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Curr. Opt. Photon. 2023; 7(1): 47-53

Published online February 25, 2023 https://doi.org/10.3807/COPP.2023.7.1.47

## Uniform-fiber-Bragg-grating-based Fabry-Perot Cavity for Passive-optical-network Fault Monitoring

Xuan Zhang1,2 , Ning Ning1, Tianfeng Yang2

1College of Electronic Science and Engineering, University of Electronic Science and Technology of China, Chengdu 610054, China
2College of Physics and Electronic Engineering, Sichuan Normal University, Sichuan, Chengdu 610101, China

Corresponding author: *xuanzhang@sicnu.edu.cn, ORCID 0000-0003-1748-2299

Received: August 17, 2022; Revised: November 6, 2022; Accepted: December 2, 2022

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

We propose a centralized passive-optical-network monitoring scheme using the resonance-spectrum properties of a Fabry-Perot cavity based on fiber Bragg gratings. Each cavity consists of two identical uniform fiber Bragg gratings and a varying cavity length or grating length, which can produce a unique single-mode resonance spectrum for the drop-fiber link. The output spectral properties of each cavity can be easily adjusted by the cavity length or the grating length. The resonance spectrum for each cavity is calculated by the transfer-matrix method. To obtain the peak wavelength of the resonance spectrum more accurately, the effective cavity length is introduced. Each drop fiber with a specific resonance spectrum distinguishes between the peak wavelength or linewidth. We also investigate parameters such as reflectivity and bandwidth, which determine the basic performance of the fiber Bragg grating used, and thus the output-spectrum properties of the Fabry-Perot cavity. The feasibility of the proposed scheme is verified using the Optisystem software for a simplified 1 × 8 passive optical network. The proposed scheme provides a simple, effective solution for passive-optical-network monitoring, especially for a high-density network with small end-user distance difference.

Keywords: Fabry-Perot cavity, Fiber Bragg grating, Network link monitoring, Passive optical network, Transfer matrix method

OCIS codes: (060.3735) Fiber Bragg gratings; (060.4257) Networks, network survivability; (060.4261) Networks, protection and restoration

Among the many technologies addressing the ever-increasing demand for high-bandwidth broadband Internet service, the passive optical network (PON) has been reckoned as the most promising technology in fiber-access-network deployment [1, 2]. Due to its various advantages such as large capacity, simple structure, flexible scalability, and transparency of support services, PONs have been widely used in access networks and are today’s access technology of choice for operators, especially when they need to build new infrastructure [3, 4]. PONs have been widely deployed worldwide; however, the large-scale deployment of PON-based access networks also increases the difficulty of network management and maintenance. The time, labor, and truck-roll for fault troubleshooting dramatically increase operational expenditure. Furthermore, long repair time would reduce quality of service (QoS). Therefore, the expeditious expansion of PON deployment across the globe has highlighted the pressing need to devise an effective optical-layer monitoring system [2, 5].

When a failure occurs on a point-to-point (P2P) network, optical time-domain reflectometry (OTDR) can be used to troubleshoot the network’s link problem. However, OTDR is ineffective in point-to-multipoint (P2MP) networks like PONs, since a branch return signal in a PON can be partially or totally masked by other branch signals [6]. That is, the return signals (i.e. backreflected and backscattered light) from each branch add up to form an aggregated or composite trace. As a direct consequence, it is difficult for the central-office (CO) network manager to identify the faulty branch from the aggregated OTDR trace. To solve this problem, many studies to monitor physical-layer faults in fiber-optic distribution networks have been presented [6]. In the early 21st century, some fault-monitoring schemes were presented for the wavelength-division multiplexer (WDM)-PON [7, 8]. A novel coding approach exploits a fiber ring with varying length and a fiber Bragg grating (FBG) with 100% reflectivity to produce a varying periodic code. The inexpensive and simple optical coding device generates a unique pseudo-orthogonal code to identify each drop-fiber (DF) link [9]. A modified optical frequency-hopping/periodic coding scheme adds an optical encoder array at a remote node (RN) and configures the identical reflector at each optical network unit (ONU). This scheme can reduce the upgrade cost and is expected to become a promising PON-monitoring solution [10]. The remote-coding scheme uses the cascaded encoder to simultaneously achieve optical splitting and encoding at the RN. Multiple FBGs and 1 × 2 power splitter/combiners (PSC) are connected according to a certain design rule, to ensure that the minimum number of gratings is used. At the same time, the use of the identical reflector at the ONU side further reduces the system’s cost and makes the scheme more competitive [11]. It should be noted that many existing schemes, such as those above, involve the time domain in the final recognition processing. The multicustomer interference probability (MCIP), first introduced in [12], provides a useful tool for system-performance evaluation of schemes involving time-domain identification. In a high-density network the length difference between DF links is very small, which may cause large MCIP. That is, the length difference between DF links affects the final recognition efficiency. Consequently, large MCIP may lead to low efficiency in final recognition.

