Design of add-drop multiplexer based on multicore optical fibers for mode-division multiplexing Ming-Yang Chen1,* and Jun Zhou2 1
Department of Optical Engineering, School of Mechanical Engineering, Jiangsu University, Zhenjiang 212013, Jiangsu Province, China 2 Institute of Photonics, Ningbo University, Ningbo 315211, Zhejiang Province, China * [email protected]
Abstract: A multi-core fiber coupler is proposed to extract one of the modes in a few-mode optical fiber from a light beam, leaving the other modes undisturbed, and allowing a new signal to be retransmitted on that mode. Selective coupling of higher-order modes from a few-mode optical fiber can be realized by increasing the coupling length difference of the modes in the fiber using the multi-core configuration. Low cross-talk and wide bandwidth operation are realized owing to the fact that only one mode can be effectively coupled. ©2014 Optical Society of America OCIS codes: (060.2330) Fiber optics communications; (060.1810) Buffers, couplers, routers, switches, and multiplexers; (060.4230) Multiplexing.
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Received 20 Sep 2013; revised 13 Dec 2013; accepted 2 Jan 2014; published 15 Jan 2014 27 January 2014 | Vol. 22, No. 2 | DOI:10.1364/OE.22.001440 | OPTICS EXPRESS 1440
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1. Introduction Space multiplexing is considered a promising technology for increasing the transmission capacity, in addition to the already exploited wavelength division multiplexing (WDM) technology. This technology can be fall into one of two categories: space-division multiplexing using multi-core fiber [1–9] and mode-division multiplexing (MDM) [10–18]. Multi-core fiber consists of a number of single mode cores, and each core acts as different channel and carries a different signal. Recently, spatial-division multiplexing has been demonstrated in ultra-high-capacity transmissions without any added signal processing for demultiplexing spatial channels because of low inter-core crosstalk of multi-core fibers (MCFs) [8, 9]. MDM based on multiple-input multiple-output (MIMO) digital signal processing (DSP) techniques allow for increased fiber capacity even in the presence of significant mode crosstalk [10–15, 19]. Peoples are also exploring the techniques to separate out specific modes in the optical domain, which can be realized by use of phase plates or spatial light modulators with free-space optics [11, 20–24], fiber or waveguide coupling devices [16, 17, 21, 25, 26], volume holographic approaches [27], optical filtering of spatial samples taken from a multi-mode fiber aperture [13], and silicon photonics [28–30]. As a basis device for MDM application, mode converters with variant configurations have been proposed [26, 31–35]. Like add-drop multiplexing in wavelength division systems, the ability to drop and add a single space channel without having to convert all the channels in and out of electronics is very useful. Mode multiplexing based on optical demultiplexing technique has been proposed and demonstrated recently [36–38]. Such technique avoids the complex DSP techniques at the demultiplexing process. Another merit of the technique is that individual mode in the fewmode optical fiber(FMF) can be extracted and inserted independently. For such systems, the modes used for multiplexing should have low cross-talks. For example, Kubota et al. [36] used the LP01, LP11, and LP21 modes for multiplexing. Very recently, reconfigurable add-drop multiplexer for spatial modes implemented with Mach-Zehnder interferometers has been investigated [39]. The proposed multiplexer can drop and add any specific spatial mode while passing through all modes orthogonal to it, all without fundamental splitting loss. All-fiber devices are advantageous for the low splicing loss and matched mode fields with the transmission fiber. However, the technique that can selectively add and drop a mode from a group of modes propagating in the fiber based on all-fiber devices with low cross-talks is still a challenge. In this article, we propose an all-fiber add-drop multiplexer which can selectively add/drop a mode to/from the transmission fiber, whereas at the same time has a little influence on the other modes in the fiber. Multiplexing is owing to the selective coupling in multi-core optical fiber composed of two types of cores. The principles and spectral coupling characteristics will be investigated in detail. 2. Numerical investigation Modes in FMF can be extracted by simply applying an index-matched single-mode optical fiber. Just as the reviewer said, demultiplexing modes in a few-mode optical fiber can be realized by applying a mode coupler which uses only one neighboring core who's propagation constant is close to the mode that is intended to be demultiplexed. However, generally it’s difficult to design the core parameters so that the two modes in the cores can be indexmatched at wide wavelength range. Therefore, we have resort to the use of few-mode fiber cores such that the modes in the two cores are always index-matched. Our main principle is to design a fiber coupler with strong mode-dependent coupling characteristics. That is, if the
#198055 - $15.00 USD (C) 2014 OSA
Received 20 Sep 2013; revised 13 Dec 2013; accepted 2 Jan 2014; published 15 Jan 2014 27 January 2014 | Vol. 22, No. 2 | DOI:10.1364/OE.22.001440 | OPTICS EXPRESS 1442
mode we wish to drop from a few-mode optical fiber has considerably shorter coupling length than all the other modes in the fiber, then the mode can be coupled to the cross-core and selectively coupled out. We will start from a simple two-core optical fiber, the configuration is shown in Fig. 1(a). The index-difference between the core and the cladding is set as 0.015. The core diameter is ds = 11 μm, and the center-to-center distance between the two cores is dcc = 15 μm. The normalized frequency V of the single-core fiber at the wavelength of 1.55 μm is 4.66, which means the fiber core can support the propagation of the LP01, LP11, LP21 and LP02 modes. Assume the mode we wish to extract is the LP11 mode, which has effective index lower than the LP01 mode and higher than the LP21 and LP02 modes. A full-vectorial finite-difference beam propagation method(BPM) [40] with transparent boundary conditions [41] is applied to investigate the coupling characteristics of the fiber. Assuming light is launched into the left core of the fiber, then the power transferring between the two cores for different modes in the fiber is shown in Fig. 1(b). We can see the coupling length of the fundamental mode (LP01 mode) are longest, whereas the LP02 mode has shortest coupling length. This is because that the higher-order mode has more field extending to the cladding, which enhance the coupling between the modes in the two cores. In this situation, the separation of the LP11 mode based on this configuration is difficult.
