Optical measurement by a dual-frequency comb based on Rayleigh scattered Stokes light

Accepted Manuscript Optical measurement by a dual-frequency comb based on Rayleigh scattered Stokes light Pei Li, Fangyuan Chen, Chao Peng, Zhengbin Li

PII: DOI: Reference:

S0030-4018(19)30096-3 https://doi.org/10.1016/j.optcom.2019.02.004 OPTICS 23849

To appear in:

Optics Communications

Received date : 14 December 2018 Revised date : 28 January 2019 Accepted date : 1 February 2019 Please cite this article as: P. Li, F. Chen, C. Peng et al., Optical measurement by a dual-frequency comb based on Rayleigh scattered Stokes light, Optics Communications (2019), https://doi.org/10.1016/j.optcom.2019.02.004 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

*Manuscript Click here to view linked References

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

Optical measurement by a dual-frequency comb based on Rayleigh scattered Stokes light Pei Li, Fangyuan Chen, Chao Peng∗, Zhengbin Li State Key Laboratory of Advanced Optical Communication Systems and Networks, School of Electronics Engineering and Computer Science, Peking University, Beijing 100871, China

Abstract The backward stimulated Brillouin scattering in the optical fiber leads to a forward peaked Rayleigh scattering light with the same frequency shift. A dual-frequency comb is proposed and experimentally demonstrated, in which the frequency difference is equal to the Brillouin frequency shift. Further, a temperature measurement scheme is design based on the novel dual-frequency comb, where the radio-frequency (RF) signal is directly detected; neither high frequency photo detector or extra Mach-Zehnder interferometer (MZI) structure is required. The beaten RF signal is of narrower linewidth because the related phases are reduced, which enhances the measurement with a higher resolution. The measurement structured is demonstrated, in which the sensitivity of temperature measurement is 1.08 MHz/◦ C, same as the MZI structure, while the resolution is improved to 4.5 times compared to the traditional structure in the experiment. Keywords: dual-frequency, Rayleigh scattering, Brillouin scattering, temperature measurement 1. Introduction Rayleigh and Brillouin scattering phenomena occur when light passes through an optical fiber. The nonuniform distribution of refractive indices in a fiber can often be treated as reflectors with a length order smaller than the wavelength of the light, which cause Rayleigh reflection. The Rayleigh reflections interfere with each other and generate Rayleigh scattering. Rayleigh scattering distributes randomly along the fiber, and has a narrower linewidth [1]. Moreover, the intensity of Rayleigh scattering is inversely proportional to the fourth power of the wavelength of the incident light [2]. The principle of generating backward stimulated Brillouin scattering (SBS) light has been discussed in many studies [3, 4, 5]. The incident light causes the partial refractive index to change with time by electrostriction. The time-varying refractive index leads to a forward propagating acoustic wave along the fiber. The key point of the SBS is the interaction between the incident light and the acoustic wave, so the linewidth of SBS light is larger than 20 MHz, which is determined by the lifetime of the phonon in the optical fiber. The SBS light in a single mode and polarization maintaining optical fiber is mainly composed of backward Stokes light [5] with a downward frequency shift of approximately 10 GHz, which is determined by the direction and speed of the acoustic wave, and consists of the main nonlinear part. The corresponding Brillouin gain when the input exceeds the threshold is determined by the type and length of the optical fiber and can be used to form a Brillouin laser [6]. Rayleigh and Brillouin scattering phenomena in optical fibers can be widely used to form narrow-linewidth light sources [7, ∗ Corresponding

author Email address: [email protected] (Chao Peng)

