## Acoustic modal analysis and control in w-shaped triple-layer optical fibers with highly-germanium-doped core and F-doped inner cladding

Optics Express, Vol. 16, Issue 14, pp. 10006-10017 (2008)

http://dx.doi.org/10.1364/OE.16.010006

Acrobat PDF (1258 KB)

### Abstract

The numerical study of acoustic modal properties in w-shaped optical fibers with high-delta germanium-doped core and F-doped inner cladding (F-HDF) is demonstrated. The cutoff conditions of acoustic modes in the F-HDF show opposite behaviors in contrast with those of optical ones because F-doped inner cladding contributes differently to acoustic and optical waveguides. The acoustic dispersion characteristics vary to a great extent with respect to the location of the acoustic modes in the fiber’s core or in the fiber’s inner cladding. The resonance frequency spacing between neighboring acoustic modes is theoretically and experimentally found to have a quadratic relation to the core’s germanium concentration. We also investigate the critical conditions to move high-order acoustic modes into the F-doped inner cladding and validate the optimal feasibility of employing *L*_{01} and *L*_{03} acoustic modes to fiber-optic Brillouin-based discriminative sensing of strain and temperature.

© 2008 Optical Society of America

## 1. Introduction

1. 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]

5. M. Nikles, L. Thevenaz, and P. A. Robert, “Simple distributed fiber sensor based on Brillouin gain spectrum analysis,” Opt. Lett. **21**, 738–740, 1996. [CrossRef]

6. K. Hotate and M. Tanaka, “Distributed fiber Brillouin strain sensing with 1-cm spatial resolution by correlation-based continuous-wave technique,” IEEE Photon. Technol. Lett. **14**, 179–181, 2002. [CrossRef]

*L*

_{01}acoustic mode, that is, Brillouin frequency shift (BFS), has a linear relationship to applied strain or temperature change. The linear relationship has been used to build a type of fully-distributed fiber-optic Brillouin sensors [5

5. M. Nikles, L. Thevenaz, and P. A. Robert, “Simple distributed fiber sensor based on Brillouin gain spectrum analysis,” Opt. Lett. **21**, 738–740, 1996. [CrossRef]

6. K. Hotate and M. Tanaka, “Distributed fiber Brillouin strain sensing with 1-cm spatial resolution by correlation-based continuous-wave technique,” IEEE Photon. Technol. Lett. **14**, 179–181, 2002. [CrossRef]

*w*-shaped triple-layer single-mode optical fiber structure with a high-delta GeO

_{2}-doped core and F-doped inner cladding (F-HDF) was recently proposed and investigated [7

7. W. Zou, Z. He, M. Kishi, and K. Hotate, “Stimulated Brillouin scattering and its dependences on temperature and strain in a high-delta optical fiber with F-doped depressed inner cladding,” Opt. Lett. **32**, 600–602, 2007. [CrossRef] [PubMed]

_{2}-doped silica, four resonance frequencies in that F-HDF from various

*L*

_{0l}longitudinal acoustic modes hold different dependence behaviors to strain and temperature. The combination of 1st-order

*L*

_{01}together with 4th-order

*L*

_{04}modes provided a lowest discriminative error. This is because the

*L*

_{04}acoustic mode locates nearest to the F-doped inner cladding although still in the GeO

_{2}-doped core. It was expected that the discriminative sensing performance could be enhanced if high-order acoustic mode, such as

*L*

_{02}or

*L*

_{03}mode, was moved into the F-doped inner cladding with comparable Brillouin gain in contrast with the fundamental

*L*

_{01}acoustic mode that is always confined in the GeO

_{2}-doped core.

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]

*L*

_{01}and

*L*

_{03}acoustic modes for discriminative sensing is verified by setting fiber parameters to let

*L*

_{03}mode below its critical condition while just close to its cutoff condition.

