The linewidth, the threshold, and frequency shift of the stimulated Rayleigh scattering (STRS) in single mode fiber (SMF-28e), large effective area fiber (LEAF) and polarization maintaining fiber (PMF) have been studied using heterodyne detection to separate the Brillouin scattering with a fiber laser for the first time to the best of our knowledge. Experimental results show that the linewidth of STRS and spontaneous Rayleigh scattering are ~9 kHz, ~10 kHz, and ~11 kHz, and ~25 kHz, ~30 kHz, and ~27 kHz for SMF-28e, LEAF and PMF, respectively. The threshold power for STRS for 2km SMF-28e, 7km LEAF, and 100m PMF are 11dBm, 4.5dBm and 16.5dBm, respectively. The measured Rayleigh gain coefficient is a 2 × 10−13 m/W for SMF-28e. Also, weak frequency shift could be observed when input power is large enough before SBS occurred. Because of the properties of narrower bandwidth and lower threshold power of STRS in fibers, some of applications, such as narrower filter, could be realized.
©2010 Optical Society of America
Optical fiber is an ideal medium to study nonlinear optical effects with enhancement factor of 109 compared with the bulk medium, due to two important factors of ultra low attenuation coefficient and very small core diameters . Among three scattering mechanisms of Rayleigh, Brillouin and Raman, stimulated Brillouin scattering (SBS) and stimulated Raman scattering have been widely investigated in optical fibers, which are also widely used in optical fiber sensing and communication systems recently [1–7]. Spontaneous Rayleigh scattering is associated with the density fluctuations partly caused by local thermal fluctuations in mediums. It has been widely studied for its birefringence and polarization properties in the optical time-domain reflectometer and communications [8–10]. The stimulated Rayleigh scattering (STRS) phenomena was firstly observed by Rank et al in liquids  and in gases by Wiggins et al  after Herman and Gray presented the theoretical prediction  of STRS to account for the absorption process. Later another type of STRS caused by entropy waves was investigated in different absorbing liquids and in some glasses . Because the absorption coefficient of optical fiber is ~0.03dB/km, which is much smaller than that of gas or liquid, the measurement length in optical fiber is often much longer than the liquid or gas samples, this means another effect, SBS can build up quickly which prevents the study of the STRS in optical fiber. While in liquid and gas, the situation is different, because of the short sample length, SBS requires much higher power than that of the STRS, even though the gain coefficient of STRS in gas or liquid is two orders lower than that of Brillouin, while in optical fiber, due to the long fiber length, the threshold power for STRS and SBS is in the same magnitude. On the other hand if a short fiber length is used, the weak Rayleigh scattering signal will be buried in the noise floor which makes it very difficult to measure the Rayleigh linewidth for the purpose of separation of the Brillouin scattering: the large bandwidth (tens of MHZ) of the Rayleigh scattering in liquid and gas  makes it possible for direct detection, while in optical fiber we find it is tens of kHz, especially long fiber length is required to observe the weak Rayleigh scattering. This requirement is the same as that of SBS for low threshold power; hence the SBS is a hurdle to study the STRS. Up to now, to our knowledge, no report is found on the STRS in optical fibers for its threshold and linewidth change process from spontaneous to stimulated Rayleigh scattering. The competition between the SBS and STRS has prevented the growth of the STRS, as the narrow linewidth STRS decreases and its power increases exponentially in long fiber with increase of the pump power until onset of the SBS process which has much higher gain coefficient (two orders of magnitude higher), hence the scattered power is dominated by the SBS which can be characterized easily by the transmitted and backscattered power, while the STRS must be characterized by the coherent detection method due to its narrow (20-30KHz) linewidth for the purpose of separating the SBS process, and STRS has very small input power range due to SBS generation .