Preprint submitted to Optics Communications

6], or to measure temperature and strain changes in the optical fiber [8, 9]. The SBS light has a frequency shift of approximately 10 GHz, so if we want to directly demodulate the signal from the Brillouin frequency shift, a high-speed photo detector (PD) should be utilized to detect the modulated signals. To reduce the requirements of the PD, a Mach-Zehnder interferometer (MZI) structure or a Michelson interferometer structure could be used to measure the radio-frequency (RF) signals. In such structures, the reference arm provides a bias with a fixed Brillouin frequency shift under a certain temperature and strain, and the signal in the measurement arm varies with the environment [10, 11]. Using the Brillouin Optical Time Domain Analysis (BOTDA) [12] or Brillouin Optical Time Domain Reflector (BOTDR) [13], distributed temperature or strain changes can be obtained with a certain spatial resolution, but the heterodyne method is also necessary to measure the Brillouin frequency shift. Thus the beat frequency between the reference and measurement signals is in general RF with a linewidth greater than 20 MHz. To improve the resolution, each arm can be designed as special structure to narrow the linewidth, e.g., a ring resonator [14]. In previous study [15], by using two light sources, the frequency interval was large enough so that the measurement system had different responses at different frequencies. Therefore, temperature and strain changes could be demodulated simultaneously. It should be noted that in the two arms, the phase of the two signals caused by the different optical paths and the independent Brillouin scattering process cannot be eliminated using the heterodyne method, which limits the resolution improvement. In this work, a dual-frequency comb is proposed based on Rayleigh scattered Stokes light. The frequency interval is relatively small, so the response difference is small enough, and by using the dual-frequency comb, the structure can be simplified January 28, 2019

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

relative to a MZI structure. The acoustic wave in the measurement arm brings related phase noise to different signals, thus the phase of the differential RF output can be simultaneously reduced. With this new design, the RF output reduces the requirements of the PD, and the simple structure has the same measurement sensitivity of 1.08 MHz/◦ C as the MZI structure, along with a resolution improved by 4.5 times.

of f1B − f0B , which contains the temperature information. The signal is RF in general, so a low-speed PD can detect it. In our scheme, we place the traditional reference arm just behind the source to get a dual-frequency comb with the frequency interval as a reference. As shown in Figure 1, the dualfrequency comb and measurement arm are similar to a singlefrequency source and Michelson interferometer measurement structure. However, the one-arm scheme has a narrower internal linewidth than the Michelson interferometer scheme. In the following analysis, the signal with frequencies of f0 and f0 − fB1 can be divided into two signals, one with the frequency f0 and another with the frequency f0 − fB1 . Thus, the signal with the frequency f0 goes through the Rayleigh and Brillouin scattering process and the output E0RB can be expressed as Eq. (2).

2. Principle and Analysis 2.1. scheme Rayleigh scttered stokes light SBS

Source

E0RB = AR (E0 ) exp[i2π f0 t + iΦ0R (t)] + AB (E0 ) exp[i2π( f0 − f0B )t + iΦ0B (t)] f1 f 0 Circulator

f0 Source

E0 is the electric amplitude of the signal with frequency f0 before the measurement arm, AR is the amplitude of Rayleigh scattering light, AB is the amplitude of Brillouin scattering light, Φ0R (t) is the phase of the Rayleigh scattering light through the measuring arm, and Φ0B (t) is the phase caused by Brillouin scattering. Similarly, the signal with frequency f0 − f0B goes through the Rayleigh and Brillouin scattering process, and the output E1RB can be expressed as Eq. (3).

f4 PD

Reference Arm

f2 f0

Measurement Arm

f4

f1 f 0

E1RB = AR (E1 ) exp[i2π( f0 − f0B )t + iΦ1R (t)]

f3 f1

+ AB (E1 ) exp[i2π( f0 − f0B − f1B )t + iΦ1B (t)]

Figure 1: The designed scheme and corresponding expected frequency shift.

Aao ef f

K (1 − exp(−αL))/α gB0

(3)

E1 is the electric amplitude of the signal with frequency f0 − f0B before the measuring arm, Φ1R (t) and Φ1B (t) are the corresponding phases and the frequency f1B is the Brillouin frequency shift in the measuring arm which changes with outside experiment. The Brillouin scattering light of the signal with frequency f0 and the Rayleigh scattering light of the signal with frequency f0 − f0B cause a RF signal with frequency f1B − f0B , and the phase of this signal can be expressed as Eq. (4).

Figure 1 shows the optical program and the expected frequency shift diagram. The single-frequency source with the isolator and the reference fiber act as a dual-frequency comb that contains the original frequency f0 and the Brillouin scattering frequency f1 . The frequency interval is the Brillouin frequency shift f0B , and the relationship between the SBS threshold and fiber length is shown in Eq. (1) [5]. Pth = κ

(2)

Φ(t) = Φ1R (t) − Φ0B (t)

(1)

(4)

The phase Φ1R (t) and Φ0B (t) are coorelated to a degree because the corresponding scattering originated from the same optical fiber, which can be shown from previous research [7].

