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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 24 — Nov. 26, 2007
  • pp: 15952–15963
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SBS gain efficiency measurements and modeling in a 1714 µm2 effective area LP08 higher-order mode optical fiber

M. D. Mermelstein, S. Ramachandran, J. M. Fini, and S. Ghalmi  »View Author Affiliations


Optics Express, Vol. 15, Issue 24, pp. 15952-15963 (2007)
http://dx.doi.org/10.1364/OE.15.015952


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Abstract

The stimulated Brillouin scattering (SBS) gain efficiencies were measured in the LP08 and LP01 modes of a higher-order-mode optical fiber. Gain efficiencies CB of 0.0085 and 0.20 (m-W)-1 were measured for the LP08 and LP01 modes at 1083 nm, respectively. CB is inversely proportional to the optical effective area Aeff and the same core-localized acoustic phonon seeds the SBS process in each case. An acoustic modal analysis and a distributed phenomenological model are presented to facilitate the data analysis and interpretation. The LP08 mode exhibits a threshold power-length product of 2.5 kW-m.

© 2007 Optical Society of America

1. Introduction

2. Experiment

The HOM fiber consists of a central core and an 86 µm diameter silica inner cladding that is surrounded by a lower index outer trench. Details of the fiber design, the LP08 and LP01 intensity profiles and a near-field image of the LP08 mode after 50 m of propagation in the HOM fiber are shown in Fig. 1.

Fig. 1. Schematic of the HOM fiber refractive index profile Δn, the intensity profiles of the LP08 [blue] and LP01 [red] modes and a near field image of the LP08 intensity pattern. The peak intensities have been normalized to one.

The experimental arrangement is shown in Fig. 2. A three-stage Yb-doped pulsed master-oscillator power-amplifier (MOPA) configuration generates the high power single frequency radiation. The seed source is a commercially available distributed feedback fiber laser exhibiting a linewidth <30 kHz and a center wavelength of ~1083.7 nm. The final amplifier stage utilizes a 20 µm mode-field-diameter Yb- doped LMA fiber. The amplifier was run at a 100 kHz repetition frequency and a pulse width of 1 µs. A mode-transformer injected the light from the LMA fiber into a SMF 1% tap where the length of the SMF was kept below 0.5 m to avoid SBS generation in the small core fiber. This arrangement provided a peak LP01 power of ~45 W at the tap output. The absence of SBS generation in the SMF was confirmed experimentally.

Fig. 2. Experimental arrangement for measuring the SBS spectra of the HOM fiber. Shown is the last LMA fiber stage of a three stage MOPA, the mode transformer MT, diagnostic tap and the LP08 HOM module with the LPG. The LPG is removed for the LP01 experiment.

Aeff=En2(r)2En4(r)
(1)

where E n r is the electric field distribution of the nth fiber mode (either LP08 or LP01) and the angular brackets <…> represent an integration over the cross section of the fiber. A SBS reflectivity equal to 10-5 is achieved at a peak power of ~25.5 W. The maximum reflectivity was determined by the available peak pump power and the need to avoid an excessive amount of counter propagating light from entering the 3rd stage amplifier and generating parasitic lasing. No pump depletion at the fiber output was observed.

Fig. 3. Backscatter spectra of the LP08 mode at the indicated peak input powers PP [W]. Inset shows extracted SBS reflectivities RSBS vs. single pass gain G data points and a two-parameter fit to the phenomenological equation for RSBS. The center wavelength λ 0 is 1082.74 nm.

In a second experiment, a 20 m length of HOM fiber was directly spliced onto the tap output to excite the LP01 mode. Figure 4 shows the growth of the backscattered LP01 Stokes spectral component as a function of the LP01 pump power and the inset shows the RSBS vs. G. In this case the SBS reflectivity equals 10-5 at a peak power of ~2.5 W.

