Quasi-single-mode optical fiber with a large effective area

Abstract

A quasi-single-mode optical fiber with a large effective area is disclosed. The quasi-single-mode fiber has a core with a radius greater than 5 μm, and a cladding section configured to support a fundamental mode and a higher-order mode. The fundamental mode has an effective area greater than 170 μm.sup.2 and an attenuation of no greater than 0.17 dB/km at a wavelength of 1530 nm. The higher-order mode has an attenuation of at least 1.0 dB/km at the wavelength of 1530 nm. The quasi-single-mode optical fiber has a bending loss of less than 0.02 dB/turn for a bend diameter of 60 mm for a wavelength of 1625 nm.

Claims

1. A quasi-single-mode (QSM) optical fiber, comprising: a core having a centerline and an outer edge, with a peak refractive index n.sub.0 on the centerline and a refractive index n.sub.1 at the outer edge; a cladding section surrounding the core, wherein the cladding section includes an inner annular moat region immediately adjacent the core; wherein the core and cladding section support a fundamental mode LP.sub.01 and a higher-order mode LP.sub.11 and define: i) for the fundamental mode LP.sub.01: an effective area A.sub.eff>170 μm.sup.2 at a wavelength of 1530 nm and an attenuation of no greater than 0.17 dB/km at a wavelength of 1530 nm; ii) for the higher-order mode LP.sub.11: an attenuation of at least 1.0 dB/km at 1530 nm; and iii) a bending loss of BL<0.02 dB/turn at 1625 nm and for a bend diameter D.sub.B=60 mm.

2. The QSM optical fiber according to claim 1, wherein the core has a radius that is greater than 5 μm.

3. The QSM optical fiber according to claim 2, wherein the core radius is greater than 7 μm.

4. The QSM optical fiber according to claim 2, further comprising a 2 m cutoff wavelength λc>1600 nm.

5. The QSM optical fiber according to claim 4, wherein the first inner annular cladding region has a minimum refractive index n.sub.2, and wherein the cladding section further includes a moat immediately adjacent the inner annular cladding region and having minimum refractive index n.sub.3.

6. The QSM optical fiber according to claim 5, wherein the cladding section further includes a ring immediately adjacent the moat, the ring having a refractive index n.sub.R, and wherein n.sub.R>n.sub.3>n.sub.2.

7. The QSM optical fiber according to claim 6, wherein the ring includes an absorbing dopant that contribute to the attenuation of the higher-order mode.

8. The QSM optical fiber according to claim 1, wherein the effective area A.sub.eff>200 μm.sup.2.

9. The QSM optical fiber according to claim 1, wherein: i) the core is made of potassium-doped silica; ii) the cladding section is made of fluorine-doped silica; and iii) neither the core nor the cladding section includes germanium.

10. The QSM optical fiber according to claim 1, wherein the attenuation of the fundamental mode LP.sub.01 is no greater than 0.165 dB/km, and wherein for the fundamental mode LP.sub.01 the bending loss BL<0.005 dB/turn at 1625 nm for the bend diameter D.sub.B=60 mm.

11. The QSM fiber according to claim 1, further comprising an axial periodic refractive-index perturbation configured to contribute to the attenuation of the higher-order mode LP.sub.11 while not substantially attenuating the fundamental mode LP.sub.01.

12. An optical transmission system, comprising: the QSM optical fiber of claim 1; an optical transmitter configured to emit light that defines an optical signal that carries information; an optical receiver optically coupled to the optical transmitter by the QSM fiber and configured to receive the light emitted by the optical transmitter and transmitted over the QSM optical fiber in the fundamental mode LP.sub.01 and the higher-order mode LP.sub.11 thereby giving rise to multipath interference (MPI), wherein the optical receiver generates an analog electrical signal from the received light; an analog-to-digital converter (ADC) that converts the analog electrical signal into a corresponding digital electrical signal; and a digital signal processor electrically connected to the ADC and configured to receive and process the digital electrical signal to mitigate the MPI and generate a processed digital signal representative of the optical signal from the optical transmitter.

13. A quasi-single-mode (QSM) optical fiber, comprising: a core having a centerline and a radius r.sub.1 greater than 5 μm, with a peak refractive index n.sub.0 on the centerline and a refractive index n.sub.1 at the radius r.sub.1; a cladding section surrounding the core, wherein the cladding section includes a first inner annular cladding region immediately adjacent the core with a minimum refractive index n.sub.2, a second inner annular cladding region immediately adjacent the first inner annular cladding region and having minimum refractive index n.sub.3, and a ring immediately adjacent the second inner annular cladding region and having a refractive index n.sub.R, wherein n.sub.0>n.sub.1>n.sub.3>n.sub.2 and n.sub.R>n.sub.3>n.sub.2; wherein the core and cladding section support a fundamental mode LP.sub.01 and a higher-order mode LP.sub.11 and define: i) for the fundamental mode LP.sub.01: an effective area A.sub.eff>150 μm.sup.2 at a wavelength of 1530 nm and an attenuation of no greater than 0.17 dB/km at a wavelength of 1530 nm; ii) for the higher-order mode LP.sub.11: an attenuation of at least 1.0 dB/km for the wavelength of 1530 nm; and iii) a bending loss of BL<0.02 dB/turn when the wavelength is 1625 nm and for a bend diameter D.sub.B=60 mm.

