mellah, hakim (2018) Design of LP01 to LPlm Mode Converters for Mode Division Multiplexing. PhD thesis, Concordia University.
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Abstract
Mode division multiplexing (MDM) over few mode fiber (FMF) has been proposed as an alternative solution to tackle the capacity limitations of optical networks based on standard single mode fiber (SMF). These limitations are caused by the fiber nonlinear effects. MDM is realized through excitation of different fiber spatial modes, each mode being an independent transmission channel. Therefore, MDM over FMF requires mode conversion (basically from fundamental mode to higher order modes and vice versa) as well as mode multiplexing and demultiplexing.
Mode conversion, multiplexing and demultiplexing can be realized through different techniques. It can be achieved using free-space optics based on matching the profile of an input mode to the profile of an output mode using phase mask or spatial light modulator. Mode conversion and (de)multiplexing can also be achieved using waveguide structures. These mode converters and (de)multiplexers are mainly based on optical fiber and planar waveguide, which include fiber grating, tapering, lanterns, planar lightwave circuit (PLC), photonic crystal fiber (PCF), mode selective coupler (MSC) and Y-junction. It is worth mentioning that more than one technique may be applied to realize a specific converter/ (de)multiplexer for a specific mode.
In general, Mode converters and (de)multiplexers based on free space optics are polarization insensitive and wavelength independent, but they result in high insertion loss and are bulky. On the other hand, all-waveguide mode converters and (de)multiplexers have high mode conversion efficiency (less insertion loss and high extinction ratio) and are compact, but they are wavelength dependent.
Recently, many research works demonstrate the design, analysis and fabrication of several types of mode converters and (de)multiplexers. However, almost all the proposed devices are specific to a certain number of modes, therefore, they result in mode-specific designs.
The explosive growth of traffic over telecommunication networks, especially in the access networks mandates that more and more modes would be (de)multiplexed to respond to the high traffic demands. As a result, proposing a universal mode converter and (de)multiplexer, that can convert and (de)multiplex any required number of modes is needed.
In this thesis, mode converters and (de)multiplexers are thoroughly investigated. A universal LP01 to LPlm mode converter and (de)multiplexer is proposed. The mode converter is based on tapered circular waveguides and the (de)multiplexer is based on symmetric directional couplers.
An LP01 to LP02 is first introduced. It consists of a tapered circular waveguide followed by a non-tapered circular waveguide. Inside the second waveguide, a circular tapered element is inserted. The initial tapered waveguide allows excitation of LP02 mode as well as other LP0m modes (m > 2). The second waveguide (comprising the circular section and the inner tapered element) is used to make conversion to be mainly from LP01 to LP02. Simulation shows that conversion efficiency of almost 100% at the central wavelength of O- S- and C-band, and above 98% over the S- and C-band is achieved. Moreover, suppression of non-desired higher order modes is more than 10 dB over the whole O-, S- and C-band. In particular, suppression is more than 19 dB over the entire C-band. The analysis also shows that the performance of the mode converter is not sensitive to slight variations of the converter’s parameters. In addition, the same converter can be used for converting LP02 back to LP01. Further, a (de)multiplexer for an LP02 and an LP01 mode is designed using the mode converter combined with a symmetric directional coupler. The multiplexer is broadband and has insertion loss less than 0.5 dB over the C-band.
The proposed design is fabricated by inscribing it in the bulk of a borosilicate glass using a femtosecond laser. The converter has an insertion loss of less than 1 dB for the entire C-band and a total length of 2.22mm. this fabricated prototype validates the proposed mode converter design.
The LP01 to LP02 mode converter structure can also be used to convert to other LP0m mode by proper tuning its parameters. After extensive simulations and optimizations, an LP01 to LP0m mode converter is proposed. The proposed converter structures are designed not only to provide high performances (low insertion losses and high extinction ratios), but also to be able to be fabricated by respecting the fabrication requirements (in terms of lengths and refractive indices). As a case study, six mode converters, converting LP01 to LP0m, with m = 2 to 7 are reported. The structures have insertion losses ranging from 0.1 dB to 2.5 dB. These performance results outperform all reported similar mode converters.
To (de)multiplex the resulting LP0m modes, a (de)multiplexer based on symmetric directional couplers is proposed. This kind of devices are easy to design and fabricate and provide low insertion loss and cross talk. As an example, the first five modes (LP01 to LP05) are (de)multiplexed with an insertion loss less than 2.5 dB and cross talk less than -15 dB at the design wavelength. These results outperform the reported results for similar devices.
