Few-Mode Fibers with Improved Mode Spacing Alexander R. May * and Michalis N. Zervas

Optoelectronics Research Centre, University of Southampton, Southampton, SO17 1BJ, UK *arm103@orc.soton.ac.uk

Abstract A simple and intuitive optimization approach is described for the design of composite rotationally asymmetric refractive index fiber profiles with substantially improved mode spacing.

Introduction Space division multiplexing (SDM)1 has been heralded as a potential solution to the forthcoming optical communication capacity crunch. SDM constitutes a drastic design departure from the currently used standard single-mode fibers (SMF). It relies on multicore or multimode fibers in order to increase the transmission degrees of freedom. Multimode-division multiplexing (MDM), in particular, relies on specially designed multimode fibres (MMFs) and uses propagating optical modes as separate communication channels. High capacity MDM has been implemented by using MMFs supporting highly-coupled, low differential mode delay (DMD) and extensive, energy-hungry digital signal processing (DSP)2. Alternatively, high performance MDM systems have also been demonstrated using MMFs with virtually uncoupled, high differential mode delay (DMD) modes, with minimum DSP requirements3,4. The major consideration in designing un-coupled MDM (UC-DMD) systems is the degree of modal cross-coupling. It is known that cross-coupling is inversely-proportional to the effective index difference5 and it is, therefore, more severe between adjacent modes. So far, UC-DMD is based primarily on optimized step-index fibers. Step-index designs offer simplicity in terms of their design and fabrication and previous authors2,3 have investigated their use in up to six-LP-mode fibers. Also, it is important for improved designs to have large mode effective areas and differential group delays (DGD) (>0.5ps/m) to limit inter-mode non-linearity as well as meeting the optimum trade-off between micro- and macro-bend losses. It has been shown that step-index fibers, despite the parameter optimization, still support modes with non-equally spaced effective indices. Due to cylindrical symmetry, this is particularly severe between LP21 and LP02 modes. As a result, strong mode cross-coupling has been measured in relatively short MMF lengths using the S2 method6. In this paper we investigate an alternative MMF refractive index (RI) design showing

substantially equalized mode effective indices, compared with state-of-the-art step-index fibers. Mode index equalization improvements are achieved by introducing optimum 1) rotationally-symmetric RI perturbations inside the core,

affecting primarily one sub-group of modes, and 2) rotationally-non-symmetric RI perturbations in the cladding, affecting primarily the rest of the supported modes. The design optimization strategy is based on simple, physically-intuitive arguments.

Design strategy for fibers with optimally distributed mode spacing Given that what we try to achieve is the effective index manipulation, where targeted RI perturbations (n) could be introduced in a known starting profile (e.g. standard step-index) in order to selectively affect the propagation constant of individual modes (), an excellent, intuitive guiding principle is the following well known perturbation formula7

Fig. 1: Refractive index distribution schematics of (a)

standard SI fiber and (b) an optimally perturbed proposed design

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2

2 A

A

n e dAk

e dA

+

(1)

where k is the free-space wavenumber, the mode propagation constant and the electric field of the known profile . As already mentioned, the main issue with the mode neff distribution in step-index fibers (see Fig. 1) stems from the small separation between LP21 and LP02 modes. The optimization takes place in two steps. Step 1: We begin by investigating the addition of a depressed inner core to a previously optimized4 four-LP-mode step-index fiber at 1550nm with index contrast 12 = 9.7103 and radius = 7.5 m. We optimize the RI depression to obtain a design with more equally spaced modes. This is achieved by fixing the outer radius, a, and index of the ring, 1 as in the above selected design and by varying the index of the core depression, 3 as well as its width, b. We then consider the objective function

3 11 3 21 302 3 3 01 3 2

( , ) ( , ) 3 ( , ) 2

( , ) ; ( , ) [ ( , ) ] / 4

f b n LP b n LP b n

LP b n b n LP b n n

= + +

= (2)

In the objective function, the effective index of each LP mode is referred to as well as the optimum spacing, , between modes defined in terms of the difference between the effective index of the LP01 mode and the cladding 2. The mode neff distribution of the optimally perturbed inner core are shown in Fig. 2 (solid lines). The inner core depression overlaps mostly with the cylindrically-symmetric LP01 and LP02 modes and as expected from Eq. (1) their neff is reduced. LP11 and LP21 on the other hand have intensity minima in the core centre and therefore the index depression leaves them almost unaffected. Although the inner core depression increases the LP21 - LP02 index difference, this is mainly achieved by lowering the LP02 index closer to the cladding refractive index, which increases the macro- and micro-bending sensitivity of the design. Fibers with depressed inner cladding have been discussed in the context of MM fibers with maximum four-wave mixing8. Step 2: In order to improve the LP02 micro- and macro-bending performance and maintain the improved LP21 LP02 effective index separation we

consider the addition of localized RI perturbations in the cladding overlapping optimally with the four intensity lobes of the LP21 mode. We have added 2 m radius high-index rods a distance of 1 m from the edge of the outer core. Such cylindrically non-symmetric perturbation increases the effective indices of LP21 and LP02 by amounts given by Eq. (1) (see Fig. 2). As expected, modes LP01 and LP11 are affected by small amounts due to negligible overlaps with the additional perturbations. Representative LP-mode field distributions of

the fully optimized (step1+step2) profiles are shown in Fig. 3. It is shown that the cylindrically non-symmetric modes LP11 and LP21 are aligned with the added cladding rods. At this point, we

should mention that the addition of RI perturbing rods in the fiber cladding breaks the rotational degeneracy of the LP11 and LP21 modes. The mode profiles with maxima falling between the RI modifying rods have effective indices close to