−11

κ ∼ 21, the gain factor gB0 = 2 × 10 m/W, and K = 1 or 2 which characterizes the polarization state of the light. In general, the light intensity at the new frequency depends on the reference fiber length. The dual-frequency comb goes through a circulator to the measuring arm. The Brillouin scattering here can reflect the temperature or strain. As shown in Figure 1, the signal with frequency f0 and f1 goes through two processes in the measuring arm, and generate Rayleigh scattering light and Brillouin scattering light respectively. Thus the output is composed of four frequencies; f0 and f1 are generated by the Rayleigh process, and f2 and f3 are generated by the Brillouin process with a shift of f1B . After the PD, the signal with four frequencies generates a RF signal in the electric domain with a frequency

 ∂t Φ p (z, t) + ∂z Φ p (z, t) = −g(Aa E B /E p )θ        (1/βA )∂t Aa (z, t) = −(E p E B /Aa )θ    1 = E p E B /Aa cos(θ)      θ = Φ B + Φa − Φ p

(5)

Aa and Φa are the amplitude and phase of the acoustic wave, respectively, E B and ΦB are the electric amplitude and phase of the Brillouin scattering light, respectively, E p and Φ p are the electric amplitude and phase of the pump light, respectively, βA represents the damping rate of the acoustic wave, and g is the coupling constant. In previous studies, g(Aa E B /E p )θ is considered perturbative, which means the relative fluctuation 2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

of the amplitude of the acoustic wave is weak. Therefore, the equations can be simplified because the phase of pump light has no relationship with that of the acoustic wave.The situation is different, however, for the dual-frequency comb. In our scheme, E0 is much larger than E1 , so the acoustic wave is mainly caused by the light with frequency f0 . Additionally, Brillouin scattering light is generated by the light with a frequency of f0 − f0B , and the acoustic wave with Aa (z, t), which means g(Aa E B /E p )θ must be considered for this light. Thus, the phase of light with frequency f0 − f0B has a relationship with the acoustic wave. By calculating the equation assuming E0 is much larger than E1 , this correlation can be determined. For simplicity, we can use Eq. (6) to approximately express the correlation. Φ1R (t) = Φ1 (t) + γΦ0B (t) (6)

fiber is strong enough for a given optical fiber length, the mathematical model should consider high order Brillouin scattering.  ∂P (x) I    = −αPI (x) − gB PI (x)PB (x)    ∂x      ∂PB (x) − = −αPB (x) + gB PI (x)PB (x) + rPRB    ∂x      ∂P (x)    RB = −αPRB (x) + rPB ∂x

PI (x), PB (x) and PRB denote the power of the incident light, the SBS light in the optical fiber and Rayleigh scattered Stokes light, respectively, α is the loss factor of the optical fiber, gB is the Brillouin gain, and r is the Rayleigh scattering factor. The signs on the left side of Eqs. (10) indicate the propagation direction of the corresponding light. In the prrevious research, a single-frequency source could be achieved using the direction of the Brillouin scattering as output. In this paper, we first choose the direction of the incident light as the output. Shown in Eq. (10), light in this direction consists of two different frequencies with an interval equivalent to the Brillouin frequency shift. The term rPRB is relatively complex, and the Rayleigh scattered Stokes light also generates backward Rayleigh scattering along the fiber, and acts as a seed light amplified by the Brillouin scattering. Counting from the SBS, the three lights form a loop. So rPRB indicates the feedback, which eventually contributes to PRB . Through this process, the forward light has two frequencies and the electric field can be expressed as Eq. (11).

