Open Access
Add to BibSonomyAbstract
We experimentally demonstrate mode conversion by exploiting optical reflection of tilted few-mode fiber Bragg grating (FM-FBG). Mode conversions from LP01 mode to higher symmetric and asymmetric modes are achieved, and more than 99.5% conversion efficiency from LP01 to LP11 mode is obtained using a 1.6°-tilted FM-FBG. Influences of the weakly tilted FM-FBG parameters on the property of mode conversion is analyzed and discussed. A simultaneous mode conversion and demultiplexing scheme for 4-mode × 3-wavelength multiplexing transmission is proposed and the modal crosstalk is analyzed based on the transmission spectra of the tilted FM-FBGs. The proposed approach shows potential applications in mode and wavelength division multiplexing communication systems.
© 2015 Optical Society of America
1. Introduction
Recent techniques including multi-level modulation, mode-division multiplexing (MDM) and space-division multiplexing have attracted increasing research interest to achieve large optical communication capacity, due to the rapid growth of traffic in optical fiber communications [1–3]. Compared to the normal single-mode fiber, few-mode fiber (FMF) supports multiplexing transmission of spatial modes. Thus, it potentially accomplishes multiple increase of capacity in a single optical fiber [4–8]. Especially, energy efficiency can be increased and cost of per bit can be relatively reduced by utilizing other degrees of freedom, such as wavelength, high-order format modulation and polarization. Since it is significant to propose new concepts and develop novel devices to realize MDM communication, mode converters (MCs) become a great research interest. The current mode selective devices may be classified into three categories. The technique referring free space optics is usually bulky, although it has low wavelength dependence [9]. Phase plates based on liquid-crystal-on-silicon spatial light modulator [10, 11] have been utilized in MDM transmission system. However, these induce large insertion loss and increase device complexity. Integrated MC based on silicon-on-insulator ring resonator [12] or planar lightwave circuit [13], can effectively reduce insertion loss, but requires complicated design and fabrication accuracy. On the contrary, fiber based mode selective components have the advantages of low cost, low insertion and coupling loss, as well as easy connection within networks. A three-mode multiplexer proposed in [14] provides a compact route to couple different modes into one multimode core in the future MDM transmission system, despite of the challenging fabrication techniques. Tilted fiber gratings have been widely utilized in fiber sensing [15], signal processing [16] and microwave photonics [17], due to the multiple cladding-mode resonances. Especially, multiple core-mode couplings in tilted multi-mode fiber gratings (MM-TFGs) have potential applications in MDM systems. Mode conversion in reflective and transmissive MM-TFGs were theoretically analyzed [18, 19], lacking of experimental evidence for mode conversion in reflective MM-TFGs. A mechanical pressure-induced transmissive fiber grating was also demonstrated as an MC in [20]. However, the output of transmissive fiber gratings contains the converted mode (LP11) as well as the residual fundamental mode, and involves precise control on the coupling length to obtain high extinction ratio.
In this paper, we demonstrate a reflective MC based on weakly tilted few-mode fiber Bragg grating (FM-FBG). Pure converted mode output is obtained and mode dropping function is provided if the MC is applied in mode and wavelength division multiplexing (WDM-MDM) systems. It has the benefits of design flexibility and simple fabrication. Furthermore, it can achieve high mode conversion efficiency between fundamental mode and higher order modes by adjusting the grating tilt angle. A conversion efficiency of more than 99.5% from LP01 to LP11 mode is experimentally demonstrated using a 1.6°-tilted FM-FBG. Influences of tilt angle on mode conversions are theoretically discussed in detail. A demultiplexer for 4-mode × 3-wavelength multiplexing transmission based on the reflective MCs is proposed, and the modal crosstalk is discussed by analyzing the spectra of each grating with various incident modes.
