Influence of Pump Light on LP₀₁ and LP₁₁ Modes in Few-Mode Fiber Brillouin Optical Time Domain Reflectometry

Abstract

The quality of pump pulse in few-mode-fiber Brillouin optical time domain reflectometry (FMF-BOTDR) is vital for the spontaneous Brillouin scattering of modes LP₀₁ and LP₁₁ because it is the comprehensive effect of the main laser linewidth and pulse width, which is firstly discussed as we know. Numerical and experimental analysis are made for the amplitude and linewidth distribution, corresponding to the signal–noise ratio (SNR) and frequency resolution in BOTDR, respectively. Simulation shows the linewidths and peak values of Brillouin scattering have the same tendency for the LP₀₁ mode and LP₁₁ mode when the laser linewidth is less than 1 MHz but decreases slowly until they are the same when the laser linewidth is wider than 1 MHz. With the pulse width widening, the Brillouin linewidths for LP₀₁ and LP₁₁ modes both decrease sharply, almost to the natural linewidth of fiber 41 MHz and 35 MHz. Experimental results show that the amplitude distribution for the LP₀₁ mode is always larger than for the LP₁₁ mode if the main laser has the same linewidth and the frequency fluctuation is at least 2 MHz with the fiber laser and LP₁₁ mode. The above results could provide improved sensing resolution for FMF-BOTDR sensing system.

1. Introduction

Brillouin optical time domain reflectometry (BOTDR)-based spontaneous Brillouin scattering has been focused on as a powerful tool for distributed fiber sensing since 1989 [1,2,3]. Different kinds of system configurations and data algorithms have been reported to improve the system performance and develop the practical applications [3,4,5]. Single-mode fiber (SMF)-based BOTDR has been well known and studied in detail in the conventional research. With the development of optical fiber technology, the few-mode fiber (FMF) has been invented. Recently, it has attracted much attention, because it offers the potential to break the capacity limit of standard SMF. It has been applied in the space-division multiplexing of optical fiber communication systems successfully [6]. Very recently, researchers around the world have turned their attention to the distributed fiber sensor-based FMF [7,8,9,10,11,12].

Compared with SMF-BOTDR sensing, the characteristic sensing spectra in FMF are multiple because every mode has its own inner-mode spontaneous Brillouin scattering, while inter-mode Brillouin scattering is weak enough to be neglected in the BOTDR field. For N-modes FMF (2 ≤ N ≤ 10), BOTDR could measure N parameters simultaneously. As temperature and strain are the two mainly concerned parameters, we performed an analysis of the two lowest order (LP₀₁, LP₁₁) modes in two-mode fiber (TMF). Similar with SMF-BOTDR, the peak values and frequency shifts of spontaneous Brillouin scattering in the sensing fiber for the LP₀₁ mode and LP₁₁ mode are linear to the temperature and strain variations. It has been reported that the temperature and strain coefficient was 1.29 MHz/°C, 58.5 KHz/με for the LP₀₁ mode and 1.25 MHz/°C, 57.6 KHz/με for the LP₁₁ mode [9]. In reference [12], the five-mode fiber BOTDR obtained 1.01690 MHz/°C and 59.24 KHz/με for the LP₀₁ mode, 0.99099 MHz/°C and 48.72 KHz/με for the LP₁₁ mode. All setups of FMF-BOTDR are similar to SMF-BOTDR, only with a mode converter inserting in front of the sensing fiber and behind the Brillouin scattering light [13,14].