Φ1 (t) here should its same distribution and has no relationship with Φ0B (t). In general, 0< γ <1. As shown in previous study [16], the relationship between the linewidth and the phase with a Gaussian distribution satisfies Eq. (7). T p0 is the period of the signal, σ2Φ (T p0 ) is the variance of the phase in one period, and ∆ f is the linewidth of the signal. (7) ∆ f = σ2Φ (T p0 )/2πT p0 Therefore, in a one-arm structure, the linewidth of the RF output and the variance of the phase can be expressed as Eq. (8). ∆ f0 = σ2Φ1R (T p0 )/2πT p0 + (1 − γ)2 σ2Φ0B (T p0 )/2πT p0

(8)

In the two-arm structure, light in the different arms goes through independent processes. In general, the linewidth can be expressed as Eq. (9) [17]. ∆ ft = σ2Φ1B (T p0 )/2πT p0 + σ2Φ0B (T p0 )/2πT p0

(10)

E(t) = E0 exp[2πi f0 t + iΦ0 (t)] + E1 exp[2πi( f0 − fB1 )t + iΦ1 (t)]

(9)

(11)

where E0 and E1 are amplitudes, Φ0 (t) and Φ1 (t) are the phases, f0 is the frequency of the light source, and fB1 is the Brillouin frequency shift.

As Eqs. (8) and (9) show, Φ1R (T p0 ) is determined by the Rayleigh process of the optical fibers of the reference and measurement arms, and the linewidth is narrower than the incident light. Generally, ithe linewidth is narrower than the Brillouin scattering. Additionally, (1 − γ)2 <1, therefore, in principle, the linewidth of the output in a one-arm structure is narrower than that in a two-arm structure. Continuing the analysis, if there is reflection at the end of the measurement arm, the correlation between the phases would be stronger and the output linewidth would be narrower.

2.3. measurement Backward Brillouin scattering can be used to measure the temperature or strain on the fiber [8], because the frequency shift of SBS light obeys the following equation Eq. (12). fB (ε, T ) = fB (ε0 , T 0 ) +

∂ fB ∂ fB (ε − ε0 ) + (T − T 0 ) ∂ε ∂T

(12)

fB (ε, T ) is the Brillouin scattering frequency at a strain ε and temperature T , and ε0 and T 0 are specific strain and temperature, respectively, as references. By monitoring the frequency shift, changes in the temperature or strain can be observed. From Eq. (12), when the measurement arm is fixed, only the temperature is variable. Different measurement systems have different response functions to frequency, and signals with different frequencies cause different outputs through a certain measurement system. Consider two systems with response functions h1 and h2 . The functions h1 and h2 correspond to a single-frequency output and a dual-frequency output, respectively, with a single-frequency input. Assuming that fin0 and fin1 are the two frequencies, the

2.2. dual-frequency comb Compared to a MZI structure, if the reference arm is placed just after the source as shown in Figure 1, a dual-frequency comb with a frequency interval equal to the Brillouin frequency shift will be achieved. Light from the single-frequency source generates backward SBS light, and then the Brillouin Stocks light generates a forward Rayleigh scattered Stokes light. This process is described in Eq. (10) [18], without considering higher order Brillouin scattering. In fact, if the power of incident light

3

response of the system with response function h1 with a singlefrequency input and a dual-frequency input can be expressed as:    Y( fout ) = h1 (X( fin0 )) (13)   Y( f , f ) = h (X( f , f )) out0 out1 1 in0 in1

SBS threshold is the major consideration in choosing the length of the single mode fiber. The max output of the laser is 80 mW, and this should exceed the SBS threshold in the single mode 2 optical fiber. With the effective area Aao e f f = 100 µm [5], the shortest length is 0.63 km from Eq. (1). In this experiment we use a 12 km optical fiber to make the Brillouin gain large enough to compensate for the effective losses in one loop.

For this system, the output includes two different frequencies fout0 and fout1 when the input is dual-frequency. When the frequency response is nonlinear, the system has different scale factors at frequencies fin0 and fin1 . By monitoring the frequency shifts fout0 − fin0 and fout1 − fin1 , simultaneous measurements of two physical quantities can be realized, such as temperature and strain. To accomplish simultaneous measurements, fin1 − fin0 should be large enough to guarantee the response is significantly different at the two frequencies. In previous study [15], simultaneous measurements of two physical quantities needed two light sources.    Y( fout0 , fout1 ) = h2 (X( fin0 )) (14)   Y( f , f , f , f ) = h (X( f , f )) out0 out1 out2 out3 2 in0 in1

Source

Circulator

EDFA

Isolator

EDFA

PD

Reference Arm (a)

(b)

(c) Measurement Arm FRM Attenuator

Figure 2: The experimental setup, (a) without facet reflection at the end of the measurement arm, (b) with facet reflection, (c) with reflection with a Faraday rotation mirror and attenuator.

