Characterization of OAM fibers using fiber Bragg gratings L. Wang,1,2 P. Vaity,1 B. Ung,1 Y. Messaddeq,1 L. A. Rusch,1 and S. LaRochelle1,* 1 2
Centre d’Optique, Photonique et Laser (COPL), Université Laval, Québec, QC, Canada on leave from Institute of Semiconductors, Chinese Academy of Sciences, Beijing, China *[email protected]
Abstract: The reflectogram of a fiber grating is used to characterize vector modes of an optical fiber supporting orbital angular momentum states. All modes, with a minimal effective index separation around 10−4, are simultaneously measured. OAM states are reflected by the FBG, along with a charge inversion, at the center wavelength of the Bragg reflection peak of the corresponding fiber vector mode. ©2014 Optical Society of America OCIS codes: (060.3735) Fiber Bragg gratings; (050.4865) Optical vortices; (060.4230) Multiplexing.
References and links 1. 2. 3. 4. 5.
6. 7. 8.
9. 10. 11. 12. 13. 14. 15.
L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992). A. E. Willner, J. Wang, and H. Huang, “Applied physics. A Different Angle on Light Communications,” Science 337(6095), 655–656 (2012). G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12(22), 5448–5456 (2004). J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012). H. Huang, G. Xie, Y. Yan, N. Ahmed, Y. Ren, Y. Yue, D. Rogawski, M. J. Willner, B. I. Erkmen, K. M. Birnbaum, S. J. Dolinar, M. P. Lavery, M. J. Padgett, M. Tur, and A. E. Willner, “100 Tbit/s free-space data link enabled by three-dimensional multiplexing of orbital angular momentum, polarization, and wavelength,” Opt. Lett. 39(2), 197–200 (2014). N. Fontaine, C. Doerr, and L. Buhl, “Efficient Multiplexing and Demultiplexing of Free-space Orbital Angular Momentum using Photonic Integrated Circuits,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2012), paper OTu1I.2. J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493(7431), 195–199 (2013). B. Guan, R. P. Scott, C. Qin, N. K. Fontaine, T. Su, C. Ferrari, M. Cappuzzo, F. Klemens, B. Keller, M. Earnshaw, and S. J. Yoo, “Free-space coherent optical communication with orbital angular, momentum multiplexing/demultiplexing using a hybrid 3D photonic integrated circuit,” Opt. Express 22(1), 145–156 (2014). N. Bozinovic, S. Golowich, P. Kristensen, and S. Ramachandran, “Control of orbital angular momentum of light with optical fibers,” Opt. Lett. 37(13), 2451–2453 (2012). P. Gregg, P. Kristensen, S. Golowich, J. Olsen, P. Steinvurzel, and S. Ramachandran, “Stable Transmission of 12 OAM States in Air-Core Fiber,” in CLEO: 2013, OSA Technical Digest (online) (Optical Society of America, 2013), paper CTu2K.2. N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “TerabitScale Orbital Angular Momentum Mode Division Multiplexing in Fibers,” Science 340(6140), 1545–1548 (2013). B. Ung, L. Wang, C. Brunet, P. Vaity, C. Jin, L. A. Rusch, Y. Messaddeq, and S. LaRochelle, “Inverse-parabolic graded-index profile for transmission of cylindrical vector modes in optical fibers,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2014), paper Tu3K.4. C. Brunet, B. Ung, Y. Messaddeq, S. LaRochelle, E. Bernier, and L. Rusch, “Design of an Optical Fiber Supporting 16 OAM Modes”, in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2014), paper Th2A.24. S. Ramachandran, P. Kristensen, and M. F. Yan, “Generation and propagation of radially polarized beams in optical fibers,” Opt. Lett. 34(16), 2525–2527 (2009). J. M. Savolainen, L. Grüner-Nielsen, P. Kristensen, and P. Balling, “Measurement of effective refractive-index differences in a few-mode fiber by axial fiber stretching,” Opt. Express 20(17), 18646–18651 (2012).