According to the optical fiber theory [15], the optical field distribution (OFD) of the LP₀₁ mode and LP₁₁ mode are different. The OFD of LP₀₁ is circular, while the LP₁₁ is two halves. When prorogating in the TMF, the acoustic field distribution originating from optical field is similar to OFD. So, the spontaneous Brillouin scattering lights for the two modes are lightly different, because the overlapped area between the optical/acoustic field distributions is not the same. Ideally, the acoustic field distributions of the LP₀₁ mode and LP₁₁ mode in TMF are standard Lorentzian functions, and researchers made Lorentzian fitting in the published papers because it is the natural shape of spontaneous Brillouin scattering. In addition, pulse sequence with different pulse width and repetition frequency is used to position accurately the temperature/strain occurrences in the sensing range in BOTDR. The power spectrum of the single pulse is of some width in the frequency domain through fast Fourier transforming (FFT). Every frequency in the pulse power spectrum has its own Brillouin scattering spectrum. So, the total and detected spontaneous Brillouin scattering is the superposition of all the Brillouin scattering components in the whole pulse power spectrum, expressed as Formula (8) in reference [16]. When the pump pulse width increases in the time domain, its power spectrum will be narrower in the frequency domain. Scientists usually change the pulse width to obtain different spatial resolution, without analyzing its influence on Brillouin scattering. All the launched pulse is regarded as having an ideal single wavelength and zero linewidth in previous work, but, as we know, the optical pulse is modulated from the continuous light of the main laser in the BOTDR system. Narrow linewidth lasers have a ~KHz or ~MHz linewidth, which is not as ideal as zero linewidth. Under an equal optical power condition, the peak values decrease with the widening of the laser linewidth. By totally combining the narrow linewidth of the laser output with the pulse power spectrum of pulse FFT, the broadening of the pump light launched into sensing fiber will be obtained in the frequency domain, which is wider than the ideal pulse power spectrum [17]. At the same time, the amplitude of Brillouin scattering would be influenced by the laser linewidth and pulse width accordingly. That is to say, the power spectrum of the launched pulse is vital for spontaneous Brillouin scattering. The effects of pump light quality on sensing spontaneous Brillouin light are similar for the modes LP₀₁ and LP₁₁.

The BOTDR sensing system has four important parameters: the spatial resolution, the response time, the sensing distance, and the sensing resolution. The first item is related to pulse width, and the last two items are essentially related to the signal–noise ratio (SNR) of the spontaneous Brillouin scattering along the sensing fiber. Higher SNR indicates better frequency resolution, i.e., temperature resolution and/or strain resolution. In this paper, the difference of Brillouin scattering between the lowest two modes LP₀₁ and LP₁₁ in the sensing few-mode fiber is presented, taking three factors including the laser linewidth, the pulse width, and the two guiding modes in the few-mode fiber into consideration. Numerical simulation for the two modes is carried out to analyze the linewidth and amplitude of Brillouin light for different laser linewidths and pulse widths in order to study the SNR and frequency fitting fluctuation. An experimental FMF-BOTDR sensing system is built to evaluate amplitudes and linewidths of spontaneous Brillouin scattering for LP₀₁/LP₁₁ modes; then, frequency fluctuation is obtained to analyze the sensing resolution performances of FMF-BOTDR. The simulation and experimental results in this work could be used to analyze the FMF-BOTDR sensing system further.

2. Theoretical Analysis and Numerical Simulations

Similar to SMF, Brillouin scattering in the FMF originates from the interaction between photons and acoustic phonons, when the pump light in the mode LP₀₁ or LP₁₁ is propagating in the fiber. Brillouin scattering is frequency downshifted from the pump light and propagated in the opposite direction in the fiber. In circular coordinates, the wave equation of the optical field is written as follows:

$$\frac{d^2{f}_o}{d{r}^2}+\frac{1}{r}\cdot \frac{d{f}_o}{dr}+k_o^2\cdot (n_o^2-n_{oeff}^2)\cdot f_o=0$$

(1)

where f_o is the optical field distribution; k_o is the optical wave number, k_o = 2π/λ; λ is the optical wavelength; n_o is the optical refractive index for the optical guided modes; and n_oeff is the optical effective refractive index of optical mode.

The thermally excited mechanical vibration can propagate as guided acoustic modes in optical fibers, so the wave equation for acoustic modes can be written as

$$\frac{d^2{f}_a}{d{r}^2}+\frac{1}{r}\cdot \frac{d{f}_a}{dr}+k_a^2\cdot (n_a^2-n_{aeff}^2)\cdot f_a=0$$

(2)

where f_a denotes the longitudinal acoustic field; k_a is the acoustic wave number; n_a is the acoustic refractive index; and n_aeff is the effective refractive index of every acoustic guided mode.

