# High-Sensitivity Fiber Fault Detection Method Using Feedback-Delay Signature of a Modulated Semiconductor Laser

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## Abstract

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## 1. Introduction

## 2. Methods

#### 2.1. Principle

_{m}is directly added on the bias current of the laser, and the laser emits the light to the fiber under test, as shown in Figure 1a. At this time, the amplitude of the laser output power is the response at the modulation frequency f

_{m}. The modulation response curve of the semiconductor laser is obtained by sweeping the frequency and then recording the response at different frequencies. When the fiber fault occurs, a reflection from the fault will feed back to the laser, and a high or low response will appear that is different from the modulation response without feedback, as shown in Figure 1b. The fluctuation period is inversely proportional to the fault distance L, e.g., F = c/2nL. By calculating the inverse Fourier transform (IFT) of the modulation response curve, one can obtain a clear peak located at t = 1/F, as plotted in Figure 1c. Thus, this peak reads out the position of the fiber fault, which we named “feedback-delay signature” (FDS), referring to the time-delay signature.

#### 2.2. Theoretical Model

_{n}is the gain coefficient, ε is coefficient of gain saturation, and N

_{0}is the transparent carrier density. τ

_{n}and τ

_{p}are carrier and photon lifetime, respectively. The round-trip time in the laser internal cavity is τ

_{in}. The amplitude feedback coefficient is k = (1 − r

_{0}

^{2})r/r

_{0}, where r and r

_{0}are the amplitude reflectivity of the fiber fault and the laser facet, respectively. We define the intensity reflectivity of the fault as feedback strength and denote it as R = 10log(r

^{2}) in dB. The feedback phase θ(t) = ωτ + f (t) − f (t−τ), and τ = 2nL/c is the round-trip time of light between the laser facet and the fiber fault located at a distance L, where ω, n, and c are the angular oscillation frequency, the refractive index of fiber, and the velocity of light in vacuum, respectively. The symbols of linewidth enhancement factor, the electron charge, and the internal cavity volume of the laser are defined as α, q, and V. The modulation current I

_{m}(t) = I

_{b}+ M(I

_{b}− I

_{th})cos(2πf

_{m}t), where I

_{b}and I

_{th}are the bias and threshold current, and M and f

_{m}are the modulation depth and modulation frequency, respectively.

_{n}= 5.89 × 10

^{−12}m

^{3}/s, N

_{0}= 0.455 × 10

^{24}m

^{−3}, ε = 5 × 10

^{−23}m

^{3}, τ

_{n}= 2.5 × 10

^{−9}s, τ

_{p}= 1.5 × 10

^{−12}s, τ

_{in}= 7 × 10

^{−12}s, α = 5, V = 3.24 × 10

^{−16}m

^{3}, r

_{0}= 0.55, ω = 1.216 × 10

^{15}rad/s, q = 1.602 × 10

^{19}C, and I

_{th}= 19 mA.

## 3. Results

#### 3.1. Sensitivity

_{th}. Under this bias current condition, the output power of the laser is much less than the laser-induced damage threshold. Even if 100% of the feedback optical power is added, the optical power inside the laser is still less than the laser-induced damage threshold. Lasers will not be destroyed by the tiniest amounts of light feedback. The relaxation oscillation frequency f

_{r}of the laser is around 3.6 GHz. Due to the modulation response curve of the laser without feedback having a Gaussian-like shape, we set the modulation frequency sweeping area as 0–20 GHz to cover the whole response frequency. Even if the increasing bias current will make the f

_{r}of the laser increase, it is still confined within the sweeping range. Considering the large-signal modulation maybe dominating the laser output oscillation in excessive amplitude and causing difficulty in finding the resonance phenomenon, we used small-signal modulation and set M at 0.05. We initially used 10 MHz as the frequency sweeping step to balance the modulation scanning speed and the fineness of the modulation response curve.

_{b}= 2I

_{th}in Figure 3a. The SNR rises with the R increase and reaches the maximum at R = −50 dB. After that, the SNR decreases until R increases to −25 dB, and then increases again when R continues to increase. According to the criterion of 3 dB, the sensitivity of the frequency-resonance method is −84.3 dB with the laser running at 2I

_{th}bias current.

_{r}, and the modulation response also changes accordingly. Figure 4a shows the modulation response subject to R = −60 dB under different bias current. Obviously, with the bias current increasing, f

_{r,}which is indicated by the maximum position in the modulation response curve, moves to the higher frequency, with the peak level decreasing. Moreover, the period fluctuation also shows a shrinking trend, which is shown in the inset of Figure 4a. The amplitude of period fluctuation decreases from 0.7 at 2I

_{th}to 0.035 at 10I

_{th}. Corresponding IFT curves are illustrated in Figure 4b. The FDS level changes with the increasing bias current, and the highest value appears at I

_{b}= 2I

_{th}. The inset shows the variation in SNR, and the SNR decreases from 13.4 dB to 10.1 dB when I

_{b}increases from 2I

_{th}to 10I

_{th}. Apparently, the sensitivity of the frequency resonance method will change with the difference in SNR under different I

_{b}. As shown in Figure 4c, the sensitivity decreases to −74 dB at I

_{b}= 10I

_{th}.

