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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 13 — Jun. 18, 2012
  • pp: 13810–13824
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Perspectives of principal mode transmission in mode-division-multiplex operation

Adrian A. Juarez, Christian A. Bunge, Stefan Warm, and Klaus Petermann  »View Author Affiliations


Optics Express, Vol. 20, Issue 13, pp. 13810-13824 (2012)
http://dx.doi.org/10.1364/OE.20.013810


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Abstract

We investigate the concept of principal modes and its application for mode division multiplexing in multimode fibers. We start by generalizing the formalism of the principal modes as to include mode dependent loss and show that principal modes overcome modal dispersion induced by modal coupling in mode division multiplexing operation, even for multi-mode-fibers guiding a large number of modes, if the product of modulation bandwidth, fiber length and differential group delay is equal or less than one in each transmission channel. If this condition is not sustained, modal dispersion and crosstalk at the receiver limit the transmission performance, setting very high constraints towards modal coupling.

© 2012 OSA

1. Introduction

The demand for capacity has been increasing exponentially over the last decade, mainly due to the large growing Internet traffic. The standard single mode fiber (SSMF), which is currently the fiber used for long-haul transmission systems, is reaching its capacity limit and new technologies are needed to confront the challenges of higher capacity transmission [1

1. R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightwave Technol. 28(4), 662–701 (2010). [CrossRef]

].

2. System modeling

2.1. Principal modes and fiber transmission matrix

Ein(x,y)=i=1IaiEi(x,y).
(1)

Hereaiis a complex weighting coefficient describing the excitation of the ith eigenmode of the unperturbed MMF and I is the total number of modes.

The eigenmodes of the unperturbed MMF are normalized so that they obey the orthonormality condition:
1ξ2Ei(x,y)·Ej*(x,y)·dxdy=δi,j,
(2)
whereδi,jis the Kronecker delta symbol. After propagating through the MMF, we can describe the output field also as a superposition of eigenmodes with different complex weighting coefficientsbi:

Eout(x,y)=i=1IbiEi(x,y).
(3)

The relation between the input excitation coefficientaiand the output coefficientbican be expressed as follows:

b=ejϕ0(ω)T(ω)·a.
(4)

Mode coupling is modeled by assuming fiber alignment mismatches at splice points as shown in Fig. 1(a). This is due to the assumption that longer terrestrial transmission systems will rely on spliced fibers which will in turn induce mode coupling. We expect mode coupling induced by micro bending along a MMF segment to be relatively small compared to the influence of splices since the segment length is only 3km and we proceed by calculating the induced mode coupling through overlap integrals as:

Kij,m=1ξ2Ei,m(x,y)·Ej,m+1*(x´,y´)dxdy.
(6)

Here Ei,m is the ith eigenmode of the unperturbed MMF in the segment m and Ej,m+1 respectively the jth eigenmode of the MMF in segment m + 1. Our transmission matrix is then given by:
T(ω)=m=1MMm(ω)·Km,
(7)
where matrix Kmdescribes the coupling between segment m and m + 1; M is the total number of MMF segments. As data signals occupy a certain bandwidth, it is necessary to consider the frequency dependence of the output vector b given a fixed input vectora. For this reason we start by evaluating the derivative of Eq. (4) with respect to the angular frequency denoted asω. This leads to:
ωb=[jT(ω)ωϕ0(ω)+ωT(ω)]ejϕ0(ω)a,
(8)
where we have assumed ωa=0 since the input vector ais fixed. By rearranging Eq. (8) and using Eq. (4) we obtain the following expression:

ωb=[jT(ω)ωϕ0(ω)+ωT(ω)]T(ω)1b.
(9)

This equation can rearranged such as:
ωb=[jτ0LI+G(ω)]b,
(10)
whereIis the identity matrix and  G(ω)=ωT(ω)·T(ω)1. The frequency derivative ofϕ0(ω)can be identified asτ0L, the group delay of the fundamental mode over the whole transmission length L. Equation (10) tells us that an output field pattern, represented by the output vectorb, changes with frequency to the first order due to the matrixG(ω). Nevertheless, it is possible to find a vectorbpthat is frequency independent to the first order if the frequency dependent matrixG(ω)acting onbcomplies with the following equation:

G(ω)·bp=γpbp.
(11)

We emphasize here that Eq. (15) and Eq. (12) are not identical sinceG(ω)F(ω)which is a direct consequence of T(ω)not being unitary. This means that Eq. (15) and Eq. (12) have different eigenvectors and as a consequence, the principal modes at the inputapare not equal to the principal modes at the outputbpand our equations differ at this point from the derivation presented in [3

3. S. Fan and J. M. Kahn, “Principal modes in multimode waveguides,” Opt. Lett. 30(2), 135–137 (2005). [CrossRef] [PubMed]

]. We will now proceed with the details of the MMF and the eigenmodes of the MMF.

2.2. Eigenmodes of the MMF

The eigenmodes of the MMF and their propagation constants depend strongly on the fiber geometry (radius and index profile) as well as on the relative index differenceΔ=(n1n2)/n1. Assuming a weakly guiding MMF, that isΔ1, with a parabolic index profile given as [9

9. H.-G. Unger, Planar Optical Waveguides and Fibers (Oxford University Press, 1977).

]:
n(r)=n1(12Δ(r/r0)2),
(16)
wheren1is the refractive index profile in the center of the core andr0the core radius, we can formulate the transverse field distribution of the MMF in good approximation in terms of the Laguerre-Gauss modes. We obtain the LP Modes (for one polarization) as given by [9

9. H.-G. Unger, Planar Optical Waveguides and Fibers (Oxford University Press, 1977).

] as:

El,q(r,φ)=Cl,q(rξ)lLql(r2ξ2)er22ξ2{sinlφcoslφ.
(17)

Here l describes de circumferential order and q the radial order, Lql the Laguerre polynomial and ξ is given as:
ξ=r0/(k0n12Δ).
(18)
Cl,qis a normalization constant, normalizing the field as shown in Eq. (2). The propagation constant and group delay coefficient are given for the Laguerre Gauss modes according to [9

9. H.-G. Unger, Planar Optical Waveguides and Fibers (Oxford University Press, 1977).

] by:
βq,l=n1k0(122Δn1k0r0(2q+2l+1))
(19)
and
τq,l=N1c(1+Δ(2q+l+1n1k0r0  )2),
(20)
where N1 is the group index in the core. Equation (20) neglects profile dispersion. Using this model, we will now proceed to analyze a simple three-mode system, in order to study the main properties of principal mode transmission in mode division multiplexing operation without the usage of MIMO equalization techniques and compare them to the traditional eigenmode transmission.

3. Performance evaluation in a three mode system

To understand some of the main limitations when using PMs for MDM purposes we investigate a three-mode system numerically. A layout of the simulated three mode transmission system is presented in Fig. 3
Fig. 3 Exemplary three mode transmission system. optical fields coming out of each modulator (MOD) are encoded and then matched to a desired spatial mode (M-MUX), which can either be a PM or EM. These are then multiplexed into the MMF. At the output of the MMF, the sum of all PMs or EMs is mode-de-multiplexed (M-DE-MUX) and detected at the receiver (Rx). The M-DE-MUX can be realized for instance by a diffractive element or a photodiode array together with a local oscillator to obtain space and phase information.
. A single coherent light source is used as transceiver and its output power is divided equally into three different modulators, resulting in three individual signals at the same wavelength. The spatial field distribution of each carrier is modified to match a specific principal mode or eigenmode in the optical domain by spatial filtering. The field conversion can be realized as mentioned in [7

7. G. Stepniak, L. Maksymiuk, and J. Siuzdak, “Binary-Phase Spatial Light Filters for Mode-Selective Excitation of Multimode Fibers,” J. Lightwave Technol. 29(13), 1980–1987 (2011). [CrossRef]

] with free space optics using a spatial light modulator, by using a mode converter similar to the one proposed in [10

10. K. Petermann, “Nonlinear distortions and noise in optical communication systems due to fiber connectors,” J. Quantum Electron. 16(7), 761–770 (1980). [CrossRef]

,11

11. N. Hanzawa, K. Saitoh, T. Sakamoto, T. Matsui, S. Tomita, and M. Koshiba, “Demonstration of mode-division multiplexing transmission over 10 km two-mode fiber with mode coupler,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OWA4.

