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Abstract
We propose what we believe is a novel format conversion scheme using a few-mode fiber Bragg grating (FM-FBG) that can perform multichannel format conversion from carrier-suppressed return-to-zero (CSRZ) to non-return-to-zero (NRZ) for both LP01 and LP11. The multichannel spectral response of FM-FBG is designed according to the algebraic difference between the CSRZ and NRZ spectra outlines. Additionally, the FM-FBG response spectra of LP11 are designed to shift with that of LP01 by the WDM-MDM channel spacing for filtering both modes together. Numerical results demonstrate the successful conversion of both LP01 and LP11 channels, carrying four channels of 200-GHz-spaced CSRZ signals at 40 Gbit/s, into NRZ signals with a high Q-factor (exceeding 14 dB), and the converted NRZ signals exhibit clean and open eye diagrams. Furthermore, the performance analysis also shown that our proposed FM-FBG is robust to central wavelength detuning.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Wavelength division multiplexing - mode division multiplexing (WDM-MDM) has emerged as a promising new technique to further increase the capacity of fiber systems. This is due to the fact that multiplexing can be done in both wavelength and spatial domains [1,2]. To better utilize the potential of fiber systems and achieve higher transmission capacities, advanced optical modulation formats also play a crucial role in the design of fiber systems [3,4]. Future WDM-MDM systems employing few-mode fiber (FMF) will adopt suitable modulation formats based on network scale, application requirements, and bit rates, similar to existing WDM systems [5].
The carrier-suppressed return-to-zero (CSRZ) format has gained widespread usage in ultra-long distance fiber transmission systems due to its superior tolerance to linear and nonlinear impairments that accumulate along fiber transmission lines, and its narrower base shape also offers advantages over conventional return-zero (RZ) codes [6–9]. On the other hand, non-return-to-zero (NRZ) format is used extensively in low-speed commercial systems due to its lower bandwidth requirements and simpler transmitter configurations [10,11]. Therefore, for the future WDM-MDM fiber systems, multichannel multimode CSRZ-to-NRZ format conversion will serve as a crucial interface technology bridging high-speed backbone networks and low-speed access networks.
However, the challenge of simultaneous format conversion for multimode multichannel scenarios remains largely unresolved. Apart from our previously reported scheme using a FM-FBG to achieve synchronous RZ-to-NRZ conversion for WDM-MDM systems, no other format conversion solution has been proposed for WDM-MDM systems [12].
In this paper, we propose a single-device scheme based on a properly designed FM-FBG for multimode multichannel CSRZ-to-NRZ format conversion. This filter possesses a multichannel reflection spectra, with each channel’s spectral response designed based on the algebraic difference between CSRZ and NRZ spectra profiles. Furthermore, the FM-FBG spectra response of ${\rm {LP_{11}}}$ is designed to shift with that of ${\rm {LP_{01}}}$ by the WDM-MDM channel spacing, enabling synchronous filtering of all channels in both modes. Numerical results demonstrate that ${\rm {LP_{01}}}$ and ${\rm {LP_{11}}}$ channels carrying 40 Gbit/s CSRZ signals with a 200-GHz-spacing can be simultaneously converted into NRZ signals. Additionally, the converted NRZ signals exhibit high Q-factors, and their eye diagrams demonstrate clean and open characteristics.
2. Constructing the spectra of the FM-FBG
Spectrum tailoring is the principle behind utilizing FM-FBG for implementing format conversion. The challenge of multichannel random CSRZ-to-NRZ data conversion for ${\rm {LP_{01}}}$ and ${\rm {LP_{11}}}$ modes can be addressed by constructing an FM-FBG filter that simultaneously converts the input CSRZ data spectra of the both modes into the desired NRZ data spectra.
The process of FM-FBG design can be divided into three key stages. Firstly, to achieve format conversion of the multichannel input CSRZ signal, the reflectance spectra of the FM-FBG needs to be designed in a comb shape, where the profile of each channel is determined based on the algebraic difference between the CSRZ and NRZ spectral profiles. Secondly, to enable simultaneous format conversion of the two modes, the specifications of the FMF must be carefully selected to obtain the desired effective refractive index between the two modes. This results in the FM-FBG response spectra of ${\rm {LP_{11}}}$ to shift with that of ${\rm {LP_{01}}}$ by the WDM-MDM channel spacing. In the final stage, based on the results from the previous two steps, the structure of the FM-FBG is determined through the utilization of a layer-peeling algorithm and then inscribed it into the FMF of the chosen specifications.