## 2. Mathematical principles

### 2.1. Optical refractive index and longitudinal acoustic index

_{2}-doped core (

*r*≤

*a*

_{1}), F-doped inner cladding (

*a*

_{1}≤

*r*≤

*a*

_{2}) and pure-silica outer cladding (

*a*

_{2}≤

*r*≤

*b*

_{0}) where

*r*is a radial coordinate in the cylindrical optical fiber,

*a*

_{1}the core radius,

*a*

_{2}the outer radius of the inner cladding and

*b*

_{0}the outer radius of the outer cladding (i.e., ~62.5

*µ*m). The optical properties of F-HDF structure such as the optical cutoff condition and the modified optical dispersion properties have been comprehensively reported by Monerie [9

9. M. Monerie, “Propagation in doubly clad single-mode fibers,” IEEE J. Quantum Electron. **QE-18**, 535–542, 1982. [CrossRef]

10. B. J. Ainslie, K. J. Beales, C. R. Day, and J. D. Rush, “The design and fabrication of monomode optical fiber,” IEEE J. Quantum Electron. **QE-18**, 514–523, 1982. [CrossRef]

*n*profile (solid curve) and the longitudinal acoustic velocity

_{i}*V*profile (dashed curve) of the F-HDF where the subscripts

_{li}*i*=1, 2, 0 correspond to the core, inner cladding and outer cladding, respectively. In this study, we introduce a longitudinal acoustic index

*N*, as also plotted in Fig. 1 (dotted curve), which is defined as the ratio of the longitudinal acoustic velocity of pure silica (

_{i}*V*

_{l0}, 5944

*m*/

*s*[11

11. Y. Koyamada, S. Sato, S. Nakamura, H. Sotobayashi, and W. Chujo, “Simulating and designing Brillouin gain spectrum in single-mode fibers,” J. Lightwave Technol. **22**, 631–639, 2004. [CrossRef]

_{2}-doped or F-doped silica (

*V*):

_{li}7. W. Zou, Z. He, M. Kishi, and K. Hotate, “Stimulated Brillouin scattering and its dependences on temperature and strain in a high-delta optical fiber with F-doped depressed inner cladding,” Opt. Lett. **32**, 600–602, 2007. [CrossRef] [PubMed]

*n*and

_{i}*N*are dependent on the

_{i}*i*th-layer dopant concentrations:

*w*

_{1}and

*w*

_{2}are the concentrations of GeO

_{2}and F in units of molecular percent (

*mol*%) and weight percent (

*wt*%), respectively. It is worth noting that the above relationships are basically referred to [11

11. Y. Koyamada, S. Sato, S. Nakamura, H. Sotobayashi, and W. Chujo, “Simulating and designing Brillouin gain spectrum in single-mode fibers,” J. Lightwave Technol. **22**, 631–639, 2004. [CrossRef]

_{2}concentration

*w*

_{1}is thought to be

*mol*% rather than

*wt*% according to Ref. [12

12. Y. Y. Huang, A. Sarkar, and P. C. Schultz, “Relationship between composition, density and refractive index for germania silica glasses,” J. Non-Cryst. Solid. **27**, 29–37, 1978. [CrossRef]

11. Y. Koyamada, S. Sato, S. Nakamura, H. Sotobayashi, and W. Chujo, “Simulating and designing Brillouin gain spectrum in single-mode fibers,” J. Lightwave Technol. **22**, 631–639, 2004. [CrossRef]

13. Y. Park, K. Oh, U. C. Paek, D. Y. Kim, and C. R. Kurkjian, “Residual stresses in a doubly clad fiber with depressed inner cladding (DIC),” J. Lightwave Technol. **17**, 1823–1834, 1999. [CrossRef]

14. W. Zou, Z. He, A. D. Yablon, and K. Hotate, “Dependence of Brillouin frequency shift in optical fibers on draw-induced residual elastic and inelastic strains,” IEEE Photon. Technol. Lett. **19**, 1389–1391, 2007. [CrossRef]

*n*

_{0}=1.444 in 1.55-

*µ*m region [15

15. T. Mito, S. Fujino, H. Takeba, K. Morinaga, S. Todoroki, and S. Sakaguchi, “Refractive index and material dispersions of multi-component oxide glasses,” J. Non-Cryst. Solid. **210**, 155–162, 1997. [CrossRef]

*N*

_{0}=1.0 correspond to pure silica.

