Abstract

Spatial light modulation can be used to address specific fiber modes, as required in mode-division multiplexed systems. We theoretically compare phase-only spatial light modulation to a combination of amplitude and phase spatial light modulation in terms of insertion loss and crosstalk for a fiber supporting 11 LP modes. We experimentally demonstrate selective mode excitation using a Liquid Crystal on Silicon (LCoS) spatial light modulator configured to as phase and amplitude modulator.

© 2013 OSA

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    [CrossRef]
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2012 (5)

2011 (3)

2010 (2)

2007 (1)

2006 (1)

W. Mohammed, M. Pitchumani, A. Mehta, and E. G. Johnson, “Selective excitation of the LP11 mode in step index fiber using a phase mask,” SPIE Opt. Eng.45(7), 74602–74602 (2006).
[CrossRef]

2002 (1)

1994 (1)

1984 (1)

1982 (1)

1971 (1)

Alam, S.

Y. Jung, S. Alam, Z. Li, A. Dhar, D. Giles, I. P. Giles, J. K. Sahu, F. Poletti, L. Grüner-Nielsen, and D. J. Richardson, “First demonstration and detailed characterization of a multimode amplifier for space division multiplexed transmission systems,” Opt. Express19(26), B952–B957 (2011).
[CrossRef] [PubMed]

Q. Kang, E. Lim, Y. Jung, J. Sahu, F. Poletti, S. Alam, and D. Richardson, “Modal gain control in a multimode erbium doped fiber amplifier incorporating ring doping,” in Proc. European Conference on Optical Communication (ECOC’12), P1.05 (2012).
[CrossRef]

Argyros, A.

Askarov, D.

D. Askarov and J. M. Kahn, “Design of multi-mode erbium-doped fiber amplifiers for low mode-dependent gain,” in Proc. IEEE Photonics Society Summer Topical Meeting Series, 220–221 (2012).
[CrossRef]

Astruc, M.

Berdagué, S.

Bigo, S.

Bland-Hawthorn, J.

Bolle, C.

Boutin, A.

Brindel, P.

Brooks, J. L.

Burrows, E. C.

Carpenter, J.

J. Carpenter, B. C. Thomsen, and T. D. Wilkenson, “Mode division multiplexing of modes with the same azimuthal index,” IEEE Photon. Technol. Lett.24(21), 1969–1972 (2012).
[CrossRef]

Cerou, F.

Chandrasekhar, S.

Charlet, G.

Corrado, B. J.

Dhar, A.

Dimarcello, F. V.

Esmaeelpour, M.

Essiambre, R.-J.

Facq, P.

Fini, J. M.

Fishteyn, M.

Foschini, G. J.

Giles, D.

Giles, I. P.

Gloge, D.

Gnauck, A. H.

Goebel, B.

Grüner-Nielsen, L.

Johnson, E. G.

W. Mohammed, M. Pitchumani, A. Mehta, and E. G. Johnson, “Selective excitation of the LP11 mode in step index fiber using a phase mask,” SPIE Opt. Eng.45(7), 74602–74602 (2006).
[CrossRef]

Jung, Y.

Y. Jung, S. Alam, Z. Li, A. Dhar, D. Giles, I. P. Giles, J. K. Sahu, F. Poletti, L. Grüner-Nielsen, and D. J. Richardson, “First demonstration and detailed characterization of a multimode amplifier for space division multiplexed transmission systems,” Opt. Express19(26), B952–B957 (2011).
[CrossRef] [PubMed]

Q. Kang, E. Lim, Y. Jung, J. Sahu, F. Poletti, S. Alam, and D. Richardson, “Modal gain control in a multimode erbium doped fiber amplifier incorporating ring doping,” in Proc. European Conference on Optical Communication (ECOC’12), P1.05 (2012).
[CrossRef]

Kahn, J. M.

D. Askarov and J. M. Kahn, “Design of multi-mode erbium-doped fiber amplifiers for low mode-dependent gain,” in Proc. IEEE Photonics Society Summer Topical Meeting Series, 220–221 (2012).
[CrossRef]

Kang, Q.

Q. Kang, E. Lim, Y. Jung, J. Sahu, F. Poletti, S. Alam, and D. Richardson, “Modal gain control in a multimode erbium doped fiber amplifier incorporating ring doping,” in Proc. European Conference on Optical Communication (ECOC’12), P1.05 (2012).
[CrossRef]

Koebele, C.