] or byusing a diffractive optics approach as shown in [12

12. N. K. Fontaine, C. R. Doerr, M. A. Mestre, R. R. Ryf, P. J. Winzer, L. L. Buhl, Y. Sun, X. Jiang, and R. Lingle, Jr., “Space-division multiplexing and all-optical MIMO demultiplexing using a photonic integrated circuit,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2012), post-deadline paper PDP5B.

]. If the spatial field distribution is matched to a PM, adaptive techniques would be required due to temporal channel variations. Here we will only consider the time interval where the channel is practically stationary so that PM estimation is required only once per simulation. The modes are then multiplexed into the MMF and de-multiplexed at the output of the MMF. Multiplexing and de-multiplexing can be considered as mirror images and it is therefore possible to apply the same concepts as mentioned for the multiplexing. After de-multiplexing, the signal is amplified to compensate for losses and direct detection is applied.

The transverse field distributions given in Eq. (17) now simplifies for the LP01 mode as:
E01(r,φ)=1πer2 2ξ2 
(21)
and the LP11 modes as:
E11(r,φ)=2/πrer2 2ξ2{sinφcosφ
(22)
for the odd and even mode respectively. The coupling matrix for a three mode system can be evaluated for a radial offset b and a rotation angleφ0as shown in Fig. 1 using Eq. (6) as:

Km=(eb22ξ2beb22ξ2(cosφ0+sinφ0)2ξbeb22ξ2(sinφ0cosφ0)2ξbeb22ξ22ξeb22ξ2(sinφ0b2+(b22ξ2)cosφ0)2ξ2eb22ξ2((b22ξ2)sinφ0b2cosφ0)2ξ2beb22ξ22ξeb22ξ2(cosφ0b2+(b22ξ2)sinφ0)2ξ2eb22ξ2(b2sinφ0(b22ξ2)cosφ0)2ξ2)
(23)

The simulation parameters are given in Table 1

Table 1. Fiber Simulation Parameters Used for MDM Simulation in Three Mode Fiber

table-icon
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and some values require explanation; αrepresents the total transmission loss induced by splices and is calculated by exciting all guided modes in the MMF input and measuring the overall loss at the output. ξ is the mode field size of the LP01 mode and can be calculated using Eq. (18), Lm is the fiber segment length in which we assume ideal propagation, b/ξ is the splice mismatch to mode field ratio and induces the splice loss α along the MMF; φ0 is used to randomize the mode coupling between two MMF segments by rotating the axis with respect to the previous. The refractive index n1 and the group index N1 were calculated using the Sellmeyer equation [13

13. E. Voges and K. Petermann, “Vielmodenfaser,” in Optische Kommunikationstechnik, (Springer Verlag 2002) 214–260.

] for a fiber with 90% SiO2 concentration andΔτmis the maximal differential group delay (DGD) between the fastest and slowest propagating mode.

B1ΔτmL0.7GHz.
(24)

We start by transmitting three random bit sequences with OOK-NRZ modulation format containing 512 symbols over the MMF at0.7Gbit/s. Each bit sequence si(t)is encoded on one spatial mode and multiplexed into the MMF as:

aT(ω)=i=1ISi(ω)ai.
(25)

Here Si(ω)=F{si(t)} denotes the Fourier transform of the bit sequencesi(t)and aidenotes the spatial mode, which can either be an EM or PM. At the output of the MMF we spatially decouple each mode as discussed further on in section 3.1, detect the output power and compute the eye opening penalty. Additive Gaussian white noise is not included in this transmission and losses are compensated at the receiver in order to study the eye opening penalty caused by inter-symbolic interference induced by mode coupling. Figure 4
Fig. 4 Eye diagram plotted for a PRBS OOK signal at 1 Gbits/s over 50 km MMF; a) using EM as carriers; b) using PMs as carriers.
shows an exemplary result for the eye opening computed at the receiver using (a) EMs as carriers and (b) PMs as carriers. We notice that the eye opening in Fig. 4(a) has several quantized amplitude levels inside of what should be a perfect eye.

