Stimulated Brillouin scattering (SBS) has proved to be useful in the generation of optically tunable acoustic grating known as Brillouin dynamic grating (BDG) in polarization maintaining fibers (PMFs) [1]. Several interesting applications have been reported based on the BDG, such as temperature and strain sensors with high sensitivity [2, 3, 4], birefringence sensors [5], tunable delay lines [6], time-domain distributed sensors with extremely high resolution [7], and all-optical signal processing [8]. So far only PMFs have been adopted for the generation and the application of the BDG, since the operation principle strongly depends on the local birefringence of the medi um. In this Letter, the operation of the BDG is carried out based on conventional single-mode fibers (SMFs), and the characterization is reported, where the experimental results show that the BDG can be generated by proper control of the polarization in the interaction of SBS within an SMF, and the bandwidth of the observed grating can be made much narrower than in the case of PMF thanks to the better uniformity of the fiber. When a $100\mathrm{m}$ SMF is used, a BDG with a maximum reflectance of 8% and a spectral bandwidth of about $2.4\mathrm{MHz}$ is achieved, which is, to the best of our knowledge, a Bragg reflector with the narrowest bandwidth ever reported in fibers.

Figure 1 shows the schematic of the BDG operation in an optical fiber. Counterpropagating pump 1 and pump 2 in one polarization (x-pol.) build up acoustic waves by SBS to be used as the BDG, and a probe wave in the orthogonal polarization (y-pol.) is propagated in the direction of pump 1 to be reflected by the grating for detection (probe reflection). The frequency offset between two pump waves is set to the Brillouin frequency (${\nu }_B$) of the fiber for SBS, and the frequency separation $\mathrm{\Delta }f$ between pump 1 and the probe linearly depends on local birefringence of the fiber [1]. When a PMF is used as a BDG medium, a $\mathrm{\Delta }f$ as large as several tens of gigahertz is typically observed, and the probe reflection is easily separable from the pump waves by applying an optical filter and a polarization beam splitter (PBS).

The operation condition is different when an SMF is used as the BDG medium. The optical frequencies of the probe and the probe reflection are expected to be the same as those of pump 1 and pump 2, respectively, which makes it difficult to separate the BDG reflection from the SBS signal (pump 2) with a good extinction ratio. Additionally, proper control of the input polarization states of the interacting waves is crucial due to the random evolution of the polarization states within the fiber. Meanwhile, one of the potential advantages of BDG operation based on SMF is the better uniformity of the medium compared to the case of PMF, which may lead to enhanced performance of the grating in terms of the bandwidth and the reflectance. In previous work, a $10\mathrm{m}$ PMF needed to be stretched with the jacket removed to achieve a section with uniform birefringence to realize a $10\mathrm{MHz}$ bandwidth [9], which may reduce the practicality of the BDG. On the contrary, the simple and symmetric internal structure of SMF is expected to provide better uniformity and easier handling.

The experimental configuration for the operation of the BDG based on SMF is depicted in Fig. 2. A distributed feedback laser diode (DFB-LD) at $1550\mathrm{nm}$ was used as a light source, and the output was split into two arms by a $70/30$ coupler. The light wave through one (30%) of the arms was directly used as pump 1, being amplified by a high-power Er-doped fiber amplifier (EDFA). A single-sideband modulator (SSBM) and a microwave generator were used to modulate the output through the other arm (70%) to generate pump 2, with the frequency downshifted from pump 1 by ${\nu }_B$ of the fiber ($\sim 10.877\mathrm{GHz}$). An EDFA was applied to control the power of pump 2, and a $30/70$ coupler was used to split the EDFA output into the directions of pump 2 (30%) and the probe (70%). In the probe direction, an electro-optic modulator (EOM) and another microwave generator were used to generate the probe wave, whose frequency can be accurately controlled and swept around that of pump 1, and another EDFA was used to control the power of the probe. In this way, the frequency offset and the power of the three optical waves (pump 1, pump 2, and the probe) can be accurately controlled with high stability. The inset in Fig. 2 shows the optical spectra of the output from the SSBM (black) and the EOM (red) measured by an optical spectrum analyzer. Pump 1 and the probe were combined by a PBS to keep the orthogonal states of the polarization along the fiber, and a polarization controller (PC) was inserted in the direction of pump 2 for both maximizing the SBS between pump 1 and pump 2 and minimizing the crosstalk of pump 2 into the direction of the probe at the same time. Two photodiodes (PD1 and PD2) were used to monitor the power of the probe reflection and pump 2, respectively. A conventional step-index SMF with a mode field diameter of $9.3\mathrm{\mu m}$, a cladding diameter of $125\mathrm{\mu m}$, and a $245\mathrm{\mu m}$ acrylate jacket was used as the fiber under test (FUT). Four different lengths ($L=11$, 20, 50, and $100\mathrm{m}$) were prepared, and the fibers were loosely wound with a radius of about $20\mathrm{cm}$. For each of the fiber examples, the reflection spectrum of the probe was measured by PD1 connected to a digital oscilloscope, while the frequency offset ($\mathrm{\Delta }\nu$) between two pump waves was controlled in the vicinity of ${\nu }_B$ and the frequency offset ($\mathrm{\Delta }f$) between pump 1 and the probe was swept within a span of $160\mathrm{MHz}$. The acquired spectra were screen-averaged 64 times to reduce noise.

