Abstract

Phase and/or intensity modulation techniques to broaden the Linewidth of an optical source are well known methods to suppress stimulated Brillouin scattering (SBS) in optical fibers. A common technique used to achieve significant bandwidth enhancement in a simple fashion is to phase modulate with a filtered noise source. We will demonstrate here that, in this case the stochastic nature of noise requires an inclusion of length dependent corrections to the SBS threshold enhancement. This effect becomes particularly significant for short fiber lengths common to most high power fiber amplifiers.

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References

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2012

2011

2010

2009

1989

E. Lichtman, R. G. Waarts, and A. A. Friesem, “Stimulated Brillouin scattering excited by a modulated pump wave in single-mode fibers,” J. Lightwave Technol.7(1), 171–174 (1989).
[CrossRef]

Augst, S. J.

Brückner, F.

Chowdhury, D.

Clarkson, W. A.

Clausnitzer, T.

Dajani, I.

Di Domenico, G.

Eberhardt, R.

Fan, T. Y.

Friesem, A. A.

E. Lichtman, R. G. Waarts, and A. A. Friesem, “Stimulated Brillouin scattering excited by a modulated pump wave in single-mode fibers,” J. Lightwave Technol.7(1), 171–174 (1989).
[CrossRef]

Goldizen, K. C.

Goodno, G. D.

Gowin, M.

Jung, M.

Kobyakov, A.

Lichtman, E.

E. Lichtman, R. G. Waarts, and A. A. Friesem, “Stimulated Brillouin scattering excited by a modulated pump wave in single-mode fibers,” J. Lightwave Technol.7(1), 171–174 (1989).
[CrossRef]

Limpert, J.

Ludewigt, K.

McComb, T. S.

McNaught, S. J.

Moore, G. T.

Mungan, C. E.

C. E. Mungan, S. D. Rogers, N. Satyan, and J. O. White, “Time-dependent modeling of Brillouin scattering in optical fibers excited by a chirped diode laser,” IEEE J. Quantum Electron.48(12), 1542–1546 (2012).
[CrossRef]

Murphy, D. V.

Naderi, S.

Nilsson, J.

Peschel, T.

Redmond, S. M.

Richardson, D. J.

Robin, C.

Rogers, S. D.

C. E. Mungan, S. D. Rogers, N. Satyan, and J. O. White, “Time-dependent modeling of Brillouin scattering in optical fibers excited by a chirped diode laser,” IEEE J. Quantum Electron.48(12), 1542–1546 (2012).
[CrossRef]

Rothenberg, J. E.

Sanchez, A.

Satyan, N.

C. E. Mungan, S. D. Rogers, N. Satyan, and J. O. White, “Time-dependent modeling of Brillouin scattering in optical fibers excited by a chirped diode laser,” IEEE J. Quantum Electron.48(12), 1542–1546 (2012).
[CrossRef]

Sauer, M.

Schilt, S.

Schmidt, O.

Schreiber, T.

Supradeepa, V. R.

ten Have, E.

Thielen, P. A.

Thomann, P.

Tsybin, I.

Tünnermann, A.

Waarts, R. G.

E. Lichtman, R. G. Waarts, and A. A. Friesem, “Stimulated Brillouin scattering excited by a modulated pump wave in single-mode fibers,” J. Lightwave Technol.7(1), 171–174 (1989).
[CrossRef]

Weber, M. E.

Weiner, A. M.

White, J. O.

C. E. Mungan, S. D. Rogers, N. Satyan, and J. O. White, “Time-dependent modeling of Brillouin scattering in optical fibers excited by a chirped diode laser,” IEEE J. Quantum Electron.48(12), 1542–1546 (2012).
[CrossRef]

Wickham, M. G.

Wirth, C.

Yu, C. X.

Zeringue, C.

Adv. Opt. Photon.

Appl. Opt.

IEEE J. Quantum Electron.

C. E. Mungan, S. D. Rogers, N. Satyan, and J. O. White, “Time-dependent modeling of Brillouin scattering in optical fibers excited by a chirped diode laser,” IEEE J. Quantum Electron.48(12), 1542–1546 (2012).
[CrossRef]

J. Lightwave Technol.

E. Lichtman, R. G. Waarts, and A. A. Friesem, “Stimulated Brillouin scattering excited by a modulated pump wave in single-mode fibers,” J. Lightwave Technol.7(1), 171–174 (1989).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Express

Opt. Lett.