In the following section, we will illustrate the above procedure for the case of 200-GHz-spaced CSRZ signals at 40 Gbit/s coverted into NRZ.
2.1 Design of the multichannel spectra for $LP_{01}$
To implement the conversion of the input CSRZ spectra into the output NRZ spectra, the algebraic difference between the CSRZ and NRZ spectra is calculated and then it will be used to design the single-channel response spectra [13]. One way to determine the outlines of the CSRZ and the NRZ spectra is by averaging the power spectra with different pseudo-random bit sequences of ${2^{31}}{\rm {}\hbox{-}{\rm }}1$ bits and then calculating their algebraic difference. As is shown in Fig. 1, the 40 Gbit/s CSRZ and NRZ are calculated ${2^{15}}$ times and are averaged.
Fig. 1. NRZ spectra (blue dashed curve, ${\lambda _{c,{\rm {NRZ}}}}=1549.96$ nm, ${T_{p}}=25$ ps), CSRZ spectra with 67% duty cycle (yellow dashed-dotted curve, ${\lambda _{c,{\rm {CSRZ}}}}=1550.12$ nm). The red dotted curve shows their algebraic difference (the ideal transfer function of the filter), and the cyan solid curve is the well-designed single-channel FM-FBG spectra.
Similar to other reported conversion schemes [13–20], one of the CSRZ sidebands (1549.96nm) should be chosen as the carrier wavelength of the converted NRZ and an appropriate attenuation (−25dB) should be set for out-of-band components. We will then be able to obtain the single-channel target spectra (cyan solid curve in Fig. 1). The well-designed single-channel simplified transfer function of FM-FBGs filter is given by [19]:
The multichannel response spectra of the FM-FBG can be derived by linearly superposing the well-designed single-channel spectral response and setting the appropriate characteristic length of the group delay. It should be kept in mind that one more channel should be designed for the response spectra of FM-FBG than carriers used in the WDM-MDM system [12]. Thus, the multichannel response spectra of ${\rm {LP_{01}}}$ can be written as:
2.2 Alignment of the reflection channels of ${LP_{\textit {01}}}$ and ${LP_{\textit {11}}}$
To achieve simultaneous format conversion for both ${\rm {LP_{01}}}$ and ${\rm {LP_{11}}}$ modes, the input ${\rm {LP_{01}}}$ and ${\rm {LP_{11}}}$ CSRZ signal spectra need to be filtered into NRZ spectra together. Due to the effective refractive index difference between the two modes, the FM-FBG response spectra of the two modes are not the same (i.e., the difference between them can be seen as a shift). One approach to implement simultaneous filtering of both ${\rm {LP_{01}}}$ and ${\rm {LP_{11}}}$ is to design the ${\rm {LP_{11}}}$ response spectra of the FM-FBG shift with that of ${\rm {LP_{01}}}$ by WDM-MDM system channel spacing, which is accomplished by selecting the appropriate few-mode fiber specification to obtain the target effective refractive index. The calculation of the shift and the restrictive condition are as follows [12]:
where $\Delta {\lambda _{{\rm shift}}}$ is the shift between the spectra of ${\rm {LP_{01}}}$ and ${\rm {LP_{11}}}$, and ${\Lambda _{{\rm c}}}$ denote the Bragg period of the central wavelength of full ${\rm {LP_{01}}}$ spectra.Using Eqs. (4), (5) with the fiber eigenvalue equation, after setting the core refractive index to 1.4681, we can obtain the relationship between the ${\rm {LP_{01}}}$ and ${\rm {LP_{11}}}$ response spectral shifts (200-GHz spacing equals 1.6 nm shift) with the cladding refractive index and core diameter (illustrated in Fig. 2).
As is shown in Fig. 2, the ideal specification for the FMF that meets our requirement is not unique (the results close to zero or deep red are what we want). In our example, the refractive indices and core diameter of the FMF are ${n_{0}}$ = 1.4681, ${n_{1}}$ = 1.4642 and ${a}$ = 16.4404 $\mu$m, and the effective refractive indices of ${\rm {LP_{01}}}$ and ${\rm {LP_{11}}}$ are 1.4670 and 1.4655, respectively (see the blue dot in Fig. 2). The specifications correspond to a type of two-mode fiber that only allows for stable transmission of ${\rm {LP_{01}}}$ and ${\rm {LP_{11}}}$ modes within the fiber.