The LP01 to LP0m mode converter structure is modified by inserting more inner elements to be able to convert to any LPlm mode. Therefore, a universal LP mode converter structure is proposed. The number and parameters of these inner elements depend on the desired LPlm mode. For instance, structures to convert LP01 to LP11, LP21 and LP31 are provided. These modes require between 5 to 6 inner elements with different radii and lengths. The simulation results for these three structures shows that an insertion loss less than 1.9 dB and an extinction ratio higher than 10 dB are achieved for the three modes at the design wavelength of 1550nm.
Furthermore, the three modes (LP11, LP21 and LP31) are (d)multiplexed using a symmetric directional coupler with an insertion loss less than 0.9 dB and a cross talk below -17 dB for the three modes at the design wavelength.
All the parameters of the presented mode converters and (de)multiplexers are designed to allow them to be fabricated using 3D femtosecond laser inscription technique.
| Divisions: | Concordia University > Gina Cody School of Engineering and Computer Science > Electrical and Computer Engineering |
|---|---|
| Item Type: | Thesis (PhD) |
| Authors: | mellah, hakim |
| Institution: | Concordia University |
| Degree Name: | Ph. D. |
| Program: | Electrical and Computer Engineering |
| Date: | June 2018 |
| Thesis Supervisor(s): | Zhang, John Xiupu |
| Keywords: | Mode Division Multiplexing, Mode Converter, Mode Multiplexer, Optical Communications |
| ID Code: | 984343 |
| Deposited By: | HAKIM MELLAH |
| Deposited On: | 31 Oct 2018 17:41 |
| Last Modified: | 31 Oct 2018 17:41 |
References:
[1] R. Essiambre and A. Mecozzi, “Capacity limits in single mode fiber and scaling for spatial multiplexing,” in Optical Fiber Communication Conference, 2012.[2] R.-J. R.-J. Essiambre et al., “Capacity Limits of Optical Fiber Networks,” J. Light. Technol., 2010.
[3] R. J. Essiambre and R. W. Tkach, “Capacity trends and limits of optical communication networks,” in Proceedings of the IEEE, 2012.
[4] J. H. Lin, A. Ellis, and D. Rafique, “Capacity Limits of Optical Fibre Based Communications,” Adv. Photonics, 2011.
[5] D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nature Photonics, vol. 7, no. 5. 2013.
[6] Y. Weng, X. He, and Z. Pan, “Space division multiplexing optical communication using few-mode fibers,” Opt. Fiber Technol., 2017.
[7] J. M. Kahn and Keang-Po Ho, “Mode-division multiplexing systems: Propagation effects, performance and complexity,” in OFC, 2013.
[8] T. Morioka, “Recent progress in space-division multiplexed transmission technologies,” in Optical Fiber Communications Conference (OFC/NFOEC), 2013.
[9] G. Li, N. Bai, N. Zhao, and C. Xia, “Space-division multiplexing: the next frontier in optical communication,” Adv. Opt. Photonics, vol. 6, no. 4, 2014.
[10] T. Mizuno and Y. Miyamoto, “High-capacity dense space division multiplexing transmission,” Opt. Fiber Technol., 2017.
[11] S. Randel, “Space-division multiplexed transmission,” in Optical Fiber Communications Conference (OFC/NFOEC), 2013.
[12] L. Wang et al., “Linearly polarized vector modes: enabling MIMO-free mode-division multiplexing,” Opt. Express, 2017.
[13] K. Shi, G. Gordon, M. Paskov, J. Carpenter, T. D. Wilkinson, and B. C. Thomsen, “Degenerate mode-group division multiplexing using MIMO digital signal processing,” in 2013 IEEE Photonics Society Summer Topical Meeting Series, PSSTMS 2013, 2013.
[14] S. O. Arik and J. M. Kahn, “Adaptive MIMO signal processing in mode-division multiplexing,” in Proceedings - 2014 Summer Topicals Meeting Series, SUM 2014, 2014.
[15] A. Al Amin, A. Li, X. Chen, and W. Shieh, “Mode division multiplexing MIMO-OFDM optical transmission,” in Technical Digest - 2012 17th Opto-Electronics and Communications Conference, OECC 2012, 2012.
