# Patent

## Title
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 μm2 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.

## Background
CROSS-REFERENCE TO RELATED APPLICATIONS
This application claims the benefit of priority under 35 U.S.C. §119 of U.S. Provisional Application Ser. No. 62/056,784 filed on Sep. 29, 2014, which is related to U.S. Provisional Patent Application Ser. No. 62/086,383, filed Dec. 2, 2014, and entitled “Optical transmission systems and methods using a QSM large-effective-area optical fiber,” which application is incorporated herein by reference.


FIELD
The present disclosure relates to optical fibers, and in particular relates to a quasi-single-mode optical fiber with a large effective area.
The entire disclosure of any publication or patent document mentioned herein is incorporated by reference, including the publication by I. Roudas, et al., “Comparison of analytical models for the nonlinear noise in dispersive coherent optical communications systems,” IEEE Photonics Conference, paper MG3.4, Bellevue, Wash., September 2013; the publication by Sui et al., “256 Gb/s PM-16-QAM Quasi-Single-Mode Transmission over 2600 km using Few-Mode Fiber with Multi-Path Interference Compensation,” OFC Conference, San Francisco, Calif., Mar. 9-13, 2014, Fiber Non-linearity Mitigation and Compensation (M3C) (ISBN: 978-1-55752-993-0); and the publication by S. J. Savory, “Digital filters for coherent optical receivers,” Optics Express, Vol. 16, No. 2, Jan. 21, 2008, pp. 804-818.
BACKGROUND
Optical fibers are used for a variety of applications, especially in long-haul, high-speed optical communications systems. Optical fibers have an optical waveguide structure that acts to confine light to within a central region of the fiber. One of the many benefits of optical fibers is their ability to carry a large number of optical signals in different channels, which provides for high data transmission rates and a large bandwidth.
The increasing demand for bandwidth and higher data transmission rates has resulted in optical fibers carrying more channels and higher amounts of optical power. At some point, however, the optical power carried by the optical fiber can give rise to non-linear effects that distort the optical signals and reduce the transmission capacity of the optical communications system. Consequently, there is a practical limit to how much optical power an optical fiber can carry.
Because the optical power is confined by the waveguide structure of the optical fiber, the intensity determines the severity of non-linear effects in the optical fiber. The intensity is defined as the amount of optical power in the guided light divided by the (cross-sectional) area over which the guided light is distributed. This area is referred to in the art as the “effective area” Aeff of the optical fiber. The effective area Aeff is calculated from the electromagnetic field distribution of the light traveling within the optical fiber using techniques and methods known in the art.
It is well-known that optical fibers with large effective areas Aeff are desirable in optical transmission systems because of their relatively high power threshold for nonlinear distortion impairments. The larger the effective area Aeff, the lower the intensity and thus the less non-linear effects. Because of this feature, an optical fiber with a large effective area Aeff may be operated at higher optical powers, thereby increasing the optical signal-to-noise ratio (OSNR).
Unfortunately, the effective area Aeff of optical fibers cannot simply be increased without bound. The conventional wisdom in the art is that an effective area Aeff of about 150 μm2 is the limit for a true single-mode fiber to maintain sufficient bend robustness, (i.e., reduced loss due to bending). In some cases, an effective area Aeff of 150 μm2 may in fact already be too large for some bending-loss requirements. However, the bending loss of an optical fiber can be reduced by increasing the mode confinement and hence the cutoff wavelength of the optical fiber associated with single-mode operation. Increasing the effective area Aeff beyond present-day values would require raising the cutoff wavelength to be above the signal wavelength, thereby resulting in few-mode operation, which gives rise to undesirable optical transmission impairments such as modal dispersion and multipath interference (MPI).
Alternatives to increasing the effective area Aeff of the optical fiber to reduce adverse non-linear effects include decreasing the effective nonlinear index n2. The nonlinear physics of an optical fiber depends on the ratio n2/Aeff. However, changing n2 is difficult and the resulting effect is likely to be very small. Reducing the fiber attenuation is another alternative for better transmission performance. A lower fiber attenuation reduces the need for amplification and thus reduces the noise of the transmission link, which in turn reduces the required signal power for a given required OSNR. However, reducing the attenuation of the optical fiber impacts the optical fiber transmission system in a different way than by changing the effective area Aeff, so that these two parameters cannot be exactly traded off.
What is needed therefore is a more robust type of large-effective-area optical fiber that reduces adverse non-linear effects while also having sufficiently small bending loss.
SUMMARY
An aspect of the disclosure is a QSM optical fiber. The QSM fiber includes a core having a centerline and an outer edge, with a peak refractive index n0 on the centerline and a refractive index n1 at the outer edge. A cladding section surrounds the core and has a first inner annular cladding region immediately adjacent the core. The core and cladding section support a fundamental mode LP01 and a higher-order mode LP11 and define: i) for the fundamental mode LP01: an effective area Aeff>170 μm2 and an attenuation of no greater than 0.17 dB/km at 1530 nm; ii) for the higher-order mode LP11: 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 DB=60 mm.
In one example of the QSM fiber described above, the effective area Aeff>200 μm2 at 1530 nm.
Another aspect of the disclosure is a QSM optical fiber that has a core having a centerline and a radius r1 greater than 5 μm, with a peak refractive index n0 on the centerline and a refractive index n1 at the radius r1; 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 n2, a second inner annular cladding region immediately adjacent the first inner annular cladding region and having minimum refractive index n3, and a ring immediately adjacent the second inner annular cladding region and having a refractive index nR, wherein n0>n1>n3>n2 and nR>n3>n2; wherein the core and cladding section support a fundamental mode LP01 and a higher-order mode LP11 and define: i) for the fundamental mode LP01: an effective area Aeff>150 μm2 and an attenuation of no greater than 0.17 dB/km at 1530 nm; ii) for the higher-order mode LP11: 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 DB=60 mm.
In one example of the QSM fiber described immediately above, the effective area Aeff>170 μm2, while in another example, the effective area Aeff>200 μm2. In another example, n1>nR, while in other examples n1=nR and n1<nR.
Another aspect of the disclosure is an optical transmission system that includes the QSM optical fiber as disclosed herein. The optical transmission system further includes 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 LP01 and the higher-order mode LP11 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.
Additional features and advantages are set forth in the Detailed Description that follows, and in part will be readily apparent to those skilled in the art from the description or recognized by practicing the embodiments as described in the written description and claims hereof, as well as the appended drawings. It is to be understood that both the foregoing general description and the following Detailed Description are merely exemplary, and are intended to provide an overview or framework to understand the nature and character of the claims.