2.3 FM-FBG design
To illustrate the operational principle of the proposed FM-FBG, we have selected four channels (1546.92, 1548.52, 1550.12, and 1551.72 nm) spaced at 200 GHz for simulating the WDM-MDM system. Based on the Eq. (3), five channels (1546.76, 1548.36, 1549.96, 1551.56 and 1553.16 nm) are selected as FM-FBGs designed channels for ${\rm {LP_{01}}}$.
Based on the multichannel objective function described by Eq. (2), the FM-FBG structure can be resynthesized using the well-known discrete layer-peeling method [21,22]. Subsequently, the reflection spectra of the ${\rm {LP_{01}}}$ and ${\rm {LP_{11}}}$ modes are simulated using the transfer matrix method [23]. In our calculations, we have set $d_{j}=[0.1450,0.1275,0.1100,0.0925,0.0750]$. The FM-FBG is uniformly divided into 4949 segments, with a total length of 10 cm.
Figure 3(a) depicts a stair-like graph, indicating the presence of local chirp with a variation span of approximately $8\times 10^{-9}$ m. The maximum refractive index modulation, as illustrated in Fig. 3(b), is approximately $4\times 10^{-4}$, which is considerably smaller than $10^{-3}$. This demonstrates the practical realizability of the FM-FBG structure.
As is shown in Fig. 4(a), the simulated ${\rm {LP_{01}}}$ response spectra of the synthesized FBG (blue dotted curve) is in excellent agreement with the target multichannel spectra (red curve) obtained from Eq. (2). For better presentation, the response spectra of ${\rm {LP_{01}}}$ and ${\rm {LP_{11}}}$ are shown together in Fig. 4(b). It is clear that the response spectra of ${\rm {LP_{01}}}$ and ${\rm {LP_{11}}}$ are mostly overlapped at all carriers (1546.92, 1548.52, 1550.12, and 1551.72 nm) used in the WDM-MDM system.
Fig. 4. (a) Simulated reflection spectra (dotted blue curve), target reflection spectra (solid red curve), and simulated group delay (dotted green curve). (b) Simulated reflection spectra of ${\rm {LP_{01}}}$ (dotted blue curve), simulated reflection spectra of ${\rm {LP_{11}}}$ (solid red curve).
3. Simulation results and discussion
To assess the performance of the designed FM-FBG, we conducted systematic simulations to evaluate its capability for multichannel CSRZ-to-NRZ format conversion of ${\rm {LP_{01}}}$ and ${\rm {LP_{11}}}$ modes, using a pseudo-random binary sequence (PRBS) with a length of ${2^{31}}-1$ bits. The flowchart for the simulations is shown in Fig. 5.
Figure 6 presents the spectra of the input CSRZ signals for both ${\rm {LP_{01}}}$ and ${\rm {LP_{11}}}$ modes, along with the corresponding output NRZ signal spectra.
Fig. 6. (a) Spectra of the input CSRZ signal and (b) spectra of the output NRZ signal for ${\rm {LP_{01}}}$ mode. (c) Spectra of the input CSRZ signal and (d) spectra of the output NRZ signal for ${\rm {LP_{11}}}$ mode.
As depicted in Fig. 6(b) and Fig. 6(d), the spectra undergo reshaping at the in-band wavelengths of all carriers, effectively suppressing the amplitude of out-of-band frequencies. Nevertheless, it is inevitable that certain frequency components remain unfiltered (indicated by the red dotted curve in Fig. 6(b) and Fig. 6(d)). This is due to the fact that we designed the FM-FBG response spectra with one additional channel compared to the transmitted carriers. The amplitude of this additional channel in the converted spectra can be mitigated or rendered negligible by carefully selecting the channel spacing between carriers based on the waveform’s duty cycle or setting a sufficiently large channel spacing, the unfiltered frequencies can fall within the partial lobe of the spectra. The converted NRZ signal waveforms and their corresponding eye diagrams are presented in Fig. 7. It is clear that the quality of the converted NRZ waveform remains largely unaffected by the presence of unfiltered frequency components when appropriate channel spacing is employed.