In this paper, we propose a novel PON-monitoring scheme using a fiber-Bragg-grating-based Fabry-Perot (FBG-FP) cavity. The output spectra of the resonant cavity constructed from two identical uniform FBGs (UFBGs) can be optically identified in peak wavelength or linewidth. The detecting signal generated by the encoder is not affected by the length difference between DF links. As mentioned earlier, the length difference between DF links is closely related to the MCIP. It is known that the periodic coding (PC) scheme is one of the earliest classic PON monitoring schemes [6]. Considering a detecting signal with pulse duration of 1 ns and code weight of 4 in the PC scheme, we can employ the Monte Carlo method with 105 iterations to calculate the MCIP of 64 randomly distributed users within a circular area with a radius of 460 m. To make the MCIP of the PC scheme not exceed 0.1, the difference between any two-branch links should not be less than 4.65 m. Thanks to the characteristics of spectrum recognition, the length difference between DF links in the proposed scheme is theoretically unrestricted. It is simple and flexible to generate a resonance spectrum with a unique peak wavelength or linewidth by changing the cavity length of the FBG-FP cavity, or the grating length of the UFBGs. Compared to the previous work [13], the current scheme is new, as mainly reflected in three aspects: (1) The encoder on the ONU side in the previous work is a single FBG with different central reflection wavelengths or reflection bandwidths, while the encoder in the current work is a resonant cavity constructed from two identical FBGs and a certain cavity length; (2) the generation principle and signal characteristics of the monitoring signal in the two works are different; and (3) the previous work is mainly devoted to solving the problem of identifying different reflection bandwidths at the same wavelength, while the current work focuses on obtaining more single-mode output spectra by investigating some parameters (cavity length, grating length, etc.). In terms of the detection sources, the optical bandwidth of the current work is smaller than that of the previous work. To reduce the difficulty of final recognition, we use the transfer-matrix method (TMM) to analyze and calculate a single-mode resonance spectrum that can be used in the proposed scheme. In addition, we use the Optisystem software to perform a simulation.

### 2.1. Principle of Operation

Figure 1(a) illustrates the principle of the proposed PON-monitoring system. Specifically, a U-band (1,625–1,675 nm) detecting signal is coupled to normal data traffic from the optical line terminal (OLT) via a wavelength-division multiplexer (WDM) and sent into the feeder fiber (FF). At the RN, the detecting signal is split into n sub signals by the PSC and broadcast to each DF link. Different resonant spectra are encoded and reflected to the CO. Each encoder located at the front of the ONU consists of an FBG-FP cavity, two circulators (CIRs), and an FBG (i.e. FBG3) with 100% reflectivity, as shown in Fig. 1(b). Finally, the spectra returned from all DFs are filtered by an optical filter (OF) for spectrum recognition.

Figure 1.System principle and structure. (a) Schematic diagram of the proposed passive optical network-monitoring system; (b) encoder with an fiber-Bragg-grating-based Fabry-Perot (FBG-FP) cavity, two circulators (CIRs), and a 100%-reflectivity FBG; (c) structure of the FBG-FP cavity.

Features of the reflected resonance peaks can be used to assess the link quality for individual DFs. An attenuated resonance peak shows that the fiber link between the CO and the ONU may be degrading. That is, the DF status can be determined by checking the reflected power level of the corresponding resonance peak. For the proposed scheme, the resonance spectrum can be different peak wavelengths with the same linewidth, or the same wavelength with different linewidths. In theory, more linewidths at the same wavelength can lead to larger monitoring capacity, but may also increase the difficulty of the final recognition process. To strike a balance between final-recognition difficulty and monitoring capacity, the number of linewidths in the proposed scheme at the same wavelength does not exceed 2.

### 2.2. Encoder Design

Recall that the encoder contains an FBG-FP cavity, two CIRs, and a FBG3 with 100% reflectivity. As illustrated in Fig. 1(b), the detecting signal is injected into the FBG-FP cavity via port 2 of CIR2 and resonates at a desired wavelength. Then the resonance wavelength is fully reflected by FBG3 and passes back through port 2 of CIR3. Port 1 of CIR2 and port 3 of CIR3 are connected by a fiber. Figure 1(b) shows that the detecting signal experiences the following optical path in the encoder: Port 2 of CIR2 → Port 3 of CIR2 → FBG-FP cavity → Port 1 of CIR3 →Port 2 of CIR3 → FBG3→ Port 2 of CIR3 → Port 3 of CIR3 → Port 1 of CIR2 → Port 2 of CIR2→output. The central reflection wavelength of FBG3 in each encoder is consistent with the resonance wavelength produced by the FBG-FP cavity. FBG3 can also be a broadband reflector; that is, the FBG can reflect the resonant signals generated by all FBG-FP cavities in the proposed PON-monitoring system. Per the ITU-T L.66 (2007) recommendation, the working wavelength of the FBG-FP cavity and FBG3 are in the U band, which is transparent to the data traffic in the C and L bands. Note that multichannel network monitoring does require multiple circulators and FBGs. However, according to the design of the proposed scheme, all circulators are the same and all FBGs can also be the same, which is obviously conducive to reducing costs.

### 2.3. Resonance-spectra Calculation

As illustrated in Fig. 1, the FBG-FP cavity is constructed from two identical UFBGs. For this cavity the effective cavity length Leff is the sum of the effective lengths Leff_FBG of both the FBGs forming the cavity plus the distance between them Ln. Thus, the effective cavity length of the FP cavity based on two identical UFBGs can be expressed as

Leff=Ln+2Leff_FBG

According to [14], Leff_FBG is determined by the group delay of light reflected from the grating, and depends on its refraction coefficient:

Leff_FBG=LFBGR/2atanh(R)

where LFBG is the physical length of the FBG, corresponding to Ln1 and Ln2 in Fig. 1(c), and R is the peak reflectivity of the FBG. The atanh function returns the inverse hyperbolic tangent of a number.