In a system with response function h2 , when the input frequency is fin0 , the output has two frequencies fout0 and fout1 , which shows that there are two processes with different responses in the system. Therefore, the output would have four frequencies with a dual-frequency input ( fin1 and fin0 ), among which fout0 and fout2 are from one process, and fout1 and fout3 are from the other process. So, an electric signal with a beat frequency of | fout2 − fout1 | can be created, and after being detected by the PD, the output can be RF. There is another signal with frequency | fout3 − fout0 | after the PD, and the frequency is different from | fout2 − fout1 |. When the frequency interval is large enough, we can achieve a simultaneous measurement of two physical quantities. By using only one light source, a dual-frequency comb with a small frequency interval of fin1 − fin0 can be designed. At this time, the frequency response is almost the same, thus the output is RF.

3.1. dual-frequency comb realization To completely elucidate the information in the dual-frequency comb, a method of delayed self-heterodyne interferometry should be used. The linewidth of the laser is 5 kHz, so the coherence length can be determined by calculating Eq. (15). It is approximately 41.2 km in the single mode optical fiber with an effective index of 1.457. In the equation, c is the light speed in vacuum. l = λ2 /∆λ = c/∆ f

(15)

-20

3. Experiments and Results TeraXion’s PS-NLL Narrow Linewidth Semiconductor Laser is used as an original source, and PXA Signal Analyzer N9030A with range from 3 Hz to 50 GHz is used to analyze the lineswidths in the experiment. This source has a narrow linewidth (< 5 kHz), so we can get an intuitive understanding of the dualfrequency comb. As Figure 2 shows, EDFA is used to amplify the signal in this experiment, because most of the Brillouin scattering light is absorbed by the isolator. Additionally, a 2 km polarization-maintaining fiber is used as the measurement arm, so the SBS threshold is low. More importantly, the difference in acoustic speed between the single mode fiber and the polarization-maintaining fiber can produce a bias that avoids low-frequency noise when the temperature of the two optical fibers is the same and there is no strain, so it is not necessary in fact. At the end of the arm shown in Figure 2(a), we circulate the fiber to avoid the reflected light from the end facet, and results of structure with reflection shown in Figure 2(b) and Figure 2(c) are also discussed as comparative experiments. The 4

Spectrum density (dBm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

-30

-40

-50

-60 -80

-40

0

40

Frequency (MHz)

80

10.55

10.57

10.59

Frequency (GHz)

Figure 3: Spectrum density from the dual-frequency comb.

The delay length of the optical fiber should be six times the coherence length (approximately 247.1 km) to effectively avoid coherence. In this experiment, the output of the reference arm has two frequencies, and there is a simple method to recognize the dual-frequency comb. As Eq. (11) shows, the electric amplitude through the fiber can be expressed in two terms with different frequencies. The Rayleigh and Brillouin scattering are distributed, so there exists an equivalent delay τ between the

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

two signals with frequencies f0 and f0 − fB1 . Therefore, Eq. (11) should be rewritten as Eq. (16).