14. The QSM optical fiber according to claim 13, wherein the core radius is greater than 7 μm.

15. The QSM optical fiber according to claim 13, further comprising a 2 m cutoff wavelength λc>1600 nm.

16. The QSM optical fiber according to claim 13, wherein the effective area A.sub.eff>170 μm.sup.2.

17. The QSM optical fiber according to claim 13, wherein the attenuation of the fundamental mode LPoi is no greater than 0.165 dB/km.

18. The QSM fiber according to claim 13, further comprising an axial periodic refractive-index perturbation configured to contribute to the attenuation of the higher-order mode LP.sub.11 while not substantially attenuating the fundamental mode LP.sub.01.

19. The QSM fiber according to claim 13, further comprising an LP.sup.01-to-LP.sub.11 coupling coefficient CC<0.002 km.sup.−1 at the wavelength of 1530 nm.

20. An optical transmission system, comprising: the QSM optical fiber of claim 13; an optical transmitter configured to emit light that defines an optical signal that carries information; an optical receiver optically coupled to the optical transmitter by the QSM fiber and configured to receive the light emitted by the optical transmitter and transmitted over the QSM optical fiber in the fundamental mode LP.sub.01 and the higher-order mode LP.sub.11 thereby giving rise to multipath interference (MPI), wherein the optical receiver generates an analog electrical signal from the received light; an analog-to-digital converter (ADC) that converts the analog electrical signal into a corresponding digital electrical signal; and a digital signal processor electrically connected to the ADC and configured to receive and process the digital electrical signal to mitigate the MPI and generate a processed digital signal representative of the optical signal from the optical transmitter.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The accompanying drawings are included to provide a further understanding, and are incorporated in and constitute a part of this specification. The drawings illustrate one or more embodiment(s), and together with the Detailed Description serve to explain principles and operation of the various embodiments. As such, the disclosure will become more fully understood from the following Detailed Description, taken in conjunction with the accompanying Figures, in which:

(2) FIG. 1 is a front elevated view of a section of quasi-single-mode (QSM) fiber as disclosed herein;

(3) FIG. 2 is a plot of the refractive index n versus radius r that illustrates an example refractive index profile for an example of the QSM fiber of FIG. 1;

(4) FIG. 3 is similar to FIG. 2 and illustrates an example refractive index profile for the QSM fiber that does not include the ring portion of the cladding section;

(5) FIG. 4 is a close-up, cross-sectional view of the QSM fiber of FIG. 1, illustrating an example where the fiber includes an axial (longitudinal) refractive-index perturbation designed to provide substantial attenuation of the higher-order mode while not substantially attenuating the fundamental mode;

(6) FIG. 5 is similar to FIG. 2 and illustrates in a single plot three different refractive index profiles p1, p2 and p3 for example QSM fibers, wherein the inner cladding for the different profiles has different depths;

(7) FIG. 6 is a plot of the bending loss BL (dB/turn) versus the bending diameter D.sub.B (mm) for the three refractive index profiles p1, p2 and p3 of FIG. 5;

(8) FIG. 7 is a plot of the ratio of the measured outputted optical power P.sub.OUT to the inputted optical power P.sub.IN (P.sub.OUT/P.sub.IN) versus the wavelength λ (nm) for the three different refractive index profiles p1, p2 and p3 of FIG. 5, wherein the plot is used to calculate the cutoff wavelength λ.sub.c from multimode to single-mode operation;

(9) FIGS. 8A and 8B plot of the signal power distribution SP in arbitrary power units (a.p.u.) as a function of the differential mode delay or DMD (ns) in a two-mode (LP.sub.01 and LP.sub.11) QSM optical fiber for the case where there is negligible mean differential modal attenuation or DMA (FIG. 8A) and for the case where there is a high DMA (FIG. 8B), wherein the solid shows the total power, the dashed line shows the power in the fundamental mode LP.sub.01, and the dashed-dotted line shows the power in the higher-order mode LP.sub.11;

(10) FIGS. 9A and 9B are plots of the effective DMD, denoted DMD.sub.Eff, versus the DMA (dB/km) for an example optical transmission system that employs an example of the QSM fiber disclosed herein, wherein for FIG. 9A the DMD units are nanoseconds whereas in FIG. 9B the DMD.sub.Eff is in units of the tap (temporal) spacing τ of the signal processor; and

(11) FIG. 10 is a schematic diagram of an optical transmission system that employs the QSM fiber as disclosed herein along with MPI compensation to recover the signal that travels in the fundamental LP.sub.01 mode of the QSM fiber.

DETAILED DESCRIPTION

(12) Reference is now made in detail to various embodiments of the disclosure, examples of which are illustrated in the accompanying drawings. Whenever possible, the same or like reference numbers and symbols are used throughout the drawings to refer to the same or like parts. The drawings are not necessarily to scale, and one skilled in the art will recognize where the drawings have been simplified to illustrate the key aspects of the disclosure.

(13) The claims as set forth below are incorporated into and constitute part of this Detailed Description.

