摘要
在光纤传输系统中,由于多种高速率应用的发展,具有更高容量的传输系统成为当今一个不断发展的研究方向。它不仅改变传统的00K调制,使之向更高阶的调制模式发展,而且采用波分复用的复用传输模式取代传统的单信道传输。但面临的问题是高速传输中不断增长的需求会令单模光纤容量很快达到饱和。模式复用被认为是解决容量问题的方案,同时也是未来光纤传输系统中一项重要的技术。
本论文对阶跃少模光纤模式复用的关键问题进行了理论和数值的研究,在此基础上分析了模式复用的理论论证,并讨论了这种新型传输系统中的一些重要器件。本文的核心要点是研究了模式耦合中的重要传输参数,模式群时延色散和模式相关损耗。通过推理讨论我们得到以上所提及参数与光纤物理参量之间的关系。本文还在数值上分析了每个参数,最后将未来系统中适用的少模光纤的最佳发展条件进行了分类。
除了根据光纤物理参量研究传输参数,作者还对群时延和模式相关损耗进行了统计性研究,这在长距离模式复用系统中起到了重要的作用。本文主要探讨了长距离模式复用系统中群时延和模式相关损耗的变量和概率分布函数。在给定场景中,本文的研究成果对接收端的最佳信号处理和计算信道容量起到关键的作用。
In optical fiber transmission systems, it is a continuous pursuit to develop higher capacity transmission systems due to development of many high speed applications. This pursuit transformed the conventional modulation formats of on-off keying to higher order modulations and single channel to multiplexed transmission in form of wavelength division multiplexing. However it is envisaged that increasing demand of high speed transmission will soon saturate the capacity of single mode optical fibers. Mode division multiplexing is assumed to be the solution of capacity problem and future of optical fiber transmission systems.
In our dissertation, we performed a theoretical and numerical study of key issues in mode division multiplexing for step index few mode fibers. We proceeded on this study by exploring theoretical reasoning of mode division multiplexing followed by discussions on important devices in this new transmission system. The core of this dissertation is the study of important transmission parameters of mode coupling, modal group delay dispersion and mode dependent losses. We laid the theoretical discussion to know about the relationship of above mentioned parameters to physical parameters of optical fiber. Numerical analysis for each parameter has been performed to sort optimum conditions for development of suitable few mode fibers for future systems.
In addition to the study of transmission parameters as a function of physical parameters of optical fibers, statistical study of group delays and mode dependent losses has also been made. Statistics of these parameters play important role in long haul mode multiplexed systems. Study of variance and probability distribution functions of group delays and mode dependent losses have been made for long haul systems. These studies are important in implementing optimum signal processing at receiver and computing channel capacities in a given scenario
引文
[1]C. P. Tsekrekos, "Mode group diversity multiplexing in multimode fiber transmission systems", dissertation at Eindhoven University of Technology, Netherlands.
[2]Reinhold Noe, "Essentials of Modern Optical Fiber Communication" Chapter 1; Berlin, Springer,2010.
[3]T. Koonen, "Fiber to the Home/Fiber to the Premises:What, Where, and When?" Proc. IEEE, vol.94, May 2006.
[4]Abid Munir, Xin Xiangjun, Liu Bo, Ashiq Hussain, Abdul Latif and Aftab Hussain, "Coherent Optical Systems:Principles, Contemporary Implementations" Recent Patents on Engineering,2011.
[5]L.G Roberts, Beyond Moore's law:Internet growth trends, USA:computer 33,1(2000).
[6]Dirk van den Borne, Vincent A. J. M. Sleiffer, Mohammad S. Alfiad, Sander L. Jansen and Torsten Wuth(1) "POLMUX-QPSK modulation and coherent detection:the challenge of long-haul 100G transmission", ECOC 2009,20-24 September,2009, Vienna, Austria.
[7]Matthias Seimetz, "High-Order Modulation for Optical Fiber Transmission" Springer-Verlag Berlin Heidelberg,2009.
[8]P. P. Mitra and J. B. Stark, "Nonlinear limits to the information capacity of optical fibre communications", Nature 411,2001.
