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Abstract
By increasing the number of modes of transmission in optical fiber, the mode-division multiplexing (MDM) technology can effectively improve the transmission capacity. The mode add-drop technology is an important part of the MDM system and a key element for realizing flexible networking. In this paper, a mode add-drop technology based on few-mode fiber Bragg grating (FM-FBG) is reported for the first time. The technology utilizes the reflection characteristics of Bragg grating to realize the add-drop function in the MDM system. The grating is written in parallel according to the optical field distribution characteristics of different modes. By changing the writing grating spacing Δa to match the optical field energy distribution of the few-mode fiber, the few-mode fiber grating with high self-coupling reflectivity for the high-order mode is fabricated, and the performance of the add-drop technology is improved. The mode add-drop technology is verified in a 3 x 3 MDM system, which uses quadrature phase shift keying (QPSK) modulation and coherence detection. The experimental results show that the excellent transmission, add, and drop of 3 x 8 Gbit/s QPSK signals in 8 km few-mode fibers are achieved. The realization of this mode add-drop technology only requires Bragg gratings, few-mode fiber circulators, and optical couplers. It has the advantages of high performance, simple structure, low cost, and easy implementation, and it can be widely used in the MDM system.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
With the rapid development of the Internet industry, the information demand of all walks of life shows explosive growth, and the increase of data volume has higher requirements on the transmission capacity of optical fiber communication networks. However, the transmission capacity of the existing single-mode fiber is limited by the Shannon limit, and there will be bandwidth exhaustion soon [1,2]. Few-mode fiber has multiple orthogonal modes, and each mode can be used as an independent channel for information transmission. The information transmission capacity can be increased exponentially using mode-division multiplexing (MDM) technology, which has developed rapidly in recent years [3–10].
Multiple modes are transmitted in a few-mode optical fiber for an MDM system. At a particular node of a long-distance transmission system, it is usually necessary to drop the information carried by a mode from the trunk line. Similarly, information needs to be added to the trunk line at the node for transmission, that is, to realize the add-drop of a particular mode at the node [11,12]. Existing add-drop technology for MDM systems can be roughly divided into spatial optical path type and on-chip waveguide type. The spatial optical path type is easy to implement but has a complex structure and large insertion loss [13–15]. The on-chip waveguide has good controllability and high integration, but it is difficult to realize [16–19]. In addition, a study has used the mode-selective coupler based on long-period gratings to realize the mode add-drop function [20], the performance is good, and the coupling interference between modes can be effectively eliminated. However, the core component of this technology, the mode-selective coupler, needs first to process the few-mode fiber and the single-mode fiber to make their effective refractive indices approximately the same and fabricate long-period gratings, respectively. And by precisely controlling the parameters of the two gratings to match the phase-matching conditions of the modes, the efficient conversion from the fundamental mode to the high-order mode is realized, which requires high fabrication accuracy and conditions.
This paper proposes a mode add-drop technology based on few-mode fiber Bragg gratings, which only needs to fabricate Bragg gratings in few-mode fibers without other processing. Using its reflection characteristics, when the phase matching condition is met, a particular mode can be reflected at a specific wavelength, while other modes are not affected, so multiple Bragg gratings can be used at a specific wavelength to achieve separation of different modes, thereby realize the mode add-drop function. The components required for the system are easy to fabricate, no pre-processing is required, the cost is low, and the performance is good. In the process of gratings fabrication, the femtosecond laser method is used to write the gratings in parallel. The self-coupling reflectivity of $LP_{01}$, $LP_{11}$, and $LP_{21}$ modes, which is 95$\%$, 87$\%$, and 83$\%$, respectively, by changing the writing position of the gratings to match the energy distribution of the mode field of the high-order mode, which effectively improves the performance of the mode add-drop technology, and is verified in the MDM system. The signal quality of the add and drop is tested experimentally, and the constellation diagrams and bit error rate curves are given.
2. Design and fabrication of few-mode fiber Bragg gratings with high self-coupling reflectivity
2.1 Fabrication principle of fiber Bragg grating
Compared with ordinary single-mode fibers, few-mode fibers have a large mode field area, allowing a small number of fiber modes to be co-transmitted in the fiber. Set the polarization direction of the optical field as y, then the expression of the Bessel equation of the mode field in the few-mode step-index fiber is as follows [21,22]:
According to the eigenequation, the optical field distribution of different modes can be simulated, among which the optical field distributions of $LP_{01}$, $LP_{11}$, and $LP_{21}$ are shown in Fig. 1.
