LCoS-based mode shaper for few-mode fiber

Transcription

1 -based mode shaper for few-mode fiber Johannes von Hoyningen-Huene, 1,,* Roland Ryf, 1 and Peter Winzer 1 1 Bell Laboratories, Alcatel-Lucent, 791 Holmdel-Keyport Rd, Holmdel, NJ, 7733, USA Chair for Communications, University of Kiel, Kaiserstr., 4143 Kiel, Germany * jhh@tf.uni-kiel.de 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 () spatial light modulator configured to as phase and amplitude modulator. 13 Optical Society of America OCIS codes: (6.6) Fiber optics and optical communications; (6.43) Multiplexing; (6.34) Fiber optics components. References and links 1. P. J. Winzer, Optical networking beyond WDM, IEEE Photon. J. 4(), (1).. R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, Capacity limits of optical fiber networks, J. Lightwave Technol. 8(4), (1). 3. S. Chandrasekhar, A. H. Gnauck, X. Liu, P. J. Winzer, Y. Pan, E. C. Burrows, T. F. Taunay, B. Zhu, M. Fishteyn, M. F. Yan, J. M. Fini, E. M. Monberg, and F. V. Dimarcello, WDM/SDM transmission of 1 x 18- Gb/s PDM-QPSK over 688-km 7-core fiber with a per-fiber net aggregate spectral-efficiency distance product of 4,3 km b/s/hz, Opt. Express (), (1). 4. 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 19x1x17-Gb/s SDM- WDM-PDM-QPSK signals at 35Tb/s, in Proc. Optical Fiber Communication Conference (OFC/NFOEC 1), PDP5C.1 (1). 5. 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, 1.1-Pb/s (1 SDM/ WDM/456 Gb/s) crosstalk-managed transmission with 91.4-b/s/Hz aggregate spectral efficiency, in Proc. European Conference on Optical Communication (ECOC 1), Th.3.C.1 (1). 6. 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 4 km 3-core microstructured fiber, in Proc. Optical Fiber Communication Conference (OFC/NFOEC 1), PDP5C. (1). 7. P. J. Winzer and G. J. Foschini, MIMO capacities and outage probabilities in spatially multiplexed optical transport systems, Opt. Express 19(17), (11). 8. S. Schöllmann, S. Soneff, and W. Rosenkranz, 1.7 Gb/s Over 3 m GI-MMF using a x MIMO system based on mode group diversity multiplexing, in Proc. Optical Fiber Communication Conference (OFC/NFOEC 7), OTuLS (7). 9. C. P. Tsekrekos and A. M. J. Koonen, Mode-selective spatial filtering for increased robustness in a mode group diversity multiplexing link, Opt. Lett. 3(9), (7). 1. H. Chen, B. H.P.A. van den, and T. Koonen, 3Gbit/s 3 3 optical mode group division multiplexing system with mode-selective spatial filtering, in Proc. Optical Fiber Communication Conference (OFC/NFOEC 11), OWB1 (11). 11. 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 (11). 1. 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 1), OW1D. (1). 13. 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 1), Th.3.A.6 (1). 14. 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 km heterogeneous spans of fewmode fiber with inline erbium-doped fiber amplifier, in Proc. Optical Fiber Communication Conference (OFC/NFOEC 1), OTuC.4 (1). (C) 13 OSA 9 July 13 Vol. 1, No. 15 DOI:1.1364/OE OPTICS EXPRESS 1897