[9]JM. Kahn, H. Keang-Po, "Spectral efficiency limits and modulation-detection techniques for DWDM systems", IEEE Jour. Quantum Elec.10, 2(2004).
[10]R. Olshansky, "Mode coupling effects in graded-index optical fibers" Appl. Opt., vol.14, no.4, pp.935-945, Apr.1975.
[11]Ivan B. Djordjevic, Murat Arabaci, Lei Xu, and Ting Wang, "Spatial-domain-based multidimensional modulation for multi-Tb/s serial optical transmission",2011 Optical Society of America.
[12]A. Li, A. Amin, Xi Chen, W. Shieh, "Transmission of 107-Gb/s mode and polarization multiplexed CO-OFDM signal over a two-mode fiber", Opt. Express.19,9(2011).
[13]S. Randel, R.Ryf,A. Sierra, P.J. Winzer, A.H. Gnauck, C. A. Bolle, R.J Essiambre, D.W. Peckham, A. Mcurdy and R. Lingle, "6×56-Gb/s mode-division multiplexed transmission over 33-km few-mode fiber enabled by 6x6 MIMO equalization", Optics Express, Vol.19, Issue 17, pp.16697-16707(2011).
[14]R. Ryf, S. Randel, A.H.Gnauck, C. Bolle, R.J.Essiambre, P.J.Winzer, "Space division multiplexing over 10 Km of three mode fiber using coherent 6x6 MIMO processing", in proceedings of optical fiber conference (Los Angeles, USA,2011).
[15]Joseph M. Kahn, Keang-Po Ho and Mahdieh Bagher Shemirani, "Mode Coupling Effects in Multi-Mode Fibers", Optical Fiber Communication Conference (OFC) 2012.
[16]S. V. Kartalopoulos, "Understanding SONET/SDH and ATM",IEEE Press, Piscataway, NJ,1999.
[17]Govind P. Agrawal, "light wave technology telecommunication systems" Wiley-Interscience, Canada,2005.
[18]Bharat Doshi "Towards Optical Core:Demand And Technology Driven Future WAN Architecture", WCC-ICCT 2000, Communication Technology Proceedings,2000.
[19]Ivan P. Kaminow, Tingye Li, Alan E. Willner, "Optical Fiber Telecommunications V B:Systems and Networks", Elsevier,2008.
[20]K. Schuh, B. Junginger, H. Rempp et al., "85.4 Gbit/s ETDM Transmission over 401km SSMF applying UFEC", in Proc. ECOC 2005, Post-deadline paper Th4.1.4,2004.
[21]K. Schuh, E. Lach, and B. Junginger, "100Gbit/s ETDM Transmission System Based on Electronic Multiplexing Transmitter and De-multiplexing Receiver," in Proc. ECOC 2006, PaperWeS.P.124,2006.
[22]M. Daikoku, I. Morita, H. Taga et al., "100 Gbit/s DQPSK Transmission Experiment without OTDM for 100G Ethernet Transport," in Proc. OFC 2006, Post-deadline paper PDP36,2006.
[23]S.J.Savory, "Digital coherent optical receivers:Algorithms and subsystems", J. of Lightwave Tech.16,5(2010).
[24]Savory S.J, "Digital filters for coherent optical receivers". Opt Express 2008; 16(2):804-817.
[25]A. D. Ellis, D. M. Patrick, D. Flannery, R. J. Manning, D. A. O. Davies, and D. M. Spirit, "Ultra-high speed OTDM networks using semiconductor amplifier-based processing nodes", J. Light wave Technol., vol.13,1995.
[26]T. Ohara, H. Takara, I. Shake, K. Mori, K. Sato, S. Kawanishi, S. Mino, T. Yamada, M. Ishii, I. Ogawa, T. Kitoh, K. Magari, M. Okamoto, R. V. Roussev, J. R. Kurz, K. R. Parameswaran, and M. M. Fejer, "160-Gb/s OTDM Transmission Using Integrated All-Optical MUX/DEMUX With All Channel Modulation and De-multiplexing" IEEE Photon. Technol. Lett. 16,650(2004).