2. Basic principle
The main function of MC is to convert optical signals from fundamental mode to higher orders, e.g. LP11 mode, or vice versa. The resonant coupling takes place between counter-propagating core modes, when Bragg grating structure is induced in FMF. According to the coupled mode theory [21], the coupled mode equations under perturbation in optical fiber can be written as:
where Aμ, Bμ are the slowly varying amplitudes of μth mode travelling in forward and backward direction. βμ, βν are the propagation constants of μth and νth modes respectively. And Ktνμ is the transverse coupling coefficient between νth and μth mode, defined aswhere, ω is the angular frequency of light, ε0 is the dielectric constant, n0 is the fiber refractive index, n is the grating refractive index profile. and are electric transverse fields of the two involved modes respectively. It can be seen that the coupling coefficient is determined by electric field overlap integral of the two modes. Bragg reflection resonance at λco-co is determined by core-core mode phase matching condition:where, are the effective refractive index of the μth forward-propagating and νth backward-propagating core mode respectively, Λ’ = Λ/cosθ, while Λ is the period and θ is the tilt angle of grating. The expressions above indicate that coupling between two core modes in FM-FBG requires mode phase matching and non-zero electric field overlap integral.3. Theoretical results and discussions
The simulation results of the transverse field intensity distributions of the utilized FMF in experiments, which is fabricated by Yangtze Optical Fiber and Cable Ltd, are shown in Fig. 1. The optical fiber has core radius rcore of 9.5 μm, core refractive index ncore of 1.4613, and cladding refractive index ncladding of 1.45601.
Fig. 1 Simulated results of intensity distributions of spatial modes in the fabricated FMF by using COMSOL toolkit.
It is obvious that the field overlap integral between fundamental mode and asymmetric modes, e.g. LP11, is zero. Consequently, the mode conversion between LP01 mode and asymmetric modes cannot occur in non-tilted FM-FBGs. However, when a weak tilt angle is induced in grating plane, the uniformity of refractive index of fiber cross section is interrupted, leading to variations of the mode field and refractive index profiles.
The structures of uniform non-tilted FBG and weakly tilted FBG are illustrated in Fig. 2(b)-2(c). It is assumed that the maximum index perturbation is 2 × 10−4 and the grating length is 10 mm. Figure 2(a) shows the calculated transmission spectra of the non-tilted, 0.8°-tilted, and 1.6°-tilted FM-FBGs under LP01 mode incident. It is shown that mode conversions from LP01 mode to asymmetric LP11 and LP21 mode are prohibited in non-tilted FM-FBG. However, in the weakly tilted FM-FBGs, LP01 mode can be converted to both symmetric LP02 mode and asymmetric higher order modes. The tilt angle of grating is an important parameter to determine refractive index distribution of fiber cross section and electric field overlap integral between different modes, and consequently governs mode conversion efficiency under certain mode incident. To realize relatively high conversion efficiency from LP01 to LP11 mode, and to maintain evident conversion from LP01 to LP02 and LP21 mode simultaneously, we choose the angle of 1.6 degree in the fabrication of the tilted FM-FBG.
Fig. 2 (a) Simulated transmission spectra of non-tiled, 0.8°-tilted and 1.6°-tilted FM-FBG with LP01 incident; schematic diagram of (b) non-tilted FM-FBG and (c) weakly tilted FM-FBG.
The relationships of the normalized coupling efficiency between LP01 and backward LP01, LP11, LP21 and LP02 mode against the tilt angles of weakly tilted FM-FBG are plotted in Fig. 3. The coupling between forward and backward fundamental modes decreases along with the increase of tilt angle. And the couplings between fundamental mode and higher order modes increase to maximum values at certain tilt angles. The simulation results provide a guidance of FM-FBGs fabrication as mode converters.
Fig. 3 The relationships of the normalized coupling efficiency between fundamental mode and backward modes against tilt angle of weakly tilted FM-FBG.
4. Experimental results of tilted FM-FBG based MC
The weakly tilted FM-FBG was fabricated using the phase mask technique by employing the 248-nm KrF excimer laser on hydrogen loading FMF. The inscription setup is shown in Fig. 4(a), and the grating plane is written with a certain tilt relatively to the longitudinal axis of the cylindrical focusing lens by adjusting the angle of the fiber through high-resolution actuators (Newport PZA12). As shown in Fig. 4(b), the coupling between core mode and cladding modes are rather small compared to the coupling between core modes, thus, the core-cladding coupling can be ignored.
Fig. 4 (a) Schematic diagram for inscription of non-tilted and weakly tilted FM-FBGs; (b) transmission spectra of EDFA ASE source (red line) and that with insertion of fabricated tilted FM-FBG.