It is well known that coupled-mode theory (CMT) is a useful mathematical tool for the analysis of the wave propagation and interactions with materials in an optical waveguide. The TMM is a simple, precise technique that is easy to integrate into coupled mode equations. Therefore, we use the TMM to calculate the output resonance spectrum of the FBG-FP cavity [15, 16]. For the TMM, the FBG-FP cavity can be divided into 3 cascaded sections (i.e. FBG1, a bare fiber, and FBG2), with each section affecting the succeeding one. That is, matrix outputs of one section are used as matrix inputs of the next. In addition, the two UFBGs in the FBG-FP cavity are connected by a fiber of length Ln. The phase-shift matrix Tps corresponding to Ln can be found in [15]. The reflection spectrum of the UFBG can be calculated using the reflection coefficient in [17].

### III. ANALYSIS AND CALCULATION

A FBG can only produce reflections within its reflection bandwidth, and the reflectivity is wavelength-dependent. When the FBG-FP cavity resonates at the central reflection wavelength λB (i.e. the Bragg condition), the cavity length Ln and period Λ satisfy Ln = (m − 1 / 2)(1 + δn / neff)Λ. Since the FBG has the strongest reflectance at its central reflection wavelength λB, at λB the “dc” self-coupling coefficient σ is zero, such that the phase angle of the reflection coefficient at this wavelength is always π/2 [17]. Obviously a FBG-FP cavity can produce different wavelengths when Ln changes in one period Λ. Figure 2 depicts spectral responses of the UFBG used, and the FBG-FP cavity for different cavity lengths. In this calculation we use an effective refractive index of n0 = 1.447, two 4.8-mm-long UFBGs (i.e. Ln1 = Ln2 = 4.8 mm) with a period of Λ = 570 nm, and an index modulation of δn = 2 × 10−4. These parameters ensure that the detecting signals generated are within the U band, as recommended by the ITU. In Fig. 2(a) the reflection spectrum is plotted, where the reflection bandwidth for the UFBG used in the FBG-FP cavity is that between the first zeros on either side of the maximum reflectivity (FZ bandwidth). Figure 2(b) shows the output spectra of the FBG-FP cavity with Ln = 0.6 mm and an increase of half a period (i.e. +0.5Λ) and one period (i.e. +Λ). When the cavity length is 0.6 mm, the FBG-FP cavity exhibits single-mode output. Clearly from the graph, the two resonance peaks generated (1,649.718 and 1,649.882 nm) with Ln = +0.5Λ are symmetric about the original peak (1,649.8 nm) with Ln = 0.6 mm. For the convenience of display, the curves with different colors and lines are stacked in one figure; Note, however, that each curve represents a single output spectral response at a specific cavity length. The resonance peak moves toward longer wavelengths when Ln is uniformly increased to 0.5Λ with a step size ΔL of 0.005Λ (2.85 nm), as shown in Fig. 2(c). Similarly, Fig. 2(d) shows the resonance peaks generated for Ln varied from 0.505Λ to Λ with ΔL = 0.005Λ. In general, when the cavity length gradually changes by about one period, the resonance peak deviates from the position of the original peak and finally reappears. For this FBG-FP cavity, 201 different peak wavelengths with an interval of about 0.1 GHz can be generated, which are bounded by two symmetric peak wavelengths. Note that a wider reflection spectrum may produce more resonance wavelengths or larger single-wavelength intervals. To reduce the manufacturing difficulty, the cavity-length interval can be appropriately increased.

Figure 2.Results for the spectral response: (a) The reflection spectrum of the uniform fiber-Bragg-gratings (FBGs) used in the FBG-FP cavity, (b) cavity lengths for Ln = 0.6 mm (red dashed-dotted line), +0.5Λ (green solid line) and +Λ (blue dashed line), and different cavity lengths varied from (c) 0.6 + 0.005Λ to 0.6 + 0.5Λ with ΔL = 0.005Λ, and (d) 0.6 + 0.505Λ to 0.6 + Λ with ΔL = 0.005Λ.

Parameters such as reflectivity and bandwidth determine the basic performance of the FBG, and thus affect the output-spectrum properties of the FBG-FP cavity. For instance, a smaller reflection bandwidth allows for fewer resonant modes to be accommodated in the FBG-FP cavity. The reflection bandwidth and maximum reflectivity of the FBG largely depend on the grating length or refractive-index modulation depth. We further investigate the reflection-spectrum performance of the UFBGs used for different grating lengths and refractive modulation depths, as listed in Table 1.