Fig. 1. Energy distribution of mode field of few-mode fiber. (a) $LP_{01}$. (b) $LP_{11}$. (c) $LP_{21}$.
By periodically changing the refractive index distribution of the few-mode fiber core, the few-mode fiber Bragg grating (FM-FBG) can be fabricated, and the effect of the grating on the beam can be described by the diffraction equation [23,24].
where n is the refractive index of the medium, $\theta _{2}$ is the diffraction Angle, m is the diffraction order, and $\lambda$ is the wavelength of light. When this beam of light is transmitted in the fiber, its propagation constant $\beta = 2\pi \cdot {n_{eff}}\sin \frac {\theta }{\lambda }$ can be substituted into Eq. (3) to obtain the phase matching condition,For FM-FBG, when two coupling modes are in the opposite direction, $\beta _{1} = -\beta _{2}$. Then Eq. (4) can be expressed as:
Therefore, when mode self-coupling reflection occurs in M-order FM-FBG gratings, the resonant condition is:
Therefore, under the condition that the effective refractive index of different modes of the few-mode fiber is known, different grating period $\Lambda$ can be selected to make the Bragg wavelength $\lambda$ of each mode grating the same to realize the self-coupling reflection of different modes at the same wavelength $\lambda$.
Select Yangtze Optical Fiber and Cable (YOFC) company’s four-mode step-index fiber to fabricate Bragg grating, the core diameter of the fiber is 18.5 $\mathrm{\mu}$m, the cladding diameter is 125 $\mathrm{\mu}$m, and the $LP_{01}$ mode effective refractive index is 1.4488. The effective refractive index of the $LP_{11}$ mode is 1.4474. The effective refractive index of $LP_{21}$ mode is 1.4456.
According to Eq. (6), at 1550.02 nm, the first-order Bragg grating periods of self-coupling reflection by $LP_{01}$, $LP_{11}$, and $LP_{21}$ are 534.93 nm, 535.45 nm, and 536.12 nm, respectively.
In fabricating Bragg gratings, the reflected light of each mode will be mixed due to the small difference in the effective refractive index of each mode and the slight difference in the period of Bragg grating of each mode, and it is difficult to distinguish effectively. Therefore, we choose to fabricate second-order Bragg grating and double its grating period so that different light modes can be effectively distinguished. Moreover, reduce the fabrication difficulty.
In this paper, at 1550.02 nm, the periods of the second-order Bragg gratings with the self-coupling reflection of $LP_{01}$, $LP_{11}$, and $LP_{21}$ are 1069.8647 nm, 1070.8995 nm, and 1072.2330 nm, respectively.
2.2 Fiber Bragg grating fabrication system
We used the femtosecond laser writing method to write Bragg grating, and its fabrication system is shown in Fig. 2.
Fig. 2. Fabrication system of fiber Bragg grating. OSA, Optical Spectrum Analyzer; CCD, Charge Coupled Device.
The laser used in this system is the Pharos series femtosecond laser (PH1-10W) produced by Light Conversion Company. The laser wavelength is 1030 nm, the pulse width is adjustable (290 fs$\sim$10 ps), and the maximum single pulse energy can reach 200 $\mathrm{\mu}$J (@10W$/$50 kHz). The short-wavelength laser is more conducive to achieving high-precision machining. The 515 nm femtosecond laser can be obtained by frequency doubling the 1030 nm femtosecond laser by $\beta$-BaB2O4 (BBO) crystal. The laser is focused into the core by an Olympus oil-immersed objective lens (60${\times }$/1.42), and a specific optical fiber fixture clamps the fiber. The lighting method is transmission lighting, and the processing can be observed in real-time through the CCD camera at the bottom. The X and Y axes of the 3D displacement platform are the ABL1000 series high-precision air floating displacement platform produced by Aerotech, with a maximum stroke of 50 mm, resolution of 2.5 nm, and repeated positioning accuracy of $\pm$50 nm. The Z-axis is also the QF46Z piezoelectric displacement table produced by the company. The closed-loop stroke is 250 $\mathrm{\mu}$m, the resolution can reach 0.5 nm, and the repeated positioning accuracy is 3 nm. In order to reduce the impact of external vibration, the entire machining system is placed on an air-floating optical platform. After the grating writing is completed, the transmission spectrum and reflection spectrum of the grating can be obtained from OSA1 and OSA2.