Fig. 4. Backscatter spectra of the LP01 mode at the indicated peak input powers PP [W]. Inset shows extracted SBS reflectivities RSBS vs. single pass gain G data points and a two-parameter fit to the phenomenological equation for RSBS. The center wavelength λ 0 is 1082.74 nm. The small change in center wavelength is related to the laser temperature setting.

The Brillouin frequency shift of the Stokes radiation was determined in a heterodyne experiment where backscattered light was combined with the seed laser radiation with a 50% 2×2 coupler. Figure 5 shows the rf spectrum for the LP08 and LP01 modes exhibiting Brillouin shifts νB of 15.19 and 15.20 GHz, respectively. These measurements were taken at an SBS reflectivity approximately equal to 10-5 which is 30 to 40 dB above the thermal Brillouin reflectivity of 10-9 to 10-8.

Fig. 5. Heterodyne spectra of SBS radiation and seed laser local oscillator for the LP08 and LP01 modes. A spectral offset is introduced for clarity and the resolution bandwidth is 3.0 MHz.

The full-width at half-maximum (FWHM) of the Stokes optical spectrum is determined by a non-linear least squares fit to the rf spectra utilizing a Gaussian trial function appropriate for the high gain G: exp[(ν-ν B)2/2σ2] where ν is the frequency and σ is a fitting parameter [10

10. R. W. Boyd et al., “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42, 5514 (1990). [CrossRef] [PubMed]

]. The FWHM is given by: Δν=2σ2ln(2) and is found to be 33 MHz for the LP08 mode at G=7.0 and 32 MHz for the LP01 mode at G=10.4. The absence of additional spectral peaks corresponding to other fiber acoustic modes in the rf spectrum and the ~30 MHz FWHM of these spectral features suggest that these measurements are taken sufficiently within the SBS regime where the scattering process is dominated by a single acoustic phonon. This indicates that the Stokes powers extracted from the low resolution OSA measurements correspond to scattering from a single acoustic mode. This is examined more closely in the following section which calculates the phonon spectra.

3. Modeling and Analysis

The SBS mechanism is illustrated in Fig. 6. Forward propagating light in either the LP08 or LP01 modes is scattered by density fluctuations exhibiting a transverse distribution ρ(r), associated with the acoustic phonons, in a thermal Brillouin scattering event and the frequency of the scattered radiation is shifted by the Doppler frequency. A fraction of the backscattered radiation is captured by the fiber modes and propagates in the backward direction The counter propagating electric fields generate a forward traveling intensity interference pattern which generates a forward propagating pressure wave by means of the electrostrictive effect. This pressure wave can induce stimulated scattering in two manners. The signal laser light is Brillouin scattered by the electrostrictively-generated pressure wave. The mixing of this scattered light with the signal radiation further enhances the pressure wave, leading to stimulated scattering. Also, the pressure wave can mechanically drive the thermal phonon that caused the original thermal Brillouin scattering event, thereby increasing the stimulated scattering [11

11. I. L. Fabelinskii, Molecular Scattering of Light, (Plenum Press, 1968).

].

Fig. 6. Schematic diagram showing thermal Brillouin scattering of the LP08 and LP01 modes by a core-localized acoustic phonon with a density fluctuation ρ(r), the electric field distributions E(r), the optical index profile n(r) and the acoustic index profile N(r)=VSi02/V(r) where VSi02 is the sound speed in silica.

The thermal phonons or normal modes of vibration of the HOM fiber are given by the solutions to the Helmholtz equation [12

12. E. Peral and A. Yariv, “Degradation of modulation and noise characteristics of semiconductor lasers after propagation in optical fiber due to phase shift induced by stimulated Brillouin scattering” IEEE J. Quantum Elect. 35, 1185 (1999). [CrossRef]

, 13

13. A. Kobyakov et al., “Design concept for optical fibers with enhanced SBS threshold,” Opt. Express 14, 5388 (2005).

] with stress-free boundary conditions:

2ρ(r)+(2πΛ0)2·N(r)2·ρ(r)=(2πΛ0)2Neff2·ρ(r)
(2)

where ∇2 is the transverse Laplacian operator, f is the acoustic frequency in Hz, Λ0 is the acoustic wavelength in silica, f·Λ0=VSiO2, VSiO2 is the speed of sound in the silica inner cladding and Neff is the effective acoustic index. The acoustic refractive index is given by N(r)=VSiO2V(r) where V(r) is the speed of sound at a radius r. Brillouin scattering also requires that the Bragg condition be satisfied to ensure that the optical field resonantly excites the acoustic field, namely:

2π·NeffΛ0=4π·neffλ0,
(3)

where λ 0 is the optical wavelength in vacuum and neff is the effective optical index. The normal modes of vibration ρ m(r)are labeled by the index m and determined by Eq. (2). Those acoustic modes that also satisfy the Bragg condition given by Eq. (3) will participate in the thermal Brillouin scattering event. The acoustic eigenfrequencies are expressed in terms of the acoustic effective index N m eff:

fm=2·neff·VSiO2Neffm·λ0.
(4)

The local sound speed in the HOM optical fiber preform was measured with a scanning acoustic microscope [14

14. Courtesy of James Hou, Sonix Inc., Springfield, VA.

]. Shown in Fig. 7 are an acoustic ‘time-of-flight’ image and the acoustic index profile of the central fiber region rescaled from the fiber preform diameter to the fiber cladding diameter. The preform measurement did not include the lower index outer trench region. The acoustic index of this region was estimated from the glass composition. The thermal Brillouin scattering will be dominated by the acoustic phonon that exhibits the maximum overlap with the optical mode intensity distribution [9

9. Y. Koyamada, et al., “Simulating and designing Brillouin Gain Spectrum in single-mode fibers,” J. Lightwave Technol. 22, 631 (2004). [CrossRef]

]. This overlap may be expressed by the normalized overlap integral Γm,n for the mth acoustic mode with the nth optical mode:

Γm,n=ρm(r)·En(r)22ρm(r)2·En(r)4.
(5)
Fig. 7. Acoustic index as a function radius in the HOM fiber in the central region of the fiber. Also shown is a ‘time-of-flight’ image of the fiber preform taken with a scanning acoustic microscope. The sound speed in silica is 5944 m/s [9].

Fig. 8. The acousto-optic overlap integral Γm,n as a function of the acoustic frequency f.

Figures 9(a) and 9(b) show the normalized optical intensity modes and the normalized acoustic density fluctuation modes showing the greatest overlap for the LP08 and LP01 optical modes, respectively. Hence, the rf spectra and phonon mode structure indicate that the acoustic phonon that seeds the SBS process is localized in the optical core region.

Fig. 9. Plots of the intensity distributions and the two acoustic eigenfunctions exhibiting the maximum overlap integral for the LP08 and LP01 modes of the HOM fiber.

The SBS gain efficiency CB may be extracted from the SBS reflectivity data presented in Figs. 3 and 4 with the aid of a modified Brillouin amplifier model. This is accomplished by including a distributed thermal Brillouin scattering source term in the coupled differential equations for the pump and Stokes radiation [8

8. G. P. Agrawal, Non-Linear Optics (Academic Press, San Diego, 1995).

]:

dPPdz=CB·PP·PSα·PPβ·PP
dPSdz=CB·PP·PS+α·Psη·βS·PP
(6)

where β is the total thermal Brillouin scattering coefficient per unit length, βS=β/2 (equal Stokes and anti-Stokes components) is the total Stokes scattering coefficient per unit length, and η is a capture fraction equal to the ratio of backscatter power captured by the fiber mode to the total thermal Stokes Brillouin scattered power. Note that the thermal Brillouin scattering coefficient is proportional to the overlap integral Γm,n [9

9. Y. Koyamada, et al., “Simulating and designing Brillouin Gain Spectrum in single-mode fibers,” J. Lightwave Technol. 22, 631 (2004). [CrossRef]

]. The quantities βS and η are left as phenomenological coefficients. The Brillouin amplifier model is illustrated in Fig. 10. Equations (6) may be solved analytically under the following conditions: i) the intrinsic fiber loss is negligible for short fiber amplifier lengths so α may be set equal to zero in Eqs.