Reflection-spectrum performance of the uniform fiber-Bragg-gratings used

 Grating Length (mm) Refractive-index Modulation Depth FZ Bandwidth (nm) Maximum Reflectivity 4 2 × 10−4 0.523 82.7% 5 2 × 10−4 0.440 91.5% 7 2 × 10−4 0.354 98.1% 4 1.8 × 10−4 0.477 77.3% 5 1.8 × 10−4 0.430 87.8% 7 1.8 × 10−4 0.340 96.8% 4 2.2 × 10−4 0.445 86.9% 5 2.2 × 10−4 0.402 94.1% 7 2.2 × 10−4 0.356 98.9%

For the UFBGs used, the maximum reflectivity increases as the grating length or refractive-index modulation depth increases. However, the reflection bandwidth decreases as the grating length increases, and is decided by the refractive-index modulation depth. A FBG with a reflectivity of at least 80% is usually adopted, to reduce the loss in the FBG-FP cavity.

Figure 3 depicts the reflection spectra of the FBG-FP cavity with Ln = 0.743093 mm for LFBG = 3.8 mm (black solid line), Ln = 0.650085 mm for LFBG = 4 mm (red dashed line), and Ln = 0.6 mm for LFBG = 4.8 mm (blue dotted line). Recall that the expression for the effective cavity length includes two parts. For different values of LFBG, Ln can be flexibly adjusted to obtain the same peak wavelength. For a 4-mm-long FBG, the precision of the cavity length is reduced from 6 digits (i.e. 0.650085 mm) to 2 digits (i.e. 0.65 mm), and the resonance-peak wavelength moves from 1,649.8 nm to 1,649.774 nm. Consequently, the cavity length may require nanoscale precision to obtain the same resonance-peak wavelength under different conditions. The 6-dB linewidths of the wavelength at 1,649.8 nm for LFBG = 3.8, 4, and 4.8 mm are roughly 2.72, 2.34, and 1.23 GHz respectively. That is, for the same peak wavelength, the 6-dB linewidth can be different when the grating lengths are different. Here we use the 6-dB linewidth, instead of the commonly used 3-dB linewidth, to further reduce the requirements for lightwave-measurement equipment. Unlike for other F-P structures, there is a tradeoff relationship between grating length LFBG and cavity length Ln to ensure that the effective cavity length Leff is consistent. Figure 4 shows the reflection spectra with FZ bandwidth for different grating lengths used in the FBG-FP cavity. The black solid line, red dashed line, and blue dotted line represent values for the grating length LFBG of 3.8, 4, and 4.8 mm respectively. Obviously the spectral linewidth is closely related to the reflectivity of the FBG at the resonance wavelength. Smaller reflectivity is seen to produce a larger resonance linewidth.

Figure 3.6-dB linewidths of the output resonance spectra for different grating lengths.

Figure 4.The reflection spectra with FZ bandwidth for different grating lengths.

Based on the above calculations and analysis, we conclude that the FBG-FP cavity can produce many optical spectra with different peak wavelengths or linewidths. Compared to other parameters, it is very easy to change the cavity length and grating length during the fabrication of the FBG-FP cavity. It is worth noting that both manufacturing errors and changes in ambient temperature may cause a wavelength shift of the FBG-FP cavity. However, as long as any two resonance wavelengths can be distinguished by the existing lightwave-measurement equipment, the feasibility of the proposed scheme will not be affected. High-precision, high-resolution lightwave-measurement equipment facilitates efficient spectrum recognition and further enhancement of network-monitoring capacity.

### IV. SIMULATION RESULTS

Figure 5.Simulation results: (a) all drop-fiber (DF) links are normal; (b) DF4, (c) DF5, and (d) DF6 experiences a break.

We have proposed a novel PON-monitoring scheme using the single-mode resonance spectra of the FBG-FP cavity. The calculated results obtained using the TMM show that many different spectra can be produced by the FBG-FP cavity. The resonance spectra with different peak wavelengths or linewidths can simplify the final recognition process, which is achieved using various cavity lengths or grating lengths. The spectrum identification used in the proposed scheme solves the problem of multiple end-users with small distance differences in a high-density network. A simulation has proved the feasibility of the proposed scheme.

The authors declare no conflicts of interest.

Data underlying the results presented in this paper are not publicly available at the time of publication, but may be obtained from the authors upon reasonable request.

National Natural Science Foundation of China (NSFC 61901289).

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### Article

#### Article

Curr. Opt. Photon. 2023; 7(1): 47-53

Published online February 25, 2023 https://doi.org/10.3807/COPP.2023.7.1.47

## Uniform-fiber-Bragg-grating-based Fabry-Perot Cavity for Passive-optical-network Fault Monitoring

Xuan Zhang1,2 , Ning Ning1, Tianfeng Yang2

1College of Electronic Science and Engineering, University of Electronic Science and Technology of China, Chengdu 610054, China
2College of Physics and Electronic Engineering, Sichuan Normal University, Sichuan, Chengdu 610101, China

Correspondence to:*xuanzhang@sicnu.edu.cn, ORCID 0000-0003-1748-2299

Received: August 17, 2022; Revised: November 6, 2022; Accepted: December 2, 2022

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/4.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

### Abstract

We propose a centralized passive-optical-network monitoring scheme using the resonance-spectrum properties of a Fabry-Perot cavity based on fiber Bragg gratings. Each cavity consists of two identical uniform fiber Bragg gratings and a varying cavity length or grating length, which can produce a unique single-mode resonance spectrum for the drop-fiber link. The output spectral properties of each cavity can be easily adjusted by the cavity length or the grating length. The resonance spectrum for each cavity is calculated by the transfer-matrix method. To obtain the peak wavelength of the resonance spectrum more accurately, the effective cavity length is introduced. Each drop fiber with a specific resonance spectrum distinguishes between the peak wavelength or linewidth. We also investigate parameters such as reflectivity and bandwidth, which determine the basic performance of the fiber Bragg grating used, and thus the output-spectrum properties of the Fabry-Perot cavity. The feasibility of the proposed scheme is verified using the Optisystem software for a simplified 1 × 8 passive optical network. The proposed scheme provides a simple, effective solution for passive-optical-network monitoring, especially for a high-density network with small end-user distance difference.