Fig. 1. Configuration (a) and normalized power transferring (b) for the two-core optical fiber.
Enhanced coupling can be realized by applying resonant coupling mechanism [42–44], such idea has been applied for polarization splitting [42], narrow band-pass filter [43], and resonant refractive index sensors [44]. It's well known that the coupling length increase with the increase of the distance between the cores. In this way, we will firstly increase the distance between the two cores and then insert an assistant core to reduce the coupling length of the LP11 mode. In this way, it's possible that the LP11 mode will have shorter coupling length than the other modes in the fiber. The center-to-center distance between the side core and the assistant core is set as dsa = 12 μm. The configuration is shown in Fig. 2(a). Firstly, we should determine the parameters of the assistant core, the fundamental mode of which should match with the LP11 mode of the side cores. The assistant core should be single-mode guided, so that the assistant core will only couple with one specified mode of the side cores. The core diameter and the index difference between the assistant core and the cladding are set as da = 3.9 μm and 0.021, respectively. Figure 2(b) shows the effective indexes of the assistant core and the side core. The index difference between the LP01 mode of the assistant core and the LP11 mode of the side cores can be kept at low level. In particular, the two curves meet at the wavelength of 1.585 μm, which means strong coupling can occur at the wavelength. In addition, there is always large index difference between the LP01 mode of the assistant core and the other modes in the side cores. Figure 3(a) and 3(b) shows the normalized power variation of the LP11 mode along the propagation distance at the wavelength of 1.55 and 1.585 μm, respectively. The matched coupling at the wavelength of 1.585 μm shows periodic coupling between the two side cores, similar to a conventional twocore fiber coupler. The exception is that the resident energy in the left core shows a flat range
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Received 20 Sep 2013; revised 13 Dec 2013; accepted 2 Jan 2014; published 15 Jan 2014 27 January 2014 | Vol. 22, No. 2 | DOI:10.1364/OE.22.001440 | OPTICS EXPRESS 1443
when the energy in the right core reach maximum. This phenomenon is owing to the fact that the assistant core acts as a bridge for the mode coupling of the two side cores, which extends the low energy range of the left core. More importantly, the introduction of the assistant core can effectively reduce the coupling length. In fact, the coupling length of the LP11 mode for the three-core configuration is 7.5 mm, whereas the elimination of the assistant core will lead to a long coupling length of 1710 mm. At the wavelength of 1.55 μm, the mode coupling shows quite different feature. Although the curves still show periodic like coupling, more complex energy transferring happens. This is owing to the fact that the LP11 mode in the side cores does not match with the LP01 mode of the assistant mode. Apparently, such feature will influence the operating bandwidth of the multiplexer.
Fig. 2. Configuration (a) and normalized power transferring (b) for the three-core optical fiber.
Fig. 3. Normalized power transferring of the LP11 mode for the three-core optical fiber at the wavelength of 1.55 μm (a) and 1.585 μm (b).
From coupled mode theory, we know that the coupling length and maximum power transferring are determined by the coupling coefficients and the phase-mismatch constant [45]. Generally, phase-match in a wide operational wavelength range for two waveguides with different structural parameters is difficult, however, increasing the coupling coefficients by reducing the core distance can also reduce the influence of phase-mismatch on the coupling characteristics [45]. This can be seem from Fig. 4, where the power variation of the LP11 mode in the three-core optical fiber with dsa = 9, and 11 μm are plotted. The power variation show periodic variation of power with modulated amplitude. From the figure, we can see strong coupling can still be achieved at the first coupling period.
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Received 20 Sep 2013; revised 13 Dec 2013; accepted 2 Jan 2014; published 15 Jan 2014 27 January 2014 | Vol. 22, No. 2 | DOI:10.1364/OE.22.001440 | OPTICS EXPRESS 1444
Fig. 4. Normalized power transferring of the LP11 mode for the three-core optical fiber with dsa = 9μm (a), and dsa = 11 μm (b) at the wavelength of 1.55 μm.
As expected, the introduction of the assistant core do not have strong effects on the coupling curves of the other modes in the side cores. Figure 5 shows the power variation of the LP01, LP02 and LP21 modes in the three-core optical fiber with dsa = 12 μm. As a comparison, the coupling characteristics of the modes in the two side cores without the assistant core is also plotted. We can see the coupling lengths of the three-core optical fiber are shorter than the fiber without the assistant core.
Fig. 5. Normalized power transferring for the LP01 mode (a), LP21 mode (b), and LP02 mode (c) at the wavelength of 1.55 μm.
As shown in Fig. 3(a), the coupling length of the three-core optical fiber at the wavelength of 1.585 μm is 7.5 mm. If we set the fiber length to be the coupling length of the LP11 mode, the launching of the light to the left core will lead to the coupling of the LP11 mode to the right core, whereas the majority of the other modes will still stay in the left core. In this way, the LP11 mode can be selectively dropped. However, mode coupling will still happen for the LP02 and LP21 modes, which will increase the insertion loss of the modes and also the crosstalk will increase. Therefore, further optimizing the configuration should be considered. In one way, we wish reduce the center-to-center distance between the side core and the assistant core to increase the operational wavelength range of the LP11 mode. In another way,
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Received 20 Sep 2013; revised 13 Dec 2013; accepted 2 Jan 2014; published 15 Jan 2014 27 January 2014 | Vol. 22, No. 2 | DOI:10.1364/OE.22.001440 | OPTICS EXPRESS 1445
we wish increase the center-to-center distance between the side cores to increase the coupling lengths of the other modes. Although it seems contradictory, the two conditions can be met by introducing more assistant cores. As shown in Fig. 6, another two assistant cores have been included. The center-to-center distance between the adjacent assistant cores is set as daa = 7.5 μm, whereas the center-to-center distance between the side core and the adjacent assistant core is set as dsa. Different dsa will lead to different coupling characteristics for the LP11 mode, this can be seen from Fig. 7, where the power variation of the LP11 mode in the five-core optical fiber with different dsa is plotted. In particular, the configuration with dsa = 10.5 μm shows quite regular periodic variation of the power in the two side cores. In order to understand the different coupling characteristics of the five-core optical fiber with different dsa, we have calculated the coupling lengths of two different optical fibers. One is a two-core optical fiber composed of a side core and the assistant core with the center-to-center distance setting as dsa, another is a two-core optical fiber composed of two assistant cores with the center-to-center distance daa = 7.5 μm. The fundamental mode coupling length of the fiber with two assistant cores is 2.03 mm at the wavelength of 1.55 μm. The coupling lengths of the first type two-core fiber for the coupling of the LP11 mode in the side core and the LP01 mode of the assistant core at dsa = 9.5, 10.5, and 11.5 μm are 1.09, 2.14, and 4.1 mm, respectively. That is, the first fiber with dsa = 10.5 μm shows lowest coupling length difference with the second fiber. We can also understand the phenomenon in another way. The appropriate choice of the dsa value makes the five core fiber works like a configuration composed of the same cores with uniform center-to-center distance, which effectively enhances the coupling effects.
