Abstract

We present extensive stimulated Brillouin scattering (SBS) results from experiments and modeling for four different photonic crystal fibers (PCFs) with core diameters ranging from 8 to 1.7μm. These results reveal several SBS characteristic features of small-core PCFs, high thresholds, and acoustic peaks, which are due to their antiguiding nature and highly multimode acoustic character. The nature of what we believe to be new acoustic modes is examined in the light of the large variations observed in the Brillouin gain, Brillouin threshold, and Brillouin shift with decreasing core diameter and optical wavelength.

© 2008 Optical Society of America

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  1. J. Toulouse, E. J. H. Davies, S. Y. Texier, R. K. Pattnaik, L. Farr, B. J. Mangan, and J. C. Knight, “Stimulated Brillouin scattering and lasing,” in Nonlinear Guided Waves and Their Applications, edited by A.Sawchuk, Vol. 80 of OSA Trends in Optics and Photonics (Optical Society of America, 2002), paper PD7.
  2. L. Zou, X. Bao, and L. Chen,“Brillouin scattering spectrum in photonic crystal fiber with a partially germanium-doped core,” Opt. Lett. 28, 2022-2024 (2003).
    [CrossRef] [PubMed]
  3. P. Dainese, P. St. J. Russell, N. Joly, J. C. Knight, G. S. Wiederhecker, H. L. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibers,” Nat. Phys. 2, 388-923 (2006).
    [CrossRef]
  4. K. Saitoh and M. Koshiba, “Numerical modeling of photonic crystal fibers,” J. Lightwave Technol. 23, 3580-3590 (2005).
    [CrossRef]
  5. V. Laude, A. Khelif, S. Benchabane, M. Wilm, T. Sylvestre, B. Kibler, A. Mussot, J. M. Dudley, and H. Maillotte, “Phononic band-gap guidance of acoustic modes in photonic crystal fibers,” Phys. Rev. B 71, 45107-1-45107-6 (2005).
    [CrossRef]
  6. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1995).
  7. D. Cotter, “Observation of stimulated Brillouin scattering in low-loss silica fibre at 1.3μm,” Electron. Lett. 18, 495-496 (1982).
    [CrossRef]
  8. A. Yeniay, J.-M. Delavaux, and J. Toulouse, “Spontaneous and stimulated Brillouin scattering gain spectra in optical fibers,” J. Lightwave Technol. 20, 1425-1432 (2002).
    [CrossRef]
  9. J. F. Berret and M. Meissner, “How universal are the low temperature acoustic properties of glasses?,” Z. Phys. B: Condens. Matter 70, 65-72 (1988).
    [CrossRef]
  10. J. Yu, B. Kwon, and K. Oh, “Analysis of Brillouin frequency shift and longitudinal acoustic wave in a silica optical fiber with a triple-layered structure,” J. Lightwave Technol. 21, 1779-1786 (2003).
    [CrossRef]
  11. I. Enomori, K. Saitoh, and M. Koshiba, “Fundamental characteristics of localized acoustic modes in photonic crystal fibers,” IEICE Trans. Electron. E88, 876-881 (2005).
    [CrossRef]
  12. A. Kobyakov, S. Kumar, D. Q. Chowdhury, A. B. Ruffin, M. Sauer, and S. R. Bickham, “Design concept for optical fibers with enhanced SBS threshold,” Opt. Express 13, 5338-5346 (2005).
    [CrossRef] [PubMed]
  13. K. Saitoh and M. Koshiba, “Full-vectorial imaginary-distance beam propagation method based on a finite element scheme: application to photonic crystal fibers,” IEEE J. Quantum Electron. 38, 927-933 (2002).
    [CrossRef]
  14. I. Bongrand, E. Picholle, and C. Montes, “Coupled longitudinal and transverse stimulated Brillouin scattering in single-mode optical fibers,” Eur. Phys. J. D 20, 121-127 (2002).
    [CrossRef]
  15. R. M. Shelby, M. D. Levenson, and P. W. Bayer, “Guided acoustic-wave Brillouin scattering,” Phys. Rev. B 31, 5244-5252 (1985).
    [CrossRef]
  16. P. Dainese, P. St. J. Russell, G. S. Wiederhecker, N. Joly, H. L. Fragnito, V. Laude, and A. Khelif, “Raman-like scattering from acoustic phonons in photonic crystal fiber,” Opt. Express 14, 4141-4150 (2006).
    [CrossRef] [PubMed]

2006

P. Dainese, P. St. J. Russell, N. Joly, J. C. Knight, G. S. Wiederhecker, H. L. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibers,” Nat. Phys. 2, 388-923 (2006).
[CrossRef]