Keywords: Fabry-Perot cavity, Fiber Bragg grating, Network link monitoring, Passive optical network, Transfer matrix method

### I. INTRODUCTION

Among the many technologies addressing the ever-increasing demand for high-bandwidth broadband Internet service, the passive optical network (PON) has been reckoned as the most promising technology in fiber-access-network deployment [1, 2]. Due to its various advantages such as large capacity, simple structure, flexible scalability, and transparency of support services, PONs have been widely used in access networks and are today’s access technology of choice for operators, especially when they need to build new infrastructure [3, 4]. PONs have been widely deployed worldwide; however, the large-scale deployment of PON-based access networks also increases the difficulty of network management and maintenance. The time, labor, and truck-roll for fault troubleshooting dramatically increase operational expenditure. Furthermore, long repair time would reduce quality of service (QoS). Therefore, the expeditious expansion of PON deployment across the globe has highlighted the pressing need to devise an effective optical-layer monitoring system [2, 5].

When a failure occurs on a point-to-point (P2P) network, optical time-domain reflectometry (OTDR) can be used to troubleshoot the network’s link problem. However, OTDR is ineffective in point-to-multipoint (P2MP) networks like PONs, since a branch return signal in a PON can be partially or totally masked by other branch signals [6]. That is, the return signals (i.e. backreflected and backscattered light) from each branch add up to form an aggregated or composite trace. As a direct consequence, it is difficult for the central-office (CO) network manager to identify the faulty branch from the aggregated OTDR trace. To solve this problem, many studies to monitor physical-layer faults in fiber-optic distribution networks have been presented [6]. In the early 21st century, some fault-monitoring schemes were presented for the wavelength-division multiplexer (WDM)-PON [7, 8]. A novel coding approach exploits a fiber ring with varying length and a fiber Bragg grating (FBG) with 100% reflectivity to produce a varying periodic code. The inexpensive and simple optical coding device generates a unique pseudo-orthogonal code to identify each drop-fiber (DF) link [9]. A modified optical frequency-hopping/periodic coding scheme adds an optical encoder array at a remote node (RN) and configures the identical reflector at each optical network unit (ONU). This scheme can reduce the upgrade cost and is expected to become a promising PON-monitoring solution [10]. The remote-coding scheme uses the cascaded encoder to simultaneously achieve optical splitting and encoding at the RN. Multiple FBGs and 1 × 2 power splitter/combiners (PSC) are connected according to a certain design rule, to ensure that the minimum number of gratings is used. At the same time, the use of the identical reflector at the ONU side further reduces the system’s cost and makes the scheme more competitive [11]. It should be noted that many existing schemes, such as those above, involve the time domain in the final recognition processing. The multicustomer interference probability (MCIP), first introduced in [12], provides a useful tool for system-performance evaluation of schemes involving time-domain identification. In a high-density network the length difference between DF links is very small, which may cause large MCIP. That is, the length difference between DF links affects the final recognition efficiency. Consequently, large MCIP may lead to low efficiency in final recognition.

In this paper, we propose a novel PON-monitoring scheme using a fiber-Bragg-grating-based Fabry-Perot (FBG-FP) cavity. The output spectra of the resonant cavity constructed from two identical uniform FBGs (UFBGs) can be optically identified in peak wavelength or linewidth. The detecting signal generated by the encoder is not affected by the length difference between DF links. As mentioned earlier, the length difference between DF links is closely related to the MCIP. It is known that the periodic coding (PC) scheme is one of the earliest classic PON monitoring schemes [6]. Considering a detecting signal with pulse duration of 1 ns and code weight of 4 in the PC scheme, we can employ the Monte Carlo method with 105 iterations to calculate the MCIP of 64 randomly distributed users within a circular area with a radius of 460 m. To make the MCIP of the PC scheme not exceed 0.1, the difference between any two-branch links should not be less than 4.65 m. Thanks to the characteristics of spectrum recognition, the length difference between DF links in the proposed scheme is theoretically unrestricted. It is simple and flexible to generate a resonance spectrum with a unique peak wavelength or linewidth by changing the cavity length of the FBG-FP cavity, or the grating length of the UFBGs. Compared to the previous work [13], the current scheme is new, as mainly reflected in three aspects: (1) The encoder on the ONU side in the previous work is a single FBG with different central reflection wavelengths or reflection bandwidths, while the encoder in the current work is a resonant cavity constructed from two identical FBGs and a certain cavity length; (2) the generation principle and signal characteristics of the monitoring signal in the two works are different; and (3) the previous work is mainly devoted to solving the problem of identifying different reflection bandwidths at the same wavelength, while the current work focuses on obtaining more single-mode output spectra by investigating some parameters (cavity length, grating length, etc.). In terms of the detection sources, the optical bandwidth of the current work is smaller than that of the previous work. To reduce the difficulty of final recognition, we use the transfer-matrix method (TMM) to analyze and calculate a single-mode resonance spectrum that can be used in the proposed scheme. In addition, we use the Optisystem software to perform a simulation.

