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Brillouin Gain Spectra of Few Mode FibresLars Grüner-Nielsen (1), and Søren Herstrøm (2)

(1) Danish Optical Fiber Innovation, (2) OFS Fitel Denmark ApS

Slide no. 1

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Introduction• Known model* for single mode fibres has been expanded to include few mode fibres

• Brillouin gain is found from the overlap between guided optical mode and guided acoustic modes

• Model is tested on a two LP mode fibre

• Simulations are compared to measurements

* A. Kobyakov et al, “Stimulated Brillouin scattering in optical fibers,” Advances in Optics and Photonics, Vol. 2, no. 1, p. 1 (2010)

Slide no. 2

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Modeling 1

Slide no. 3

Acoustic modes are found by solving the acoustic wave equation:

)r()r(vkdr

)r(d

r

v

dr

)r(dv 2

B

2

A

2

B

2

A

2

22

A

The acoustic velocity vA(r) is found from the index profile Dn(r):

DD

DD

0)r(nfor)r(n1v

0)r(nfor)r(n1v)r(v

F2SiO,A

2GeO2SiO,A

A

GeO2 is > 0 and F is < 0. I.e. both GeO2 doping and F doping will lead to acoustic guided regions

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Modeling 2

Slide no. 4

Only modes with velocity lower than in the cladding are guided: 2SiO,A

B

m,B

m vk

v

2m,Bbw

2

m,B

2

m,Bbw

m,0m2/

2/G)(G

D

D

2r

0

2

0

m

2

Bm,Bbw

3

2

12

8

effm,0

f

rdrdEc

pn4G

DDm

m )(G)(G

Calculation of Brillouin gain efficiency G:

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Measurement setup

Slide no. 5

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Results

Slide no. 6

Fibre under test: two LP mode graded index fibre: L. Grüner-Nielsen et al., “Few Mode Transmission Fiberwith low DGD, low Mode Coupling, and low Loss,” J. Lightwave Technol., Vol. 30, no. 23, p. 3693 (2012)

Mode no.(m)

nB, LP01 G0,m

LP01

nB, LP11 G0,m

LP11

GHz (Wm)-1 GHz (Wm)-1

1 10.768 0.144 10.747 0.010

2 10.776 - 10.756 -

3 10.801 - 10.780 -

4 10.824 0.031 10.804 0.037

5 10.842 - 10.822 -

6 10.882 0.007 10.861 0.025

7 10.899 - 10.878 -

Mode no.(m)

nB, LP01 G0,m

LP01

nB, LP11 G0,m

LP11

GHz (Wm)-1 GHz (Wm)-1

8 10.940 0.002 10.920 0.012

9 10.969 - 10.949 -

10 10.999 - 10.978 0.005

11 11.051 - 11.031 -

12 11.057 - 11.037 0.002

13 11.115 - 11.094 0.001

14 11.137 - 11.117 -

14 guided acoustic modes found

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Index profile and mode distribution optical and all guided acoustic modes

Slide no. 7

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Index profile and mode distribution optical and acoustic core modes

Slide no. 8

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Index profile and mode distribution optical and acoustic ring modes

Slide no. 9

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Index profile and mode distribution optical and acoustic core & ring modes

Slide no. 10

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Modelled and measured Brillouin spectra

Slide no. 11

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Conclusion• The Brillouin gain efficiency and its spectrum is determined from the overlap between the

optical mode and the guided acoustic modes

• The Brillouin gain spectra differ between different optical modes due to dissimilar overlap between optical and acoustic modes

Slide no. 12