[27]M.Saruwatari, "All-optical signal processing for terabit/second optical transmission", IEEE J. Sel. Topics Quantum Electron., vol.6,2000.
[28]E. Bgdtker and John E. Bowers, "Techniques for Optical Demultiplexing in High Bit Rate Communication Systems" J. Lightwave Technol.13,1809 (1995).
[29]B. Mikkelsen, G. Raybon, R.-J. Essiambre, J. E. Johnson, K. Dreyer, and L F. Nelson, "Un repeatered transmission of 150Km over non zero Dispersion shifted fiber at 100Gbits/s with semiconductor based pulse source, De-multiplexer and clock recovery", Electron. Lett.35,1866 (1999).
[30]Y. Su, L. Moller, C. Xie et al., "Ultra high-speed data signals with alternating and pair wise alternating optical phases," J. Lightw. Technol., 23(1),2005.
[31]A. H. Gnauck, G. Raybon, P. G. Bernasconi et al., "(1 Tb/s 6170.6 Gb/s) transmission over 2000 km NZDF using OTDM and RZ-DPSK", IEEE Photon. Technol. Lett.,15(11),2003.
[32]S. Weisser, S. Ferber, L. Raddatz et al., "Single- and alternating polarization 170 Gbit/s transmission up to 4000 km using dispersion-managed fiber and all-Raman amplification", Photon. Technol. Lett.,18(6), 2006.
[33]G. P. Agarwal, Fiber Optic Communication Systems:3rd edition, (John willey & Sons, New york,2002.
[34]Jean-Pierre Laude, "DWDM Fundamentals, Components and Applications", Artech House, Norwood,2002.
[35]N. A. Olsson, J. Hegarty, R. A. Logan, L. F. Johnson, K. L. Walker, L. G. Cohen, B. L. Kasper, and J. C. Campbell, Electron, "68.3 km transmission with 1.37 Tbit km/s capacity using wavelength division multiplexing of ten single-frequency lasers at 1.5 um",. Lett.21,105,1985.
[36]A. Ghatak, K. Thayagarajan, "Introduction to Optical fiber", Cambridge university press,1997.
[37]J-P Goure and I Verrier, "Optical Fibre Devices",lOP Publishing,2002
[38]A. R. Chraplyvy, "Limitations on lightwave systems due to optical nonlinearities", J. Lightwave Technol.8,1548,1990.
[39]M. Wu and W. I. Way, "Fiber nonlinearity limitations in ultra-dense WDM systems," J. Lightwave Technol.22,1483 (2004).
[40]D. N. Christodoulides and R. B. Jander, "Evolution of stimulated Raman crosstalk in wavelength division multiplexed systems", Photon. Technol. Lett.8,1722 (1996).
[41]X. Zhang, B. F. Jorgensen, F. Ebskamp, and R. J. Pedersen, "Input power limits and maximum capacity in long-haul WDM lightwave systems due to stimulated Raman scattering",Opt. Commun.107,358(1994).
[42]G. P. Agrawal, Nonlinear Fiber Optics,3rd ed., Academic Press, San Diego, CA,2001.
[43]F. Forghieri, R. W. Tkach, and A. R. Chraplyvy, in Optical Fiber Telecommunications Vol.3A, I. P. Kaminow and T. L. Koch, Eds., Academic Press, San Diego, CA,1997.
[44]T.-K. Chiang, N. Kagi, M. E. Marhic, and L. G. Kazovsky, "Cross-phase modulation in fiber links with multiple optical amplifiers and dispersion compensators", J. Lightwave Technol., vol.14,1996.
[45]G. Goeger. M. Wrage and W. Fischler, "Cross-phase modulation in multispan WDM systems with arbitrary modulation formats", IEEE Photon. Technol. Lett.16,1858 (2004).
[46]Ciaramella E. "Nonlinear impairments in extremely dense WDM systems" IEEE Photon.Technol. Lett.,14,14,804-806,2002.
[47]G. L. Woods, P. Papaparaskeva, M. Shtaif, Member, I. Brener, and D. A. Pitt, "Reduction of cross-phase modulation-induced impairments in long-haul WDM telecommunication systems via spectral inversion" IEEE Photon. Technol. Lett.16,677 (2004).
