Investigation of dynamic properties of erbium fiber laser for ultrasonic sensing

Qi Wu; Yoji Okabe; Junqiang Sun

doi:10.1364/OE.22.008405

1. Introduction

The erbium fiber laser (EFL) as an optical light source has been researched and utilized in communication and sensing in these decades. Then, some researchers proposed the potential application of the EFL as a sensing element. When the Bragg wavelength of the cavity-inbuilt fiber Bragg grating (FBG) shifts, the lasing wavelength will change accordingly [1]. These applications are usually based on EFL’s static properties. As a result, the dynamic properties of the EFL are always treated as negative effects, which should be avoided in practical applications [2, 3]. However, several researchers explored the potential sensing application of EFL based on its dynamic properties recently. For example, Barmenkov et al. proposed a hydrogen sensor based on measurement of buildup time of his EFL [4]. Stewart et al. proposed a gas sensor based on measurement of evolution of spectra distribution [5]. Because these researches still focus on using EFL to detect static physical parameters, EFL’s properties to dynamic parameters, such as ultrasonic wave, have not been explained in detail until now.

On the other hand, researchers developed ultrasonic sensor based on FBG [6], and recently improved it to phase-shifted fiber Bragg grating (PS-FBG). PS-FBG has broader ultrasonic bandwidth and higher sensitivity, making it suitable for ultrasonic detection [7]. Theoretically, the sensitivity of PS-FBG sensor can be improved further by increasing its slope (narrowing its FWHM). However, it is not practical in reality. The narrow peak in the PS-FBG makes the demodulation system instable, because quasi-static environmental change, such as temperature and strain, will easily shifts the Bragg wavelength of the PS-FBG out of its dynamic range. Although feedback controller or the Pound-Drever-Hall method can stabilize sensing systems, these methods require complex configuration and high costs [8, 9]. Furthermore, the reported highest detectable frequency in Pound-Drever-Hall method is only 20 kHz, far from enough in ultrasonic detection [9]. Therefore, using normal external independent tunable laser source (TLS) to demodulate PS-FBG should be carefully considered in harsh-environment application.

Tsuda has recently proposed optical fiber lasers incorporated with FBG to achieve temperature or quasi-static strain robustness [10]. It is believed that this system is not sensitive enough due to its principle on uneven slope of the amplified spontaneous emission (ASE) spectrum of erbium doped fiber (EDF). Han et al. also integrated EFL with FBG to detect ultrasonic wave [11]. In their design, the lasing wavelength is decided by a tunable Fabry-Perot filter, which is controlled and stabilized by an external electrical signal, i.e., it does not have high temperature robustness. Furthermore, fiber grating laser sensor was proposed to detect isotropic strain with very high frequency [12]. These sensors usually need extra demodulation system with high cost, and they may be not suitable to be used in certain ultrasonic nondestructive testing (NDT), such as acousto-ultrasonic method [6]. To our knowledge, there is no ultrasonic optical fiber sensor which can simultaneously solve the problems among sensitivity, ultrasonic bandwidth, robustness, and cost.

In this research, we proposed and demonstrated a novel ultrasonic optical fiber sensing system based on an EFL with an inbuilt PS-FBG. In section 2, the system setup is explained. In section 3, the theory of this EFL is briefly introduced. In section4, a numerical model of the EFL is used to explain EFL’s dynamic properties, and the EFL’s ultrasonic response is found to be similar as the forced single degree of freedom (1-DOF) vibration with damping. In section 5, the experimental results fit the simulation results well, showing that this design has high sensitivity and broad bandwidth to ultrasonic wave, and robustness to quasi-static environmental change.

2. System setup

Figure 1 shows the experimental setup of this EFL and spectra of FBGs. As shown in Fig. 1(a), an erbium doped fiber amplifier (EDFA) (FiberLabs, AMP-FL8013) with 980-nm pump generates enough gain for laser oscillation. Two polarization controllers are used to control the polarization status in the EFL. 10 percent of the laser power is lead out of the ring cavity by an optical coupler, then monitored by an optical spectrum analyzer (OSA) (Anritsu, MS9710C) and detected by a photo-detector (Thorlabs, PDA10CS-EC) with gain setting of 10. After the photo-detector, an electrical spectrum analyzer (ESA) (Advantest, R3131A) and an oscilloscope (Yokogawa, DL708E) are connected for observing EFL’s response to ultrasonic wave. A PS-FBG with grating length of 5 mm and an apodized FBG (AFBG) connected after a circulator are inbuilt in the ring cavity. Figure 1(b) shows the transmitted spectrum of the PS-FBG and the reflected spectrum of the AFBG, observed by OSA. The AFBG and the PS-FBG have approximately the same Bragg wavelength, and the reflected peak of the AFBG almost covers the transmitted peak area of the PS-FBG. The inset of Fig. 1(b) shows the detailed observation of the peak area of the PS-FBG with about 1.6-pm full-width-half-maximum (FWHM), obtained by wavelength sweeping of a TLS. According to Fig. 1(b), these two FBGs constitute a filter with ultra-narrow FWHM for laser wavelength determination; however, their insertion losses are high. Besides being used as a filter, the PS-FBG is also used to receive the ultrasonic waves. Acousto-ultrasonic method is used to investigate the dynamic responses of the EFL to ultrasonic wave. A broadband lead-zirconate-titanate (PZT) (Fuji Ceramics, 1045S) is used as an actuator, glued on an aluminum plate. The PS-FBG in the EFL is glued about 8 cm away from the actuator in line. The other same type PZT sensor and another PS-FBG with relative broad FWHM of 0.02 nm demodulated by the balanced sensing technique [7], are also glued near to the PS-FBG in the EFL as references. All the sensors are glued using high-acoustic impedance ultrasonic couplant.

