1 Introduction

Stimulated Brillouin scattering (SBS) has attracted great attention in recent years because of its broad range of applications [1–3]. The SBS can be realized in gases, liquids, and solids. Gaseous media are difficult to handle due to high pressure. Organic liquids such as CS2 have high Brillouin gain and low absorption in a wide spectral range. However, ordinary focusing geometry can cause optical breakdown, which results in low SBS reflectivity and stability [4]. Although heavy fluorocarbon (FC) and Perfluoropolyether (HT) liquids have high threshold for optical breakdown, they have low gain coefficient, and SBS temporal modulations easily occur due to a short phonon lifetime [5, 6]. Single-mode or multimode quartz fibers are the common solid media. They have advantages of easy handling and low SBS threshold. Unfortunately, the SBS pulses and transmitted pulses of these fibers display serious modulations [7, 8]. Moreover, the Brillouin gain of quartz glasses is very low and needs to be compensated by large length. In some applications, the temporal waveform of the SBS should be preserved [9], whereas it is difficult to achieve in the ordinary SBS phase conjugating mirror (PCM) because of modulations mentioned above and a steep rising edge. High-fidelity SBS pulses have been obtained using a prepulse injection [10] and Stokes seed injection [11], but their optical configurations were more complicated.

Liquid-core optical fiber (LCOF) consists of flexible capillary tubing filled with liquids characterized by sufficiently high refractive indices. Experiments have demonstrated that the threshold peak power of the SBS was as low as 70 W, and the reflectivity and phase fidelity reached 50 % and 80 % in LCOF contained CS2 with 500 ns pulses at 1064 nm wavelength, respectively [12]. Nevertheless, the spectral characteristics of the backscattered beam, the SBS reflectivity, the pulse-shape (PS) fidelity, and phase conjugation (PC) fidelity in LCOF with a short pump pulse were not observed experimentally. In addition, the thresholds for stimulated Raman scattering (SRS) in LCOFs also decrease dramatically for a laser with the pulse width of the order of several ns [13]. The relationship between SBS and backward SRS (BSRS) was not clearly understood. These are of great importance for applications of SBS in LCOF such as phase conjugation or pulse shaping. In this work, we experimentally demonstrate that the LOCF can synthesize the advantages of liquid media and quartz fibers, and use short LOCF filled with CS2 to achieve simultaneously high SBS reflectivity, PS fidelity, and PC fidelity.

2 Experimental results and discussions

The experimental setup is depicted in Fig. 1. A passively Q-switched ND:YAG laser produces single longitudinal quasi-Gaussian pulses with a duration of 10 ns and linear polarization at 1 Hz repetition rate. An aperture of 1.5 mm is inserted into the cavity to limit the higher transversal modes. After passing through second harmonic generator (SHG) and short-wave pass filter, the output light has a wavelength of 532 nm. The laser energy is continuously varied by means of an attenuator, which consisted of a rotatable half-wave plate (λ/2) and a polarizer (P). The laser radiation transmitted through a beam splitter (BS) can be considered as the pump beam, which can be monitored in real time on ED1 and PD1. The pump energy E P is coupled into the LCOF by a lens L1 at a certain coupling efficiency C eff. The input energy E in can be defined as C eff E P. The part of the backscattered beam from the LCOF is reflected by the BS, and is directed into detectors or an optical spectrum analyzer (OSA). In order to measure the pump spectrum, a mirror M1 is located in the dashed box and used to reflect the laser beam back. The reflected beam transmitting through the BS is also introduced into the OSA. CS2 is contained in fused silica capillary tubing (Polymicro TSP) because of its high Brillouin gain coefficient (∼70 cm/GW) and high refractive index (1.6). As a result, this LCOF has a large acceptance angle or numerical aperture (0.68).