Figure 5 shows the transmission spectra of our fabricated FM-FBG and the theoretical simulation of a 1.6°-tilted FM-FBG with a length of 10 mm, a maximum refractive index modulation of 2.4 × 10−4, a grating pitch of 531.06 nm, and the input light is launched with LP01 mode.
Fig. 5 Transmission spectra of the experimentally fabricated weakly tilted FM-FBG and theoretical result of a 1.6°-tilted FM-FBG with LP01 mode incident.
An amplified spontaneous emission (ASE) source is injected into the FMF with an SMF pigtail, which is spliced to the FMF with no angle and no lateral core-offset, therefore the light travelling in the FMF can be considered mainly fundamental mode. Thus the resonant dips in Fig. 5 represent the core to core mode coupling of LP01 to LP01, LP01 to LP11, LP01 to LP21 and LP01 to LP02 respectively. The slightly mismatch between the theoretical and experimental data can be ascribed to the difference of modes effective refractive index between the simulation and the practical value. The utilized FMF does not support LP02 mode very well, which largely decreases the coupling between LP01 to LP02 mode compared to the simulation result.
The experimental setup shown in Fig. 6 is used to observe the intensity patterns of the exporting modes reflected by the fabricated FM-FBG. A tunable laser diode (TLD) emitting a continuous wave (CW) beam with a SMF pigtail is connected to a fiber polarization beam splitter (PBS) and then a polarization controller (PC), to optimize the polarization state, to which the intensity distribution patterns of the converted modes are sensitive. The light is then launched into free space through a collimating lens. The reflection light from beam splitter (BS) goes into the FMF through another collimating lens. When the fundamental mode propagates through the FM-FBG, mode coupling happens, and the reflected mode propagates backward to the free space and is observed by a CCD through the BS.
Fig. 6 Experimental setup to observe the intensity distributions of exporting modes reflected by the weakly tilted FM-FBG with fundamental mode incident (the arrows show the light direction).
Different orders of coupled modes are obtained by tuning wavelength of TLD. Figure 7(a)-7(c) display the mode intensity distributions viewed on CCD when the TLD is tuned to be 1551.8 nm, 1551 nm, 1550.05 nm respectively, which correspond to wavelengths nearby the transmission dips. Figure 7(d) illustrates that the conversion efficiency is determined by the transmittivity of FBG. Since there is no coupling resonance at wavelength of 1552 nm, its output is set to be reference power. Power of the converted mode is assumed to be the difference between the practical and the reference power, due to that the reflective MC has a nearly 100% extinction ratio with the restriction of phase matching condition. Transmittivity of −23 dB at 1551 nm corresponds to a conversion efficiency of 99.5% from LP01 to LP11. The operation bandwidth of the MC is determined by the resonance bandwidth of the fabricated FM-FBG, which can be effectively broadened by inducing linear chirp into the grating period.
Fig. 7 Intensity patterns of the exporting (a) LP01; (b) LP11; (c) LP21 mode; (d) transmission optical spectra corresponding to wavelengths (transmission power: −16.1 dBm @1550.05 nm, −28.5 dBm @1551.0 nm, −14.1 dBm @1551.8 nm; reference power: −5.5 dBm @1552.0 nm).
5. 4-mode × 3-wavelength demultiplexer
From the results discussed above, different modal coupling efficiencies can be realized by adjusting the tilt angle of weakly tilted FM-FBGs, and the resonances of mode coupling primarily depend on the input wavelength. A 4-mode × 3-wavelength demultiplexer is proposed and the configuration is shown in Fig. 8. It consists of four groups of FM-FBGs with specific Λ, θ and Δnmax to convert the launched LP01, LP11, LP02, LP21 mode to counter-propagating LP01 modes respectively, and they are connected by few-mode optics circulators (FM-OCs). Each of the four output access fibers exports LP01 modes in three wavelengths.
Fig. 8 Schematic diagram of proposed 4-mode × 3-wavelength (4 modes in 3 wavelengths respectively) demultiplexer based on a series of FM-FBGs.