In this letter, we report on the experimental study of spontaneous and stimulated Rayleigh scattering in normal single mode fiber (SMF-28e, the mode field area is about 83.7μm2), large effective area fiber (LEAF, the mode area is ~72.2μm2) and polarization maintaining fiber (Panda PMF, the mode field area is about 86.54μm2). Experimental results show that the bandwidths (FWHM, full bandwidth at half maximum) of STRS are 9 kHz, 10 kHz, and 11 kHz, compared with that of spontaneous Rayleigh scattering (SponRS) of ~25 kHz, ~30 kHz, and ~27 kHz for SMF-28e, LEAF and PMF, respectively. The threshold power for 2km SMF-28e, 7km LEAF, and 100m PMF are 11dBm, 4.5dBm and 16.5dBm, respectively. For SMF, LEAF and PMF the product of the threshold power and the fiber length is a constant, which are about 21, 15 and 4.5 mW·km, respectively. This difference may be explained by the effective core and polarization factors. The measured Rayleigh gain coefficient is about 2 × 10−13 m/W, 2.8 × 10−13 m/W, and 1.0 × 10−12 m/W for SMF-28e, LEAF and PMF, respectively. Also, some frequency shift characteristics of STRS are studied in the paper. Because of the narrow bandwidth of STRS in fibers, some applications, such as narrow filter and super narrow laser source, could be realized using STRS. Furthermore, it is very important to understand the properties of STRS in fibers to optimize higher power fiber laser system and power limit of OTDR.
2. Linewidth and gain spectra of STRS
The experimental setup of measuring Rayleigh signal of PMF is shown in Fig. 1 . A fiber laser with bandwidth of 11.2 kHz and wavelength of 1.55μm is used as a CW signal. An attenuator is used to adjust the power value after the output signal of fiber laser is amplified by using an erbium-doped fiber amplifier (EDFA), whose maximum gain could be up to 30dB. One beam with linear polarization status can be generated by using the polarization beam splitter (PBS) because PBS can split to two beams with orthogonal linear polarization from input light. The backward Rayleigh signal is dropped from polarization maintaining circulator and is launched into a Mach-Zehnder interferometer (MZI) which is realized by two 3dB couplers. An acoustic optic modulator (AOM, Brimrose) is added into upper arm of MZI to generate frequency shift of ~200MHz, and the normal single mode fiber of 75km is used to generate ~125μs delay which is larger than the coherent length of the fiber laser. Because of beating between the Rayleigh signal with frequency shift of ~200MHz and the delayed Rayleigh signal, the lower central frequency of the output signal from MZI should be ~200MHz, which can be detected and amplified by using photon detector (PD, Thorlabs PDB130C-AC) with frequency response range of 100Hz~350MHz. And finally, the spectra of Rayleigh signal could be measured by using electrical spectrum analyzer (ESA, Agilent E4446A). Considering that the length of delaying fiber is 75km, the frequency resolution of MZI is about ~0.9kHz according to ref. . Obviously, if Rayleigh signal of non-polarization maintaining fiber is measured, PC1 and PBS should be removed and polarization maintaining circulator should be replaced by a normal circulator in Fig. 1. The measurement principle is the same as aforementioned.