[16] S. O. Arik, D. Askarov, and J. M. Kahn, “MIMO DSP Complexity in Mode-Division Multiplexing,” in Optical Fiber Communication Conference, 2015.
[17] I. P. Giles, R. Chen, and V. Garcia-Munoz, “Fiber based multiplexing and demultiplexing devices for few mode fiber space division multiplexed communications,” in Conference on Optical Fiber Communication, Technical Digest Series, 2014.
[18] Y. Xie, S. Fu, M. Zhang, M. Tang, P. Shum, and D. Liu, “Optimization of few-mode-fiber based mode converter for mode division multiplexing transmission,” Opt. Commun., 2013.
[19] P. Sillard, D. Molin, M. Bigot-Astruc, K. De Jongh, and F. Achten, “Rescaled Multimode Fibers for Mode-Division Multiplexing,” J. Light. Technol., 2017.
[20] M. Kasahara et al., “Design of few-mode fibers for mode-division multiplexing transmission,” IEEE Photonics J., 2013.
[21] Y. Sun, R. Lingle, A. McCurdy, D. Peckham, R. Jensen, and L. Gruner-Nielsen, “Few-mode fibers for mode-division multiplexing,” in 2013 IEEE Photonics Society Summer Topical Meeting Series, PSSTMS 2013, 2013.
[22] P. Sillard, M. Bigot-Astruc, D. Boivin, H. Maerten, and L. Provost, “Few-Mode Fiber for Uncoupled Mode-Division Multiplexing Transmissions,” Eur. Conf. Exhib. Opt. Commun., 2011.
[23] M. Salsi, C. Koebele, G. Charlet, and S. Bigo, “Mode Division Multiplexed Transmission with a weakly-coupled Few-Mode Fiber,” Opt. Fiber Commun. Conf., 2012.
[24] H. Kubota and T. Morioka, “Few-mode optical fiber for mode-division multiplexing,” Opt. Fiber Technol., 2011.
[25] S. Matsuo, Y. Sasaki, I. Ishida, K. Takenaga, K. Saitoh, and M. Koshiba, “Recent Progress on Multi-Core Fiber and Few-Mode Fiber,” 2013 Opt. Fiber Commun. Conf. Expo. Natl. Fiber Opt. Eng. Conf., 2013.
[26] Y. Sasaki, K. Takenaga, S. Matsuo, K. Aikawa, and K. Saitoh, “Few-mode multicore fibers for long-haul transmission line,” Opt. Fiber Technol., 2017.
[27] S. Matsuo, Y. Sasaki, I. Ishida, K. Takenaga, K. Saitoh, and M. Koshiba, “Recent Progress in Multi core and Few mode Fiber,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference 2013, 2013.
[28] K. Nakajima, Y. Goto, T. Matsui, and S. Tomita, “Multi-core fiber technologies for extremely advanced transmission,” 16th Opto-Electronics Commun. Conf., 2011.
[29] B. J. Puttnam et al., “High capacity multi-core fiber systems,” in 2016 21st European Conference on Networks and Optical Communications (NOC), 2016.
[30] K. Nakajima, Y. Goto, and S. Tomita, “Recent progress on multi-core fiber,” in Opto-Electronics and Communications Conference (OECC), 2012 17th, 2012.
[31] R. Ryf et al., “Mode-division multiplexing over 96 km of few-mode fiber using coherent 6×6 MIMO processing,” J. Light. Technol., 2012.
[32] M. Salsi et al., “Mode Division Multiplexing of 2 x 100Gb/s Channels using an LCOS based Spatial Modulator,” J. Light. Technol., 2011.
[33] N. K. Fontaine, “Devices and Components for Space-Division Multiplexing in Few-Mode Fibers,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference 2013, 2013.
[34] J. Carpenter, B. J. Eggleton, and J. Schröder, “Applications of spatial light modulators for mode-division multiplexing,” in European Conference on Optical Communication, ECOC, 2014.
[35] M. Salsi et al., “Mode-division multiplexing of 2 × 100 Gb/s channels using an LCOS-based spatial modulator,” J. Light. Technol., 2012.
[36] J. A. Carpenter, B. J. Eggleton, and J. B. Schroeder, “LCOS Based Devices for Mode-division Multiplexing,” in Optical Fiber Communication Conference, 2015.