(14) Terminology

(15) The term “relative refractive index,” as used herein in connection with the multimode fibers and fiber cores discussed below, is defined as:
Δ(r)=[n(r).sup.2−n.sub.S.sup.2)]/(2n.sub.S.sup.2)
where n(r) is the refractive index at radius r, unless otherwise specified and n.sub.S is the reference index. The relative refractive index is defined at the operating wavelength λ.sub.p. In another aspect, n.sub.S is the index of undoped silica (SiO.sub.2). The maximum index of the index profile is denoted n.sub.0, and in most cases, n.sub.0=n(0).

(16) As used herein, the relative refractive index is represented by Δ and its values are given in units of “%,” unless otherwise specified. In the discussion below, the reference index n.sub.REF is that for pure silica.

(17) The term “dopant” as used herein generally refers to a substance that changes the relative refractive index of glass relative to pure (undoped) SiO.sub.2 unless otherwise indicated.

(18) The term “mode” is short for a guided mode or optical mode. A “multimode” optical fiber means an optical fiber designed to support the fundamental guided mode and at least one higher-order guided mode over a substantial length of the optical fiber, such as 2 meters or longer. A “single-mode” optical fiber is an optical fiber designed to support a fundamental guided mode only over a substantial length of the optical fiber, such as 2 meters or longer. A “few mode” or “few-moded” optical fiber is an optical fiber designed to support a fundamental guided mode and one or two higher-order modes over a substantial length of the optical fiber, such as 2 meters or longer. A “quasi-single mode” fiber is distinguished from a “few-mode” fiber in that the former seeks to use only the fundamental mode to carry information while the latter seeks to use all of the few modes to carry information.

(19) The term “cutoff” is used herein refers to the cutoff wavelength λ.sub.c that defines the boundary for single-mode and multimode operation of an optical fiber, wherein single-mode operation of the fiber occurs for wavelengths λ>λ.sub.c. The cutoff wavelength λ.sub.c as the term is used herein can be measured by the standard 2 m fiber cutoff test, FOTP-80 (EIA-TIA-455-80), to yield the “fiber cutoff wavelength,” also known as the “2 m fiber cutoff” or “measured cutoff”. The FOTP-80 standard test is performed to either strip out the higher order modes using a controlled amount of bending, or to normalize the spectral response of the fiber to that of a multimode fiber.

(20) For examples of the QSM fiber disclosed herein, the cutoff wavelength λ.sub.c>1600 nm, or more preferably λ.sub.c>1700 nm, or more preferably λ.sub.c>1750 nm, or even more preferably λ.sub.c>1800 nm.

(21) The number of propagating modes and their characteristics in a cylindrically symmetric optical fiber with an arbitrary refractive index profile is obtained by solving the scalar wave equation (see for example T. A. Lenahan, “Calculation of modes in an optical fiber using a finite element method and EISPACK,” Bell Syst. Tech. J., vol. 62, no. 1, p. 2663, February 1983). The light traveling in an optical fiber is usually described (approximately) in terms of combinations of LP (linear polarization) modes. The LP.sub.0p modes with p>0 have two polarization degrees of freedom and are two-fold degenerate. The LP.sub.mp modes with m>0, p>0 have both two polarization and two spatial degrees of freedom. They are four-fold degenerate. In the discussion herein, polarization degeneracies are not counted when designating the number of LP modes propagating in the fiber. For example, an optical fiber in which only the LP.sub.01 mode propagates is a single-mode fiber, even though the LP.sub.01 mode has two possible polarizations. A few-mode (or “few moded”) optical fiber in which the L.sub.01 and LP.sub.11 modes propagate supports three spatial modes but nevertheless is referred herein as having two modes for ease of discussion.

(22) As used herein, the “effective area” A.sub.eff of an optical fiber is the cross-sectional area of the optical fiber through which light is propagated and is defined as:

(23) $A_{\mathrm{eff}}=2\pi \frac{{\left({\int }_0^{\infty }{E}^2\mathrm{rdr}\right)}^2}{{\int }_0^{\infty }{E}^4\mathrm{rdr}},$
where E is the electric field associated with light propagated in the fiber and r is the radius of the fiber. The effective area A.sub.eff is determined at a wavelength of 1550 nm, unless otherwise specified.

(24) Macrobend performance of the example QSM fibers disclosed herein was determined according to FOTP-62 (IEC-60793-1-47) by wrapping 2 turns around a mandrel having a diameter D.sub.B(e.g., D.sub.B=60 mm) and measuring the increase in attenuation due to the bending using an encircled flux (EF) launch condition.

(25) In the discussion below, any portion of the optical fiber that is not the core is considered part of the cladding, which can have multiple sections. In some of the Figures (e.g., FIG. 1 and FIG. 4), the cladding is shown has having a limited radial extent (e.g., out to radius r.sub.g) for ease of illustration even though the cladding in principle extends beyond this limit.

(26) The C-band is defined as the wavelength range from 1530 nm to 1565 nm; The L-band is defined as the wavelength range from 1565 nm to 1625 nm; and the C+L wavelength band is defined as the wavelength range from 1530 nm to 1625 nm.

(27) The limits on any ranges cited herein are considered to be inclusive and thus to lie within the stated range, unless otherwise specified.