### 2.2. Optical scalar-wave equation

^{2}

_{a}=∂

^{2}/∂

*x*′

^{2}+∂

^{2}/∂

*y*′

^{2}is the transverse Laplacian in a coordinate normalized to the outer radius of the inner cladding

*a*

_{2}(i.e.,

*x*′=

*x*/

*a*

_{2},

*y*′=

*y*/

*a*

_{2});

*E*, the transverse electric field of the fundamental

_{i}*LP*

_{01}optical mode [i.e.,

*E*(

_{x}*x*′,

*y*′) for

*HE*

^{x}_{11}mode and

*E*(

_{y}*x*′,

*y*′) for

*HE*

^{y}_{11}mode]. v

_{op},

*P*, and

_{op}*W*are the optical normalized frequency, the normalized refractive index distribution, and the normalized optical transverse wave number, respectively, which are given by

_{op}*k*

_{0}(=2

*π*/

*λ*

_{0}) is the free-space optical wave number with

*λ*

_{0}(=1.549

*µm*in this study) the optical wavelength in vacuum,

*n*(

_{i}*r*′) with

*r*′=

*r*/

*a*

_{2}is the radial refractive index distribution in the normalized coordinates, and

*n*is the optical effective refractive index that determines the effective propagation constant

_{eff}*β*=

_{op}*k*

_{0}

*n*.

_{eff}*n⃗*is the outward pointing normal on the boundary and

*K*(

_{m}*W*) is the

_{op}*m*th-order second-kind modified Bessel function.

### 2.3. Acoustic scalar-wave equation

*l*th-order

*L*

_{0l}acoustic displacement field distributions (

*u*) follow the eigenvalue equation [1

_{z}1. 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]

17. E. Peral and A. Yariv, “Degradation of modulation and noise characteristics of semiconductor lasers after propagation in optical fiber due to shift induced by stimulated Brillouin scattering,” IEEE J. Quantum Electron. **35**, 1185–1195, 1999. [CrossRef]

^{2}=∂

^{2}/∂

*x*

^{2}+∂

^{2}/∂

*y*

^{2},

*β*is the propagation constant of the longitudinal acoustic modes decided by the Bragg-like phase-matching condition as

_{ac}*β*=2

_{ac}*β*, and

_{op}*ω*

^{(l)}

_{ac}is the

*l*th-order angular resonance frequency that is relative to

*β*and the effective

_{ac}*l*th-order longitudinal acoustic velocity

*V*

^{(l)}

_{a}as

*w*

^{(l)}

_{ac}=

*V*

^{(l)}

_{a}

*β*.

_{ac}_{ac},

*P*, and

_{ac}*W*denote the normalized acoustic frequency, the normalized acoustic index distribution, and the normalized acoustic transverse wavenumber, respectively, which are defined by:

_{ac}*N*(

_{i}*r*′) is the longitudinal acoustic index distribution and

*N*

^{(l)}

_{eff}is the effective acoustic index of the longitudinal

*l*th-order

*L*

_{0l}acoustic mode that determines the

*L*

_{0l}mode’s effective acoustic velocity as

*V*

^{(l)}

_{a}=

*V*

_{l0}/

*N*

^{(l)}

_{eff}. As follows, the

*l*th-order resonance frequency

*ν*

^{(l)}

_{ac}=

*β*·

_{ac}*V*

^{(l)}

_{a}/2

*π*in the F-HDF’s BGS can be expressed as:

*L*

_{0l}acoustic mode also satisfies the Eq. (6) except for the substitution of the acoustic eigenvalue

*W*for the optical eigenvalue

_{ac}*W*.

_{op}### 2.4. Numerical method

18. W. Zou, Z. He, and K. Hotate, “Two-dimensional finite element modal analysis of Brillouin gain spectra in optical fibers,” IEEE Photon. Technol. Lett. **18**, 2487–2489, 2006. [CrossRef]

*l*th-order

*L*

_{0l}acoustic resonance frequency in Eq. (10) is quantified; the

*l*th-order Brillouin gain (

*g*) is evaluated which is inversely proportional to the acousto-optic effective area

_{l}*A*

^{ao(l)}

_{eff}[1

1. 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]

*f*>=∫∫

*f*(

*x*′,

*y*′)d

*x*′d

*y*′ is over all the calculated core and cladding regions.