Due to the interaction between the acoustic modes and optical modes, a fraction of light is backscattered. The normalized modal overlap integral I_u between the optical field and acoustic field is expressed as

$$I_{\mathrm{u}}=\frac{{\left({\displaystyle \int E_{\mathrm{o}}{E}_{\mathrm{o}}^{\ast }{\rho }_u^{\ast }rdrd\theta }\right)}^2}{{\displaystyle \int {\left(E_{\mathrm{o}}{E}_{\mathrm{o}}^{\ast }\right)}^{2}rdrd\theta \cdot {\displaystyle \int \rho {\rho }^{\ast }rdrd\theta }}}$$

(3)

where the integral brackets are the integration of optical modes over the polar coordinates (r, θ); E_o is the electric field distribution associated with the fundamental mode; ρ_u is the field of a longitudinal acoustic eigenmode of order u; and ρ is the acoustic density variation for the acoustic modes.

In FMF, the optical intensity profile and acoustic intensity profile match well for the LP₀₁ mode, so the overlap area is bigger than the LP₁₁ mode when making the integral. This caused the slight difference of Brillouin scattering between the two modes, because the Brillouin light originates from the optical and acoustic modes. The modes with different OFD in FMF have vital influence on their Brillouin scattering.

In the FMF-BOTDR sensing system, the continuous output of the main laser is modulated to the pulses’ sequences with a different pulse width and repetition frequency in order to position the temperature/strain accurately in the sensing range and, then, this is launched into the long-sensing FMF. The total Brillouin power spectrum for every mode is the superposition of many Brillouin power spectra for every single frequency in the launched pulse power spectrum in the frequency domain. In fact, Brillouin scattering is the product of the pulse power spectrum and the natural Brillouin transfer function. So, the frequency-dependent factor H(ν) for the backscattering Brillouin light [16] is expressed as

$$H\left(v\right)={\displaystyle {\int }_{-\infty }^{+\infty }{\mathrm{P}}_p}\left(f\right)\frac{h{\left(\omega /2\right)}^2}{{\left\{v-\left(f-\Delta v_B\right)\right\}}^2+{\left(\omega /2\right)}^2}df$$

(4)

where h is constant; Δν_B is the Brillouin frequency shift (about 10.88 GHz); P_P(f) is the power spectrum of the pump pulse; ω is full width at half maximum (FWHM, different for mode LP₀₁ and mode LP₁₁, around 33 MHz); and ν is the frequency in the Brillouin power spectrum. P_p(f) in the integral is the pump pulse power spectrum related to the laser linewidth and the pulse width, which is the key points in BOTDR; and h, Δν_B, and ω are correlated to two guiding modes LP₀₁ and LP₁₁.

About P_p(f), the previous work all regarded the simple FFT of the modulated pulse without considering the linewidth of the laser itself. The pulse laser with a zero linewidth is not ideal because it derives from the narrow linewidth continuous laser. So, the pump light includes two aspects: the main laser linewidth and the pulse width.

In a word, the above mentioned three parameters, including the propagating modes, the laser linewidth, and the pulse width, all have an important influence on the spontaneous Brillouin scattering in FMF-BOTDR.

2.1. Brillouin Frequency Shifts for LP₀₁ and LP₁₁ Modes

The backwards spontaneous Brillouin scattering light is frequency downshifted from the pump light, expressed as

$$\Delta v_B=\frac{2\pi \cdot n_{eff}\cdot V_a}{\lambda }$$

(5)

where λ is the main laser wavelength, n_eff is the effective refractive index of modes LP₀₁ or LP₁₁, and V_a is the acoustic velocity in FMF. Inner-mode Brillouin scattering and inter-mode Brillouin scattering between the LP₀₁ mode and LP₁₁ mode happens simultaneously, but we focused on inner-mode Brillouin scattering in this paper, which is the mutual interaction of OFD and its acoustic field for one mode. Values of n_eff, linewidths@3dB, and frequency shifts for mode LP₀₁ and mode LP₁₁ are listed in

Table 1. Parameters for Brillouin scattering for LP₀₁ and LP₁₁ modes.