(28) QSM Optical Fiber

(29) FIG. 1 is an elevated view of a section of a QSM fiber 10 as disclosed herein. The QSM fiber 10 has a body 11 configured as described below and includes a centerline 12 that runs longitudinally down the center of the QSM fiber.

(30) FIG. 2 is a plot of the refractive index n versus radius r of QSM fiber 10 as measured from centerline 12, illustrating an example refractive index configuration (profile) for the QSM fiber. The QSM fiber 10 has a central core (“core”) 20 with a cladding section 30 surrounding the core. In an example, core 20 is made primarily silica and preferably alkali doped, e.g., potassium doped silica. Core 20 is preferably substantially free, and preferably entirely free, of GeO.sub.2. Core 20 may also include fluorine as a dopant.

(31) The cladding section 30 includes a number of regions, namely a first inner annular cladding region or “inner cladding” 32, a second inner annular cladding region or “moat” 34 surrounding the inner cladding, and an annular outer cladding region or “ring”38 surrounding moat 34. The shape of the core 20 is approximately triangular, but can vary from a step profile to an alpha profile. The core 20 has an outer edge 21 at a radius r.sub.e, which can be considered the core radius, which in example is also equal to radius r.sub.1. In one example, the core radius r.sub.e or r.sub.1>5 μm, while in another example, r.sub.e or r.sub.1>7 μm.

(32) In an example, neither the core 20 nor the cladding section 30 includes germanium. The different regions of cladding section 30 may be made of fluorine-doped silica. In an example, cladding section 30 is doped with fluorine while core 20 is doped with potassium.

(33) The example refractive index profile of the example QSM fiber 10 of FIG. 2 can be described by nine fiber parameters (P): Five refractive indices n.sub.0, n.sub.1, n.sub.2, n.sub.3 and n.sub.R, and four radii r.sub.1, r.sub.2, r.sub.3 and r.sub.R. The refractive index n.sub.0 is the peak refractive index and occurs at r=0, i.e., on centerline 12 within core 20. The refractive index n.sub.1 represents the refractive index at the interface between the core 20 and the adjacent inner cladding 32, i.e., at the core edge 21, which in an example is associated with radius r.sub.e. The refractive index n.sub.2 represents the minimum refractive index for inner cladding 32. The refractive index n.sub.3 represents the minimum refractive index for moat 34. The refractive index n.sub.R represents the refractive index of ring 38.

(34) In an example, the radius r.sub.1 represents both the radius of core 20 and the inner radius of inner cladding 32, while the radius r.sub.2 represents the outer radius of the inner cladding. The radius r.sub.3 represents the outer radius of moat 34. The radius r.sub.R represents the inner radius of ring 38. The radius r.sub.g represents the radius where ring 38 ends and the glass coating 39 of refractive index n.sub.g that makes up the rest of the QSM fiber 10 begins.

(35) In an example, the nine fiber parameters P are designed for a nominal glass radius r.sub.g=62.5 μm. Small adjustments, to especially the cladding parameters (r.sub.3, n.sub.3) and ring parameters (n.sub.R, r.sub.R) may be required if the fiber glass radius r.sub.g is changed, which is optional for reducing bending loss. In FIG. 1, the core edge radius r.sub.e is slightly smaller than the inner cladding radius r.sub.1 due to shortcomings in the refractive index measurement. In the plot of FIG. 5 discussed below, the transition from core 20 to inner cladding 32 is vertical so that r.sub.e=r.sub.1.

(36) In an example embodiment of QSM fiber 10, n.sub.0>n.sub.1>n.sub.3>n.sub.2. In another example, n.sub.1>n.sub.R, while another example n.sub.1≦n.sub.R. Also in an example, n.sub.R>n.sub.3>n.sub.2.

(37) FIG. 3 is similar to FIG. 2 and illustrates an example refractive index profile for an example QSM fiber 10 wherein the cladding region 30 does not include the outer ring 38. For the “no-ring” profile of FIG. 3, the inner radius of inner cladding 32 is denoted r.sub.i and has an associated refractive index n.sub.i. The shape of the core 20 is approximately step-like in the example, but can vary from a step profile to an alpha profile. The small bumps bi and b2 in the refractive index profile of FIG. 3 are features arising from the expected draw stress distribution and are not critical to the design. As noted above, the inner radius r.sub.i of inner cladding 32 can be equal to the radius r.sub.1 of core 20.

(38) The QSM fiber 10 disclosed herein has a relatively large effective area A.sub.eff, which in one example is A.sub.eff>150 μm.sup.2, while in another example is A.sub.eff>170 μm.sup.2, while yet in another example is A.sub.eff>200 μm.sup.2. The QSM fiber 10 is designed to be operated using only the fundamental mode LP.sub.01 just as in single-mode fiber, while the one additional higher-order mode LP.sub.11 is not used. The one additional higher-order mode LP.sub.11 can impair the transmission of optical signals traveling in the QSM fiber unless appropriate MP-compensating digital signal processing is applied to the received (transmitted) signal.

(39) In an example, the fundamental mode LP.sub.01 has a fundamental-mode effective index, the higher-order mode LP.sub.11 has a higher-order-mode effective index, and wherein a difference Δn.sub.eff between the fundamental-mode effective index and the higher-order-mode effective index is |Δn.sub.eff|>0.001 at a wavelength of 1550 nm.