Kogelnik, H.

Koonen, A. M. J.

Kramer, G.

Leeb, W. R.

Leon-Saval, S. G.

Li, Z.

Lim, E.

Q. Kang, E. Lim, Y. Jung, J. Sahu, F. Poletti, S. Alam, and D. Richardson, “Modal gain control in a multimode erbium doped fiber amplifier incorporating ring doping,” in Proc. European Conference on Optical Communication (ECOC’12), P1.05 (2012).
[CrossRef]

Lingle, R.

Liu, X.

Mardoyan, H.

McCurdy, A. H.

Mehta, A.

W. Mohammed, M. Pitchumani, A. Mehta, and E. G. Johnson, “Selective excitation of the LP11 mode in step index fiber using a phase mask,” SPIE Opt. Eng.45(7), 74602–74602 (2006).
[CrossRef]

Mohammed, W.

W. Mohammed, M. Pitchumani, A. Mehta, and E. G. Johnson, “Selective excitation of the LP11 mode in step index fiber using a phase mask,” SPIE Opt. Eng.45(7), 74602–74602 (2006).
[CrossRef]

Monberg, E. M.

Mumtaz, S.

Pan, Y.

Peckham, D. W.

Pitchumani, M.

W. Mohammed, M. Pitchumani, A. Mehta, and E. G. Johnson, “Selective excitation of the LP11 mode in step index fiber using a phase mask,” SPIE Opt. Eng.45(7), 74602–74602 (2006).
[CrossRef]

Poletti, F.

Y. Jung, S. Alam, Z. Li, A. Dhar, D. Giles, I. P. Giles, J. K. Sahu, F. Poletti, L. Grüner-Nielsen, and D. J. Richardson, “First demonstration and detailed characterization of a multimode amplifier for space division multiplexed transmission systems,” Opt. Express19(26), B952–B957 (2011).
[CrossRef] [PubMed]

Q. Kang, E. Lim, Y. Jung, J. Sahu, F. Poletti, S. Alam, and D. Richardson, “Modal gain control in a multimode erbium doped fiber amplifier incorporating ring doping,” in Proc. European Conference on Optical Communication (ECOC’12), P1.05 (2012).
[CrossRef]

Provost, L.

Randel, S.

Richardson, D.

Q. Kang, E. Lim, Y. Jung, J. Sahu, F. Poletti, S. Alam, and D. Richardson, “Modal gain control in a multimode erbium doped fiber amplifier incorporating ring doping,” in Proc. European Conference on Optical Communication (ECOC’12), P1.05 (2012).
[CrossRef]

Richardson, D. J.

Ryf, R.

Sahu, J.

Q. Kang, E. Lim, Y. Jung, J. Sahu, F. Poletti, S. Alam, and D. Richardson, “Modal gain control in a multimode erbium doped fiber amplifier incorporating ring doping,” in Proc. European Conference on Optical Communication (ECOC’12), P1.05 (2012).
[CrossRef]

Sahu, J. K.

Salsi, M.

Shaw, H. J.

Sierra, A.

Sillard, P.

Sperti, D.

Taunay, T. F.

Thomsen, B. C.

J. Carpenter, B. C. Thomsen, and T. D. Wilkenson, “Mode division multiplexing of modes with the same azimuthal index,” IEEE Photon. Technol. Lett.24(21), 1969–1972 (2012).
[CrossRef]

Thornburg, W. Q.

Tran, P.

Tsekrekos, C. P.

Verluise, F.

Wallner, O.

Wilkenson, T. D.

J. Carpenter, B. C. Thomsen, and T. D. Wilkenson, “Mode division multiplexing of modes with the same azimuthal index,” IEEE Photon. Technol. Lett.24(21), 1969–1972 (2012).
[CrossRef]

Winzer, P. J.

Yan, M. F.

Youngquist, R. C.

Zhu, B.

Zhu, X. D.