Other

G. P. Agrawal, “Nonlinear fiber optics, 4th ed,” (Academic Press, 2007).

A. Kanno, S. Honda, R. Yamanaka, H. Sotobayashi, and T. Kawanishi, “2.56 x10 ^{17} Hz/s frequency chirp signal generation using DSB-SC optical modulation without optical filters,” In The European Conference on Lasers and Electro-Optics. Optical Society of America (2011).

S. M. Kay, Fundamentals of statistical signal processing, volume I: estimation theory (Prentice-Hall, 1993), Vol. 1.

R. G. Gallager, “Stochastic processes: theory for applications,” (Draft, 2012) http://www.rle.mit.edu/rgallager/notes.htm .

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Figures (5)

Fig. 1
Fig. 1

Schematic showing a narrow linewidth input source to a power amplifier. The narrow linewidth source is generated by intensity (IM) and/or phase modulation (PM) with noise of a Single frequency (SF) seed. A low pass filter (LP) is used to control the bandwidth.

Fig. 2
Fig. 2

An instance of the filtered noise time domain waveform used to modulate the phase of the optical carrier. Actual power spectrum and the power spectral density.

Fig. 3
Fig. 3

The fiber (and the time domain waveform) used for intensity or phase modulation is considered in L B sized segments. The effective spectrum for a specific fiber length is the mean of the power spectrum of every segment preceding it. The effective spectrum smoothens out as the fiber length increases.

Fig. 4
Fig. 4

Plot showing enhancement reduction (relative to ideal value) versus normalized length of the fiber.

Fig. 5
Fig. 5

Comparison between this work and the numerical results from ref [12].

Equations (25)

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EF= σ(S(f) g B (f)) σ( g B (f))
EF=1+ Δf Δ υ B
S k (f) = lim k 1 k k S k (f) = S ¯ (f)
L B = c n fiber Δ υ B
X k r ( f n )= a(t) cos(2π f n t) W k (t) g i (t) dt X k c ( f n )= a(t) sin(2π f n t) W k (t) g j (t) dt
1 2 sin(2*2π f n t) | W k (t) | 2 dt
X k r ( f n )= cosϕ(t)cos(2π f n t) W k (t)dt sinϕ(t)sin(2π f n t) W k (t)dt X k c ( f n )= cosϕ(t)sin(2π f n t) W k (t)dt+ sinϕ(t)cos(2π f n t) W k (t)dt
S k ( f n )= i=1 k | X i r ( f n ) | 2 + i=1 k | X i c ( f n ) | 2
σ= ( S k (f)df ) 2 S k 2 (f)df
σ=Δ υ B ( n S k ( f n ) ) 2 n S k 2 ( f n )
σ=Δ υ B ( n S ¯ ( f n ) ) 2 n S k 2 ( f n ) =Δ υ B ( n S ¯ ( f n ) ) 2 n S k 2 ( f n )
S k 2 ( f n ) = 2k(2k+2) (2k) 2 S ¯ 2 ( f n )= k+1 k S ¯ 2 ( f n )
σ= k k+1 Δ υ B ( n S ¯ ( f n ) ) 2 n S ¯ 2 ( f n ) = k k+1 σ ideal
EF= k k+1 E F ideal
EF= (L/ L B ) (L/ L B )+1 E F ideal
EF= Δ υ B Δ υ B + c n fiber L E F ideal
S k ( f n )= i=1 k w i | X i r ( f n ) | 2 + i=1 k w i | X i c ( f n ) | 2
w i = E i i=1 k E i = P i i=1 k P i
S k ( f n )= i=1 k w i S 2 ( f n )
S k 2 ( f n ) =(1+ i=1 k w i 2 ) S ¯ 2 ( f n )
i=1 k w i 2 = i=1 k P i 2 ( i=1 k P i ) 2
L eff = ( P(z)dz ) 2 P (z) 2 dz
σ= L eff / L B 1+ L eff / L B σ ideal
EF= L eff / L B 1+ L eff / L B E F ideal = Δ υ B Δ υ B + c n fiber L eff E F ideal
L eff = ( g B (z)P(z) A eff (z) dz ) 2 ( g B (z)P(z) A eff (z) ) 2 dz

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