(40) Higher-Order-Mode Impairments

(41) The main two impairments caused by the presence of the higher-order mode LP.sub.11 in QSM fiber 10 are multipath interference (MPI) and excess loss (EL). An aspect of the disclosure includes using QSM fiber 10 for optical signal transmission while electronically mitigating MPI of the optical signal using digital signal processing techniques that are known in the art and as described in greater detail. The electronic mitigation of MPI effects enables the deployment of QSM fiber 10 in an optical transmission system. To this end, in an example, the aforementioned parameters P of QSM fiber 10 are substantially optimized, while the excess loss EL, which cannot be compensated, is substantially minimized (e.g., made substantially zero). This avoids having the excess loss EL reduce the benefit of having a relatively large effective area A.sub.eff used to overcome detrimental non-linear effects, as explained above.

(42) Because the higher-order mode LP.sub.11 of QSM fiber 10 is undesirable and unused, the design and configuration of QSM fiber 10 is different than that for conventional few-mode optical fibers that seek to transmit information in the higher-order modes. In particular, because conventional few-mode optical fibers seek to utilize the information transmitted in the few higher-order modes, these modes need to have relatively low differential modal attenuation (DMA). As is explained in greater detail below, the QSM fiber 10 disclosed herein has relatively high DMA, i.e., the higher-order mode LP.sub.11 is intentionally subjected to a relatively large attenuation to reduce the degree of optical transmission impairment caused by this higher-order mode.

(43) Ideally, QSM fiber 10 would have a relatively large phase index difference between all supported modes to minimize mode-coupling, while at the same time having a small group index difference between all supported modes. This latter attribute minimizes the digital signal processing required to remove MPI artifacts from the received signal. Unfortunately, this is not possible in fibers with large effective area A.sub.eff. Qualitatively, this is because, for any mode, the group index (n.sub.g) is related to phase index (or “effective index” n.sub.e) as follows:

(44) $n_g=n_e-\lambda \frac{{\mathrm{dn}}_e}{d\lambda }$
The difference in the group index n.sub.g between two modes is therefore given by:

(45) $\Delta n_g=\Delta n_e-\lambda \Delta \frac{{\mathrm{dn}}_e}{d\lambda }$

(46) In the limit of very large effective area A.sub.eff, the wavelength dispersion of all modes approaches that of the bulk glass, in which case the last term in the equation for Δn.sub.g vanishes so that Δn.sub.g≈Δn.sub.e. Consequently, one cannot simultaneously have a low mode coupling (large Δn.sub.e) and a small differential mode delay (DMD, small Δn.sub.g).

(47) In the QSM fiber 10 disclosed herein, low mode coupling is substantially preserved while, as noted above, the DMD is managed by intentionally designing the QSM fiber to have as much loss (i.e., a high DMA) as possible for the higher-order mode LP.sub.11. A high DMA reduces the number of equalizer taps (i.e., memory) required in the digital signal processor used for MPI compensation, thereby reducing system complexity, as described below. High DMA values also reduce the total MPI level, which may have an upper limit in terms of the efficacy of the MPI compensation digital signal processing.

(48) In one example, the DMA for a wavelength of 1530 nm is DMA≧1.0 dB/km, while in another example, the DMA≧4.0 dB/km. Also in one example, the coupling coefficient CC between the fundamental mode LP.sub.01 and the higher-order mode LP.sub.11 at a wavelength of 1530 nm is CC<0.002 km.sup.−1, while in another example, the coupling coefficient CC<0.001 km.sup.−1.

(49) One way to increase the DMA for the higher-order mode LP.sub.11 is to shift the cutoff wavelength λ.sub.c to its lowest possible value consistent with macrobend requirements. Another way is to make the higher-order modes lossy in a mode-selective way. FIG. 4 is a close-up cross-sectional view of a portion of an example QSM fiber 10 that includes an axial (longitudinal) refractive-index perturbation 52. FIG. 4 includes a plot of refractive index n versus the axial distance z down the QSM fiber that illustrates an example form of the refractive-index perturbation having a constant period Λ. The refractive-index perturbation 52 is configured to increase the attenuation (DMA) of the higher-order mode LP.sub.11 while not substantially increasing the attenuation of the fundamental mode LP.sub.01. In an example, refractive-index perturbation 52 is in the form of a long-period grating that substantially matches a difference in the effective indices of the higher-order mode LP.sub.11 and a radiative cladding mode at the operating wavelength, i.e., a period Λ≈1/Δn, where Δn is the effective index difference between the higher-order mode LP.sub.11 and the radiative cladding mode).

(50) In an example, axial refractive-index perturbation 52 has a wavelength resonance and includes a non-constant (e.g., chirped) period Λ that serves to to widen the bandwidth of the resonance as compared to the constant period configuration. In an example, axial refractive-index perturbation 52 can be formed in QSM fiber 10 using known methods, such as laser irradiation. In an example, the axial refractive-index perturbation 52 can be formed as the fiber is being drawn, such as by irradiating the fiber with one or more lasers. In an example, the period Λ of the refractive-index perturbation is chosen such that there is substantially no resonant coupling of the LP.sub.01 and LP.sub.11 modes in the C+L bands, and in an example at a wavelength of 1530 nm.