### 2.1. Principle of Operation

Figure 1(a) illustrates the principle of the proposed PON-monitoring system. Specifically, a U-band (1,625–1,675 nm) detecting signal is coupled to normal data traffic from the optical line terminal (OLT) via a wavelength-division multiplexer (WDM) and sent into the feeder fiber (FF). At the RN, the detecting signal is split into n sub signals by the PSC and broadcast to each DF link. Different resonant spectra are encoded and reflected to the CO. Each encoder located at the front of the ONU consists of an FBG-FP cavity, two circulators (CIRs), and an FBG (i.e. FBG3) with 100% reflectivity, as shown in Fig. 1(b). Finally, the spectra returned from all DFs are filtered by an optical filter (OF) for spectrum recognition.

Figure 1. System principle and structure. (a) Schematic diagram of the proposed passive optical network-monitoring system; (b) encoder with an fiber-Bragg-grating-based Fabry-Perot (FBG-FP) cavity, two circulators (CIRs), and a 100%-reflectivity FBG; (c) structure of the FBG-FP cavity.

Features of the reflected resonance peaks can be used to assess the link quality for individual DFs. An attenuated resonance peak shows that the fiber link between the CO and the ONU may be degrading. That is, the DF status can be determined by checking the reflected power level of the corresponding resonance peak. For the proposed scheme, the resonance spectrum can be different peak wavelengths with the same linewidth, or the same wavelength with different linewidths. In theory, more linewidths at the same wavelength can lead to larger monitoring capacity, but may also increase the difficulty of the final recognition process. To strike a balance between final-recognition difficulty and monitoring capacity, the number of linewidths in the proposed scheme at the same wavelength does not exceed 2.

### 2.2. Encoder Design

Recall that the encoder contains an FBG-FP cavity, two CIRs, and a FBG3 with 100% reflectivity. As illustrated in Fig. 1(b), the detecting signal is injected into the FBG-FP cavity via port 2 of CIR2 and resonates at a desired wavelength. Then the resonance wavelength is fully reflected by FBG3 and passes back through port 2 of CIR3. Port 1 of CIR2 and port 3 of CIR3 are connected by a fiber. Figure 1(b) shows that the detecting signal experiences the following optical path in the encoder: Port 2 of CIR2 → Port 3 of CIR2 → FBG-FP cavity → Port 1 of CIR3 →Port 2 of CIR3 → FBG3→ Port 2 of CIR3 → Port 3 of CIR3 → Port 1 of CIR2 → Port 2 of CIR2→output. The central reflection wavelength of FBG3 in each encoder is consistent with the resonance wavelength produced by the FBG-FP cavity. FBG3 can also be a broadband reflector; that is, the FBG can reflect the resonant signals generated by all FBG-FP cavities in the proposed PON-monitoring system. Per the ITU-T L.66 (2007) recommendation, the working wavelength of the FBG-FP cavity and FBG3 are in the U band, which is transparent to the data traffic in the C and L bands. Note that multichannel network monitoring does require multiple circulators and FBGs. However, according to the design of the proposed scheme, all circulators are the same and all FBGs can also be the same, which is obviously conducive to reducing costs.

### 2.3. Resonance-spectra Calculation

As illustrated in Fig. 1, the FBG-FP cavity is constructed from two identical UFBGs. For this cavity the effective cavity length Leff is the sum of the effective lengths Leff_FBG of both the FBGs forming the cavity plus the distance between them Ln. Thus, the effective cavity length of the FP cavity based on two identical UFBGs can be expressed as

$Leff=Ln+2Leff_FBG$

According to [14], Leff_FBG is determined by the group delay of light reflected from the grating, and depends on its refraction coefficient:

$Leff_FBG=L FBGR/2atanh(R)$

where LFBG is the physical length of the FBG, corresponding to Ln1 and Ln2 in Fig. 1(c), and R is the peak reflectivity of the FBG. The atanh function returns the inverse hyperbolic tangent of a number.

It is well known that coupled-mode theory (CMT) is a useful mathematical tool for the analysis of the wave propagation and interactions with materials in an optical waveguide. The TMM is a simple, precise technique that is easy to integrate into coupled mode equations. Therefore, we use the TMM to calculate the output resonance spectrum of the FBG-FP cavity [15, 16]. For the TMM, the FBG-FP cavity can be divided into 3 cascaded sections (i.e. FBG1, a bare fiber, and FBG2), with each section affecting the succeeding one. That is, matrix outputs of one section are used as matrix inputs of the next. In addition, the two UFBGs in the FBG-FP cavity are connected by a fiber of length Ln. The phase-shift matrix Tps corresponding to Ln can be found in [15]. The reflection spectrum of the UFBG can be calculated using the reflection coefficient in [17].