2 15. 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, 1 (1). 16. 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 1), P1.5 (1). 17. 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. Express 19(6), B95 B957 (11). 18. A. Li, A. Al Amin, X. Chen, and W. Shieh, Reception of mode and polarization multiplexed 17-Gb/s CO- OFDM signal over a two-mode fiber, in Proc. Optical Fiber Communication Conference (OFC/NFOEC 11), PDPB8 (11). 19. R. C. Youngquist, J. L. Brooks, and H. J. Shaw, Two-mode fiber modal coupler, Opt. Lett. 9(5), (1984).. 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 modemultiplexed transmission in few-mode fiber, in Proc. Optical Fiber Communication Conference (OFC/NFOEC 1), PDP5B.5 (1). 1. S. G. Leon-Saval, A. Argyros, and J. Bland-Hawthorn, Photonic lanterns: A study of light propagation in multimode to single-mode converters, Opt. Express 18(8), (1).. 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 1), Th..D.6 (1). 3. 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, 1 x 1 MIMO transmission over 13-km few-mode fiber, in Proc. Frontiers in Optics Conference (FiO 1), FW6C.4 (1). 4. S. Berdagué and P. Facq, Mode division multiplexing in optical fibers, Appl. Opt. 1(11), (198). 5. R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R.-J. Essiambre, P. J. Winzer, D. W. Peckham, A. H. McCurdy, and R. Lingle, Mode-division multiplexing over 96 km of few-mode fiber using coherent 6 6 MIMO processing, J. Lightwave Technol. 3(4), (1). 6. W. Q. Thornburg, B. J. Corrado, and X. D. Zhu, Selective launching of higher-order modes into an optical fiber with an optical phase shifter, Opt. Lett. 19(7), (1994). 7. 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), (6). 8. C. Koebele, M. Salsi, D. Sperti, P. Tran, P. Brindel, H. Mardoyan, S. Bigo, A. Boutin, F. Verluise, P. Sillard, M. Astruc, L. Provost, F. Cerou, and G. Charlet, Two mode transmission at 1 Gb/s, over 4 km-long prototype few-mode fiber, using LCOS-based programmable mode multiplexer and demultiplexer, Opt. Express 19(17), (11). 9. 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 '4), IEEE, vol., (4). 3. J. Carpenter, B. C. Thomsen, and T. D. Wilkenson, Mode division multiplexing of modes with the same azimuthal index, IEEE Photon. Technol. Lett. 4(1), (1). 31. D. Marcuse, Theory of Dielectric Optical Waveguides (Academic, 1974). 3. D. Gloge, Weakly guiding fibers, Appl. Opt. 1(1), 5 58 (1971). 33. O. Wallner, W. R. Leeb, and P. J. Winzer, Minimum length of a single-mode fiber spatial filter, J. Opt. Soc. Am. A 19(1), (). 34. 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 1), Tu.3.F.3 (1). 35. H. Kogelnik and P. J. Winzer, Modal birefringence in weakly guiding fibers, J. Lightwave Technol. 3(14), 4 45 (1). 36. H. Kogelnik, Guided-Wave Optoelectronics (Springer, 1988). 1. Introduction In order to support the exponential growth of the Internet traffic demand in fiber optic communication systems, multiple degrees of freedom for the optical signal have been exploited over the past decades [1], such as increased symbol rates, wavelength-division multiplexing (WDM), polarization-division multiplexing (PDM) and higher-order modulation formats. However, recent studies that include fiber nonlinearity into the Shannon capacity framework [] have shown that the transmission capacity over single mode fiber (SMF) is rapidly approaching fundamental limits. To overcome the capacity limit, a new degree of freedom must be exploited for multiplexing, and space has been identified as the next (C) 13 OSA 9 July 13 Vol. 1, No. 15 DOI:1.1364/OE OPTICS EXPRESS 1898

3 accessible dimension [1]. In space-division multiplexing (SDM), a number of signals are sent over parallel uncoupled or coupled transmission paths. SDM can be used in combination with other known techniques like WDM, PDM, and higher-order modulation formats, and two SDM approaches are currently being investigated: In multi-core fibers (MCFs) several fiber cores are arranged within the same cladding and are being used as different, either coupled or uncoupled communication channels [3 6]. In few-mode fibers (FMFs) the size and the refractive index profile of a single fiber core is chosen such that several propagation modes are supported by the fiber. Owing to their mutual orthogonality, these modes, albeit coupled by fiber imperfections, can then be used as individual communication channels through multiple-input multiple-output (MIMO) digital signal processing [7]. Note that the full set of modes supported by the FMF has to be addressed individually at transmitter and receiver in order to achieve reliable long-distance transmission [7], in contrast to shorter-reach mode-group multiplexing applications that have been reported for multimode fibers [8 1]. To enable mode multiplexing systems that can replace SMF systems with parallel fibers both few-mode amplifiers [11 17] and mode multiplexers and demultiplexers [18 9] have to be developed or enhanced. The purpose of a mode multiplexer is to couple light from a set of SMF sources into different FMF propagation modes (or to specific unitary combinations thereof). At the receiver a mode demultiplexer is required to separate the different modes of the FMF into a set of parallel SMF. Over the past years, several multiplexer and demultiplexer techniques have been reported. These techniques include physically stressed fiber [18,19], spot couplers [], photonic lanterns [1 3], 3D-waveguides [3], and spatial phase shaping of the optical profile with glass plates [4 7]. Alternatively to the above static mode shaping techniques, dynamic and adaptive spatial light modulators (SLMs), such as reflective liquid crystal on silicon () devices can also be used for mode shaping [8 3]. Regarding the latter, mode multiplexers that shape the phase but not the amplitude of the spatial optical profile to be coupled into the FMF have so far been used. In this work we theoretically investigate and experimentally demonstrate beam shaping of both phase and amplitude using a modulator and discuss its relevance for coupling into higher-order modes of few-mode fibers.. Modes of a step-index few-mode fiber The guided modes of a step-index profile fiber are determined by the diameter of the core, the refractive index profile of the fiber, and the wavelength of the optical signal [31,3]. In a SMF these parameters are chosen such that only a single spatial mode (consisting of two degenerate polarization modes) can propagate along the fiber. All other modes do not propagate over extended distances in the fiber. Their power is radiated off quickly and cannot be received at the end of the fiber [33]. However, with increased core diameter, increased refractive index difference between core and cladding, or decreased wavelength, an increasing number of higher-order modes can also be guided in the fiber. In this work we assume a step-index fiber with 16-µm core diameter, a refractive index of 1.46, and a relative difference between core and cladding refractive index of.5%. At 155 nm, and as shown in Fig. 1, this fiber supports six true waveguide modes, namely the twofold degenerate HE 11 mode as well as the TE 1, TM 1, and the twofold degenerate HE 1. The twofold degenerate HE 11 -modes (labeled a and b in Fig. 1) are also known as the two polarization modes making up the fiber s fundamental mode. Due to its Gaussian-like intensity profile, its flat phase front, and its linear polarization, the HE 11 can be excited with high efficiency by using linearly polarized Gaussian beams. The twofold degenerate HE 1 -modes (labeled a and b in Fig. 1), as well as TE 1 and TM 1 have a donut-shaped intensity profile and a polarization distribution that changes across the beam profile. In contrast to the fundamental mode, these (C) 13 OSA 9 July 13 Vol. 1, No. 15 DOI:1.1364/OE OPTICS EXPRESS 1899

