Stimulated Brillouin scattering properties in a single-mode tellurite glass fiber were studied using a cw laser with an operating wavelength of 1.54 µm. The Brillouin frequency shift vB and the gain linewidth Δv B were 7.882 GHz and 23.6 MHz, respectively. A Brillouin gain coefficient gB in the range of 1.47×10-10-2.16×10-10 m/W was measured. The higher gain coefficient of the tellurite fiber, together with its relatively low loss compared with other non-silica fibers, makes it a suitable candidate for realizing efficient, all-optical, slow-light devices.
©2006 Optical Society of America
When narrow-band laser radiation propagates inside an optical fiber, some of the incident light scatters backward due to the nonlinear process called stimulated Brillouin scattering (SBS) [1, 2]. This scattering creates problems for some nonlinear signal processing applications that involve using a strong continuous wave (cw) pump . SBS can however be used for amplification of light propagating in a direction opposite to the pump light. This has lead to many applications, such as in Brillouin amplifiers, lasers, and microwave signal processors [4–6]. The large Brillouin amplification that occurs in a narrow spectral region can lead to a large increase in the group index in the fiber core, which can be utilized to control the transit time inside the fiber [7, 8]. Such SBS-assisted slowing down of light has drawn considerable attention lately for its potential applications to optical buffers in future all-optical networks.
In applications involving the SBS process, it is desirable to have a medium that has a large Brillouin gain coefficient g B to lower the power requirements and also to shorten the length of fiber devices. Recently, chalcogenide fiber is reported to have a gB coefficient about two orders of magnitude larger than that of silica-based fibers . Another promising non-silica glass material that has been successfully drawn into single-mode fibers is tellurite glass, which has a high refractive index, high optical nonlinearity, and transparency region that extends to wavelengths beyond 2 µm [10–13]. Tellurite glass fibers doped with erbium reportedly have a wider gain bandwidth in the L-band region, extending to beyond 1610 nm , which is not possible with erbium-doped silica fibers Research has also been conducted to develop a photonic crystal fiber from tellurite glass with the aim of further enhancing the nonlinearity coefficient of the fiber .
A tellurite fiber with a relatively large refractive index of about 2.028 , which is about 40% higher than that of silica, is expected to exhibit a large Brillouin scattering coefficient since it is proportional to the material refractive index raised to the power of 7, i.e. n7 . To our knowledge, there are no reports on the study of SBS in tellurite fiber. In this paper, we investigate for the first time the Brillouin scattering in a tellurite glass single-mode optical fiber. The Brillouin gain coefficient was determined independently from the spontaneous Brillouin spectrum, the Brillouin threshold power, and small-signal gain measurement. The Stokes frequency shift and the Brillouin gain linewidth were also measured experimentally. Furthermore, the suitability of the fiber for application to slow light devices is also discussed.
The tellurite fiber used here was a single-mode fiber with a core diameter of 2.6 µm, Δn of 1.6%, and cutoff wavelength of about 1.3 µm. It was developed by NTT Electronics particularly for use in L-band amplifiers, and consequently, the core was doped with erbium at a concentration of about 1000 ppm (wt%). The details of the fabrication of tellurite fiber has been reported in Ref 11. The tellurite fiber was coupled to a silica fiber using a tilted Vgroove connection  with an estimated coupling loss of about 0.6 dB. In the experiments, two pieces of SMF-pigtailed fibers 2 and 3 m in length were used.
Transmission properties of the tellurite fiber were studied at the operating wavelength of 1542 nm using cw light from an external-cavity tunable laser that was amplified to a maximum power level of 30 dBm.
To study the Brillouin scattering, the 1542-nm cw light was launched into a 2-m-long tellurite glass fiber though an optical circulator, and the backscattered radiation from the fiber was observed with an optical spectrum analyzer. The intensity of the Stokes component at different pump power levels could be directly read from the optical spectrum analyzer. Heterodyne measurement [9, 16] was performed to measure the Brillouin shift with a high resolution, as well as the 3-dB gain linewidth. To this end, the backscattered light was amplified using an erbium amplifier and detected using a fast photodiode and broadband electrical amplifier. The Stokes component and a small fraction of the pump light reflected in the backward direction caused optical beating, which could be observed in an RF spectrum analyzer. We could measure the 3-dB Brillouin gain linewidth Δv B from the RF beat spectrum.