[48]Damask JN, "Polarization optics in telecommunications", Springer:USA 2005.
[49]Ted Schmidt, Christian Malouin, Samuel Liu, "100G Module and Subsystems for Long Haul DWDM Applications" LEOS Annual Meeting Conference Proceedings,2009.
[50]D.Marcuse, "Theory of dielectric optical waveguides", Academic press, New York,1974.
[51]H.G. Unger, "Planar Optical Waveguides and fibers", Clarendon, Oxford, 1977.
[52]E.Snitzer, "Cylindrical Dielectric waveguides modes", J. Opt. Soc. Amer., 51,1979.
[53]Gerd Keiser, "Optical Fiber Communications", Mcgraw-Hill,1991.
[54]J. A. Buck, "Fundamentals of optical fibers:second edition", John Willey & Sons, New Jersy,2004.
[55]D. Gloge, "weakly guiding fibers", Appl. Opt.10,1(1971).
[56]A. Yariv, P. Yeh, "Photonics:Optical electronics in modern communications", Oxford 2007.
[57]Marcuse,"Light Transmission Optics",. (JTan Nostrand, New York,1972).
[58]H. E. Rowe, "Electromagnetic propagation in multimode random media" Wiley-Interscience,1999.
[59]C. Chen, "Foundations for guided-wave optics", John Willey & Sons, New Jersy,2007.
[60]M.Salsil, C.Koebelel, D.Spertil, P.Tran, P.Brindel, H.Mardoyan, S.Bigo, A.Boutin, F.Verluise, P.Sillard, M.Astruc, L.Provost, F. Cerou, G. Charlet, 'Transmission of 2×100Gb/s PDM QPSK over two modes over 20km of prototype few-mode fiber, using LCOS-based mode mux/demux" in proceedings of optical fiber conference (Los Angeles,USA,2011).
[61]Raman Kashyap:"Fiber Bragg Gratings,2nd edition", Academic Press Elsevier.
[62]M. Sumetsky and S. Ramachandran:"Conversion and focusing of optical fiber modes with superimposed long period gratings", OFC/NOFC 2008.
[63]Kyung Shik Lee:"Fiber mode conversion with tilted gratings in an optical fiber" J. Opt. Soc. Am. A/Vol.18, No.5/May 2001.
[64]Kikuchi K, Kaminow IP, Li T, Willner AE. "Optical fiber telecommunications", Elsevier:USA 2008:vol. B.
[65]S. Berdague and P. Facq. "Mode division multiplexing in optical fibers", Applied Optics,1982,21(11).
[66]R. Ryf, C. Bolle, J. von Hoyningen-Huene, "Optical Coupling Components for Spatial Multiplexing in Multi-Mode Fibers", ECOC Technical Digest 2011 OSA.
[67]Hamed Dalir, Yasushi Yokota, and Fumio Koyama, "Spatial Mode Multiplexer/Demultiplexer Basedon Tapered Hollow Waveguide", The 16th Opto-Electronics And Communications Conference, OECC 2011.
[68]C.P. Tsekrekos, A.M.J. Koonen, H.P.A. van den Boom, "Selective Excitation of Graded-Index Multimode Fibres Resulting in Annular Near Field Patterns", Proceedings Symposium IEEE/LEOS Benelux Chapter, 2004.
[69]H. S. Chen, H. P. A. van den Boom and A. M. J. Koonen, "30Gbit/s 3×3 Optical Mode Group Division Multiplexing System with Mode-Selective Spatial Filtering", OSA/OFC/NFOEC 2011.
[70]W. Rosenkranz, S.Schollmann, "Optical MIMO processing and mode multiplexing:Experimental achievements and future prospective" OECC 2010.
[71]Chin-ping Yu, Jia-hong Liou, Yi-jen Chiu, and Hidenori Taga,"Mode multiplexer for multimode transmission in multimode fibers", Vol.19, No. 13 OPTICS EXPRESS,2011.