Fig. 1 Experimental setup and spectra of FBGs. (a) Configuration of the EFL. (b) The transmitted spectrum of the PS-FBG and the reflected spectrum of the AFBG. The inset shows the peak area of the PS-FBG has a FWHM of approximately 1.6 pm.

Download Full Size | PDF

3. Theory

Figure 2 shows the principles of EFL. First, the laser emits when the gain generated by the EDFA and tailored by both the PS-FBG and AFBG exceeds the loss in the ring cavity. Because of the ultra-narrow FWHM of the PS-FBG and the dominantly homogeneous broadening property of the EDF, single longitudinal mode will oscillate under the ideal steady-state condition. The exact lasing wavelength is determined by both the Bragg wavelength of the PS-FBG and the longitudinal mode positions of the ring cavity, i.e., the longitudinal mode which is nearest to the Bragg wavelength of the PS-FBG is the exact lasing mode.

Fig. 2 Sensing and self-adjustment principles.

Download Full Size | PDF

After the laser is established, the sensing principle of the EFL is similar to FBG demodulation by an external independent TLS [8]. The output power of the EFL changes when ultrasonic strain shifts the Bragg wavelength of the PS-FBG, because the insertion loss from the PS-FBG is varied. Mainly due to the short effective grating length and the ultra-steep peak area slope of the PS-FBG [13], the achievable sensing bandwidth and sensitivity of this EFL will be much better than that of traditional FBG sensing system. However, EFL’s ultrasonic dynamic responses show several unique properties, such as waveform deformation and frequency-dependent amplitude.

Besides the high sensitivity and the broad bandwidth, the EFL is very robust. When temperature or quasi-static strain significantly shifts the Bragg wavelength of the PS-FBG, the lasing longitudinal mode will hop to a neighboring position, emitting light with different wavelength. From another view point, the intra-cavity PS-FBG is still interrogated in the save way by the light within the cavity after the mode hop(s), giving a solution between high sensitivity and temperature-induced instability.

4. Simulation

4.1 Numerical model

Table 1 gives some basic parameters and their values used in the dynamic model of this EFL. In order to simplify the model, certain assumptions are applied to the PS-FBG in the EFL. Although the spectrum of the PS-FBG is complex, Gaussian function can approach its transmittance due to the similarity. The longitudinal mode spacing (LMS) of the EFL calculated by $λ^{2} / n L$ has value about 0.06 pm. In our simulation, we consider the wavelength range from 1549.997 - 1550.003 nm. Thus, m = 100 longitudinal modes are considered. The transmittance of the PS-FBG at each longitudinal mode position is given by:

F_{m} = \exp (- {(\frac{λ_{m} - λ}{Δ λ})}^{2}) .

where

λ_{m}

is the wavelength of the m^th longitudinal mode,

Δ λ

= 1.6 pm is the FWHM of the filter,

λ

≈1550 nm is the initial Bragg wavelength, and

F_{m}

is the transmittance at

λ_{m}

. Although the response of the PS-FBG to ultrasonic wave also shows complicate behavior especially when the ultrasonic wave has high frequency, we simply assume the PS-FBG shifts its Bragg wavelength following the input signal and maintains its spectrum shape herein.

Table 1. Parameters used in the simulation

View Table

Two-level model and averaged parameters are used to describe the EDFA in the EFL [5, 14]. Because only dozens of longitudinal modes may exist in the ultra-narrow FWHM of the filter, the absorption and emission coefficients of the EDF at the wavelengths of these longitudinal modes have very small differences. As a result, these parameters in our model are treated as constants rather than wavelength-dependent ones. Unlike the Eqs. in reference [11, 15] where mode groups are used, we treat the longitudinal modes individually because of few numbers of longitudinal modes. Therefore, the dynamic property of the EFL can be described by differential equations with length averaged inversion level $N_{2}$ and photon numbers of the m^th longitudinal mode $M_{m}$ as variables, given by:

\begin{array}{l} (ρ S l) \frac{d N_{2}}{d t} = P_{p} (1 - e^{g_{p} l}) - (ρ S l) \frac{N_{2}}{τ_{0}} \\ - \sum_{1}^{m} \frac{M_{m}}{τ} (1 - e^{- g_{g} l}) - 4 m \frac{γ_{g} l N_{2}}{τ} (A_{g} - 1) . \end{array}

