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Two-core fiber based mode coupler for single-mode excitation in a two-mode fiber for quasi-single-mode operation
Optical Fiber Technology 52 (2019) 101970
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Optical Fiber Technology journal homepage: www.elsevier.com/locate/yofte
Two-core fiber based mode coupler for single-mode excitation in a twomode fiber for quasi-single-mode operation
T
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Thomas Joseph , Joseph John Electrical Engineering Department, IIT Bombay, Mumbai 400076, India
A R T I C LE I N FO
A B S T R A C T
Keywords: Quasi-single mode operation Fiber coupler Single mode fibers Few mode fibers
Quasi-single mode operation in few-mode fibers is a promising technique for extending the Kerr nonlinearity threshold of standard single mode fibers. Under this operation the design goals of few-mode fibers used for mode division multiplexing can be relaxed. Based on the MinΔneff , we calculated the maximum core radius of twomode and four-mode fibers for quasi-single-mode operation, and is found to be 8 μm and 9.7 μm respectively. We also propose the design of a two-core fiber coupler, based on thermally diffused core technique, for effective excitation of the fundamental mode alone in the above two-mode fiber for the entire C-band. The robustness of the proposed design is studied by varying the design parameters and observing their sensitivity to coupling efficiency and extinction ratios and are found to be well above −0.5 dB and 25 dB respectively.
1. Introduction The meteoric growth of Internet traffic over optical networks around the world drives the research in capacity enhancing methods such as employing few mode fibers (FMFs) [1], multicore fibers (MCFs) [2], high spectral-efficient modulation formats, large effective area fibers etc. By employing mode division multiplexing (MDM) in FMFs and space division multiplexing (SDM) in MCFs, large spectral efficiency can be achieved. Further, by combining FMF and MCF technologies, multicore few mode fibers (MC-FMFs) are developed which support transmission of more than 100 spatial channels over a single fiber [3]. However, FMFs and MC-FMFs require complex and expensive signal processing to recover the data [4]. On the other hand spectrally efficient modulation schemes require more optical signal to noise ratio (OSNR) to get the same bit error rate (BER) as compared to ON-OFF keying [5,6]. One straight forward option to increase OSNR is to launch higher signal power into the fiber. However this can lead to Kerr nonlinearity in standard single mode fibers (SSMFs) which is due to the limited effective area of these fibers. Increasing the effective area of SMF by reducing the core-cladding index difference is restricted by the bending losses [7]. In SSMFs the effective area of the fundamental mode is ∼80 μm2 [8]. By introducing a trench in the cladding this can even be raised to ∼160 μm2 [9–11]. To the best of our knowledge the above limit has not been crossed so far in standard 125 μm grade SMFs (Fibers with Aeff larger than 160 μm2 have more than 125 μm diameter to compensate for micro-bend losses [12]). In order to increase the
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effective area, low index differences and large core diameters are required which in turn introduce higher bending losses and affect the cutoff conditions. An easier method for extending this limit is to use few mode fibers and excite only the fundamental mode [13–16]. This allows us to obtain large Aeff , at the same time limiting the fiber diameter to 125 μm . Marianne et. al fabricated a few mode fiber with fundamental mode area, Aeff , of 220 μm2 with trench assisted refractive index profile [13]. The trench results in a reduction of bending loss. Yaman et. al demonstrated long distance transmission in a few mode fiber at 1310 nm which was actually a large effective area SMF at 1550 nm [15]. Quasi-single mode operation in an FMF leads to multi-path interference (MPI) [17]. Impact of MPI on few mode fiber transmission is discussed in [18]. Frequency domain equalization method for mitigating MPI on FMF is theoretically and experimentally demonstrated in [19]. Yaman et. al demonstrated first quasi-single mode transmission over transoceanic distance using FMFs [20]. Quasi-single mode transmission for long-haul and submarine optical communication is demonstrated by Downie et. al by concatenating large-mode-area single mode fibers and FMFs [21]. However investigations on the effective index difference between the supporting modes (Δneff ), bending loss, and effective area ( Aeff ) of each mode for quasi-single mode operation in a few mode fiber have not been conducted so far to the best of our knowledge. Also the current method used for single mode excitation in FMFs is direct launching from an SMF pigtail which is prone to misalignments that result in power coupling to higher order modes leading to increased MPI. In this paper we calculate the maximum core radius
Corresponding author. E-mail addresses: [email protected] (T. Joseph), [email protected] (J. John).
https://doi.org/10.1016/j.yofte.2019.101970 Received 19 March 2019; Received in revised form 7 June 2019; Accepted 28 June 2019 1068-5200/ © 2019 Elsevier Inc. All rights reserved.
Optical Fiber Technology 52 (2019) 101970
T. Joseph and J. John
in two and four-mode step-index fibers for fundamental mode operation when the loss and MinΔneff of the higher order modes are relaxed. We also propose the design of a two-core fiber based mode coupler for effective excitation of the fundamental mode alone in a two-mode fiber. The remaining part of this paper is organized as follows. Section 2 explains fiber figure of merit which shows the impact of increasing mode effective area. In Section 3 few mode fibers and quasi-single mode operation in these fibers are presented. Section 4 describes the design of a two-core fiber based coupler for single mode excitation in a two-mode fiber followed by the conclusions in Section 5.
7 40 km spans 60 km spans 80 km spans 100 km spans
FIber FOM (dB)
6 5 4 3 2 1
2. Fiber figure of merit
0
The reach and capacity of single mode fibers mainly depend on two factors: attenuation and nonlinear tolerance (governed by the nonlinear refractive index coefficient, n2 and the effective area, Aeff ). It was found that a minor improvement in attenuation significantly improves the link performance [22]. By using pure silica core fibers instead of Ge doped core, a small reduction in attenuation is possible. Besides, the nonlinear coefficient, n2 , of pure silica core is slightly lower (2.1 × 10−20 m2/W) than Ge doped core (2.2–2.3 × 10−20 m2/W) which is an additional advantage. The impact of fiber attenuation, Aeff and n2 can be expressed using the figure of merit (FOM) given by the following equation [22]
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Fiber Effective Area (μm ) Fig. 2. Fiber figure of merit vs. effective area ( Aeff ). Both fibers have the same attenuation but different nonlinear coefficients, n2 .
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FIber FOM (dB)
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FOM (dB ) Aeff . n2, ref 2⎛ = ⎜10log ⎡ − [α (dB / km) − αref (dB / km)]. L⎞⎟ ⎢ 3 Aeff , ref . n2 ⎠ ⎣ ⎝ Leff ⎤ ⎞ 1⎛ − ⎜10log ⎛⎜ ⎥⎟ 3 L ⎝ eff , ref ⎦ ⎠ ⎝
100
5 4 3 40 km spans 60 km spans 80 km spans 100 km spans
2
(1)
1
where L is the span length, Leff the effective nonlinear length, approximately given by 1/α . α is the attenuation of the fiber in linear units of km−1. The term ‘ref’ in the subscript refers to the reference fiber. The above FOM indicates the difference in Q factor or 20log (Q) between the fiber under consideration and the reference fiber. Since the quasi-single mode operation is for extending the Aeff of the fundamental mode, we are concentrating only on the effect of Aeff , even though the fiber attenuation and n2 has impact on FOM. Fig. 1 shows the FOM of fiber as a function of Aeff for different span lengths. Following are the parameters considered in the simulation: α = 0.153 dB/km, αref = 0.2 dB/km, n2 = 2.1 × 10−20 m2/W, n2, ref = 2.3 × 10−20 m2/W, Aeff , ref = 80 μm2 [5]. These values correspond to pure silica core fiber and GeO2 doped fiber (standard single mode fiber, which is the reference fiber, falls in this category) respectively. We studied the influence of n2 and attenuation separately for the same fiber by varying one of them at a time from the reference value. These results are shown in
0 80
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Fig. 3. Fiber figure of merit (FOM) vs. effective area ( Aeff ). Both fibers have the same n2 but different attenuation.
Fig. 2 and Fig. 3 respectively. It was found that the reduction in n2 results in an FOM increment of 0.22 dB while the reduction in attenuation improves the FOM by 0.9 dB (the state of the art pure silica core fiber has an attenuation ∼0.146 dB/km which will give an additional FOM improvement of 0.1 dB). Considering these into account an increase in Aeff from 80 μm2 to 160 μm2 results in an FOM improvement of 2–4 dB. It was also found that a reduction in attenuation increases the reach of the fiber link, i.e. for larger span length the FOM improvement is more for smaller attenuation values. These results show that an increase in Aeff has greater influence on fiber capacity.