(51) The so-called “Gaussian Noise (GN)” model of optical transmission posits that the launch-power-optimized system Q-factor scales with the effective area A.sub.eff as:
Q.sup.2∝A.sub.eff.sup.2/3
so that increasing the effective area A.sub.eff from 150 to 175 μm.sup.2 increases Q.sup.2 by about 11% or 0.45 dB. Increasing the effective area A.sub.eff from 150 to 250 μm.sup.2 increases Q.sup.2 by 41% or 1.5 dB. An example simulation was carried out for an erbium-doped fiber-amplified (EDFA) polarization-multiplexed (PM)-16QAM (Quadrature Amplitude Modulation) optical transmission system having 80 channels, a 32 GHz (Nyquist) channel spacing, a 50 km span length, ideal (noise and distortion-free) transmitter and receivers and a QSM fiber 10 with span loss of 0.158 dB/km. The simulation shows that increasing the effective area A.sub.eff from 150 μm.sup.2 to 250 μm.sup.2 increases the reach at 11.25 dB from 3000 km to 4000 km. Hence, while a 1.5 dB increase in optimal Q.sup.2 seems small, it can lead to a significant reach improvement.

(52) This simulation suggests that with 50 km spans, increasing the effective area A.sub.eff from 150 μm.sup.2 to 250 μm.sup.2 and increasing the span loss from 0.158 dB/km to 0.215 dB/km produces no net change in Q.sup.2. Hence the excess loss EL (i.e., the additional loss resulting from mode coupling above the intrinsic LP.sub.01 attenuation) of just 0.057 dB/km can completely erase the advantage of the increase in effective area A.sub.eff. An excess loss EL of even 0.01 dB/km can decrease the reach of QSM fiber 10 with an effective area A.sub.eff=250 μm.sup.2 by about 200 km. The advantage of large effective area fibers with an effective area A.sub.eff of less than 250 μm.sup.2 would likewise be reduced.

(53) It was found through modeling that conventional refractive index profiles cannot achieve sufficiently large DMA and effective areas A.sub.eff exceeding 175 μm.sup.2 without also introducing excess macrobend loss. However, it was also found that the judicious addition of the ring 38 of increased refractive index n.sub.R relative to the refractive index n.sub.c of the outer cladding 34 can enhance the LP.sub.11 mode coupling to the glass coating 39, thereby increasing the DMA without significantly impacting bend performance. In this regard, the index n.sub.R of the ring 38 must not exceed the effective index n.sub.eff of the fundamental mode. In an example, ring 38 includes at least one absorbing dopant that contribute to the attenuation of the higher-order mode LP.sub.11. Examples of absorbing dopants include titanium or other transition metals. In another example, ring 38 does not include any absorbing dopants. In an example, ring 38 includes fluorine dopant, which is not an absorbing dopant.

(54) Example QSM Fibers

(55) Table 1 below sets forth example QSM fiber parameters P for three examples of QSM fiber 10. In the Tables below, P stands for the given parameter, “MIN1” and “MAX1” stand for first example minimum and maximum values for the given parameter, “MIN2” and “MAX2” for second example minimum and maximum values for the given parameter, and “MIN3” and “MAX3” for third example minimum and maximum values for the given parameter. The parameters P in the following Tables are based on QSM fiber 10 having a nominal radius r.sub.g=62.5 μm.

(56) TABLE-US-00001 TABLE 1 EXAMPLE 1 P MIN0 MAX0 MIN1 MAX1 MIN2 MAX2 n.sub.0 1.4430 1.4450 1.4436 1.4448 1.4438 1.4447 n.sub.1 1.4430 1.4450 1.4430 1.4436 1.4432 1.4434 n.sub.2 1.4400 1.4430 1.4406 1.4419 1.4408 1.4415 n.sub.3 1.4390 1.4430 1.4406 1.4422 1.4408 1.4412 r.sub.1 [μm] 5 15 7 12 8 11 r.sub.2 [μm] 25 38 28 35 31 33 r.sub.3 [μm] 40 62.5 45 55 48 52 r.sub.R [μm] 40 62.5 47 57 50 54

(57) Table 2 below is an alternative representation of the refractive index data of Table 1. In Table 2, the refractive index change relative to pure silica is used. This refractive index change is represented by the relative refractive index Δ, which is given by

(58) $\Delta =\frac{n^2-n_s^2}{2n_s^2},$
where n is the refractive index value from the tables above (at 1550 nm) and n.sub.S=1.444374, the refractive index of pure silica.