\frac{d M_{m}}{d t} = \frac{M_{m}}{τ} (F_{m} e^{g_{g} l - α} - 1) + \frac{2}{τ} γ_{g} l N_{2} A_{g} .

where

τ = n L / c

is the round trip time of the laser cavity,

g_{p} = - α_{p} (1 - N_{2})

is the length-averaged pump absorption coefficient,

g_{g} = (γ_{g} + α_{g}) N_{2} - α_{g}

is the length-averaged gain coefficient for laser mode, and

A_{g} = (e^{g_{g} l} - 1) / g_{g} l

is the ASE amplification factor for laser mode. In the Eq. (2), the left-hand side (LHS) represents the total photon changes in the upper state of the EDF; the first term in the right-hand side (RHS) represents the pump absorption rate; the second term in the RHS represents spontaneous emission rate; the third term in the RHS represents the stimulated emission rate; the forth term in the RHS represents the change rate of

N_{2}

caused by the ASE. In the Eq. (3), the LHS represents the photon change of certain longitudinal mode; the first term in the RHS represents the photon number change in each circulation of the EFL; the second term in the RHS represents the influence from ASE. The pump power

P_{p}

in unit of photons/second has relation to the pump power

P

, as

P_{p} = P λ / h c

, where

c

and

h

are light speed and Planck constant, respectively. Then, according to the same relation, the output power detected by photo-detector is proportional to the power given by:

P_{o u t} = \frac{h c}{τ λ} \sum_{1}^{m} M_{m} .

where

\sum_{1}^{m} M_{m}

stands for the summation of all the photons.

4.2 Initial steady-state condition

Figure 3 shows the transmittance of the filter (red line) and the simulated lasing wavelength of the EFL (blue dots) in steady-state condition. Although the transmittances near to the peak of the filter are very similar, only the longitudinal mode which processes the largest transmittance oscillates, fitting the dominantly homogeneous broadening property of the EDF well, i.e., the EDF usually only supports single longitudinal mode laser oscillation in ideal steady-state condition. Because the longitudinal modes have the identical LMS, the wavelength of the laser will always be near to the peak of the filter in the range of one LMS (from –LMS/2 to LMS/2), as shown in the inset of Fig. 3. However, the exact position is uncontrollable in practice. Thus, we consider 9 different positions with equal interval of LMS/20 in the left side of the filter marked as 1 to 9 in our simulation. These different positions will influence the sensing results, as discussed in the section 4.5 and 4.6. Due to the symmetric property of the PS-FBG filter, the other side of the filter should have the same waveform results albeit with opposite phase.

Fig. 3 Transmittance of the filter and lasing wavelength of the EFL. Red line is the transmittance of the filter; blue dots are the laser output power in each longitudinal mode positions. Inset shows 9 different initial lasing longitudinal mode positions near to the peak of the filter.

Download Full Size | PDF

Figure 4 shows the laser establishing process. When a step pump is applied at 0 ms, after a certain delay, the laser output shows a number of spikes and undergoes damped relaxation oscillation (RO) before the steady state is reached. The simulated laser will finally get stable, as shown in the inset of Fig. 4. The exact laser wavelength determined by the longitudinal mode position has little influence on the DC output of the laser, because the transmittance of the filter has negligible differences in the range of one LMS. The final stable output of the laser at different initial lasing longitudinal mode positions is used as initial conditions in the dynamic simulations in section 4.4 - 4.6.

Fig. 4 Laser establishing process at different initial longitudinal mode positions shows spikes and damped ROs. The inset shows different DC output when the laser is stable.

Download Full Size | PDF

4.3 Response to quasi-static change

Firstly, we consider the dynamic response of the EFL to quasi-static change, corresponding to the environmental influences from strain and temperature. Under the quasi-static change, we assume the Bragg wavelength of the PS-FBG shifts as a half-cycle cosine curve shown in Fig. 5(a). The Bragg wavelength changes 0.25 pm (about 5 LMSs) in 20 ms, equaling to 1.25 degree temperature change or 10.5-με strain change per second. Figure 5(b) shows each longitudinal mode changes in the time domain. When the Bragg wavelength of the filter is within one LMS (over 0 – 5ms), the output intensity of the lasing longitudinal mode varies due to the changing transmittance of the PS-FBG. Once the Bragg wavelength shift exceeds one LMS (around 6 ms), the longitudinal mode at initial position will decrease rapidly due to the large loss; however, the neighboring longitudinal mode ( + LMS) will lase because the gain of the EDFA exceeds the loss of the cavity. This physical phenomenon repeats, once the Bragg wavelength caused by quasi-static change shifts out the range of one LMS. In our simulation, 5 longitudinal modes lase one by one. Although, the lasing modes are different, the power output (proportional to voltage) is almost stable as shown in Fig. 5(c). The vibration of the power output is smaller than 0.2% of the DC voltage. Owing to the low-frequency negligible change, it will have no influence to the ultrasonic detection of this EFL. Thus, this EFL is robust due to its adjustment ability.

