.6
7.3
21.0
90.5
−16.4
−313.4
−121.2

Ex65
17.8
46.0
−58.0
10.9
22.5
119.9
−14.5
−272.2
−127.0

Ex66
21.0
68.7
−54.3
7.7
21.4
91.7
−14.5
−272.2
−121.5

Ex67
20.1
62.2
−55.6
9.8
22.9
113.6
−14.5
−272.2
−129.2

Ex68
16.5
44.3
−52.5
11.7
22.4
122.9
−14.5
−272.2
−126.6

Ex69
18.4
54.7
−53.0
10.8
22.7
128.7
−18.3
−358.1
−131.8

Ex70
18.2
51.1
−55.5
10.3
22.1
111.9
−20.6
−430.5
−131.1

Ex71
24.2
92.4
−49.4
3.8
19.5
50.5
−25.1
−535.0
−122.8

Ex72
21.7
72.1
−54.6
7.2
21.2
85.7
−18.0
−355.5
−124.2

Ex73
20.7
73.5
−47.4
5.5
18.9
69.6
−25.1
−535.0
−119.6

Ex74
21.1
72.8
−50.7
6.9
20.6
90.0
−30.0
−652.8
−132.9

Ex75
20.2
67.4
−51.0
5.5
18.7
70.9
−30.0
−652.8
−123.4

Ex76
18.4
54.8
−52.6
9.5
21.5
107.4
−20.6
−430.5
−127.9

Ex77
24.3
91.1
−51.3
5.8
21.6
75.3
−16.4
−313.4
−124.3

Ex78
21.4
71.8
−53.5
7.5
21.4
87.4
−18.0
−355.5
−125.1

Ex79
18.4
54.8
−53.1
11.1
23.1
125.6
−16.4
−313.4
−131.7

Ex80
20.4
68.6
−50.6
7.7
21.0
94.9
−21.2
−428.5
−126.0

Ex81
20.5
71.7
−48.2
5.7
19.0
70.8
−25.1
−535.0
−120.1

Ex82
20.7
70.1
−51.3
5.5
19.0
68.5
−25.1
−535.0
−120.1

Ex83
21.0
74.1
−48.8
7.2
20.8
93.7
−24.7
−510.5
−128.9

Ex84
20.8
71.9
−49.6
6.8
20.3
86.1
−24.7
−510.5
−126.2

Ex85
19.1
57.4
−54.2
8.6
21.0
103.1
−24.7
−510.5
−129.5

Ex86
22.9
77.8
−56.3
6.1
21.0
74.8
−20.6
−430.5
−125.8

Ex87
19.8
65.8
−50.2
6.4
19.3
77.9
−30.0
−652.8
−126.3

Ex88
23.0
80.9
−53.9
7.3
22.3
96.8
−18.3
−358.1
−129.9

Ex89
23.4
86.5
−50.6
6.4
21.6
82.2
−16.4
−313.4
−124.5

Ex90
22.3
79.4
−50.9
5.8
20.3
71.9
−18.0
−355.5
−119.6

Ex91
20.5
65.6
−54.4
7.6
20.9
95.6
−24.7
−510.5
−129.4

Ex92
18.2
54.4
−52.0
8.7
20.6
99.3
−25.1
−535.0
−127.9

Ex93
21.0
71.3
−51.8
7.2
20.9
89.1
−24.7
−510.5
−129.0

Ex94
23.4
81.4
−55.6
7.2
22.5
87.7
−14.5
−272.2
−126.9

TABLE 13

CD
CD
CD
MFD
MFD
Cable

No
ZDW
ZDS
1267.5
1310
1374.5
1310
1550
Cutoff

(Units)
(nm)
(ps/(nm²· km))
(ps/(nm · km))
(ps/(nm · km))
(ps/(nm · km))
(μm)
(μm)
(nm)