Fiber FOM (dB)
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3. Quasi-single mode operation in few mode fibers
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Few mode fibers (FMFs) are of two types: weakly coupled and strongly coupled. Weakly coupled FMFs have step index refractive index profiles while the strongly coupled ones have graded index refractive index profiles [23]. Since FMFs are designed for exploring spatial diversity, design of FMFs have to consider many factors, such as loss of each supporting mode, effective index difference between the adjacent modes, effective area of each mode, differential mode delay (DMD), etc. When we are concentrating only on the fundamental mode of FMFs, many design criteria for higher order modes can be relaxed or modified. In order to avoid mode coupling between adjacent modes, the minimum effective index difference between any two modes should be ⩾0.5 × 10−3 [24,25]. This value is higher than the x and y polarized modes of a polarization maintaining fiber. Also bending loss of each LP mode should be less than 10 dB/turn at 10 mm bending radius for good
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2 1 0 100
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Fiber Effective Area (μm2) Fig. 1. Fiber figure of merit (FOM) vs. effective area ( Aeff ). 2
Optical Fiber Technology 52 (2019) 101970
T. Joseph and J. John −3
600
x 10 7
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mode robustness [23]. The above two are the main design requirements for a spatial mode in an FMF. All propagating modes should satisfy this criteria when used for MDM. However, if we operate an FMF in the quasi-single mode regime, we can relax these criteria for higher order propagating modes, i.e. in a two LP mode fiber, these requirements can be relaxed for the LP11 mode. We studied the feasibility of quasi-single mode operation in two-mode and four-mode fibers by relaxing the design requirements. The design relaxations are calculated by varying different parameters such as core radius, Δneff and Aeff . These calculations are done at an operating wavelength of 1550 nm with a core refractive index value of 1.444. Fig. 4 shows variations of effective index difference (Δneff ) between the two propagating modes (LP01& LP11) as a function of the core radius for a two mode fiber (TMF). The Δneff is > 0.5 × 10−3 for all the core radius values considered. It was found that up to 14 μm core radius the Δneff is higher than the required limit of 0.5 × 10−3 . Bending loss for each mode of a step index fiber can be calculated using the following relation [23,26]. Calculated losses for the two supporting modes of the TMF are shown in Fig. 5.
Aeff , mn =
2 2 k 2 − β 2 and γ = β 2 − nclad k 2 are the field decay rates where κ = ncore in the core and cladding regions respectively, k = 2π /λ the free space propagation constant, β the propagation constant of the considered LP mode of an unbent fiber, R the bend radius, em is a constant depending 20
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∬ |Fm (x , y )|2 dxdy ∬ |Fn (x , y )|2 dxdy ∬ |Fm (x , y )|2 |Fn (x , y )|2 dxdy
(3)
Aeff of the LP01 mode is found to be more than 340 μm2 when the core radius is 11.6 μm , with loss and Δneff satisfying the design requirements. If we require a minimum Δneff of 1 × 10−3 , the core radius corresponding to this value is 10.4 μm and the loss of LP01 mode at this point is less than 2 dB/turn. The Aeff corresponding to this value is 275 μm2 which is far higher than that of an SSMF. These results show that the quasi-single mode regime operation of TMF can be utilized to overcome the Aeff limitations of an SSMF. A recently reported work fabricated a TMF having an Aeff of 215 μm2 for the LP01 mode with very low macro-bend losses and an equivalent micro-bend losses as that of SSMFs [14]. However, the multi-path interference (MPI) level of this fiber was found to be −24 dB, even with a Δneff of 1.3 × 10−3 on an 85 km fiber. An MPI level below −35 dB is required to eliminate system degradation which can be obtained through increased Δneff value. This can be done by tailoring the effective refractive index of LP11 mode to a lower value without affecting that of the LP01 mode. Also higher order mode filters can be employed to reduce the MPI [18]. The loss of LP01 mode can be further reduced by using a four-LP mode fiber and operating it in the quasi-single mode regime. The V number of a four-LP mode fiber can go up to 5.1 (V = 3.8 in TMF), enabling us to increase either the refractive index difference or the Aeff (by increasing core radius) of the fiber modes. When the V number increases the confinement of the mode also increases resulting in a reduction in the loss which can be used to overcome the loss drawback of the TMF. The calculated macro-bending losses of each fiber mode of a four-LP mode fiber is shown in Fig. 7. The loss of LP01 mode is far lower than the ITU recommendations at a core radius of 14 μm ; however the loss of the higher order modes are more than 10 dB/turn at this point. Δneff of the supporting modes of the four-LP mode fiber are shown in Fig. 8. At 14 μm core radius the Δneff between the fundamental mode and the LP11 mode is 0.8 × 10−3 , which shows that in a four-mode fiber the limiting factor in core radius is the Δneff rather than the macro-bending loss as in the TMF. Calculated Aeff of the four-mode fiber is shown in Fig. 9. Aeff of the LP01 mode is 437 μm2 when the core radius is 14 μm . This is approximately 100 μm2 higher than that of the TMF. Also the Aeff is 354 μm2 when we fix the Δneff between the
(2)
10
12
on the order of the LPmn mode (em = 2 for m = 0 and em = 1 for m ≠ 0), Km ± 1 are the modified Bessel functions. The loss of LP01 mode is found to be less than 10 dB/turn up to a core radius of 11.6 μm . For quasi-single mode operation in a TMF, the maximum core radius is determined by the loss rather than Δneff . The effective area of the fiber modes can be calculated using the following relations [27] and are shown in Fig. 6.
−2γ 3 (R + a)
10
8 10 Core radius (μm)
Fig. 6. Variations of Aeff of the two supporting modes (LP01 and LP11) of a two mode fiber with core radius.
Fig. 4. Variation of Δneff as a function of core radius for a two mode fiber.
eff − 2γa⎤ 4.34π 1/2κ 2exp ⎡ 3β2 ⎣ ⎦ 2α (dB / m) = 3/2V 2K em (R + a)1/2 m − 1 (γa) Km + 1 (γa) eff γ
6
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Fig. 5. Bending loss variations for the two supporting modes (LP01 and LP11) of a two-mode fiber with core radius. 3
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for Δneff ⩾1.7 × 10−3 , mode coupling coefficient converges to a constant value [28]. In view of this our later designs fixed the MinΔneff to be 1.7 × 10−3 in a TMF. Core radii corresponding to this Δneff (1.7 × 10−3 ) for a TMF is 8 μm and 9.7 μm for a four-mode fiber. Effective areas of fundamental mode of TMF and four-mode fiber for the above mentioned core radius is 162 μm2 and 210 μm2 respectively. The core radius and effective area can be further increased by proper index profile tailoring. Since the quasi-single mode operation in FMF is considered in this work, the inter-modal dispersion is not present; only chromatic dispersion is applicable. We calculated the chromatic dispersion of the two-mode and four-mode fibers at 8 μm and 9.7 μm core radii and found them to be 22.8 ps/nm-km and 23.3 ps/nm-km respectively.
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LP01 LP11 LP21
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Loss (dB)
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4. Two-core fiber mode coupler for single mode excitation in a two-mode fiber
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Quasi-single mode operation in TMFs requires the effective excitation of the fundamental mode alone with good extinction ratio between the supporting LP01 and LP11 modes to reduce cross-talk. Yaman et. al used light launching from an SMF for effective excitation of the fundamental mode in a TMF. The SMF and TMF used in their experiment have comparable core diameters which result in an effective excitation with good extinction ratio. However for larger TMF core diameters, direct launching from an SMF will couple power to the higher order modes resulting in much lower extinction ratios, and hence special launching methods are required for efficient excitation of the fundamental mode. Power coupling coefficients of the excited modes in an MMF with center launching show that significant power gets coupled to the higher order modes even for smaller misalignments [29]. In a TMF even after effective excitation, power coupling will take place from the excited LP01 to the LP11 mode during propagation. This cross-talk can be reduced by making the effective index differences between the two modes as large as possible. But Maruyama et. al experimentally verified that under normal working conditions increasing the Δneff beyond 1.7 × 10−3 will not have much impact [28]. This threshold value depends on the fiber working environments, such as winding tension on the fiber. In our fiber design we fixed the value of MinΔneff to be 1.7 × 10−3 for quasi-single mode operation of the TMF. Under these conditions the cross-talk and the resulting multi-path interference (MPI) can be reduced by effective suppression of LP11 mode excitation at the transmitter side. For this purpose high precision launching is a must and any misalignments will lead to the excitation of the LP11 mode which will increase the MPI. To alleviate this problem we propose the design of a two-core fiber coupler which excites the LP01 mode alone in a TMF with a large extinction ratio. The proposed two-core coupler has two cores; one is a single-mode core and the other one two-mode. Input is given to the single-mode core and is coupled to the fundamental mode of the two-mode core in a thermally expanded core (TEC) region which is obtained by thermally diffused core technique (TDCT) [30]. In the TDCT technique, fiber under consideration is heated above the temperature of 1200 °C, leading to the diffusion of dopants from core into the cladding resulting in an expanded core [31,32]. The heating can be done by employing an oxy-hydrogen flame of a fiber-tapering machine or using an electric arc. The two cores are designed in such a way that the effective indices of the fundamental modes of both the cores are matching. This leads to effective power coupling between the LP01 modes of the two cores in the TEC region. Design details of this two-core fiber coupler is described below.