4 polarization and intensity profiles are difficult to generate experimentally [34]. However linear polarized linear combinations of ± = or HE 11a = LP 1y HE 1a TE 1 LP 11ay LP 11bx ± = or HE 11b = LP 1y HE 1b TM 1 LP 11by LP 11ax Fig. 1. Intensity and electrical field orientation of the LP 1 and the two degenerate LP 11 modes propagating in the fiber. The LP 1 mode and both LP 11 modes appear in vertical and horizontal polarizations. the waveguide modes HE 1, TE 1, and TM 1, can be approximated by the so called linear polarized (LP) modes. Note that even though the resulting LP 11 modes are not true waveguide modes, they are still orthogonal but undergo unitary transformations upon propagation. For example, if LP 11ay is launched into the fiber, it couples into the waveguide modes HE 1a + TE 1, which propagate with slightly different phase velocities, resulting in an increasing phase shift between HE 1a and TE 1. At some distance, which can be in the range from centimeters to kilometers depending on the fiber properties, HE 1a and TE 1 are out of phase by π, resulting in the field distribution of LP 11bx, which has a 9-degree rotated intensity profile and polarization compared to the launched LP 11ay. Figure (a) shows the steady exchange of power between LP 11ay and LP 11bx along the fiber when LP 11ay is launched, and Fig. (b) shows the power exchange between LP 11ax and LP 11by when LP 11ax is launched. In our simulations total power exchange was observed every 11.5 cm (for LP 11ay LP 11bx ) respectively.7 m (for LP 11ax LP 11by ). This effect of modal birefringence is studied in detail in [35]. As a consequence, even under ideal conditions, a receiver will always see a random mixture of the true waveguide modes making up the LP 11 modes, and MIMO processing is required to recover the individual information streams [7]. LP 11ay LP 11bx LP 11ay a) b) LP 11ax LP 11by LP 11ax Power distribution [db] LP 11ay LP 11bx -3 LP 11ax LP 11by L [m] L [m] Power distribution [db] -1 Fig.. Simulated power distribution between different LP 11 -modes at different propagation distances when coupled into the fiber. (a) LP 11ay and LP 11bx exchange power within 11.5 cm. (b) LP 11ax and LP 11by (b) exchange power within 5.4m..1. Coupling into few-mode fiber Mode-multiplexed systems require the ability to address individual fiber modes (or unitary combinations thereof) at the transmitter and at the receiver. Since it is often preferable to (C) 13 OSA 9 July 13 Vol. 1, No. 15 DOI:1.1364/OE OPTICS EXPRESS 181