	LP01	LP11
neff	1.4552	1.4463
ΔνB (GHz)	10.905	10.913
linewidth@3dB (MHz)	33.03	33.10

.

2.2. Influence of Laser Linewidth on Brillouin Scattering for the LP₀₁ and LP₁₁ Mode

In the FMF-BOTDR sensing system, pump lasers are not generally ideal with a single frequency with zero linewidth. Assuming the laser output is the Lorentzian shape in nature, it could be written as

$$E(f)=\frac{{({\omega }_s/2)}^2}{{(f-f_s)}^2+{({\omega }_s/2)}^2}$$

(6)

where E(f) is the intensity, f_s is the central frequency of the optical source, f is the frequency around f_s in the frequency domain, and ω_s is the laser linewidth@3dB.

Taking the main laser linewidths 50 KHz, 500 KHz, and 10 MHz for numerical simulation, the optical spectra for the three laser outputs are shown in Figure 1, where the optical intensities are the same for the three lasers and the optical intensities are normalized to the narrowest linewidth laser output. Obviously, peaks and the extended range of the launched laser have a noticeable difference in the frequency domain, especially in comparison between 50 KHz and 1 MHz. When they are substituted into Equation (4), the P_p(f) item is different from the ideal single-frequency laser (ω_s = 0); then, the peak-values and linewidths of spontaneous Brillouin scattering will be totally different consequently.

According to Equation (4), the OFDs of modes LP₀₁ and LP₁₁ are related to the second item in the integral. Next, we made the simulation for the two lowest modes. When the laser linewidth varies from 1 KHz to 100 MHz, the peak value and linewidth distributions of Brillouin scattering for the LP₀₁/LP₁₁ mode are demonstrated in Figure 2a and Figure 2b, respectively. During the simulation, the natural linewidths are 33.03 MHz and 33.10 MHz, and the Brillouin gain coefficients are 1 and 0.989, for the LP₀₁ mode and the LP₁₁ mode; the pulse width is set as 100 ns.

From Figure 2a,b, the peak values and linewidths of Brillouin scattering have the same tendency for the LP₀₁ mode and LP₁₁ mode. For a single-mode LP₀₁ or LP₁₁, the peak value almost stays constant and the linewidth is nearly the same when the laser linewidth is narrower than 1 MHz. However, when the laser linewidth is wider than 1 MHz, the peak value drops, and the linewidth broadens seriously. As to the difference between mode LP₀₁ and mode LP₁₁, the peak values difference between them is 0.07 dB, as shown in the insert figure in Figure 3a, and the linewidth@3dB difference between them is approximately 0.2 MHz when the laser linewidth is less than 1 MHz. With the increasing of the main laser linewidth (wider than 1 MHz), the difference in peak values and linewidths becomes smaller until they are same. However, the linewidths of Brillouin scattering for the two modes are the same when the laser linewidth is widened far beyond 1 MHz. The above results can be explained by the fact that the optical field and acoustic field overlap much more until they totally overlap with the widening laser linewidth.

2.3. Influence of Pulse Width on Brillouin Scattering for the LP₀₁ and LP₁₁ Mode

The pulse is injected into the sensing FMF in BOTDR. In the time domain, the mathematical expression for different pulse widths is as follows:

$$\mathrm{P}\left(t\right)=\left\{\begin{array}{cc}0\hfill & t<-\tau /2\\ 1\hfill & -\tau /2\le t\le \tau /2\\ 0\hfill & t>\tau /2\end{array}\right.$$

(7)

where the pulse width τ denotes the full width at half peak and the pulse intensity is uniformed; the pulse is symmetrical for t = 0.