P. Dainese, P. St. J. Russell, G. S. Wiederhecker, N. Joly, H. L. Fragnito, V. Laude, and A. Khelif, “Raman-like scattering from acoustic phonons in photonic crystal fiber,” Opt. Express 14, 4141-4150 (2006).
[CrossRef] [PubMed]

2005

I. Enomori, K. Saitoh, and M. Koshiba, “Fundamental characteristics of localized acoustic modes in photonic crystal fibers,” IEICE Trans. Electron. E88, 876-881 (2005).
[CrossRef]

A. Kobyakov, S. Kumar, D. Q. Chowdhury, A. B. Ruffin, M. Sauer, and S. R. Bickham, “Design concept for optical fibers with enhanced SBS threshold,” Opt. Express 13, 5338-5346 (2005).
[CrossRef] [PubMed]

K. Saitoh and M. Koshiba, “Numerical modeling of photonic crystal fibers,” J. Lightwave Technol. 23, 3580-3590 (2005).
[CrossRef]

V. Laude, A. Khelif, S. Benchabane, M. Wilm, T. Sylvestre, B. Kibler, A. Mussot, J. M. Dudley, and H. Maillotte, “Phononic band-gap guidance of acoustic modes in photonic crystal fibers,” Phys. Rev. B 71, 45107-1-45107-6 (2005).
[CrossRef]

2003

2002

A. Yeniay, J.-M. Delavaux, and J. Toulouse, “Spontaneous and stimulated Brillouin scattering gain spectra in optical fibers,” J. Lightwave Technol. 20, 1425-1432 (2002).
[CrossRef]

K. Saitoh and M. Koshiba, “Full-vectorial imaginary-distance beam propagation method based on a finite element scheme: application to photonic crystal fibers,” IEEE J. Quantum Electron. 38, 927-933 (2002).
[CrossRef]

I. Bongrand, E. Picholle, and C. Montes, “Coupled longitudinal and transverse stimulated Brillouin scattering in single-mode optical fibers,” Eur. Phys. J. D 20, 121-127 (2002).
[CrossRef]

1988

J. F. Berret and M. Meissner, “How universal are the low temperature acoustic properties of glasses?,” Z. Phys. B: Condens. Matter 70, 65-72 (1988).
[CrossRef]

1985

R. M. Shelby, M. D. Levenson, and P. W. Bayer, “Guided acoustic-wave Brillouin scattering,” Phys. Rev. B 31, 5244-5252 (1985).
[CrossRef]

1982

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

Electron. Lett.

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

Eur. Phys. J. D

I. Bongrand, E. Picholle, and C. Montes, “Coupled longitudinal and transverse stimulated Brillouin scattering in single-mode optical fibers,” Eur. Phys. J. D 20, 121-127 (2002).
[CrossRef]

IEEE J. Quantum Electron.

K. Saitoh and M. Koshiba, “Full-vectorial imaginary-distance beam propagation method based on a finite element scheme: application to photonic crystal fibers,” IEEE J. Quantum Electron. 38, 927-933 (2002).
[CrossRef]

IEICE Trans. Electron.

I. Enomori, K. Saitoh, and M. Koshiba, “Fundamental characteristics of localized acoustic modes in photonic crystal fibers,” IEICE Trans. Electron. E88, 876-881 (2005).
[CrossRef]

J. Lightwave Technol.

Nat. Phys.

P. Dainese, P. St. J. Russell, N. Joly, J. C. Knight, G. S. Wiederhecker, H. L. Fragnito, V. Laude, and A. Khelif, “Stimulated Brillouin scattering from multi-GHz-guided acoustic phonons in nanostructured photonic crystal fibers,” Nat. Phys. 2, 388-923 (2006).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. B

V. Laude, A. Khelif, S. Benchabane, M. Wilm, T. Sylvestre, B. Kibler, A. Mussot, J. M. Dudley, and H. Maillotte, “Phononic band-gap guidance of acoustic modes in photonic crystal fibers,” Phys. Rev. B 71, 45107-1-45107-6 (2005).
[CrossRef]

R. M. Shelby, M. D. Levenson, and P. W. Bayer, “Guided acoustic-wave Brillouin scattering,” Phys. Rev. B 31, 5244-5252 (1985).
[CrossRef]

Z. Phys. B: Condens. Matter

J. F. Berret and M. Meissner, “How universal are the low temperature acoustic properties of glasses?,” Z. Phys. B: Condens. Matter 70, 65-72 (1988).
[CrossRef]

Other

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1995).

J. Toulouse, E. J. H. Davies, S. Y. Texier, R. K. Pattnaik, L. Farr, B. J. Mangan, and J. C. Knight, “Stimulated Brillouin scattering and lasing,” in Nonlinear Guided Waves and Their Applications, edited by A.Sawchuk, Vol. 80 of OSA Trends in Optics and Photonics (Optical Society of America, 2002), paper PD7.