Fig. 7. Variations of bending loss of a four-mode fiber with core radius.
0.012 n
−n
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Fig. 8. Variations of Δneff of a four-mode fiber with core radius.
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Fig. 9. Variations of Aeff of supporting modes of a four-mode with core radius.
fundamental mode and the LP11 mode to be 1 × 10−3 , which is approximately 80 μm2 larger than the TMF. This way the Aeff of a fiber can be increased to any arbitrary higher value by operating an FMF in the fundamental mode regime. To ensure low mode coupling to the LP11 mode, a large Δneff must be maintained between the fundamental mode and the next higher order mode while keeping the benefits of larger Aeff as such. This can be done by proper refractive index profile tailoring. While tailoring the refractive index profile, the Δneff between the fundamental mode and the higher order modes must be kept high to avoid any coupling from the fundamental mode. However it was found that
4.1. Design of two-core fiber coupler As described in the previous section first we fixed the MinΔneff as 1.7 × 10−3 for the two-mode core. This corresponds to a core radius of 8 μm and the resulting Aeff is greater than 160 μm2 . The core refractive index is 1.4546 and the cladding refractive index 1.45. For the singlemode core we fixed the core diameter to be 9.8 μm , core refractive 4
Optical Fiber Technology 52 (2019) 101970
T. Joseph and J. John
Fig. 10. Schematic representation of thermally expanded core (TEC) fiber coupler.
index = 1.4548, and the cladding refractive index = 1.45, which is the same as that of the two-mode core. The core refractive indices are chosen for effective index matching of the two fundamental modes at the operating wavelength of 1530 nm. Normalized frequency or the V number of the single-mode core is 2.37 and that of the two-mode core is 3.79. Therefore they support one, and two modes respectively at 1530 nm. The initial center to center separation between the two cores is 22 μm and the gap between them is 9.1 μm. Under this condition there is no or negligibly small coupling between the two cores. This two-core fiber is heated for a duration of 16 min at a temperature of 1650 °C so that the dopants in the cores diffuse into the cladding. This results in the TEC region and the separation between the cores becoming very small leading to interaction of modes between the cores. Since the effective index of the fundamental modes of the two cores are matched, power from the single-mode core couples only to the fundamental mode of the two-mode core. The expanded core radius can be calculated using the relation ΔA = Dt , where D is the diffusion coefficient of the dopant and t the heating duration in seconds. For GeO2 the value of D is 2.1 × 10−14 m2 /s at 1650 °C [30]. Fig. 10 shows the schematic diagram of the proposed TEC coupler. Input is given to the singlemode core (Pin ) and output obtained through the two-mode core (Pout2 ). For simulation purpose we considered the following device structure. The single-mode core is placed at −10 μm and the two-mode core at 12 μm , with a total scan length of 3.8 mm and a taper length of 13.8 mm. These values correspond to a power coupling from the singlemode core to the two-mode core with no power coupling back into the single-mode core. For our simulations, the two-core fiber is assumed to have a total length of 28.8 mm which is assumed to be heated for a sufficient duration (16 min using TDCT) to obtain the required core diameter expansion of 9 μm . Thus the total core diameter of the singlemode core becomes 18.8 μm and the two-mode core 25 μm . The final gap between the two cores in the TEC region is 0.1 μm resulting in strong coupling between the fundamental modes. As shown in Fig. 11 the input to the coupler is to the single-mode core placed at −10 μm . The corresponding output intensity of the two-mode core is shown in Fig. 12. Comparison of input and output intensities shows that the effective area of the output is larger (since the two-mode core has larger diameter). Measured power in each of the modes of the two-core fiber along the light propagation direction is shown in Fig. 13. We used two parameters to evaluate the performance of the converter, viz. the coupling efficiency, CLP01, and the extinction ratio, ER. CLP01 is defined as ratio of the coupled power in the LP01 mode of the two-mode core to the input power of the LP01 of the single-mode core; ER is the ratio of power in the LP01 mode to the LP11 mode power of the two-mode core.
CLP01 = 10. log10 ER = 10. log10
PLP01 Pin
PLP01 PLP11
Fig. 11. Input of the two-core coupler simulated using Beamprop (given to the single-mode core at −10 μm ).
Fig. 12. Output of the mode converter simulated using Beamprop. More than 94% of input power gets coupled to the two-mode core LP01 mode.
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Fig. 13. Measured power in each of the modes of thermally expanded two-core fiber. Negligibly small power coupled to the LP11 mode of the two-mode core.
coupled to the LP11 mode of the two-mode core.
(4) 4.2. CLP01 and ER variations with scan length (5)
When the scan length was 3.8 mm, more than 94% of the input power got coupled to the LP01 mode of the two-mode core which is the maximum value obtained in our design. In this section the effect of scan
where Pin is the input power to the single-mode core, PLP01 the power coupled to the LP01 mode of two-mode core, and PLP11 the power 5
Optical Fiber Technology 52 (2019) 101970
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Fig. 14. Coupling efficiency (CLP01) variations of two-core coupler with scan length.
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Fig. 16. Coupling efficiency (CLP01) variations of two-core coupler with wavelength.
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Fig. 15. Extinction ratio (ER) variations of two-core coupler with scan length.
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Fig. 17. Extinction ratio (ER) variations of two-core coupler with wavelength.
−0.2
length variations on the extinction ratio and the power coupling efficiency are calculated. Scan length variations are considered only in a range over which power coupled to the LP01 mode is greater than 90%. Calculated CLP01 and ER values are shown in Fig. 14 and Fig. 15 respectively. It is evident that the coupling efficiency is well above −0.5 dB for a wide range (∼1.7 mm) of scan lengths. Besides, ER is greater than 24 dB. The ER values show nonuniform variation with scan length; however power coupled to the LP11 mode in all the cases were ⩽0.3% which is negligibly small. Nonuniform variations in the ER is due to the small changes in the LP11 mode coupled power which is negligibly small as evident from the large ER values.
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01
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4.3. CLP01 and ER variations with wavelength
−1 8.5
Performance of the coupler to changes in the wavelength is evaluated in this section. The proposed two-core fiber coupler is designed for 1530 nm which is the starting wavelength of the C-band. Variations in the coupling efficiency and extinction ratio are calculated and shown in Fig. 16 and Fig. 17 respectively. For the entire C-band CLP01 is found to be higher than −0.45 dB, and gradually decreasing with increasing wavelength. Even though ER shows nonlinear variations, it is important to note that the ER value is more than 26 dB for the entire C band. Reduction in the CLP01 and ER values are due to the phase mismatch for wavelength changes.
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8.9
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Fig. 18. Coupling efficiency (CLP01) variations of two-core coupler with coreexpansion.
