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Optics Express

  • Editor: Michael Duncan
  • Vol. 13, Iss. 6 — Mar. 21, 2005
  • pp: 2019–2024
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SBS threshold for single mode and multimode GRIN fibers in an all fiber configuration

A. Mocofanescu, L. Wang, R. Jain, K. D. Shaw, A. Gavrielides, P. Peterson, and M. P. Sharma  »View Author Affiliations


Optics Express, Vol. 13, Issue 6, pp. 2019-2024 (2005)
http://dx.doi.org/10.1364/OPEX.13.002019


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Abstract

We investigate stimulated Brillouin scattering (SBS) threshold in single mode and multimode fibers in an all fiber network. The pump is a single mode fiber pigtail attached to a diode. We find the theory and experiment agree for both single mode and multimode GRIN fibers. We modify the bulk SBS threshold equation for use with fibers by properly accounting for mode sizes and modal dispersion.

© 2005 Optical Society of America

1. Introduction

We begin by reiterating the development of reference [4

4. V. I. Kovalev and R. G. Harrison, “Waveguide-induced inhomogeneous spectral broadening of stimulated Brillouin scattering in optical fiber,” Opt. Lett. 27, 2022–2025 (2002). [CrossRef]

]. In their paper they include inhomogeneous broadening of the SBS spectrum resulting from the angular confinement of the pump by up to twice the critical angle. These authors [4

4. V. I. Kovalev and R. G. Harrison, “Waveguide-induced inhomogeneous spectral broadening of stimulated Brillouin scattering in optical fiber,” Opt. Lett. 27, 2022–2025 (2002). [CrossRef]

] apply their formula to several different fibers and find that the measured linewidths agree with their predictions. However, we are interested in the effects of the area on SBS operation. Thus, in the following we extend their work by measuring the threshold of multimode GRIN fibers and single mode fibers in an all fiber network, and compare these results with theory. This type of network is highly desirable in an industrial setting, for example.

2. Experiment

The experimental setup is shown in Fig. 1. The pump source is a single mode narrow-linewidth (150 KHz), 5W fiber laser operating at a wavelength of 1550nm. A single mode circulator couples the pump into the SBS fiber and outcouples the backwards-propagating Stokes radiation. We investigate SBS in two different fibers. The first is a single-mode fiber (Corning SMF-28) of length 1 km. The second is a multimode GRIN fiber (Corning 50/125) of length 4.4 km. Both fibers are butt-coupled to the pump source using FC/APC connectors. These connectors are used throughout the optical chain to minimize reflection of light. In order to assess the effectiveness of coupling between multimode fibers and single mode fibers we measured the transmission between two short fibers. We found that single mode to multimode has a transmission of 98%, and that the transmission of multimode to single mode is 60%.

Prior to the SBS experiments we investigated the excited mode structure in the multimode fiber. This was done by butt-coupling a short (2 meter) length of MM fiber to the pump source and imaging the fiber end onto a CCD array camera. The spot had a 1/e 2 radius of 7.8µm and an M2 of 1.15. Thus, only the lowest-order mode in the multimode (MM) fiber is excited under butt coupling. Using the same technique the mode radius of the single-mode (SM) fiber was found to be 4.9µm. These results agree with the theoretical predictions, see Table 1 and the following section.

SBS thresholds were measured for both fibers. Table 1 shows the measured and calculated thresholds and mode waists; we will discuss the theoretical calculations in a moment. The mode waists agree within 1%. Additionally, for the single mode fiber we measure the reflectivity RSM=Pc/Pp(0) as a function of the input pump power Pp(0), see Fig. 2, where Pc is the Stokes power exiting circulator. For the multimode fiber we calculate the reflectivity RMM=Ps(0)/Pp(0)=(Pp(0)-Pp(L))/Pp(0) from Pp(z) which is the pump power measured at both ends of the fiber at z=0, and z=L with Ps(L)=0. Note, that RMM depends only on the measured pump inside the fiber at z=0, L, and hence does not represent a conjugation property. Further, we determine the multimode fidelity from FMM=Pc/Ps(0)=Pc/Pp(0)/RMM where Pc is the Stokes power exiting the circulator. FMM depends on the Stokes power Pc measured external to the fiber compared to Pp(0) which is internal to the fiber. Thus, FMM represents a measurement of phase conjugation. This definition of phase fidelity is consistent with the standard definition based on overlap integrals. These two quantities are shown in Fig. 2 as a function of input pump power. In both figures we also show, as the solid line, our theoretical calculations for the threshold and the reflectivity R=Ps(0)/Pp(0) obtained from the well known plane wave model [11

11. W. Kaiser and M. Maier, Laser HandbookVol. 2,ed. by F. T. Arecchi and E. O. Schulz-Dubois (Northland-Holland Publishing Company, 1972),pp. 1118.

