Abstract

Polarization dependence in microbend gratings is an inherent problem. We formulate simple analytical expressions to describe it, and demonstrate their effectiveness via a comparison with experimental results on a standard transmission fiber. The ability to control polarization dependence with fiber design potentially enables replacing UV-LPGs within low-cost, tunable microbend gratings.

© 2005 Optical Society of America

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References

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  1. C. B. Probst, A. Bjarklev, and S. B. Andreasen, “Experimental Verification of Microbending Theory Using Mode Coupling to Discrete Cladding Modes,” J. Lightwave Technol. 7, 55–61 (1989).
    [CrossRef]
  2. S. Savin, M. J. F. Digonnet, G. S. Kino, and H. J. Shaw, “Tunable Mechanically Induced Long Period Fiber Gratings,” Opt. Lett. 25, 710–712 (2000).
    [CrossRef]
  3. S. H. Yun, H. K. Lee, H. K. Kim, and B. Y. Kim, “Dynamic Erbium-Doped Fiber Amplifier Based on Active Gain Flattening with Fiber Acousto-optic Tunable Filters,” IEEE Photonics Technol. Lett. 11, 1229–1231 (1999).
    [CrossRef]
  4. S. Ramachandran, M. F. Yan, E. Monberg, F. Dimarcello, P. Wisk, and S. Ghalmi, “Record Bandwidth Microbend Gratings for Spectrally Flat Variable Optical Attenuators,” IEEE Photonics Technol. Lett. 15, 1561–1563 (2003).
    [CrossRef]
  5. Q. Li, A. A. Au, C.-H. Lin, E. R. Lyons, and H. P. Lee, “An Efficient All-Fiber Variable Optical Attenuator via Acoustooptic Mode Coupling,” IEEE Photonics Technol. Lett. 14, 1563–1565 (2002).
    [CrossRef]
  6. C. D. Pool, C. D. Townsend, and K. T. Nelson, “Helical-Grating Two-Mode Fiber Spatial-Mode Coupler,” J. Lightwave Technol. 9, 598–604 (1991).
    [CrossRef]
  7. T. E. Dimmick, G. Kakarantzas, T. A. Birks, A. Diez, and P. S. J. Russell, “Compact All-Fiber Acoustooptic Tunable Filters with Small Bandwidth-Length Product,” IEEE Photonics Technol. Lett. 12, 1210–1212 (2000).
    [CrossRef]
  8. S. Ramachandran, S. E. Golowich, M. F. Yan, E. Monberg, F. Dimarcello, J. Fleming, S. Ghalmi, and P. Wisk, “Lifting Polarisation Degeneracy Of Modes By Fiber Design: A Platform for Polarisation Insensitive Microbend Fiber Gratings,” Opt. Lett. (in press).
    [PubMed]
  9. S. Ramachandran, Z. Wang, and M. F. Yan, “Bandwidth Control of Long-Period Grating-Based Mode Converters in Few-Mode Fibers,” Opt. Lett. 27, 698–700 (2002).
    [CrossRef]
  10. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983).
  11. D. Chowdhury and D. Wilcox, “Comparison Between Optical Fiber Birefringence Induced by Stress Anisotriipy and Geometric Deformation,” IEEE J. Sel. Top. Quantum Electron. 6, 227–232 (2000).
    [CrossRef]

2003 (1)

S. Ramachandran, M. F. Yan, E. Monberg, F. Dimarcello, P. Wisk, and S. Ghalmi, “Record Bandwidth Microbend Gratings for Spectrally Flat Variable Optical Attenuators,” IEEE Photonics Technol. Lett. 15, 1561–1563 (2003).
[CrossRef]

2002 (2)

Q. Li, A. A. Au, C.-H. Lin, E. R. Lyons, and H. P. Lee, “An Efficient All-Fiber Variable Optical Attenuator via Acoustooptic Mode Coupling,” IEEE Photonics Technol. Lett. 14, 1563–1565 (2002).
[CrossRef]