Fig. 10. Brillouin amplifier model for the SBS generation from a distributed thermal Brillouin source in the low SBS reflectivity limit.

(6), ii) the thermal Brillouin scattering coefficient β is also small, so it can be neglected in Eq. (6a) and iii) at the onset of SBS (i.e. RSBS≪1) there is negligible pump depletion. In this case the pump power is nearly constant and equal to the injected power, i.e. P P(L)=P P(0). Note that βS is retained in Eq. (6b) since it provides the distributed source. Eq. (6b) may be solved analytically with the additional boundary condition that no Stokes power is provided at the far end of the amplifier, i.e. P S (L)=0. The SBS reflectivity R SBS=P S(0)/P P(0) can then be written as:

RSBS=η·βS·L·(eG1)G.
(7)

CB·(AefforAm,nao)=γ·gB
(8)

where Eq. (8) considers both possibilities for the effective area. The SBS gain coefficient gB is given by [8

8. G. P. Agrawal, Non-Linear Optics (Academic Press, San Diego, 1995).

]:

gB=2πn7p122cλ02ρVSΔνph,
(9)

where p12 is the Pockel’s coefficient, ρ is the density, VS is the sound speed and Δν ph is the thermal phonon full-width at half-maximum (FWHM). The thermal phonon linewidths (FWHM) Δν ph are determined from the rf spectral linewidth Δν by accounting for the gain-narrowing with the relation: Δνph=Δνln(2)G [10

10. R. W. Boyd et al., “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42, 5514 (1990). [CrossRef] [PubMed]

]. They are found to be 123 and 105 MHz for the LP08 and LP01 modes, respectively. The independently measured optical effective areas and the smallest calculated acousto-optic effective areas are shown in columns 2 and 3 of Table I for the LP08 and LP01 modes. Equation (8) suggests that the gain efficiency-area product is nearly a constant. This is consistent with the experimentally determined gain efficiency-optical effective area products for the two modes shown in column 4, which are nearly equal. However, when the acousto-optic effective area is used, the product for LP08 mode is 5.4 times greater than that for the LP01 mode, conflicting with Eq. (8). Therefore, the measured SBS gain efficiency CB for the HOM fiber scales with the optical effective area Aeff.

Table ICB [m-W]-1
 Aeff [µm2]Am,n ao [µm2]CB Aeff CBAao m,n meas.calc.
LP08 1714716614.6870.00850.0077
LP01 61.58013.1160.200.21

The last two columns show the measured gain efficiencies (taken from Fig. 3 and 4) and the calculated gain efficiencies using measured thermal phonon linewidths and known parameters [15

15. See ref. [8], the refractive index n=1.48, the Pockel’s coefficient p12=0.27, c is the speed of light in vacuum, λ=1083 nm is the wavelength, ρ=2221 kg/m3 is the density, VS=5661 m/s is the sound speed and the phonon FWHM is 123 MHz for the LP08 mode and 105 MHz for the LP01 mode.

] with γ=1. The calculated results for CB presented in Table I are in good agreement with the measured values. Calculated results for ηβS are not presented since the capture fractions η and scattering coefficients βS are not available for Brillouin scattering in an HOM fiber.

Pth=ln(RSBSηβS·γgBAeffPth)·AeffγgBL
(10)

where the gain coefficient CB is written in terms of the fundamental parameters and e G≫1. Eq. (10) is a transcendental equation for the threshold powers Pth and is of similar form to that first introduced by Smith [16

16. R.G. Smith, “Optical power handling capacity of low loss optical fibers as determined by stimulated Raman and Brillouin scattering,” Appl. Opt. 11, 2489–2494 (1972). [CrossRef] [PubMed]