5 excite and detect LP spatial profiles instead of the true waveguide modes directly, mode shaping needs to take place before coupling into the fiber to adapt the usually single-mode source to the amplitude and phase profile of the respective LP mode. For lower-order modes, the phase profile is the most prominent differentiator between modes. For example [4 8], use only a simple phase pattern to launch a specific mode. When only the phase profile but not the amplitude profile of the incident light is matched to the desired fiber LP mode not all the optical power will couple into this target LP mode. Some fraction of the incident power will then couple into other typically higher order LP modes. If these unwanted LP modes are not supported by the FMF the mismatch of the amplitude profile upon coupling only results in an insertion loss. However, if propagation of these unwanted LP modes is supported by the fiber as well in the context of a mode multiplexing system, the corresponding spurious power will reach the receiver and act as (non-unitary, hence capacitydegrading) crosstalk [7,]. Furthermore, lack of amplitude shaping results in higher insertion loss for each individually shaped mode. The insertion loss and crosstalk of the mode coupler is evaluated according to the arrangement shown in Fig. 3, where a fiber with a core diameter of 3-µm is assumed, that has a V-value of 8.87 and supports 11 LP modes. This is done, because modal crosstalk by phase-only mode shaping only arises when modes higher than LP 11 are supported by the FMF. Vertical polarized light from a SMF source is collimated to a Gaussian beam with waist radius W and a plane phase front. W 3-µm π Gaussian beam with plane phase front Phase profile of SLM (here: LP 11 ) Phase modulated beam LP 11 LP 31 LP 51 LP 1 LP 3 Excited LP 'modes' in FMF 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). The incident Gaussian beam can be expressed by its electrical and magnetic field E μ 1 x + y ( ey, 4 Gauss xy, ) = o exp π W W (1) H 1 x + y (, ) = exp ex, 4 Gauss xy π μo W W where the total optical beam power is normalized to 1. The phase profile of the beam is changed by the spatial light modulator. Assuming a plane phase front of the incident beam, the phase profile of the SLM is defined by the phase profile of the LP (µ,υ) mode to be shaped: ( i ( ELP( μν, ) ( x y )) f( x, y) = exp arg, ). (3) Thus, the electromagnetic field of the shaped beam is given by: E ( x, y) = E f( x, y), Gauss () (4) (C) 13 OSA 9 July 13 Vol. 1, No. 15 DOI:1.1364/OE OPTICS EXPRESS 1811

6 H ( x, y) = H f( x, y), Gauss Neglecting reflection effects at the fiber surface, the optical field in the FMF can be described as a sum of guided and radiated LP modes each weighted with a complex coupling coefficient C (µ,υ) [36] (, ) Exy C, ( µ, ν) ELP( µ. ν) (6) = µ ν H( x, y) C( µ, ν) HLP( µ. ν). = The electro-magnetic field of the LP mode is normalized as µ E LP( μν, ) xy H LP( μν, ) xydxdyez ν (, ) (, ) = 1. The coupling coefficient C (µ,υ) from an electro-magnetic field Exy (, ) and H ( xy, ) into a LP mode, defined by its electro-magnetic field E LP( μν, ) ( x, y) and H LP( μν, ) ( xy, ), can be calculated as C = Exy (, ) H ( x, y) + E ( x, y) H( x, y) dxdye, (9) ( ) ( μν, ) LP( μν, ) LP( μν, ) where * denotes complex conjugation and is the outer product. The coupling efficiency from the incident beam power to the power of an excited LP mode is finally given by ( μν, ) C( μν, ). z (5) (7) (8) η = (1) As an example, we calculate coupling efficiencies for a FMF with a core diameter of 3 µm that has a V-number of 8.87 and supports 11 different LP modes. The waist radius W of the Gaussian beam is varied from 5 to 3 µm. Figure 4(a) shows the coupling efficiencies into several LP modes supported by the fiber, if phase shaping for the LP 11 mode is used. Both the insertion loss into the desired LP 11 mode and the crosstalk into other LP modes depend on the waist radius W of the Gaussian beam. The optimal waist radius W,opt in terms of minimal insertion loss for LP 11 is 13.4 µm. Figure 4(a) also depicts the waist radius with lowest maximal crosstalk into an individual mode. However, at this waist radius LP 31 and LP 1 are excited with similar coupling efficiency, so the total power in undesired LP modes is higher compared to W,opt. This simulation is repeated for all supported LP modes of the FMF. Figure 4(b) shows insertion loss and crosstalk values better than 3 db visualized in grey scale (brightness of area is proportional to absolute coupling coefficient). For each desired LP mode the optimal waist radius W,opt in terms of insertion loss is retrieved. With phase-only spatial shaping of a Gaussian beam, coupling efficiency values between.1 db (LP 1 ) and 3. db (LP 51 ) are obtained. The highest crosstalk from a beam with LP 11 phase profile into the fiber LP 31 mode is 1 db. Note that no crosstalk between LP 1 and LP 11 is observed, thus phase-only mode shaping is sufficient for an FMF supporting only these LP modes. In a FMF supporting more LP modes phase-only shaping results in crosstalk, which degrades the system performance. When the SLM allows spatial attenuation to also match the amplitude profile of the launch signal to that of the desired LP mode the crosstalk of the mode shaper can be significantly reduced. In this case the complex spatial shaping profile is chosen as: (C) 13 OSA 9 July 13 Vol. 1, No. 15 DOI:1.1364/OE OPTICS EXPRESS 181