[72]Fumiya Saitoh, Kunimasa Saitoh, and Masanori Koshiba, "A design method of a fiber-based mode multi/demultiplexer for mode-division multiplexing", Vol.18, No.5, OPTICS EXPRESS,2010
[73]Joel Carpenter, Timothy D. Wilkinson, "Holographic Mode-Group Division Multiplexing", OSA/OFC/NFOEC 2011.
[74]Kazuyuki Morita, Atsushi Okamoto and Junya Tanaka, "Volume Holographic Demultiplexer for Spatial Mode Division Multiplexing in Optical Fiber Communication", ACP 2009.
[75]S. Ramachandran, "Dispersion-Tailored Few-Mode Fibers:A Versatile Platform for In-Fiber Photonic Devices", J. Lightwave Technol.23, (2005).
[76]K. Hill, B. Malo, K. Vineberg, F. Bilodeau, D. Johnson, and I. Skinner, "Efficient mode conversion in telecommunication fibre using externally written gratings" Electron. Lett.26 (16), (1990).
[77]Andermahr and C. Fallnich:"Optically induced long-period fiber gratings for guided mode conversion in few-mode fibers" 2010 Optical Society of America.
[78]H. Kubota, H. Takara, T. Nakagawa, M. Matsui, T. Morioka, "Intermodal group velocity dispersion of few mode fiber", Electr. express,17,20 (2010).
[79]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", Journal of Lightwave Technology,2009, 27(10).
[80]D. Marcuse. "Theory of dielectric optical waveguides", Boston, Academic Press,1991.
[81]D. Marcuse. "Coupled mode theory of round optical fibers", The Bell system technical journal,25(6),1973.
[82]D.Gloge. "Optical power flow in multimode fibers", The Bell system technical journal,51(8),1971.
[83]S. Fan and J. M. Kahn, "Principal modes in multimode waveguides,"Opt. Lett., vol.30, no.2, pp.135-137, Jan.2005.
[84]A. B. Carlson, P. B. Crilly, and J. C. Rutledge, "Communication Systems, 4th ed", New York:McGraw-Hill,2002.
[85]"Carrier Sense Multiple Access With Collision Detection (CSMA/CD) Access Method and Physical Layer Specifications", IEEE 802.3 Standard, 2008.
[86]"Carrier Sense Multiple Access With Collision Detection (CSMA/CD) Access Method and Physical Layer Specifications Amendment 2:Physical Layer and Management Parameters for 10 Gb/s Operation, Type 10 GBASE-LRM", IEEE Standard 802.3aq,2006.
[87]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. Opt. Fiber Commun.,2011.
[88]N. J. Kapanyand, J. J. Burke, "Optical Waveguides", Academic press, New York,1972.
[89]H. Kogelnik and T. Li, "Laser beams and resonators", Appl.Opt.5,1(1966).
[90]B.E.A. Saleh, M. C. Teich, "Fundamentals of photonics" John willey & Sons, Newyork,1991.
[91]D.R. Anderson, "Troubleshooting optical-fiber networks:understanding and using your optical time domain reflectrometer:second edition" Elsevier Academic press, San Diego,2004.
[92]D. Gloge, "Propagation Effects in Optical Fibers", IEEE Trans, on microwave theory and techniques,23,1(1975).
[93]Keang-Po Ho, and Joseph M. Kahn, "Statistics of Group Delays in Multimode Fiber WithStrong Mode Coupling", journal of lightwave technology, vol.29, no.21, november 1,2011.
[94]S. S.-H. Yam, F.-T. An, M. E. Marhic, and L. G. Kazovsky, "Polarization sensitivity of 40 Gb/s transmission over short-reach 62.5 m multimode fiber," presented at the Opt. Fiber Commun., Los Angeles, CA,2011, Paper FA-5
[95]C. D. Poole and R. E. Wagner, "Phenomenological approach to polarization dispersion in long single-mode fibers," Electron. Lett., vol.22, pp.1029-1030,1986.
[96]C. D. Poole and J. A. Nagel, "Polarization effects in lightwave systems," in Optical Fiber Telecommunications IIIA, I. P. Kaminow and T. L. Koch, Eds. San Diego, CA:Academic,1997, pp.114-161.