Fig. 6. Configuration of the five-core optical fiber.
#198055 - $15.00 USD (C) 2014 OSA
Received 20 Sep 2013; revised 13 Dec 2013; accepted 2 Jan 2014; published 15 Jan 2014 27 January 2014 | Vol. 22, No. 2 | DOI:10.1364/OE.22.001440 | OPTICS EXPRESS 1446
Fig. 7. Normalized power transferring of the LP11 mode for the five-core optical fiber with dsa = 9.5 μm (a), dsa = 10.5 μm (a), and dsa = 11.5 μm (c) at the wavelength of 1.55 μm.
As shown in Fig. 7(b), the LP11 mode will be coupled to the right core with little energy left in the left core if the fiber length is set as 4.5 mm, the coupling length of the mode. In addition, little energy of the other modes will be coupled to the right core. Figure 8 shows the power variation of the other modes in the two side cores for the five-core optical fiber with dsa = 10.5 μm at the wavelength of 1.55 μm. The power in the left core shows a modulated variation which is caused by the mismatched coupling [45]. The large modulated amplitude for the LP21 and LP02 modes are owing to the fact that the two modes have more mode fields extending to the cladding, which increases the coupling coefficient. But still, most of the energy stayed in the left core. The main trend of the power in the right core is increasing with the increase of the propagation distance, which is also modulated for the same reason. At a short distance, the coupling energy of the LP01, LP21 and LP02 modes is always small. Therefore, the LP11 mode can be dropped from the other modes with low cross-talk.
Fig. 8. Normalized power transferring for the five-core optical fiber with dsa = 10.5 μm (a) at the wavelength of 1.55 μm.
Figure 9 shows the spectral coupling characteristics of the proposed five-core fiber coupler. We can see from Fig. 9(a) that the LP11 mode can be coupled to the right core with transmission loss lower than 1 dB at a wavelength range from 1.525 to 1.595 μm, which
#198055 - $15.00 USD (C) 2014 OSA
Received 20 Sep 2013; revised 13 Dec 2013; accepted 2 Jan 2014; published 15 Jan 2014 27 January 2014 | Vol. 22, No. 2 | DOI:10.1364/OE.22.001440 | OPTICS EXPRESS 1447
corresponding to a 70-nm bandwidth. The polarization-dependent losses are lower than 0.12 dB in the wavelength range. The wavelength range is denoted as the operating wavelength range. Simultaneously, the other modes can still stay at the left core with low loss. In fact, as shown in Fig. 9(b), the losses for the LP01, LP21, and LP02 modes at the operating wavelength range are lower than −0.0015, −0.15, and −0.23 dB, respectively. The modes show polarization-dependent losses lower than 0.00015, 0.014, and 0.04 dB for the LP01, LP21, and LP02 modes, respectively. The low losses are owing to the weak coupling between the modes in the side core and the LP01 mode in the assistant core. More importantly, low cross-talk can be achieved, this can be seen from Fig. 10. The cross-talk, that is, the LP11 mode output from the left core is also lower than −17 dB. For the wavelength range from 1.534 to 1.595 μm, the LP11 mode stay at the left core can be lower than −20 dB. The main reason for the low crosstalk is that the assistant cores work as bridge for the two side cores, that is, the energy will firstly coupled to the assistant core, then coupled to the side core. As a result, there is a period that the left core has low LP11 mode field, which lead to low cross-talk. We can also see the cross-talk induced by the coupling of the LP01, LP21, and LP02 modes from the left core to the right core is low. In fact, the normalized power transferring to the right core for the LP01, LP21, and LP02 modes at the operating wavelength range are lower than −75, −36, and −31 dB, respectively. We can easily understand that the configuration can be readily applied to add the mode to the few-mode optical fiber. The only difference is the LP11 mode would be launched from the right core. At this stage, the results shown in Fig. 9(a) and Fig. 9(b) would be the output power of the LP11 mode from the left core and right core, respectively. The cross-talk will not be a problem. Therefore, the operating wavelength range can be extended as long as higher losses are allowed.
Fig. 9. Spectral coupling characteristics at the right core for the LP11 mode (a) and the left core (b) for the five-core optical fiber.
Fig. 10. Spectral coupling characteristics at the left core for the LP11 mode (a) and the right core (b) for the five-core optical fiber.