Fig. 1
figure 1

Experimental setup, SHG, second harmonic generator; F, short-wave pass filter; P, polarizer; BS, beam splitter; ED’s, energy detectors; PD’s, photodiodes; L 1, lens; Ms, mirrors; LCOF, liquid-core optical fiber; OSA, optical spectrum analyzer

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We firstly analyze the spectral component of the reflected beam from the LCOF using a spectrometer or a Fabry–Perot (F-P) etalon at the location of OSA shown in Fig. 1. The normalized spectrum shown in Fig. 2 is recorded by the spectrometer (Ocean optics USB4000), which are obtained using the input energy of 200 μJ and the LCOF with an internal diameter (ID) of 300 μm and a 2 m length. We can see that two peaks are shown. One is at 532 nm consisting of Rayleigh and Brillouin scattering; the other is at 551 nm corresponding to the first Stokes line involved in the Raman scattering. There is no anti-Stokes component in it, which indicates that SRS occurs [13]. To distinguish spectral detail in the peak at 532 nm, F-P etalon with the free spectral range of 10 GHz is used. Figure 3 shows the measured results. The spectrum of the backscattered light from the LCOF is given in Fig. 3(a). Only one set of interference fringe is recorded by CCD(MTV1881EX). To analyze its spectrum characteristics, the partial pump beam is also directed into F-P etalon. Figure 3(b) shows F-P interferogram of the pump. The backward scattered light and the pump beam simultaneously enter into the F-P etalon for measuring the frequency shift between them; the measured spectrum is depicted in Fig. 3(c). By comparison, we can see that the inner circle is the backscattered component and the outer one is the pump component. Their frequency difference is calculated as 7.7 GHz, which is typical Brillouin shift of CS2 at room temperature [8]. Therefore, the SBS dominates in the backward scattering from the LCOF at this time. Compared to the SBS, spontaneous Rayleigh scattering is too weak to be recorded in the CCD (as shown in Fig. 3(a)), while the intensity of the BSRS is much lower in the measured range. The maximum BSRS reflectivity is approximately 1 % (see below). These experimental results are similar to those in the water cell [14, 15]. Differently, the thresholds for the SBS and BSRS decrease sharply owing to the special structure of the LCOF.

Fig. 2
figure 2

Normalized spectrum of the reflected beam from the LCOF using the spectrometer

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Fig. 3
figure 3

Measured spectra using the F-P etalon. (a) SBS spectrum, (b) pump spectrum, and (c) SBS and pump spectra

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We next measure the reflectivity of the LCOF. A prism is used to split the backscattered beam into a SBS and BSRS which are detected by ED3 and ED4, respectively. Taking into account the losses ε of the quartz window of the end cell of the LCOF, the energy E S can be expressed as E refl/[r(1−ε)], where E refl is measured energy on ED3, and r is the reflection factor of the BS. Therefore, the SBS reflectivity of the LCOF is the ratio of E S on E in [16]. The reflectivity of BSRS can be obtained with the similar way. In the experiment, the energy detectors used are Newport 818E-10-25-S and Ophir PE-9, PD-10, respectively. The pulse shape is recorded with a digital oscilloscope Tektronix DPO4032.

The LCOFs with different IDs and lengths have been used to study the SBS and BSRS reflectivity as well as threshold. The dependences of the SBS and BSRS reflectivity on the input energy for 300 μm ID and 2 m length are illustrated in Fig. 4. The behavior of the LCOFs with IDs of 100, 200, and 300 μm and 1 m length is similar. It can be seen that for a single longitudinal mode laser with the ns-order pulse width, the BSRS is not completely suppressed. The main reason for this may be the pumping effect of SBS on BSRS transmitted synchronously [14]. The strong SBS can excite its own BSRS,and amplify the inhibited BSRS. However, the BSRS has extremely lower reflectivity (about 2 orders lower than the SBS reflectivity) and higher threshold, and hence has little influence on the SBS.

Fig. 4
figure 4

SBS and BSRS reflectivity versus input energy for the LCOF of 300 μm ID and 2 m length

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A comparison of the dependence of the experimental LCOF reflectivities against the input energy is shown in Fig. 5. The SBS threshold E SBSth is determined according to the literature [17]. Among these LCOFs, the 100 μm ID one has a minimum threshold of 2.5 μJ and a maximum reflectivity of 92 %. Obviously, this SBS threshold is higher than the result reported in [12], since the shorter pump pulse and wavelength are used [18]. For 100, 200, 300 μm ID, 1 m long LCOFs, 90 % reflectivity is achieved at over 20 times threshold. Here, optical breakdown is not observed because of lower threshold and longer interaction length. We theoretically simulate the dependence of the SBS reflectivity on E in/E SBSth based on the transient SBS model including its spontaneous initiation from noise [19], as shown in Fig. 4. It can be seen that the experimental result is in agreement with the theoretical one. However, in a traditional bulk PCM, the reflectivity is usually limited to below 80 % at high pump energy owing to optical breakdown, and cannot reach the maximum value predicted theoretically [4].

