Optics Communications

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1 Optics Communications 283 (2010) Contents lists available at ScienceDirect Optics Communications journal homepage: Studies on multi-wavelength fiber Bragg grating laser strain sensor Zuowei Yin a,, Shengchun Liu a,b,c, Liang Zhang a, Liang Gao a, Xiangfei Chen a, a The National Laboratory of Microstructures, Nanjing University, Nanjing , China b Institute of Fiber Optics, Heilongjiang University, Harbin , China c The Laboratory of Modern Acoustics and Institute of Acoustics, Nanjing University, Nanjing , China article info abstract Article history: Received 17 March 2010 Received in revised form 3 July 2010 Accepted 3 July 2010 A novel stable multi-wavelength fiber Bragg grating laser is achieved and its sensing characteristic with the strain is studied. The beat signals generated by the multi-wavelength fiber laser are measured under different strains. Four-wave mixing (FWM) is firstly observed in such a short-cavity fiber laser Elsevier B.V. All rights reserved. Keywords: Beat frequency Four-wave mixing (FWM) Fiber laser strain sensor Nonlinear effect 1. Introduction In the recent years, fiber laser sensors using beat frequency demodulation have attracted significant interest and a lot of papers have been published to address such issues [1 5]. This type of fiber laser sensors has opened a new way for pursing simple, but powerful fiber-optic sensors. However, more investigations are still needed to study the fiber laser sensors better, such as the generation of the beat frequency signal, the response to the strain, and so on. In this paper, a multi-wavelength fiber laser with wavelength spacing of about 43 pm (equal to 5.3 GHz in the frequency field) has been obtained. The intensities of the five modes vary differently with the pump power. One of the modes shows its nonlinear response to the pump power. Four beat sensing signals generated by the multi-wavelength fiber laser under different strains are studied. It is experimentally shown that the responses of the beat frequencies to the strain have some abnormalities. Two beat frequencies are varied with the strain linearly when the strain is changed from 0 to 630 με, but the slope of the fitting line is different under different pump powers. The other two of the beat signals are nonlinearly varied with the strain. These strange phenomena indicate that there is nonlinear effect existing in the establishment of the laser, which can be thought to be four-wave mixing (FWM) in terms of detailed experiments. To the best of our knowledge, the FWM phenomenon is firstly observed in such a short fiber laser (the length is about 6.2 cm). The present investigations are Corresponding authors. addresses: yinzuowei@gmail.com (Z. Yin), chenxf@nju.edu.cn (X. Chen). believed to benefit for more knowledge of the fiber laser sensor with beat frequency demodulation. 2. Principle and experiments The experimental setup is shown in Fig. 1. The multi-wavelength fiber laser is formed using a fiber Bragg grating (FBG) structure. There are two 23 mm fiber Bragg gratings (FBGs) with spacing of 16 mm written in the Erbium doped fiber (Coractive EDF-HCO-4000). The round-trip wavelength spacing of the fiber laser is about 43 pm corresponding to 5.3 GHz in the frequency field. Pumped by the 980 nm light through the wavelength division multiplexer (WDM), the multi-wavelength fiber laser will be established. The output of the multi-wavelength fiber laser is split by a coupler. One light is injected into a photodetector (PD) to generate the beat signal, which can be observed by a radio frequency spectrum analyzer (RFSA). The other is observed by the optical spectrum analyzer (OSA). The isolator is used to prevent the reflective light and the Erbium doped fiber amplifier (EDFA) is used to amplify the light. Under a pump power of about 17 mw, we can observe a dualwavelength fiber laser in the OSA as shown in Fig. 2. While increasing the pump power from 17 mw to 43 mw, 75 mw, 95 mw, 120 mw and 150 mw, we can gradually get a multi-wavelength fiber laser as shown in Fig. 2. When the pump power is high enough, five stable modes can be established with frequencies of f m (m=1 to 5). Here mode f 4 is the weakest under a low pump power. However, when the pump power is increased to 75 mw, mode f 4 suddenly becomes strong. That is to say, mode f 4 has a high threshold and high slope efficiency when the pump power is higher than 75 mw /$ see front matter 2010 Elsevier B.V. All rights reserved. doi: /j.optcom