[97]J. P. Gordon and H. Kogelnik, "PMD fundamentals:Polarization mode dispersion in optical fibers," Proc. Natl. Acad. Sci., vol.97,9,2000.
[98]G. H. Golub and C. F. Van Loan, "Matrix Computations,3rd ed",. Baltimore, MD:The Johns Hopkins Univ. Press,1996.
[99]M. L. Mehta, "Random Matrices",3rd ed. San Diego, CA:Academic, 2004.
[100]T. Tao and V. H. Vu, "From the Littlewood-Offord problem to the circular law:Universality of the spectral distribution of random matrices", Bull. Amer. Math. Soc., vol.46,3,2009.
[101]L. Erdos, J. Ramirez, B. Schlein, T. Tao, V. H. Vu, and H.-T. Yau,"Bulk universality for Wigner hermitian matrices with sub exponential decay" Math. Res. Lett., vol.17, no.4,2010.
[102]D. Voiculescu, K. Dykema, and A. Nica, "Free Random Variables, CRM Monograph Series",. Providence, RI:AmericanMathematical Society, 1992, vol.1.
[103]J.M Kahn, K.P Ho and M.B Shemirani, "mode coupling effects in multimode fibers", OFC 2012.
[104]D. V Borne, T. Duthel, C. R. S. Fludger, E. D. Schmidt, T. Wuth, C. Schulien, E. Gottwald, G. D. Khoe and H. de Waardt, "Electrical PMD Compensation in 43-Gb/s POLMUX-NRZ-DQPSK enabled by Coherent Detection and Equalization" ECOC,2007.
[105]Diego E. Crivelli, Hugo S. Carrer and Mario R. Hueda, "Adaptive Digital Equalization in the Presence of Chromatic Dispersion, PMD, and Phase Noise in Coherent Fiber Optic Systems", Globecom 2004.
[106]S. Hellerbrand and N. Hanik, "Techniques for Electronic Mitigation of Transmission Impairments in Fiber-Optic Communication Systems" ICTON 2008.
[107]K.P. Ho and J.M. Kahn, "Mode-dependent loss and gain:statistics and effect on mode-division multiplexing" OPTICS EXPRESS, Vol.19, No. 17,2011.
[108]B.C.Bagley, C.R. Kurkjian, J.W. Mitchell, G.E. Peterson and A.R. Tynes, "Materials, properties and choices" in "Optical fiber telecommunications" Academic, New York,1979.
[109]S.E Miller and I.P Kaminow, "Optical fiber Telecommunications-Ⅱ" Academic, New York,1988.
[110]R.Olshansky, "propagation in glass optical waveguides" Rev. Mod. Physics, Vol 51,1979.
[111]V.Miya, Y.Terunuma, T.Hosaka and T.Miyashita,'Ultra low loss single mode fibers at 1.55 μm", electronics letters, Vol.51,1979.
[112]S.R.Nagel, J.B.MacChesney and K.L.Walker,'An overviewof the MCVD process and performance", IEEE J.Quantum Electronics, vol.QE-18,1982.
[113]G. A. Thomas, B. L. Shraiman, P. F. Glodis, and M. J. Stephan,"Toward the clarity limit in optical fibre", Nature 404,262 (2000).
[114]P. K. Tien, "Light waves in thin films and integrated optics," Appl. Opt., Vol.10,pp.2395-2413,1971.
[115]D. Marcuse, "Mode conversion caused by surface imperfections of a dielectric slab waveguide" B. S. T. J., Vol.48, pp.3187-3215, (1969)
[116]M. Born and E. Wolf, "Principles of Optics,7th ed.", Cambridge University Press, New York,1999.
[117]D. K. Myanbaev,L. L. Schiener, "Fiber-Optic Communications Technology", Prentice Hall,2001.
[118]E. G. Neumann and H. D. Rudolphl "Radiation from bends in dielectric rod transmission lines," IEEE transactions on mircrow'ave theory and techniques january 1975.
[119]D. Gloge, "Mode fields and loss in curved optical fibers," unpublished work
[120]A. W. Snvderand D.J. Mitchell. "Leaky rays cause failure of geometrical optics on optical fibers" Electronics Letters, Vol.9,1973.