].We note that for the single mode fiber the reflectivities agree within 3% and for the multimode GRIN fiber the agreement in reflectivities is within 10%. We now discuss the theory which incorporates the effects of the mode area and inhomogeneous gain which we used for the curves in Fig. 2.

Fig. 1. Schematic for measuring SBS performance.

Table 1. Summary of calculated and measured radius and threshold for single mode and multimode fibers.

table-icon
View This Table

3. Theory

In the cited paper[4

4. V. I. Kovalev and R. G. Harrison, “Waveguide-induced inhomogeneous spectral broadening of stimulated Brillouin scattering in optical fiber,” Opt. Lett. 27, 2022–2025 (2002). [CrossRef]

] the SBS gain coefficient gi for inhomogeneous broadening due to waveguiding is derived as

gi(f)=g0Γ02F0Fc×[tan1(F0fΓ02)tan1(FcfΓ02)].
(1)
Fig. 2. Upper figure: single mode fiber reflectivity for a length of 1.0km; lower figure: multimode reflectivity and fidelity for a length of 4.4km. The horizontal axis is input pump power, in watts, and the g0IL product.

Also they show that the FWHM of the inhomogeneous spontaneous Brillouin spectrum is

ΓΓ02+F02(NA)44nco4.
(2)

In these equations the frequency shift of the SBS field is given by FB(ϕ)=2ncov sin(ϕ/2)/λ, v is the velocity of sound, λ is the pump wavelength in vacuum, nco is the core index-of-refraction, and ϕ is the backward Stokes angle with respect to the pump. The on-axis frequency is F0=FB(π), and the frequency at the critical angle is Fc=FB(π2θc)=2ncov1(NA)2nco2λ where the complement of the critical angle is θc=sin-1((NA)/nco). Kovalev and Harrison [4

4. V. I. Kovalev and R. G. Harrison, “Waveguide-induced inhomogeneous spectral broadening of stimulated Brillouin scattering in optical fiber,” Opt. Lett. 27, 2022–2025 (2002). [CrossRef]

] use the values: Γ0=36MHz for the Brillouin linewidth, λ=1.06µm, v=5.96km/s, nco=1.46 and the bulk gain g 0=5×10-11m/W for their calculations. The above equations are applied to step index fibers where all ray directions are assumed to be equally probable up to the critical angle. This assumption is based on the uniformity of the index profile which is not valid for GRIN fibers. They find that the bandwidth in Eq. (2) compares favorably with their experiment.

In our experiments we are interested in the SBS threshold in fibers. For this we assume the standard threshold equation

Pth=21πω2leffgi(fs)
(3)

For our experiment we use: v=5960m/s, λ=1.5µm, nco=1.4682, F 0=2ncov/λ, g 0=2.5×10-11m/W this gain is half of the bulk gain value given in reference (10). Since our wavelength is λ=1.5µm the value of Γ0 is determined from the scaling Γ0=38.4/λ 2MHz [10

10. D. Cotter, “Observation of stimulated Brillouin scattering in low loss silica fiber at 1.3µm,” Electron. Lett. 18, 495–496 (1982). [CrossRef]

]. This gives 36MHz for λ=1.06µm and 17MHz for Erbium at λ=1.5µm.

