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Abstract
We proposed and experimentally demonstrated a new scheme for enhancing the sensitivity of a fiber laser sensor using Brillouin slow light. The Brillouin laser was exposed to environmental vibrations, producing fluctuations at 408 kHz frequency, which were then interrogated using a Mach–Zehnder interferometer. By introducing Brillouin slow light into one arm of the interferometer, the sensitivity increased by 1.57 times that of a device without slow light. We believe this scheme may provide a new way of using Brillouin slow light and that it has some important implications regarding the use of fiber sensors for measuring the vibration, temperature, strain and so on.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Optical fiber sensors have attracted significant interest owing to their high sensitivity, compactness, multiplexing capabilities, and low cost. Many types of fiber sensors have been proposed and used for measuring various parameters, such as the refractive index [1], temperature [2], strain [3], and bend [4]. In addition, fiber laser sensors have received widespread attention owing to their excellent high signal-to-noise ratio and narrow bandwidth [5]. By contrast, slow and fast light has received considerable interest in the development of various applications in numerous fields including optical buffering [6] and nonlinearity enhancements [7]. Control of the light group velocity can be used to improve the sensitivity of an optical sensor [8]. The phase change induced through perturbations is inversely proportional to the group velocity of the wave. The use of slow light in an optical fiber can therefore increase the phase change induced through an external perturbation applied to the fiber, and thus increase the sensitivity of a fiber sensor [9]. The enhancing effect on the sensitivity has been experimentally observed in the fields of spectroscopy [10], laser gyroscopes [11], and strain sensors [12–14]. Recent research, in particular, has demonstrated that slow light can be an extremely useful approach to improving the spectral sensitivity and measuring the laser frequency with unprecedented precision [15]. Sternklar et al. reported that kilohertz laser frequency sensing using Brillouin mutually modulated cross-gain modulation [16]. However, it requires a long interaction length for a low modulation frequency [17]. Otherwise, it can only be used for a high modulation frequency [18]. Zhang et al. reported a sensitivity enhancement using a Mach–Zehnder interferometer coupled with a fiber ring resonator. However, the laser wavelength should be chosen extremely carefully, namely, approximately within the resonant region of the resonator [19].
In this study, we experimentally demonstrated a novel scheme to enhance the sensitivity of a fiber laser sensor with a slow light effect using a single-frequency Brillouin fiber laser as the sensing element. The frequency of the Brillouin fiber laser was interrogated using a Mach–Zehnder readout interferometer (MZRI) [3]. By increasing the group index of one arm of the interferometer using Brillouin slow light, the sensitivity is increased by a factor of 1.56. To the best of our knowledge, this is the first demonstration of Brillouin slow light improving the sensitivity of a fiber laser sensor. In addition, our scheme using Brillouin slow light with certain inherent characteristics has several advantages, namely, a large signal bandwidth range and operation at room temperature and at any wavelength. Moreover, the proposed scheme may provide a new way for applying Brillouin slow light.
2. Theory
The frequency deviation of a fiber laser sensor [20,21] can be written as follows [3]:
where L is the length of the sensing fiber, $\Delta L$ is its change caused by the signal to be detected, ${L_{FL}}$ is the cavity length of the fiber laser, $\zeta \approx 0.78$ is a constant that depends on the photoelastic properties of the fiber [3], and v is the central frequency of the fiber laser. Applying the derivative of v to the sensing fiber length, the following expression is obtained [3]: For an unbalanced Mach–Zehnder readout interferometer, the difference in phase of the two beams passing through two different routes is given by [10,15] where n denotes the refractive index, ${L_{MZ}}$ is the physical difference in fiber length of the interferometer, and c is the velocity of light in a vacuum. Taking the derivative of $\Delta \phi$ with respect to the frequency, we obtain the following expression: where ${n_g}\ =\ n + vdn/dv$ is the group index of the medium [10]. Substituting Eq. (2) into Eq. (4), we obtain the following expression: The sensitivity is proportional to the group index ${n_g}$ inside the interferometer [15].The process of stimulated Brillouin scattering (SBS) is the most widely used mechanism for generating a slow light effect in fibers with the incomparable advantages of a low pump power, as well as operation at room temperature and at any wavelength [22]. At the peak of the Brillouin gain, the group index is given by the following [23]:
where ${g_0}$ is the center gain factor, ${\Gamma _B}$ is the SBS linewidth, and ${I_p}$ is the pump intensity. The group index increases with the pump power. Therefore, we can improve the sensitivity of the sensor by increasing this power. It is worth noting that we ignore the variance in ${n_g}$ with the Stokes frequency for simplicity. It is reasonable for $\Delta v$ to be less than 0.5 MHz and the Brillouin gain bandwidth to be approximately 30 MHz.3. Experiments and results
Figure 1 shows the experiment setup. The light source is a self-made narrow linewidth fiber laser (NLFL) with a wavelength of 1,541 nm and an output power of 100 mW. After passing through an isolator, the laser light is split using a 95:5 coupler, in which the 95% port is sent to the Brillouin fiber laser as a Brillouin pump and the 5% port is sent to EDFA 2 at a maximum output power of 2 W. The BFL consists of a circulator, a 6-m long highly non-linear fiber (HNLF, YOFC NL-1550-ZERO), a polarization controller, a PZT, an isolator, and an 80:20 coupler.