The small-signal SBS gain was determined by measuring the intensity change of a probe signal that was launched into the tellurite glass fiber in a direction opposite to the strong pump wave. The probe signal was created from the output of the same laser used for pumping, by generating optical sidebands using an electro-optic phase modulator. The change in the intensity of the lower frequency sideband was measured using the optical spectrum analyzer while the modulation frequency was varied over a frequency range of ~200 MHz centered on the Stokes frequency shift v B.
Figure 1 shows the transmission loss measured at 1542 nm at different launched powers using two pigtailed tellurite fibers 2 m and 3 m in length. At low power the fiber exhibited large loss due to the presence of erbium doping in the core. However, as the launched power exceeded ~5 dBm, the fiber became increasingly transparent as the loss began to saturate. For a pump power of 25 dBm, we estimated a loss of 0.51 dB/m (i.e. α=0.117 m-1).
The Brillouin scattering properties of the tellurite fiber were studied at 1542 nm. Figure 2 shows the optical spectra of the back-scattered light from the 2-m-long (effective length L eff was 1.78 m) fiber observed with different launched pump powers. A Stokes wavelength component at a separation of 0.063 nm at longer wavelengths could be easily observed when the power exceeded ~300 mW, and it grew by more than 40 dB as the pump power was raised to 1260 mW. Figure 3 shows the power level of the light backscattered from the two fibers, 2 m and 3 m in length, as a function of the launched pump power. Brillouin threshold powers, defined at pump power when the Stokes began to grow exponentially, were found to be about 1000 mW and 630 mw for the 2-m and 3-m fibers, respectively, as shown in the inset of Fig. 3.
According to the small-signal steady-state theory of stimulated Brillouin scattering , the pump power Pth required to reach the Brillouin threshold in a single-pass scheme is related to the Brillouin gain coefficient g B by the following equation:
Here, Pth is power corresponding to the Brillouin threshold, A eff is the effective cross-sectional area defined as Aeff =π (ωo is the 1/e2-intensity radius of a Gaussian distribution), Leff is the effective length. K is a constant that depends on the polarization properties of the fiber, which is 1 if the polarization is maintained and 0.5 otherwise [15, 18]. However a later report  showed that a value of 0.667 instead of 0.5 is more appropriate for K, when the fiber is lowbirefringence and much longer than the polarization beat length. Although the fibers used in the experiment are rather short, (2–3 m) using K=0.667, P th=1000 mW, A eff=9.18 µm2, and Leff =1.78 m, and in Eq. (1), we obtained the peak Brillouin gain coefficient gB=1.62×10-10 m/W. Similarly, using the threshold power for the 3-m long fiber, we obtained gB=1.81×10-10 m/W.
The Brillouin shift and linewidth could be observed with a higher resolution from the heterodyne measurement. The RF spectra that resulted from the beating between the pump laser and the Stokes component for the 2-m long fiber is shown in Fig. 4. The Brillouin gain spectrum showed a peak at 7.882 GHz (v B). By fitting the spectrum with a Lorentzian spectral profile (dashed curve), we obtained a 3-dB Brillouin gain linewidth (Δv B) of 23.6 MHz.
where n is the refractive index, p12 is the longitudinal elastooptic coefficient, c is the velocity of light, λP is the wavelength, ρ is the material density, v A is the acoustic velocity, Δv B is the linewidth of spontaneous Brillouin scattering, and M 1 is a material figure of merit that is related to the acousto-optic diffraction efficiency. Using the measured value of Δv B=23.6 MHz and the published value of M 1=58.1×10-8 m2s/kg , gB of tellurite glass for a pump wavelength of 1.542 µm was determined to be 2.17×10-10 m/W, which was close to the value obtained from the Brillouin threshold measurement.