#208042 - $15.00 USD (C) 2014 OSA
Received 11 Mar 2014; revised 7 Jun 2014; accepted 11 Jun 2014; published 19 Jun 2014 30 June 2014 | Vol. 22, No. 13 | DOI:10.1364/OE.22.015653 | OPTICS EXPRESS 15653
16. S. Ramachandran, S. Golowich, M. F. Yan, E. Monberg, F. V. Dimarcello, J. Fleming, S. Ghalmi, and P. Wisk, “Lifting polarization degeneracy of modes by fiber design: a platform for polarization-insensitive microbend fiber gratings,” Opt. Lett. 30(21), 2864–2866 (2005). 17. F. Stutzki, C. Jauregui, J. Limpert, and A. Tünnermann, “Real-time characterisation of modal content in monolithic few-mode fibre lasers,” Electron. Lett. 47(4), 274–275 (2011). 18. F. Stutzki, C. Jauregui, C. Voigtländer, J. U. Thomas, J. Limpert, S. Nolte, and A. Tünnermann, “Passively stabilized 215 W monolithic CW LMA-fiber laser with innovative transversal mode filter,” Proc. SPIE 7580(75801K), 75801K (2010). 19. J. M. O. Daniel, J. S. P. Chan, J. W. Kim, J. K. Sahu, M. Ibsen, and W. A. Clarkson, “Novel technique for mode selection in a multimode fiber laser,” Opt. Express 19(13), 12434–12439 (2011). 20. C. Jocher, C. Jauregui, C. Voigtländer, F. Stutzki, S. Nolte, J. Limpert, and A. Tünnermann, “Fiber based polarization filter for radially and azimuthally polarized light,” Opt. Express 19(20), 19582–19590 (2011). 21. T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15(8), 1277–1294 (1997). 22. S. Roychowdhury, V. K. Jaiswal, and R. P. Singh, “Implementing controlled NOT gate with optical vortex,” Opt. Commun. 236(4-6), 419–424 (2004). 23. G. Molina-Terriza, J. Recolons, J. P. Torres, L. Torner, and E. Wright, “Observation of the dynamical inversion of the topological charge of an optical vortex,” Phys. Rev. Lett. 87(2), 023902 (2001).
1. Introduction Orbital angular momentum (OAM) of light is represented by an electrical field with a helical phase proportional to exp(ilφ) where l is an integer and φ is the azimuthal angle [1]. The unique property of OAM light beams is that an infinite number of orthogonal OAM states can be supported in principle [2]. It is therefore possible to use them as carriers to transport data in optical communications in addition to wavelength division multiplexing (WDM). In the past decade, OAM-based optical free space communications has been extensively studied. The reported data-transferring capacity rapidly increased from 2 Tbit/s to 100 Tbit/s [3–5]. Photonic integrated techniques were also implemented to achieve more compact systems [6– 8]. After initial studies in free space communication links, OAM modes are now being considered for spatial multiplexing in optical fibers [9, 10]. Terabit-scale data-transferring capacity in specially designed optical “vortex” fibers has been demonstrated by multiplexing two OAM modes over 10 wavelengths, which is a huge step forward in efforts to develop this technology as an efficient means to scale the capacity of current fiber optic networks [11]. OAM beams are generally considered to be unstable in conventional optical few mode fibers because of the presence of mode coupling. Therefore, specialty fibers that support OAM states are a critical technology for future OAM-WDM systems and several designs have been proposed [10, 12–14]. One key parameter in the performance of such OAM guiding fibers is the separation of the effective refractive indices, ∆neff, of the fiber vector modes. Large ∆neff values alleviate the problem of mode coupling and enable the stable copropagation of multiple OAM states. Efficient techniques that accurately and rapidly measure the vector modal effective indices are highly desirable for the characterization of OAM fibers and subsequent optimization of their designs. Savolainen et al. measured the difference in modal effective indices by stretching the fiber and monitoring the interference pattern [15]. This method works well for few mode fibers in which only few modes propagate. When the number of propagating modes increases, the