Before we proceed to scale the bit rate in the MMF transmission we define a 2 dB eye opening penalty criterion which allows us to define whether a transmission mode is usable for transmission. In other words a mode is adequate for transmission if its eye opening penalty is less than 2 dB. Using this criterion we obtain the results for the usable modes as presented in Fig. 6 (a)
Fig. 6 EOP of MDM transmission for various bitrates in a three mode fiber; a) Using EM as carriers, b) using PM as carriers.
where EMs are used as carriers and (b) where PMs are used as carriers.

3.1. Crosstalk limitations and spatial filtering

In order to operate the MMF in a MDM operation, it is necessary to demultiplex each transmission mode at the receiver. This has been realized using lenses [2

2. R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R. Essiambre, P. J. Winzer, D. W. Peckham, A. McCurdy, and R. Lingle, “Mode-division multiplexing over 96 km of few-mode fiber using coherent 6 x 6 MIMO processing,” J. Lightwave Technol. 30(4), 521–531 (2012). [CrossRef]

], holograms [14

14. J. Carpenter and T. D. Wilkinson, “Precise modal excitation in multimode fiber for control of modal dispersion and mode-group division multiplexing,” in Proceedings of European Conf. Opt. Commun. (2011), paper We.10.P1.

] and diffractive gratings [12

12. N. K. Fontaine, C. R. Doerr, M. A. Mestre, R. R. Ryf, P. J. Winzer, L. L. Buhl, Y. Sun, X. Jiang, and R. Lingle, Jr., “Space-division multiplexing and all-optical MIMO demultiplexing using a photonic integrated circuit,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2012), post-deadline paper PDP5B.

]. The goal of this is to modify the output field distribution in such a way, that the orthogonality condition can be applied to discriminate the mode of interest. In our model, where each vector component represents the weighting coefficient for each eigenmode of the unperturbed MMF, it reduces to a scalar multiplication of the output vector b with a detection vectord.This means for instance, that if we would want to discriminate the LP01 mode at the receiver, we would have to scalar multiply the output vectorbwithd=g1(1,0,0)T,whereg1is the gain factor needed to compensate for transmission loses, which are different for each transmission mode. In the case of PM detection, this would extend to the scalar multiplication of the output PM bp,iwith its conjugate complex vectorbp,i*.This is only correct if the PMs form a complete orthogonal basis, which in our case they do not, as mentioned in section 2.1. Computing bp,i·bp,j0 at the output would then lead to residual crosstalk from the remaining PMs at the receiver. Crosstalk at the jth channel can be defined as [15

15. A. A. Juarez, S. Warm, C.-A. Bunge, P. Krummrich, and K. Petermann, “Perspectives of principal mode transmission in a multi-mode fiber,” in Proceedings of European Conf. Opt. Commun. (2010), paper P.4.10.

