Strong stimulated Brillouin scattering in single-mode As2Se3 chalcogenide fiber is observed using a cw laser at 1.55 μm wavelength region. Brillouin threshold for a 5-m-long fiber is as small as 85 mW. The Brillouin frequency shift v B and the gain linewidth Δv B are 7.95 GHz and 13.2 MHz, respectively, measured with heterodyne detection and an RF spectrum analyzer. A Brillouin gain coefficient g B of 6.0 × 10-9 m/W, about 134 times larger than that of fused silica fiber, is obtained for As2Se3 single mode fiber from measurements of Brillouin threshold power and the gain linewidth.
©2005 Optical Society of America
When a narrow band laser radiation is propagated through optical fiber, a part of light is seen to scatter in the backward direction when the power exceeds a certain limit . This phenomenon known as stimulated Brillouin scattering (SBS) imposes a limit to the amount of optical power that can be transmitted thorough an optical fiber and has been considered detrimental to optical communication systems and in many nonlinear fiber-optic applications involving cw light. However, the SBS can be useful to amplify a narrow band optical signal by propagating in a direction opposite to the pump, and this has lead applications in many places such as Brillouin amplifiers, lasers, distributed fiber sensors, as well as phase conjugators . Using the intensity-dependent refractive index change associated with SBS process, tunable optical delays via slowing of light has been demonstrated in optical fiber , which has drawn considerable attention lately for its potential applications in optical networks. For applications involving SBS, it is desirable to have medium that has large Brillouin gain coefficient, g B in order to reduce the threshold power and also the device length. Although many crystals and organic materials are reported to have large Brillouin gain coefficients , many are difficult to draw in the form of optical fibers. So far a number of non-silica based fibers are successfully drawn into optical fibers, which include tellurite, bismuth and chalcogenide glass fibers. These fibers are reported to have large nonlinear Kerr and Raman gain coefficients, and already found to have potential applications in high-speed optical signal processing [5,6].
The chalcogenide glasses contain S, Se that has transparency beyond 2 μm and nonlinear coefficients over two-three order of magnitudes larger than that of silica glass [6–9]. Within the As-S-Se chalcogenide glass family, As2Se3 glass is reported to have 500 times larger nonlinear coefficient n 2 than that of silica . Low loss multimode As2Se3 fiber has been fabricated that exhibited large Raman gain coefficients [9,10]. Also optical regeneration in single mode As2Se3 fiber is also been demonstrated recently using the large Kerr nonlinearity . Besides, Ogusu et al. estimated the Brillouin gain coefficient in As2Se3 glass using the phonon lifetime time and reported a value about 25 times large than that of fused silica . However, to our knowledge so far no experimental observation of Brillouin scattering effect and its characterization in As2Se3 optical fiber has been reported.
This paper reports the first observation of SBS in single mode As2Se3 chalcogenide fiber in the 1.55 μm wavelength region. Strong SBS is observed from a fiber merely 5 m in length when pumped with a continuous wave (cw) laser with a threshold power of only 85 mW. The Brillouin frequency shift is 7.95 GHz that has a 3-dB linewidth of 13.2 MHz. A Brillouin gain coefficient g B of 6.2 × 10-9 m/W, as much as 134 times larger than fused silica fiber is measured.
The chalcogenide fiber was drawn at CorActive HighTech Inc. from high-purity material using double-crucible process , where the core was made from As39Se61 and the cladding from one that had slightly reduced As content . The core diameter of the fiber was 6 μm and the NA was 0.18, which resulted in a V number of 2.2, and allowed the lowest mode to propagate through the fiber in the 1.55 μm wavelength. Because of the large refractive index of ~2.8 in chalcogenide glass, the fibers had large Fresnel reflection (22%), which was suppressed by antireflection coating for operation at 1.55μn. Two pieces of single mode silica fibers, tapered at their ends, were used to couple light into and out from the fiber.
Since the index of chalcogenide glass is relatively large compared to silica, light that did not coupled into the core could partly reached the other end of the fiber. However, by coupling light at the output of AS2Se3 fiber using a lensed fiber, it was possible to accurately determine the light that travel in a single mode inside the core. Using a superluminescence laser source, the transmission spectra were measured for two pieces of As2Se3 fibers, 2 and 10 m in length, and were used for determining the transmission loss α in the 1360-1660 nm region and also the coupling loss.
The experimental setup used to study the Brillouin scattering in As2Se3 fiber is shown in Fig. 1. Light from an external cavity tunable cw laser operating at 1560 nm was amplified and launched into the fiber though am optical circulator, and light that was backscattered from the As2Se3 fiber was collected at the port #3 of the circulator and used for diagnosis. The intensity of Stokes component could be measured using an optical spectrum analyzer with a resolution of 0.01 nm. The pump power was gradually changed while the peak of the Stokes component was recorded using the optical spectrum analyzer. From the threshold power we determined the Brillouin gain coefficients using the small-signal steady-state theory of stimulated Brillouin scattering [14, 15].