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Figures (17)

Fig. 1
Fig. 1

Measured attenuation (using cut-back technique) in the small-core (a) RB65 fiber and (b) crystal fiber. Note that the attenuation in both fibers is in excess of 20 dB km at 1550 nm .

Fig. 2
Fig. 2

Effective area of the optical mode (solid) and geometric core area (open) as a function of core size for a d Λ of (a) 0.60 matching that of the CF and (b) 0.49 matching that of the RB65 fiber.

Fig. 3
Fig. 3

Schematics of the Brillouin scattering measurement setup.

Fig. 4
Fig. 4

Output and reflected power in the large-core RB61 fiber. The Brillouin scattering becomes stimulated when the input power exceeds 24 dB m .

Fig. 5
Fig. 5

Brillouin spectrum of the RB61 fiber with pump wavelength at 1550 nm for different input powers. The spectral shape is symmetric and does not reveal any unusual features. The peak is at 11.1 GHz .

Fig. 6
Fig. 6

Brillouin shift as a function of inverse pump wavelength. The speed of sound waves is estimated from the slope of the linear fit. A refractive index of 1.439 is assumed in this estimation.

Fig. 7
Fig. 7

Reflected (solid) and transmitted (open) power for RB65 fiber ( λ P = 1550 nm ) .

Fig. 8
Fig. 8

Brillouin spectrum of the RB65 fiber with pump wavelength at 1550 nm . Signal for different input powers. The spectrum reveals an extra peak on the high frequency end. The main peak is at 10.96 GHz , while the second one is at 11.043 GHz .

Fig. 9
Fig. 9

Brillouin shift in RB65 fiber for different pump wavelengths. The speed of sound waves is estimated from the slope of the linear fit. An effective refractive of 1.42 was used in this estimation. A linear fit to the second peak curve does not pass through the origin.

Fig. 10
Fig. 10

Reflected (solid) and transmitted (open) powers in the CF ( λ P = 1550 nm ) .

Fig. 11
Fig. 11

Brillouin spectrum of the crystal fiber with pump wavelength at 1540 nm for different input powers. The spectrum reveals three peaks with the largest peak shifted to lower frequency, 10.65 GHz , the small second peak at 10.74 GHz , and the third peak at 11.04 GHz .

Fig. 12
Fig. 12

Pump wavelength dependence of the Brillouin shift in CF. A linear fit to the first peak passes through the origin, as expected for longitudinal waves in solids. An effective refractive index of 1.359 was used in this estimation. A linear fit to the second peak, however, does not pass through the origin.

Fig. 13
Fig. 13

Dependence of the Brillouin gain on core diameter. Values of the ratio d H Λ are indicated above each data point.

Fig. 14
Fig. 14

Brillouin shift frequency as a function of core diameter. The connecting lines are a visual guide only. The solid curve shows the dependence of the main peak on the core size while the dashed curve shows the dependence of the second peak. The open triangle is indicates the frequency of the third peak of the CF.

Fig. 15
Fig. 15

Brillouin gain calculated from Eq. (6) for RB61, RB65, and CF, respectively.

Fig. 16
Fig. 16

a)–c) u z component of the acoustic displacement distribution at the main Brillouin peak frequency, 11.044, 10.920, 10.622 GHz, for RB61, RB65, and CF, respectively. d)–f) Corresponding optical mode field distribution for 1550 nm .

Fig. 17
Fig. 17

a) and b) Acoustic displacement distribution components u x and u y [ u z in Fig. 16c] of CF at the main Brillouin peak frequency, 10.622 GHz . c)–e) Acoustic displacement distribution components u x , u y , u z , respectively, at the third peak frequency, 10.96 GHz .

Tables (1)

Tables Icon

Table 1 Fiber Parameters at 1550 nm and Threshold SBS Powers Calculated Using Eq. (1), Assuming a Brillouin Coefficient g B = 5 × 10 11 W m

Equations (6)

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A eff opt = ( F ( x , y ) 2 d x d y ) 2 F ( x , y ) 4 d x d y ,
P th = 21 A eff g B L eff .
ν B = 2 n eff V A λ ,
g i ( f ) = 4 π n eff 8 p 12 2 λ 3 ρ c f B i Δ f B i Δ f B i 2 4 ( f f B i ) 2 + Δ f B i 2 1 A eff , i ao
A eff , i ao = [ ϕ 2 ( x , y ) d x d y ] 2 [ u z i ( x , y ) ϕ 2 ( x , y ) d x d y ] 2 u z i 2 ( x , y ) d x d y ,
g ( f ) = i g i ( f ) .

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