]:

PjC(ω)=i=1,ijI(bi·dj)(bi·dj)*.
(27)

P·D=I.
(28)

HerePis the matrix containing in its rows the principal modes at the outputbp,Iis the identity matrix andDis the detection matrix in which each column represents one detection vector used to detect the ith PM crosstalk free. It is worthwhile noting here that the definition of the detection vectors in Eq. (28) automatically implies the compensation of mode dependent losses. Figure 7
Fig. 7 Left: Crosstalk of: (a) LP11 (b) PM 2 and (c) PM 2 at the output of the MMF for three different splice losses. Right: Crosstalk for each guided (a) EM (b) PM and (c) PM using the detection vectors for constant total splice loss of 0.5 dB; Fig. (b) and (c) differ only at the demultiplexing stage at the receiver; (b) uses the conjugate complex of the PMs as mode filter whereas (c) uses the detection vector defined in Eq. (28). Each EM or PM exited at the input of the MMF contains unit power.
shows the crosstalk at the receiver for three different transmission scenarios; (a) represents the crosstalk at the receiver when eigenmodes are used as carriers, (b) is the crosstalk at the receiver when PMs are used as carriers using their complex conjugate di=gibifor spatial de-multiplexing (gi = gain factor to compensate for their losses) and (c) is the crosstalk at the receiver when PMs are used as carriers and Eq. (28) is used for spatial de-multiplexing.

4. Scaling properties for systems with larger number of modes

The bit sequence is 512 bits long using NRZ-OOK modulation format. Spatial demultiplexing is realized applying Eq. (28) at the receiver, which means zero crosstalk at the carrier frequencyω0/2π. The results are presented in Fig. 8
Fig. 8 Number of usable principal modes in a 36 mode fiber for various bitrates. The maximal differential group delay has the value ofΔτm=134ps/km and limits the maximal transmission rate down to0.1Gbit/s.
.

The transmission rate per channel assumed for this MDM transmission is10Gbit/s. Here we point out that these results are an extension of the results already presented in [17

17. A. A. Juarez, S. Warm, C.-A. Bunge, and K. Petermann, “Number of usable principal modes in a mode division multiplexing transmission for different multi-mode fibers,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper JTHA34.

] and additionally correct the splice loss values given there. The results presented in Fig. 9
Fig. 9 Usable principal modes in a 50 km transmission link, at 10Gbit/s. This implies 16 splicing points. Results represent an enhanced version of the results presented in [17].
show that the number of usable PMs is very low even if we use the new allowable total splice loss value of 0.16 dB (this curve would be in between of the green and purple curve).

5. Conclusion

We pointed out that crosstalk at the receiver influences the transmission performance, especially at higher bitrates, since the frequency independence of the PMs does no longer hold and each PM interferes with one another at the frequency independent receiver. This could be well compensated using MIMO equalization as realized in [19

19. A. Tarighat, R. C. J. Hsu, A. Shah, A. H. Sayed, and B. Jalali, “Fundamentals and challenges of optical multiple-input multiple-output multimode fiber links [Topics in Optical Communications],” IEEE Commun. Mag. 45(5), 57–63 (2007). [CrossRef]

] and the questions arises if the receiver complexity can be reduced by using the principal modes as carriers compared to using the eigenmodes of the unperturbed MMF as carriers.

References and links

1.

R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightwave Technol. 28(4), 662–701 (2010). [CrossRef]

2.

R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R. Essiambre, P. J. Winzer, D. W. Peckham, A. McCurdy, and R. Lingle, “Mode-division multiplexing over 96 km of few-mode fiber using coherent 6 x 6 MIMO processing,” J. Lightwave Technol. 30(4), 521–531 (2012). [CrossRef]

3.

S. Fan and J. M. Kahn, “Principal modes in multimode waveguides,” Opt. Lett. 30(2), 135–137 (2005). [CrossRef] [PubMed]

4.

M. B. Shemirani, W. Mao, R. A. Panicker, and J. M. Kahn, “Principal modes in graded-index multimode fiber in presence of spatial- and polarization-mode coupling,” J. Lightwave Technol. 27(10), 1248–1261 (2009). [CrossRef]

5.

N. W. Spellmeyer, “Communications performance of a multimode EDFA,” IEEE Photon. Technol. Lett. 12(10), 1337–1339 (2000). [CrossRef]

6.

P. Krummrich and K. Petermann, “Evaluation of potential optical amplifier concepts for coherent mode multiplexing,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OMH5.

7.