## 3. Modal analysis and modal control

### 3.1. Cutoff conditions

*n*but also to the GeO

_{eff}_{2}concentration

*w*

_{1}since

*n*

_{1}and

*N*

_{1}are both proportional to

*w*

_{1}as given in Eq. (2) and Eq. (3), respectively.

_{ac}is 5.37 to 6.00 times of v

_{op}, which means that the longitudinal acoustic modes sense better confinement than the optical mode. This characteristic is responsible for the existence of multiple-peak BGS in a GeO

_{2}-doped single-mode fiber (SMF) and even in the standard step-index SMF [18

18. W. Zou, Z. He, and K. Hotate, “Two-dimensional finite element modal analysis of Brillouin gain spectra in optical fibers,” IEEE Photon. Technol. Lett. **18**, 2487–2489, 2006. [CrossRef]

*L*

_{01}acoustic mode among the multiple-peak BGS.

_{0op}for

*LP*

_{01}and

*LP*

_{11}modes are quantified at different concentration ratio

*R*=

*w*

_{2}/

*w*

_{1}and radius ratio

*S*=

*a*

_{2}/

*a*

_{1}. To do that, the optical cutoff condition of

*W*=0 (i.e.,

_{op}*n*=

_{eff}*n*

_{0}) in Eq. (5) is preset for the boundary condition of Eq. (6) as follows:

*LP*

_{01}or

*LP*

_{11}.

_{0op}is increased when the concentration ratio

*R*or radius ratio

*S*is increased, and further the fundamental

*LP*

_{01}optical mode has a nonzero cutoff v

_{0op}. Our results are in good agreement with previously-reported ones [9

9. M. Monerie, “Propagation in doubly clad single-mode fibers,” IEEE J. Quantum Electron. **QE-18**, 535–542, 1982. [CrossRef]

*L*

_{02}or

*L*

_{03}acoustic mode. The cutoff v

_{0ac}becomes reductive when the concentration ratio

*R*or radius ratio

*S*increases, which coincides with our previous estimation that F-doped inner cladding acts as an enhanced waveguide layer for acoustic modes [see Fig. 1].

### 3.2. Acoustic dispersion properties

_{ac}at different concentration ratio

*R*or radius ratio

*S*to evaluate the dispersion curves of

*L*

_{0l}acoustic modes in the F-HDF which denote the relations between

*W*/

_{ac}*S*and v

_{ac}.

*L*

_{01}(blue solid curves),

*L*

_{02}(green dashed curves) and

*L*

_{03}(red dotted curves) acoustic modes for the concentration ratio

*R*=0.05 and the GeO

_{2}concentration

*w*

_{1}=10

*mol*% are plotted in Fig. 4(a) where a cluster of curves in the same color corresponds to different radius ratios

*S*(=1.0, 2.0, 3.5, and 5.0 from right side to left side). Similarly, Fig. 4(b) denotes the corresponding acoustic dispersion curves at the same parameters as those of Fig. 4(a) except for

*R*=0.10. In Figs. 4(a) or (b), a black solid linear curve as a based line corresponds to the case when

*N*=

_{eff}*N*

_{2}, which means that the acoustic mode is just cutoff at the interface between the physical core and the physical inner cladding.

*A*with

_{l}*l*=1, 2 or 3) between

*l*th-order acoustic dispersion curve and the based line in Fig. 4 determines a critical value of v

^{(l)}

_{c-ac}. If v

_{ac}is just below the v

^{(l)}

_{c-ac}then

*N*

^{(l)}

_{eff}<

*N*

_{2}, which means that the

*l*th-order acoustic mode enters into the F-doped physical inner cladding; vice versa, the

*l*th-order acoustic mode still exists in the GeO

_{2}-doped physical core. For example, when

*w*

_{1}=10

*mol*%,

*R*=0.05 and

*S*=1.5, v

^{(3)}

_{c-ac}=8.12 for the 3

*rd*-order

*L*

_{03}acoustic mode. Figure 5 illustrates our evaluated field distributions of the fundamental

*LP*

_{01}optical mode and all

*L*

_{0l}acoustic modes in the calculated core region for the above fiber parameters of

*w*

_{1},

*R*and

*S*but at different acoustic v

_{ac}. It can be clearly seen that when v

_{ac}becomes smaller than v

^{(3)}

_{c-ac}the

*L*

_{03}field enters more into the F-doped physical inner cladding.