S. Ramachandran, Z. Wang, and M. F. Yan, “Bandwidth Control of Long-Period Grating-Based Mode Converters in Few-Mode Fibers,” Opt. Lett. 27, 698–700 (2002).
[CrossRef]

2000 (3)

D. Chowdhury and D. Wilcox, “Comparison Between Optical Fiber Birefringence Induced by Stress Anisotriipy and Geometric Deformation,” IEEE J. Sel. Top. Quantum Electron. 6, 227–232 (2000).
[CrossRef]

T. E. Dimmick, G. Kakarantzas, T. A. Birks, A. Diez, and P. S. J. Russell, “Compact All-Fiber Acoustooptic Tunable Filters with Small Bandwidth-Length Product,” IEEE Photonics Technol. Lett. 12, 1210–1212 (2000).
[CrossRef]

S. Savin, M. J. F. Digonnet, G. S. Kino, and H. J. Shaw, “Tunable Mechanically Induced Long Period Fiber Gratings,” Opt. Lett. 25, 710–712 (2000).
[CrossRef]

1999 (1)

S. H. Yun, H. K. Lee, H. K. Kim, and B. Y. Kim, “Dynamic Erbium-Doped Fiber Amplifier Based on Active Gain Flattening with Fiber Acousto-optic Tunable Filters,” IEEE Photonics Technol. Lett. 11, 1229–1231 (1999).
[CrossRef]

1991 (1)

C. D. Pool, C. D. Townsend, and K. T. Nelson, “Helical-Grating Two-Mode Fiber Spatial-Mode Coupler,” J. Lightwave Technol. 9, 598–604 (1991).
[CrossRef]

1989 (1)

C. B. Probst, A. Bjarklev, and S. B. Andreasen, “Experimental Verification of Microbending Theory Using Mode Coupling to Discrete Cladding Modes,” J. Lightwave Technol. 7, 55–61 (1989).
[CrossRef]

Andreasen, S. B.

C. B. Probst, A. Bjarklev, and S. B. Andreasen, “Experimental Verification of Microbending Theory Using Mode Coupling to Discrete Cladding Modes,” J. Lightwave Technol. 7, 55–61 (1989).
[CrossRef]

Au, A. A.

Q. Li, A. A. Au, C.-H. Lin, E. R. Lyons, and H. P. Lee, “An Efficient All-Fiber Variable Optical Attenuator via Acoustooptic Mode Coupling,” IEEE Photonics Technol. Lett. 14, 1563–1565 (2002).
[CrossRef]

Birks, T. A.

T. E. Dimmick, G. Kakarantzas, T. A. Birks, A. Diez, and P. S. J. Russell, “Compact All-Fiber Acoustooptic Tunable Filters with Small Bandwidth-Length Product,” IEEE Photonics Technol. Lett. 12, 1210–1212 (2000).
[CrossRef]

Bjarklev, A.

C. B. Probst, A. Bjarklev, and S. B. Andreasen, “Experimental Verification of Microbending Theory Using Mode Coupling to Discrete Cladding Modes,” J. Lightwave Technol. 7, 55–61 (1989).
[CrossRef]

Chowdhury, D.

D. Chowdhury and D. Wilcox, “Comparison Between Optical Fiber Birefringence Induced by Stress Anisotriipy and Geometric Deformation,” IEEE J. Sel. Top. Quantum Electron. 6, 227–232 (2000).
[CrossRef]

Diez, A.

T. E. Dimmick, G. Kakarantzas, T. A. Birks, A. Diez, and P. S. J. Russell, “Compact All-Fiber Acoustooptic Tunable Filters with Small Bandwidth-Length Product,” IEEE Photonics Technol. Lett. 12, 1210–1212 (2000).
[CrossRef]

Digonnet, M. J. F.

Dimarcello, F.