G. Stepniak, L. Maksymiuk, and J. Siuzdak, “Binary-Phase Spatial Light Filters for Mode-Selective Excitation of Multimode Fibers,” J. Lightwave Technol. 29(13), 1980–1987 (2011). [CrossRef]

8.

C. P. Tsekrekos and A. M. J. Koonen, “Mode-selective spatial filtering for increased robustness in a mode group diversity multiplexing link,” Opt. Lett. 32(9), 1041–1043 (2007). [CrossRef] [PubMed]

9.

H.-G. Unger, Planar Optical Waveguides and Fibers (Oxford University Press, 1977).

10.

K. Petermann, “Nonlinear distortions and noise in optical communication systems due to fiber connectors,” J. Quantum Electron. 16(7), 761–770 (1980). [CrossRef]

11.

N. Hanzawa, K. Saitoh, T. Sakamoto, T. Matsui, S. Tomita, and M. Koshiba, “Demonstration of mode-division multiplexing transmission over 10 km two-mode fiber with mode coupler,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OWA4.

12.

N. K. Fontaine, C. R. Doerr, M. A. Mestre, R. R. Ryf, P. J. Winzer, L. L. Buhl, Y. Sun, X. Jiang, and R. Lingle, Jr., “Space-division multiplexing and all-optical MIMO demultiplexing using a photonic integrated circuit,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2012), post-deadline paper PDP5B.

13.

E. Voges and K. Petermann, “Vielmodenfaser,” in Optische Kommunikationstechnik, (Springer Verlag 2002) 214–260.

14.

J. Carpenter and T. D. Wilkinson, “Precise modal excitation in multimode fiber for control of modal dispersion and mode-group division multiplexing,” in Proceedings of European Conf. Opt. Commun. (2011), paper We.10.P1.

15.

A. A. Juarez, S. Warm, C.-A. Bunge, P. Krummrich, and K. Petermann, “Perspectives of principal mode transmission in a multi-mode fiber,” in Proceedings of European Conf. Opt. Commun. (2010), paper P.4.10.

16.

R. K. Bocek, J. Hartpence, Y. Qian, and T. Lian OFS. “Ensuring low splice loss with high quality fibers”. [Online] http://stage.ofsinfo.com/resources/splice.pdf (2012).

17.

A. A. Juarez, S. Warm, C.-A. Bunge, and K. Petermann, “Number of usable principal modes in a mode division multiplexing transmission for different multi-mode fibers,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper JTHA34.

18.

A. Li, A. A. Amin, X. Chen, S. Chen, G. Gao, and W. Shieh, “Reception of dual-spatial-mode CO-OFDM signal over a two-mode fiber,” J. Lightwave Technol. 30(4), 634–640 (2012). [CrossRef]

19.

A. Tarighat, R. C. J. Hsu, A. Shah, A. H. Sayed, and B. Jalali, “Fundamentals and challenges of optical multiple-input multiple-output multimode fiber links [Topics in Optical Communications],” IEEE Commun. Mag. 45(5), 57–63 (2007). [CrossRef]

OCIS Codes
(030.4070) Coherence and statistical optics : Modes
(060.0060) Fiber optics and optical communications : Fiber optics and optical communications
(060.4230) Fiber optics and optical communications : Multiplexing

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: February 22, 2012
Revised Manuscript: April 28, 2012
Manuscript Accepted: May 18, 2012
Published: June 6, 2012

Citation
Adrian A. Juarez, Christian A. Bunge, Stefan Warm, and Klaus Petermann, "Perspectives of principal mode transmission in mode-division-multiplex operation," Opt. Express 20, 13810-13824 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-13-13810