#198055 - $15.00 USD (C) 2014 OSA
Received 20 Sep 2013; revised 13 Dec 2013; accepted 2 Jan 2014; published 15 Jan 2014 27 January 2014 | Vol. 22, No. 2 | DOI:10.1364/OE.22.001440 | OPTICS EXPRESS 1448
The selective coupling of the other modes can be achieved by simply adjusting the parameters of the assistant cores. For example, if we wish to selectively drop the LP21 mode, then the core diameter and index difference of the assistant cores can be set as 2.5 μm and 0.023, respectively. In order to reduce the coupling of the other modes, the center-to-center distance between the assistant cores is set as 8.8 μm. The corresponding center-to-center distance between the side core and the assistant core is set as 11.5 μm. The coupling length of the LP21 mode is 5.2 mm. Figure 11 shows the spectral coupling characteristics of the proposed five-core fiber coupler with a fiber length of 5.2 mm. It's found the LP21 mode can be coupled to the right core with transmission loss lower than 1 dB at a wavelength range from 1.523 to 1.564 μm, which corresponding to a 41-nm bandwidth. Simultaneously, the other modes can still stay at the left core with low loss. In this situation, the LP01 and LP11 modes in the left core have little coupling with the other cores, whereas the coupling loss for the LP02 mode is lower than −0.44 dB. Such coupling characteristics are owing to the fact that there are low index difference between the effective indexes of the LP21 and LP02 modes for the side cores, whereas the LP21 mode has large index difference with the LP01 and LP11 modes. As shown in Fig. 12, the cross-talk at the right core is higher owing to the strong coupling of the LP02 mode, but still the coupling power is lower than −20 dB for the LP02 mode. The cross-talk at the left core can be lower than −19 dB at the operating wavelength range.
Fig. 11. Spectral coupling characteristics at the right core for the LP21 mode (a) and the left core (b) for the five-core optical fiber.
Fig. 12. Spectral coupling characteristics at the left core for the LP21 mode (a) and the right core (b) for the five-core optical fiber.
For the above proposed five-core optical fiber, mode converters should be applied to convert the higher-order mode to the fundamental mode. Mode converter based long period grating (LPG) configuration would be a good choice [46]. The conversion efficiency of infiber LPG can be higher than 99% coupling efficiency over bandwidths as large as 94 nm, and peak efficiencies can be >99.9%. Alternatively, the output fiber core can be replaced by another assistant core. The cross-section of the fiber is shown in Fig. 13. The fiber, which is
#198055 - $15.00 USD (C) 2014 OSA
Received 20 Sep 2013; revised 13 Dec 2013; accepted 2 Jan 2014; published 15 Jan 2014 27 January 2014 | Vol. 22, No. 2 | DOI:10.1364/OE.22.001440 | OPTICS EXPRESS 1449
composed of one few-mode core and four assistant cores with single-mode operation, is denoted as Fiber A. The fiber parameters are set as the same as the five-core optical fiber for LP11 mode separation. The distance between the left core and the adjacent assistant core is set as dsa = 10.5 μm and the the center-to-center distance between the assistant cores is daa = 7.5 μm. The fiber length is also set to be 4.5 mm. As a comparison, the results of the five-core optical fiber with two side cores, which is denoted as Fiber T, is also presented. Figure 14-15 shows the spectral coupling characteristics of the five-core fiber couplers. We can see, compared with the five-core optical fiber with two side-cores, the five-core optical fiber with four assistant-cores shows higher loss for the LP11 mode, whereas the cross-talks at both the left and right side-cores are higher.
Fig. 13. Configuration of the five-core optical fiber with four assistant cores.
Fig. 14. Spectral coupling characteristics at the right core for the LP11 mode (a) and the left core (b) for the five-core optical fiber.
Fig. 15. Spectral coupling characteristics at the left core for the LP11 mode (a) and the right core (b) for the five-core optical fiber.
#198055 - $15.00 USD (C) 2014 OSA
Received 20 Sep 2013; revised 13 Dec 2013; accepted 2 Jan 2014; published 15 Jan 2014 27 January 2014 | Vol. 22, No. 2 | DOI:10.1364/OE.22.001440 | OPTICS EXPRESS 1450
Technically, the four modes in LP11 groups can be divided into the LP11a and LP11b modes by using the proposed add-drop device, which is based on the fact that the LP11a mode will have strong coupling between the two few-mode optical fibers, whereas the LP11b modes in the FMFs have weak coupling. In fact, numerical results show that the launching of the LP11b mode from one of the FMFs in the add-drop device will lead to the output of LP11b mode power lower than −60 dB at another FMF. In this situation, only the LP11a mode is applied for multiplexing. Similar condition hold for the LP21 mode. It’s also possible to apply both of the modes in the LP11 or LP21 mode group for mode multiplexing. At this situation, the separation of the LP11a or LP11b mode can be achieved by considering the mode orientation. Similar condition have been investigated by Nielson et al [5]. 4. Conclusion In conclusion, an all-fiber based add-drop multiplexer for mode-division multiplexing application is proposed. Selective coupling for the mode in a few-mode optical fiber is achieved by applying multiply assistant cores to selectively enhance the mode coupling between the two side cores. The assistance cores work as a bridge for the coupling of the selected mode. The long distance between the two side cores can effectively reduce the coupling of the other modes in the fiber. As a result, wide bandwidth and low cross-talk can be achieved. The proposed technique can also be achieved by applying the silica waveguide configuration, the design and experimental demonstration will be the task of our future work. Acknowledgments This work is supported by the Qing Lan Project of Jiangsu Province and the National Natural Science Foundation of China (NNSFC) (Grant No. 61275153, 61320106014).
#198055 - $15.00 USD (C) 2014 OSA
Received 20 Sep 2013; revised 13 Dec 2013; accepted 2 Jan 2014; published 15 Jan 2014 27 January 2014 | Vol. 22, No. 2 | DOI:10.1364/OE.22.001440 | OPTICS EXPRESS 1451
Department of Optical Engineering, School of Mechanical Engineering, Jiangsu University, Zhenjiang 212013, Jiangsu Province, China 2 Institute of Photonics, Ningbo University, Ningbo 315211, Zhejiang Province, China * [email protected]
Abstract: A multi-core fiber coupler is proposed to extract one of the modes in a few-mode optical fiber from a light beam, leaving the other modes undisturbed, and allowing a new signal to be retransmitted on that mode. Selective coupling of higher-order modes from a few-mode optical fiber can be realized by increasing the coupling length difference of the modes in the fiber using the multi-core configuration. Low cross-talk and wide bandwidth operation are realized owing to the fact that only one mode can be effectively coupled. ©2014 Optical Society of America OCIS codes: (060.2330) Fiber optics communications; (060.1810) Buffers, couplers, routers, switches, and multiplexers; (060.4230) Multiplexing.