Fig. 1. Experiment setup: ISO, polarization independent isolator; BFL, Brillouin fiber laser; C1–C6, coupler; EDFA, Erbium-doped fiber amplifier; HNLF, high nonlinearity fiber; PC, polarization controller; PZT, piezoelectric transducer; VOA, variable optical attenuator.
The group delay of the Brillouin slow light was first measured. The output of the BFL was modulated using an electro-optic modulator (EOM) to produce a signal of a 10 MHz sinusoidal pulse train. This pulse train then passes through a 6-m HNLF in one arm of the interferometer. The output of EDFA 2 severs as the Brillouin slow light pump. The group delay is measured using an oscilloscope after opto-electrical conversion. Figure 2 shows the traces under different pump powers. When the pump power is 2 W, a controllable delay of up to 15 ns is obtained. The group index is given by ${n_g} = \frac{c}{{{L_{MZ}}}}(\frac{{n{L_{MZ}}}}{c} + \tau )$, where $\tau$ is the group delay. In our experiments, where the length of the HNLF is approximately 6 m, the refractive index of the HNLF is ∼1.6 and the maximum group delay is 15 ns; thus, the maximum group index is calculated as 2.35, which is 1.49-times the refractive index.
We then removed the EOM and used the Brillouin fiber laser as the sensing element. As shown in Fig. 1, a 2 m long single mode fiber was wound on the PZT to sweep the ring cavity length of the Brillouin laser. When this sensing fiber is impacted by a vibration signal, its length and refractive index change accordingly, which will consequently change the equivalent length of the ring cavity and the output laser frequency. Thus, when the peak-to-peak voltage of the PZT is constant, the relative frequency beat can be scanned from zero to the maximal frequency deviation through a frequency modulation [24].
Figure 3(a) shows the optical spectra of the self-made narrow linewidth fiber laser and the Brillouin fiber laser. The BFL wavelength is shifted by approximately 0.08 nm from the Brillouin pump. Figure 3(b) shows the homodyne spectra of the two lasers when using a delayed self-homodyne technique [24]. The free spectrum range (FSR) of the BFL is 21.44 MHz. The first three peaks in the homodyne spectrum are caused by the NLFL. The FSR of the NLFL is 4.28 MHZ. By applying a sinuously modulated voltage of 600 mV peak-to-peak at a frequency of 1 kHz on the PZT, the maximum deviation of the Brillouin laser frequency is 408 kHz, as shown in the inset of Fig. 3(b).
Generally, for a frequency-based fiber laser sensor, the frequency deviation is interrogated using a MZRI [3]. Here, we introduce Brillouin slow light into one arm of the MZRI. The difference in optical path between the two arms of the MZRI is equal to the optical path length of the HNLF. Because the group index of the HNLF varies with the Brillouin slow light pump, an appreciable sensitivity enhancement can be obtained by increasing the pump power. The interferometer output was measured with a photodetector and a spectrum analyzer. The VOA and two couplers (C4 and C5) in the interferometer were used to maintain the optical power of the two arms at the same level.