In our experiments, 2km SMF-28e, 7km LEAF and 100m PMF are used. Figure 2 shows the experimental results about evolution of spectra, the bandwidth variation and contrast of Rayleigh signal for the three kinds of fibers. Figure 2(a), (c) and (e) show the transmission spectrum at different input power. It shows that the contrast of Rayleigh scattering signal increases at first, and then decreases when the background level is increased, which means the SBS signal occurred when input power reaches the SBS power region. Figure 2(b), (d) and (f) clearly show the relationship among the bandwidth of fiber laser and Rayleigh scattering, contrast of Rayleigh signal, and input power. The bandwidth of fiber laser after it is amplified by using EDFA is ~11.2kHz (blue curve). And the bandwidth of the SponRS is ~25kHz (shown in Fig. 2(b)), ~30kHz (shown in Fig. 2(d)), and ~27 kHz (shown in Fig. 2(f)), respectively. It is noted that the bandwidth measurement error of the SponRS is about ± 1.5kHz because the Rayleigh power is too low to measure 3dB bandwidth, even for 2km fiber length. The bandwidth of Rayleigh (the part of curves marked error bar in Fig. 2 (b), (d) and (f)) is measured by using the bandwidth at half energy when input power is very low. When input power is more than 11dBm, 4.5dBm and 16.5dBm, but it is less than 17dBm, 11.6dBm, and 26dBm, for SMF-28e, LEAF and PMF, respectively, the bandwidth of Rayleigh scattering signal vary very little. We think STRS occurred in the region, which is about 6dB except for PMF with 10dB power range. This power range is much smaller than that in the SBS. The bandwidth 1/τR of the three kinds of fibers are 9 kHz, 10 kHz and 11 kHz, respectively, and the threshold power of STRS for the fibers are respectively 11dBm, 4.5dBm and 16.5dBm. However, when input power is more than 17dBm, 11.6dBm and 26dBm for SMF-28e, LEAF and PMF, respectively, input power is transferred to SBS process because the gain factor of SBS is two orders larger than that of STRS, finally STRS disappeared. We can see from Fig. 2(b), (d) and (f) that the bandwidth of Rayleigh signal begins to increase and the contrast begins to sharply decrease and finally disappeared. The large background or baseline accounts for the growing of Brillouin scattering of 20MHz bandwidth at 1550nm. In order to study the threshold power dependence of STRS to the fiber length, we did the threshold measurement for 2km SMF-28e, 7km LEAF and 100m PMF, they are 10.2 dBm, 3.4 dBm and 9.4 dBm, respectively. The products of threshold power and length are approximately constants for long and short fiber lengths of three kinds of fibers: 21, 15 and 4.5 mW·km for SMF-28e, LEAF and PMF, respectively, which has the same properties as that of the SBS [1, 15]. Two reasons account for large difference among SMF-28e, LEAF and PMF on their threshold. 1) threshold power depends on the fiber length, effective core area and polarizations, with different lengths and effective core areas of SMF-28e, LEAF and PMF, their thresholds are expected to be different; 2) The efficiency of simulated Rayleigh scattering in PMF fiber are higher compared with the normal optical fibers, such as SMF-28e and LEAF. By calculating the contrast change in the STRS power of three fibers we find that the Rayleigh gain coefficient is about 2 × 10−13 m/W, 2.8 × 10−13 m/W, and 1.0 × 10−12 m/W for SMF-28e, LEAF and PMF, respectively, in which PD transform efficiency and the attenuation coefficient of ESA should also be considered. The gain coefficient of SBS for the three kinds of fibers in our experiments are 2.14 × 10−11 m/W, 1.29 × 10−11 m/W, and 3.20 × 10−11 m/W, they are similar to 5x10-11m/W for SMF-28e , and they are two orders higher than that of STRS except for PMF which is of only one order of magnitude difference between STRS and SBS.
We also can see from Fig. 2 that the threshold value of STRS is 6dB lower than that of SBS, and 3dB line width of STRS is four orders lower than that of SBS in optical fiber, while in liquid and gas it is of two orders of magnitude difference. Among SMF-28e, LEAF and PMF fibers, the 3dB line width including STRS and SBS are almost the same as they are determined by the relaxation time (τR) with the similar fiber core materials. Because the polarization state in single mode optical fiber changes and Rayleigh scattering is polarization dependent [1, 17], this is not the case in PMF; hence the gain coefficient of PMF is much larger than that of SMF-28e and LEAF.
For SponRS, entropy fluctuation is the dominating factor. Because entropy waves do not propagate, the nonlinear polarization is proportional to entropy fluctuations which can give rise only to an unshifted component of the scattered light. This model does not consider the local polarization state change in optical fiber, which is special in optical fiber due to birefringence, not for the case of bulk glass. The bandwidth of this component in glass can be given by δSTRS :18], ρ = 1g/cm3, cp = 0.25 cal/g·°C, κ = 0.0064cal/s·cm·°C, k = 2π/λ. η is the limited factor of fiber, which is on the order of 10−4 by our experimental results because the bandwidth of Rayleigh is about 25 kHz in optical fibers. This factor can be considered as the waveguide and birefringence contributions.