7 ELP(, ) ( xy, ) μν f( x, y) = exp( i arg ( ELP( μν, ) ( xy, ))) min,1. (11) EGauss ( x, y) The clipping of the amplitude profile to 1 takes into account that only spatial attenuation but no amplification is considered. This clipping is the only source of the residual crosstalk of the mode shaper. An alternative choice for the spatial shape profile is to normalize it to a maximum amplitude of 1. This would result in further reduced crosstalk but also significantly increased insertion loss, which should be avoided. We choose clipping as a good compromise Coupling efficiency [db] at W,opt W,opt a) - LP11 LP11 b) LP µm Coupling efficiency (db) optimal insertion loss minimal crosstalk LP LP LP LP LP LP LP LP Waist radius of Gaussian beam (µm) Desired mode (mode shaper) LP µm LP µm LP µm LP 31 LP µm 13.8 µm LP µm LP µm LP µm LP µm LP µm LP 1 LP 11 LP 1 LP LP 31 LP 1 LP 41 LP LP 3 LP 51 LP 3 Fiber mode Fig. 4. (a) Simulated coupling efficiency for phase-only mode shaping assuming the coupling of a target LP 11 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. Coupling efficiency [db] at W,opt W,opt a) b) LP µm - LP11 LP11 LP µm -4 LP µm -6 LP µm optimal insertion loss -8 LP µm -1 LP µm -1 LP µm LP11 LP1-14 LP µm -16 LP µm LP11 LP31-18 LP µm - LP µm Waist radius of Gaussian beam (µm) Fiber mode Coupling efficiency (db) Desired mode (mode shaper) Fig. 5. (a) Simulated coupling efficiencies for complex (phase and amplitude) mode shaping assuming the coupling of a target LP 11 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. LP 1 LP 11 LP 1 LP LP 31 LP 1 LP 41 LP LP 3 LP 51 LP 3 (C) 13 OSA 9 July 13 Vol. 1, No. 15 DOI:1.1364/OE OPTICS EXPRESS 1813

8 between insertion loss and crosstalk. Figures 5(a) and 5(b) show simulation results for coupling efficiency and crosstalk when complex (phase and amplitude) shaping is applied instead of phase-only spatial light modulation. Due to the spatial attenuation the insertion loss is increased by between.1 db and 1. db for the various modes. But the crosstalk into undesired modes is significantly reduced to a maximal value of 19 db instead of 1 db with phase-only mode shaping. Thus, the net improvement is approximately 6 db. The simulation results also show, that the optimal waist radius of the incident beam increases slightly for the lower-order LP modes and decreases for higher-order LP modes... Amplitude shaping using a modulator Spatial light modulation of phase and amplitude can be realized by combining a spatial phase modulator (eq. glass plates with different thicknesses, or a modulator) with an additional structure that provides spatial attenuation; devices that perform both functions in a single step are difficult to realize. A more practical approach is to use a phase-only modulator f 1 f 1 f f r core FMF L 1 L Pinhole SMF Fig. 6. Optical setup for complex spatial light modulation and coupling into FMF in combination with a spatial filter, consisting in its simplest form of a two-lens system with a pinhole located in between. The spatial filter converts spatial phase-modulation (PM) to spatial amplitude-modulation (AM) and thus generates complex light modulation if an adequate phase profile is used. The concept is shown in Fig. 6. The optical signal from a SMF is collimated generating a Gaussian-like beam. The optical beam is reflected on a modulator, where its optical phase profile can be adjusted by the pixels. For efficient fiber coupling the beam has to be adapted to the fiber core radius r core (see Figs. 4(a)-4(b) and 5(a)-5(b)) using a double telecentric system consisting of two lenses (L 1, L ). The optical profile at the FMF surface is scaled down by ( f 1 / f ) relative to the profile on the modulator, where f 1 and f are the focal lengths of the lenses. By placing a pinhole in the Fourier plane, which is located in the common focal plane between the lenses, a low pass filter for spatial frequency can be implemented. Regions on the modulator having a relative slow change in phase profile will generate low spatial frequency that are transferred to the field profile at the fiber facet at a corresponding position. On the other hand, region where the phase changes rapidly, will generate large spatial frequencies that are attenuated by the spatial filter and the amplitude at the corresponding position on the fiber facet is attenuated. The diameter of the pinhole is chosen so that the patterns with highest spatial frequency (i.e. checkerboard pattern) are blocked. In Fig. 6, for example, the part of the incident beam that is phase shaped with a checkerboard pattern is highly attenuated. The use of checkerboard pattern is advantageous because it generates the largest spatial frequency that the device is capable of, therefore maximizing the spatial frequency transfer for the desired phase and amplitude profile. By using a checkerboard with two independent pixel values the intensity and the phase of a reflected beam can be adjusted. While the intensity of the beam can be controlled by the difference of the pixel values, the phase shift can be set by (C) 13 OSA 9 July 13 Vol. 1, No. 15 DOI:1.1364/OE OPTICS EXPRESS 1814