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References

  1. R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, “Capacity limits of optical fiber networks,” J. Lightwave Technol.28(4), 662–701 (2010). [CrossRef]
  2. R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R. Essiambre, P. J. Winzer, D. W. Peckham, A. McCurdy, and R. Lingle, “Mode-division multiplexing over 96 km of few-mode fiber using coherent 6 x 6 MIMO processing,” J. Lightwave Technol.30(4), 521–531 (2012). [CrossRef]
  3. S. Fan and J. M. Kahn, “Principal modes in multimode waveguides,” Opt. Lett.30(2), 135–137 (2005). [CrossRef] [PubMed]
  4. M. B. Shemirani, W. Mao, R. A. Panicker, and J. M. Kahn, “Principal modes in graded-index multimode fiber in presence of spatial- and polarization-mode coupling,” J. Lightwave Technol.27(10), 1248–1261 (2009). [CrossRef]
  5. N. W. Spellmeyer, “Communications performance of a multimode EDFA,” IEEE Photon. Technol. Lett.12(10), 1337–1339 (2000). [CrossRef]
  6. P. Krummrich and K. Petermann, “Evaluation of potential optical amplifier concepts for coherent mode multiplexing,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OMH5.
  7. G. Stepniak, L. Maksymiuk, and J. Siuzdak, “Binary-Phase Spatial Light Filters for Mode-Selective Excitation of Multimode Fibers,” J. Lightwave Technol.29(13), 1980–1987 (2011). [CrossRef]
  8. C. P. Tsekrekos and A. M. J. Koonen, “Mode-selective spatial filtering for increased robustness in a mode group diversity multiplexing link,” Opt. Lett.32(9), 1041–1043 (2007). [CrossRef] [PubMed]
  9. H.-G. Unger, Planar Optical Waveguides and Fibers (Oxford University Press, 1977).
  10. K. Petermann, “Nonlinear distortions and noise in optical communication systems due to fiber connectors,” J. Quantum Electron.16(7), 761–770 (1980). [CrossRef]
  11. N. Hanzawa, K. Saitoh, T. Sakamoto, T. Matsui, S. Tomita, and M. Koshiba, “Demonstration of mode-division multiplexing transmission over 10 km two-mode fiber with mode coupler,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper OWA4.
  12. N. K. Fontaine, C. R. Doerr, M. A. Mestre, R. R. Ryf, P. J. Winzer, L. L. Buhl, Y. Sun, X. Jiang, and R. Lingle, Jr., “Space-division multiplexing and all-optical MIMO demultiplexing using a photonic integrated circuit,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2012), post-deadline paper PDP5B.
  13. E. Voges and K. Petermann, “Vielmodenfaser,” in Optische Kommunikationstechnik, (Springer Verlag 2002) 214–260.
  14. J. Carpenter and T. D. Wilkinson, “Precise modal excitation in multimode fiber for control of modal dispersion and mode-group division multiplexing,” in Proceedings of European Conf. Opt. Commun. (2011), paper We.10.P1.
  15. A. A. Juarez, S. Warm, C.-A. Bunge, P. Krummrich, and K. Petermann, “Perspectives of principal mode transmission in a multi-mode fiber,” in Proceedings of European Conf. Opt. Commun. (2010), paper P.4.10.
  16. R. K. Bocek, J. Hartpence, Y. Qian, and T. Lian OFS. “Ensuring low splice loss with high quality fibers”. [Online] http://stage.ofsinfo.com/resources/splice.pdf (2012).
  17. A. A. Juarez, S. Warm, C.-A. Bunge, and K. Petermann, “Number of usable principal modes in a mode division multiplexing transmission for different multi-mode fibers,” in Optical Fiber Communication Conference, OSA Technical Digest (CD) (Optical Society of America, 2011), paper JTHA34.
  18. A. Li, A. A. Amin, X. Chen, S. Chen, G. Gao, and W. Shieh, “Reception of dual-spatial-mode CO-OFDM signal over a two-mode fiber,” J. Lightwave Technol.30(4), 634–640 (2012). [CrossRef]
  19. A. Tarighat, R. C. J. Hsu, A. Shah, A. H. Sayed, and B. Jalali, “Fundamentals and challenges of optical multiple-input multiple-output multimode fiber links [Topics in Optical Communications],” IEEE Commun. Mag.45(5), 57–63 (2007). [CrossRef]

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