S. Ramachandran, M. F. Yan, E. Monberg, F. Dimarcello, P. Wisk, and S. Ghalmi, “Record Bandwidth Microbend Gratings for Spectrally Flat Variable Optical Attenuators,” IEEE Photonics Technol. Lett. 15, 1561–1563 (2003).
[CrossRef]

S. Ramachandran, S. E. Golowich, M. F. Yan, E. Monberg, F. Dimarcello, J. Fleming, S. Ghalmi, and P. Wisk, “Lifting Polarisation Degeneracy Of Modes By Fiber Design: A Platform for Polarisation Insensitive Microbend Fiber Gratings,” Opt. Lett. (in press).
[PubMed]

Dimmick, T. E.

T. E. Dimmick, G. Kakarantzas, T. A. Birks, A. Diez, and P. S. J. Russell, “Compact All-Fiber Acoustooptic Tunable Filters with Small Bandwidth-Length Product,” IEEE Photonics Technol. Lett. 12, 1210–1212 (2000).
[CrossRef]

Fleming, J.

S. Ramachandran, S. E. Golowich, M. F. Yan, E. Monberg, F. Dimarcello, J. Fleming, S. Ghalmi, and P. Wisk, “Lifting Polarisation Degeneracy Of Modes By Fiber Design: A Platform for Polarisation Insensitive Microbend Fiber Gratings,” Opt. Lett. (in press).
[PubMed]

Ghalmi, S.

S. Ramachandran, M. F. Yan, E. Monberg, F. Dimarcello, P. Wisk, and S. Ghalmi, “Record Bandwidth Microbend Gratings for Spectrally Flat Variable Optical Attenuators,” IEEE Photonics Technol. Lett. 15, 1561–1563 (2003).
[CrossRef]

S. Ramachandran, S. E. Golowich, M. F. Yan, E. Monberg, F. Dimarcello, J. Fleming, S. Ghalmi, and P. Wisk, “Lifting Polarisation Degeneracy Of Modes By Fiber Design: A Platform for Polarisation Insensitive Microbend Fiber Gratings,” Opt. Lett. (in press).
[PubMed]

Golowich, S. E.

S. Ramachandran, S. E. Golowich, M. F. Yan, E. Monberg, F. Dimarcello, J. Fleming, S. Ghalmi, and P. Wisk, “Lifting Polarisation Degeneracy Of Modes By Fiber Design: A Platform for Polarisation Insensitive Microbend Fiber Gratings,” Opt. Lett. (in press).
[PubMed]

Kakarantzas, G.

T. E. Dimmick, G. Kakarantzas, T. A. Birks, A. Diez, and P. S. J. Russell, “Compact All-Fiber Acoustooptic Tunable Filters with Small Bandwidth-Length Product,” IEEE Photonics Technol. Lett. 12, 1210–1212 (2000).
[CrossRef]

Kim, B. Y.

S. H. Yun, H. K. Lee, H. K. Kim, and B. Y. Kim, “Dynamic Erbium-Doped Fiber Amplifier Based on Active Gain Flattening with Fiber Acousto-optic Tunable Filters,” IEEE Photonics Technol. Lett. 11, 1229–1231 (1999).
[CrossRef]

Kim, H. K.

S. H. Yun, H. K. Lee, H. K. Kim, and B. Y. Kim, “Dynamic Erbium-Doped Fiber Amplifier Based on Active Gain Flattening with Fiber Acousto-optic Tunable Filters,” IEEE Photonics Technol. Lett. 11, 1229–1231 (1999).
[CrossRef]

Kino, G. S.

Lee, H. K.

S. H. Yun, H. K. Lee, H. K. Kim, and B. Y. Kim, “Dynamic Erbium-Doped Fiber Amplifier Based on Active Gain Flattening with Fiber Acousto-optic Tunable Filters,” IEEE Photonics Technol. Lett. 11, 1229–1231 (1999).
[CrossRef]

Lee, H. P.

Q. Li, A. A. Au, C.-H. Lin, E. R. Lyons, and H. P. Lee, “An Efficient All-Fiber Variable Optical Attenuator via Acoustooptic Mode Coupling,” IEEE Photonics Technol. Lett. 14, 1563–1565 (2002).
[CrossRef]

Li, Q.