Fig. 5 (a) Bragg wavelength shift of the PS-FBG under the quasi-static strain change or temperature change. (b) Lasing mode hopping. (c) Amount output change shows very small power fluctuation.

Download Full Size | PDF

4.4 Responses to continuous ultrasonic wave

Then, we consider the dynamic response of the EFL to continuous ultrasonic sinusoidal wave. Herein we assume the ultrasonic wave has frequency of 1 MHz, and shifts the Bragg wavelength of 0.005 pm. As shown in Fig. 6, the output of the EFL shows clear and periodic waveforms after transition time. The inset of Fig. 6 amplifies one small section of time for clearly manifesting the output curve. The output sinusoidal waveform has the same frequency of the input signals, demonstrating the dynamic response of the EFL to ultrasonic wave, because the EFL demodulates the Bragg wavelength shift of the PS-FBG filter.

Fig. 6 Dynamic response of the EFL to continuous sinusoidal wave. The inset shows a short time range of the dynamic response.

Download Full Size | PDF

4.5 Responses to burst signal

Next, we simulate the response of the EFL when the input burst signal is ten-cycle sinusoidal wave with a Hamming window. The input middle frequency is 1 MHz. Figs. 7(a) and 7(b) show the different responses of the EFL with different initial lasing longitudinal mode positions when the Bragg wavelength shift are 0.1 fm and 0.01 pm, (corresponding to 0.083 nε and 8.3 nε [16]), respectively. Compared with the ultrasonic waveform, the output intensity waveform from the EFL has small deformations, such as the areas marked by the dotted circles. The decaying tail-like oscillation after the main envelope has the same frequency as the RO.

Fig. 7 Dynamic response of the EFL to burst sinusoidal wave. (a) When the input strain signal is small; (b) when the input strain signal is relative large.

Download Full Size | PDF

It is better that the deformation can be removed in order to perfectly recover the actual ultrasonic waveform for performing analysis of ultrasonic NDT. Figure 8(a) shows the normalized input waveform (red line) and the detected waveform (blue line). Figure 8(b) shows the corresponding spectra, which clearly contain 1-MHz signals. However, there is a large 350-kHz peak in the EFL caused by the RO. This deformation in the detected waveform can be removed by applying a supposed high-pass filter. Figure 8(c) shows the recovered waveform after this supposed high-pass filter with suitable 500-kHz cut-off frequency, which perfectly matches the actual input waveform. In Fig. 8(b), the small peak in 2 MHz (twofold frequency of the input single) is probably caused by nonlinear slope of the PS-FBG, because the slope of the filter is not completely linear around the peak area. However, it will not influence our analysis in the ultrasonic NDT due to its very low energy; thus, the higher order peak is ignored in the following experiment and data process.

Fig. 8 (a) Original normalized burst signals; (b) the corresponding spectra; (c) burst signals after high-pass filter.

Download Full Size | PDF

4.6 Ultrasonic response properties

Figure 9 shows the effective estimated sensitivity of the detected waveforms from the EFL and from the same PS-FBG but demodulated by external independent TLS under different strains. The effective estimated sensitivity is evaluated by:

Sensitivity = \frac{(V_{\max} - V_{\min})}{V_{D C} \cdot S} .

where

V_{\max}

and

V_{\min}

are the maximum and minimum values of the output voltage,

V_{D C}

is the DC output voltage, and

S

is the input ultrasonic strain. In Fig. 9, neither small strain (0.083-nε) nor large strain (8.3-nε) affects on the sensitivities detected by this EFL. When the lasing longitudinal mode is at position 9, although 8.3-nε strain will shift the Bragg wavelength out of one LMS, the ultrasonic signal is still detectable. Because the neighboring longitudinal mode does not have enough time to oscillate due to the high frequency of the ultrasonic signal, the actual dynamic range of the EFL to ultrasonic signal is larger than one LMS. According to Fig. 9 as well as Fig. 7, the sensitivities of the detected ultrasonic signals are influenced by the initial lasing longitudinal mode positions. When the position approaches to the peak of the filter (such as position 1), the sensitivity decreases due to the relative gentle slope. However, the sensitivity is still very high due to the steep slope and the broad ultrasonic bandwidth. In practice, the exact lasing wavelength of the EFL is unknown and uncontrollable due to the environmental quasi-static change. Therefore, the sensitivity of the detected ultrasonic signal always vibrates, which is a bad side-effect of the self-adjustment. As a result, this EFL is suitable to be used in application based on mode analysis rather than amplitude analysis in ultrasonic NDT, such as the technique demonstrated in reference [17].