2 Z. Yin et al. / Optics Communications 283 (2010) Fig. 1. Experimental setup with beat frequency demodulation. Fig. 3 shows the relationship between the intensity of individual mode and the pump power. The intensity is measured directly from the OSA under different pump powers. It is obvious that the intensity of mode f 4 changes more quickly than the other four modes. It is the total contribution of the pump power and the FWM effect. In addition, the intensities of modes f 1 and f 5 vary little with the pump power. The five modes of the multi-wavelength fiber laser are coherent because they are established in the same resonant cavity and thus any two of them will generate a beat signal. The beat frequency ν of the two modes can be written as ν=f m f n, where f m and f n are the frequencies of two arbitrary modes of the fiber laser. When a strain ε is applied on the fiber laser, the wavelength of the fiber laser will shift as follows δλ m λ m = ð1 p e Þε ð1þ where p e =0.22 is the strain-optic coefficient, m denotes the mode of the fiber laser. Thus the beat frequency shift can be written as follows δν = ν δλ m λ m = νð1 p e Þε ð2þ It is obvious that the beat frequency varies linearly with the strain applied on the fiber laser sensor. Fig. 4 shows the beat frequency signals around 5.3 GHz measured by the RFSA. Under the pump power of 75 mw, four beating signals are obtained as shown in Fig. 4. Seen from the generating sequence of the five wavelengths and subsequently four beat frequencies, signal v a is the beating signal generated by modes f 1 and f 2, signal v b by modes f 4 and f 5, signal v c by modes f 2 and f 3, and signal v d by modes f 4 and f 3. As shown in Fig. 4, when the pump power increases, the four beat signals will shift due to the shift of the five wavelengths. Seen from the figure, signals v a, v c and v d shift to the left while signal v b shifts to the right. It is just the result of the nonlinear effect in the fiber laser which Fig. 3. Intensities of the five modes versus the pump power. The inset shows the nonlinear response of mode f 4 (the unit of the vertical axis is a.u.). proves the existence of FWM. It should be mentioned that when the pump power is tuned to 120 mw, signal v b will coincide with signal v c around 5287 MHz. Fig. 5 shows the responses of the four beat signals to the strain under different pump powers. Signal v a and signal v c have the linear responses to the strain while signals v b and v d have nonlinear responses. Under the low pump power, the sensing characteristics of signal v a and signal v c are linear and close to the theoretical prediction with the slopes of 4.08 khz/με and 4.13 khz/με respectively from Eq. (2). Signal v b shows its nonlinear positive-going response and signal v d shows its linear fitting slope of about khz/με under a pump power of 75 mw, which is much larger than the theoretical value. When the pump power is increased, the slope value of response of signal v a to the strain becomes small, while that of signal v c changes little and that of signal v b gradually becomes negative. The fitting slope value of signal v d becomes smaller when the pump power is increased. These abnormal phenomena should be related to the nonlinear effect in the laser cavity. That is to say, the multi-wavelength fiber laser can be affected by the FWM in the laser cavity, which leads to the abnormal responses of the beat sensing signals. The detailed reason can be indicated in the following. According to the theory of FWM process [6,7], three waves with frequencies f i,f j, and f k (j k) will generate a new frequency f F =f i + f j f k. Based on the theory of FWM, the phase matching for the FWM effect can be easily satisfied and FWM plays a role of amplitude equalizer, broadening and stabilizing the output spectrum [8,9]. The output power of FWM light is written as follows [7,10] P F = 1024π6 n 4 λ 2 c ðdχ P i P j P k Þ2 e αl ð1 e αl Þ 2 η ð3þ α 2 A 2 eff Fig. 2. Optical spectra under different pump powers. Fig. 4. Beat frequency spectra under different pump powers.

3 4998 Z. Yin et al. / Optics Communications 283 (2010) Fig. 5. Responses of the four beat frequency signals to the strain under different pump powers. where n is the refractive index of the fiber, λ is the wavelength, c is the light velocity in the vacuum, Dχ 1111 is the degeneracy factor, P i, P j and P k are the light powers of modes f i,f j and f k, A eff is the effective mode area of the fiber, α is the fiber loss coefficient, L is the fiber length which is corresponding to the whole laser cavity, and the FWM efficiency η is equal to 1 when the phase mismatching Δβ=0. Thus the power of the FWM mode is proportional to the powers of the three pump modes. In our laser sensor, the mixing of f 2 +f 3 f 4,f 2 +f 4 f 5,2f 2 f 3, and 2f 3 f 5 can lead to a FWM laser frequency f 1 which can be called FWM f 1 for convenience in this paper and these mixing can be written as f 234,f 245,f 223, and f 335 respectively. Moreover, we use FWM f 1 = (f 234,f 245,f 223,f 335 ) to indicate FWM f 1. Therefore, FWM f 2 =(f 143,f 154, f 345,f 334 ), FWM f 3 =(f 142,f 254,f 221,f 445 ), FWM f 4 =(f 152,f 231,f 253, f 332 ), and FWM f 5 =(f 241,f 342,f 331,f 443 ). Under the low pump power, mode f 4 is difficult to establish because of the low gain in the laser cavity and when the pump power is increased, the intensity of mode f 4 will change in a more nonlinear way and thus we think there is a strong nonlinear effect occurring in mode f 4. When the pump power is high enough, mode f 4 is established stably by the combination of conventional laser resonant cavity and the nonlinear effect of FWM. According to Eq. (3), the power of the FWM mode is proportional to the intensities of the three modes. As we referred above, FWM f 4 =(f 152,f 231,f 253,f 332 ) which is mainly constituted by modes f 2 and f 3. Due to the high intensity, modes f 2 and f 3 contribute a lot to FWM f 4. On the other hand, due to the low intensity, mode f 1 and mode f 5 will have a little contribution to the intensity of mode f 4 with the increasing pump power. The FWM f 4 of f 231,f 253, and f 332 may significantly enhance mode f 4 and then the power of mode f 4 increases nonlinearly and quickly. The light with this frequency just meets the phase matched condition and thus can be established under the high pump power with the help of the FWM effect. Therefore, mode f 4 has a high slope efficiency, as shown in Fig. 3. In such situation, the signals v b and v d related to f 4 will vary with