We also performed a heterodyne detection to measure the Brillouin shift with a higher resolution and also the gain linewidth . The backscattered light was amplified using an erbium amplifier and detected using a fast photodiode and broadband electrical amplifier as shown in Fig. 1(b). The Stokes component and a fraction of light pump light reflected in the backward direction from the coupling optics caused optical beating, which could be observed in an RF spectrum analyzer. We could measure the Brillouin gain spectrum with high resolution (300 KHz), which yielded the gain linewidth.
Figure 2 shows the loss per meter versus wavelength, which indicates a loss lower than 1.0 dB/m over a wide wavelength range. The transmission loss at 1.55 μm is about 0.84 dB/m. The coupling loss between single mode fiber (SMF28) and the As2Se3 fiber was estimated to be 2.2 dB.
Figure 3 shows the optical spectra of the back-scattered light from a 4.92-m (effective length L eff is 3.2 m) long fiber observed with pump powers of 60 and 88 mW. A Stokes wavelength component at a separation of 0.06 nm in the longer wavelength side could be seen in the optical spectra. Figure 4 plots the power level of the light back scattered from the fiber as a function of the launched pump power. We could see the Stokes component with pump power as small as 6 mW. Brillouin threshold was observed at a power of 85 mW, when a sharp increase in the Stokes component could be seen.
According to the small-signal steady-state theory of stimulated Brillouin scattering , the pump power Pth required to reach 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 defined as Leff = α-1(1-exp[-αL]), and K is a constant that depends on the polarization property of the fiber which is 1 if the polarization is maintained and 0.5 otherwise . Note that with this definition of Aeff , the exponential Brillouin gain along a fiber becomes g B LeffP/Aeff (P is the incident pump power). Radius ωo can be calculated from the core radius a and the V parameter using, ωo ≈ a(0.65+1.619/V1.5+2.879/V6) 
Using, P th = 85 mW, A eff = 39 μm2, Leff = 3.17 m and K = 0.5 in Eq. (1) we obtained the peak Brillouin gain coefficient gB = 6.0 × 10-9 m/W.
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 is shown in Fig. 5. The Brillouin gain spectrum shows a peak at 7.95 GHz (ν B) and a 3-dB linewidth of Brillouin scattering (Δν B) of 13.2 MHz.
We also calculated the peak value of Brillouin gain coefficient from the linewidth of Brillouin gain using the following equation .
where n is the refractive index, p12 is the longitudinal elastooptic coefficient, c is the velocity of light, λ is the wavelength, ρ is the material density, V A is the acoustic velocity, Δν B is the linewidth of spontaneous Brillouin scattering. Using the measured value of Δν B = 13.2 MHz, and also the published values of n = 2.81, ρ = 4.64 × 103 kg/m3, v A= 2250 m/s, p12 = 0.266, gB for As2Se3 was determined to be 6.08 × 10-9 m/W.
The Brillouin gain coefficients measured experimentally using linewidth and threshold of single pass Brillouin scattering are in agreement with each other. The following table compares the Brillouin gain coefficients for As2Se3 and silica glass fiber and the parameters that are used to calculate the gain coefficients. As shown in the table the Brillouin gain in As2Se3 single mode fiber is about 134 times larger than that of fused silica.
It is worth comparing the experimental value of gB with that estimated recently by Ogusu et al. for bulk As2Se3 glass in Ref. 12. They calculated the Brillouin gain coefficient from phonon lifetime T B, which was estimated from the attenuation coefficient αA reported for acoustic wave at 200 MHz for bulk As2Se3  and the acoustic velocity v A . As the experimental data αA of acoustic waves in the 11 GHz range was not available, it was approximated from αA measured at 200 MHz through an extrapolation made under the assumption that αA ∝ . They obtained a g B in bulk As2Se3 that was 25 times larger than that of bulk silica.
We can think of several possible sources that might have caused this discrepancy between the estimated g B for bulk As2Se3, and experimentally determined g B for single mode As2Se3 fiber, which include differences in the exact guided nature of optical modes (transverse distribution of the electric field) and damping time of acoustic waves between bulk sample and cylindrical optical waveguide [2, 22], exact composition (e.g. As39Se61 in the core of the fiber we used) of the core and clad, the purity of material, and also any possible deviation in the estimation of attenuation coefficient for higher acoustic frequency using αA ∝ . For example the gB estimated for fused silica (2.24 × 10-11 m/W) in Ref. 12 from αA is about half of what measured in fused silica fiber . Also equation 2 is derived under the assumption of no reflections from the Brillouin fiber. However, there can exist some weak feedback due to residual reflections from the fiber ends despite the ends being antireflection coated, which might effect the threshold power measurements  and the calculated value of the gain coefficient. These effects are currently under investigation.
In conclusion, we report our observation of a strong SBS from As2Se3 single mode optical fiber. The threshold power for single Brillouin scattering from a 4.92 m long fiber was about 80 mW. The Brillouin shift was measured to be 7.95 GHz, which has a bandwidth of 13.2 MHz. A Brillouin gain coefficient of 6.0 × 10-9 m/W, about 134 times larger than that of fused silica fiber, was obtained from both the gain linewidth and Brillouin threshold measurements.
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