We wrote three Bragg gratings in parallel; the spacing between the gratings is $\Delta a$, as shown in Fig. 3. Set the pulse width of the laser to 290fs, the repetition frequency to 400 HZ, the pulse energy to 190 nJ, and the grating length to 8 mm. In order to obtain the intensity distribution of self-coupling reflection peaks of different modes, we built the test system, as shown in Fig. 4. The output wavelength of the tunable laser source is adjusted to the corresponding Bragg wavelength of the grating. Modes $LP_{01}$, $LP_{11}$, and $LP_{21}$ are excited by the photonic lantern, respectively, and coupled into the Bragg grating to be tested through the circulator port 2. The beam quality analyzer observes the mode field intensity distribution of the reflected light signal at the circulator port 3.
2.3 Fiber Bragg grating test results
According to the relevant parameters of the few-mode fiber used, we simulated the optical field distribution of different modes in the fiber, as shown in Fig. 1, and the relevant parameters of the fiber are shown in Table 1. After analyzing Fig. 1, it is found that the mode optical field energy distribution of different modes in the fiber is different. The optical field of the $LP_{01}$ mode is mainly concentrated in the range of 0 $\mathrm{\mu}$m-6 $\mathrm{\mu}$m from the center of the fiber. When the grating is written at the center of the fiber and 3 $\mathrm{\mu}$m on both sides of the center of the fiber, it can better match the mode optical energy distribution of the $LP_{01}$ mode and realize the high reflectivity of $LP_{01}$ mode; the optical field of the $LP_{11}$ mode is mainly concentrated in the range of 2.5 $\mathrm{\mu}$m-7.5 $\mathrm{\mu}$m from the center of the fiber. When the grating is written at 5 $\mathrm{\mu}$m on both sides of the center of the fiber, it can better match the mode optical energy distribution of the $LP_{11}$ mode and realize the high reflectivity of $LP_{11}$ mode; the optical field of the $LP_{21}$ mode is mainly concentrated in the range of 0 $\mathrm{\mu}$m-2.75 $\mathrm{\mu}$m and 5 $\mathrm{\mu}$m-9 $\mathrm{\mu}$m from the center of the fiber. When the grating is written at the center of the fiber and 7 $\mathrm{\mu}$m on both sides of the center of the fiber, it can better match the mode optical energy distribution of the $LP_{21}$ mode and realize the high reflectivity of $LP_{21}$ mode.
Table 1. Relevant parameters of the fiber.
Since the high-order mode optical field distribution consists of several different light spots, we choose to write three Bragg gratings in parallel to better match the optical field intensity distribution and improve the self-coupling reflectivity of the high-order mode of the gratings. For $LP_{11}$ mode, although the optical field energy at the center was 0, to maintain the experiment’s consistency, three Bragg gratings were written in parallel during the fabrication of $LP_{01}$ mode, $LP_{11}$ mode, and $LP_{21}$ mode gratings.
To sum up, in order to achieve high self-coupling reflectivity of the three modes, we selected three $\Delta a$ values of 3 $\mathrm{\mu}$m, 5 $\mathrm{\mu}$m, and 7 $\mathrm{\mu}$m. Respectively. Few-mode fiber gratings were fabricated to achieve high self-coupling reflectivity for $LP_{01}$, $LP_{11}$, and $LP_{21}$ modes. Figure 5 shows the grating transmission spectrum when the grating writing position $\Delta a$ changes, and the transmission depth is shown in Table 2 when $\Delta a$ = 3 $\mathrm{\mu}$m, the optical field energy distribution of $LP_{01}$ mode is matched; when $\Delta a$ = 5 $\mathrm{\mu}$m, the optical field energy distribution of $LP_{11}$ mode is matched; and when $\Delta a$ = 7 $\mathrm{\mu}$m, the optical field energy distribution of $LP_{21}$ mode is matched. At this time, the reflection effect of modes $LP_{01}$, $LP_{11}$, and $LP_{21}$ is the best. The transmission depth is −13.01 dB, −8.89 dB, and −7.69 dB, respectively.