Appl. Opt. (2)

IEEE Photon. J. (1)

P. J. Winzer, “Optical networking beyond WDM,” IEEE Photon. J.4(2), 647–651 (2012).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

J. Carpenter, B. C. Thomsen, and T. D. Wilkenson, “Mode division multiplexing of modes with the same azimuthal index,” IEEE Photon. Technol. Lett.24(21), 1969–1972 (2012).
[CrossRef]

J. Lightwave Technol. (3)

J. Opt. Soc. Am. A (1)

Opt. Express (5)

Opt. Lett. (3)

SPIE Opt. Eng. (1)

W. Mohammed, M. Pitchumani, A. Mehta, and E. G. Johnson, “Selective excitation of the LP11 mode in step index fiber using a phase mask,” SPIE Opt. Eng.45(7), 74602–74602 (2006).
[CrossRef]

Other (19)

S. Ramachandran, N. Bozinovic, P. Gregg, S. Golowich, and P. Kristensen, “Optical vortices in fibres: A new degree of freedom for mode multiplexing,” in Proc. European Conference on Optical Communication (ECOC’12), Tu.3.F.3 (2012).
[CrossRef]

H. Kogelnik, Guided-Wave Optoelectronics (Springer, 1988).

D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, 1974).

J. Sakaguchi, B. J. Puttnam, W. Klaus, Y. Awaji, N. Wada, A. Kanno, T. Kawanishi, K. Imamura, H. Inaba, K. Mukasa, R. Sugizaki, T. Kobayashi, and M. Watanabe, “19-core fiber transmission of 19x100x172-Gb/s SDM-WDM-PDM-QPSK signals at 305Tb/s,” in Proc. Optical Fiber Communication Conference (OFC/NFOEC’12), PDP5C.1 (2012).

H. Takara, A. Sano, T. Kobayashi, H. Kubota, H. Kawakami, A. Matsuura, Y. Miyamoto, Y. Abe, H. Ono, K. Shikama, Y. Goto, K. Tsujikawa, Y. Sasaki, I. Ishida, K. Takenaga, S. Matsuo, K. Saitoh, M. Koshiba, and T. Morioka, “1.01-Pb/s (12 SDM/222 WDM/456 Gb/s) crosstalk-managed transmission with 91.4-b/s/Hz aggregate spectral efficiency,” in Proc. European Conference on Optical Communication (ECOC’12), Th.3.C.1 (2012).
[CrossRef]

R. Ryf, R.-J. Essiambre, A. Gnauck, S. Randel, M. A. Mestre, C. Schmidt, P. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, T. Hayashi, T. Taru, and T. Sasaki, “Space-division multiplexed transmission over 4200 km 3-core microstructured fiber,” in Proc. Optical Fiber Communication Conference (OFC/NFOEC’12), PDP5C.2 (2012).

S. Schöllmann, S. Soneff, and W. Rosenkranz, “10.7 Gb/s Over 300 m GI-MMF using a 2 x 2 MIMO system based on mode group diversity multiplexing,” in Proc. Optical Fiber Communication Conference (OFC/NFOEC’07), OTuL2S (2007).

H. Chen, B. H.P.A. van den, and T. Koonen, “30Gbit/s 3 × 3 optical mode group division multiplexing system with mode-selective spatial filtering,” in Proc. Optical Fiber Communication Conference (OFC/NFOEC’11), OWB1 (2011).
[CrossRef]

P. M. Krummrich and K. Petermann, “Evaluation of potential optical amplifier concepts for coherent mode multiplexing,” in Proc. Optical Fiber Communication Conference (OFC/NFOEC’11), OMH5 (2011).
[CrossRef]

R. Ryf, R.-J. Essiambre, J. von Hoyningen-Huene, and P. Winzer, “Analysis of mode-dependent gain in Raman amplified few-mode fiber,” in Proc. Optical Fiber Communication Conference (OFC/NFOEC’12), OW1D.2 (2012).
[CrossRef]

M. Salsi, D. Peyrot, G. Charlet, S. Bigo, R. Ryf, N. K. Fontaine, M. A. Mestre, S. Randel, X. Palou, C. Bolle, B. Guan, G. Le Cocq, L. Bigot, and Y. Quiquempois, “A six-mode erbium-doped fiber amplifier,” in Proc. European Conference on Optical Communication (ECOC’12), Th.3.A.6 (2012).
[CrossRef]