BRIEF DESCRIPTION OF THE DRAWINGS
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:
FIG. 1 is a front elevated view of a section of quasi-single-mode (QSM) fiber as disclosed herein;
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;
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;
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;
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;
FIG. 6 is a plot of the bending loss BL (dB/turn) versus the bending diameter DB (mm) for the three refractive index profiles p1, p2 and p3 of FIG. 5;
FIG. 7 is a plot of the ratio of the measured outputted optical power POUT to the inputted optical power PIN (POUT/PIN) 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 λc from multimode to single-mode operation;
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 (LP01 and LP11) 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 LP01, and the dashed-dotted line shows the power in the higher-order mode LP11;
FIGS. 9A and 9B are plots of the effective DMD, denoted DMDEff, 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 DMDEff is in units of the tap (temporal) spacing τ of the signal processor; and
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 LP01 mode of the QSM fiber.



DETAILED DESCRIPTION
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.
The claims as set forth below are incorporated into and constitute part of this Detailed Description.
Terminology
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)2−nS2)]/(2nS2)

where n(r) is the refractive index at radius r, unless otherwise specified and nS is the reference index. The relative refractive index is defined at the operating wavelength λp. In another aspect, nS is the index of undoped silica (SiO2). The maximum index of the index profile is denoted n0, and in most cases, n0=n(0).

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 nREF is that for pure silica.
The term “dopant” as used herein generally refers to a substance that changes the relative refractive index of glass relative to pure (undoped) SiO2 unless otherwise indicated.
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.
The term “cutoff” is used herein refers to the cutoff wavelength λc 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>λc. The cutoff wavelength λc 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.
For examples of the QSM fiber disclosed herein, the cutoff wavelength λc>1600 nm, or more preferably λc>1700 nm, or more preferably λc>1750 nm, or even more preferably λc>1800 nm.
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 LP0p modes with p>0 have two polarization degrees of freedom and are two-fold degenerate. The LPmp 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 LP01 mode propagates is a single-mode fiber, even though the LP01 mode has two possible polarizations. A few-mode (or “few moded”) optical fiber in which the L01 and LP11 modes propagate supports three spatial modes but nevertheless is referred herein as having two modes for ease of discussion.
As used herein, the “effective area” Aeff of an optical fiber is the cross-sectional area of the optical fiber through which light is propagated and is defined as:




  
    
      A
      eff
    
    =
    
      2
      ⁢
      
        
      
      ⁢
      π
      ⁢
      
        
      
      ⁢
      
        
          
            (
            
              
                ∫
                0
                ∞
              
              ⁢
              
                
                  E
                  2
                
                ⁢
                
                  
                
                ⁢
                rdr
              
            
            )
          
          2
        
        
          
            ∫
            0
            ∞
          
          ⁢
          
            
              E
              4
            
            ⁢
            
              
            
            ⁢
            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 Aeff is determined at a wavelength of 1550 nm, unless otherwise specified.