analysis becomes rather complicated. The index separations can also be measured by using mechanically-induced micro-bend long period fiber gratings (LPGs) [16]. ∆neff is deduced from the center wavelength of the mode conversion peak. However, a number of micro-bend LPGs with different periods are required for the measurement in the wavelength range of interest, e.g. the C-band, due to the large separation of the mode conversion peaks (around 100 nanometers), making this technique practically inconvenient. Fiber Bragg gratings (FBGs) can spectrally filter fiber modes over a much smaller wavelength region. FBGs have been successfully used to characterize and monitor fiber modes, but most of them are in conventional multi-mode fibers and for measuring linearly polarized modes [17–20]. Until now FBGs written in fewmode fibers supporting OAM modes have never been reported to the best of our knowledge. In this paper we demonstrate a FBG-based technique for characterizing vector modes in OAM fibers. The OAM fiber under test was designed to suppress OAM mode coupling and was fabricated in our laboratory [12]. Weak FBGs were photoinduced in the OAM fibers and
#208042 - $15.00 USD (C) 2014 OSA
Received 11 Mar 2014; revised 7 Jun 2014; accepted 11 Jun 2014; published 19 Jun 2014 30 June 2014 | Vol. 22, No. 13 | DOI:10.1364/OE.22.015653 | OPTICS EXPRESS 15654
all the fiber vector modes were simultaneously measured by analyzing the FBG reflectogram. The measured effective index separations are in good agreement with numerical simulations of the fiber refractive index profile. Furthermore, Bragg reflections of OAM states by the FBG are also demonstrated and analyzed. 2. OAM fiber with an inverse-parabolic graded-index profile The OAM fiber under test presents an inverse-parabolic graded refractive index profile (Fig. 1 (a)) written as
n( r ) = n 1 − N ∆(r 2 / r 2 ) core 1 n2
0 ≤ r ≤ rcore
(1)
r ≥ rcore
where n1 and n2 are the refractive indices at the center core (r = 0) and in the cladding respectively, N is the curvature parameter, and = ∆ ( n12 − n22 ) / 2n12 [12]. Inverse-parabolic profiles are obtained with N
Centre d’Optique, Photonique et Laser (COPL), Université Laval, Québec, QC, Canada on leave from Institute of Semiconductors, Chinese Academy of Sciences, Beijing, China *[email protected]
Abstract: The reflectogram of a fiber grating is used to characterize vector modes of an optical fiber supporting orbital angular momentum states. All modes, with a minimal effective index separation around 10−4, are simultaneously measured. OAM states are reflected by the FBG, along with a charge inversion, at the center wavelength of the Bragg reflection peak of the corresponding fiber vector mode. ©2014 Optical Society of America OCIS codes: (060.3735) Fiber Bragg gratings; (050.4865) Optical vortices; (060.4230) Multiplexing.
References and links 1. 2. 3. 4. 5.
6. 7. 8.
9. 10. 11. 12. 13. 14. 15.
L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of laguerre-gaussian laser modes,” Phys. Rev. A 45(11), 8185–8189 (1992). A. E. Willner, J. Wang, and H. Huang, “Applied physics. A Different Angle on Light Communications,” Science 337(6095), 655–656 (2012). G. Gibson, J. Courtial, M. Padgett, M. Vasnetsov, V. Pas’ko, S. Barnett, and S. Franke-Arnold, “Free-space information transfer using light beams carrying orbital angular momentum,” Opt. Express 12(22), 5448–5456 (2004). J. Wang, J. Yang, I. M. Fazal, N. Ahmed, Y. Yan, H. Huang, Y. Ren, Y. Yue, S. Dolinar, M. Tur, and A. Willner, “Terabit free-space data transmission employing orbital angular momentum multiplexing,” Nat. Photonics 6(7), 488–496 (2012). H. Huang, G. Xie, Y. Yan, N. Ahmed, Y. Ren, Y. Yue, D. Rogawski, M. J. Willner, B. I. Erkmen, K. M. Birnbaum, S. J. Dolinar, M. P. Lavery, M. J. Padgett, M. Tur, and A. E. Willner, “100 Tbit/s free-space data link enabled by three-dimensional multiplexing of orbital angular momentum, polarization, and