[121]A. M. Tulino and S. Verdu, "Random Matrix Theory and Wireless Communications", (Nov,2004).
[122]D. Tse and P. Viswanath, "Fundamentals of Wireless Communication", Cambridge Univ. Press,2005.
[123]M. A. Berger, "Central limit theorem for products of random matrices," Trans. Am. Math. Soc.285(2),777-803,1984.
[124]A. Mecozzi and M. Shtaif, "The statistics of polarization-dependent loss in optical communication systems," IEEE Photon. Technol. Lett.14(3),313-315(2002).
[125]A. Glatarossa and L. Palmieri, "The exact statistics of polarization-dependent loss in fiber-optic links," IEEE Photon. Technol. Lett.15(1),57-59 (2003).
[126]D. Voiculescu, K. Dykema, and A. Nica, "Free Random Variables", CRM Monograph Series, vol.1, (American Mathematical Society,1992.
[127]A. Nica and R. Speicher, "Lectures on the Combinatorics of Free Probability", London Mathematical Society Lecture Note Series, vol.335, Cambridge Univ. Press,2006.
[128]K.-P. Ho, "Central limits for the products of free random variables,' http://arxiv.org/abs/1101.5220.
[129]A. Amin, A. Li, X. Chen and W.Shieh, "spatial mode division multiplexing for overcoming capacity barrier of optical fiber", Optoelectronics and communication conference (OECC),2011.
[130]Y. Awaji, N. Wada, Y. Toda,"demonstration of spatial mode division multiplexing using laguerre-gaussian beam in telecom wavelength", IEEE Photonics Society,2010.
[131]W. Rosenkranz, S. Schollmann, "Optical MIMO-Processing and Mode-Multiplexing:Experimental Achievements and Future Perspectives",15th Optoelectronics and communication conference (OECC),2010.
[132]M. Silva-Lopez, W. Gaberl, W. Rosenkranz, H. Zimmermann, "Segmented Photo-Detection for a MIMO Multi-Mode Fiber Transmission System", J. Opt. Commun.31 (2010).
[133]G. Nykolak, S. A. Kramer, J. R. Simpson, D. J. DiGiovanni, C. R. Giles, H. M. Presby:"An Erbium-Doped Multimode Fiber Amplifier", IEEE Trans. Phot. Technol. Lett. (1991), Vol.3, No.12.
[134]C. D. Stacey, J. M. Jenkins:"Demonstration of fundamental mode propagation in highly multimode fibre for high power EDFAs", Conference on Lasers and Electro-Optics Europe (CLEO 2005), Munich, Germany, June 17, p.558.
[1]A. Selvarajan, Subrat Kar, T. Srinivas, "Optical Fiber Communication: Principles and Systems", Tata-McgrawHill 2006.
[2]G.Keiser "Optical Fiber Communications", McGraw-Hill Education (India) Pvt Ltd, Oct 7,2008.
[3]A. J. Rogers, "Understanding Optical Fiber Communications", Artech House 2001.
[4]Masataka Nakazawa, "High Spectral Density Optical Communication Technologies" Springer 2010.
[5]Tolga M. Duman, Ali Ghrayeb, "Coding for MIMO Communication Systems", Wiley,2007.
[6]Gregory J. Gbur, "Mathematical Methods for Optical Physics and Engineering", Cambridge university press.
[7]J. K. Shaw "Mathematical Principles of Optical Fiber Communications", SIAM.
[8]B. Vucetic and J. Yuan, "Space-Time Coding", Wiley,2003.
[9]Antonia M. Tulino, Sergio Verdu, "Random Matrix Theory And Wireless Communications", NowPublishers,2004.
[10]Percy Deift, Dimitri Gioev "Random Matrix Theory:Invariant Ensembles and Universality", AMS 2009.
[11]Pavel Bleher, Alexander R, "Random Matrix Models and Their Applications", Cambridge university press.
[12]Dan V. Voiculescu, "Free Probability Theory", AMS,1995.
[13]S. R. S. Varadhan,"Probability Theory", AMS,2001.