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 DB(e.g., DB=60 mm) and measuring the increase in attenuation due to the bending using an encircled flux (EF) launch condition.
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 rg) for ease of illustration even though the cladding in principle extends beyond this limit.
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.
The limits on any ranges cited herein are considered to be inclusive and thus to lie within the stated range, unless otherwise specified.
QSM Optical Fiber
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.
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 GeO2. Core 20 may also include fluorine as a dopant.
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 re, which can be considered the core radius, which in example is also equal to radius r1. In one example, the core radius re or r1>5 μm, while in another example, re or r1>7 μm.
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.
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 n0, n1, n2, n3 and nR, and four radii r1, r2, r3 and rR. The refractive index n0 is the peak refractive index and occurs at r=0, i.e., on centerline 12 within core 20. The refractive index n1 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 re. The refractive index n2 represents the minimum refractive index for inner cladding 32. The refractive index n3 represents the minimum refractive index for moat 34. The refractive index nR represents the refractive index of ring 38.
In an example, the radius r1 represents both the radius of core 20 and the inner radius of inner cladding 32, while the radius r2 represents the outer radius of the inner cladding. The radius r3 represents the outer radius of moat 34. The radius rR represents the inner radius of ring 38. The radius rg represents the radius where ring 38 ends and the glass coating 39 of refractive index ng that makes up the rest of the QSM fiber 10 begins.
In an example, the nine fiber parameters P are designed for a nominal glass radius rg=62.5 μm. Small adjustments, to especially the cladding parameters (r3, n3) and ring parameters (nR, rR) may be required if the fiber glass radius rg is changed, which is optional for reducing bending loss. In FIG. 1, the core edge radius re is slightly smaller than the inner cladding radius r1 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 re=r1.
In an example embodiment of QSM fiber 10, n0>n1>n3>n2. In another example, n1>nR, while another example n1≦nR. Also in an example, nR>n3>n2.
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 ri and has an associated refractive index ni. 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 ri of inner cladding 32 can be equal to the radius r1 of core 20.
The QSM fiber 10 disclosed herein has a relatively large effective area Aeff, which in one example is Aeff>150 μm2, while in another example is Aeff>170 μm2, while yet in another example is Aeff>200 μm2. The QSM fiber 10 is designed to be operated using only the fundamental mode LP01 just as in single-mode fiber, while the one additional higher-order mode LP11 is not used. The one additional higher-order mode LP11 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.
In an example, the fundamental mode LP01 has a fundamental-mode effective index, the higher-order mode LP11 has a higher-order-mode effective index, and wherein a difference Δneff between the fundamental-mode effective index and the higher-order-mode effective index is |Δneff|>0.001 at a wavelength of 1550 nm.
Higher-Order-Mode Impairments
The main two impairments caused by the presence of the higher-order mode LP11 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 Aeff used to overcome detrimental non-linear effects, as explained above.
Because the higher-order mode LP11 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 LP11 is intentionally subjected to a relatively large attenuation to reduce the degree of optical transmission impairment caused by this higher-order mode.
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 Aeff. Qualitatively, this is because, for any mode, the group index (ng) is related to phase index (or “effective index” ne) as follows:




  
    n
    g
  
  =
  
    
      n
      e
    
    -
    
      λ
      ⁢
      
        
          dn
          e
        
        
          d
          ⁢
          
            
          
          ⁢
          λ
        
      
    
  




The difference in the group index ng between two modes is therefore given by:





  
    Δ
    ⁢
    
      
    
    ⁢
    
      n
      g
    
  
  =
  
    
      Δ
      ⁢
      
        
      
      ⁢
      
        n
        e
      
    
    -
    
      λ
      ⁢
      
        
      
      ⁢
      Δ
      ⁢
      
        
          dn
          e
        
        
          d
          ⁢
          
            
          
          ⁢
          λ
        
      
    
  




