1 Introduction

With the development of modern industry, the requirement for the long-distance fiber sensor system is highly desirable. As we all know, the common method to achieve this objective is applying the Erbium-Doped Fiber Amplifier (EDFA). However, if there is no electric power supply to drive the EDFA between two long fiber-links, we cannot realize the long-distance sensing. In addition, the maximum transmission distance with a broadband light source is limited up to 25 km due to Rayleigh scattering and attenuation effect along the fiber [1]. Although a long-distance sensor system with a linear cavity Raman laser configuration based on a fiber Bragg grating (FBG) and a fiber loop mirror was proposed, the long-distance fiber served as the role of the laser cavity in their setup. This will bring out the thermal stability issue along the fiber [2]. Hence, in order to solve the above-mentioned issues, hybrid EDF and Raman amplification technique [3, 4] was proposed. Recently, our group demonstrated a 100-km long-distance fiber Sensor system based on erbium-doped fiber and Raman amplification [4]. For the above systems, a section of EDF has to be connected to the long fiber link. If do not considering the thermal effect of the Raman amplification on the fiber link, the additional inserted EDF may affect the sensing performance since, as we all know, the pumped EDF is also sensitive to the temperature.

Here, without using the additional EDF, we demonstrate a novel technique to realize a long-distance fiber sensor system based on the second-order Raman pump and amplification. With a 1395-nm high power pump served as the first Raman pump to pump a 50-km SMF, a gain spectrum around 1480 nm will be generated. With the other low power 1480-nm pump, as the signal light, to pump the same SMF, it will be simultaneously amplified by the above 1480-nm gain spectrum. The amplified 1480 nm light will serve as the second-order pump to further pump the SMF, and generate a gain spectrum around 1582-nm. The gain spectrum around 1582-nm has a Gauss gain spectrum of 20-dB SNR, with two steep slopes, and a side gain spectrum, with a quasi-linear slope. The gain spectrum serves as the optical source and the filter, simultaneously, for the remote fiber sensor. We demonstrated their applications for a remote fiber Fabry–Pérot (F–P) strain sensor. Experimental results show that when the strain is applied on the sensor, the wavelength shift of the resonance peak is simultaneously intensity modulated by the steep slope with a high sensitivity, while the sensor is temperature insensitive. Moreover, the side gain spectrum can serve as a quasi-linear filter to intensity-modulate the wavelength shift of the sensor. It should be noted that the system is also applicable for the fiber Bragg grating (FBG) sensors to realize a long-distance sensing. Using the second order Raman amplification is convenient for the local operation since it is no need to connect an additional EDF in the long fiber end as using the first order Raman amplification. The thermal stability of the sensor system will be improved since it has not the thermal problem induced by the pumped EDF as using the first order Raman amplification.

2 Principle of operation

Figure 1 shows the schematic configuration of the sensor system. With a high power 1395-nm Raman laser pumped a 50-km SMF via a 1395/1550 nm wavelength division multiplexer (WDM), a gain spectrum around 1480 nm will be generated along the fiber by the first-order stimulated Raman scattering (SRS). The other low power 1480-nm pump, as the signal light, is coupled into the 50-km SMF via a 1480/1550 nm WDM, will be simultaneously amplified by the above 1480-nm gain spectrum. The amplified 1480 nm pump will serve as the second-order pump to further pump the SMF, and generate the second-order SRS along the fiber, then a gain spectrum around 1582 nm will be obtained.

Fig. 1
figure 1

Schematic configuration of the sensor system

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The reflection spectrum is captured with an optical spectrum analyzer (OSA) under the wavelength resolution of 0.02 nm. A hollow core photonic-crystal fiber (HCPCF) type F–P sensor [5, 6] is selected to demonstrate the applications of the system since it has been proved to be a good strain sensor candidate and the resonance peaks of the F–P type sensor can cover the gain spectrum around 1582 nm. The inset is the microscope image of the F–P sensor. It is constructed with a 0.4-mm HCPCF, with a free-spectral range of about 3 nm. Figure 2 shows the reflection spectra of the sensor system under a 30-dBm 1395-nm pump and different powers of the 1480-nm pump. Under a same 1395-nm high power pump of 30 dBm, the SNR of the F–P sensor will increase accordingly with the enlargement of the 1480-nm pump power. With the 22.75-dBm 1480-nm pump, a Gauss gain spectrum of 20-dB SNR around 1582 nm with two steep slopes is obtained, and the 3-dB bandwidth of the Gauss gain spectrum is ∼2 nm, as shown in Fig. 3. Without the F–P sensor, the reflection spectrum is the gain spectrum around 1582 nm, which is reflected by the 50-km SMF end surface, and the reflectivity of the end surface is <4 %. With the F–P sensor connected to the SMF, it can be seen that the SNR is increased. This is because the reflectivity of the F–P sensor is bigger than that of the end surface of the SMF. Note that, if just with the high power 1395-nm pump or the low power 1480-nm pump to pump the 50-km SMF, no distinct gain spectrum around 1582 nm can be seen. When a strain ε is applied to the sensor and ambient temperature variation ΔT occurs, the wavelength shift of the ith resonance peak of the sensor can be expressed as

$$ \frac{\Delta \lambda_{i}}{\lambda_{i}} = \biggl(1 + \frac{1}{n}\frac{\partial n}{\partial \varepsilon} \biggr) \varepsilon + \biggl(\frac{1}{L}\frac{\partial L}{\partial T} + \frac{1}{n} \frac{\partial n}{\partial T}\biggr)\Delta T, $$
(1)

where n and L are the effective refractive index and length of the F–P cavity, respectively; ε=ΔL/L, indicates the applied strain, ΔL is the strain-induced change in cavity length; \(\frac{1}{n}\frac{\partial n}{\partial \varepsilon} \varepsilon\) is the strain-induced change in index; \(\frac{1}{L}\frac{\partial L}{\partial T}\Delta T\) and \(\frac{1}{n}\frac{\partial n}{\partial T}\Delta T\) are the temperature-induced changes in cavity length and index, respectively.