For different pulse widths, their power spectra in the frequency domain are obtained by FFT. Taking 50 ns, 100 ns, and 200 ns pulse widths as examples, as shown in Figure 3a, the power spectrum distribution is much more centralized when the pulse is wider in the time domain, as shown in Figure 3b. According to Equation (3), the energy distribution in the frequency domain has vital influence on the acoustic field area for each mode.

Taking the multiplication of the natural Brillouin optical field and pulse power spectrum, we obtain Brillouin properties for modes LP₀₁ and LP₁₁. The comparison figures of linewidths and peak values are shown in Figure 4a and Figure 4b, respectively, where the laser linewidth is set as 1 KHz.

From Figure 4a, the linewidths of Brillouin scattering for the LP₀₁ mode and LP₁₁ mode decrease sharply almost to the natural linewidth. Linewidth difference between the two modes increases with the pulse widening. When the pulse width is 10 ns and 100 ns, the linewidth difference of Brillouin scattering is 4.12 MHz and 7.05 MHz, respectively. When the pulse is wider than 100 ns, the linewidth difference between modes LP₀₁ and LP₁₁ is almost the same at 7.05 MHz. The above results originate from the optical field variation of the LP₀₁ mode and LP₁₁ mode. Similarly, the peak values of modes LP₀₁ and LP₁₁, as shown in Figure 4b, both increase with the pulse width widening, and their peak value difference also increases. A wider pulse means that much more optical energy is launched into the sensing FMF fiber, so the peak values of its Brillouin scattering are higher for every mode. Meanwhile, the pump optical field area and the corresponding acoustic field area are both enlarged, then the overlapped area difference between the LP₀₁ mode and LP₁₁ mode becomes larger. So, the peak values difference of Brillouin light between the two modes also rises.

3. Experimental Results and Discussions

To analyze the influence of the pump light on FMF-BOTDR, an experimental sensing system is built, which is shown in Figure 5. According to the theoretical analysis in Section 2, various pump pulse and pulse power spectra are constituted by different linewidth lasers and different pulse widths. Together with the two different guiding modes in the sensing FMF fiber, Brillouin scattering of modes LP₀₁ and LP₁₁ and their sensing characteristics are studied in detail.

Two individual narrow linewidth optical sources with different linewidths are set as the main lasers in the FMF-BOTDR sensing system for generating different laser linewidths, including a fiber laser with a 4 KHz linewidth [18] and a DFB laser with a 3 MHz linewidth (FITEL, FURUKAWA Solutions, Norcross, State of Georgia, USA). The two lasers are adjusted to have the same power of 28 mw. The continuous lights of the main lasers are modulated to pulses 500 ns via AOM (Model MT160-IIR10-FIO, AA Opto-Electronic, Orsay, France). These modulated pump pulses are launched into the sensing FMF (two-mode fiber with step index, OFS-FITEL, Norcross, State of Georgia, USA) to generate the spontaneous Brillouin scattering of every mode. The pulses are amplified properly (avoiding stimulated Brillouin/Raman scattering in the sensing fiber) by EDFA (Model AMP-FL8015-CB-30, FiberLabs Inc., Saitama, Japan), and then are injected into the 5 km fiber through a three-port circulator. A mode converter [19] (built by Hoya Tech, Shenzhen, China) is inserted at the front end of the sensing FMF in order to convert mode LP₀₁ to mode LP₁₁, whose mode coupling efficiency is 85% and insert loss is 3.3 dB for mode LP₁₁ and 12.1 dB for mode LP₀₁. To compare the mode influence on Brillouin scattering equally, a tunable attenuator (Hanyu Fiber Optic Communication Technology Company, Shanghai, China) is also inserted at the same position to attenuate 3.3 dB for the LP₀₁ mode. Spontaneous Brillouin scattering transmits to port 3 via port 2 of the circulator. A compact Brillouin fiber laser [20] is designed to serve as the local oscillator, who has a fixed and unchanging frequency shift to the main laser. The spontaneous Brillouin light from FMF and the local Brillouin laser interfere with each other through a 1:1 fiber coupler. The beat frequency between them is decreased to several hundred MHz, from ~11 GHz, and the beat signals can be detected using a double-balanced photo diode (DB-PD, New Focus 1617-AC, Newport Economic Development Commission, Newport, State of Arkansas, USA) with a 10 KHz~700 MHz bandwidth. Then, all of the Brillouin scattering information along the sensing fiber is collected and processed by a computer acquisition system with a high-speed data acquisition card (DAQ, Model CS82G, sample rate 3GS/s, National Instrument, Austin, State of Texas, USA). A home-built program based on LabVIEW is used to make FFT of all the sampled data in every single spatial resolution, and then Lorentz fittings are carried out to extract the amplitudes, linewidths, and central beat frequencies of these discrete interference signals. So, the amplitude, linewidth, and frequency distribution of Brillouin interference along the sensing FMF fiber can be obtained quickly without any extra optical component. The digital coherent detection scheme in this structure depends on the DAQ and algorithm; the 3D Brillouin gain spectra (BGS) are not necessary to construct because the parameter of BGS have been extracted in the data processing, which is different from the traditional frequency scanning scheme.