The detected signal frequency spectra at different pump powers are shown in Fig. 4. We calculated the differences in amplitude between the fundamental and third harmonics. The phase difference between the two arms can be written as $\phi \ =\ {\phi _m}\cos (\Omega t + {\phi _0})$, where ${\phi _m}$ is the amplitude of the phase difference, $\Omega $ is the vibration frequency of the PZT, and ${\phi _0}$ is a constant. The value of ${\phi _m}$ can be calculated using the ratio of the Bessel function [25], which can be written as $\left|{\frac{{{J_1}({\phi_m})}}{{{J_3}({\phi_m})}}} \right|= {10^{\alpha /20}}$, where ${J_1}$ and ${J_3}$ are the fundamental and third harmonic Bessel functions of the first kind, and $\alpha$ is the difference in intensity between the fundamental and third harmonic spectra. By increasing the slow light pump power, the phase difference amplitude increases from 0.394 to 0.618 radian.
Figure 5 shows the group index in the HNLF and the phase difference of the MZRI as a function of the pump power. The inset of Fig. 5 indicates that the phase difference is proportional to the group index under certain change in the sensing fiber length, which confirms Eq. (3). In our system, the maximum group index is 1.49-times the refractive index. Accordingly, the maximum phase difference with slow light is 1.57-times larger than that without slow light. The theoretical model fits the experimental data well. Generally, the sensitivity of the fiber laser sensor can be enhanced by introducing Brillouin slow light into the MZRI.
We can also adopted a phase generation carrier demodulation method into our system to recover a 1 kHz vibration signal [26]. As shown in Fig. 6(a), when the pump power increased from 0 mW to 2 W, the peak-to-peak voltage of the detected signal increased from 616 to 941 mV. Figure 6(b) shows the spectrum of the demodulated signal. The signal-to-noise ratio of this sensor is approximately 40 dB. This indicates that the vibration signal can be recovered correctly in our fiber laser sensor system using a Brillouin slow light MZRI.
Fig. 6. Output signal after phase generated carrier demodulation: (a) waveform and (b) spectrum of the recovered signal.
The enhancement of the signal-to-noise ratio is not significant here because a maximum change in the group index of only 1.49-fold was found in our experiment. However, a higher sensitivity could be obtained by further increasing the group index of the Brillouin slow light. In fact, the group index value is a key parameter, and can be further enhanced if using a shorter fiber to avoid the saturation effect during the SBS process [27]. Indeed, a much larger group index can be achieved by optimizing the Brillouin slow light scheme. For example, Pant et al. reported the use of Brillouin slow light using a rib waveguide based on chalcogenide glass [28], and achieved a group index change of 130. Dong reported the light storage using Brillouin-scattering induced transparency in a whispering-gallery mode microresonator [29]. Thus, we could obtain a signal enhancement of 100 fold or even more by further increasing the group index. It is important that our experiment verify the feasibility of Brillouin slow-light enhancement regarding the sensitivity. Meanwhile, the phase difference of the MZRI is also affected by the outside temperature, vibration, and phase noise of the laser. The smaller difference in the optical path of the MZRI means a lower noise floor. Furthermore, by further increasing the group index in our Brillouin slow-light sensor system, we could greatly reduce the difference in fiber length of the interferometer without sacrificing the signal amplitude. This will be extremely useful for reducing the noise floor of a sensor and may have some important applications.
4. Conclusion
In conclusion, we experimentally demonstrated a sensitivity enhancement of a fiber laser sensor using Brillouin slow light. The sensitivity of the fiber laser sensor is proportional to the group index of the slow light medium in one arm of the readout interferometer while the group index increases with the Brillouin pump power. A sensitivity enhancement of approximately 1.57 fold was observed during our experiment. By further increasing the group index, we may be able to obtain a more significant signal enhancement in future experiments. We believe this scheme may provide a new way of using Brillouin slow light and that it has some important implications regarding the use of fiber sensors for measuring the vibration, temperature, strain, and other factors.
Funding
National Natural Science Foundation of China (61665002, 61463014, 61705001); Natural Science Foundation of Hubei Province (2015CFB609); Hubei Provincial Department of Education (Q20151903); Special Funds for “Double First-Class” Construction in Hubei Province (2019).
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