^{(l)}

_{c-ac}is almost independent on the radius ratio

*S*; however, it is sensitive to the concentration ratio

*R*: when

*R*is increased, it is correspondingly increased. These dependences can be further understood from Fig. 6 where the

*l*th-order acoustic mode’s critical value v

^{(l)}

_{c-ac}and the (

*l*+1)th-order acoustic mode’s cutoff value v

^{(l+1)}

_{0ac}are plotted together as functions of the concentration ratio

*R*for different radius ratio

*S*.

*l*th-order acoustic dispersion curve from the horizontal axis in Fig. 4 corresponds to its cutoff value v

^{(l)}

_{0ac}. From it, we can clearly see that the cutoff value v

^{(l)}

_{0ac}is reduced when the radius ratio

*S*is increased, which means that the higher-order acoustic modes become more difficult to be cut off by the pure-silica outer cladding. Further, when the radius ratio

*S*is increased, the parts of the dispersion curves below the based line become closer, which results in closer acoustic modes existing in the F-doped inner cladding. These analyzed properties can well explain the experimental observation in Ref. [8

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]

_{2}-doped core but the other group including three closer peaks due to its location in the F-doped region. Figure 7 depicts our simulated BGS of the F-HDF demonstrated by Yeniay

*et al.*[8

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]

_{2}-doped core and the F-doped inner cladding, respectively.

*w*

_{1}of 3.65

*mol*% and 10

*mol*%. From it, we know that they match each other within less than 1% difference. This similarity further shows that the distinction of

*W*/

_{ac}*S*between neighboring acoustic modes is almost independent on

*w*

_{1}for a constant v

_{ac}. From Eq. (10) together with Eq. (5) and Eq. (9), we can deduce

*b*=

*W*

^{2}

_{op}/v

^{2}

_{op}is the normalized optical propagation constant. The resonance frequency spacing (Δ

*v*

^{(l)}

_{ac}≡

*v*

^{(l+1)}

_{ac}-

*v*

^{(l)}

_{ac}) between neighboring longitudinal acoustic modes can be further deduced to be

_{ac}in Eq. (9), for a fixed v

_{ac}meaning a fixed v

_{op}and

*b*approximately, an increase of

*w*

_{1}corresponds to a reduction of the core size

*a*

_{1}resulting in a smaller resonance frequency

*v*

^{(l)}

_{ac}[see Eq. (14)]. Furthermore, according to Eq. (15), a quadratic increase of the neighboring resonance frequency spacing arises from a increase of

*w*

_{1}or a reduction of

*a*

_{1}. This is the reason why a high-delta optical fiber (HDF) with highly GeO

_{2}-doped core is preferred in this study since the enlarged frequency spacing is helpful to improve the measurement system performance in discriminative sensing of strain and temperature [7

7. W. Zou, Z. He, M. Kishi, and K. Hotate, “Stimulated Brillouin scattering and its dependences on temperature and strain in a high-delta optical fiber with F-doped depressed inner cladding,” Opt. Lett. **32**, 600–602, 2007. [CrossRef] [PubMed]

*mol*% step-index SMF and in a 17.0-

*mol*% HDF via pump-probe SBS-based experimental configuration [7

**32**, 600–602, 2007. [CrossRef] [PubMed]

## 4. Application for discriminative sensing

*L*

_{01}and

*L*

_{02}acoustic modes for discriminative sensing, for which

*L*

_{03}acoustic mode is cutoff by the pure-silica outer cladding and

*L*

_{02}acoustic mode is moved into the F-doped inner cladding. Note that the fundamental

*L*

_{01}acoustic mode is always located in the GeO

_{2}-doped core since its critical v

^{(1)}

_{c-ac}is extremely low, such as less than 1.9 as illustrated in Fig. 4, which corresponds to v