Additionally, an experiment was performed to determine gB directly from the small-signal gain measurement. Single-frequency laser radiation at 1.542 µm from an external-cavity semiconductor laser was divided into two parts. One part was amplified with an erbium-doped fiber amplifier for use as a pump, and the other part was phase-modulated at a frequency approximately equal to the Brillouin frequency shift (vB) for use as the probe signal. The intensity of the lower frequency sideband was measured using an optical spectrum analyzer and plotted against the modulation frequency, which was varied around the Stokes frequency shift v B of 7.882 GHz. Figure 5 shows the variation of the intensity of the amplified probe signal with the modulation frequency (fm). The launched pump power was kept constant at 360 mW, and the length of the tellurite fiber was 2 m. A peak Brillouin gain, 10log [exp (g B L eff PK/A eff)], of 30 dB was obtained at a modulation frequency of 7.882 GHz, which corresponded to a gain of 0.083 dB/mW of the pump power. This yielded a Brillouin gain coefficient of 1.47×10-10 m/W using the effective area Aeff =9.18 µm2 and effective length Leff =1.78 m of the fiber and a polarization factor K=0.667.
By fitting the Brillouin gain spectrum with a Lorentzian profile, we obtained a 3-dB Brillouin gain linewith of 23.8 MHz, which was in excellent agreement with the value obtained from the spontaneous Brillouin spectrum.
We performed measurements of the Brillouin gain coefficient of a tellurite fiber by three different methods: spontaneous Brillouin-gain spectrum, Brillouin threshold power, and direct measurement of small-signal Brillouin gain, and the coefficients were found to be 2.17×10-10, 1.62×10-10 and 1.47×10-10 m/W, respectively.
In table 1, the linear and nonlinear optical properties of tellurite fibers are compared with those of two other non-silica fibers, bismuth and chalcogenide, which also have attracted widespread attention lately due to their large nonlinearity.
The tellurite fiber with its large Brillouin gain coefficient and low scattering loss can be useful for realizing efficient SBS-assisted slow light generators. The induced delay per unit length and per unit power that one would expect from slow light fiber devices can be expressed as [7, 8, and 16],
Table 1 also shows that the delay per unit length and unit power in tellurite, bismuth and chalcogenide glasses calculated for fibers with the smallest core size reported to date. This delay generation efficiency in tellurite fiber is about the same as that for bismuth fiber, while chalcogenide fiber is seen to exhibit the highest efficiency. When a dithered broadband pump is used for bandwidth enhancement in slow light generation , the gain coeffecient becomes the only parameter that determines the efficiency of slow light generation. For such cases, the figure of merit (FOM) taking into account of the response time of the devices  has been expressed as Gain (dB)/(Aeff.PPump.n), which becomes proportional to gB/(Aeff.n). The values of the parameter are calculated for tellurite, bismuth and chalcogenide fibers and are compared in table 1. Tellurite and bismuth fibers exhibit almost similar values, which are about one-fifth of that of chalcogenide fiber. It is to be noted here that the efficiencies of slow light fiber devices made from different glasses but with identical core size can be compared by simply considering the factor, gB/n.
One important aspect of tellurite fiber compared to other non-silica fibers used so far for slow light generation is its relatively low loss. The saturated loss of the fiber at high pump power was 0.5 dB/m, which was due to the doping of the core with erbium. A previous report showed that a tellurite glass fiber with a scattering loss of only 0.054 dB/m at 1.2 µm was possible . It should be possible to realize a fiber with a similarly low scattering loss at 1.55 µm by drawing from an undoped core using existing technologies. Further research towards successful drawing of low-loss tellurite fibers with smaller core size will make it possible the realization of slow light fiber devices with a much higher efficiency.
In conclusion, we report our observation of strong SBS from a tellurite glass single-mode optical fiber. The threshold power for single-pass Brillouin scattering from a 2-m-long fiber was about 1000 mW. The Brillouin shift was measured to be 7.882 GHz, with a bandwidth of 23.6 MHz. Brillouin gain coefficient of 1.47-2.16×10-10 m/W was obtained from the 3-dB gain linewidth, Brillouin threshold power and from small-signal Brillouin gain measurements.
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