In the limit of very large effective area Aeff, the wavelength dispersion of all modes approaches that of the bulk glass, in which case the last term in the equation for Δng vanishes so that Δng≈Δne. Consequently, one cannot simultaneously have a low mode coupling (large Δne) and a small differential mode delay (DMD, small Δng).
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 LP11. 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.
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 LP01 and the higher-order mode LP11 at a wavelength of 1530 nm is CC<0.002 km−1, while in another example, the coupling coefficient CC<0.001 km−1.
One way to increase the DMA for the higher-order mode LP11 is to shift the cutoff wavelength λc 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 LP11 while not substantially increasing the attenuation of the fundamental mode LP01. 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 LP11 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 LP11 and the radiative cladding mode).
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 LP01 and LP11 modes in the C+L bands, and in an example at a wavelength of 1530 nm.
The so-called “Gaussian Noise (GN)” model of optical transmission posits that the launch-power-optimized system Q-factor scales with the effective area Aeff as:

Q2∝Aeff2/3 

so that increasing the effective area Aeff from 150 to 175 μm2 increases Q2 by about 11% or 0.45 dB. Increasing the effective area Aeff from 150 to 250 μm2 increases Q2 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 Aeff from 150 μm2 to 250 μm2 increases the reach at 11.25 dB from 3000 km to 4000 km. Hence, while a 1.5 dB increase in optimal Q2 seems small, it can lead to a significant reach improvement.

This simulation suggests that with 50 km spans, increasing the effective area Aeff from 150 μm2 to 250 μm2 and increasing the span loss from 0.158 dB/km to 0.215 dB/km produces no net change in Q2. Hence the excess loss EL (i.e., the additional loss resulting from mode coupling above the intrinsic LP01 attenuation) of just 0.057 dB/km can completely erase the advantage of the increase in effective area Aeff. An excess loss EL of even 0.01 dB/km can decrease the reach of QSM fiber 10 with an effective area Aeff=250 μm2 by about 200 km. The advantage of large effective area fibers with an effective area Aeff of less than 250 μm2 would likewise be reduced.
It was found through modeling that conventional refractive index profiles cannot achieve sufficiently large DMA and effective areas Aeff exceeding 175 μm2 without also introducing excess macrobend loss. However, it was also found that the judicious addition of the ring 38 of increased refractive index nR relative to the refractive index nc of the outer cladding 34 can enhance the LP11 mode coupling to the glass coating 39, thereby increasing the DMA without significantly impacting bend performance. In this regard, the index nR of the ring 38 must not exceed the effective index neff 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 LP11. 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.
Example QSM Fibers
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 rg=62.5 μm.







TABLE 1







EXAMPLE 1













P
MIN0
MAX0
MIN1
MAX1
MIN2
MAX2
















n0
1.4430
1.4450
1.4436
1.4448
1.4438
1.4447


n1
1.4430
1.4450
1.4430
1.4436
1.4432
1.4434


n2
1.4400
1.4430
1.4406
1.4419
1.4408
1.4415


n3
1.4390
1.4430
1.4406
1.4422
1.4408
1.4412


r1 [μm]
5
15
7
12
8
11


r2 [μm]
25
38
28
35
31
33


r3 [μm]
40
62.5
45
55
48
52


rR [μm]
40
62.5
47
57
50
54









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




  
    Δ
    =
    
      
        
          n
          2
        
        -
        
          n
          s
          2
        
      
      
        2
        ⁢
        
          
        
        ⁢
        
          n
          s
          2
        
      
    
  
  ,




where n is the refractive index value from the tables above (at 1550 nm) and nS=1.444374, the refractive index of pure silica.








TABLE 2







EXAMPLE 1 USING Δ VALUES













P
MIN
MAX
MIN1
MAX1
MIN2
MAX2





Δ0
−9.5082E−04
  4.3350E−04
−5.3573E−04
  2.9498E−04
−3.9733E−04
  2.2573E−04


Δ1
−9.5082E−04
  4.3350E−04
−9.5082E−04
−5.3573E−04
−8.1248E−04
−6.7411E−04


Δ2
−3.0237E−03
−9.5082E−04
−2.6095E−03
−1.7114E−03
−2.4714E−03
−1.9878E−03


Δ3
−3.7137E−03
−9.5082E−04
−2.6095E−03
−1.5040E−03
−2.4714E−03
−2.1951E−03


r1 [μm]
5
15
7
12
8
11


R2 [μm]
25
38
28
35
31
33


r3 [μm]
40
62.5
45
55
48
52


rR [μm]
40
62.5
47
57
50
54









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.