Fig. 9 Comparison results of the effective estimated sensitivity between the EFL and the same PS-FBG demodulated by external independent TLS.

Download Full Size | PDF

Unlike demodulation by an external TLS, the slope of the response curve for the EFL in Fig. 9 is influenced by ultrasonic frequency, i.e., the EFL has different responses to different frequencies. The open dots shown in Fig. 10 are the intensities (square of the amplitude) of the detected signals from the EFL. Figure 10 can be roughly divided into three areas. In area 1, the intensity decreases with the increase in frequency, exactly fitting to Lorentz curve with central frequency of 350-kHz, which is the frequency of RO. In the area 1, all the waveforms detected by the EFL can be recovered by the data process method mentioned in section 4.5. In area 2, the detected intensity is very large, marked by red square. The waveform in this area has frequency so close to the frequency of RO, that it cannot be recovered by data process based on frequency analysis, such as the waveform with 350-kHz shown in the inset of Fig. 10. Thus, the frequency in area 2 is not suitable for ultrasonic NDT, but maybe has other applications. In area 3, the intensity decreases rapidly with decrease in frequency and deviate from the Lorentz curve, although the waveform can be recovered.

Fig. 10 Intensity of the detected signals from the EFL to different frequencies shows Lorentz curve with resonance equal to the frequency of RO.

Download Full Size | PDF

4.7 Similarities between EFL and vibration

According to the above simulation and analysis, the ultrasonic response of the EFL resembles the behavior of the forced 1-DOF vibration with damping [18] to a certain extent. The resonance of the vibration model is the frequency of the RO of the EFL, and the force corresponds to the dynamic loss from the PS-FBG in the ring cavity. This result can be partially seen according to the equation of the EFL in reference [15]. We cite this Eq.:

\frac{d^{2} (δ M_{g})}{d t^{2}} + 2 α \frac{d (δ M_{g})}{d t} + ω_{0}^{2} δ M_{g} = 0.

where

ω_{0}

is the frequency of RO,

α

is the decay constant. Equation (6) has similar format of 1-DOF vibration with damping. If the laser is disturbed by small and random vibrations, such as the case when the laser is in stable condition but with very small pump instability, the RHS of Eq. (6) is 0. In this case, the noise of the EFL shows peaks at RO [19]. When the ultrasonic loss in the ring cavity disturbs the EFL relative largely, 0 in the RHS of Eq. (6) is replaced by the function of the dynamic loss. Thus, the dynamic response of the system can be predicted from vibration view point. For example, when the input frequency is much larger than resonance, the dynamic response of this EFL shows same frequency as the input continuous wave (the case in section 4.4). For another example, the response of the EFL to non-period ultrasonic signal is the convolution of EFL’s impulse response and the format of the input signal (the case in section 4.5). Furthermore, it also explains why the intensity of the detected signal has Lorentz relation to the frequency in Fig. 10 in section 4.6. We believe these results are universal in all the intensity-modulated EFL, which is a very helpful direction in the ultrasonic sensing application.

5. Experimental results

5.1 Characteristics of the EFL

Figure 11(a) shows a number of spikes and damped ROs occurred in the experimental laser establishing process. The estimated parameters in the numerical model and the linear increasing pump power in the experiment cause the differences between the simulation results and the experimental results. Figure 11(b) shows the output voltage of the EFL in environmental quasi-steady-state conditions (small and low frequency temperature change). The output voltage is usually constant at about 0.32 V. When we were conducting this experiment, there was a 5 degree temperature fluctuation in the lab. Therefore this system can resistant at least 5 degree quasi-static change without feedback controller. However, sometimes burst signals with very similar and unique format were observed, as shown in the inset of Fig. 11(b). They are caused by the mode hopping, we think. This is one problem in this EFL. Figure 11(c) shows the observed optical spectrum of the EFL. Lasing wavelength is around 1550 nm, matching to the Bragg wavelength of the PS-FBG. The output power of this EFL is about −27 dBm (2 μW), which is much smaller than the pump power, meaning low efficiency of the EFL caused by the large insertion loss of the FBGs. However, it is essential for guaranteeing the ultrasonic detection, because single longitudinal mode oscillates when the ring cavity loss is large or pump power is small. Otherwise, more sidelobe longitudinal modes with large output power will oscillate due to the partial inhomogeneous broadening property of EDF, destructing the sensing ability of this EFL.

Fig. 11 Characteristics of the EFL. (a) A number of spikes and damped ROs were observed in laser establishing process. (b) Stable DC output voltage in the quasi-steady-state condition with sometimes mode hopping signals. Inset shows a typical mode hopping signal in short time period. (c) Optical spectrum shows low efficiency of the EFL caused by large insertion loss.