The pump pulse width is 500 ns in the experiment, corresponding to the 50 m spatial resolution, which is much wider than the pulse width in the literature. Because the inserting loss of the mode converter is 3.3 dB, causing the pump pulse energy and the optical intensity of spontaneous Brillouin scattering to be attenuated more than in the SMF-BOTDR, more optical energy injected into the mode converter and the sensing FMF is needed. It is worth noting that the pulse width is not changed in this experiment because the performance comparison between the different spatial resolution in BOTDR is meaningless, though the comparison between the two modes at a fixed pulse width is made in the numerical simulation.

The amplitude distribution along the whole 5 km sensing distance is shown in Figure 6. In comparison, the amplitude distribution curve for the LP₀₁ mode is always larger than the amplitude for the LP₁₁ mode, with the same laser linewidth, whether the main laser is the DFB laser or the fiber laser, as shown in the upper two graphs for the fiber laser or the two lower graphs for the DFB laser in Figure 6a,b. Larger optical intensity indicates higher SNR in BOTDR. According to the relation between SNR and sensing frequency resolution, $\delta \nu$: $\frac{\delta \nu }{\Delta \nu }\propto \frac{1}{\sqrt{2}(\mathrm{SNR}{)}^{1/4}}$, along with the relations between temperature/strain resolution ($\delta T$/$\delta \epsilon$) and frequency resolution $\delta \nu$: $\frac{\delta T}{T}=\frac{\delta \nu }{C_T}$, $\frac{\delta \epsilon }{\epsilon }=\frac{\delta \nu }{C_{\epsilon }}$ [21], we can conclude that the sensing resolution would be improved for the LP₀₁ mode in the subsequent temperature/strain sensing for the FMF-BOTDR system. Meanwhile, for the same guiding mode LP₀₁ or LP₁₁ in TMF, the narrower linewidth fiber laser, serving as the main laser, is beneficial for SNR enhancement, as shown in the two graphs in Figure 6a or Figure 6b, respectively.

The frequency distribution along the FMF sensing fiber is demonstrated in Figure 7. For the 500 ns pump pulse, when the main laser is the DFB laser, as shown in the upper graphs of Figure 7a,b, the linewidth of Brillouin scattering for the LP₁₁ mode is distributed approximately 40 MHz and the linewidth for the LP₀₁ mode is approximately 46 MHz, resulting in a ~6 MHz linewidth difference. Similarly, when the main laser is the fiber laser, the linewidth distribution for LP₁₁ mode is approximately 43 MHz and the linewidth for the LP₀₁ mode is approximately 37 MHz, resulting in the same ~6 MHz linewidth difference, as shown in the lower two graphs of Figure 7a,b. With the different main laser in the sensing system, the fiber laser linewidth is much narrower than DFB. As to the same guiding mode, the corresponding Brillouin scattering linewidths of the fiber laser and DFB laser are 43 MHz and 46 MHz for the LP₀₁ mode and 37 MHz and 40 MHz for the LP₁₁ mode, as shown in the left and right in Figure 7a,b. Together with the amplitude results in Figure 6a,b, the Lorentzian fitting curves can be generated. The above amplitude and beat frequency linewidth distributions are in accordance with the numerical simulation in Section 2. Though the amplitude is weaker for the LP₁₁ mode than the amplitude for the LP₀₁ mode for the same linewidth, the Brillouin linewidth is narrower for the LP₁₁ mode. So, the fitting accuracy of the beat frequency signals and extraction of the central frequencies for all the generated Lorentz curves would be the comprehensive effects of the two factors.