3. Frequency shift of spectra of STRS
Herman and Gray predicted that STRS of pulse light in absorbing liquids would experience an anti-Stokes shift due to a coupling between spontaneous thermal fluctuations and the incident light . On the other hand, the STRS of pulse light would experience a Stokes shift due to electrostriction . The maximum gain gR(max) could be given by :Eq. (2) could be obtained, respectively. Whether the frequency of STRS spectra shifts mainly depends on the synergism of thermal fluctuations and electrostriction.
The measurement system shown in Fig. 3(a) is used to measure frequency shift of STRS in optical fibers. Compared with the system shown in Fig. 1, the difference is that the two input beams of MZI come from fiber laser and Rayleigh scattering signal, respectively. 100km SMF-28e fiber was used to delay upper beam of MZI, which makes the frequency resolution is ~0.6kHz according to ref. . The frequency shift ∆f can be calculated by subtracting the central frequencies measured by using systems shown in Fig. 1 and Fig. 3(a) under the same power of input for the fiber under test, respectively. Here we measure central frequency by getting much more symmetrical points in the symmetrical profile, and the frequency shift is the difference of the two measured central frequency, it can be smaller than the laser linewidth. The positive ∆f means anti-Stokes frequency shift occurred, and the minus ∆f means Stokes frequency shift. Experimental results show that there is no frequency shift when input power is in the range of −10dBm~15dBm and −30dBm~10dBm for 2km SMF-28e and 7km LEAF (shown in Fig. 3 (b)), respectively. For 100m PMF, when input power is in the range of −10dBm~20dBm, there is also no frequency shift, however, when input power is larger than 20dBm, the frequency shift ∆f begin to decrease and finally, it is up to ~-1.0kHz. The reason of the observed different phenomena for the three kinds of fibers is that the role of absorption and electrostriction are the same magnitude at low input power, however, when input power keeps increasing, the electrostriction effect is dominant, the frequency of STRS will shift to lower frequency. For 100m PMF, when input power is larger than 25dBm, the SBS occurred, which quickly occupied the input power because its gain coefficient is two orders higher than that of STRS. The stimulated Brillouin scattering will quickly build up if the fiber is longer, such as 2km SMF-28e or 7km LEAF, so we cannot observe the frequency shift in 2km SMF-28e or 7km LEAF fiber. If SBS threshold value can be largely suppressed for fibers, we believe a much higher frequency shift could be observed. The detailed frequency shift of STRS of optical fibers is currently being studied in our lab because some suppression methods of SBS threshold value should be provided in order to measure the small frequency shift.
In conclusions, we investigated the SponRS and STRS in three kinds of optical fibers: SMF-28e, LEAF and PMF by using fiber laser with 1.55μm and 11.2 kHz bandwidth. The bandwidth of STRS for three kinds of fibers is about 9 kHz, 10 kHz, and 11 kHz, which is narrower than that of SponRS. Also, the threshold powers are measured for the three fibers and the values are 11dBm, 4.5dBm and 16.5dBm, respectively, which are 6-10 dB lower than that of SBS. And the measured Rayleigh gain coefficient is about 2 × 10−13 m/W, 2.8 × 10−13 m/W, and 1 × 10−12 m/W for SMF-28e, LEAF and PMF, respectively, which are about two orders lower than that of SBS except for PMF which is of only one order magnitude difference due to the polarization maintaining property. This indicates that, STRS in optical fibers is a weak effect; however, because of its properties of narrower bandwidth and lower threshold power, some of applications, such as narrower filter, could be realized.
This work was supported by NSERC Strategic Grant and Discovery Grant of Canada.
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