Download Full Size | PDF

5.2 Response to continuous signals

Figures 12(a) and 12(b) show the dynamic responses of the traditional PZT sensor and the EFL, respectively, when the input continuous sinusoidal signal has 10MHz frequency and 5-V peak-to-peak voltage. Both sensors can detect ultrasonic wave. Figure 12(c) shows the spectra of the detected signal from the EFL observed via ESA. In 1-MHz frequency, clear signal peaks are observed; however, the signal level has about 22 dB instability, caused by the uncontrollable initial longitudinal mode position and uneven slope of the PS-FBG around the peak area. Furthermore, small peaks are observed in about 6.8 MHz, caused by the longitudinal mode beating due to the partial inhomogeneous broadening property of the EDF. However, due to the very small energy, the lasing sidelobe longitudinal modes do not affect the sensing ability of the EFL, which can be ignored. In 2-MHz, very small higher order peaks are also shown, as predicted in simulation.

Fig. 12 Typical dynamic response of (a) the traditional PZT sensor and (b) the EFL to continuous sinusoidal wave. (c) Spectra of the detected signals from the EFL.

Download Full Size | PDF

For further analysis on the properties of the sensitivity and the bandwidth of the EFL, we changed the input frequency with 0.1-MHz step. Figure 13 shows the results from the EFL (red) and from the traditional PZT sensor (blue) when preamplifier is not connected after it. In Fig. 13(a), the noise level detected from the PZT is lower than that from the EFL, and has equivalent value to every frequency. The electrical noise in the ESA perhaps is the main noise source in the results from the PZT. However, the noise in the EFL decreases with frequency increment, and resembles the Lorentz curve. The peak of the noise in EFL is at 150-kHz, which is the frequency of RO. According to Fig. 13(a), both sensors have a broad bandwidth up to 6.5 MHz It is very high for applications of acousto-ultrasonic detection in NDT. The ultrasonic bandwidth is limited by the longitudinal mode beating of the EFL, and can be improved by using shorter laser cavity. In the traditional PZT sensor, blind areas exist around the frequency multiples of 2.5 MHz where the PZT cannot detect ultrasonic waves. These blind areas greatly influence PZT’s practical performance. However, the EFL detects every frequency ultrasonic signals.

Fig. 13 Response of the PZT and the EFL to every frequency. (a) Original data of detected energy and noise in the PZT and the EFL. (b) Sensitivity of the PZT and the EFL obtained after data process method.

Download Full Size | PDF

The detected energies shown in Fig. 13(a) are influenced by the piezoelectricity efficiency of the PZT actuator; thus data process should be done to obtain the correct sensitivity of the EFL. Thanks to the same piezoelectric coefficient in the same type of PZT actuator and PZT sensor, we can evaluate the sensitivity of the PZT [20]. Then, we use the energy detected from the EFL to subtract the influence from PZT actuator in order to evaluate the sensitivity of the EFL. These results are shown as open dots in Fig. 13(b). Lastly, we use adjacent-averaging method with window of 10 to smooth the data, as the red line and the blue line for the EFL and the PZT in Fig. 13(b), respectively. Although the signal data from the EFL in Fig. 13 were collected when they were in large level, the sensitivity of the EFL is larger than that of the PZT, even by considering the 22-dB amplitude instability of the EFL. The high sensitivity of the EFL is beneficial for the sensing distance and sensing accuracy, important for ultrasonic detection. Furthermore, both curves decrease with increase in frequency. However, 2.5-MHz periodic resonant property is shown in PZT rather than in EFL. The sensitivity of the EFL decreases about 27 dB gently, which has similar value to the decrease of the noise level in EFL shown in Fig. 13(a). Although this measurement is not so precisely due to the influence from the propagating efficiency of Lamb wave in aluminum plate, the trend of the curve of the EFL is similar to area 3 shown in Fig. 10. Therefore, we believe the sensitivity of the EFL does depend on the frequency as Lorentz function.

5.3 Response to burst signals

Then we evaluated the response of the EFL to burst signals. The input signal with 5-V peak-to-peak voltage has the same waveform as that used in simulation in section 4.5. Figure 14(a) shows the waveform detected by the traditional PZT sensor after 1024 times averaging. The dot line in Fig. 14(a) shows the waveform detected by the PZT without averaging. Figure 14(b) shows the waveform detected by our previous PS-FBG balanced sensing system after 1024 times averaging. Figure 14(c) shows typical waveforms detected by this EFL when the ultrasonic wave amplitude is relatively large. Clearly, previous systems need amount data averaging with time-consuming for clear waveform presentation; only the EFL achieved real-time ultrasonic detection with good resolutions. All the detected signals have the same arrival time, which means that the ultrasonic detection ability of the EFL is derived from the Bragg wavelength shift rather than the polarimetric heterodyning [12]. If the detected signals are caused by the polarization change of the optical fiber, the EFL will be more sensitive to the ultrasonic wave propagated in the transverse direction, which is caused by the reflection of the aluminum plate edges. This will delay the arrival time of the detected wave. The waveform in Fig. 14(c) fits the simulation result shown in Fig. 7 very well, showing small waveform deformation and low frequency vibration behind the wave envelop.