TABLE 3







EXAMPLE (NO RING)













P
MIN
MAX
MIN1
MAX1
MIN2
MAX2
















n0
1.4435
1.4445
1.4437
1.4443
1.4438
1.4442


n1
1.4430
1.4450
1.4427
1.4438
1.4430
1.4435


ni
1.4410
1.4420
1.4412
1.4418
1.4413
1.4417


n2
1.4397
1.4413
1.4400
1.4412
1.4402
1.4409


n3
1.4380
1.4410
1.4387
1.4405
1.4390
1.4402


r1[μm]
5
12
5
10
6
9


ri [μm]
6
13
7
12
7
11


r2 [μm]
18
33
19
29
20
25









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







TABLE 4







EXAMPLE 3 (NO RING)













P
MIN
MAX
MIN1
MAX1
MIN2
MAX2
















n0
1.4435
1.4445
1.4437
1.4443
1.4438
1.4442


n1
1.4425
1.4435
1.4426
1.4433
1.4427
1.4432


ni
1.4410
1.4420
1.4412
1.4418
1.4405
1.4409


n2
1.4397
1.4413
1.4400
1.4412
1.4402
1.4409


n3
1.4380
1.4410
1.4387
1.4405
1.4390
1.4402


r1[μm]
6
14
6
12
7
10


ri [μm]
7
15
8
14
9
13


r2 [μm]
25
35
20
34
25
30









QSM Properties of Example Profiles

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 DB (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 DB of 60 mm.
FIG. 7 is a plot of the ratio of the measured outputted optical power POUT to the inputted optical power PIN (POUT/PIN) 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 λc from multimode to single-mode operation.
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 λc are estimated from the power trace plots of FIG. 7. The effective area Aeff is measured in μm2 at λ=1550 nm. The straight fiber LP11 mode cutoff wavelength λc is measured in nanometers (nm). The straight-fiber LP11 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 DB=60 mm.







TABLE 5







PREDICTED OPTICAL PROPERTIES FOR 3 EXAMPLE PROFILES











Profile
Aeff [μm2]
λc [nm]
RL [dB/km]
BL [dB/turn]














p1
237
1800
11.4
1.9 × 10−3


p2
232
1850
5.1
0.9 × 10−3


p3
227
1885
2.3
0.6 × 10−3









Relationship Between DMA and NT 

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 (LP01 and LP11) QSM fiber 10. The solid shows the total power; the dashed line shows the power in the fundamental mode LP01; the dashed-dotted line shows the power in the higher-order mode LP11.
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 LP01 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 NT of taps as compared to conventional MPI compensation.
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 NT of taps as compared to conventional MPI compensation.
FIGS. 9A and 9B plot the effective DMD, denoted DMDEff, versus the DMA (dB/km) for an example optical transmission system that utilizes the QSM fiber 10 disclosed herein. In FIG. 9A, the DMDEff has units of nanoseconds (ns) while in FIG. 9B the DMDEff 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.
The plots of FIGS. 9A and 9B show the effect of the non-zero DMA on the number NT 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 NT 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 NT of taps.
Optical Transmission System with QSM Fiber
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.
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.
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.
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 LP01. 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 (LP01) while a portion of the light travels in the higher-order mode LP11. 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.
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.
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 NT 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.
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.

## Claims

1. A quasi-single-mode (QSM) optical fiber, comprising: a core having a centerline and an outer edge, with a peak refractive index n0 on the centerline and a refractive index n1 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 LP01 and a higher-order mode LP11 and define: i) for the fundamental mode LP01: an effective area Aeff>170 μm2 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 LP11: 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 DB=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 n2, and wherein the cladding section further includes a moat immediately adjacent the inner annular cladding region and having minimum refractive index n3.

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 nR, and wherein nR>n3>n2.

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 Aeff>200 μm2.

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 LP01 is no greater than 0.165 dB/km, and wherein for the fundamental mode LP01 the bending loss BL<0.005 dB/turn at 1625 nm for the bend diameter DB=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 LP11 while not substantially attenuating the fundamental mode LP01.

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 LP01 and the higher-order mode LP11 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 r1 greater than 5 μm, with a peak refractive index n0 on the centerline and a refractive index n1 at the radius r1; 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 n2, a second inner annular cladding region immediately adjacent the first inner annular cladding region and having minimum refractive index n3, and a ring immediately adjacent the second inner annular cladding region and having a refractive index nR, wherein n0>n1>n3>n2 and nR>n3>n2; wherein the core and cladding section support a fundamental mode LP01 and a higher-order mode LP11 and define: i) for the fundamental mode LP01: an effective area Aeff>150 μm2 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 LP11: 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 DB=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 Aeff>170 μm2.

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 LP11 while not substantially attenuating the fundamental mode LP01.

19. The QSM fiber according to claim 13, further comprising an LP01-to-LP11 coupling coefficient CC<0.002 km−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 LP01 and the higher-order mode LP11 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.