the linewidth of Brillouin scattering light which is wider than 20 MHz in the optical fiber. The one-arm structure compresses the output linewidth to 22.5% of the MZI structure without narE(t) = E0 exp[2πi f0 t + iΦ0 (t)] rowing the linewidth. When dividing the 9MHz linewidth by (16) the sum of the 20 MHz SBS linewidth and the 2.1MHz input + E1 exp[2πi( f0 − fB1 )(t − τ) + iΦ1 (t − τ)] signal linewidth from before the measurement arm, the calcuThis equation is mathematically the same form as the delated percentage of 40.7% reflects the phase noise without any layed self-heterodyne interferometer[19]. As introduced in Eq. (5) correlation between the signals with frequencies of f0 − f0B and , Φ1 (t) is the phase noise of the Rayleigh scattered Stokes light. f0 − f1B before the PD. Compared to Eq. (6), γ ≈ 0.41, which is Φ1 (t) and Φ0 (t) only have week correlation, considering the declose to 0.5, the result shown above. The difference between the lay τ, Φ1 (t + τ) and Φ0 (t) have almost no correlation. Since two results is mainly because distributed Rayleigh scattering we are concerned with the linewidth of the comb, we can use can narrow the linewidth further, and SBS linewidth is approxia high-speed PD to directly detect the light as the dotted box mately 20 MHz. Thus, measurements using the dual-frequency shows in Figure 2. comb can intrinsically improve the resolution (narrow the outThe signal from the spectrometer is shown as Figure 3. The put linewidth) and keep the sensitivity equal to the traditional light intensity at frequency 0 Hz is E02 + E12 , and the spectromstructure. eter shows −23.6 dBm. The light intensity at frequency f1B is As shown in Figure 4 (b), the frequency difference decreases 2E0 E1 , and the spectrometer shows −28.9 dBm. The linewidth as increasing temperature until it reaches zero at 36 ◦ C, gives corresponding to the phase noise Φ1 (t + τ) − Φ0 (t) is 2.1 MHz. a static temperature bias that is governed by the acoustic wave As introduced above, σ2Φ = σ2Φ0 +σ2Φ1 , so the linewidth of signal speeds of the fibers. Such bias can be tuned by choosing difwith the frequency f0 − fB1 is approximately 2.1 MHz in the curferent types of fibers or applying strain on them. The extraporent structure and has been narrowed to 0.1 times the linewidth lation shows that the frequency difference further increases as of the Brillouin scattering light. By calculating Eq. (5) and increasing temperature, makes the setup capable of measuring Eq. (6) , we can calculate γ ≈ 0.5. the temperatures above the bias. However, due to the practical limit in detecting frequency, there exists a range of temperature 3.2. temperature measurement and linewidth narrowing in which the frequency difference is too small to measure; we As Eq. (12) shows, when the reference and measurement refer it as to “dead zone” (28.0 − 42.0◦ C given by lowest dearms are fixed, the frequency of the RF output can be expressed tectable frequency of 6 MHz in our setup). The measurement as Eq. (17). range is determined by the detector bandwidth, for instance, it is −55.8 − 129.1◦ C assuming 100 MHz bandwidth. Besides, ∂ f1B the measurement precision is estimated as 0.09◦ C from the un(17) (T − T 0 ) f = f1B (T ) − f0B (T 0 ) = fBias + ∂T certainty of Brillouin frequency shift of 0.1MHz [20, 21, 22]. The measurement arm is placed in the thermostat, and the temIn the current structure, the circle at the end of the measureperature is successively set to 0◦ C, -10◦ C, -20◦ C, -30◦ C, and ◦ ment arm can avoid the facet reflection, and it is more conve-40 C. The frequency of the RF output moves with the tempernient to verify that the one-arm structure can improve the resature, shown in Figure 4(a). The temperature can be demoduolution. By introducing the facet reflection, the linewidth of lated only by the central frequency of the output, so in the figure the output should be further narrowed and the output should be we have normalized the output intensities. stronger because of interference and Eq. (10). Reflection can The corresponding center frequencies are shown in Table 1. be introduced by releasing the circle, or by adding an attenuator and a Faraday mirror at the end of the measurement arm. Table 1: Central frequencies at different temperatures The attenuator is used to adjust the strength of reflection, and Temp /◦ C 0 -10 -20 -30 -40 the comparison results with different reflections are shown in Figure 5. Freq /MHz 39.3 50.9 61.7 71.5 83.1 The red line in the figure corresponds to the structure of releasing the circle. In this situation, facet reflection is relatively From the corresponding data, we can fit the relationship weak, with a strength approximately −37 dBm and a linewidth between the central frequency and temperature as Eq. (18), as of 2 MHz, which is narrower than linewidth of output without shown in Figure 4(b). reflection. The blue line in the figure corresponds to a structure with an attenuator and a Faraday mirror at the end of the f = −1.082T + 39.66 (18) measurement arm. The strength is about −10.3 dBm and the The correlation coefficient is 0.9996, which shows a strong corlinewidth is 1.5 MHz. By improving the reflection, the strength relation. The coefficient of −1.082 means that the frequency of the output can obviously be enhanced and the resolution can shift is equal to 1.082 MHz when the temperature changes one be improved, as we mentioned in the Section 2. This can also degree Celsius. Thus, we can directly measure the RF signal, be used in the following distributed measurement. and the average linewidth of the output signal is 9 MHz without any additional methods to compress it. This is narrower than 5