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#198055 - $15.00 USD (C) 2014 OSA
Received 20 Sep 2013; revised 13 Dec 2013; accepted 2 Jan 2014; published 15 Jan 2014 27 January 2014 | Vol. 22, No. 2 | DOI:10.1364/OE.22.001440 | OPTICS EXPRESS 1440
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#198055 - $15.00 USD (C) 2014 OSA
Received 20 Sep 2013; revised 13 Dec 2013; accepted 2 Jan 2014; published 15 Jan 2014 27 January 2014 | Vol. 22, No. 2 | DOI:10.1364/OE.22.001440 | OPTICS EXPRESS 1441
44. D. K. C. Wu, B. T. Kuhlmey, and B. J. Eggleton, “Ultrasensitive photonic crystal fiber refractive index sensor,” Opt. Lett. 34(3), 322–324 (2009). 45. W.-P. Huang, “Coupled-mode theory for optical waveguides: an overview,” J. Opt. Soc. Am. A 11(3), 963–983 (1994). 46. S. Ramachandran, J. M. Fini, M. Mermelstein, J. W. Nicholson, S. Ghalmi, and M. F. Yan, “Ultra-large effective-area, higher-order mode fibers: a new strategy for high-power lasers,” Laser Photon. Rev. 2(6), 429– 448 (2008).
1. Introduction Space multiplexing is considered a promising technology for increasing the transmission capacity, in addition to the already exploited wavelength division multiplexing (WDM) technology. This technology can be fall into one of two categories: space-division multiplexing using multi-core fiber [1–9] and mode-division multiplexing (MDM) [10–18]. Multi-core fiber consists of a number of single mode cores, and each core acts as different channel and carries a different signal. Recently, spatial-division multiplexing has been demonstrated in ultra-high-capacity transmissions without any added signal processing for demultiplexing spatial channels because of low inter-core crosstalk of multi-core fibers (MCFs) [8, 9]. MDM based on multiple-input multiple-output (MIMO) digital signal processing (DSP) techniques allow for increased fiber capacity even in the presence of significant mode crosstalk [10–15, 19]. Peoples are also exploring the techniques to separate out specific modes in the optical domain, which can be realized by use of phase plates or spatial light modulators with free-space optics [11, 20–24], fiber or waveguide coupling devices [16, 17, 21, 25, 26], volume holographic approaches [27], optical filtering of spatial samples taken from a multi-mode fiber aperture [13], and silicon photonics [28–30]. As a basis device for MDM application, mode converters with variant configurations have been proposed [26, 31–35]. Like add-drop multiplexing in wavelength division systems, the ability to drop and add a single space channel without having to convert all the channels in and out of electronics is very useful. Mode multiplexing based on optical demultiplexing technique has been proposed and demonstrated recently [36–38]. Such technique avoids the complex DSP techniques at the demultiplexing process. Another merit of the technique is that individual mode in the fewmode optical fiber(FMF) can be extracted and inserted independently. For such systems, the modes used for multiplexing should have low cross-talks. For example, Kubota et al. [36] used the LP01, LP11, and LP21 modes for multiplexing. Very recently, reconfigurable add-drop multiplexer for spatial modes implemented with Mach-Zehnder interferometers has been investigated [39]. The proposed multiplexer can drop and add any specific spatial mode while passing through all modes orthogonal to it, all without fundamental splitting loss. All-fiber devices are advantageous for the low splicing loss and matched mode fields with the transmission fiber. However, the technique that can selectively add and drop a mode from a group of modes propagating in the fiber based on all-fiber devices with low cross-talks is still a challenge. In this article, we propose an all-fiber add-drop multiplexer which can selectively add/drop a mode to/from the transmission fiber, whereas at the same time has a little influence on the other modes in the fiber. Multiplexing is owing to the selective coupling in multi-core optical fiber composed of two types of cores. The principles and spectral coupling characteristics will be investigated in detail. 2. Numerical investigation Modes in FMF can be extracted by simply applying an index-matched single-mode optical fiber. Just as the reviewer said, demultiplexing modes in a few-mode optical fiber can be realized by applying a mode coupler which uses only one neighboring core who's propagation constant is close to the mode that is intended to be demultiplexed. However, generally it’s difficult to design the core parameters so that the two modes in the cores can be indexmatched at wide wavelength range. Therefore, we have resort to the use of few-mode fiber cores such that the modes in the two cores are always index-matched. Our main principle is to design a fiber coupler with strong mode-dependent coupling characteristics. That is, if the
#198055 - $15.00 USD (C) 2014 OSA
Received 20 Sep 2013; revised 13 Dec 2013; accepted 2 Jan 2014; published 15 Jan 2014 27 January 2014 | Vol. 22, No. 2 | DOI:10.1364/OE.22.001440 | OPTICS EXPRESS 1442
mode we wish to drop from a few-mode optical fiber has considerably shorter coupling length than all the other modes in the fiber, then the mode can be coupled to the cross-core and selectively coupled out. We will start from a simple two-core optical fiber, the configuration is shown in Fig. 1(a). The index-difference between the core and the cladding is set as 0.015. The core diameter is ds = 11 μm, and the center-to-center distance between the two cores is dcc = 15 μm. The normalized frequency V of the single-core fiber at the wavelength of 1.55 μm is 4.66, which means the fiber core can support the propagation of the LP01, LP11, LP21 and LP02 modes. Assume the mode we wish to extract is the LP11 mode, which has effective index lower than the LP01 mode and higher than the LP21 and LP02 modes. A full-vectorial finite-difference beam propagation method(BPM) [40] with transparent boundary conditions [41] is applied to investigate the coupling characteristics of the fiber. Assuming light is launched into the left core of the fiber, then the power transferring between the two cores for different modes in the fiber is shown in Fig. 1(b). We can see the coupling length of the fundamental mode (LP01 mode) are longest, whereas the LP02 mode has shortest coupling length. This is because that the higher-order mode has more field extending to the cladding, which enhance the coupling between the modes in the two cores. In this situation, the separation of the LP11 mode based on this configuration is difficult.