expansion. Variations in the coupled power due to core expansion and the resulting CLP01 and ER are calculated in this section. Fig. 18 and Fig. 19 show CLP01 and ER values as a function of core expansion. It is found that the conversion efficiency is maximum for the designed value of 9 μm and decreases for smaller expansion values. For core expansion variations ER changes gradually as compared to other parameter variations, and is maximum for the 8.95 μm expansion case. For the designed expansion value the two cores literally touch each other (to be
4.4. CLP01 and ER variations with core expansion Interaction between the two cores depends on the extent of core 6
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27.5
31–42. [6] Q. Sui, H. Zhang, J.D. Downie, W.A. Wood, J. Hurley, S. Mishra, A.P.T. Lau, C. Lu, H.-Y. Tam, P.K.A. Wai, Long-haul quasi-single-mode transmissions using few-mode fiber in presence of multi-path interference, Opt. Express 23 (3) (2015) 3156–3169. [7] P. Sillard, New fibers for ultra-high capacity transport, Opt. Fiber Technol. 17 (2011) 495–502. [8] P. Sillard, S. Richard, L.A. De Montmorillon, M. Bigot-Astruc, Micro-bend losses of trench-assisted single-mode fibers, Proceedings of European Conference on Optical Communication (ECOC), Torino, Italy, 2010 paper We.8.F.3. [9] M. Bigot-Astruc, F. Gooijer, N. Montaigne, P. Sillard, Trench-assisted profiles for large-effective-area single-mode fibers, in Proceedings of European Conference on Optical Communication (ECOC), Brussels, Belgium, 2008, paper Mo.4.B.1. [10] M. Bigot-Astruc, L. Provost, G. Krabshuis, P. Dhenry, P. Sillard, 125 m glass diameter single-mode fiber with Aeff of 155 μm2, in: Proceedings of Optical Fiber Communication Conference/National Fiber Optic Engineers Conference (OFC/ NFOEC) Los Angeles, CA, USA, 2011, paper OTuJ2. [11] Y. Yamamoto, M. Hirano, K. Kuwahara, T. Sasaki, OSNR-enhancing pure-silica-core fiber with large effective area and low attenuation, Proceedings of Optical Fiber Communication Conference/National Fiber Optic Engineers Conference (OFC/ NFOEC), San Diego, CA, USA, (2010) paper OTuI2. [12] M. Tsukitani, M. Matsui, K. Nagayama, E. Sasaoka, Ultra low nonlinearity puresilica-core fiber with an effective area of 211 m2 and Transmission Loss of 0.159dB/ km, in Proceedings of European Conference on Optical Communication, Copenhagen, Denmark, 2002, paper Tu3.2.2. [13] M. Bigot-Astruc, P. Sillard, Realizing large effective area fibers, in: Proceedings of Optical Fiber Communication Conference (OFC) Los Angeles, CA, USA, 2012, paper OTh4I.1. [14] D. Boivin, M. Bigot-Astruc, M. Travagnin, P. Sillard, Weakly-coupled few-mode fibers for single-mode and mode-division-multiplexed transmissions, in: Proceedings of Optical Fiber Communication Conference/National Fiber Optic Engineers Conference (OFC/NFOEC) Anaheim, CA, USA, 2013, paper OTh3K.6. [15] F. Yaman, N. Bai, B. Zhu, T. Wang, G. Li, Long distance transmission in few-mode fibers, Opt. Express 18 (12) (2010) 13250–13257. [16] Q. Sui, H. Zhang, J.D. Downie, W.A. Wood, J. Hurley, S. Mishra, A.P.T. Lau, C. Lu, H.-Y. Tam, P. Wai, 256 Gb/s PM-16-QAM quasi-single-mode transmission over 2600 km using few-mode fiber with multi-path interference compensation, in: Proceedings of Optical Fiber Communication Conference (OFC) San Francisco, CA, USA, 2014, paper M3C.5. [17] M. Mlejnek, I. Roudas, J.D. Downie, N. Kaliteevskiy, K. Koreshkov, Coupled-mode theory of multipath interference in quasi-single mode fibers, IEEE Photonics J. 7 (1) (2015) 1–16. [18] F. Yaman, E. Mateo, T. Wang, Impact of modal crosstalk and multi-path interference on few-mode fiber transmission, in: Proceedings of Optical Fiber Communication Conference/National Fiber Optic Engineers Conference (OFC/NFOEC), Los Angeles, CA, USA 2012, paper otu1d.2. [19] N. Bai, C. Xia, G. Li, Adaptive frequency-domain equalization for the transmission of the fundamental mode in a few-mode fiber, Opt. Express 20 (11) (2012) 241010–24017. [20] F. Yaman, S. Zhang, Y.K. Huang, E. Ip, J.D. Downie, W.A. Wood, A. Zakharian, S. Mishra, J. Hurley, Y. Zhang, I.B. Djordjevic, M.F. Huang, E. Mateo, K. Nakamura, T. Inoue, Y. Inada, T. Ogata, First quasi-single-mode transmission over transoceanic distance using few-mode fibers, Proceedings of Optical Fiber Communication Conference (OFC), Los Angeles, CA, USA, 2015 paper Th5C-7.. [21] J.D. Downie, M. Mlejnek, W.A. Wood, J. Hurley, A. Zakharian, I. Roudas, S. Mishra, F. Yaman, S. Zhang, E. Ip, Y.K. Huang, Quasi-single-mode transmission for longhaul and submarine optical communications, in: Proceedings of Conference on Lasers and Electro-Optics (CLEO), San Jose, CA, USA, 2016, paper SM4F.6. [22] S. Makovejs, J.D. Downie, J.E. Hurley, J.S. Clark, I. Roudas, C.C. Roberts, H.B. Matthews, F. Palacios, D.A. Lewis, D.T. Smith, P.G. Diehl, J.J. Johnson, C.R. Towery, S.Y. Ten, Towards superior transmission performance in submarine systems: leveraging ultralow attenuation and large effective area, J. Lightwave Technol. 34 (1) (2016) 114–120. [23] J. Han, G. Gao, Y. Zhao, S. Hou, Bend performance analysis of few-mode fibers with high modal multiplicity factors, J. Lightwave Technol. 35 (13) (2017) 2526–2534. [24] J. Liu, J. Zhang, J. Han, G. Gao, Y. Zhao, W. Gu, Design and optimization of weaklycoupled few-mode fiber with low nonlinearity, Chin. Opt. Lett. 12 (3) (2014) pp. 030601–1–030601-3. [25] M. Bigot-Astruc, D. Boivin, P. Sillard, Design and fabrication of weakly-coupled fewmodes fibers, Proceedings of IEEE Photonics Society Summer Topical Meeting Series (2012) paper TuC1.1. [26] R.T. Schermer, J.H. Cole, Improved bend loss formula verified for optical fiber by simulation and experiment, IEEE J. Quantum Electron. 43 (10) (2007) 899–909. [27] C. Koebele, M. Salsi, G. Charlet, S. Bigo, Nonlinear effects in mode-division-multiplexed transmission over few-mode optical fiber, IEEE Photonics Technol. Lett. 23 (18) (2011) 1316–1318. [28] R. Maruyama, N. Kuwaki, S. Matsuo, M. Ohashi, Experimental investigation of relation between mode-coupling and fiber characteristics in few-mode fibers, in: Proceedings of Optical Fiber Communication Conference (OFC), Los Angeles, CA, USA, 2015 paper M2C.1. [29] T. Joseph, J. John, Mode-field matched twin spot launch for enhancing data rates in multimode fibers, 2016 22nd National Conference on Communication (NCC), 2016. [30] Y. Zhao, A. Zhou, X. Ouyang, Y. Ouyang, C. Zhou, L. Yuan, A stable twin-core-fiberbased integrated coupler fabricated by thermally diffused core technique, J. Lightwave Technol. 35 (24) (2017) 5473–5478. [31] K. Shiraishi, Y. Aizawa, S. Kawakami, Beam expanding fiber using thermal diffusion of the dopant, J. Lightwave Technol. 8 (8) (1990) 1151–1161. [32] H. Yamada, H. Hanafusa, Mode shape convertor produced by the thermal diffusion of different dopants, Photon. Technol. Lett. 6 (4) (1994) 531–533.
ER (dB)
27
26.5
26
25.5 8.5
8.6
8.7 8.8 Core Expansion (μm)
8.9
9
Fig. 19. Extinction ratio (ER) variations of two-core coupler with core expansion.
more specific, there is a gap of 0.1 μm between the cores). Reduction in the CLP01 and ER values for smaller expansions is mainly due to the weaker interaction between the two coupling modes. 5. Conclusions Quasi-single mode operation in few mode fibers is an interesting method for extending the Aeff and the Kerr nonlinearity threshold. For quasi-single mode operation, design criteria for the higher order modes in a few mode fiber can be relaxed. This enables an extended core radius and corresponding increase in the fundamental mode Aeff of few mode fibers used for MDM. This relaxation helps us to extend the core radius of a two-mode fiber to 8 μm and the Aeff to ⩾160 μm2 . The mode coupling between the supporting modes along the propagation direction depends on the power coupled to the higher order modes at the input end. We proposed the design of a two-core fiber coupler which can effectively excite only the fundamental mode of a two-mode fiber with large extinction ratio which is essential for avoiding mode coupling. The extinction ratio and conversion efficiency of the proposed design were well above 25 dB and −0.5 dB respectively for a wider scan length over the entire C-band. Acknowledgement This work was supported by facilities from the Bharti Center for Communication. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, athttps://doi.org/10.1016/j.yofte.2019.101970. References [1] P. Sillard, M. Bigot-Astruc, D. Molin, Few-mode fibers for mode-division-multiplexed systems, J. Lightwave Technol. 32 (16) (2014) 2824–2829. [2] K. Saitoh, S. Matsuo, Multicore fiber technology, J. Lightwave Technol. 34 (1) (2016) 55–66. [3] J. Sakaguchi, W. Klaus, J.-M.D. Mendinueta, B.J. Puttnam, R.S. Luis, Y. Awaji, N. Wada, T. Hayashi, T. Nakanishi, T. Watanabe, Y. Kokubun, T. Takahata, T. Kobayashi, Realizing a 36-core, 3-mode fiber with 108 spatial channels, Proceedings of Optical Fiber Communications Conference and Exhibition (OFC), Los Angeles, CA, USA, Los Angeles, CA, USA, 2015paper Th5C.2. [4] Y. Sasaki, S. Saitoh, Y. Amma, K. Takenaga, S. Matsuo, K. Saitoh, T. Morioka, Y. Miyamoto, Quasi-single-mode homogeneous 31-core fibre, in Proceedings of European Conference on Optical Communication (ECOC), Valencia, Spain, 2015, paper We. 1.4.4. [5] J.D. Downie, M. Mlejnek, I. Roudas, W.A. Wood, A. Zakharian, J.E. Hurley, S. Mishra, F. Yaman, S. Zhang, E. Ip, Y. Huang, Quasi-single-mode fiber transmission for optical communications, IEEE J. Sel. Top. Quantum Electron. 23 (3) (2017)
7
Contents lists available at ScienceDirect
Optical Fiber Technology journal homepage: www.elsevier.com/locate/yofte
Two-core fiber based mode coupler for single-mode excitation in a twomode fiber for quasi-single-mode operation
T
⁎
Thomas Joseph , Joseph John Electrical Engineering Department, IIT Bombay, Mumbai 400076, India
A R T I C LE I N FO
A B S T R A C T
Keywords: Quasi-single mode operation Fiber coupler Single mode fibers Few mode fibers
Quasi-single mode operation in few-mode fibers is a promising technique for extending the Kerr nonlinearity threshold of standard single mode fibers. Under this operation the design goals of few-mode fibers used for mode division multiplexing can be relaxed. Based on the MinΔneff , we calculated the maximum core radius of twomode and four-mode fibers for quasi-single-mode operation, and is found to be 8 μm and 9.7 μm respectively. We also propose the design of a two-core fiber coupler, based on thermally diffused core technique, for effective excitation of the fundamental mode alone in the above two-mode fiber for the entire C-band. The robustness of the proposed design is studied by varying the design parameters and observing their sensitivity to coupling efficiency and extinction ratios and are found to be well above −0.5 dB and 25 dB respectively.