Q. Li, A. A. Au, C.-H. Lin, E. R. Lyons, and H. P. Lee, “An Efficient All-Fiber Variable Optical Attenuator via Acoustooptic Mode Coupling,” IEEE Photonics Technol. Lett. 14, 1563–1565 (2002).
[CrossRef]

Lin, C.-H.

Q. Li, A. A. Au, C.-H. Lin, E. R. Lyons, and H. P. Lee, “An Efficient All-Fiber Variable Optical Attenuator via Acoustooptic Mode Coupling,” IEEE Photonics Technol. Lett. 14, 1563–1565 (2002).
[CrossRef]

Love, J. D.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983).

Lyons, E. R.

Q. Li, A. A. Au, C.-H. Lin, E. R. Lyons, and H. P. Lee, “An Efficient All-Fiber Variable Optical Attenuator via Acoustooptic Mode Coupling,” IEEE Photonics Technol. Lett. 14, 1563–1565 (2002).
[CrossRef]

Monberg, E.

S. Ramachandran, M. F. Yan, E. Monberg, F. Dimarcello, P. Wisk, and S. Ghalmi, “Record Bandwidth Microbend Gratings for Spectrally Flat Variable Optical Attenuators,” IEEE Photonics Technol. Lett. 15, 1561–1563 (2003).
[CrossRef]

S. Ramachandran, S. E. Golowich, M. F. Yan, E. Monberg, F. Dimarcello, J. Fleming, S. Ghalmi, and P. Wisk, “Lifting Polarisation Degeneracy Of Modes By Fiber Design: A Platform for Polarisation Insensitive Microbend Fiber Gratings,” Opt. Lett. (in press).
[PubMed]

Nelson, K. T.

C. D. Pool, C. D. Townsend, and K. T. Nelson, “Helical-Grating Two-Mode Fiber Spatial-Mode Coupler,” J. Lightwave Technol. 9, 598–604 (1991).
[CrossRef]

Pool, C. D.

C. D. Pool, C. D. Townsend, and K. T. Nelson, “Helical-Grating Two-Mode Fiber Spatial-Mode Coupler,” J. Lightwave Technol. 9, 598–604 (1991).
[CrossRef]

Probst, C. B.

C. B. Probst, A. Bjarklev, and S. B. Andreasen, “Experimental Verification of Microbending Theory Using Mode Coupling to Discrete Cladding Modes,” J. Lightwave Technol. 7, 55–61 (1989).
[CrossRef]

Ramachandran, S.

S. Ramachandran, M. F. Yan, E. Monberg, F. Dimarcello, P. Wisk, and S. Ghalmi, “Record Bandwidth Microbend Gratings for Spectrally Flat Variable Optical Attenuators,” IEEE Photonics Technol. Lett. 15, 1561–1563 (2003).
[CrossRef]

S. Ramachandran, Z. Wang, and M. F. Yan, “Bandwidth Control of Long-Period Grating-Based Mode Converters in Few-Mode Fibers,” Opt. Lett. 27, 698–700 (2002).
[CrossRef]

S. Ramachandran, S. E. Golowich, M. F. Yan, E. Monberg, F. Dimarcello, J. Fleming, S. Ghalmi, and P. Wisk, “Lifting Polarisation Degeneracy Of Modes By Fiber Design: A Platform for Polarisation Insensitive Microbend Fiber Gratings,” Opt. Lett. (in press).
[PubMed]

Russell, P. S. J.

T. E. Dimmick, G. Kakarantzas, T. A. Birks, A. Diez, and P. S. J. Russell, “Compact All-Fiber Acoustooptic Tunable Filters with Small Bandwidth-Length Product,” IEEE Photonics Technol. Lett. 12, 1210–1212 (2000).
[CrossRef]

Savin, S.

Shaw, H. J.

Snyder, A. W.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983).

Townsend, C. D.

C. D. Pool, C. D. Townsend, and K. T. Nelson, “Helical-Grating Two-Mode Fiber Spatial-Mode Coupler,” J. Lightwave Technol. 9, 598–604 (1991).
[CrossRef]

Wang, Z.