Fig. 5. Grating transmission spectrum of each mode when the writing position of the grating is adjusted. (a) $LP_{01}$. (b) $LP_{11}$. (c) $LP_{21}$.
Table 2. Grating transmission spectrum depth of each mode when the grating writing position is adjusted.
Figure 6 shows each mode’s reflection spectrum and optical field distribution when the grating spacing $\Delta a$ is 3 $\mathrm{\mu}$m, 5 $\mathrm{\mu}$m, and 7 $\mathrm{\mu}$m, respectively. It can be seen that when the grating spacing is 3 $\mathrm{\mu}$m, the self-coupling reflectivity of mode $LP_{01}$ is the maximum at 1550.02 nm, which is 95$\%$. When the grating spacing is 5 $\mathrm{\mu}$m, the self-coupling reflectivity of mode $LP_{11}$ reaches the maximum at 1550.02 nm, which is 87$\%$. When the grating spacing is 7 $\mathrm{\mu}$m, the self-coupling reflectivity of mode $LP_{21}$ reaches its maximum at 1550.02 nm, which is 83$\%$.
Fig. 6. Reflection spectrum of fabricated Bragg gratings. (a) $LP_{01}$. (b) $LP_{11}$. (c) $LP_{21}$.
3. Demonstration of mode add-drop technology
3.1 Principle of mode add-drop technology
Figure 7 shows how to implement the mode add-drop technology. When the selected mode is not dropped, the switches are not connected to the circulator and grating, and all mode signals are transmitted normally; when the selected mode is dropped, switch 1 is connected to the circulator port 1, and switch 2 is connected to the grating. By using the reflection characteristics of the grating, when the mode signal is incident through port 1 of the circulator and is emitted from port 2 of the circulator, it will be reflected by the grating. However, the other mode’s signals will pass through normally without being affected, and the reflected signal is incident at port 2 of the circulator and emitted at port 3 to drop; when the selected mode is added, the optical coupler is added after the grating, and the selected mode is transmitted to the trunk line through the optical coupler to add.
3.2 Demonstration of mode add-drop technology based on few-mode fiber gratings in mode-division multiplexing system
The demonstration of mode add-drop technology based on few-mode fiber gratings in the MDM system is shown in Fig. 8. In this demonstration, we fixed the Bragg gratings in a constant temperature chamber, other devices in the system were fixed on the optical platform, and vibration isolation measures were taken to ensure that it was not interfered with by external factors. Moreover, a polarization controller is used to control the polarization state of the beam to remain unchanged. Three tunable lasers are used as the light source of the MDM system, and the central wavelength is set to 1550.02 nm. The tunable laser 1 is connected to the IQ modulator, and the tunable laser 3 is connected to the coherent receiver as the local oscillator light source. The DAC (Fujitsu LEIA-DK) sends two 4 Gbit/s binary pseudo-random sequences connected to the IQ modulator’s I and Q channels (FTM7962EP). After modulation, 8 Gbit/s quadrature phase shift keying (QPSK) signals are formed and loaded onto the beam emitted by the laser. $LP_{01}$, $LP_{11}$, and $LP_{21}$ modes are excited by connecting photonic lantern 1 through the optical splitter. A time delay between modes is generated by adding fiber of different lengths before connecting the photonic lantern so that the three optical signals are not correlated. After transmission by 8 km few-mode fiber, the three modes are demultiplexed through photonic Lantern 3, and the signals carried by the three modes are obtained respectively and then processed by offline DSP.
Fig. 8. Implementation of mode add-drop technology in the MDM system. DAC, Digital to Analog Converter; IQ modulator, In-phase and Quadrature modulator; OS, optical splitter; PD, photodetector.
The DSP composition is shown in Fig. 9, which mainly includes orthogonalization, clock recovery, re-sampling, channel equalization, frequency offset recovery, and phase noise compensation. Among them, the Gram-Schmidt algorithm is used to compensate and orthogonalize the IQ imbalance, the Gardner algorithm is used to restore the clock, the Constant-Modulus Algorithm (CMA) algorithm is used to balance and compensate for the channel noise, and finally, the Viterbi-Viterbi algorithm is used to compensate the frequency offset and phase noise.