1. Introduction The meteoric growth of Internet traffic over optical networks around the world drives the research in capacity enhancing methods such as employing few mode fibers (FMFs) [1], multicore fibers (MCFs) [2], high spectral-efficient modulation formats, large effective area fibers etc. By employing mode division multiplexing (MDM) in FMFs and space division multiplexing (SDM) in MCFs, large spectral efficiency can be achieved. Further, by combining FMF and MCF technologies, multicore few mode fibers (MC-FMFs) are developed which support transmission of more than 100 spatial channels over a single fiber [3]. However, FMFs and MC-FMFs require complex and expensive signal processing to recover the data [4]. On the other hand spectrally efficient modulation schemes require more optical signal to noise ratio (OSNR) to get the same bit error rate (BER) as compared to ON-OFF keying [5,6]. One straight forward option to increase OSNR is to launch higher signal power into the fiber. However this can lead to Kerr nonlinearity in standard single mode fibers (SSMFs) which is due to the limited effective area of these fibers. Increasing the effective area of SMF by reducing the core-cladding index difference is restricted by the bending losses [7]. In SSMFs the effective area of the fundamental mode is ∼80 μm2 [8]. By introducing a trench in the cladding this can even be raised to ∼160 μm2 [9–11]. To the best of our knowledge the above limit has not been crossed so far in standard 125 μm grade SMFs (Fibers with Aeff larger than 160 μm2 have more than 125 μm diameter to compensate for micro-bend losses [12]). In order to increase the
⁎
effective area, low index differences and large core diameters are required which in turn introduce higher bending losses and affect the cutoff conditions. An easier method for extending this limit is to use few mode fibers and excite only the fundamental mode [13–16]. This allows us to obtain large Aeff , at the same time limiting the fiber diameter to 125 μm . Marianne et. al fabricated a few mode fiber with fundamental mode area, Aeff , of 220 μm2 with trench assisted refractive index profile [13]. The trench results in a reduction of bending loss. Yaman et. al demonstrated long distance transmission in a few mode fiber at 1310 nm which was actually a large effective area SMF at 1550 nm [15]. Quasi-single mode operation in an FMF leads to multi-path interference (MPI) [17]. Impact of MPI on few mode fiber transmission is discussed in [18]. Frequency domain equalization method for mitigating MPI on FMF is theoretically and experimentally demonstrated in [19]. Yaman et. al demonstrated first quasi-single mode transmission over transoceanic distance using FMFs [20]. Quasi-single mode transmission for long-haul and submarine optical communication is demonstrated by Downie et. al by concatenating large-mode-area single mode fibers and FMFs [21]. However investigations on the effective index difference between the supporting modes (Δneff ), bending loss, and effective area ( Aeff ) of each mode for quasi-single mode operation in a few mode fiber have not been conducted so far to the best of our knowledge. Also the current method used for single mode excitation in FMFs is direct launching from an SMF pigtail which is prone to misalignments that result in power coupling to higher order modes leading to increased MPI. In this paper we calculate the maximum core radius
Corresponding author. E-mail addresses: [email protected] (T. Joseph), [email protected] (J. John).
https://doi.org/10.1016/j.yofte.2019.101970 Received 19 March 2019; Received in revised form 7 June 2019; Accepted 28 June 2019 1068-5200/ © 2019 Elsevier Inc. All rights reserved.
Optical Fiber Technology 52 (2019) 101970
T. Joseph and J. John
in two and four-mode step-index fibers for fundamental mode operation when the loss and MinΔneff of the higher order modes are relaxed. We also propose the design of a two-core fiber based mode coupler for effective excitation of the fundamental mode alone in a two-mode fiber. The remaining part of this paper is organized as follows. Section 2 explains fiber figure of merit which shows the impact of increasing mode effective area. In Section 3 few mode fibers and quasi-single mode operation in these fibers are presented. Section 4 describes the design of a two-core fiber based coupler for single mode excitation in a two-mode fiber followed by the conclusions in Section 5.
7 40 km spans 60 km spans 80 km spans 100 km spans
FIber FOM (dB)
6 5 4 3 2 1
2. Fiber figure of merit
0
The reach and capacity of single mode fibers mainly depend on two factors: attenuation and nonlinear tolerance (governed by the nonlinear refractive index coefficient, n2 and the effective area, Aeff ). It was found that a minor improvement in attenuation significantly improves the link performance [22]. By using pure silica core fibers instead of Ge doped core, a small reduction in attenuation is possible. Besides, the nonlinear coefficient, n2 , of pure silica core is slightly lower (2.1 × 10−20 m2/W) than Ge doped core (2.2–2.3 × 10−20 m2/W) which is an additional advantage. The impact of fiber attenuation, Aeff and n2 can be expressed using the figure of merit (FOM) given by the following equation [22]
80
120
140
160
180
200
220
240
2
Fiber Effective Area (μm ) Fig. 2. Fiber figure of merit vs. effective area ( Aeff ). Both fibers have the same attenuation but different nonlinear coefficients, n2 .
7
FIber FOM (dB)
6
FOM (dB ) Aeff . n2, ref 2⎛ = ⎜10log ⎡ − [α (dB / km) − αref (dB / km)]. L⎞⎟ ⎢ 3 Aeff , ref . n2 ⎠ ⎣ ⎝ Leff ⎤ ⎞ 1⎛ − ⎜10log ⎛⎜ ⎥⎟ 3 L ⎝ eff , ref ⎦ ⎠ ⎝
100
5 4 3 40 km spans 60 km spans 80 km spans 100 km spans
2
(1)
1
where L is the span length, Leff the effective nonlinear length, approximately given by 1/α . α is the attenuation of the fiber in linear units of km−1. The term ‘ref’ in the subscript refers to the reference fiber. The above FOM indicates the difference in Q factor or 20log (Q) between the fiber under consideration and the reference fiber. Since the quasi-single mode operation is for extending the Aeff of the fundamental mode, we are concentrating only on the effect of Aeff , even though the fiber attenuation and n2 has impact on FOM. Fig. 1 shows the FOM of fiber as a function of Aeff for different span lengths. Following are the parameters considered in the simulation: α = 0.153 dB/km, αref = 0.2 dB/km, n2 = 2.1 × 10−20 m2/W, n2, ref = 2.3 × 10−20 m2/W, Aeff , ref = 80 μm2 [5]. These values correspond to pure silica core fiber and GeO2 doped fiber (standard single mode fiber, which is the reference fiber, falls in this category) respectively. We studied the influence of n2 and attenuation separately for the same fiber by varying one of them at a time from the reference value. These results are shown in
0 80
100
120 140 160 180 200 2 Fiber Effective Area (μm )
220
240
Fig. 3. Fiber figure of merit (FOM) vs. effective area ( Aeff ). Both fibers have the same n2 but different attenuation.
Fig. 2 and Fig. 3 respectively. It was found that the reduction in n2 results in an FOM increment of 0.22 dB while the reduction in attenuation improves the FOM by 0.9 dB (the state of the art pure silica core fiber has an attenuation ∼0.146 dB/km which will give an additional FOM improvement of 0.1 dB). Considering these into account an increase in Aeff from 80 μm2 to 160 μm2 results in an FOM improvement of 2–4 dB. It was also found that a reduction in attenuation increases the reach of the fiber link, i.e. for larger span length the FOM improvement is more for smaller attenuation values. These results show that an increase in Aeff has greater influence on fiber capacity.