Fig. 14 (a) Waveform detected by the PZT after 1024 times averaging. Dot line shows the detected signal without averaging. (b) Waveform detected by the PS-FBG balanced sensing system after 1024 times averaging. (c) Waveform detected by the EFL in real time. (d) Corresponding spectra. (e) Recovered waveform after high-pass filter detected by the EFL.

Download Full Size | PDF

By performing Fourier transform, we obtained the corresponding spectra of the detected waveforms, as shown in Fig. 14(d). At about 1 MHz, there are clear ultrasonic signals. In the EFL, there are also low-frequency peaks with relative large energy caused by RO and higher order small signals as we predicted in simulation. The detected ultrasonic signal level and the noise level of the EFL and the PS-FBG balanced sensing system are marked. After recalling the sensitivity of the PS-FBG balanced sensing system of $ε_{\min}$ = 9 nε/Hz^1/2 and considering the 1024 times averaging, the sensitivity of the EFL to the waveform in Fig. 14 is evaluated as $ε_{\min}$ = 5.6 pε/Hz^1/2. If adding the influence of instability of the amplitude, the sensitivity of the EFL varies from 0.9 nε/Hz^1/2 to 5.6 pε/Hz^1/2 in 1-MHz frequency. This evaluation is just a reference, because the sensitivity of the ultrasonic detection is related to the frequency, influenced by the attachment condition and so on.

We then applied a high-pass filter with cut-off frequency of 200 kHz to the detected signal from EFL. The recovered signal shown in Fig. 14(e) resembles the waveform in Fig. 14(b), also resembles the results in Fig. 8. It demonstrates the practice of this data process method. Actually, we have applied this EFL to practical acousto-ultrasonic detection for impact damage evaluation of carbon fiber reinforced plastics (CFRP). The high sensitivity and broad ultrasonic bandwidth of the EFL makes the impact damage evaluation easier, showing large advantage in ultrasonic NDT field. Because certain acousto-ultrasonic method is based on Lamb wave mode analysis, the amplitude instability is not a problem. Furthermore, the self-adjustment ability of this EFL contributes the real-time ultrasonic detection when CFRP is working, because CFRP is widely applied to aerospace in harsh environment.

Conclusion

In this research, we investigated the dynamic properties of an EFL, and applied it to ultrasonic detection for NDT. In the ring cavity of the EFL, a PS-FBG with ultra-narrow FWHM is inbuilt to fully receive the ultrasonic signal. We simulated the EFL’s response to quasi-static change, continuous ultrasonic wave and burst ultrasonic wave based on a numerical model and explained its ultrasonic response properties. One important characteristic of the EFL is its robustness to quasi-static environmental change, which is beneficial for practical applications. The detected ultrasonic amplitude of the EFL depends on the initial lasing longitudinal mode positions. The amplitude is also influenced by ultrasonic frequency, showing approximate Lorentz curve. We found that EFL has similar dynamic properties as the forced 1-DOF vibration with damping, when the resonance is the frequency of RO, and the force is the dynamic loss from the PS-FBG in the cavity. Experimental results fit the simulation results very well, and demonstrated that the ultrasonic responses of the EFL have broad ultrasonic bandwidth, high sensitivity and good ultrasonic response curve. Furthermore, the waveform can be recovered by filtering out the frequency of RO, which is useful for applications based on mode analysis in NDT. In conclusion, the EFL shows high potential in ultrasonic detections.

References and Links

1. L. Talaverano, S. Abad, S. Jarabo, and M. Lopez-Amo, “Multiwavelength fiber laser sources with Bragg-grating sensor multiplexing capability,” J. Lightwave Technol. 19(4), 553–558 (2001). [CrossRef]

2. E. Lacot, F. Stoeckel, and M. Chenevier, “Dynamics of an erbium-doped fiber laser,” Phys. Rev. A 49(5), 3997–4008 (1994). [CrossRef] [PubMed]

3. M. Ding and P. K. Cheo, “Analysis of Er-doped fiber laser stability by suppressing relaxation oscillation,” IEEE Photonic. Tech. L. 8(9), 1151–1153 (1996). [CrossRef]

4. Y. O. Barmenkov, A. Ortigosa-Blanch, A. Diez, J. L. Cruz, and M. V. Andrés, “Time-domain fiber laser hydrogen sensor,” Opt. Lett. 29(21), 2461–2463 (2004). [CrossRef] [PubMed]