Ex61
1354
0.096
−9.3
−4.5
2.0
8.90
10.24
1247

Ex62
1350
0.098
−9.0
−4.2
2.4
9.16
10.52
1244

Ex63
1352
0.094
−8.9
−4.2
2.1
8.87
10.20
1170

Ex64
1348
0.094
−8.4
−3.8
2.5
8.84
10.13
1200

Ex65
1352
0.099
−9.4
−4.5
2.2
9.18
10.58
1209

Ex66
1342
0.096
−7.9
−3.3
3.0
9.03
10.30
1212

Ex67
1342
0.097
−8.0
−3.3
3.1
9.16
10.44
1259

Ex68
1341
0.096
−7.8
−3.2
3.1
9.16
10.45
1224

Ex69
1350
0.095
−8.7
−4.0
2.3
9.04
10.39
1239

Ex70
1354
0.095
−9.0
−4.4
2.0
8.86
10.20
1260

Ex71
1342
0.093
−7.6
−3.1
3.0
8.64
9.82
1244

Ex72
1347
0.095
−8.3
−3.7
2.6
8.82
10.08
1233

Ex73
1340
0.094
−7.5
−3.0
3.2
8.97
10.21
1200

Ex74
1345
0.096
−8.2
−3.6
2.8
9.10
10.40
1246

Ex75
1354
0.092
−8.7
−4.3
1.9
8.62
9.92
1175

Ex76
1343
0.096
−8.0
−3.4
3.0
9.18
10.48
1260

Ex77
1342
0.094
−7.7
−3.1
3.0
8.77
9.97
1252

Ex78
1341
0.092
−7.4
−3.0
3.0
8.65
9.83
1256

Ex79
1342
0.094
−7.7
−3.2
3.0
9.02
10.29
1259

Ex80
1342
0.095
−7.8
−3.2
3.0
9.00
10.26
1240

Ex81
1341
0.093
−7.4
−3.0
3.1
8.83
10.06
1204

Ex82
1350
0.092
−8.3
−3.9
2.2
8.61
9.88
1185

Ex83
1342
0.095
−7.8
−3.2
3.1
9.06
10.33
1247

Ex84
1341
0.092
−7.3
−3.0
3.1
8.76
9.97
1239

Ex85
1359
0.092
−9.3
−4.8
1.4
8.61
9.95
1211

Ex86
1352
0.093
−8.7
−4.2
2.1
8.63
9.89
1245

Ex87
1342
0.090
−7.3
−3.0
2.9
8.63
9.83
1220

Ex88
1350
0.094
−8.6
−4.0
2.3
8.83
10.13
1250

Ex89
1341
0.093
−7.6
−3.1
3.1
8.79
10.01
1252

Ex90
1341
0.094
−7.6
−3.1
3.1
8.84
10.06
1226

Ex91
1359
0.093
−9.3
−4.8
1.5
8.60
9.93
1216

Ex92
1348
0.093
−8.2
−3.7
2.4
8.80
10.09
1222

Ex93
1341
0.090
−7.3
−3.0
3.0
8.61
9.80
1257

Ex94
1347
0.093
−8.2
−3.6
2.6
8.65
9.87
1260

TABLE 14

R15BL
R10BL
R7.5BL
R15BL
R10BL
R7.5BL

No
at 1550
at 1550
at 1550
at 1625
at 1625
at 1625

(Units)
(dB/10turn)
(dB/turn)
(dB/turn)
(dB/10turn)
(dB/turn)
(dB/turn)
BL Type

Ex61
0.009
0.07
0.54
0.057
0.23
1.24
A1

Ex62
0.037
0.12
0.58
0.180
0.34
1.16
A1

Ex63
0.072
0.25
1.22
0.370
0.70
2.49
A1

Ex64
0.021
0.11
0.63
0.121
0.33
1.38
A1

Ex65
0.098
0.32
1.53
0.459
0.84
2.97
A1

Ex66
0.027
0.14
0.81
0.149
0.40
1.73
A1

Ex67
0.011
0.08
0.60
0.067
0.25
1.34
A1

Ex68
0.035
0.17
0.95
0.183
0.47
1.97
A1

Ex69
0.021
0.11
0.65
0.117
0.32
1.37
A1

Ex70
0.008
0.04
0.25
0.048
0.14
0.57
A2

Ex71
0.002
0.01
0.09
0.013
0.05
0.22
A2

Ex72
0.008
0.05
0.33
0.050
0.16
0.77
A2

Ex73
0.027
0.07
0.28
0.136
0.20
0.58
A2

Ex74
0.015
0.04
0.19
0.078
0.13
0.38
A2

Ex75
0.019
0.05
0.18
0.103
0.13
0.37
A2

Ex76
0.021
0.08
0.38
0.107
0.22
0.80
A2

Ex77
0.002
0.02
0.23
0.013
0.08
0.57
A2

Ex78
0.001
0.02
0.15
0.010
0.06
0.39
A2

Ex79
0.006
0.06
0.43
0.042
0.18
0.98
A2

Ex80
0.013
0.06
0.35
0.076
0.19
0.76
A2

Ex81
0.014
0.05
0.21
0.080
0.14
0.46
A2

Ex82
0.013
0.04
0.20
0.079
0.14
0.45
A2

Ex83
0.014
0.06
0.29
0.075
0.17
0.62
A2

Ex84
0.005
0.03
0.18
0.032
0.10
0.41
A2

Ex85
0.012
0.05
0.27
0.074
0.16
0.59
A2

Ex86
0.003
0.02
0.15
0.020
0.07
0.37
A2

Ex87
0.004
0.02
0.10
0.029
0.06
0.23
A2

Ex88
0.004
0.04
0.31
0.030
0.13
0.75
A2

Ex89
0.002
0.02
0.24
0.015
0.09
0.60
A2

Ex90
0.008
0.05
0.33
0.053
0.17
0.76
A2

Ex91
0.008
0.04
0.23
0.053
0.13
0.52
A2

Ex92
0.012
0.05
0.21
0.070
0.14
0.47
A2

Ex93
0.001
0.01
0.11
0.011
0.05
0.27
A2

Ex94
0.001
0.01
0.18
0.007
0.06
0.48
A2