[37] D. Askarov and J. M. Kahn, “Long-period fiber gratings for mode coupling in mode-division-multiplexing systems,” J. Light. Technol., 2015.
[38] H. Mellah, X. Zhang, and D. Shen, “LP01 to LP0m mode converters using all-fiber two-stage tapers,” Opt. Commun., vol. 354, 2015.
[39] S. G. Leon-Saval, “Photonic lanterns for mode division multiplexing,” in MOC 2015 - Technical Digest of 20th Microoptics Conference, 2016.
[40] K. Saitoh et al., “PLC-based mode multi/demultiplexers for mode division multiplexing,” Opt. Fiber Technol., 2017.
[41] J. B. Driscoll, R. R. Grote, B. Souhan, J. I. Dadap, M. Lu, and R. M. Osgood, “Asymmetric Y junctions in silicon waveguides for on-chip mode-division multiplexing,” Opt. Lett., 2013.
[42] H. Mellah, X. Zhang, and D. Shen, “Analysis of optical fiber-based LP01<--> LP02 mode converters for the O-, S-, and C-Band,” Appl. Opt., vol. 54, no. 17, 2015.
[43] A. Li, X. Chen, A. Al Amin, J. Ye, and W. Shieh, “Space-division multiplexed high-speed superchannel transmission over few-mode fiber,” J. Light. Technol., 2012.
[44] C. P. Tsekrekos and D. Syvridis, “All-fiber broadband LP 02 mode converter for future wavelength and mode division multiplexing systems,” IEEE Photonics Technol. Lett., 2012.
[45] D. Dai, “Silicon-based Multi-channel Mode (de)multiplexer for On-chip Optical Interconnects,” in Advanced Photonics for Communications, 2014.
[46] N. Riesen, J. D. Love, and J. W. Arkwright, “Few-core spatial-mode multiplexers/demultiplexers based on evanescent coupling,” IEEE Photonics Technol. Lett., 2013.
[47] J. Xing, Z. Li, X. Xiao, J. Yu, and Y. Yu, “Two-mode multiplexer and demultiplexer based on adiabatic couplers,” Opt. Lett., 2013.
[48] Y. Ding, H. Ou, J. Xu, and C. Peucheret, “Silicon photonic integrated circuit mode multiplexer,” IEEE Photonics Technol. Lett., 2013.
[49] S. H. Chang et al., “Mode division multiplexed optical transmission enabled by all–fiber mode multiplexer,” Opt. Express, 2014.
[50] M. Yin, Q. Deng, Y. Li, X. Wang, and H. Li, “Compact and broadband mode multiplexer and demultiplexer based on asymmetric plasmonic–dielectric coupling,” Appl. Opt., 2014.
[51] N. Hanzawa et al., “Two-mode PLC-based mode multi/demultiplexer for mode and wavelength division multiplexed transmission,” Opt. Express, 2013.
[52] N. Hanzawa et al., “Mode multi/demultiplexing with parallel waveguide for mode division multiplexed transmission,” Opt. Express, vol. 22, no. 24, 2014.
[53] W. Chang et al., “Ultra-compact mode (de) multiplexer based on subwavelength asymmetric Y-junction,” Opt. Express, 2018.
[54] Z. Zhang, Y. Yu, and S. Fu, “Broadband On-Chip Mode-Division Multiplexer Based on Adiabatic Couplers and Symmetric Y-Junction,” IEEE Photonics J., 2017.
[55] H.-C. Chung, K.-S. Lee, and S.-Y. Tseng, “Short and broadband silicon asymmetric Y-junction two-mode (de)multiplexer using fast quasiadiabatic dynamics,” Opt. Express, 2017.
[56] M. Lan, S. Yu, S. Cai, L. Gao, and W. Gu, “Mode multiplexer/demultiplexer based on tapered multi-core fiber,” IEEE Photonics Technol. Lett., 2017.
[57] S. G. Leon-Saval, N. K. Fontaine, and R. Amezcua-Correa, “Photonic lantern as mode multiplexer for multimode optical communications,” Opt. Fiber Technol., 2017.
[58] Z. S. Eznaveh, J. E. Antonio-Lopez, J. C. A. Zacarias, A. Schülzgen, C. M. Okonkwo, and R. A. Correa, “All-fiber few-mode multicore photonic lantern mode multiplexer,” Opt. Express, 2017.