Wilcox, D.

D. Chowdhury and D. Wilcox, “Comparison Between Optical Fiber Birefringence Induced by Stress Anisotriipy and Geometric Deformation,” IEEE J. Sel. Top. Quantum Electron. 6, 227–232 (2000).
[CrossRef]

Wisk, P.

S. Ramachandran, M. F. Yan, E. Monberg, F. Dimarcello, P. Wisk, and S. Ghalmi, “Record Bandwidth Microbend Gratings for Spectrally Flat Variable Optical Attenuators,” IEEE Photonics Technol. Lett. 15, 1561–1563 (2003).
[CrossRef]

S. Ramachandran, S. E. Golowich, M. F. Yan, E. Monberg, F. Dimarcello, J. Fleming, S. Ghalmi, and P. Wisk, “Lifting Polarisation Degeneracy Of Modes By Fiber Design: A Platform for Polarisation Insensitive Microbend Fiber Gratings,” Opt. Lett. (in press).
[PubMed]

Yan, M. F.

S. Ramachandran, M. F. Yan, E. Monberg, F. Dimarcello, P. Wisk, and S. Ghalmi, “Record Bandwidth Microbend Gratings for Spectrally Flat Variable Optical Attenuators,” IEEE Photonics Technol. Lett. 15, 1561–1563 (2003).
[CrossRef]

S. Ramachandran, Z. Wang, and M. F. Yan, “Bandwidth Control of Long-Period Grating-Based Mode Converters in Few-Mode Fibers,” Opt. Lett. 27, 698–700 (2002).
[CrossRef]

S. Ramachandran, S. E. Golowich, M. F. Yan, E. Monberg, F. Dimarcello, J. Fleming, S. Ghalmi, and P. Wisk, “Lifting Polarisation Degeneracy Of Modes By Fiber Design: A Platform for Polarisation Insensitive Microbend Fiber Gratings,” Opt. Lett. (in press).
[PubMed]

Yun, S. H.

S. H. Yun, H. K. Lee, H. K. Kim, and B. Y. Kim, “Dynamic Erbium-Doped Fiber Amplifier Based on Active Gain Flattening with Fiber Acousto-optic Tunable Filters,” IEEE Photonics Technol. Lett. 11, 1229–1231 (1999).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

D. Chowdhury and D. Wilcox, “Comparison Between Optical Fiber Birefringence Induced by Stress Anisotriipy and Geometric Deformation,” IEEE J. Sel. Top. Quantum Electron. 6, 227–232 (2000).
[CrossRef]

IEEE Photonics Technol. Lett. (4)

S. H. Yun, H. K. Lee, H. K. Kim, and B. Y. Kim, “Dynamic Erbium-Doped Fiber Amplifier Based on Active Gain Flattening with Fiber Acousto-optic Tunable Filters,” IEEE Photonics Technol. Lett. 11, 1229–1231 (1999).
[CrossRef]

S. Ramachandran, M. F. Yan, E. Monberg, F. Dimarcello, P. Wisk, and S. Ghalmi, “Record Bandwidth Microbend Gratings for Spectrally Flat Variable Optical Attenuators,” IEEE Photonics Technol. Lett. 15, 1561–1563 (2003).
[CrossRef]

Q. Li, A. A. Au, C.-H. Lin, E. R. Lyons, and H. P. Lee, “An Efficient All-Fiber Variable Optical Attenuator via Acoustooptic Mode Coupling,” IEEE Photonics Technol. Lett. 14, 1563–1565 (2002).
[CrossRef]

T. E. Dimmick, G. Kakarantzas, T. A. Birks, A. Diez, and P. S. J. Russell, “Compact All-Fiber Acoustooptic Tunable Filters with Small Bandwidth-Length Product,” IEEE Photonics Technol. Lett. 12, 1210–1212 (2000).
[CrossRef]

J. Lightwave Technol. (2)

C. B. Probst, A. Bjarklev, and S. B. Andreasen, “Experimental Verification of Microbending Theory Using Mode Coupling to Discrete Cladding Modes,” J. Lightwave Technol. 7, 55–61 (1989).
[CrossRef]

C. D. Pool, C. D. Townsend, and K. T. Nelson, “Helical-Grating Two-Mode Fiber Spatial-Mode Coupler,” J. Lightwave Technol. 9, 598–604 (1991).
[CrossRef]

Opt. Lett. (2)

Other (2)

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, London, 1983).