]. It can be used to extrapolate the threshold powers to arbitrary reflectivities and fiber lengths, and yields the same results shown in Fig. 11. It is worth noting that the logarithmic term in the numerator of Eq. (10) evaluates to be 19.8 and 20.4 for the two optical modes at their respective threshold values. These values are close the value of 21 frequently quoted for unity reflectivity [8

8. G. P. Agrawal, Non-Linear Optics (Academic Press, San Diego, 1995).

]. Note that the threshold power Pth exhibits a weak logarithmic dependence on the overlap integral Γm,n through the scattering coefficient βS. Eq. (10) may also be written in a more compact form in terms of the threshold gain Gth and thermal Brillouin reflectivity: G th=In[(R SBS/R 0G th] where G th=C B·P th·L. Ref. [13

13. A. Kobyakov et al., “Design concept for optical fibers with enhanced SBS threshold,” Opt. Express 14, 5388 (2005).

] introduces a correction factor to the value 21 accounting for the possible contribution to SBS my several acoustic phonons. However, this correction is small for the HOM fiber acoustic mode spectra presented in Fig. 8.

Fig. 11. Plot of SBS reflectivities for the LP08 and LP01 modes as a function of pump powershowing the 0.01% and 1% reflectivity SBS thresholds for a 20 m length of HOM fiber.

4. Conclusion

Acknowledgments

The authors thank Clifford Headley, David DiGiovanni and Alan McCurdy for helpful discussions.

References

1.

A. Liem et al., “100-W single-frequency master-oscillator fiber power amplifier,” Opt. Lett. 28, 1537 (2003). [CrossRef] [PubMed]

2.

W. S. Wong et al., “Breaking the limit of maximum effective area for robust single-mode propagation in optical fibers,” Opt. Lett. 30. 2855 (2005). [CrossRef] [PubMed]

3.

Ming-Jun Li et al., “Al/Ge co-doped large mode area fiber with high SBS threshold,” Opt. Express 15.8290 (2007). [CrossRef] [PubMed]

4.

S. Ramachandran et al., “Light propagation with ultralarge modal areas in optical fibers,” Opt. Lett. 31, 1797 (2006). [CrossRef] [PubMed]

5.

J. M. Fini and S. Ramachandran, “Natural bend-distortion immunity of higher-order-mode large-mode-area fibers,” Opt. Lett. 32, 748 (2007). [CrossRef] [PubMed]

6.

M. D. Mermelstein, S. Ramachandran, and S. Ghalmi, “SBS Gain Efficiency Measurements in a 1714 µm2 Effective Area LP08 Higher Order Optical Fiber,” in Conference on Lasers and Electro- Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper CTuS1.

7.

M. O. van Deventer and A. J. Boot, “Polarization properties of stimulated Brillouin scattering in single-mode fibers,” J. Lightwave Technol. 12, 585 (1994) [CrossRef]

8.

G. P. Agrawal, Non-Linear Optics (Academic Press, San Diego, 1995).

9.

Y. Koyamada, et al., “Simulating and designing Brillouin Gain Spectrum in single-mode fibers,” J. Lightwave Technol. 22, 631 (2004). [CrossRef]

10.

R. W. Boyd et al., “Noise initiation of stimulated Brillouin scattering,” Phys. Rev. A 42, 5514 (1990). [CrossRef] [PubMed]

11.

I. L. Fabelinskii, Molecular Scattering of Light, (Plenum Press, 1968).

12.

E. Peral and A. Yariv, “Degradation of modulation and noise characteristics of semiconductor lasers after propagation in optical fiber due to phase shift induced by stimulated Brillouin scattering” IEEE J. Quantum Elect. 35, 1185 (1999). [CrossRef]

13.

A. Kobyakov et al., “Design concept for optical fibers with enhanced SBS threshold,” Opt. Express 14, 5388 (2005).

14.

Courtesy of James Hou, Sonix Inc., Springfield, VA.

15.