Fig. 2
figure 2

Reflection spectra of the sensor system under a 30-dBm 1395-nm pump and different powers of the 1480-nm pump

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Fig. 3
figure 3

Reflection spectra of the sensor system with and without the F–P sensor

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The gain spectrum of 20-dB SNR around 1582 nm and one of the resonance spectra of the F–P sensor can be regarded as a Gauss spectrum. When the reflection spectrum of the F–P sensor shifts, the ith resonance peak power of the sensor is simultaneously intensity modulated by the slope of the gain spectrum, and it can be given by

$$ P_{Ri} = \alpha\int_{0}^{\infty} I_{S}R_{R}(\lambda)T_{G}(\lambda) d\lambda, $$
(2)

where I S is the light intensity of the input light, R R (λ) is the spectral reflectance function of the resonance spectra of the sensor, and T G (λ) is the spectral transmittance function of the gain spectrum of 20-dB SNR around 1582 nm.

From Fig. 3, it can also be seen that the side gain spectrum, within the range of 1565–1576 nm, has a quasi-linear slope, and it can be regarded as a quasi-linear filter. The resonance peak, located in the above wavelength range, is simultaneously quasi-linearly intensity modulated by the side gain spectrum when the spectrum of the F–P sensor shifts. When a wavelength shift of Δλ occurs, a corresponding intensity variation ΔP RL is detected, which can be expressed as

$$ \Delta P_{\mathrm{RL}} \approx k\Delta\lambda, $$
(3)

where k is a coefficient, describing the quasi-linear effect of the quasi-linear slope.

3 Experimental results and discussions

Figure 4 shows the measured reflection spectral response of the sensor to strain. When a longitudinal strain is applied to the sensor, the reflection spectrum will experience a red shift. The resonance peaks of the F–P sensor are simultaneously intensity modulated by the slope of the gain spectrum. Figure 5 shows the measured relationship between the resonance wavelength/peak power and strain for the resonance peak with mark 1. The wavelength of the resonance peak varies linearly with the increase of the strain, with a correlation coefficient square of 0.9991, and the strain sensitivity reaches 2.44 pm/με, while the resonance peak power varies quadratically with the increase of the strain. Moreover, it is highly sensitive to the strain, a big power variation of 14 dB occurs when the strain changes from 0 to 625.2 με. We also tested the thermal response of the sensor.Figure 6 shows the measured relationship between the resonance wavelength/peak power and temperature. A good linear relationship between the wavelength and temperature is obtained, with a correlation coefficient square of 0.9969. The temperature sensitivity is 0.87 pm/°C. Under the 0.02-nm wavelength resolution of the OSA, the strain resolution is 8.2 με while the temperature resolution is 23 °C. The sensor can be regarded as temperature insensitive when the ambient temperature variation range is <23 °C. It can be seen that the resonance peak power varies quadratically with the increase of the temperature. Only 0.168-dB power variation occurs when the temperature changes from 30 to 100 °C. It is negligible. The low thermal characteristic of the sensor is attributed to its hollow core structure. It can be seen that the resonance peak with mark 2 is located within the quasi-linear slope of the side gain spectrum. Figure 7 shows measured relationship between the peak power and strain for the resonance peak with mark 2. The intensity sensitivity is 0.0038 dB/με.To detect the power variation of the sensor with a photo-detector, a tunable band filter can be used to select the band of the monitored resonance peak. Here, the Raman-effect induced gain spectrum served as the optical source and also a filter simultaneously. Moreover, the second-order Raman pump and amplification technique based system makes the low reflectivity F–P sensor for long-distance sensing possible. The low reflectivity F–P sensors can also be space division multiplexed [6] in a long-distance based on the system. It should be noted that the system is also applicable for the FBG sensors, with the central wavelength located in the wavelength range of the gain spectrum. Since we do not have the suitable FBG sensors, with the central wavelength located in the wavelength range of the gain spectrum, we just demonstrate its applications for F–P sensors since their resonance peaks locate in the wavelength range of the gain spectrum. Due to the power limitation of the two Raman pumps, we just demonstrated a 50-Km fiber sensor system. Longer fiber sensor system can be realized by adopting the Raman pumps with higher power.

Fig. 4
figure 4

Reflection spectral response to strain

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Fig. 5
figure 5

Measured relationship between the resonance wavelength/peak power and strain

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Fig. 6
figure 6

Measured relationship between the resonance wavelength/peak power and temperature

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Fig. 7
figure 7

Measured relationship between the peak power and strain

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4 Conclusions

In conclusion, we have demonstrated a novel technique to realize a long-distance fiber sensor system based on the second-order Raman pump and amplification. The Raman-effect induced gain spectrum could serve as the optical source for the long-distance fiber sensor. Moreover, it could also serve as the filter to intensity modulated the wavelength shift of the fiber sensor. It is expected to have practical application for the long-distance fiber sensor system.