wavelength,” Opt. Lett. 39(2), 197–200 (2014). N. Fontaine, C. Doerr, and L. Buhl, “Efficient Multiplexing and Demultiplexing of Free-space Orbital Angular Momentum using Photonic Integrated Circuits,” in Optical Fiber Communication Conference, OSA Technical Digest (Optical Society of America, 2012), paper OTu1I.2. J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493(7431), 195–199 (2013). B. Guan, R. P. Scott, C. Qin, N. K. Fontaine, T. Su, C. Ferrari, M. Cappuzzo, F. Klemens, B. Keller, M. Earnshaw, and S. J. Yoo, “Free-space coherent optical communication with orbital angular, momentum multiplexing/demultiplexing using a hybrid 3D photonic integrated circuit,” Opt. Express 22(1), 145–156 (2014). N. Bozinovic, S. Golowich, P. Kristensen, and S. Ramachandran, “Control of orbital angular momentum of light with optical fibers,” Opt. Lett. 37(13), 2451–2453 (2012). P. Gregg, P. Kristensen, S. Golowich, J. Olsen, P. Steinvurzel, and S. Ramachandran, “Stable Transmission of 12 OAM States in Air-Core Fiber,” in CLEO: 2013, OSA Technical Digest (online) (Optical Society of America, 2013), paper CTu2K.2. N. Bozinovic, Y. Yue, Y. Ren, M. Tur, P. Kristensen, H. Huang, A. E. Willner, and S. Ramachandran, “TerabitScale Orbital Angular Momentum Mode Division Multiplexing in Fibers,” Science 340(6140), 1545–1548 (2013). B. Ung, L. Wang, C. Brunet, P. Vaity, C. Jin, L. A. Rusch, Y. Messaddeq, and S. LaRochelle, “Inverse-parabolic graded-index profile for transmission of cylindrical vector modes in optical fibers,” in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2014), paper Tu3K.4. C. Brunet, B. Ung, Y. Messaddeq, S. LaRochelle, E. Bernier, and L. Rusch, “Design of an Optical Fiber Supporting 16 OAM Modes”, in Optical Fiber Communication Conference, OSA Technical Digest (online) (Optical Society of America, 2014), paper Th2A.24. S. Ramachandran, P. Kristensen, and M. F. Yan, “Generation and propagation of radially polarized beams in optical fibers,” Opt. Lett. 34(16), 2525–2527 (2009). J. M. Savolainen, L. Grüner-Nielsen, P. Kristensen, and P. Balling, “Measurement of effective refractive-index differences in a few-mode fiber by axial fiber stretching,” Opt. Express 20(17), 18646–18651 (2012).
#208042 - $15.00 USD (C) 2014 OSA
Received 11 Mar 2014; revised 7 Jun 2014; accepted 11 Jun 2014; published 19 Jun 2014 30 June 2014 | Vol. 22, No. 13 | DOI:10.1364/OE.22.015653 | OPTICS EXPRESS 15653
16. S. Ramachandran, S. Golowich, M. F. Yan, E. Monberg, F. V. Dimarcello, J. Fleming, S. Ghalmi, and P. Wisk, “Lifting polarization degeneracy of modes by fiber design: a platform for polarization-insensitive microbend fiber gratings,” Opt. Lett. 30(21), 2864–2866 (2005). 17. F. Stutzki, C. Jauregui, J. Limpert, and A. Tünnermann, “Real-time characterisation of modal content in monolithic few-mode fibre lasers,” Electron. Lett. 47(4), 274–275 (2011). 18. F. Stutzki, C. Jauregui, C. Voigtländer, J. U. Thomas, J. Limpert, S. Nolte, and A. Tünnermann, “Passively stabilized 215 W monolithic CW LMA-fiber laser with innovative transversal mode filter,” Proc. SPIE 7580(75801K), 75801K (2010). 19. J. M. O. Daniel, J. S. P. Chan, J. W. Kim, J. K. Sahu, M. Ibsen, and W. A. Clarkson, “Novel technique for mode selection in a multimode fiber laser,” Opt. Express 19(13), 12434–12439 (2011). 20. C. Jocher, C. Jauregui, C. Voigtländer, F. Stutzki, S. Nolte, J. Limpert, and A. Tünnermann, “Fiber based polarization filter for radially and azimuthally polarized light,” Opt. Express 19(20), 19582–19590 (2011). 21. T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15(8), 1277–1294 (1997). 22. S. Roychowdhury, V. K. Jaiswal, and R. P. Singh, “Implementing controlled NOT gate with optical vortex,” Opt. Commun. 236(4-6), 419–424 (2004). 23. G. Molina-Terriza, J. Recolons, J. P. Torres, L. Torner, and E. Wright, “Observation of the dynamical inversion of the topological charge of an optical vortex,” Phys. Rev. Lett. 87(2), 023902 (2001).