9 the mean of the individual phase shifts. For complex spatial light modulation the surface can be divided into small areas, each having a checkerboard pattern with two pixel values for amplitude and phase shaping. 3. Experimental mode shaping using a modulator Experimental investigation of mode shaping was performed according to the setup presented in Fig. 6. A SMF continuous-wave laser source with 5.4 dbm power is collimated to a Gaussian beam with a waist radius W = 314 μm. After beam splitting (BS, 5/5), one part is spatially modulated by the modulator, the other part is used for coherent phase measurement in a Michelson interferometer type arrangement. The modulator (Aurora Systems ASI61, optimized for 155 nm) provides phase modulation of 18x19 pixels with 8 µm pitch. At 155 nm the phase shift is adjustable in a π range. The incident Gaussian beam illuminates around 8x8 pixels on the modulator, which is sufficient for complex spatial light modulation. The FMF has a core diameter of 16 µm and supports only LP 1 and LP 11 modes. If a FMF is used that supports more LP modes a larger beamsize and more pixel might be required. In addition the focal length of the lenses and the pinhole have to be adjusted to ensure, that the phase pattern of the highest order mode still passes the pinhole, while a checkerboard pattern with a phase shift of π still leads to attenuation Device characteristics and calibration To verify the capabilities of the complex SLM setup the optical profile is detected with an infrared sensitive InGaAs sensor array. For this purpose a different lens combination (f 1 = 75 mm, f = mm) is chosen to magnify the optical profile. The calibration setup is shown in Figs. 7(a) and 7(b) for two exemplary patterns. Our measurements revealed several imperfections of the SLM: The phase shift is not exactly linearly proportional to the pixel values written to the device. A small intensity modulation of about 1.5 db is observed in addition to the phase modulation at phase shifts around π. The phase shift of a pixel is affected not only by its own voltage but partially also by that of the neighboring pixels. Hence, to calibrate the complex light modulation of the modulator, we wrote a checkerboard pattern formed by two independent phase values to the modulator. The spatially modulated beam and the reference beam are projected on the sensor array at the a) Mirror b) Mirror L 1 Mask L L 1 Mask L Sensor array Sensor array SMF from laser source SMF from laser source Fig. 7. Optical setup for calibrating the spatial phase and amplitude modulation characteristics. With uniform 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). interferometer output. By varying both phase values of the checkerboard pattern, the observed light amplitude is changed by factor a and the phase is changed by φ. In the general (C) 13 OSA 9 July 13 Vol. 1, No. 15 DOI:1.1364/OE OPTICS EXPRESS 1815

10 case, where the phase front of both beams is not exactly parallel to the sensor array, the complex envelope of the electrical fields E ( x, y ), E (, ) Ref x y on the sensor surface can be expressed as: ( x + ϕ ) ( ) E ( xy, ) = a E ( x, y) exp j( k + yk ), (1),x,y E ( xy, ) = E ( x, y) exp j( x k + yk + ϕ ), (13) Ref Ref Ref,x Ref,y Ref where E (, ) x y corresponds to the beam profile that is reflected from the modulator and E ( x, y) to the unshaped reference beam that is reflected from the mirror. E (, ) Ref x y is the field profile of the reflected from a blank modulator (e.g. without shaping), k,x, k,y, k Ref,x, k Ref,y depend on the angle between the phase front of both beam and the sensor surface in x- and y-direction. The phase offset φ Ref of the reference beam is constant, while the phase offset of the shaped beam φ depends on the pixel values. Since the sensor array cannot detect the optical phase, it detects the intensity profiles xy = (, ) ( = I (, ) a I x y E x, y) a E ( x, y), (14) (, ) (, ), R ef Ref I xy E x y (15) if only one beam illuminates the sensor array at once (the other beam is blocked in this case). If the shaped beam is superposed with the reference beam, the intensity profile captured by the sensor consists of lines of constructive and destructive interference. The measured intensity on the sensor is shown in Fig. 7(a) and can be expressed as I( x, y ) E ( x, y) + E ( x, y) Ref * { ef ( x, )} (, ) Ref (, ) + (, ) R = E x y + E x y Re E x y E y, (16) ( y ) I( x, y) = a I ( x, y) + I ( x, y) + a I ( x, y) I ( x, y) cos xδ k + Δ k + ϕ, Ref Ref x y (17) with Δ k = k k, x,x Ref,x Δ ky = k,y kref,y and ϕ = ϕ ϕ. Ref The optical components (lenses, mirror, modulator) are adjusted so that the interference profile has only vertical lines with a periodicity of about.5 mm ( Δkx 4π mm 1, Δky mm 1 ). By applying a checkerboard pattern to the modulator, the amplitude and the position of the interference lines change according to Eq. (17). Figure 8(a) shows horizontal cross sections of the intensity patterns captured on the sensor. Intensity curves of the reference beam, the shaped beam, and the interference of both are detected. The attenuation and the phase shift of this pixel pair can be retrieved by minimizing the following function: min ( ) ( ) x a, ϕ I( x) a I ( x) IRef ( x) a I x IRef x cos( x Δ kx + ϕ ).(18) Figure 8(b) shows graphically how the weighted cosine is fitted to the intensity profile of the interference. This phase and attenuation estimation is done for all possible combinations of the two pixel values. (C) 13 OSA 9 July 13 Vol. 1, No. 15 DOI:1.1364/OE OPTICS EXPRESS 1816