Fig. 2: Mode effective-index distribution for standard SI

fiber (+), optimally-depressed core (step-1 solid) and fully optimized RI distribution (step1 + step2 - dashed)

1.3 1.4 1.5 1.6 1.7 1.81.444

1.446

1.448

1.45

1.452

1.454

1.456

1.458

Wavelength (m)

n eff

Step LP01Step LP11Step LP21Step LP02Optimum ring LP01Optimum ring LP11Optimum ring LP21Optimum ring LP02Rod LP01Rod LP11Rod LP21Rod LP02

Fig. 3: Orientation of equalized effective-index modes with respect to index modifying rods (a) LP01 , (b) LP11,

(c) LP21 and (d) LP02

(a)

LP01

(b)

LP11

(c)

LP21

(d)

LP02

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the unperturbed case. In addition to shifting the mode effective index, the RI modifying rods lock the optimum separation modes spatially inside the fiber. This avoids unwanted modal rotation which complicates enormously the efficient mode demultiplexing and detection at the end of the optical link. The benefits of such spatial mode locking in the case of dual-moded fiber have been achieved by using elliptical core fibers. In the case of single-mode fiber, this is equivalent to fixing mode polarization by using high-bi fibers. The performance of the new fiber designs, with optimally spaced mode effective indices, and the comparison with state-of-the-art SI fibers4 are summarized in Tab. 1 and Tab. 2. In addition to the discussed mode spacings, we compare the differential group delays (DGD) and mode effective areas. The last two parameters define the nonlinear performance of the fibers. It is shown that in addition to improved mode effective-index distribution the new designs provide substantially larger mode effective areas. The DGDs are in excess of 4ns/km for all the supported modes. It is therefore expected to have superior non-linear performance in comparison with standard SI fibers.

Conclusions We have proposed a new MMF design with improved mode spacing, suitable for UC-MDM optical communications. The design involves two steps and it is based on fundamental and

intuitive waveguide principles. The new design incorporates first an optimized core depression, which affects primarily LP01 and LP02 mode effective indices. This optimized perturbation increases the LP21-LP02 mode spacing but can potentially compromise the fiber micro- and macro-bending behaviour. This effect has been counter-balanced by incorporating four optimally placed thin high-index rods in close proximity with the fiber core. This increases primarily the effective indices of the LP21 and LP02 modes without affecting significantly their spacing. The small LP21-LP02 mode spacing limitation, encountered in standard SI profiles, has been substantially improved by 40-100%. In addition, the new fiber design shows increased effective areas, in excess of 150 m2 for all supported modes, which is expected to give superior nonlinear performance.

Acknowledgements We gratefully acknowledge funding support for this work from the Engineering and Physical Sciences Research Council (EPSRC) through the EPSRC Centre for Innovative Manufacturing in Photonics (grant EP/H02607X/1). References [1] D. J. Richardson, et al., "Space-division

multiplexing in optical fibres," Nat. Photon., vol. 7, p. 354 (2013).

[2] M. Bigot-Astruc, et al., "Design and fabrication of weakly-coupled few-mode fibers," IEEE Photonics Soc. Summer Top. Meet. Ser., vol. 1, p. 189 (2012).

[3] D. Boivin, et al., "Weakly-coupled few-mode fibers for single-mode and mode-division-multiplexed transmissions," Proc. OFC, OTh3K.6, Anaheim (2013).

[4] P. Sillard, et al., "Few-mode fiber for uncoupled mode-division multiplexing transmissions," Proc. ECOC, Tu.5.LeCervin.7, Geneva (2011).

[5] R. Olshansky, "Mode coupling effects in graded-index optical fibers," Appl. Opt., vol. 14, no. 4, p. 935 (1975).

[6] K. Jespersen, et al., "Measuring distributed mode scattering in long, few-moded fibers," Proc. OFC, OTh3l.4, Los Angeles (2012).

[7] A. Snyder and J. Love, Optical Waveguide Theory. Chapman and Hall (1983).

[8] R. Stolen, "Modes in fiber optical waveguides with ring index profiles," Appl. Opt., vol. 14, no. 7, p. 1533 (1975).

Tab. 1: Performance comparison of new designs with state-of-the-art step-index fibers4 (@ =1550nm)

Mode LP01 LP11 LP21 LP02 neff-ncl (ring - step 1) 7.7x10

-3 5.7x10-3 3.0x10-3 1.9x10-3 neff-ncl (rods step1+step 2) 7.7x10

-3 6.0x10-3 3.9x10-3 2.7x10-3 neff-ncl ref

4 8.3x10-3 6.0x10-3 3.2x10-3 2.4x10-3 DGD w.r.t LP01 (ns/km) (step1+step2) - 4.4 6.2 3.9 DGD w.r.t LP01 (ns/km) ) ref

4 - 4.4 8.5 7.2 Aeff (m2) (step1+step2) 151 203 172 171 Aeff (m2) ref4 124 118 133 127

Tab. 2: Mode spacing comparison of new designs with state-of-the-art step-index fibers (@ =1550nm)

Mode Spacing LP01-LP11 LP11-LP21 LP21-LP02

Ring (step1) 2.0x10-3 2.7x10-3 1.1x10-3

Rods (step1+step 2)

1.7x10-3 2.1x10-3 1.2x10-3

ref4 2.3x10-3 2.8x10-3 0.8x10-3

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Few-Mode Fibers with Improved Mode SpacingAlexander R. May * and Michalis N. ZervasOptoelectronics Research Centre, University of Southampton, Southampton, SO17 1BJ, UK *arm103@orc.soton.ac.ukIntroductionDesign strategy for fibers with optimally distributed mode spacing