The design parameters of the FM-FBGs are obtained by realizing the maximum coupling efficiency between LP01, LP11, LP02, LP21 mode and backward fundamental mode for the 4 groups of FM-FBGs at different wavelengths (1548, 1550 and 1552 nm) at a certain physical realizable Δnmax according to the coupled mode theory. The calculated grating parameters are given in Table 1. It is shown that the demodulation efficiency of LP01, LP11, LP02 and LP21 mode are 99.97%, 99.96%, 99.96% and 99.95% respectively from the transmission spectra of FM-FBGs used in DEMUX as shown in Fig. 9.
Table 1. Parameters of FM-FBGs in the demultiplexer
Fig. 9 Transmission spectra of FM-FBGs in demultiplexer demodulating (a) LP01 mode; (b) LP11 mode; (c) LP02 mode; (d) LP21 mode (blue line for 1548 nm, black line for 1550 nm, red line for 1552 nm).
Each tilted FM-FBG can execute undesired mode conversion which may induce crosstalk. For example, residual LP01 modes of each wavelength are likely to be converted into LP11 mode by 1.4°-tilted FM-FBGs of group 2, thus, mode conversion with different incident modes are required to be considered. The transmission spectra of G12, G22, G32 and G42 (1550 nm) with incident mode of LP11, LP21 and LP02; LP01, LP21 and LP02; LP01, LP11 and LP21; LP01, LP11 and LP02 are shown in Fig. 10(a)-10(d) respectively. The green spots represent undesired mode conversions at working wavelengths, which may cause modal crosstalk. Table 2 gives data of mode conversion that take place in the DEMUX device.
Table 2. Mode coupling efficiency (dB) at working wavelengths
The conversion efficiency from LP01 to higher order modes, e.g. LP11, is as much as that from LP11 to LP01 in group 2 and it is similar in group 3 and 4. However, the residual signal power of LP01 modes become trivial after a reflectivity of over 34 dB in group 1. Moreover, the output pigtail of the DEMUX is single-mode fiber (SMF) which has a matched fundamental mode field of the FMF, and the higher order modes converted from LP01 undergoes a relatively large attenuation, then convert into fundamental mode. Therefore, due to the small input power and large loss, the modal crosstalk caused by FM-FBGs is negligible in this case.
6. Conclusions
In conclusion, we demonstrated a mode converter based on a 1.6°-tilted FM-FBG and observed the exporting modes in reflection. Mode conversion from LP01 to LP11 with conversion efficiency of 99.5% is realized by the MC. The relationships between mode conversion from fundamental mode to backward modes and physical parameters of FM-FBGs are also analyzed. The proposed 4-mode × 3-wavelength DEMUX based on a series of FM-FBGs has negligible modal cross talk induced by gratings. It provides a promising route for reflective mode dropping applications in mode and wavelength division multiplexing systems.
Acknowledgments
This work is supported by the National Natural Science Foundation of China under Grant No. 61377074 and 61404056.
References and links
1. D. Qian, M. Huang, E. Ip, Y. Huang, Y. Shao, J. Hu, and T. Wang, “101.7-Tb/s (370×294-Gb/s) PDM-128QAM-OFDM transmission over 3×55-km SSMF using pilot-based phase noise mitigation,” in Proc. OFC(Los Angeles, CA, USA2011), paper PDPB5.