The ranges of the values of the different parameters used in the 94 examples listed in the above tables are presented hereinafter, in [Table 15], [Table 16], [Table 17] and [Table 18].

TABLE 15

Parameter

r₀
r₁
r_eq
r₂
r₃
Δn₀
Δn₂
Δn₃

Unit
r₀/r₁
μm
μm
μm
μm
μm
(×1000)
(×1000)
(×1000)

Minimum value
0.05
0.19
2.61
1.94
7.83
10.88
5.86
1.18
−8.39

Maximum value
0.95
2.99
5.06
3.26
8.70
13.05
8.42
2.39
−3.95

TABLE 16

Parameter
V₀₁
V₁₁
V₀₂
V₁₂
V₀₃
V₁₃
K₁
K₂
K₃

Unit
(μm)
(μm²)
(μm²)
(μm)
(μm)
(μm²)
(μm)
(μm²)
(μm)

Minimum
16.3
42.4
3.8
50.5
−30
−652.8
−58.3
18.7
−132.9

value

Maximum
24.3
92.4
11.8
128.7
−14.5
−277.2
−47.4
23.3
−118.8

value

TABLE 17

CD
CD
CD
MFD
MFD
Cable

Parameter
ZDW
ZDS
1267.5
1310
1374.5
1310
1550
cutoff

Unit
nm
(ps/(nm²· km)
(ps/(nm²-km)
(ps/(nm²· km)
(ps/(nm²· km)
μm
μm
nm

Minimum
1340
0.090
−9.5
−4.8
1.4
8.6
9.8
1170

value

Maximum
1359
0.099
−7.3
−3
3.2
9.2
10.6
1260

value

TABLE 18

R15BL
R10BL
R7.5BL
R15BL
R10BL
R7.5BL

Parameter
at 1550
at 1550
at 1550
at 1625
at 1625
at 1625

(Units)
(dB/10turn)
(dB/turn)
(dB/turn)
(dB/10turn)
(dB/turn)
(dB/turn)

Minimum value
0.001
0.013
0.090
0.007
0.048
0.224

Maximum value
0.150
0.32
1.53
0.64
0.84
2.97

Thus, it can be observed from the examples of [Table 3] to [Table 14] and the ranges presented in [Table 15] to [Table 18], that the parameters of radiuses and indexes of the core and cladding of the optical fiber according to the invention, allow to obtain a ZDW which is shifted towards higher wavelengths compared to prior art optical fibers according to the G.652 and G.657 recommendations.

Indeed, the standard fibers, according to the G.657.A1 recommendation, present a ZDW comprised between 1300 and 1324 nm, while the optical fiber according to the invention presents a ZDW comprised between 1340 and 1359 nm, as illustrated by [Table 17]. Such a shift in the ZDW allows to obtain an optical fiber optimized for a use in the O- and E-bands.

Furthermore, the Zero Dispersion Slope (ZDS) of the optical fibers according to the invention is mostly below 0.092 ps/(nm²·km) in Examples 1 to 94, contrarily to the G652 or G657 attributes. Therefore, the optical fibers according to the invention are not compliant with chromatic dispersion attributes of G652 and G657, in particular for the ZDW which is completely different, and for the ZDS in most of the cases.

Moreover, the present invention also allows to obtain an optical fiber with an MFD, a cable cutoff, and bend losses similar to the ones of the G.652 and G.657 recommendations. More particularly, as illustrated by [Table 1] and [Table 18], the optical fibers according to the invention comply with the macrobend requirements of G657A1 or G657A2.

Therefore, the present invention allows to obtain a single-mode optical fiber similar to the standard optical fibers of the G.652 and G.657 recommendations, but optimized to operate with higher wavelength in the O- and E-bands due to a higher ZDW which is obtained with specific radiuses (r₀, r₁, r₂, r₃) and indexes (Δn₀, Δn₂, Δn₃) in the core 10 and cladding 20 of the optical fiber 1.

SINGLE MODE OPTICAL FIBER OPTIMIZED TO OPERATE IN O AND E BAND, AND CORRESPONDING OPTICAL TRANSMISSION SYSTEM

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