5. G. Stewart, G. Whitenett, K. Vijayraghavan, and S. Sridaran, “Investigation of the dynamic response of erbium fiber lasers with potential application for sensors,” J. Lightwave Technol. 25(7), 1786–1796 (2007). [CrossRef]

6. G. Wild and S. Hinckley, “Acousto-ultrasonic optical fiber sensors: overview and state-of-the-art,” IEEE Sens. J. 8(7), 1184–1193 (2008). [CrossRef]

7. Q. Wu and Y. Okabe, “High-sensitivity ultrasonic phase-shifted fiber Bragg grating balanced sensing system,” Opt. Express 20(27), 28353–28362 (2012). [CrossRef] [PubMed]

8. B. Lissak, A. Arie, and M. Tur, “Highly sensitive dynamic strain measurements by locking lasers to fiber Bragg gratings,” Opt. Lett. 23(24), 1930–1932 (1998). [CrossRef] [PubMed]

9. S. Avino, J. A. Barnes, G. Gagliardi, X. Gu, D. Gutstein, J. R. Mester, C. Nicholaou, and H. P. Loock, “Musical instrument pickup based on a laser locked to an optical fiber resonator,” Opt. Express 19(25), 25057–25065 (2011). [CrossRef] [PubMed]

10. H. Tsuda, “Fiber Bragg grating vibration-sensing system, insensitive to Bragg wavelength and employing fiber ring laser,” Opt. Lett. 35(14), 2349–2351 (2010). [CrossRef] [PubMed]

11. M. Han, T. Liu, L. Hu, and Q. Zhang, “Intensity-demodulated fiber-ring laser sensor system for acoustic emission detection,” Opt. Express 21(24), 29269–29276 (2013). [CrossRef] [PubMed]

12. B. O. Guan, L. Jin, Y. Zhang, and H. Y. Tam, “Polarimetric heterodyning fiber grating laser sensors,” J. Lightwave Technol. 30(8), 1097–1112 (2012). [CrossRef]

13. T. Liu and M. Han, “Analysis of π-phase-shifted fiber Bragg gratings for ultrasonic detection,” IEEE Sens. J. 12(7), 2368–2373 (2012). [CrossRef]

14. Y. Sun, J. Zyskind, and A. Srivastava, “Average inversion level, modeling, and physics of erbium-doped fiber amplifiers,”IEEE J Sel. Top. Quant. 3(4), 991–1007 (1997). [CrossRef]

15. M. A. Mirza and G. Stewart, “Multiwavelength operation of erbium-doped fiber lasers by periodic filtering and phase modulation,” J. Lightwave Technol. 27(8), 1034–1044 (2009). [CrossRef]

16. A. Othonos, “Fiber Bragg gratings,” Rev. Sci. Instrum. 68(12), 4309–4341 (1997). [CrossRef]

17. Y. Okabe, K. Fujibayashi, M. Shimazaki, H. Soejima, and T. Ogisu, “Delamination detection in composite laminates using dispersion change based on mode conversion of Lamb waves,” Smart Mater. Struct. 19(11), 115013 (2010). [CrossRef]

18. W. Thomson, Theory of Vibration with Applications (Prentice-Hall, 1996).

19. E. Rønnekleiv, “Frequency and intensity noise of single frequency fiber Bragg grating lasers,” Opt. Fiber Technol. 7(3), 206–235 (2001). [CrossRef]

20. V. Giurgiutiu, Structural Health Monitoring: with Piezoelectric Wafer Active Sensors (Elsevier Academic Press, 2008).

Symbol	Definition	Unit	Value
$n$	index of the fiber		1.456
$L$	cavity length of the EFL	m	28
$ρ$	erbium ion density	ions/m³	2e24
$S$	core cross sectional area of the fiber	μm2	8.04
$l$	length of the EDF	m	3.6
$τ_{0}$	lifetime of the upper state	ms	10
$P$	pump power	mW	225
$α_{p}$	absorption coefficient at the pump wavelength	dB/m	4.64
$γ_{g}$	emission coefficient at the signal wavelength	dB/m	3.7
$α_{g}$	absorption coefficient at the signal wavelength	dB/m	3
$α$	loss in the ring cavity excluding the EDF	dB	10

Investigation of dynamic properties of erbium fiber laser for ultrasonic sensing

Abstract

1. Introduction

2. System setup

3. Theory

4. Simulation

4.1 Numerical model

4.2 Initial steady-state condition

4.3 Response to quasi-static change

4.4 Responses to continuous ultrasonic wave

4.5 Responses to burst signal

4.6 Ultrasonic response properties

4.7 Similarities between EFL and vibration

5. Experimental results

5.1 Characteristics of the EFL

5.2 Response to continuous signals

5.3 Response to burst signals

Conclusion

References and Links

Cited By

Figures (14)

Tables (1)

Equations (6)

Optics Express