11 Optical intensity (a.u.) a) b) IRef ( x) I( x) I( x) x [mm] Optical intensity (a.u.) I( x) a I ( x) I ( x) Ref ( k φ ) a I ( x) I ( x) cos x Δ + Ref x x [mm] Fig. 8. a) Optical intensity of one camera sensor row. Overlay of measured profiles of the beam reflected by the mirror and the modulator and the interference of both. b) Cosine function fitted to measured profile to estimate amplitude and phase of the spatially modulated beam. Figure 9(a) shows a contour plot of the resulting attenuation a and Fig. 9(b) shows the contour plot of the phase shift φ. The measurements reveal that the phase can be varied in a range of π and the attenuation in a range of 16 db. a) 1-16 db a db b) 1 φ -π Pixel value Pixel value -π db -16 db 1 1 Pixel value 1 Pixel value 1 Fig. 9. Normalized attenuation a (a) and phase shift φ (b) for possible pixel value pairs for the checker board phase pattern generated by the modulator. 3. Mode shaping using spatial phase modulation If phase-only mode shaping is used, only a phase jump in vertical or horizontal direction is applied to match the Gaussian input beam to the LP 11 mode shape. In this case the width of the incident beam should be approximately the width of the desired LP mode. Experimental images of the modulated profiles of the LP 1 and both degenerate LP 11 modes with vertical polarization before fiber launching are shown in Fig. 1. The upper row of images gives the intensity patterns and the lower row gives the phase patterns, as obtained through interference with the reference beam in the Michelson setup of Figs. 7(a) and 7(b). The phase shift of π between both halves of the LP 11 mode is clearly visible. (C) 13 OSA 9 July 13 Vol. 1, No. 15 DOI:1.1364/OE OPTICS EXPRESS 1817

12 LP 1 LP 11a LP 11b LCos pattern π π Mod. beam + ref. Modulated beam Fig. 1. Measured intensity profiles after mode shaping for LP 1 and LP 11 with both vertical and horizontal orientations of the phase jump, without (upper row) and with (lower row) Michelson interference with a reference beam Mode shaping using spatial phase and amplitude modulation For the demonstration of the complex SLM structure, the incident beam widened much more. The corresponding intensity image without modulation is depicted in Fig. 11(a). The complex modulation profile is given by Eq. (11). This required modulation profile is divided into small regions equivalent to x pixels on the modulator. For each region a checkerboard with x pixels (the smallest possible checkerboard size) with the required pair of pixel values is calculated. Figure 11(b) shows the pattern that is written to the modulator. In regions with high attenuation, neighboring pixels have a phase difference of approximately π, while neighboring pixels have similar values in regions with less attenuation. In the right half of the shaped area the mean phase shift is π/ and in the left half it is 3π/. Since the incident beam is much wider than the LP 11 mode to be shaped, significant power is lost within the areas of high attenuation. Figure 11(c) shows the intensity profile after complex SLM that fits more precisely to the desired LP 11a mode. The interference of the shaped beam with the reference beam is depicted in Fig. 11(d) and visualizes the phase jump of π between both LP 11a parts. a) b) c) d) Fig. 11. Captured image of beam profile before modulation (a), phase shift pattern written to the modulator (b), intensity profile after LP 11a modulation without (c) and with interference (d). Figures 1(a) and 1(b) show the horizontal and vertical cross-sections of the measured intensity profiles with phase-only (PM) and additional amplitude modulation (AM + PM) together with the simulated curve. The intensity and the diameter are normalized in each case. (C) 13 OSA 9 July 13 Vol. 1, No. 15 DOI:1.1364/OE OPTICS EXPRESS 1818