#### 3.2. Sensitivity Improvement Potential

_{in}, linewidth enhancement factor α, and facet reflectivity r

_{0}. Therefore, there is still potential to enhance the sensitivity with the frequency resonance method. In order to express the structural parameters of the laser conveniently, here, we used internal cavity length instead of τ

_{in}. The internal cavity length’s influence on the sensitivity is shown in Figure 5a. With the increase in internal cavity length from 200 to 400 μm, the sensitivity almost appears to linearly decrease from −88 to −81.6 dB.

_{0}on the sensitivity of the frequency resonance method, and it also shows a linear trend. When the facet reflectivity is decreased, the sensitivity can reach a high value, to −91 dB and even at 0.7 reflectivity, and the sensitivity just decreases to −79 dB.

#### 3.3. Modulation Parameters

_{b}= 2I

_{th}and R = −60 dB.

_{r}oscillates smoothly like a sine curve with a stable period. The calculation result of IFT also shows a significant peak at the FDS position. These are the typical results of this method. However, as the modulation depth increases, the modulation response curve and IFT curve deteriorate by harmonic frequencies, which are plotted by red and blue in Figure 6a,b, where the modulation depth is 0.15 and 0.35, respectively. The deterioration also makes the FDS shift left slightly. The trend in Figure 6c shows that the SNR rapidly drops to 4 dB as M increases to 0.5. It is also suggested that the small signal modulation should be kept by setting M < 0.1 to make the SNR higher than 18 dB.

_{r}. The large fluctuation will achieve more significant FDS. We, thus, choose the frequency sweeping range centered at f

_{r}, as shown in Figure 7a. The corresponding IFT curves are demonstrated in Figure 7b, and the FDS decreases from 0.39 to 0.09, while the ΔF changes from 0.5f

_{r}to 2.5f

_{r}. This decreasing trend can be explained by the large amount of smaller and smaller amplitude period fluctuations on both sides of f

_{r}, which averages the value of FDS.

_{r}, corresponding to 4.68 GHz. In addition, Δf of modulation frequency actually acts as a sampling interval of the modulation response curve, and thus there should be an optimum frequency sweeping step when the external frequency F is fixed. Figure 8b shows the SNR as a function of the product F/Δf, which is obtained with ΔF =1.3f

_{r}. The SNR increases first and then becomes stable as F/Δf increases beyond 10, which means ten sampling points are measured in one fluctuation period of the modulation response curve.

_{max}of the modulation resonance method is c/(4nΔf).

_{b}= 2I

_{th}, α = 5, r

_{0}= 0.1, 200 μm internal cavity length, ΔF = 4.68 GHz, and Δf = 0.1F, respectively. In this case, the sensitivity reached the highest level at −118.1 dB.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Schematic of fiber fault detection by frequency resonance method. (

**a**) Setup: a modulated laser receiving its own delayed feedback from the fault point; (

**b**) modulation response curve and (

**c**) its inverse Fourier transform.

**Figure 2.**Typical results of frequency-resonance method with laser running at 2 I

_{th}with different feedback strength R. (

**a1**,

**b1**,

**c1**,

**d1**) the modulation response curves and (

**a2**,

**b2**,

**c2**,

**d2**) IFT curves when R is −90 dB, −60 dB, −30 dB, and −20 dB, respectively.

**Figure 3.**(

**a**) The SNR of the frequency-resonance method versus R under 2I

_{th}bias current, and (

**b**) a bifurcation diagram of the laser with variable R.

**Figure 4.**(

**a**) Modulation response curve, (

**b**) the IFT curves, and (

**c**) the sensitivity of frequency resonance method versus laser bias current I

_{b}. The insets are the period fluctuation amplitude of modulation response curve and SNR of FDS versus I

_{b}, respectively.

**Figure 5.**Effects of laser parameters on sensitivity: (

**a**) internal cavity length; (

**b**) linewidth enhancement factor; (

**c**) facet reflectivity.

**Figure 6.**(

**a**) Modulation response curve and (

**b**) IFT with different modulation depths of 0.05, 0.15, and 0.35; (

**c**) SNR versus modulation depth.

**Figure 7.**(

**a**) Modulation response curve and (

**b**) corresponding IFT curve under ΔF = 0.5f

_{r}and 2.5 f

_{r}.

**Figure 9.**SNR versus feedback strength with optimized parameters, which are I

_{b}= 2I

_{th}, α = 5, r

_{0}= 0.33, 200 μm internal cavity length, ΔF = 4.68 GHz, and Δf = 0.1F, respectively.

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## Share and Cite

**MDPI and ACS Style**

Shi, Z.; Zhao, T.; Wang, Y.; Wang, A. High-Sensitivity Fiber Fault Detection Method Using Feedback-Delay Signature of a Modulated Semiconductor Laser. *Photonics* **2022**, *9*, 454.
https://doi.org/10.3390/photonics9070454

**AMA Style**

Shi Z, Zhao T, Wang Y, Wang A. High-Sensitivity Fiber Fault Detection Method Using Feedback-Delay Signature of a Modulated Semiconductor Laser. *Photonics*. 2022; 9(7):454.
https://doi.org/10.3390/photonics9070454

**Chicago/Turabian Style**

Shi, Zixiong, Tong Zhao, Yuncai Wang, and Anbang Wang. 2022. "High-Sensitivity Fiber Fault Detection Method Using Feedback-Delay Signature of a Modulated Semiconductor Laser" *Photonics* 9, no. 7: 454.
https://doi.org/10.3390/photonics9070454