Fig. 1. Configuration (a) and normalized power transferring (b) for the two-core optical fiber.
Enhanced coupling can be realized by applying resonant coupling mechanism [42–44], such idea has been applied for polarization splitting [42], narrow band-pass filter [43], and resonant refractive index sensors [44]. It's well known that the coupling length increase with the increase of the distance between the cores. In this way, we will firstly increase the distance between the two cores and then insert an assistant core to reduce the coupling length of the LP11 mode. In this way, it's possible that the LP11 mode will have shorter coupling length than the other modes in the fiber. The center-to-center distance between the side core and the assistant core is set as dsa = 12 μm. The configuration is shown in Fig. 2(a). Firstly, we should determine the parameters of the assistant core, the fundamental mode of which should match with the LP11 mode of the side cores. The assistant core should be single-mode guided, so that the assistant core will only couple with one specified mode of the side cores. The core diameter and the index difference between the assistant core and the cladding are set as da = 3.9 μm and 0.021, respectively. Figure 2(b) shows the effective indexes of the assistant core and the side core. The index difference between the LP01 mode of the assistant core and the LP11 mode of the side cores can be kept at low level. In particular, the two curves meet at the wavelength of 1.585 μm, which means strong coupling can occur at the wavelength. In addition, there is always large index difference between the LP01 mode of the assistant core and the other modes in the side cores. Figure 3(a) and 3(b) shows the normalized power variation of the LP11 mode along the propagation distance at the wavelength of 1.55 and 1.585 μm, respectively. The matched coupling at the wavelength of 1.585 μm shows periodic coupling between the two side cores, similar to a conventional twocore fiber coupler. The exception is that the resident energy in the left core shows a flat range
#198055 - $15.00 USD (C) 2014 OSA
Received 20 Sep 2013; revised 13 Dec 2013; accepted 2 Jan 2014; published 15 Jan 2014 27 January 2014 | Vol. 22, No. 2 | DOI:10.1364/OE.22.001440 | OPTICS EXPRESS 1443
when the energy in the right core reach maximum. This phenomenon is owing to the fact that the assistant core acts as a bridge for the mode coupling of the two side cores, which extends the low energy range of the left core. More importantly, the introduction of the assistant core can effectively reduce the coupling length. In fact, the coupling length of the LP11 mode for the three-core configuration is 7.5 mm, whereas the elimination of the assistant core will lead to a long coupling length of 1710 mm. At the wavelength of 1.55 μm, the mode coupling shows quite different feature. Although the curves still show periodic like coupling, more complex energy transferring happens. This is owing to the fact that the LP11 mode in the side cores does not match with the LP01 mode of the assistant mode. Apparently, such feature will influence the operating bandwidth of the multiplexer.
Fig. 2. Configuration (a) and normalized power transferring (b) for the three-core optical fiber.
Fig. 3. Normalized power transferring of the LP11 mode for the three-core optical fiber at the wavelength of 1.55 μm (a) and 1.585 μm (b).
From coupled mode theory, we know that the coupling length and maximum power transferring are determined by the coupling coefficients and the phase-mismatch constant [45]. Generally, phase-match in a wide operational wavelength range for two waveguides with different structural parameters is difficult, however, increasing the coupling coefficients by reducing the core distance can also reduce the influence of phase-mismatch on the coupling characteristics [45]. This can be seem from Fig. 4, where the power variation of the LP11 mode in the three-core optical fiber with dsa = 9, and 11 μm are plotted. The power variation show periodic variation of power with modulated amplitude. From the figure, we can see strong coupling can still be achieved at the first coupling period.
#198055 - $15.00 USD (C) 2014 OSA
Received 20 Sep 2013; revised 13 Dec 2013; accepted 2 Jan 2014; published 15 Jan 2014 27 January 2014 | Vol. 22, No. 2 | DOI:10.1364/OE.22.001440 | OPTICS EXPRESS 1444
Fig. 4. Normalized power transferring of the LP11 mode for the three-core optical fiber with dsa = 9μm (a), and dsa = 11 μm (b) at the wavelength of 1.55 μm.
As expected, the introduction of the assistant core do not have strong effects on the coupling curves of the other modes in the side cores. Figure 5 shows the power variation of the LP01, LP02 and LP21 modes in the three-core optical fiber with dsa = 12 μm. As a comparison, the coupling characteristics of the modes in the two side cores without the assistant core is also plotted. We can see the coupling lengths of the three-core optical fiber are shorter than the fiber without the assistant core.
Fig. 5. Normalized power transferring for the LP01 mode (a), LP21 mode (b), and LP02 mode (c) at the wavelength of 1.55 μm.