We now consider the fiber mode structure. Because of the uncertainty in the launching conditions the exact fiber mode structure is unknown. In order to estimate the mode area we turn to the work of Marcuse [9

9. D. Marcuse “Loss analysis of single-mode fiber splices,” The Bell Sys. Tech. J. 56, No. 6, 703–718 (1977).

]. He assumes the field distribution is Gaussian, composed of more than the lowest mode, from which he derives an optimum Gaussian mode radius ω for both step index and GRIN fibers. He finds for a step index fiber of core radius a, the optimum beam radius ω is given by

ωa=.65+1.619V32+2.879V6,
(4)

and for GRIN a fiber the optimum beam radius is given by

ωa=2V+0.23V32+18.01V6.
(5)

Note that these waists correspond to the e -2 value of the measured intensity. In these equations the V-number is V=ka(NA)SI, k=2π/λ, where (NA)SI is the step index numerical aperture. For the GRIN fiber the numerical aperture is (NA(r))=(NA)SI1r2a2.

Table 1 summarizes the experimental and theoretical results. The calculated beam mode sizes ω are obtained using Eqs. (4),(5). The corrected threshold uses Eq. (3). However, the uncorrected threshold retains the same mode size, but uses only the gain g 0 to illustrate the effect of dispersion. If, on the other hand, the core area is used instead of the mode area, along with g 0, the threshold increases to 400mW.

We end this section by noting that not only does Eq. (3) fit our experiment satisfactorily but it also agrees with focused pump experiments. Cotter’s [10

10. D. Cotter, “Observation of stimulated Brillouin scattering in low loss silica fiber at 1.3µm,” Electron. Lett. 18, 495–496 (1982). [CrossRef]

] experiment measures a threshold of 5.6mW for a 13.6km single mode fiber at a wavelength of λ=1.32µm. Our simulation gives within 15% agreement with a threshold of 6.5mW. The experiments of Harrison et al. [5

5. R. G. Harrison, V. I. Kovalev, W. Lu, and Dejin Yu, “SBS self-phase conjugation of CW Nd”YAG laser radiation in an optical fiber,” Opt. Commun. 163, 208–211 (1999). [CrossRef]

] offer another comparison. They measure a threshold of 70mW and we simulate a threshold of 77mW for a 4.23km multimode fiber at wavelength of λ=1.06µm. This brings us to an experiment by Chen, et al. [7

7. L. Chen and X. Bao,“Analytical and numerical solutions for steady state stimlulated Brillouin scattering in a singel-mode fiber,” Opt. Commun. 152, 65–70 (1998). [CrossRef]

]. Here they measure a threshold of 14mW and we calculate 16mW for a 7.2km single mode fiber cw pumped at λ=1.31µm. All of these experiments use a focused pump.

Our theoretical approach to SBS threshold in fibers has been to modify the bulk equations. We made two changes which brought the fiber theory in agreement with experiments. For the GRIN fiber we modified the radial dependent numerical aperture by introducing an average numerical aperture in the inhomogeneous gain equation. The second alteration, applicable to both single mode and multimode fibers, was to replace the core radius by the optimum Gaussian radius. For the step index fiber the experiment and theory agree to within a few percent and for the GRIN fiber the agreement is within 10%.

Acknowledgments

One of the authors A. M. would like to gratefully acknowledge the contractual support of the Air Force Research Laboratories. She is also affiliated with Institute of Atomic Physics, Dept. of Lasers, P.O. Box MG-56, Bucharest 76900, Romaina.

References and links

1.

V. I. Kovalev, R. G. Harrison, and A. M. Scott, “The build-up of stimulated Brillouin scattering excited by pulsed pump radiation in a long optical fibre,” Opt. Commun. 185, 185–189 (2000). [CrossRef]

2.

K. Tei, Y. Tsuruoka, T. Uchiyama, and T. Fujioka, “Critical power of stimulated Brillouin scattering in multimode optical fibers,” Jpn. J. Phys. 40, 3191–3194 (2001). [CrossRef]

3.

Y. Tsuruoka, K. Tei, and T. Fujioka, “Influence of mode dispersion on critical power of stimulated Brillouin scattering in multimode optical fibers,” Jpn. J. Phys. 41, 5166–5169 (2002). [CrossRef]

4.

V. I. Kovalev and R. G. Harrison, “Waveguide-induced inhomogeneous spectral broadening of stimulated Brillouin scattering in optical fiber,” Opt. Lett. 27, 2022–2025 (2002). [CrossRef]

5.

R. G. Harrison, V. I. Kovalev, W. Lu, and Dejin Yu, “SBS self-phase conjugation of CW Nd”YAG laser radiation in an optical fiber,” Opt. Commun. 163, 208–211 (1999). [CrossRef]

6.