[59] D. Dai, Y. Tang, and J. E. Bowers, “Mode conversion in tapered submicron silicon ridge optical waveguides,” Opt. Express, 2012.
[60] S. Gross, N. Riesen, J. D. Love, and M. J. Withford, “Three-dimensional ultra-broadband integrated tapered mode multiplexers,” Laser Photonics Rev., vol. 8, no. 5, 2014.
[61] N. Riesen, S. Gross, J. D. Love, and M. J. Withford, “Femtosecond direct-written integrated mode couplers,” Opt. Express, vol. 22, no. 24, 2014.
[62] R. Ryf et al., “Photonic-lantern-based mode multiplexers for few-mode-fiber transmission,” in Conference on Optical Fiber Communication, Technical Digest Series, 2014.
[63] a Witkowska, S. G. Leon-Saval, A. Pham, and T. a Birks, “All-fiber LP11 mode convertors.,” Opt. Lett., 2008.
[64] K. Lai, S. G. Leon-Saval, a Witkowska, W. J. Wadsworth, and T. a Birks, “Wavelength-independent all-fiber mode converters.,” Opt. Lett., 2007.
[65] S. Yerolatsitis and T. A. Birks, “Three-mode multiplexer in photonic crystal fibre,” in 39th European Conference and Exhibition on Optical Communication (ECOC 2013), 2013.
[66] M. Skorobogatiy et al., “Quantitative characterization of higher-order mode converters in weakly multimoded fibers.,” Opt. Express, 2003.
[67] A. Al Amin, A. Li, S. Chen, X. Chen, G. Gao, and W. Shieh, “Dual-LP_11 mode 4x4 MIMO-OFDM transmission over a two-mode fiber,” Opt. Express, 2011.
[68] N. Riesen and J. D. Love, “Tapered velocity mode-selective couplers,” J. Light. Technol., 2013.
[69] S. Yerolatsitis and T. a Birks, “Tapered Mode Multiplexers for Single Mode to Multi Mode Fibre Mode Transitions,” Opt. Fiber Commun. Conf., 2015.
[70] A. M. Velazquez-Benitez et al., “Six Spatial Modes Photonic Lanterns,” in Optical Fiber Communication Conference, 2015.
[71] T. Uematsu et al., “Low-loss and broadband PLC-type mode (de)multiplexer for mode-division multiplexing transmission,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference 2013, 2013.
[72] N. Hanzawa et al., “PLC-based four-mode multi/demultiplexer with LP11 mode rotator on one chip,” J. Light. Technol., 2015.
[73] J. Wang et al., “Ultrabroadband silicon-on-insulator polarization beam splitter based on cascaded mode-sorting asymmetric Y-junctions,” IEEE Photonics J., 2014.
[74] C. P. Tsekrekos and D. Syvridis, “Symmetric few-mode fiber couplers as the key component for broadband mode multiplexing,” J. Light. Technol., vol. 32, no. 14, 2014.
[75] W. Klaus et al., “Advanced Space Division Multiplexing Technologies for Optical Networks,” J. Opt. Commun. Netw., 2017.
[76] K. N. Fontaine, “Devices and components for space-division multiplexing in few-mode fibers,” in Optical Fiber Communications Conference (OFC/NFOEC), 2013.
[77] J.-P. Bérubé and R. Vallée, “Femtosecond laser direct inscription of surface skimming waveguides in bulk glass,” Opt. Lett., 2016.
[78] J.-P. Bérubé et al., “Femtosecond laser direct inscription of mid-IR transmitting waveguides in BGG glasses,” Opt. Mater. Express, 2017.
[79] D. Marcuse, “Coupled‐Mode Theory for Anisotropic Optical Waveguides,” Bell Syst. Tech. J., 1975.
[80] J. R. Grenier, L. A. Fernandes, and P. R. Herman, “Femtosecond laser inscription of asymmetric directional couplers for in-fiber optical taps and fiber cladding photonics,” Opt. Express, 2015.
[81] a. Fuerbach et al., “Direct writing of photonic devices using femtosecond laser pulses,” Transparent Opt. Networks (ICTON), 2010 12th Int. Conf., 2010.
[82] C. Florea and K. A. Winick, “Fabrication and characterization of photonic devices directly written in glass using femtosecond laser pulses,” J. Light. Technol., 2003.