As shown in Fig. 3(a), the coupling length of the three-core optical fiber at the wavelength of 1.585 μm is 7.5 mm. If we set the fiber length to be the coupling length of the LP11 mode, the launching of the light to the left core will lead to the coupling of the LP11 mode to the right core, whereas the majority of the other modes will still stay in the left core. In this way, the LP11 mode can be selectively dropped. However, mode coupling will still happen for the LP02 and LP21 modes, which will increase the insertion loss of the modes and also the crosstalk will increase. Therefore, further optimizing the configuration should be considered. In one way, we wish reduce the center-to-center distance between the side core and the assistant core to increase the operational wavelength range of the LP11 mode. In another way,
#198055 - $15.00 USD (C) 2014 OSA
Received 20 Sep 2013; revised 13 Dec 2013; accepted 2 Jan 2014; published 15 Jan 2014 27 January 2014 | Vol. 22, No. 2 | DOI:10.1364/OE.22.001440 | OPTICS EXPRESS 1445
we wish increase the center-to-center distance between the side cores to increase the coupling lengths of the other modes. Although it seems contradictory, the two conditions can be met by introducing more assistant cores. As shown in Fig. 6, another two assistant cores have been included. The center-to-center distance between the adjacent assistant cores is set as daa = 7.5 μm, whereas the center-to-center distance between the side core and the adjacent assistant core is set as dsa. Different dsa will lead to different coupling characteristics for the LP11 mode, this can be seen from Fig. 7, where the power variation of the LP11 mode in the five-core optical fiber with different dsa is plotted. In particular, the configuration with dsa = 10.5 μm shows quite regular periodic variation of the power in the two side cores. In order to understand the different coupling characteristics of the five-core optical fiber with different dsa, we have calculated the coupling lengths of two different optical fibers. One is a two-core optical fiber composed of a side core and the assistant core with the center-to-center distance setting as dsa, another is a two-core optical fiber composed of two assistant cores with the center-to-center distance daa = 7.5 μm. The fundamental mode coupling length of the fiber with two assistant cores is 2.03 mm at the wavelength of 1.55 μm. The coupling lengths of the first type two-core fiber for the coupling of the LP11 mode in the side core and the LP01 mode of the assistant core at dsa = 9.5, 10.5, and 11.5 μm are 1.09, 2.14, and 4.1 mm, respectively. That is, the first fiber with dsa = 10.5 μm shows lowest coupling length difference with the second fiber. We can also understand the phenomenon in another way. The appropriate choice of the dsa value makes the five core fiber works like a configuration composed of the same cores with uniform center-to-center distance, which effectively enhances the coupling effects.
Fig. 6. Configuration of the five-core optical fiber.
#198055 - $15.00 USD (C) 2014 OSA
Received 20 Sep 2013; revised 13 Dec 2013; accepted 2 Jan 2014; published 15 Jan 2014 27 January 2014 | Vol. 22, No. 2 | DOI:10.1364/OE.22.001440 | OPTICS EXPRESS 1446
Fig. 7. Normalized power transferring of the LP11 mode for the five-core optical fiber with dsa = 9.5 μm (a), dsa = 10.5 μm (a), and dsa = 11.5 μm (c) at the wavelength of 1.55 μm.
As shown in Fig. 7(b), the LP11 mode will be coupled to the right core with little energy left in the left core if the fiber length is set as 4.5 mm, the coupling length of the mode. In addition, little energy of the other modes will be coupled to the right core. Figure 8 shows the power variation of the other modes in the two side cores for the five-core optical fiber with dsa = 10.5 μm at the wavelength of 1.55 μm. The power in the left core shows a modulated variation which is caused by the mismatched coupling [45]. The large modulated amplitude for the LP21 and LP02 modes are owing to the fact that the two modes have more mode fields extending to the cladding, which increases the coupling coefficient. But still, most of the energy stayed in the left core. The main trend of the power in the right core is increasing with the increase of the propagation distance, which is also modulated for the same reason. At a short distance, the coupling energy of the LP01, LP21 and LP02 modes is always small. Therefore, the LP11 mode can be dropped from the other modes with low cross-talk.
Fig. 8. Normalized power transferring for the five-core optical fiber with dsa = 10.5 μm (a) at the wavelength of 1.55 μm.
Figure 9 shows the spectral coupling characteristics of the proposed five-core fiber coupler. We can see from Fig. 9(a) that the LP11 mode can be coupled to the right core with transmission loss lower than 1 dB at a wavelength range from 1.525 to 1.595 μm, which
#198055 - $15.00 USD (C) 2014 OSA
Received 20 Sep 2013; revised 13 Dec 2013; accepted 2 Jan 2014; published 15 Jan 2014 27 January 2014 | Vol. 22, No. 2 | DOI:10.1364/OE.22.001440 | OPTICS EXPRESS 1447
corresponding to a 70-nm bandwidth. The polarization-dependent losses are lower than 0.12 dB in the wavelength range. The wavelength range is denoted as the operating wavelength range. Simultaneously, the other modes can still stay at the left core with low loss. In fact, as shown in Fig. 9(b), the losses for the LP01, LP21, and LP02 modes at the operating wavelength range are lower than −0.0015, −0.15, and −0.23 dB, respectively. The modes show polarization-dependent losses lower than 0.00015, 0.014, and 0.04 dB for the LP01, LP21, and LP02 modes, respectively. The low losses are owing to the weak coupling between the modes in the side core and the LP01 mode in the assistant core. More importantly, low cross-talk can be achieved, this can be seen from Fig. 10. The cross-talk, that is, the LP11 mode output from the left core is also lower than −17 dB. For the wavelength range from 1.534 to 1.595 μm, the LP11 mode stay at the left core can be lower than −20 dB. The main reason for the low crosstalk is that the assistant cores work as bridge for the two side cores, that is, the energy will firstly coupled to the assistant core, then coupled to the side core. As a result, there is a period that the left core has low LP11 mode field, which lead to low cross-talk. We can also see the cross-talk induced by the coupling of the LP01, LP21, and LP02 modes from the left core to the right core is low. In fact, the normalized power transferring to the right core for the LP01, LP21, and LP02 modes at the operating wavelength range are lower than −75, −36, and −31 dB, respectively. We can easily understand that the configuration can be readily applied to add the mode to the few-mode optical fiber. The only difference is the LP11 mode would be launched from the right core. At this stage, the results shown in Fig. 9(a) and Fig. 9(b) would be the output power of the LP11 mode from the left core and right core, respectively. The cross-talk will not be a problem. Therefore, the operating wavelength range can be extended as long as higher losses are allowed.
Fig. 9. Spectral coupling characteristics at the right core for the LP11 mode (a) and the left core (b) for the five-core optical fiber.
Fig. 10. Spectral coupling characteristics at the left core for the LP11 mode (a) and the right core (b) for the five-core optical fiber.