Set a node 4 km away from the transmitter to perform the mode add-drop function. Three FM-FBGs and three few-mode circulators realize the drop function. The drop function of a particular mode can be realized by controlling the switching state, When switch k1 is connected to a and switch k2 is connected to c, circulator 1 and $FBG-LP_{01}$ are connected to the system to realize the drop function of $LP_{01}$ mode. When switch k1 is connected to b and switch k2 is connected to d, circulator 1 and $FBG-LP_{01}$ are not connected to the system, then the drop function of $LP_{01}$ mode is not implemented; when switch k3 is connected to e and switch k4 is connected to g, circulator 2 and $FBG-LP_{11}$ are connected to the system to realize the drop function of $LP_{11}$ mode. When switch k3 is connected to f and switch k4 is connected to h, circulator 2 and $FBG-LP_{11}$ are not connected to the system, then the drop function of $LP_{11}$ mode is not implemented; when switch k5 is connected to i and switch k6 is connected to k, circulator 3 and $FBG-LP_{21}$ are connected to the system to realize the drop function of $LP_{21}$ mode. When switch k5 is connected to j and switch k6 is connected to l, circulator 3 and $FBG-LP_{21}$ are not connected to the system, then the drop function of $LP_{21}$ mode is not implemented. Through the optical coupler, the mode signal, which needs to be added, is transmitted back to the trunk to realize the add function of the system. At the receiving end, the photonic lantern is used for demultiplexing and mode conversion of the signal, and the signal is processed offline by DSP to detect its constellation diagram. We verified the performance of mode add-drop for $LP_{01}$, $LP_{11}$, and $LP_{21}$. The constellation diagrams and bit error rate curves are given.
3.3 Experimental results
When the $LP_{01}$ mode performs the add-drop function, other modes are transmitted normally. The constellation diagram of the $LP_{01}$ mode at the receiving end of the drop node and the constellation diagrams of the $LP_{01}$, $LP_{11}$, and $LP_{21}$ modes at the receiving end of the MDM system are given, as shown in Fig. 10, where (a) is the constellation diagram of each mode signal without adding equalization processing, and (b) is the signal constellation diagram of each mode after adding equalization processing.
Fig. 10. Signal constellation diagram of each mode when $LP_{01}$ mode is added and dropped. (a) Equalization processing is not added. (b) Equalization processing is added.
When the $LP_{11}$ mode performs the add-drop function, other modes are transmitted normally. The constellation diagram of the $LP_{11}$ mode at the receiving end of the drop node and the constellation diagrams of the $LP_{01}$, $LP_{11}$, and $LP_{21}$ modes at the receiving end of the MDM system are given, as shown in Fig. 11, where (a) is the constellation diagram of each mode signal without adding equalization processing, and (b) is the signal constellation diagram of each mode after adding equalization processing.
Fig. 11. Signal constellation diagram of each mode when $LP_{11}$ mode is added and dropped. (a) Equalization processing is not added. (b) Equalization processing is added.
When the $LP_{21}$ mode performs the add-drop function, other modes are transmitted normally. The constellation diagram of the $LP_{21}$ mode at the receiving end of the drop node and the constellation diagrams of the $LP_{01}$, $LP_{11}$, and $LP_{21}$ modes at the receiving end of the MDM system are given, as shown in Fig. 12, where (a) is the constellation diagram of each mode signal without adding equalization processing, and (b) is the signal constellation diagram of each mode after adding equalization processing.
Fig. 12. Signal constellation diagram of each mode when $LP_{21}$ mode is added and dropped. (a) Equalization processing is not added. (b) Equalization processing is added.