_{op}=~0.35 according to Fig. 2. The modal control conditions can be understood from Fig. 6(a) in which the crossing point decides a set of

*R*and v

_{ac}-value (v

_{op}-value correspondingly). A smaller

*S*gives a greater v

_{ac}-value or v

_{op}-value providing better waveguiding efficiency. In this case, our calculation shows that the v

_{op}is necessarily small, for instance, v

_{ac}=~4.82 (or v

_{op}=~0.85) and

*R*=0.05 when

*S*=2 and

*w*

_{1}=10

*mol*%. The corresponding optical effective area defined by

^{3}

*µm*

^{2}, which means that the optical waveguiding efficiency in the physical core is extremely weak. In fact, this fiber design is impractical even although the Brillouin gain of

*L*

_{02}acoustic mode located in the F-doped inner cladding could be even greater than that of the fundamental

*L*

_{01}acoustic mode located in the GeO

_{2}-doped core.

*L*

_{03}acoustic mode together with the fundamental

*L*

_{01}acoustic mode for discriminative sensing, for which

*L*

_{04}acoustic mode is cutoff by the outer cladding and

*L*

_{03}acoustic mode is moved into the inner cladding while

*L*

_{01}and

*L*

_{02}acoustic modes are maintained in the core. Again, as depicted in Fig. 6(b), a smaller radius ratio

*S*(e.g.,=1.5) is chosen to get a greater crossed v

_{ac}-value of ~8.12 corresponding to v

_{op}-value of ~1.43 and a larger

*R*=0.05 when

*w*

_{1}=10

*mol*%.

_{op}from v

_{op}=1.43 to v

_{op}=1.15, which corresponds to the range from below the crossed v

_{ac}-value (~8.12) to beyond the

*L*

_{03}mode’s cutoff v

^{(3)}

_{0ac}(~5.93). The resonance frequency change of the

*L*

_{03}acoustic mode is ~7 times as that of the fundamental

*L*

_{01}acoustic mode providing a higher sensitivity to the fiber parameter’s change. The Brillouin gain ratios (

*g*

_{1}/

*g*

_{2}and

*g*

_{1}/

*g*

_{3}) and the optical effective area (

*A*) are also evaluated and thus plotted in Fig. 9(b), respectively. When v

_{eff}_{op}(v

_{ac}correspondingly) decreases, the optical effective area (

*A*) increases because the optical confinement is weakened as can be seen from Fig. 5. On the other hand, the Brillouin gain (

_{eff}*g*3) of the 3

*rd*-order

*L*

_{03}acoustic mode becomes more comparable to the fundamental

*L*

_{01}acoustic mode when compared to the

*g*

_{2}of the 2

*rd*-order

*L*

_{02}acoustic mode. This is because the displacement field of the 3

*rd*-order

*L*

_{03}acoustic mode enters more into the F-doped inner-cladding region for a smaller acoustic v

_{ac}(<v

^{(3)}

_{c-ac}) while the field of

*L*

_{02}acoustic mode dominantly confined in the GeO

_{2}-doped core has tiny change with v

_{ac}(see Fig. 5). Consequently, comparing to

*L*

_{02}acoustic mode,

*L*

_{03}acoustic mode has greater acousto-optic overlapping efficiency with the weakly-guided

*LP*

_{01}optical mode.

*L*

_{01}and

*L*

_{03}acoustic mode for discriminative sensing of strain and temperature by choosing v

_{op}=1.15 or v

_{ac}=6.53. Firstly,

*A*can be kept to be as low as ~53

_{eff}*µm*

^{2}. Secondly, the simulated BGS of the optimized fiber design illustrated in Fig. 10 shows that the Brillouin gain of

*L*

_{03}acoustic mode is only ~-5 dB lower than that of the fundamental

*L*

_{01}acoustic mode. This is because the acoustic v

_{ac}=6.53 is very close to the

*L*

_{03}acoustic mode’s cutoff v

^{(3)}

_{0ac}=~5.93, so that the existence of the

*L*

_{03}acoustic field in the F-doped inner cladding is significantly enhanced (see Fig. 5(d)).