See ref. [8], the refractive index n=1.48, the Pockel’s coefficient p12=0.27, c is the speed of light in vacuum, λ=1083 nm is the wavelength, ρ=2221 kg/m3 is the density, VS=5661 m/s is the sound speed and the phonon FWHM is 123 MHz for the LP08 mode and 105 MHz for the LP01 mode.

16.

R.G. Smith, “Optical power handling capacity of low loss optical fibers as determined by stimulated Raman and Brillouin scattering,” Appl. Opt. 11, 2489–2494 (1972). [CrossRef] [PubMed]

OCIS Codes
(060.2320) Fiber optics and optical communications : Fiber optics amplifiers and oscillators
(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: August 22, 2007
Revised Manuscript: October 2, 2007
Manuscript Accepted: October 12, 2007
Published: November 16, 2007

Citation
M. D. Mermelstein, S. Ramachandran, J. M. Fini, and S. Ghalmi, "SBS gain efficiency measurements and modeling in a 1714 μm2 effective area LP08 higher-order mode optical fiber," Opt. Express 15, 15952-15963 (2007)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-24-15952


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References

  1. A. Liem, et al., "100-W single-frequency master-oscillator fiber power amplifier," Opt. Lett. 28, 1537 (2003). [CrossRef] [PubMed]
  2. W. S. Wong, et al., "Breaking the limit of maximum effective area for robust single-mode propagation in optical fibers," Opt. Lett. 30. 2855 (2005). [CrossRef] [PubMed]
  3. Ming-Jun Li, et al., "Al/Ge co-doped large mode area fiber with high SBS threshold," Opt. Express 15. 8290 (2007). [CrossRef] [PubMed]
  4. S. Ramachandran et al., "Light propagation with ultralarge modal areas in optical fibers," Opt. Lett. 31, 1797 (2006). [CrossRef] [PubMed]
  5. J. M. Fini and S. Ramachandran, "Natural bend-distortion immunity of higher-order-mode large-mode-area fibers," Opt. Lett. 32, 748 (2007). [CrossRef] [PubMed]
  6. M. D. Mermelstein, S. Ramachandran, and S. Ghalmi, " SBS Gain Efficiency Measurements in a 1714 µm2 Effective Area LP08 Higher Order Optical Fiber," in Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper CTuS1.
  7. M. O. van Deventer and A. J. Boot, "Polarization properties of stimulated Brillouin scattering in single-mode fibers," J. Lightwave Technol. 12, 585 (1994) [CrossRef]
  8. G. P. Agrawal, Non-Linear Optics (Academic Press, San Diego, 1995).
  9. Y. Koyamada,  et al., "Simulating and designing Brillouin Gain Spectrum in single-mode fibers," J. Lightwave Technol. 22, 631 (2004). [CrossRef]
  10. R. W. Boyd et al., "Noise initiation of stimulated Brillouin scattering," Phys. Rev. A 42, 5514 (1990). [CrossRef] [PubMed]
  11. I. L. Fabelinskii, Molecular Scattering of Light, (Plenum Press, 1968).
  12. E. Peral and A. Yariv, "Degradation of modulation and noise characteristics of semiconductor lasers after propagation in optical fiber due to phase shift induced by stimulated Brillouin scattering" IEEE J. Quantum Elect. 35, 1185 (1999). [CrossRef]
  13. A. Kobyakov, et al., "Design concept for optical fibers with enhanced SBS threshold," Opt. Express 14, 5388 (2005).
  14. Courtesy of James Hou, Sonix Inc., Springfield, VA.
  15. See Ref. [8], the refractive index n=1.48, the Pockel’s coefficient p12=0.27, c is the speed of light in vacuum, λ=1083 nm is the wavelength, ρ=2221 kg/m3 is the density, VS=5661 m/s is the sound speed and the phonon FWHM is 123 MHz for the LP08 mode and 105 MHz for the LP01 mode.
  16. R. G. Smith, "Optical power handling capacity of low loss optical fibers as determined by stimulated Raman and Brillouin scattering," Appl. Opt. 11, 2489-2494 (1972). [CrossRef] [PubMed]

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