Finally, the central frequencies extraction of fitting Loretz curves for different laser linewidths and different sensing modes along the 5 Km sensing FMF are shown in Figure 8. Frequency fluctuations of BOTDR itself are the frequency resolution in BOTDR. In Figure 8a, the sensing modes are both the LP₀₁ mode, but the main lasers are the 1 MHz linewidth DFB laser and 4 KHz linewidth fiber laser, respectively. The frequency fluctuates from 418 MHz to 422 MHz for DFB and fluctuates from 418 MHz to 420 MHz for the fiber laser. Clearly, a 2 MHz frequency resolution improvement for the LP₀₁ mode is obtained for the narrower linewidth main laser. Meanwhile, for the LP₁₁ mode, the frequency fluctuates from 408 MHz to 411 MHz for DFB and from 409 MHz to 411 MHz for the fiber laser; a 1 MHz frequency resolution improvement is obtained. In addition, for the same main laser in BOTDR, the frequency fluctuations of 418 MHz~420 MHz for the LP₀₁ mode and 408 MHz~411 MHz for the LP₁₁ mode in the upper graph in Figure 8a,b show that the fitting accuracy for the LP₁₁ mode is better than the LP₀₁ mode. This results from the narrower linewidth in Figure 7, despite the larger amplitude in Figure 6, which indicates that the linewidth plays a more important role than the weak amplitude difference. A similar situation is also demonstrated for the LP₁₁ mode in the lower two graphs in Figure 8a,b. According to the linear relations between frequency resolution and temperature/strain resolution, the temperature resolution and/or strain resolution would be best for the LP₁₁ mode and the fiber laser.

4. Conclusions

The pump pulse launched into the sensing fiber in FMF-BOTDR is modulated from the continuous laser with some linewidths and pulses with different widths that are generated. Pump pulse power spectra is, in essence, an important item in the Brillouin scattering formula. The overlapping of OFD and its acoustic field distribution is slightly different for the two modes LP₀₁ and LP₁₁, which is the other item in the Brillouin scattering formula. Taking laser linewidth, pump pulse width, and the OFD of the LP₀₁ mode and LP₁₁ mode into consideration, their influence on the Brillouin scattering is numerically simulated and the FMF-BOTDR sensing experiment is created in detail. According to the simulation, the linewidths and peak values of the LP₀₁ mode and LP₁₁ mode have the same tendency, but the difference is 0.2 MHz and 0.07 dB, respectively. When the laser linewidth is wider than 1 MHz, the linewidth difference of Brillouin scattering decreases until it is the same. With the pulse width increasing, the linewidths of Brillouin light for the LP₀₁ mode and LP₁₁ mode decrease almost to the natural linewidth, but the linewidth difference between them increases; the peak values of modes LP₀₁ and LP₁₁ increase but the peak values difference between them becomes larger. The sensing results show that the amplitude distribution for the LP₀₁ mode is always larger than for the LP₁₁ mode if the main laser has the same linewidth; the linewidth of pump pulse plays a more important role in frequency resolution than the weak amplitude difference while making Lorentz fitting, and the frequency oscillation is 2 MHz, at least for the fiber laser and LP₁₁ mode. As a further step, a low-inserting-loss mode transverse component between modes LP₀₁ and LP₁₁ will be researched to decrease the pulse width and improve the spatial resolution; the structural optimization of the FMF-BOTDR sensing system will be experimented with to make multi-parameter sensing and discrimination occur simultaneously, such as with the temperature and strain, for use in pipelines or electrical lines monitoring, etc.