## 5. Conclusions

*L*

_{03}longitudinal acoustic mode into the F-doped inner cladding effectively with comparable Brillouin gain in contrast with the fundamental

*L*

_{01}longitudinal acoustic mode and with more sensitive change (~6 times) of the resonance frequency than that of the fundamental

*L*

_{01}mode. When the

*L*

_{01}and

*L*

_{03}resonance BGS in the optimally designed F-HDF are utilized for fiber-optic Brillouin sensors, an improvement of our preliminarily investigated accuracy of discriminative measurement of strain and temperature (e.g., strain error of 44

*µε*and temperature error of 1.8 °C [7

**32**, 600–602, 2007. [CrossRef] [PubMed]

## 6. Acknowledgment

## References and links

1. | 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 |

2. | M. J. Li, S. Li, and D. A. Nolan, “Nonlinear fibers for signal processing using Kerr effects,” J. Lightwave Technol. |

3. | S. R. Bickham, X. Chen, M. J. Li, and D. T. Walton, “High SBS threshold optical fiber with fluorine dopant,” U. S. Patent 7228039 (June 2007). |

4. | I. Flammer, “Optical fiber with reduced stimulated Brillouin scattering,” U. S. Patent application, 2007/0081779 (April 2007) |

5. | M. Nikles, L. Thevenaz, and P. A. Robert, “Simple distributed fiber sensor based on Brillouin gain spectrum analysis,” Opt. Lett. |

6. | K. Hotate and M. Tanaka, “Distributed fiber Brillouin strain sensing with 1-cm spatial resolution by correlation-based continuous-wave technique,” IEEE Photon. Technol. Lett. |

7. | W. Zou, Z. He, M. Kishi, and K. Hotate, “Stimulated Brillouin scattering and its dependences on temperature and strain in a high-delta optical fiber with F-doped depressed inner cladding,” Opt. Lett. |

8. | A. Yeniay, J. M. Delavaux, and J. Toulouse, “Spontaneous and stimulated Brillouin scattering gain spectra in optical fibers,” J. Lightwave Technol. |

9. | M. Monerie, “Propagation in doubly clad single-mode fibers,” IEEE J. Quantum Electron. |

10. | B. J. Ainslie, K. J. Beales, C. R. Day, and J. D. Rush, “The design and fabrication of monomode optical fiber,” IEEE J. Quantum Electron. |

11. | Y. Koyamada, S. Sato, S. Nakamura, H. Sotobayashi, and W. Chujo, “Simulating and designing Brillouin gain spectrum in single-mode fibers,” J. Lightwave Technol. |

12. | Y. Y. Huang, A. Sarkar, and P. C. Schultz, “Relationship between composition, density and refractive index for germania silica glasses,” J. Non-Cryst. Solid. |

13. | Y. Park, K. Oh, U. C. Paek, D. Y. Kim, and C. R. Kurkjian, “Residual stresses in a doubly clad fiber with depressed inner cladding (DIC),” J. Lightwave Technol. |

14. | W. Zou, Z. He, A. D. Yablon, and K. Hotate, “Dependence of Brillouin frequency shift in optical fibers on draw-induced residual elastic and inelastic strains,” IEEE Photon. Technol. Lett. |

15. | T. Mito, S. Fujino, H. Takeba, K. Morinaga, S. Todoroki, and S. Sakaguchi, “Refractive index and material dispersions of multi-component oxide glasses,” J. Non-Cryst. Solid. |

16. | C. Su, “Eigenproblems of radially inhomogeneous optical fibers from the scalar formulation,” IEEE J. Quantum Electron. |

17. | E. Peral and A. Yariv, “Degradation of modulation and noise characteristics of semiconductor lasers after propagation in optical fiber due to shift induced by stimulated Brillouin scattering,” IEEE J. Quantum Electron. |

18. | W. Zou, Z. He, and K. Hotate, “Two-dimensional finite element modal analysis of Brillouin gain spectra in optical fibers,” IEEE Photon. Technol. Lett. |