(59) TABLE-US-00002 TABLE 2 EXAMPLE 1 USING Δ VALUES P MIN MAX MIN1 MAX1 MIN2 MAX2 Δ.sub.0 −9.5082E−04   4.3350E−04 −5.3573E−04   2.9498E−04 −3.9733E−04   2.2573E−04 Δ.sub.1 −9.5082E−04   4.3350E−04 −9.5082E−04 −5.3573E−04 −8.1248E−04 −6.7411E−04 Δ.sub.2 −3.0237E−03 −9.5082E−04 −2.6095E−03 −1.7114E−03 −2.4714E−03 −1.9878E−03 Δ.sub.3 −3.7137E−03 −9.5082E−04 −2.6095E−03 −1.5040E−03 −2.4714E−03 −2.1951E−03 r.sub.1 [μm] 5 15 7 12 8 11 R.sub.2 [μm] 25 38 28 35 31 33 r.sub.3 [μm] 40 62.5 45 55 48 52 r.sub.R [μm] 40 62.5 47 57 50 54

(60) The second example of QSM fiber 10 is set forth in Table 3 below and represents an example of the “no ring” configuration such as shown in FIG. 3.

(61) TABLE-US-00003 TABLE 3 EXAMPLE (NO RING) P MIN MAX MIN1 MAX1 MIN2 MAX2 n.sub.0 1.4435 1.4445 1.4437 1.4443 1.4438 1.4442 n.sub.1 1.4430 1.4450 1.4427 1.4438 1.4430 1.4435 n.sub.i 1.4410 1.4420 1.4412 1.4418 1.4413 1.4417 n.sub.2 1.4397 1.4413 1.4400 1.4412 1.4402 1.4409 n.sub.3 1.4380 1.4410 1.4387 1.4405 1.4390 1.4402 r.sub.1[μm] 5 12 5 10 6 9 r.sub.i [μm] 6 13 7 12 7 11 r.sub.2 [μm] 18 33 19 29 20 25

(62) The third example of QSM fiber 10 is set forth in Table 4 below and represents another example of the “no ring” configuration.

(63) TABLE-US-00004 TABLE 4 EXAMPLE 3 (NO RING) P MIN MAX MIN1 MAX1 MIN2 MAX2 n.sub.0 1.4435 1.4445 1.4437 1.4443 1.4438 1.4442 n.sub.1 1.4425 1.4435 1.4426 1.4433 1.4427 1.4432 n.sub.i 1.4410 1.4420 1.4412 1.4418 1.4405 1.4409 n.sub.2 1.4397 1.4413 1.4400 1.4412 1.4402 1.4409 n.sub.3 1.4380 1.4410 1.4387 1.4405 1.4390 1.4402 r.sub.1[μm] 6 14 6 12 7 10 r.sub.i [μm] 7 15 8 14 9 13 r.sub.2 [μm] 25 35 20 34 25 30
QSM Properties of Example Profiles

(64) FIG. 5 is similar to FIG. 2 and shows first, second and third example refractive index profiles p1, p2 and p3 (solid, dashed and dotted lines, respectively) for example QSM fibers 10, wherein the different index profiles have different depths for inner cladding 32. FIG. 6 is a plot of the predicted bend loss BL (dB/turn) versus bend diameter D.sub.B (mm) at a wavelength of 1625 nm as obtained using optical modeling. The three solid straight lines in FIG. 5 are approximate upper bounds for the example profiles p1, p2 and p3 based on fitting the oscillation peaks. All three example profiles p1, p2 and p3 yield a bending loss BL<5 mdB/turn at a bend diameter D.sub.B of 60 mm.

(65) FIG. 7 is a plot of the ratio of the measured outputted optical power P.sub.OUT to the inputted optical power P.sub.IN (P.sub.OUT/P.sub.IN) versus the wavelength λ (nm) for the three different refractive index profiles p1, p2 and p3 of FIG. 5, wherein the plot is used to calculate the cutoff wavelength λ.sub.c from multimode to single-mode operation.

(66) Table 5 below summarizes the predicted optical properties of the three example profiles p1, p2 and p3 of FIG. 5. The values for the bending loss BL are obtained from the straight-line fits of FIG. 6 while the cut-off wavelengths λ.sub.c are estimated from the power trace plots of FIG. 7. The effective area A.sub.eff is measured in μm.sup.2 at λ=1550 nm. The straight fiber LP.sub.11 mode cutoff wavelength λ.sub.c is measured in nanometers (nm). The straight-fiber LP.sub.11 mode radiative loss at 1550 nm is denoted RL and is measured in dB/km. The fundamental mode macro-bend loss BL is measured in dB/turn at λ=1625 nm and a bend diameter D.sub.B=60 mm.

(67) TABLE-US-00005 TABLE 5 PREDICTED OPTICAL PROPERTIES FOR 3 EXAMPLE PROFILES Profile A.sub.eff [μm.sup.2] λ.sub.c [nm] RL [dB/km] BL [dB/turn] p1 237 1800 11.4 1.9 × 10.sup.−3 p2 232 1850 5.1 0.9 × 10.sup.−3 p3 227 1885 2.3 0.6 × 10.sup.−3
Relationship Between DMA and N.sub.T

(68) One of the advantages of QSM fiber 10 is that it reduces the number of taps needed for the digital signal processor used for MPI compensation in an optical transmission system. FIGS. 8A and 8B plot the signal power distribution SP in arbitrary power units (a.p.u.) as a function of the DMD (ns) in a two-mode (LP.sub.01 and LP.sub.11) QSM fiber 10. The solid shows the total power; the dashed line shows the power in the fundamental mode LP.sub.01; the dashed-dotted line shows the power in the higher-order mode LP.sub.11.