Fig. 5
figure 5

Comparison of the SBS reflectivity of the LCOFs

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The reflectivities of 300 μm ID, 2 m long LCOF are near and somewhat below those of 1 m long one. The reason for this tendency is associated with the free gain length (FGL) in medium [20]. In experiment, the FGL in CS2 is about 95 cm. If the LCOF length L≥FGL, the effective interaction length L eff=FGL, or else, L eff=L. Thereby, 1 m and 2 m long LCOFs have the same interaction length. The reflectivity of 2 m long one is slightly lower because of more absorption losses.

Finally, we study the PS and PC fidelities of SBS in LCOFs. Figure 6(a) shows the waveforms of input pump and SBS pulses for three different input energies as well as the transmitted pump pulse. We see that the temporal shape of the SBS pulse approaches more and more the shape of the input pulse with increasing pulse energy. However, in the usual bulk liquid or optical fiber PCM, optical breakdown or pulse modulations are easy to occur at the high pump energy, resulting in bad SBS waveforms. In our experiment, no modulations are observed, and PS fidelity (is defined as the energy ratio of peak-power-normalized SBS pulse to that of the pump pulse [11]) of over 94 % is achieved at the input energy of 110 μJ corresponding to the SBS reflectivity of 77 %. Similar phenomena are observed for LCOFs with other lengths and IDs. There are four reasons for these: Firstly, CS2 has a longer phonon lifetime which can provide a better suppression of pulse modulations [5]; secondly, the LCOF structure reduces the SBS threshold, and as a result, the leading edge of the SBS pulse is no longer so steep; thirdly, waveform instability and modulations caused by optical breakdown can be avoid effectively; fourthly, increasing the input pump energy results in faster build up of acoustic grating, and hence conjugating wave, i.e., the initial delay with respect to the incident light pulse becomes shorter. Consequently, the SBS pulse closing to the pump is obtained, and a good flat-top waveform of the transmitted pump is also generated as shown in Fig. 6(b), which may have the application in the optical limiting.

Fig. 6
figure 6

Pump and SBS pulses for the input energy of 18 μJ, 30 μJ, and 110 μJ observed when 10-ns input pump pulses are transmitted through a 1 m-long and 200 μm ID LCOF (a) and transmitted pump pulse (b)

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The SBS PC fidelity is measured using energy-in-the-bucket technique, which is defined as the ratio of the backscattered SBS transmission through a far-field aperture to the input-beam transmission (84 %) through that same aperture [21]. We find that this fidelity is also improved with increasing input energy, as shown in Fig. 7. It increases from ∼70 % at 2 times threshold to 93 % at 20 times threshold. Figure 8 gives the far-field images of the input beam and the SBS wave. Their spot profiles are basically consistent. The PC fidelity is sensitive to the slope of the rising edge of the input pulse [22]. When the rising time of the incoming pulse (experimentally, 3–4 ns) is comparable with or longer than the phonon lifetime (CS2: 1.6 ns at 532 nm), the PC mode is first amplified early in the pump pulse, which saturates the input pump, suppressing other modes that cause fidelity degradation as the input energy increases. Therefore, high PS and PC fidelities are achieved simultaneously at the high pump energy.

Fig. 7
figure 7

PC fidelity versus input energy for the LCOF of 300 μm ID and 1 m length

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Fig. 8
figure 8

Far-field images of (a) the input beam and (b) the SBS wave

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3 Conclusions

The experimental results have demonstrated that SBS dominates over other scatterings in a LCOF for a ns-order laser when the input energy exceeds the threshold for stimulated scattering. It has a maximum reflectivity of 92 %, and a threshold energy of 2.5 μJ at 532 nm wavelength. High PS and PC fidelities of over 90 % are also obtained. In addition, the LCOF structure has advantages of small volume and flexible operation. It has potential applications in high reflectivity and fidelity PCM, pulse shaping, amplification of weak signals, light storage, and so on.