Figures 10, 11, and 12 show that when the equalization algorithm is not added, because of the different reflectivity of the FM-FBGs of $LP_{01}$, $LP_{11}$, and $LP_{21}$ modes, the residual signal after the drop will have different interference on the add signal of $LP_{01}$, $LP_{11}$, and $LP_{21}$. The lower the reflectivity, the more severe the interference and the more scattered the constellation diagram. In order to eliminate the influence of unsatisfactory channel and FM-FBG reflection residual on signal quality, the CMA equalization algorithm is added to DSP. The process of the CMA algorithm is shown in Fig. 13.
e(n) is the error function, and the tap coefficient update can be expressed as $W(n+1)=W(n)-\mu e(n)^{\ast } (n)$, where $\mu$ is the step size. Selecting the appropriate step size parameter is the key to the performance of the CMA algorithm. The different step size iteration operation has different adjustment amplitude to the tap coefficient. When the step size is large, the algorithm convergence speed and tracking speed are fast, but the tap coefficient will jitter in a large range near the optimal value, and the steady-state residual error is large. When the step size is small, although the algorithm’s convergence speed and tracking speed are slow, the tap coefficient will jitter within a small range near the optimal value, and the steady-state residual error is small. Therefore, it is necessary to dynamically adjust the step size in the CMA algorithm according to the processing situation. For $LP_{01}$ mode, the self-coupling reflectivity of the FM-FBG is 95$\%$, and the reflectivity is high. Therefore, the residual signal after the grating reflection is less, which will cause less interference to the transmission, and the mode is selected with a longer step size. For the $LP_{11}$ and $LP_{21}$ modes, because the self-coupling reflectivity of the FM-FBGs is 87$\%$ and 83$\%$, respectively, the residual signal after the grating reflection is more than that of the $LP_{01}$ mode, which will cause greater interference to the transmission, so the small step length is chosen. The different step size of the CMA algorithm was selected, and the processing effect was compared. When the step size parameters of $LP_{01}$, $LP_{11}$, and $LP_{21}$ are set as 1, 0.5, and 0.1, respectively, the convergence speed and equalization effect can be well balanced. It can be seen that after adding equalization processing, the noise and interference in the channel are compensated, and the signal quality is improved. Figure 14 shows the bit error rate curves of each mode after equalization.
As can be seen from Fig. 14, when the transmission rate is 8 Gbit/s, the bit error rate is lower than $10^{-3}$ when the received power of the drop signal is higher than −34.88 dBm, and the received power of the add signal is higher than −34.86 dBm in mode $LP_{01}$. To achieve the same bit error rate, the received power of $LP_{11}$ and $LP_{21}$ mode signals needs to be higher than −34.91 dBm and −34.82 dBm.
When the received power of the drop signal is higher than −34.80 dBm, and the received power of the add signal is higher than −34.57 dBm in mode $LP_{11}$, the bit error rate is lower than $10^{-3}$. To achieve the same bit error rate, the received power of $LP_{01}$ and $LP_{21}$ mode signals needs to be higher than −34.96 dBm and −34.81 dBm.
When the received power of the drop signal is higher than −34.66 dBm, and the received power of the add signal is higher than −34.37 dBm in mode $LP_{21}$, the bit error rate is lower than $10^{-3}$. To achieve the same bit error rate, the received power of $LP_{01}$ and $LP_{11}$ mode signals needs to be higher than −35.01 dBm and −34.89 dBm.
When the received optical power is higher than the above, the bit error rate of each mode signal is lower than $10^{-3}$, which meets the threshold requirement of error-free transmission after the hard decision of forward error correction (20$\%$ overhead). Therefore, the mode add-drop technology based on the few-mode fiber Bragg gratings can be well applied in the MDM system.
4. Conclusion
This paper proposes a mode add-drop technology based on few-mode fiber Bragg gratings. By using the reflection characteristics of gratings to realize the mode add-drop at a specific node, the femtosecond laser method is used to write the gratings in parallel during the fabricating process, and the self-coupling reflectivity of the high-order mode is improved by adjusting the writing position of the gratings to match the energy distribution of the high-order mode optical field. Furthermore, the performance of the mode add-drop technology is improved. The performance of the mode add-drop technology is verified in the MDM system using QPSK modulation and coherent detection technology. The experimental results show that the MDM system using this add-drop technology is simple in structure, easy to implement, can achieve good signal transmission and low bit error rate, and can meet the requirements of an optical fiber communication system. Therefore, this add-drop technology has a good application prospect in the MDM system.
Funding
National Key Scientific Instrument and Equipment Development Projects of China (62227819); National Natural Science Foundation of China (62075080).
Disclosures
The authors declare there are no conflicts of interest.
Data availability
No data were generated or analyzed in the presented research.
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