(69) In FIG. 8A, there is negligible mean DMA, while in FIG. 8B here is a high mean DMA. All other fiber parameters P were kept the same, and in both cases the signal was launched into the fundamental mode LP.sub.01 only. The amount of significantly delayed contributions (the tail of the dashed black line) is decreased as the DMA increases. This enables use of a QSM fiber 10 having a relatively large DMD with a digital signal processor having a reduced number N.sub.T of taps as compared to conventional MPI compensation.

(70) The amount of significantly delayed contributions (the tail of the dashed black line) is decreased as the DMA increases. This enables use of a QSM fiber 10 having a relatively large DMD with a digital signal processor having a reduced number N.sub.T of taps as compared to conventional MPI compensation.

(71) FIGS. 9A and 9B plot the effective DMD, denoted DMD.sub.Eff, versus the DMA (dB/km) for an example optical transmission system that utilizes the QSM fiber 10 disclosed herein. In FIG. 9A, the DMD.sub.Eff has units of nanoseconds (ns) while in FIG. 9B the DMD.sub.Eff is in units of the tap (temporal) spacing τ of the signal processor, wherein each tap has duration of 31.25 ps. The effective DMD is defined as the time interval that includes 99.95% of the interfering pulse energy and represents the amount of delay the digital signal processor needs to compensate for MPI. The calculations used to generate FIGS. 9A and 9B assume a DMD of 1 ns/km and a length L=100 km of QSM fiber 10.

(72) The plots of FIGS. 9A and 9B show the effect of the non-zero DMA on the number N.sub.T of taps needed to compensate for the optical transmission impairment of the information-carrying optical signal traveling in the fundamental mode. The calculation of the required number N.sub.T of equalizer taps is approximate. The calculation is based on a mean MPI compensation, so the results can be considered as establishing a lower bound on the number N.sub.T of taps.

(73) Optical Transmission System with QSM Fiber

(74) FIG. 10 is a schematic diagram of an example optical transmission system (“system”) 100 that employs the QSM fiber 10 as disclosed herein. System 100 includes an optical transmitter 110, a section of QSM fiber 10, an optical receiver 130, an analog-to-digital converter ADC electrically connected to the optical receiver and a digital signal processor DSP electrically connected to the analog-to-digital converter. Also optionally included in system 100 is a decision circuit 150 electrically connected to the digital signal processor DSP.

(75) The digital signal processor DSP includes an MPI mitigation system 134 that in example includes a plurality of equalizer taps 136. System 10 and in particular MPI mitigation system 134 is configured to perform electronic equalization of optical transmission impairments to the optical signal using methods known in the art. In one example, MPI mitigation system 134 includes four finite impulse response (FIR) filters in a butterfly structure (not shown), wherein each filter has a number of taps 136, which are recursively adjusted based on a least-mean-square (LMS) algorithm.

(76) The QSM fiber section 10 includes an input end 112 optically connected to optical transmitter 110 and an output end 114 optically connected to optical receiver 130, thereby establishing an optical connection between the optical transmitter and the optical receiver. In an example, QSM fiber 10 includes an amplifier 160, e.g., an EDFA.

(77) In the operation of system 100, transmitter 110 generates light 200 that defines an input analog optical signal OS that carries information only in the fundamental mode LP.sub.01. Light 200 enters the input end 112 of QSM fiber 10 and travels the length of the fiber to output end 114. Most of light 200 travels in the fundamental mode (LP.sub.01) while a portion of the light travels in the higher-order mode LP.sub.11. The light 200 is denoted as 200′ at the output end of QSM fiber 10 due the light having impairments described above by virtue of having traveled through QSM fiber 10.

(78) Optical receiver 130 receives light 200′ as emitted from the output end 114 of QSM fiber 10 and converts this light into a corresponding analog electrical signal SA. The analog electrical signal SA passes through analog-to-digital converter ADC, which forms therefrom a corresponding digital electrical signal SD. The digital electrical signal SD is then received by digital signal processor DSP, which performs digital processing of the digital electrical signal. In particular, the digital signal processor DSP is configured to perform equalization of MPI using MPI mitigation system 134 and the equalizer taps 136 therein based on techniques known in the art. The digital signal processor DSP outputs a processed digital electrical signal SDP that is representative (to within the limits of MPI mitigation system 134) of the initial optical signal OS generated by transmitter 110. The processed digital electrical signal SDP, which includes the information originally encoded into optical system OS, continues downstream to be processed as needed (e.g., by a decision circuit 150) for the given application.

(79) As noted above, the relatively high DMA of ≧1 dB/km or >4 dB/km results in less complex digital signal processing, i.e., the number N.sub.T of equalizer taps 136 is reduced as compared to conventional optical transmission systems that employ MPI compensation. Also, as noted above, high DMA values also reduce the total MPI level, which may have an upper limit in terms of the efficacy of the MPI compensation digital signal processing.

(80) It will be apparent to those skilled in the art that various modifications to the preferred embodiments of the disclosure as described herein can be made without departing from the spirit or scope of the disclosure as defined in the appended claims. Thus, the disclosure covers the modifications and variations provided they come within the scope of the appended claims and the equivalents thereto.