Fiber FOM (dB)
7 6
3. Quasi-single mode operation in few mode fibers
5
Few mode fibers (FMFs) are of two types: weakly coupled and strongly coupled. Weakly coupled FMFs have step index refractive index profiles while the strongly coupled ones have graded index refractive index profiles [23]. Since FMFs are designed for exploring spatial diversity, design of FMFs have to consider many factors, such as loss of each supporting mode, effective index difference between the adjacent modes, effective area of each mode, differential mode delay (DMD), etc. When we are concentrating only on the fundamental mode of FMFs, many design criteria for higher order modes can be relaxed or modified. In order to avoid mode coupling between adjacent modes, the minimum effective index difference between any two modes should be ⩾0.5 × 10−3 [24,25]. This value is higher than the x and y polarized modes of a polarization maintaining fiber. Also bending loss of each LP mode should be less than 10 dB/turn at 10 mm bending radius for good
4 3
40 km spans 60 km spans 80 km spans 100 km spans
2 1 0 100
150
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Fiber Effective Area (μm2) Fig. 1. Fiber figure of merit (FOM) vs. effective area ( Aeff ). 2
Optical Fiber Technology 52 (2019) 101970
T. Joseph and J. John −3
600
x 10 7
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LP01 LP11
X: 11.6 Y: 342.2
300
eff
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Core radius (μm)
mode robustness [23]. The above two are the main design requirements for a spatial mode in an FMF. All propagating modes should satisfy this criteria when used for MDM. However, if we operate an FMF in the quasi-single mode regime, we can relax these criteria for higher order propagating modes, i.e. in a two LP mode fiber, these requirements can be relaxed for the LP11 mode. We studied the feasibility of quasi-single mode operation in two-mode and four-mode fibers by relaxing the design requirements. The design relaxations are calculated by varying different parameters such as core radius, Δneff and Aeff . These calculations are done at an operating wavelength of 1550 nm with a core refractive index value of 1.444. Fig. 4 shows variations of effective index difference (Δneff ) between the two propagating modes (LP01& LP11) as a function of the core radius for a two mode fiber (TMF). The Δneff is > 0.5 × 10−3 for all the core radius values considered. It was found that up to 14 μm core radius the Δneff is higher than the required limit of 0.5 × 10−3 . Bending loss for each mode of a step index fiber can be calculated using the following relation [23,26]. Calculated losses for the two supporting modes of the TMF are shown in Fig. 5.
Aeff , mn =
2 2 k 2 − β 2 and γ = β 2 − nclad k 2 are the field decay rates where κ = ncore in the core and cladding regions respectively, k = 2π /λ the free space propagation constant, β the propagation constant of the considered LP mode of an unbent fiber, R the bend radius, em is a constant depending 20
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Loss (dB)
X: 11.6 Y: 8.977
−20
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LP01 LP11
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∬ |Fm (x , y )|2 dxdy ∬ |Fn (x , y )|2 dxdy ∬ |Fm (x , y )|2 |Fn (x , y )|2 dxdy
(3)
Aeff of the LP01 mode is found to be more than 340 μm2 when the core radius is 11.6 μm , with loss and Δneff satisfying the design requirements. If we require a minimum Δneff of 1 × 10−3 , the core radius corresponding to this value is 10.4 μm and the loss of LP01 mode at this point is less than 2 dB/turn. The Aeff corresponding to this value is 275 μm2 which is far higher than that of an SSMF. These results show that the quasi-single mode regime operation of TMF can be utilized to overcome the Aeff limitations of an SSMF. A recently reported work fabricated a TMF having an Aeff of 215 μm2 for the LP01 mode with very low macro-bend losses and an equivalent micro-bend losses as that of SSMFs [14]. However, the multi-path interference (MPI) level of this fiber was found to be −24 dB, even with a Δneff of 1.3 × 10−3 on an 85 km fiber. An MPI level below −35 dB is required to eliminate system degradation which can be obtained through increased Δneff value. This can be done by tailoring the effective refractive index of LP11 mode to a lower value without affecting that of the LP01 mode. Also higher order mode filters can be employed to reduce the MPI [18]. The loss of LP01 mode can be further reduced by using a four-LP mode fiber and operating it in the quasi-single mode regime. The V number of a four-LP mode fiber can go up to 5.1 (V = 3.8 in TMF), enabling us to increase either the refractive index difference or the Aeff (by increasing core radius) of the fiber modes. When the V number increases the confinement of the mode also increases resulting in a reduction in the loss which can be used to overcome the loss drawback of the TMF. The calculated macro-bending losses of each fiber mode of a four-LP mode fiber is shown in Fig. 7. The loss of LP01 mode is far lower than the ITU recommendations at a core radius of 14 μm ; however the loss of the higher order modes are more than 10 dB/turn at this point. Δneff of the supporting modes of the four-LP mode fiber are shown in Fig. 8. At 14 μm core radius the Δneff between the fundamental mode and the LP11 mode is 0.8 × 10−3 , which shows that in a four-mode fiber the limiting factor in core radius is the Δneff rather than the macro-bending loss as in the TMF. Calculated Aeff of the four-mode fiber is shown in Fig. 9. Aeff of the LP01 mode is 437 μm2 when the core radius is 14 μm . This is approximately 100 μm2 higher than that of the TMF. Also the Aeff is 354 μm2 when we fix the Δneff between the
(2)
10
12
on the order of the LPmn mode (em = 2 for m = 0 and em = 1 for m ≠ 0), Km ± 1 are the modified Bessel functions. The loss of LP01 mode is found to be less than 10 dB/turn up to a core radius of 11.6 μm . For quasi-single mode operation in a TMF, the maximum core radius is determined by the loss rather than Δneff . The effective area of the fiber modes can be calculated using the following relations [27] and are shown in Fig. 6.
−2γ 3 (R + a)
10
8 10 Core radius (μm)
Fig. 6. Variations of Aeff of the two supporting modes (LP01 and LP11) of a two mode fiber with core radius.
Fig. 4. Variation of Δneff as a function of core radius for a two mode fiber.
eff − 2γa⎤ 4.34π 1/2κ 2exp ⎡ 3β2 ⎣ ⎦ 2α (dB / m) = 3/2V 2K em (R + a)1/2 m − 1 (γa) Km + 1 (γa) eff γ
6
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Fig. 5. Bending loss variations for the two supporting modes (LP01 and LP11) of a two-mode fiber with core radius. 3
Optical Fiber Technology 52 (2019) 101970
T. Joseph and J. John 20
for Δneff ⩾1.7 × 10−3 , mode coupling coefficient converges to a constant value [28]. In view of this our later designs fixed the MinΔneff to be 1.7 × 10−3 in a TMF. Core radii corresponding to this Δneff (1.7 × 10−3 ) for a TMF is 8 μm and 9.7 μm for a four-mode fiber. Effective areas of fundamental mode of TMF and four-mode fiber for the above mentioned core radius is 162 μm2 and 210 μm2 respectively. The core radius and effective area can be further increased by proper index profile tailoring. Since the quasi-single mode operation in FMF is considered in this work, the inter-modal dispersion is not present; only chromatic dispersion is applicable. We calculated the chromatic dispersion of the two-mode and four-mode fibers at 8 μm and 9.7 μm core radii and found them to be 22.8 ps/nm-km and 23.3 ps/nm-km respectively.
10
LP01 LP11 LP21
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Loss (dB)
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LP02
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X: 14 Y: 6.6e−08 −10
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4. Two-core fiber mode coupler for single mode excitation in a two-mode fiber
−20
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Quasi-single mode operation in TMFs requires the effective excitation of the fundamental mode alone with good extinction ratio between the supporting LP01 and LP11 modes to reduce cross-talk. Yaman et. al used light launching from an SMF for effective excitation of the fundamental mode in a TMF. The SMF and TMF used in their experiment have comparable core diameters which result in an effective excitation with good extinction ratio. However for larger TMF core diameters, direct launching from an SMF will couple power to the higher order modes resulting in much lower extinction ratios, and hence special launching methods are required for efficient excitation of the fundamental mode. Power coupling coefficients of the excited modes in an MMF with center launching show that significant power gets coupled to the higher order modes even for smaller misalignments [29]. In a TMF even after effective excitation, power coupling will take place from the excited LP01 to the LP11 mode during propagation. This cross-talk can be reduced by making the effective index differences between the two modes as large as possible. But Maruyama et. al experimentally verified that under normal working conditions increasing the Δneff beyond 1.7 × 10−3 will not have much impact [28]. This threshold value depends on the fiber working environments, such as winding tension on the fiber. In our fiber design we fixed the value of MinΔneff to be 1.7 × 10−3 for quasi-single mode operation of the TMF. Under these conditions the cross-talk and the resulting multi-path interference (MPI) can be reduced by effective suppression of LP11 mode excitation at the transmitter side. For this purpose high precision launching is a must and any misalignments will lead to the excitation of the LP11 mode which will increase the MPI. To alleviate this problem we propose the design of a two-core fiber coupler which excites the LP01 mode alone in a TMF with a large extinction ratio. The proposed two-core coupler has two cores; one is a single-mode core and the other one two-mode. Input is given to the single-mode core and is coupled to the fundamental mode of the two-mode core in a thermally expanded core (TEC) region which is obtained by thermally diffused core technique (TDCT) [30]. In the TDCT technique, fiber under consideration is heated above the temperature of 1200 °C, leading to the diffusion of dopants from core into the cladding resulting in an expanded core [31,32]. The heating can be done by employing an oxy-hydrogen flame of a fiber-tapering machine or using an electric arc. The two cores are designed in such a way that the effective indices of the fundamental modes of both the cores are matching. This leads to effective power coupling between the LP01 modes of the two cores in the TEC region. Design details of this two-core fiber coupler is described below.