E. Ip, N. Bai, Y. Huang, E. Mateo, F. Yaman, M. Li, S. Bickham, S. Ten, Y. Luo, G. Peng, G. Li, T. Wang, J. Linares, C. Montero, and V. Moreno, “6x6 MIMO transmission over 50+25+10 km heterogeneous spans of few-mode fiber with inline erbium-doped fiber amplifier,” in Proc. Optical Fiber Communication Conference (OFC/NFOEC’12), OTu2C.4 (2012).
[CrossRef]

D. Askarov and J. M. Kahn, “Design of multi-mode erbium-doped fiber amplifiers for low mode-dependent gain,” in Proc. IEEE Photonics Society Summer Topical Meeting Series, 220–221 (2012).
[CrossRef]

Q. Kang, E. Lim, Y. Jung, J. Sahu, F. Poletti, S. Alam, and D. Richardson, “Modal gain control in a multimode erbium doped fiber amplifier incorporating ring doping,” in Proc. European Conference on Optical Communication (ECOC’12), P1.05 (2012).
[CrossRef]

A. Li, A. Al Amin, X. Chen, and W. Shieh, “Reception of mode and polarization multiplexed 107-Gb/s CO-OFDM signal over a two-mode fiber,” in Proc. Optical Fiber Communication Conference (OFC/NFOEC’11), PDPB8 (2011).

R. Ryf, M. A. Mestre, A. Gnauck, S. Randel, C. Schmidt, R.-J. Essiambre, P. Winzer, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, X. Jiang, D. Peckham, A. H. McCurdy, and R. Lingle, “Low-loss mode coupler for mode-multiplexed transmission in few-mode fiber,” in Proc. Optical Fiber Communication Conference (OFC/NFOEC’12), PDP5B.5 (2012).

N. K. Fontaine, R. Ryf, S. G. Leon-Saval, and J. Bland-Hawthorn, “Evaluation of photonic lanterns for lossless mode-multiplexing,” in Proc. European Conference on Optical Communication (ECOC’12), Th.2.D.6 (2012).
[CrossRef]

R. Ryf, N. K. Fontaine, M. A. Mestre, S. Randel, X. Palou, C. Bolle, A. H. Gnauck, S. Chandrasekhar, X. Liu, B. Guan, R.-J. Essiambre, P. J. Winzer, S. Leon-Saval, J. Bland-Hawthorn, R. Delbue, P. Pupalaikis, A. Sureka, Y. Sun, L. Grüner-Nielsen, R. V. Jensen, and R. Lingle, “12 x 12 MIMO transmission over 130-km few-mode fiber,” in Proc. Frontiers in Optics Conference (FiO’12), FW6C.4 (2012).
[CrossRef]

E. Alon, V. Stojanovic, J. M. Kahn, S. Boyd, and M. Horowitz, “Equalization of modal dispersion in multimode fiber using spatial light modulators,” in Proc. of Global Telecommunications Conference (GLOBECOM '04), IEEE, vol. 2, 1023–1029 (2004).
[CrossRef]

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Figures (14)

Fig. 1
Fig. 1

Intensity and electrical field orientation of the LP01 and the two degenerate LP11 ‘modes’ propagating in the fiber. The LP01 mode and both LP11 ‘modes’ appear in vertical and horizontal polarizations.

Fig. 2
Fig. 2

Simulated power distribution between different LP11-modes at different propagation distances when coupled into the fiber. (a) LP11ay and LP11bx exchange power within 11.5 cm. (b) LP11ax and LP11by (b) exchange power within 5.4m.

Fig. 3
Fig. 3

Setup to evaluate insertion loss and modal crosstalk for phase-only LP ‘mode’ shaping and coupling into FMF (core area depicted in blue).

Fig. 4
Fig. 4

(a) Simulated coupling efficiency for phase-only ‘mode’ shaping assuming the coupling of a target LP11 ‘mode’ into a FMF supporting 11 LP ‘modes’. (b) Coupling efficiency (showing insertion loss and crosstalk) for all LP ‘mode’ shaped beams into all supported fiber LP ‘modes’.

Fig. 5
Fig. 5

(a) Simulated coupling efficiencies for complex (phase and amplitude) ‘mode’ shaping assuming the coupling of a target LP11 ‘mode’ into a FMF supporting 11 LP ‘modes’. (b) Coupling efficiency (showing insertion loss and crosstalk) for all LP ‘mode’ shaped beams into all supported fiber LP ‘modes’.