(b) -40°C -30°C -20°C -10°C 0°C

0

-10

-20

20

50

80

100 Experimental

Central frequency (MHz)

Normalized spetrum density (dB)

(a)

60 f = -1.082T + 39.66

40

20

0 -80

110

Fitted

80

Frequency (MHz)

Dead zone -40

0

40

80

Temperature (°C)

Figure 4: (a) Normalized spectrum density in different temperatures of 0◦ C, -10◦ C, -20◦ C, -30◦ C, and -40◦ C; (b) fitted line of central frequency and temperature.

Normalized spetrum density (dB)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

1.5MHz

0

-10

directly get RF output with distributed information.

With FRM and Atte. With refle. Without refle.

5. Conclusion In this work, we design a dual-frequency comb with a frequency interval equal to the Brillouin shift based on the Rayleigh scattered stokes light in the optical fiber. The theoretical description of the dual-frequency comb is given, and it is produced with a very simple structure and a linewidth 2.1 MHz at the new frequency. Measurement principles based on the dual-frequency comb are introduced, and the reason why such a measurement scheme can improve the resolution without additional designs to narrow the linewidth is given. We verify this in the experimentally. When measuring temperatures based on the Brillouin frequency shift, the comb can be used to simplify the measurement structure, reduce the requirements of the PD and improve the resolution simultaneously. In our experiment, the sensitivity is 1.08 MHz/◦ C, which is the same as that of a two-arm structure, and because of the phase correlation, the linewidth is compressed to 22.5% of that of the two-arm structure. When a reflection is introduced at the end of the measurement arm, the output can be stronger and has a higher resolution.

2MHz

9MHz

-20

-22.5

-7.5 7.5 Frequency (MHz)

22.5

Figure 5: The 3 dB linewidth of different structures.

4. Discussion The Rayleigh scattered Stokes light and the incident light constitute the dual-frequency comb. Here we verify this through a simple structure. Also, by using two circulators, the backward SBS light can be fully used by injecting it to the fiber again [23]. By adjusting the fiber length or type, the intensity and linewidth of the dual-frequency comb can be further controlled. In this scheme, there is no special design to narrow the linewidth in the measurement arm, and we improve the resolution to 4.5 times. Special design can also be used to improve the resolution furthermore. In addition, we have pointed out that there are two different processes in the measurement arm, which provide the possibility to get more information about outside environment by using the characteristic of Rayleigh scattering at the same time. In this experiment, a method to directly produce RF output using a dual-frequency comb is shown. Using this principle, the structure of BOTDA or BOTDR can also be retrofitted to

Acknowledgment This work was funded by the National Natural Science Foundation of China (NSFC) under Grants 91736207 and 61575002; the State Administration for Science, Technology and Industry for National Defense under Grant D020403. The authors wish to thank Rongya Luo and Yulin Li for their valuable comments. References [1] A. F. Sadreev, Enhancement of Rayleigh scattering in a two-dimensional Fabry–Perot resonator loaded with impurities, J. Opt. Soc. Am. A 33 (7) (2016) 1277–1282.