### III. ANALYSIS AND CALCULATION

A FBG can only produce reflections within its reflection bandwidth, and the reflectivity is wavelength-dependent. When the FBG-FP cavity resonates at the central reflection wavelength λB (i.e. the Bragg condition), the cavity length Ln and period Λ satisfy Ln = (m − 1 / 2)(1 + δn / neff)Λ. Since the FBG has the strongest reflectance at its central reflection wavelength λB, at λB the “dc” self-coupling coefficient σ is zero, such that the phase angle of the reflection coefficient at this wavelength is always π/2 [17]. Obviously a FBG-FP cavity can produce different wavelengths when Ln changes in one period Λ. Figure 2 depicts spectral responses of the UFBG used, and the FBG-FP cavity for different cavity lengths. In this calculation we use an effective refractive index of n0 = 1.447, two 4.8-mm-long UFBGs (i.e. Ln1 = Ln2 = 4.8 mm) with a period of Λ = 570 nm, and an index modulation of δn = 2 × 10−4. These parameters ensure that the detecting signals generated are within the U band, as recommended by the ITU. In Fig. 2(a) the reflection spectrum is plotted, where the reflection bandwidth for the UFBG used in the FBG-FP cavity is that between the first zeros on either side of the maximum reflectivity (FZ bandwidth). Figure 2(b) shows the output spectra of the FBG-FP cavity with Ln = 0.6 mm and an increase of half a period (i.e. +0.5Λ) and one period (i.e. +Λ). When the cavity length is 0.6 mm, the FBG-FP cavity exhibits single-mode output. Clearly from the graph, the two resonance peaks generated (1,649.718 and 1,649.882 nm) with Ln = +0.5Λ are symmetric about the original peak (1,649.8 nm) with Ln = 0.6 mm. For the convenience of display, the curves with different colors and lines are stacked in one figure; Note, however, that each curve represents a single output spectral response at a specific cavity length. The resonance peak moves toward longer wavelengths when Ln is uniformly increased to 0.5Λ with a step size ΔL of 0.005Λ (2.85 nm), as shown in Fig. 2(c). Similarly, Fig. 2(d) shows the resonance peaks generated for Ln varied from 0.505Λ to Λ with ΔL = 0.005Λ. In general, when the cavity length gradually changes by about one period, the resonance peak deviates from the position of the original peak and finally reappears. For this FBG-FP cavity, 201 different peak wavelengths with an interval of about 0.1 GHz can be generated, which are bounded by two symmetric peak wavelengths. Note that a wider reflection spectrum may produce more resonance wavelengths or larger single-wavelength intervals. To reduce the manufacturing difficulty, the cavity-length interval can be appropriately increased.

Figure 2. Results for the spectral response: (a) The reflection spectrum of the uniform fiber-Bragg-gratings (FBGs) used in the FBG-FP cavity, (b) cavity lengths for Ln = 0.6 mm (red dashed-dotted line), +0.5Λ (green solid line) and +Λ (blue dashed line), and different cavity lengths varied from (c) 0.6 + 0.005Λ to 0.6 + 0.5Λ with ΔL = 0.005Λ, and (d) 0.6 + 0.505Λ to 0.6 + Λ with ΔL = 0.005Λ.

Parameters such as reflectivity and bandwidth determine the basic performance of the FBG, and thus affect the output-spectrum properties of the FBG-FP cavity. For instance, a smaller reflection bandwidth allows for fewer resonant modes to be accommodated in the FBG-FP cavity. The reflection bandwidth and maximum reflectivity of the FBG largely depend on the grating length or refractive-index modulation depth. We further investigate the reflection-spectrum performance of the UFBGs used for different grating lengths and refractive modulation depths, as listed in Table 1.

Reflection-spectrum performance of the uniform fiber-Bragg-gratings used.

 Grating Length (mm) Refractive-index Modulation Depth FZ Bandwidth (nm) Maximum Reflectivity 4 2 × 10−4 0.523 82.7% 5 2 × 10−4 0.440 91.5% 7 2 × 10−4 0.354 98.1% 4 1.8 × 10−4 0.477 77.3% 5 1.8 × 10−4 0.430 87.8% 7 1.8 × 10−4 0.340 96.8% 4 2.2 × 10−4 0.445 86.9% 5 2.2 × 10−4 0.402 94.1% 7 2.2 × 10−4 0.356 98.9%

For the UFBGs used, the maximum reflectivity increases as the grating length or refractive-index modulation depth increases. However, the reflection bandwidth decreases as the grating length increases, and is decided by the refractive-index modulation depth. A FBG with a reflectivity of at least 80% is usually adopted, to reduce the loss in the FBG-FP cavity.