13 While both profiles fit quite good to the theoretical profile in horizontal direction, the optical profile using PM is significantly larger in vertical direction than the measured profile of AM + PM and theory. Thus, higher crosstalk into other modes can be expected with the measured PM profile compared to the AM + PM profile. a) 1 b) AM+PM Theory.8 Normalized intensity.6.4. PM xr / core Normalized intensity PM AM+PM Theory yr / core Fig. 1. Horizontal (a) and vertical (b) cross-section of the measured LP 11 intensity profiles with phase-only modulation, complex modulation and the theoretical curve. 3.4 Fiber Coupling Results For launching the LP 11 mode into the fiber, the setup according to Fig. 13 is used. The optical beam is vertically polarized at the transmitter side. The incident beam power onto the modulator is. dbm and the optical power before fiber launching is 4.7 dbm. After spatial light modulation the beam is demagnified with two lenses with focal length of mm and 9.5 mm to fit the FMF dimension. All optical components and the fiber are carefully aligned in three dimensions and two tilt angles. Slight misalignments result in crosstalk into other than desired modes. The FMF with a length of 5 cm is fixed straight and without significant stress. After propagation the outcoming beam is enlarged again with a 9.5-mm lens and a 3-mm lens and detected with the infrared sensitive sensor. The reference beam bypasses the fiber and is interfered with the shaped beam after the fiber with a second BS in a Mach-Zehnder structure. Power measurement is also used at one side of this BS (reference beam blocked in this case). A second polarization filter allows signal detection in vertical and horizontal polarizations, respectively. Figures 14(a)-14(f) show the measured profiles of LP 1, LP 11a, and LP 11b together with the measured optical power values in both polarizations. A difference of the insertion loss of 3 db between LP 1 and LP 11 modes can be seen. Possible reasons are that the incident beam diameter fits more to LP 1 than to LP 11 and that the required phase jump for LP 1 leads to additional attenuation in the non-perfectly aligned optical setup. By looking at Mirror Unmodulated reference beam Mirror Pol. filter BS FMF (5 cm) Pol. filter BS Sensor array SMF from laser source Optical power meter Fig. 13. Setup for a FMF coupling experiment of LP 1, LP 11a, and LP 11b. the different polarizations after the fiber separately, the impact of the mode coupling as explained in section is evident. Since only vertical polarized light is launched, the optical profiles with horizontal polarization filter after the fiber corresponds to cross coupling within (C) 13 OSA 9 July 13 Vol. 1, No. 15 DOI:1.1364/OE OPTICS EXPRESS 1819

14 the fiber. Noteworthy is that even for such a short fiber (5 cm), some coupling between LP 11ay and LP 11bx is observed. The coupling between LP 11by and LP 11ax is however much smaller. Qualitatively, this observation is in agreement with the simulated coupling values in Figs. (a) and (b) because the length of power exchange of LP 11ay and LP 11bx is in the range of centimeters, while for LP 11by and LP 11ax are expected to exchange power in the range of meters, which is significantly longer than the used fiber length of 5 cm. The detection of small portions of LP 11bx in the case of LP 1 and LP 11b mode shaping could be explained with nonperfect alignment of the components (small amount of LP 11ay is launched as well) and limited selectivity of the polarization filters (LP 11by is detected as LP 11bx ). Vertical polarization LP shaped LP shaped LP shaped 1 11a 11b LP detected LP detected LP detected 1y 11ay 11by a) b) c) P = -14. dbm P = -17. dbm P = dbm 4. Conclusion Horizontal polarization d) LP detected LP detected LP + LP detected 11bx 11bx 11ax 11bx e) P = dbm P = -3. dbm P = dbm Fig. 14. Measured intensity profile of shaped LP 1 (a + d), LP 11a (b + e) and LP 11b (c + f) after 5 cm of FMF with vertical (a-c) and horizontal (d-f) polarization filter at the receiver. We analyzed the crosstalk properties of mode multiplexers based on spatial light modulators, and numerically showed that the crosstalk into higher order modes can significantly be reduced by using amplitude shaping in addition to the already discussed phase-only shaping of the optical profile. Complex spatial light modulation comes at the price of slightly increased insertion loss and system complexity but improves the performance of mode multiplexing systems supporting a large number of modes. A practical realization for a complex spatial-light modulator is proposed and experimentally demonstrated. The proposed device uses a phase-only spatial light modulator, and a simple spatial filter. The device is adaptive which is advantageous in early stage of research where the flexibility to support multiple different fiber types is required. For practical application in optical communication, the use of fixed phase plates instead of the modulator might be preferable in terms of loss, physical size and costs, at the expense of adaptability Finally, we theoretically analyzed and experimentally demonstrated the presence of coupling between the LP 11 modes of a fewmode fiber even for a very short 5 cm long fiber. The capability to precisely excite fiber modes could be of interest in other fields like optical sensing or image transfer over multimode fibers. f) (C) 13 OSA 9 July 13 Vol. 1, No. 15 DOI:1.1364/OE OPTICS EXPRESS 1811