6

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

[2] R. B. Miles, W. R. Lempert, J. N. Forkey, Laser Rayleigh scattering, Meas. Sci. Technol. 12 (5) (2001) R33. [3] N. Goldblatt, Stimulated Brillouin Scattering, Appl. Opt. 8 (8) (1969) 1559–1566. [4] E. Ippen, R. Stolen, Stimulated Brillouin scattering in optical fibers, Appl. Phys. Lett. 21 (11) (1972) 539–541. [5] A. Kobyakov, M. Sauer, D. Chowdhury, Stimulated Brillouin scattering in optical fibers, Adv. Opt. Photon. 2 (1) (2010) 1–59. [6] S. Huang, T. Zhu, G. Yin, T. Lan, L. Huang, F. Li, Y. Bai, D. Qu, X. Huang, F. Qiu, Tens of hertz narrow-linewidth laser based on stimulated Brillouin and Rayleigh scattering, Opt. Lett. 42 (24) (2017) 5286– 5289. [7] A. Debut, S. Randoux, J. Zemmouri, Experimental and theoretical study of linewidth narrowing in Brillouin fiber ring lasers, J. Opt. Soc. Am. B 18 (4) (2001) 556–567. [8] T. R. Parker, M. Farhadiroushan, R. Feced, V. A. Handerek, A. J. Rogers, Simultaneous distributed measurement of strain and temperature from noise-initiated Brillouin scattering in optical fibers, IEEE J. Quantum Electron. 34 (4) (1998) 645–659. [9] L. Zou, X. Bao, S. A. V, L. Chen, Dependence of the Brillouin frequency shift on strain and temperature in a photonic crystal fiber, Opt. Lett. 29 (13) (2004) 1485–1487. [10] D. Culverhouse, F. Farahi, C. N. Pannell, D. A. Jackson, Stimulated Brillouin scattering: A means to realise tunable microwave generator or distributed temperature sensor, Electron. Lett. 25 (14) (1989) 915–916. [11] B. Culshaw, A. Kersey, Fiber-Optic Sensing: A Historical Perspective, J. Lightw. Technol. 26 (9) (2008) 1064–1078. [12] T. Horiguchi, M. Tateda, BOTDA-nondestructive measurement of singlemode optical fiber attenuation characteristics using Brillouin interaction: Theory, J. Light. Technol. 7 (8) (1989) 1170–1176. [13] H. Ohno, H. Naruse, M. Kihara, A. Shimada, Industrial Applications of the BOTDR Optical Fiber Strain Sensor, Opt. Fiber Technol. 7 (1) (2001) 45–64. [14] C. E. Preda, A. A. Fotiadi, P. M´egret, Numerical approximation for Brillouin fiber ring resonator, Opt. Express 20 (5) (2012) 5783–5788. [15] M. G. Xu, J. L. Archambault, L. Reekie, J. P. Dakin, Discrimination between strain and temperature effects using dual-wavelength fibre grating sensors, Electron. Lett. 30 (13) (1994) 1085–1087. [16] R. Tkach, A. Chraplyvy, Phase noise and linewidth in an InGaAsP DFB laser, J. Lightw. Technol. 4 (11) (1986) 1711–1716. [17] A. Yeniay, J.-M. Delavaux, J. Toulouse, Spontaneous and Stimulated Brillouin Scattering Gain Spectra in Optical Fibers, J. Lightw. Technol. 20 (8) (2002) 1425. [18] M. Pang, S. Xie, X. Bao, D.-P. Zhou, Y. Lu, L. Chen, Rayleigh scatteringassisted narrow linewidth Brillouin lasing in cascaded fiber, Opt. Lett. 37 (15) (2012) 3129–3131. [19] L. Richter, H. Mandelberg, M. Kruger, P. McGrath, Linewidth determination from self-heterodyne measurements with subcoherence delay times, IEEE J. Quantum Electron. 22 (11) (1986) 2070–2074. [20] Z. Weiwen, H. Zuyuan, K. Masato, H. Kazuo, Stimulated brillouin scattering and its dependences on strain and temperature in a high-delta optical fiber with f-doped depressed inner cladding, Opt. Lett. 32 (6) (2007) 600–2. [21] W. Zou, Z. He, K. Hotate, Complete discrimination of strain and temperature using brillouin frequency shift and birefringence in a polarizationmaintaining fiber, Opt. Express 17 (3) (2009) 1248–1255. [22] J. Fang, G. Milione, J. Stone, G. Peng, M.-J. Li, E. Ip, Y. Li, Y.-K. Huang, P. N. Ji, M.-F. Huang, et al., Distributed temperature and strain sensing using brillouin optical time-domain reflectometry over a few-mode elliptical-core optical fiber, in: Optical Fiber Sensors, Optical Society of America, 2018, p. TuD1. [23] S. P. Smith, F. Zarinetchi, S. Ezekiel, Narrow-linewidth stimulated Brillouin fiber laser and applications, Opt. Lett. 16 (6) (1991) 393–395.

7