#198055 - $15.00 USD (C) 2014 OSA
Received 20 Sep 2013; revised 13 Dec 2013; accepted 2 Jan 2014; published 15 Jan 2014 27 January 2014 | Vol. 22, No. 2 | DOI:10.1364/OE.22.001440 | OPTICS EXPRESS 1448
The selective coupling of the other modes can be achieved by simply adjusting the parameters of the assistant cores. For example, if we wish to selectively drop the LP21 mode, then the core diameter and index difference of the assistant cores can be set as 2.5 μm and 0.023, respectively. In order to reduce the coupling of the other modes, the center-to-center distance between the assistant cores is set as 8.8 μm. The corresponding center-to-center distance between the side core and the assistant core is set as 11.5 μm. The coupling length of the LP21 mode is 5.2 mm. Figure 11 shows the spectral coupling characteristics of the proposed five-core fiber coupler with a fiber length of 5.2 mm. It's found the LP21 mode can be coupled to the right core with transmission loss lower than 1 dB at a wavelength range from 1.523 to 1.564 μm, which corresponding to a 41-nm bandwidth. Simultaneously, the other modes can still stay at the left core with low loss. In this situation, the LP01 and LP11 modes in the left core have little coupling with the other cores, whereas the coupling loss for the LP02 mode is lower than −0.44 dB. Such coupling characteristics are owing to the fact that there are low index difference between the effective indexes of the LP21 and LP02 modes for the side cores, whereas the LP21 mode has large index difference with the LP01 and LP11 modes. As shown in Fig. 12, the cross-talk at the right core is higher owing to the strong coupling of the LP02 mode, but still the coupling power is lower than −20 dB for the LP02 mode. The cross-talk at the left core can be lower than −19 dB at the operating wavelength range.
Fig. 11. Spectral coupling characteristics at the right core for the LP21 mode (a) and the left core (b) for the five-core optical fiber.
Fig. 12. Spectral coupling characteristics at the left core for the LP21 mode (a) and the right core (b) for the five-core optical fiber.
For the above proposed five-core optical fiber, mode converters should be applied to convert the higher-order mode to the fundamental mode. Mode converter based long period grating (LPG) configuration would be a good choice [46]. The conversion efficiency of infiber LPG can be higher than 99% coupling efficiency over bandwidths as large as 94 nm, and peak efficiencies can be >99.9%. Alternatively, the output fiber core can be replaced by another assistant core. The cross-section of the fiber is shown in Fig. 13. The fiber, which is
#198055 - $15.00 USD (C) 2014 OSA
Received 20 Sep 2013; revised 13 Dec 2013; accepted 2 Jan 2014; published 15 Jan 2014 27 January 2014 | Vol. 22, No. 2 | DOI:10.1364/OE.22.001440 | OPTICS EXPRESS 1449
composed of one few-mode core and four assistant cores with single-mode operation, is denoted as Fiber A. The fiber parameters are set as the same as the five-core optical fiber for LP11 mode separation. The distance between the left core and the adjacent assistant core is set as dsa = 10.5 μm and the the center-to-center distance between the assistant cores is daa = 7.5 μm. The fiber length is also set to be 4.5 mm. As a comparison, the results of the five-core optical fiber with two side cores, which is denoted as Fiber T, is also presented. Figure 14-15 shows the spectral coupling characteristics of the five-core fiber couplers. We can see, compared with the five-core optical fiber with two side-cores, the five-core optical fiber with four assistant-cores shows higher loss for the LP11 mode, whereas the cross-talks at both the left and right side-cores are higher.
Fig. 13. Configuration of the five-core optical fiber with four assistant cores.
Fig. 14. Spectral coupling characteristics at the right core for the LP11 mode (a) and the left core (b) for the five-core optical fiber.
Fig. 15. Spectral coupling characteristics at the left core for the LP11 mode (a) and the right core (b) for the five-core optical fiber.
#198055 - $15.00 USD (C) 2014 OSA
Received 20 Sep 2013; revised 13 Dec 2013; accepted 2 Jan 2014; published 15 Jan 2014 27 January 2014 | Vol. 22, No. 2 | DOI:10.1364/OE.22.001440 | OPTICS EXPRESS 1450
Technically, the four modes in LP11 groups can be divided into the LP11a and LP11b modes by using the proposed add-drop device, which is based on the fact that the LP11a mode will have strong coupling between the two few-mode optical fibers, whereas the LP11b modes in the FMFs have weak coupling. In fact, numerical results show that the launching of the LP11b mode from one of the FMFs in the add-drop device will lead to the output of LP11b mode power lower than −60 dB at another FMF. In this situation, only the LP11a mode is applied for multiplexing. Similar condition hold for the LP21 mode. It’s also possible to apply both of the modes in the LP11 or LP21 mode group for mode multiplexing. At this situation, the separation of the LP11a or LP11b mode can be achieved by considering the mode orientation. Similar condition have been investigated by Nielson et al [5]. 4. Conclusion In conclusion, an all-fiber based add-drop multiplexer for mode-division multiplexing application is proposed. Selective coupling for the mode in a few-mode optical fiber is achieved by applying multiply assistant cores to selectively enhance the mode coupling between the two side cores. The assistance cores work as a bridge for the coupling of the selected mode. The long distance between the two side cores can effectively reduce the coupling of the other modes in the fiber. As a result, wide bandwidth and low cross-talk can be achieved. The proposed technique can also be achieved by applying the silica waveguide configuration, the design and experimental demonstration will be the task of our future work. Acknowledgments This work is supported by the Qing Lan Project of Jiangsu Province and the National Natural Science Foundation of China (NNSFC) (Grant No. 61275153, 61320106014).
#198055 - $15.00 USD (C) 2014 OSA
Received 20 Sep 2013; revised 13 Dec 2013; accepted 2 Jan 2014; published 15 Jan 2014 27 January 2014 | Vol. 22, No. 2 | DOI:10.1364/OE.22.001440 | OPTICS EXPRESS 1451