**OCIS Codes**

(060.2270) Fiber optics and optical communications : Fiber characterization

(060.2280) Fiber optics and optical communications : Fiber design and fabrication

(060.2310) Fiber optics and optical communications : Fiber optics

(060.2370) Fiber optics and optical communications : Fiber optics sensors

(290.5830) Scattering : Scattering, Brillouin

**ToC Category:**

Fiber Optics and Optical Communications

**History**

Original Manuscript: May 16, 2008

Revised Manuscript: June 18, 2008

Manuscript Accepted: June 18, 2008

Published: June 23, 2008

**Citation**

Weiwen Zou, Zuyuan He, and Kazuo Hotate, "Acoustic modal analysis and control in w-shaped triple-layer optical fibers with highly-germanium-doped core and F-doped inner cladding," Opt. Express **16**, 10006-10017 (2008)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-16-14-10006

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### References

- 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]
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- S. R. Bickham, X. Chen, M. J. Li, and D. T. Walton, "High SBS threshold optical fiber with fluorine dopant," U. S. Patent 7228039 (June 2007).
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- M. Nikles, L. Thevenaz, P. A. Robert, "Simple distributed fiber sensor based on Brillouin gain spectrum analysis," Opt. Lett. 21, 738-740 (1996). [CrossRef]
- K. Hotate and M. Tanaka, "Distributed fiber Brillouin strain sensing with 1-cm spatial resolution by correlationbased continuous-wave technique," IEEE Photon. Technol. Lett. 14, 179-181 (2002). [CrossRef]
- W. Zou, Z. He, M. Kishi, and K. Hotate, "Stimulated Brillouin scattering and its dependences on temperature and strain in a high-delta optical fiber with F-doped depressed inner cladding," Opt. Lett. 32, 600-602 (2007). [CrossRef] [PubMed]
- 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]
- M. Monerie, "Propagation in doubly clad single-mode fibers," IEEE J. Quantum Electron. QE-18, 535-542 (1982). [CrossRef]
- B. J. Ainslie, K. J. Beales, C. R. Day, and J. D. Rush, "The design and fabrication of monomode optical fiber," IEEE J. Quantum Electron. QE-18, 514-523 (1982). [CrossRef]
- Y. Koyamada, S. Sato, S. Nakamura, H. Sotobayashi, and W. Chujo, "Simulating and designing Brillouin gain spectrum in single-mode fibers," J. Lightwave Technol. 22, 631-639 (2004). [CrossRef]
- Y. Y. Huang, A. Sarkar, and P. C. Schultz, "Relationship between composition, density and refractive index for germania silica glasses," J. Non-Cryst. Solid. 27, 29-37 (1978). [CrossRef]
- Y. Park, K. Oh, U. C. Paek, D. Y. Kim, and C. R. Kurkjian, "Residual stresses in a doubly clad fiber with depressed inner cladding (DIC)," J. Lightwave Technol. 17, 1823-1834 (1999). [CrossRef]
- W. Zou, Z. He, A. D. Yablon, and K. Hotate, "Dependence of Brillouin frequency shift in optical fibers on draw-induced residual elastic and inelastic strains," IEEE Photon. Technol. Lett. 19, 1389-1391 (2007). [CrossRef]
- T. Mito, S. Fujino, H. Takeba, K. Morinaga, S. Todoroki, and S. Sakaguchi, "Refractive index and material dispersions of multi-component oxide glasses," J. Non-Cryst. Solid. 210, 155-162 (1997). [CrossRef]
- C. Su, "Eigenproblems of radially inhomogeneous optical fibers from the scalar formulation," IEEE J. Quantum Electron. QE-10, 1554-1557 (1985).
- E. Peral and A. Yariv, "Degradation of modulation and noise characteristics of semiconductor lasers after propagation in optical fiber due to shift induced by stimulated Brillouin scattering," IEEE J. Quantum Electron. 35, 1185-1195 (1999). [CrossRef]
- W. Zou, Z. He, and K. Hotate, "Two-dimensional finite element modal analysis of Brillouin gain spectra in optical fibers," IEEE Photon. Technol. Lett. 18, 2487-2489 (2006). [CrossRef]

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