[83] R. Osellame et al., “Femtosecond laser writing of symmetrical optical waveguides by astigmatically shaped beams,” Integr. Opt. Photonic Integr. Circuits, 2004.
[84] R. Osellame et al., “Femtosecond writing of active optical waveguides with astigmatically shaped beams,” J. Opt. Soc. Am. B, 2003.
[85] S. Ghosh, B. P. Pal, R. K. Varshney, and G. P. Agrawal, “Transverse localization of light and its dependence on the phase front curvature of the input beam in a disordered optical waveguide lattice,” J. Opt., 2012.
[86] S. Ghosh, B. P. Pal, and R. K. Varshney, “Role of optical nonlinearity on transverse localization of light in a disordered one-dimensional optical waveguide lattice,” Opt. Commun., 2012.
[87] N. Bhatia, K. C. Rustagi, and J. John, “Single LP(0,n) mode excitation in multimode fibers.,” Opt. Express, 2014.
[88] J. Carpenter, B. C. Thomsen, and T. D. Wilkinson, “Mode division multiplexing of modes with the same azimuthal index,” IEEE Photonics Technol. Lett., 2012.
[89] N. Hanzawa; K. Saitosh; T. Sakamoto; K. Tsujikawa; T. Uematsu; M.Koshiba; F. Yamamoto, “Three-mode PLC-type multi/demultiplexer for mode-division multiplexing transmission,” 9th Eur. Conf. Exhib. Opt. Commun. (ECOC 2013), pp. 1–3, 2013.
[90] D. Gloge, “Weakly guiding fibres,” Appl. Opt., 1971.
[91] A. W. Snyder, “Weakly guiding optical fibers,” J. Opt. Soc. Am., 1980.
[92] J. Arnaud, “Optical waveguide theory,” Optical and Quantum Electronics. 1980.
[93] K. Okamoto, “Wave Theory of Optical Waveguides,” in Fundamentals of Optical Waveguides, 2006.
[94] C. Freude, Wolfgang; Koos, “Optical Waveguides and Fibers,” Fundam. Photonics, 2000.
[95] R. Lingle, D. W. Peckham, A. McCurdy, and J. Kim, “Light-Guiding Fundamentals and Fiber Design,” in Specialty Optical Fibers Handbook, 2007.
[96] K. Okamoto, Fundamentals of Optical Waveguides. 2006.
[97] K. Okamoto, “Optical Fibers,” in Fundamentals of Optical Waveguides, 2006.
[98] S. Pillay, D. Kumar, H. Azhar, and A. B. Rashid, “Weakly Guiding Fibers and LP Modes in Circular and Elliptical Waveguides,” J. Electromagn. Anal. Appl., 2013.
[99] A. W. Snyder and W. R. Young, “Modes of optical waveguides,” J. Opt. Soc. Am., 1978.
[100] J. R. Qian and W. P. Huang, “LP Modes and Ideal Modes on Optical Fibers,” J. Light. Technol., 1986.
[101] J. R. Qian and W. P. Huang, “Coupled-Mode Theory for LP Modes,” J. Light. Technol., 1986.
[102] D. G. Hall, “Vector-beam solutions of Maxwell’s wave equation,” Opt. Lett., 1996.
[103] C. Yeh, “Guided-Wave modes in cylindrical optical fibers,” IEEE Trans. Educ., 1987.
[104] X. Q. Jin, R. Li, D. C. O’Brien, and F. P. Payne, “Linearly polarized mode division multiplexed transmission over ring-index multimode fibres,” in 2013 IEEE Photonics Society Summer Topical Meeting Series, PSSTMS 2013, 2013.
[105] J. Bures, “1 Vector Wave Equations,” Guid. Opt., 2009.
[106] “LP modes.” [Online]. Available: https://www.rp-photonics.com/lp_modes.html. [Accessed: 20-Aug-2004].
[107] K. Thyagarajan, A. K. Ghatak, and A. Sharma, “Vector modes of an optical fiber in the weakly guiding approximation,” J. Light. Technol., 1989.
[108] I. Gómez-Castellanos, “Intensity distributions and cutoff frequencies of linearly polarized modes for a step-index elliptical optical fiber,” Opt. Eng., 2007.
[109] A. W. Snyder and J. D. Love, Optical Waveguide Theory. 1983.
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