Some examples of the measured spectra of the probe reflection for each of the FUTs are depicted in Figs. 3a, 3b, 3c, 3d as a function of $\mathrm{\Delta }f$. It is seen that the reflection spectrum decently fits with a Gaussian curve (red) for each case, and the bandwidth is decreased as the fiber length increases, which is a similar feature also observed in the BDG based on PMF [9]. It should be noted that the polarization of pump 2 was carefully controlled for each measurement to minimize its crosstalk to the probe port, which was limited by the polarization extinction of the PBS ($\sim 20\mathrm{dB}$) and was subtracted from the original data in the construction of the reflection spectrum.

The variation of the reflectance and the bandwidth (FWHM) of the BDG with respect to the power of pump 1 and pump 2 are shown in Figs. 4, 5, respectively. In Figs. 4a, 5a, the increase of the reflectance is clearly seen as more pump power is applied, and the slope becomes larger as the length of the fiber increases. The gradual drop of the slope in the case of the $100\mathrm{m}$ FUT in Fig. 5a is attributed to the effect of the pump depletion, which is confirmed by a similar drop in the Brillouin gain of pump 2 from 9.9 to $7.1\mathrm{dB}$ as pump 2 increases. On the contrary, the variation in the reflection bandwidth of the BDG is negligible with respect to the pump power, even regardless of the occurrence of the pump depletion as confirmed in Figs. 4b, 5b.

Figure 6a depicts the measured reflectance as a function of the fiber length with pump 1 of $250\mathrm{mW}$ and pump 2 of $14\mathrm{mW}$, where the reflectance becomes larger as the length of the fiber is increased, with a maximum reflectance of 8% with the $100\mathrm{m}$ FUT. Figure 6b shows the measured bandwidth (FWHM) of the BDG as a function of the length of the fiber compared to the theoretical graph (curve) of a weak and uniform FBG [9], where the overall drop of the measured bandwidth according to the grating length is clearly seen. It is notable that a large deviation, as much as $1.85\mathrm{MHz}$, from theory is observed, particularly in the cases of $50\mathrm{m}$ and $100\mathrm{m}$ fibers. Such a large difference may be attributed to the combined effects of the intrinsic linewidth of the DFB-LD ($\sim 1\mathrm{MHz}$) and the bending-induced birefringence of the fiber. In current configuration, the birefringence ($\mathrm{\Delta }n$) induced by a bending radius of $20\mathrm{cm}$ is calculated to be $\sim 1.3\times {10}^{-8}$ [10], which corresponds to a deviation of $\sim 1.7\mathrm{MHz}$ in the center frequency of the BDG [1], similar to the observed errors.

It is also remarkable that a measured maximum reflectance of 8% is only about $1/10$ of the expected value ($\sim 77\%$) based on the basic theory of the BDG [9]. It seems the origin of such a large discrepancy cannot be fully explained at present, even considering the broadening of the reflection spectrum, and requires further investigation. Another notable factor that may influence both the bandwidth and the reflectance of the generated BDG is the nonuniformity of the grating. It is obvious that the generated BDG in the long fibers ($50\mathrm{m}$ and $100\mathrm{m}$) is not uniform, considering a Brillouin gain of pump 2 as large as $10\mathrm{dB}$. It seems further study is also necessary to clarify this point.

As a final experiment, the reflection spectra of the BDG from the $100\mathrm{m}$ fiber were measured while sweeping the frequency offset $\mathrm{\Delta }\nu$ between two pump waves with a step of $4\mathrm{MHz}$. As depicted in Fig. 7a, the variation of the maximum reflectance of the BDG faithfully reflects the shape of a Brillouin gain spectrum (black curve), while the bandwidth of each spectrum remains less than 10% of the Brillouin gain bandwidth ($\sim 29\mathrm{MHz}$) as confirmed in Fig. 7b (squares). Additionally, the center frequency shift of the BDG reflection was negligible ($<0.2\mathrm{MHz}$) under the sweep of $\mathrm{\Delta }\nu$. This is a reasonable result considering that the sweep was applied only to pump 2 and the frequency of pump 1 was kept constant, which determines the center of the BDG.

In conclusion, the observation and the characterization of a Brillouin dynamic grating in a conventional SMF was demonstrated for the first time (to our knowledge). This grating was shown to be advantageous with the narrower reflection bandwidth, the larger reflectance, and the easier handling compared to the PMF-based BDG. It is expected that the SMF-based BDG could provide a powerful tool for sensing applications as an ultranarrowband tunable filter or an indirect way of measuring Brillouin gain spectrum [7].

This work was supported by the National Research foundation of Korea (NRF) grant funded by the Korean Ministry of Education, Science, and Technology (MEST) (2011-0003429).

 

Fig. 1 Schematic of the BDG operation in an optical fiber.

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Fig. 2 Experimental setup of the BDG based on the SMF. SSBM, single-sideband modulator; EOM, electro-optic modulator; PBS, polarization beam splitter; EDFA, Er-doped fiber amplifier.

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Fig. 3 Examples of the reflection spectrum from the BDG written in the SMF with a length of (a) $11\mathrm{m}$, (b) $20\mathrm{m}$, (c) $50\mathrm{m}$, and (d) $100\mathrm{m}$.

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Fig. 4 (a) Reflectance and (b) FWHM of the BDG as a function of the power of pump 1.

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Fig. 5 (a) Reflectance and (b) FWHM of the BDG as a function of the power of pump 2.

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Fig. 6 (a) Reflectance and (b) FWHM of the BDG with respect to the fiber length. Red curve shows the theory of a uniform grating.

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Fig. 7 (a) Brillouin gain spectrum (black) and BDG spectrum as a function of $\mathrm{\Delta }\nu$; (b) FWHM (square) and center frequency shift (circles) of the BDG as a function of $\mathrm{\Delta }\nu$.

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