2. D. J. Richardson, J. M. Fini, and L. E. Nelson, “Space-division multiplexing in optical fibres,” Nat. Photonics 7(5), 354–362 (2013). [CrossRef]
3. R. Ryf, S. Randel, A. H. Gnauck, C. Bolle, A. Sierra, S. Mumtaz, M. Esmaeelpour, E. C. Burrows, R. 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. 30(4), 521–531 (2012). [CrossRef]
4. A. Li, A. A. Amin, X. Chen, S. Chen, G. Gao, and W. Shieh, “Reception of dual-spatial-mode CO-OFDM signal over a two-mode fiber,” J. Lightwave Technol. 30(4), 634–640 (2012). [CrossRef]
5. E. Ip, N. Bai, Y. Huang, E. Mateo, F. Yaman, S. Bickham, H. Tam, C. Lu, M. Li, and S. Ten, “88x3x112-Gb/s WDM transmission over 50-km of three-mode fiber with inline multimode fiber amplifier,” in 37th European Conference and Exposition on Optical Communications, OSA Technical Digest (CD) (Optical Society of America,2011), paper Th.13.C.2. [CrossRef]
6. T. Morioka, Y. Awaji, R. Ryf, P. Winzer, D. Richardson, and F. Poletti, “Enhancing optical communications with brand new fibers,” IEEE Commun. Mag. 50(2), S31–S42 (2012). [CrossRef]
7. N. Riesen, J. D. Love, and J. W. Arkwright, “Few-mode elliptical-core fiber data transmission,” IEEE Photon. Technol. Lett. 24(5), 344–346 (2012). [CrossRef]
8. S. H. Murshid, A. Chakravarty, and R. Biswas, “Simultaneous transmission of two channels operating at the same wavelength in standard multimode fibers,” Lasers and Electro-Optics, 2008 and 2008 Conference on Quantum Electronics and Laser Science.CLEO/QELS Conference, 2008, pp. 1–2. [CrossRef]
9. T. Isoda, H. Terauchi, K. Tatsumi, A. Maruta, R. Maruyama, N. Kuwaki, S. Matsuo, and K. Kitayama, “Mode division multiplexed transmission through two-mode fiber using space-optics based mode multiplexer/demultiplexer,” in 2013 18th OptoElectronics and Communications Conference held jointly with 2013 International Conference on Photonics in Switching (Optical Society of America, 2013), paper TuS4_3.
10. 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 2×100 Gb/s, over 40 km-long prototype few-mode fiber, using LCOS-based programmable mode multiplexer and demultiplexer,” Opt. Express 19(17), 16593–16600 (2011). [CrossRef] [PubMed]
11. D. Sinefeld, C. R. Doerr, and D. M. Marom, “A photonic spectral processor employing two-dimensional WDM channel separation and a phase LCoS modulator,” Opt. Express 19(15), 14532–14541 (2011). [CrossRef] [PubMed]
12. B. A. Dorin and W. N. Ye, “Two-mode division multiplexing in a silicon-on-insulator ring resonator,” Opt. Express 22(4), 4547–4558 (2014). [CrossRef] [PubMed]
13. N. Hanzawa, K. Saitoh, T. Sakamoto, T. Matsui, K. Tsujikawa, M. Koshiba, and F. Yamamoto, “Two-mode PLC-based mode multi/demultiplexer for mode and wavelength division multiplexed transmission,” Opt. Express 21(22), 25752–25760 (2013). [CrossRef] [PubMed]
14. S. Yerolatsitis, I. Gris-Sánchez, and T. A. Birks, “Adiabatically-tapered fiber mode multiplexers,” Opt. Express 22(1), 608–617 (2014). [CrossRef] [PubMed]
15. J. Albert, L. Y. Shao, and C. Caucheteur, “Tilted fiber Bragg grating sensors,” Laser Photonics Rev. 7(1), 83–108 (2013). [CrossRef]
16. M. Li, L. Y. Shao, J. Albert, and J. P. Yao, “Continuously tunable photonic fractional temporal differentiator based on a tilted fiber Bragg grating,” IEEE Photon. Technol. Lett. 23(4), 314–316 (2011). [CrossRef]
17. M. Li, L. Y. Shao, J. Albert, and J. P. Yao, “Tilted fiber Bragg grating for chirped microwave waveform generation,” IEEE Photon. Technol. Lett. 23(5), 251–253 (2011). [CrossRef]
18. K. S. Lee and T. Erdogan, “Fiber mode coupling in transmissive and reflective tilted fiber gratings,” Appl. Opt. 39(9), 1394–1404 (2000). [CrossRef] [PubMed]
19. K. S. Lee and T. Erdogan, “Fiber mode conversion with tilted gratings in an optical fiber,” J. Opt. Soc. Am. A 18(5), 1176–1185 (2001). [CrossRef] [PubMed]
20. A. Li, X. Chen, A. Al Amin, and W. Shieh, “Mode converters and couplers for Few-mode transmission,” in 2012 IEEE Photonics Society Summer Topical Meeting Series, 2012, pp. 197–198.
21. A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. 9(9), 919–933 (1973). [CrossRef]