4 Z. Yin et al. / Optics Communications 283 (2010) the strain nonlinearly, as shown in Fig. 5. From Fig. 2, modes f 1 and f 5 are so weak that FWM f 3 mainly related to modes f 1 and f 5 is very weak. Therefore only f 334 has a relatively great contribution to FWM f 2. However, FWM f 2 is still weak compared with strong powers of modes f 2 and f 3. Thus the FWM effect is still weak to beat signal v c which is generated by modes f 2 and f 3 even if the pump power is high. In the other way, due to the great contribution of f 234 and f 223 to FWM f 1 and the low power of mode f 1,FWMf 1 will be a considerable part compared with mode f 1. In this situation, the response of signal v a to the strain will change with the pump power with large degree. From the above analysis, the experiment result shows the beat frequencies related to mode f 4 are different from the others. It is just the result of the combination of the FWM and the laser resonant cavity. Under a low pump power, because of the mode competition, there is not enough gain for mode f 4 to establish. While the pump power is increased, the other four modes subsequently increase their outputs and therefore the FWM can be stronger and stronger. Mode f 4 is generated when the pump power is increased higher to 75 mw. Because of the nonlinear effect, its characteristic is different from the others and thus the responses of the beat signals related to it are also different. However, when the pump power is high enough, mode f 4 is mainly established by the conventional resonant cavity and thus the beat frequency responses can be closer to the theoretical value. 3. Discussion and conclusion Another decisive proof to support the above illustrations can be discussed in the following. It is well known that there are three main nonlinear optical effects in the fiber, namely, self-phase modulation (SPM), cross-phase modulation (XPM) and FWM. When two laser modes are generated in the cavity, even under high pump power, the beat frequency between them is varied completely linearly with the strain. Thus we can conclude that the SPM and XPM will affect the beat frequency little. When more modes are generated in the fiber, some beat frequency signals will change nonlinearly. These phenomena mean that FWM is the only main element to contribute a lot to the nonlinearity. Therefore, we can conclude that a multi-wavelength FBG laser sensor is firstly studied and strong FWM is found in such a short laser cavity. The beat signals generated by the five-wavelength laser show different responses to the strains. It is the combination of the nonlinear FWM effect and the laser resonant cavity. It is believed that the present study will benefit for developing more complex fiber laser sensors. Acknowledgements This work is supported in part by the National Nature Science Foundation of China under Grant and in part by the National 863 project under Grant 2007AA01Z274. References [1] O. Hadeler, E. Rønnekleiv, M. Ibsen, R.I. Laming, Appl. Opt. 38 (1999) [2] O. Hadeler, M. Ibsen, M.N. Zervas, Appl. Opt. 40 (2001) [3] J.T. Kringlebotn, W.H. Loh, R.I. Laming, Opt. Lett. 21 (1996) [4] B. Guan, H. Tam, S. Lau, H.L.W. Chan, IEEE Photon. Technol. Lett. 17 (2005) 169. [5] L. Shao, X. Dong, A.P. Zhang, H. Tam, S. He, IEEE Photon. Technol. Lett. 19 (2007) [6] K. Inoue, J. Lightwave Technol. 10 (1992) [7] K.O. Hill, D.C. Johnson, B.S. Kawasaki, R.I. MacDonald, J. Appl. Phys. 49 (1978) [8] Y.G. Han, T.V.A. Tran, S.B. Lee, Opt. Lett. 31 (2006) 697. [9] M.P. Fok, C. Shu, Opt. Express 15 (2007) [10] N. Shibata, R.P. Braun, R.G. Waarts, IEEE J. Quantum Electron. 23 (1987) 1205.

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