Fig. 6
Fig. 6

Optical setup for complex spatial light modulation and coupling into FMF

Fig. 7
Fig. 7

Optical setup for calibrating the LCoS spatial phase and amplitude modulation characteristics. With uniform LCoS modulator pattern the modulated and the reference beam pass the mask (a). With checkerboard phase pattern higher harmonics in the spatial Fourier transform of the shaped beam are blocked by the mask (b).

Fig. 8
Fig. 8

a) Optical intensity of one camera sensor row. Overlay of measured profiles of the beam reflected by the mirror and the LCoS modulator and the interference of both. b) Cosine function fitted to measured profile to estimate amplitude and phase of the spatially modulated beam.

Fig. 9
Fig. 9

Normalized attenuation aLCoS (a) and phase shift φLCoS (b) for possible pixel value pairs for the checker board phase pattern generated by the LCoS modulator.

Fig. 10
Fig. 10

Measured intensity profiles after mode shaping for LP01 and LP11 with both vertical and horizontal orientations of the phase jump, without (upper row) and with (lower row) Michelson interference with a reference beam.

Fig. 11
Fig. 11

Captured image of beam profile before modulation (a), phase shift pattern written to the LCoS modulator (b), intensity profile after LP11a modulation without (c) and with interference (d).

Fig. 12
Fig. 12

Horizontal (a) and vertical (b) cross-section of the measured LP11 intensity profiles with phase-only modulation, complex modulation and the theoretical curve.

Fig. 13
Fig. 13

Setup for a FMF coupling experiment of LP01, LP11a, and LP11b.

Fig. 14
Fig. 14

Measured intensity profile of shaped LP01 (a + d), LP11a (b + e) and LP11b (c + f) after 5 cm of FMF with vertical (a-c) and horizontal (d-f) polarization filter at the receiver.

Equations (18)

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E Gauss (x,y)= 2 π μ o ϵ 0 4 1 W 0 exp( x 2 + y 2 W 0 2 ) e y ,
H Gauss (x,y)= 2 π ϵ 0 μ o 4 1 W 0 exp( x 2 + y 2 W 0 2 ) e x ,
f(x,y)=exp( iarg( E LP(μ,ν) (x,y) ) ).
E (x,y)= E Gauss f(x,y),
H (x,y)= H Gauss f(x,y),
E (x,y)= µ ν C (µ,ν) E LP(µ.ν) ,
H (x,y)= µ ν C (µ,ν) H LP(µ.ν) .
E LP(μ,ν) (x,y)× H LP(μ,ν) (x,y)dxdy e z =1.
C (μ,ν) = ( E (x,y)× H LP(μ,ν) (x,y)+ E LP(μ,ν) (x,y)× H (x,y) )dxdy e z ,
η (μ,ν) = | C (μ,ν) | 2 .
f(x,y)=exp( iarg( E LP(μ,ν) (x,y) ) )min{ | E LP(μ,ν) (x,y) E Gauss (x,y) |,1 }.
E LCoS (x,y)= a LCoS | E 0 (x,y) |exp( j(x k LCoS,x +y k LCoS,y + φ LCoS ) ),
E Ref (x,y)=| E Ref (x,y) |exp( j(x k Ref,x +y k Ref,y + φ Ref ) ),
I LCoS (x,y)= a LCoS 2 I 0 (x,y) | E LCoS (x,y) | 2 = a LCoS 2 | E 0 (x,y) | 2 ,
I Ref (x,y) | E Ref (x,y) | 2 ,
I(x,y) | E LCoS (x,y)+ E Ref (x,y) | 2 = | E LCoS (x,y) | 2 + | E Ref (x,y) | 2 +2Re{ E LCoS (x,y) E Ref * (x,y) },
I(x,y)= a LCoS 2 I 0 (x,y)+ I Ref (x,y)+2 a LCoS I 0 (x,y) I Ref (x,y) cos( xΔ k x +yΔ k y + φ 0 ),
min a LCoS , φ LCoS { x | I(x) a LCoS 2 I 0 (x) I Ref (x)2 a LCoS I 0 (x) I Ref (x) cos( xΔ k x + φ 0 ) | }.

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