V. I. Kovalev and R. G. Harrison, “Diffraction limited output form a CW Nd”YAG master oscillator/power amplifier with fibre phase conjugate SBS mirror,” Opt. Commun. 166, 89–99 (1999). [CrossRef]

7.

L. Chen and X. Bao,“Analytical and numerical solutions for steady state stimlulated Brillouin scattering in a singel-mode fiber,” Opt. Commun. 152, 65–70 (1998). [CrossRef]

8.

Robert W. Boyd, Nonlinnear Optics (Academic Press, Inc, 1992), pp. 339.

9.

D. Marcuse “Loss analysis of single-mode fiber splices,” The Bell Sys. Tech. J. 56, No. 6, 703–718 (1977).

10.

D. Cotter, “Observation of stimulated Brillouin scattering in low loss silica fiber at 1.3µm,” Electron. Lett. 18, 495–496 (1982). [CrossRef]

11.

W. Kaiser and M. Maier, Laser HandbookVol. 2,ed. by F. T. Arecchi and E. O. Schulz-Dubois (Northland-Holland Publishing Company, 1972),pp. 1118.

OCIS Codes
(190.4370) Nonlinear optics : Nonlinear optics, fibers
(290.5830) Scattering : Scattering, Brillouin

ToC Category:
Research Papers

History
Original Manuscript: January 7, 2005
Revised Manuscript: February 28, 2005
Published: March 21, 2005

Citation
A. Mocofanescu, L. Wang, R. Jain, K. Shaw, A. Gavrielides, P. Peterson, and M. Sharma, "SBS threshold for single mode and multimode GRIN fibers in an all fiber configuration," Opt. Express 13, 2019-2024 (2005)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-13-6-2019


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References

  1. V. I. Kovalev and R. G. Harrison, A. M. Scott, "The build-up of stimulated Brillouin scattering excited by pulsed pump radiation in a long optical fibre,�?? Opt. Commun. 185, 185-189 (2000). [CrossRef]
  2. K. Tei, Y. Tsuruoka, T. Uchiyama, T. Fujioka, "Critical power of stimulated Brillouin scattering in multimode optical fibers,�?? Jpn. J. Phys. 40, 3191-3194 (2001). [CrossRef]
  3. Y. Tsuruoka, K. Tei, and T. Fujioka, "Influence of mode dispersion on critical power of stimulated Brillouin scattering in multimode optical fibers,�?? Jpn. J. Phys. 41, 5166-5169 (2002). [CrossRef]
  4. V. I. Kovalev and R. G. Harrison, "Waveguide-induced inhomogeneous spectral broadening of stimulated Brillouin scattering in optical fiber,�?? Opt. Lett. 27, 2022-2025 (2002). [CrossRef]
  5. R. G. Harrison, V. I. Kovalev, W. Lu, Dejin Yu, "SBS self-phase conjugation of CW Nd�??YAG laser radiation in an optical fiber,�?? Opt. Commun. 163, 208-211 (1999). [CrossRef]
  6. V. I. Kovalev, R. G. Harrison, "Diffraction limited output form a CW Nd�??YAG master oscillator/power amplifier with fibre phase conjugate SBS mirror,�?? Opt. Commun. 166, 89-99 (1999). [CrossRef]
  7. L. Chen, X. Bao, "Analytical and numerical solutions for steady state stimlulated Brillouin scattering in a single-mode fiber,�?? Opt. Commun. 152, 65-70 (1998). [CrossRef]
  8. Robert W. Boyd, Nonlinear Optics (Academic Press, Inc, 1992), pp. 339.
  9. D. Marcuse, "Loss analysis of single-mode fiber splices,�?? The Bell Sys. Tech. J. 56, No. 6, 703-718 (1977).
  10. D. Cotter, "Observation of stimulated Brillouin scattering in low loss silica fiber at 1.3 µm,�?? Electron. Lett. 18, 495-496 (1982). [CrossRef]
  11. W. Kaiser, M. Maier, Laser Handbook Vol. 2, ed. by F. T. Arecchi, E. O. Schulz-Dubois (Northland-Holland Publishing Company, 1972), pp. 1118.

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