Figure 3 depicts the reflection spectra of the FBG-FP cavity with Ln = 0.743093 mm for LFBG = 3.8 mm (black solid line), Ln = 0.650085 mm for LFBG = 4 mm (red dashed line), and Ln = 0.6 mm for LFBG = 4.8 mm (blue dotted line). Recall that the expression for the effective cavity length includes two parts. For different values of LFBG, Ln can be flexibly adjusted to obtain the same peak wavelength. For a 4-mm-long FBG, the precision of the cavity length is reduced from 6 digits (i.e. 0.650085 mm) to 2 digits (i.e. 0.65 mm), and the resonance-peak wavelength moves from 1,649.8 nm to 1,649.774 nm. Consequently, the cavity length may require nanoscale precision to obtain the same resonance-peak wavelength under different conditions. The 6-dB linewidths of the wavelength at 1,649.8 nm for LFBG = 3.8, 4, and 4.8 mm are roughly 2.72, 2.34, and 1.23 GHz respectively. That is, for the same peak wavelength, the 6-dB linewidth can be different when the grating lengths are different. Here we use the 6-dB linewidth, instead of the commonly used 3-dB linewidth, to further reduce the requirements for lightwave-measurement equipment. Unlike for other F-P structures, there is a tradeoff relationship between grating length LFBG and cavity length Ln to ensure that the effective cavity length Leff is consistent. Figure 4 shows the reflection spectra with FZ bandwidth for different grating lengths used in the FBG-FP cavity. The black solid line, red dashed line, and blue dotted line represent values for the grating length LFBG of 3.8, 4, and 4.8 mm respectively. Obviously the spectral linewidth is closely related to the reflectivity of the FBG at the resonance wavelength. Smaller reflectivity is seen to produce a larger resonance linewidth.

Figure 3. 6-dB linewidths of the output resonance spectra for different grating lengths.

Figure 4. The reflection spectra with FZ bandwidth for different grating lengths.

Based on the above calculations and analysis, we conclude that the FBG-FP cavity can produce many optical spectra with different peak wavelengths or linewidths. Compared to other parameters, it is very easy to change the cavity length and grating length during the fabrication of the FBG-FP cavity. It is worth noting that both manufacturing errors and changes in ambient temperature may cause a wavelength shift of the FBG-FP cavity. However, as long as any two resonance wavelengths can be distinguished by the existing lightwave-measurement equipment, the feasibility of the proposed scheme will not be affected. High-precision, high-resolution lightwave-measurement equipment facilitates efficient spectrum recognition and further enhancement of network-monitoring capacity.

### IV. SIMULATION RESULTS

Figure 5. Simulation results: (a) all drop-fiber (DF) links are normal; (b) DF4, (c) DF5, and (d) DF6 experiences a break.

### V. CONCLUSION

We have proposed a novel PON-monitoring scheme using the single-mode resonance spectra of the FBG-FP cavity. The calculated results obtained using the TMM show that many different spectra can be produced by the FBG-FP cavity. The resonance spectra with different peak wavelengths or linewidths can simplify the final recognition process, which is achieved using various cavity lengths or grating lengths. The spectrum identification used in the proposed scheme solves the problem of multiple end-users with small distance differences in a high-density network. A simulation has proved the feasibility of the proposed scheme.

### DISCLOSURES

The authors declare no conflicts of interest.

### DATA AVAILABILITY

Data underlying the results presented in this paper are not publicly available at the time of publication, but may be obtained from the authors upon reasonable request.

### FUNDING

National Natural Science Foundation of China (NSFC 61901289).

### Fig 1.

Figure 1.System principle and structure. (a) Schematic diagram of the proposed passive optical network-monitoring system; (b) encoder with an fiber-Bragg-grating-based Fabry-Perot (FBG-FP) cavity, two circulators (CIRs), and a 100%-reflectivity FBG; (c) structure of the FBG-FP cavity.
Current Optics and Photonics 2023; 7: 47-53https://doi.org/10.3807/COPP.2023.7.1.47

### Fig 2.

Figure 2.Results for the spectral response: (a) The reflection spectrum of the uniform fiber-Bragg-gratings (FBGs) used in the FBG-FP cavity, (b) cavity lengths for Ln = 0.6 mm (red dashed-dotted line), +0.5Λ (green solid line) and +Λ (blue dashed line), and different cavity lengths varied from (c) 0.6 + 0.005Λ to 0.6 + 0.5Λ with ΔL = 0.005Λ, and (d) 0.6 + 0.505Λ to 0.6 + Λ with ΔL = 0.005Λ.
Current Optics and Photonics 2023; 7: 47-53https://doi.org/10.3807/COPP.2023.7.1.47

### Fig 3.

Figure 3.6-dB linewidths of the output resonance spectra for different grating lengths.
Current Optics and Photonics 2023; 7: 47-53https://doi.org/10.3807/COPP.2023.7.1.47

### Fig 4.

Figure 4.The reflection spectra with FZ bandwidth for different grating lengths.
Current Optics and Photonics 2023; 7: 47-53https://doi.org/10.3807/COPP.2023.7.1.47

### Fig 5.

Figure 5.Simulation results: (a) all drop-fiber (DF) links are normal; (b) DF4, (c) DF5, and (d) DF6 experiences a break.
Current Optics and Photonics 2023; 7: 47-53https://doi.org/10.3807/COPP.2023.7.1.47

Table 1 Reflection-spectrum performance of the uniform fiber-Bragg-gratings used

 Grating Length (mm) Refractive-index Modulation Depth FZ Bandwidth (nm) Maximum Reflectivity 4 2 × 10−4 0.523 82.7% 5 2 × 10−4 0.440 91.5% 7 2 × 10−4 0.354 98.1% 4 1.8 × 10−4 0.477 77.3% 5 1.8 × 10−4 0.430 87.8% 7 1.8 × 10−4 0.340 96.8% 4 2.2 × 10−4 0.445 86.9% 5 2.2 × 10−4 0.402 94.1% 7 2.2 × 10−4 0.356 98.9%

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Wonshik Choi,
Editor-in-chief