1. Introduction Orbital angular momentum (OAM) of light is represented by an electrical field with a helical phase proportional to exp(ilφ) where l is an integer and φ is the azimuthal angle [1]. The unique property of OAM light beams is that an infinite number of orthogonal OAM states can be supported in principle [2]. It is therefore possible to use them as carriers to transport data in optical communications in addition to wavelength division multiplexing (WDM). In the past decade, OAM-based optical free space communications has been extensively studied. The reported data-transferring capacity rapidly increased from 2 Tbit/s to 100 Tbit/s [3–5]. Photonic integrated techniques were also implemented to achieve more compact systems [6– 8]. After initial studies in free space communication links, OAM modes are now being considered for spatial multiplexing in optical fibers [9, 10]. Terabit-scale data-transferring capacity in specially designed optical “vortex” fibers has been demonstrated by multiplexing two OAM modes over 10 wavelengths, which is a huge step forward in efforts to develop this technology as an efficient means to scale the capacity of current fiber optic networks [11]. OAM beams are generally considered to be unstable in conventional optical few mode fibers because of the presence of mode coupling. Therefore, specialty fibers that support OAM states are a critical technology for future OAM-WDM systems and several designs have been proposed [10, 12–14]. One key parameter in the performance of such OAM guiding fibers is the separation of the effective refractive indices, ∆neff, of the fiber vector modes. Large ∆neff values alleviate the problem of mode coupling and enable the stable copropagation of multiple OAM states. Efficient techniques that accurately and rapidly measure the vector modal effective indices are highly desirable for the characterization of OAM fibers and subsequent optimization of their designs. Savolainen et al. measured the difference in modal effective indices by stretching the fiber and monitoring the interference pattern [15]. This method works well for few mode fibers in which only few modes propagate. When the number of propagating modes increases, the analysis becomes rather complicated. The index separations can also be measured by using mechanically-induced micro-bend long period fiber gratings (LPGs) [16]. ∆neff is deduced from the center wavelength of the mode conversion peak. However, a number of micro-bend LPGs with different periods are required for the measurement in the wavelength range of interest, e.g. the C-band, due to the large separation of the mode conversion peaks (around 100 nanometers), making this technique practically inconvenient. Fiber Bragg gratings (FBGs) can spectrally filter fiber modes over a much smaller wavelength region. FBGs have been successfully used to characterize and monitor fiber modes, but most of them are in conventional multi-mode fibers and for measuring linearly polarized modes [17–20]. Until now FBGs written in fewmode fibers supporting OAM modes have never been reported to the best of our knowledge. In this paper we demonstrate a FBG-based technique for characterizing vector modes in OAM fibers. The OAM fiber under test was designed to suppress OAM mode coupling and was fabricated in our laboratory [12]. Weak FBGs were photoinduced in the OAM fibers and
#208042 - $15.00 USD (C) 2014 OSA
Received 11 Mar 2014; revised 7 Jun 2014; accepted 11 Jun 2014; published 19 Jun 2014 30 June 2014 | Vol. 22, No. 13 | DOI:10.1364/OE.22.015653 | OPTICS EXPRESS 15654
all the fiber vector modes were simultaneously measured by analyzing the FBG reflectogram. The measured effective index separations are in good agreement with numerical simulations of the fiber refractive index profile. Furthermore, Bragg reflections of OAM states by the FBG are also demonstrated and analyzed. 2. OAM fiber with an inverse-parabolic graded-index profile The OAM fiber under test presents an inverse-parabolic graded refractive index profile (Fig. 1 (a)) written as
n( r ) = n 1 − N ∆(r 2 / r 2 ) core 1 n2
0 ≤ r ≤ rcore
(1)
r ≥ rcore
where n1 and n2 are the refractive indices at the center core (r = 0) and in the cladding respectively, N is the curvature parameter, and = ∆ ( n12 − n22 ) / 2n12 [12]. Inverse-parabolic profiles are obtained with N