Fig. 7. Variations of bending loss of a four-mode fiber with core radius.
0.012 n
−n
n
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n
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Fig. 8. Variations of Δneff of a four-mode fiber with core radius.
500 X: 14 Y: 437.4
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Fig. 9. Variations of Aeff of supporting modes of a four-mode with core radius.
fundamental mode and the LP11 mode to be 1 × 10−3 , which is approximately 80 μm2 larger than the TMF. This way the Aeff of a fiber can be increased to any arbitrary higher value by operating an FMF in the fundamental mode regime. To ensure low mode coupling to the LP11 mode, a large Δneff must be maintained between the fundamental mode and the next higher order mode while keeping the benefits of larger Aeff as such. This can be done by proper refractive index profile tailoring. While tailoring the refractive index profile, the Δneff between the fundamental mode and the higher order modes must be kept high to avoid any coupling from the fundamental mode. However it was found that
4.1. Design of two-core fiber coupler As described in the previous section first we fixed the MinΔneff as 1.7 × 10−3 for the two-mode core. This corresponds to a core radius of 8 μm and the resulting Aeff is greater than 160 μm2 . The core refractive index is 1.4546 and the cladding refractive index 1.45. For the singlemode core we fixed the core diameter to be 9.8 μm , core refractive 4
Optical Fiber Technology 52 (2019) 101970
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Fig. 10. Schematic representation of thermally expanded core (TEC) fiber coupler.
index = 1.4548, and the cladding refractive index = 1.45, which is the same as that of the two-mode core. The core refractive indices are chosen for effective index matching of the two fundamental modes at the operating wavelength of 1530 nm. Normalized frequency or the V number of the single-mode core is 2.37 and that of the two-mode core is 3.79. Therefore they support one, and two modes respectively at 1530 nm. The initial center to center separation between the two cores is 22 μm and the gap between them is 9.1 μm. Under this condition there is no or negligibly small coupling between the two cores. This two-core fiber is heated for a duration of 16 min at a temperature of 1650 °C so that the dopants in the cores diffuse into the cladding. This results in the TEC region and the separation between the cores becoming very small leading to interaction of modes between the cores. Since the effective index of the fundamental modes of the two cores are matched, power from the single-mode core couples only to the fundamental mode of the two-mode core. The expanded core radius can be calculated using the relation ΔA = Dt , where D is the diffusion coefficient of the dopant and t the heating duration in seconds. For GeO2 the value of D is 2.1 × 10−14 m2 /s at 1650 °C [30]. Fig. 10 shows the schematic diagram of the proposed TEC coupler. Input is given to the singlemode core (Pin ) and output obtained through the two-mode core (Pout2 ). For simulation purpose we considered the following device structure. The single-mode core is placed at −10 μm and the two-mode core at 12 μm , with a total scan length of 3.8 mm and a taper length of 13.8 mm. These values correspond to a power coupling from the singlemode core to the two-mode core with no power coupling back into the single-mode core. For our simulations, the two-core fiber is assumed to have a total length of 28.8 mm which is assumed to be heated for a sufficient duration (16 min using TDCT) to obtain the required core diameter expansion of 9 μm . Thus the total core diameter of the singlemode core becomes 18.8 μm and the two-mode core 25 μm . The final gap between the two cores in the TEC region is 0.1 μm resulting in strong coupling between the fundamental modes. As shown in Fig. 11 the input to the coupler is to the single-mode core placed at −10 μm . The corresponding output intensity of the two-mode core is shown in Fig. 12. Comparison of input and output intensities shows that the effective area of the output is larger (since the two-mode core has larger diameter). Measured power in each of the modes of the two-core fiber along the light propagation direction is shown in Fig. 13. We used two parameters to evaluate the performance of the converter, viz. the coupling efficiency, CLP01, and the extinction ratio, ER. CLP01 is defined as ratio of the coupled power in the LP01 mode of the two-mode core to the input power of the LP01 of the single-mode core; ER is the ratio of power in the LP01 mode to the LP11 mode power of the two-mode core.
CLP01 = 10. log10 ER = 10. log10
PLP01 Pin
PLP01 PLP11
Fig. 11. Input of the two-core coupler simulated using Beamprop (given to the single-mode core at −10 μm ).
Fig. 12. Output of the mode converter simulated using Beamprop. More than 94% of input power gets coupled to the two-mode core LP01 mode.
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Fig. 13. Measured power in each of the modes of thermally expanded two-core fiber. Negligibly small power coupled to the LP11 mode of the two-mode core.
coupled to the LP11 mode of the two-mode core.
(4) 4.2. CLP01 and ER variations with scan length (5)
When the scan length was 3.8 mm, more than 94% of the input power got coupled to the LP01 mode of the two-mode core which is the maximum value obtained in our design. In this section the effect of scan
where Pin is the input power to the single-mode core, PLP01 the power coupled to the LP01 mode of two-mode core, and PLP11 the power 5
Optical Fiber Technology 52 (2019) 101970
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Fig. 14. Coupling efficiency (CLP01) variations of two-core coupler with scan length.
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Fig. 16. Coupling efficiency (CLP01) variations of two-core coupler with wavelength.
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Fig. 15. Extinction ratio (ER) variations of two-core coupler with scan length.
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Fig. 17. Extinction ratio (ER) variations of two-core coupler with wavelength.
−0.2
length variations on the extinction ratio and the power coupling efficiency are calculated. Scan length variations are considered only in a range over which power coupled to the LP01 mode is greater than 90%. Calculated CLP01 and ER values are shown in Fig. 14 and Fig. 15 respectively. It is evident that the coupling efficiency is well above −0.5 dB for a wide range (∼1.7 mm) of scan lengths. Besides, ER is greater than 24 dB. The ER values show nonuniform variation with scan length; however power coupled to the LP11 mode in all the cases were ⩽0.3% which is negligibly small. Nonuniform variations in the ER is due to the small changes in the LP11 mode coupled power which is negligibly small as evident from the large ER values.
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4.3. CLP01 and ER variations with wavelength
−1 8.5
Performance of the coupler to changes in the wavelength is evaluated in this section. The proposed two-core fiber coupler is designed for 1530 nm which is the starting wavelength of the C-band. Variations in the coupling efficiency and extinction ratio are calculated and shown in Fig. 16 and Fig. 17 respectively. For the entire C-band CLP01 is found to be higher than −0.45 dB, and gradually decreasing with increasing wavelength. Even though ER shows nonlinear variations, it is important to note that the ER value is more than 26 dB for the entire C band. Reduction in the CLP01 and ER values are due to the phase mismatch for wavelength changes.
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Fig. 18. Coupling efficiency (CLP01) variations of two-core coupler with coreexpansion.