In the third and sixth row of Fig. 7, the clean and open eye diagrams demonstrate the simultaneous conversion of the input four-channel CSRZ signals to NRZ signals with a high Q-factor exceeding 14 dB. This successful conversion is attributed to the well-designed multichannel spectral response of the FM-FBG filter and the appropriate selection of channel spacing. Importantly, the Q-factor of the different channels exhibits no significant variation with respect to the carrier wavelength or spatial mode utilized. It is noteworthy that all Q-factors in our simulations are calculated using 170 sampled points within a period ranging from 0.33T to 0.67T. Based on these findings, we conclude that the proposed FM-FBG filter enables high Q-factor CSRZ-to-NRZ format conversion for both ${\rm {LP_{01}}}$ and ${\rm {LP_{11}}}$ modes.
Fig. 7. From top to bottom, the rows correspond to input CSRZ waveforms, the spectra, and the eye diagrams for the output NRZ signals, respectively. From left to right, the columns correspond to channels 1-4. The first three rows of the figure correspond to channels 1-4 of ${\rm {LP_{01}}}$. Rows 4 to 6 correspond to channels 5-8 of ${\rm {LP_{11}}}$.
Additionally, to better analyze the robustness of this scheme, we consider the detuning of the central wavelength of the FM-FBG reflection band. Figure 8 shows eight channels average Q-factor as a function of the filter wavelength detuning.
Fig. 8. Average Q-factor of eight channels as a function of filter detuning. Insets (a), (b) show the waveforms and the eye diagrams for the output NRZ signals in the case of −0.032 and 0.032 nm filter detuning, respectively.
As is shown in Fig. 8, the variation of the Q-factor is asymmetric since the spectra of both the FM-FBG and the input signal are asymmetric with respect to the selected carrier wavelength. With the detuning of the FM-FBG reflection spectra toward the short wavelength side, the Q-factor will decline because both the sideband of the input CSRZ signals will be overfiltered [10]. In the case of −0.032 nm detuning, the output NRZ waveform is similar to existing DI scheme [15], as shown inset (a) in Fig. 8. In the case of detuning of FM-FBG reflection spectra toward the long wavelength side, the Q-factor will also decrease. The reason for this phenomenon can be attributed to the fact that the sidebands of the input CSRZ signal are not well filtered out [10], resulting in a slight fluctuation of power in the output NRZ waveform in multiple consecutive "1" bits (see Fig. 7 and Fig. 8(b)). In summary, to achieve acceptable performance (i.e., Q-factor greater than 12 dB and acceptable fluctuation of the power in the consecutive "1" bits), the detuning of filters should be between −0.032 and 0.032 nm (i.e., 10% of the originally designed bandwidth).
4. Conclusion
In conclusion, we have proposed a single FM-FBG-based scheme for achieving multichannel format conversion from CSRZ-to-NRZ for both ${\rm {LP_{01}}}$ and ${\rm {LP_{11}}}$ modes. By constructing the comb spectra of the FM-FBG based on the algebraic difference between the optical spectra of CSRZ and NRZ signals, we successfully implemented format conversion for all spatial mode channels. The response spectra of ${\rm {LP_{11}}}$ and ${\rm {LP_{01}}}$ were appropriately shifted by the WDM-MDM channel spacing, achieved through careful selection of the FMF specifications to meet the effective refractive index difference requirements between the modes. Our simulations demonstrate the simultaneous conversion of four-channel two-mode 200-GHz-spaced CSRZ signals operating at 40 Gbit/s into NRZ signals, resulting in high Q-factor converted signals with clean and open eye diagrams. Compared with the existing active format conversion scheme such as DI-based scheme and SOA-based scheme [24–26], our FM-FBG-based scheme is superior due to the passive nature of the FM-FBG and the absence of active components that eliminate ASE noise issues. Furthermore, the system structure of our scheme is simpler, because it uses one FM-FBG to implement multichannel multimode format conversion. Additionally, our scheme offers great flexibility for network interfaces and reduces the need for redundant parallel structures and per-channel processing.
Funding
Tertiary Education Scientific Research Project of Bureau of Education of Guangzhou Municipality (202234641); Project of Construction Discipline Scientific Research Capability Improvement of Guangdong Province (2022ZDJS096, 2022ZDJS098); Research Project of Construction National Science and Technology Think Tank of Guangdong Province (SXK20220201035); Education and Science Program of Guangdong Province (2022GXJK308); Key Technologies Research and Development Program of Department of Education of Guangdong Province (2020ZDZX3072, 2021KTSCX098).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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