expansion. Variations in the coupled power due to core expansion and the resulting CLP01 and ER are calculated in this section. Fig. 18 and Fig. 19 show CLP01 and ER values as a function of core expansion. It is found that the conversion efficiency is maximum for the designed value of 9 μm and decreases for smaller expansion values. For core expansion variations ER changes gradually as compared to other parameter variations, and is maximum for the 8.95 μm expansion case. For the designed expansion value the two cores literally touch each other (to be
4.4. CLP01 and ER variations with core expansion Interaction between the two cores depends on the extent of core 6
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31–42. [6] Q. Sui, H. Zhang, J.D. Downie, W.A. Wood, J. Hurley, S. Mishra, A.P.T. Lau, C. Lu, H.-Y. Tam, P.K.A. Wai, Long-haul quasi-single-mode transmissions using few-mode fiber in presence of multi-path interference, Opt. Express 23 (3) (2015) 3156–3169. [7] P. Sillard, New fibers for ultra-high capacity transport, Opt. Fiber Technol. 17 (2011) 495–502. [8] P. Sillard, S. Richard, L.A. De Montmorillon, M. Bigot-Astruc, Micro-bend losses of trench-assisted single-mode fibers, Proceedings of European Conference on Optical Communication (ECOC), Torino, Italy, 2010 paper We.8.F.3. [9] M. Bigot-Astruc, F. Gooijer, N. Montaigne, P. Sillard, Trench-assisted profiles for large-effective-area single-mode fibers, in Proceedings of European Conference on Optical Communication (ECOC), Brussels, Belgium, 2008, paper Mo.4.B.1. [10] M. Bigot-Astruc, L. Provost, G. Krabshuis, P. Dhenry, P. Sillard, 125 m glass diameter single-mode fiber with Aeff of 155 μm2, in: Proceedings of Optical Fiber Communication Conference/National Fiber Optic Engineers Conference (OFC/ NFOEC) Los Angeles, CA, USA, 2011, paper OTuJ2. [11] Y. Yamamoto, M. Hirano, K. Kuwahara, T. Sasaki, OSNR-enhancing pure-silica-core fiber with large effective area and low attenuation, Proceedings of Optical Fiber Communication Conference/National Fiber Optic Engineers Conference (OFC/ NFOEC), San Diego, CA, USA, (2010) paper OTuI2. [12] M. Tsukitani, M. Matsui, K. Nagayama, E. Sasaoka, Ultra low nonlinearity puresilica-core fiber with an effective area of 211 m2 and Transmission Loss of 0.159dB/ km, in Proceedings of European Conference on Optical Communication, Copenhagen, Denmark, 2002, paper Tu3.2.2. [13] M. Bigot-Astruc, P. Sillard, Realizing large effective area fibers, in: Proceedings of Optical Fiber Communication Conference (OFC) Los Angeles, CA, USA, 2012, paper OTh4I.1. [14] D. Boivin, M. Bigot-Astruc, M. Travagnin, P. Sillard, Weakly-coupled few-mode fibers for single-mode and mode-division-multiplexed transmissions, in: Proceedings of Optical Fiber Communication Conference/National Fiber Optic Engineers Conference (OFC/NFOEC) Anaheim, CA, USA, 2013, paper OTh3K.6. [15] F. Yaman, N. Bai, B. Zhu, T. Wang, G. Li, Long distance transmission in few-mode fibers, Opt. Express 18 (12) (2010) 13250–13257. [16] Q. Sui, H. Zhang, J.D. Downie, W.A. Wood, J. Hurley, S. Mishra, A.P.T. Lau, C. Lu, H.-Y. Tam, P. Wai, 256 Gb/s PM-16-QAM quasi-single-mode transmission over 2600 km using few-mode fiber with multi-path interference compensation, in: Proceedings of Optical Fiber Communication Conference (OFC) San Francisco, CA, USA, 2014, paper M3C.5. [17] M. Mlejnek, I. Roudas, J.D. Downie, N. Kaliteevskiy, K. Koreshkov, Coupled-mode theory of multipath interference in quasi-single mode fibers, IEEE Photonics J. 7 (1) (2015) 1–16. [18] F. Yaman, E. Mateo, T. Wang, Impact of modal crosstalk and multi-path interference on few-mode fiber transmission, in: Proceedings of Optical Fiber Communication Conference/National Fiber Optic Engineers Conference (OFC/NFOEC), Los Angeles, CA, USA 2012, paper otu1d.2. [19] N. Bai, C. Xia, G. Li, Adaptive frequency-domain equalization for the transmission of the fundamental mode in a few-mode fiber, Opt. Express 20 (11) (2012) 241010–24017. [20] F. Yaman, S. Zhang, Y.K. Huang, E. Ip, J.D. Downie, W.A. Wood, A. Zakharian, S. Mishra, J. Hurley, Y. Zhang, I.B. Djordjevic, M.F. Huang, E. Mateo, K. Nakamura, T. Inoue, Y. Inada, T. Ogata, First quasi-single-mode transmission over transoceanic distance using few-mode fibers, Proceedings of Optical Fiber Communication Conference (OFC), Los Angeles, CA, USA, 2015 paper Th5C-7.. [21] J.D. Downie, M. Mlejnek, W.A. Wood, J. Hurley, A. Zakharian, I. Roudas, S. Mishra, F. Yaman, S. Zhang, E. Ip, Y.K. Huang, Quasi-single-mode transmission for longhaul and submarine optical communications, in: Proceedings of Conference on Lasers and Electro-Optics (CLEO), San Jose, CA, USA, 2016, paper SM4F.6. [22] S. Makovejs, J.D. Downie, J.E. Hurley, J.S. Clark, I. Roudas, C.C. Roberts, H.B. Matthews, F. Palacios, D.A. Lewis, D.T. Smith, P.G. Diehl, J.J. Johnson, C.R. Towery, S.Y. Ten, Towards superior transmission performance in submarine systems: leveraging ultralow attenuation and large effective area, J. Lightwave Technol. 34 (1) (2016) 114–120. [23] J. Han, G. Gao, Y. Zhao, S. Hou, Bend performance analysis of few-mode fibers with high modal multiplicity factors, J. Lightwave Technol. 35 (13) (2017) 2526–2534. [24] J. Liu, J. Zhang, J. Han, G. Gao, Y. Zhao, W. Gu, Design and optimization of weaklycoupled few-mode fiber with low nonlinearity, Chin. Opt. Lett. 12 (3) (2014) pp. 030601–1–030601-3. [25] M. Bigot-Astruc, D. Boivin, P. Sillard, Design and fabrication of weakly-coupled fewmodes fibers, Proceedings of IEEE Photonics Society Summer Topical Meeting Series (2012) paper TuC1.1. [26] R.T. Schermer, J.H. Cole, Improved bend loss formula verified for optical fiber by simulation and experiment, IEEE J. Quantum Electron. 43 (10) (2007) 899–909. [27] C. Koebele, M. Salsi, G. Charlet, S. Bigo, Nonlinear effects in mode-division-multiplexed transmission over few-mode optical fiber, IEEE Photonics Technol. Lett. 23 (18) (2011) 1316–1318. [28] R. Maruyama, N. Kuwaki, S. Matsuo, M. Ohashi, Experimental investigation of relation between mode-coupling and fiber characteristics in few-mode fibers, in: Proceedings of Optical Fiber Communication Conference (OFC), Los Angeles, CA, USA, 2015 paper M2C.1. [29] T. Joseph, J. John, Mode-field matched twin spot launch for enhancing data rates in multimode fibers, 2016 22nd National Conference on Communication (NCC), 2016. [30] Y. Zhao, A. Zhou, X. Ouyang, Y. Ouyang, C. 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ER (dB)
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Fig. 19. Extinction ratio (ER) variations of two-core coupler with core expansion.
more specific, there is a gap of 0.1 μm between the cores). Reduction in the CLP01 and ER values for smaller expansions is mainly due to the weaker interaction between the two coupling modes. 5. Conclusions Quasi-single mode operation in few mode fibers is an interesting method for extending the Aeff and the Kerr nonlinearity threshold. For quasi-single mode operation, design criteria for the higher order modes in a few mode fiber can be relaxed. This enables an extended core radius and corresponding increase in the fundamental mode Aeff of few mode fibers used for MDM. This relaxation helps us to extend the core radius of a two-mode fiber to 8 μm and the Aeff to ⩾160 μm2 . The mode coupling between the supporting modes along the propagation direction depends on the power coupled to the higher order modes at the input end. We proposed the design of a two-core fiber coupler which can effectively excite only the fundamental mode of a two-mode fiber with large extinction ratio which is essential for avoiding mode coupling. The extinction ratio and conversion efficiency of the proposed design were well above 25 dB and −0.5 dB respectively for a wider scan length over the entire C-band. Acknowledgement This work was supported by facilities from the Bharti Center for Communication. Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, athttps://doi.org/10.1016/j.yofte.2019.101970. References [1] P. Sillard, M. Bigot-Astruc, D. Molin, Few-mode fibers for mode-division-multiplexed systems, J. Lightwave Technol. 32 (16) (2014) 2824–2829. [2] K. Saitoh, S. Matsuo, Multicore fiber technology, J. Lightwave Technol. 34 (1) (2016) 55–66. [3] J. Sakaguchi, W. Klaus, J.-M.D. Mendinueta, B.J. Puttnam, R.S. Luis, Y. Awaji, N. Wada, T. Hayashi, T. Nakanishi, T. Watanabe, Y. Kokubun, T. Takahata, T. Kobayashi, Realizing a 36-core, 3-mode fiber with 108 spatial channels, Proceedings of Optical Fiber Communications Conference and Exhibition (OFC), Los Angeles, CA, USA, Los Angeles, CA, USA, 2015paper Th5C.2. [4] Y. Sasaki, S. Saitoh, Y. Amma, K. Takenaga, S. Matsuo, K. Saitoh, T. Morioka, Y. Miyamoto, Quasi-single-mode homogeneous 31-core fibre, in Proceedings of European Conference on Optical Communication (ECOC), Valencia, Spain, 2015, paper We. 1.4.4. [5] J.D. Downie, M. Mlejnek, I. Roudas, W.A. Wood, A. Zakharian, J.E. Hurley, S. Mishra, F. Yaman, S. Zhang, E. Ip, Y. Huang, Quasi-single-mode fiber transmission for optical communications, IEEE J. Sel. Top. Quantum Electron. 23 (3) (2017)
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