S. Ramachandran, S. E. Golowich, M. F. Yan, E. Monberg, F. Dimarcello, J. Fleming, S. Ghalmi, and P. Wisk, “Lifting Polarisation Degeneracy Of Modes By Fiber Design: A Platform for Polarisation Insensitive Microbend Fiber Gratings,” Opt. Lett. (in press).
[PubMed]

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Figures (3)

Fig. 1.
Fig. 1.

Measurements of transmitted power as a function of wavelength, for two orthogonal input SOPs. The fiber under test is TWRS™.

Fig. 2.
Fig. 2.

(a) Phase matching curves. The lines denote the predictions from theory; the symbols are the experimentally measured values. (b)Polarization splitting: δλ ℓ,m is the maximal difference in resonance wavelength between the fundamental and LP ℓm modes obtained by varying the input polarization.

Fig. 3.
Fig. 3.

(a) Fiber index profile plotted along with radial mode fields for the LP12 to LP15 modes; (b) index profile near the cladding-coating boundary, again with mode fields.

Equations (32)

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δλ = β 12 β ˙ 20 λ = λ 0 .
E t x t z t = e i ( βz ωt ) e t ( x t )
( t 2 k 2 n 2 + V ( vect ) + β 2 ) e t = 0
V ( vect ) e t = t ( e t · t ln n 2 ) .
n 2 ( x t ) = n 0 2 ( r ) + n ell 2 r θ
n 0 2 ( r ) = n co 2 ( 1 2 Δ f ( r ) )
n ell 2 ( r , θ ) = c ell r cos ( 2 θ ) f ( r )
c ell = 1 2 e 2 Δ n co 2
( t 2 k 2 n 0 2 + V ( ell ) + V ( vect ) + β 2 ) e t = 0
( t 2 + k 2 n 0 2 β 2 ) e t = 0 .
φ , m , ν , p ̂ r θ = F , m ( r ) ν ( ℓθ ) p ̂ ,
F , m 1 r F , m + ( 2 r 2 k 2 n 0 2 ) F , m = β 2 F , m .
I 1 = rdrdθF ( r ) F ( r ) f ( r )
I 2 ( ) = rdrdθ 1 r F ( r ) 2 f ( r )
I 3 = rdrdθrF ( r ) 2 f ( r ) .
= 1 , m , · , · V ( ell ) = 1 , m , · , · = π 2 k 2 c ell I 3 ( 1 1 1 1 ) .
= 0 , m , · , · V ( vect ) = 0 , m , · , · = 2 Δπ ( I 1 I 1 )
= 0 , m , · , · V ( vect ) = 0 , m , · , · =
2 Δ π 4 ( 3 I 1 + I 2 ( 1 ) I 1 + 3 I 2 ( 1 ) I 1 I 2 ( 1 ) I 1 I 2 ( 1 ) I 1 I 2 ( 1 ) I 1 I 2 ( 1 ) I 1 + 3 I 2 ( 1 ) 3 I 1 + I 1 ( 1 ) )
> 1 , m , · , · V ( vect ) > 1 , m , · , · = 2 Δ π 4 ( I 1 I 2 ( ) I 1 I 2 ( ) I 2 ( ) I 1 I 2 ( ) I 1 ) .
δ β TE 2 = 0 e t ( TE ) = 1 , m , sin , x ̂ + 1 , m , cos , y ̂
δ β TM 2 = 2 πΔ ( I 1 + I 2 ( 1 ) ) e t ( TM ) = 1 , m , cos , x ̂ + 1 , m , sin , y ̂
δ β HE 2 = πΔ ( I 1 I 2 ( 1 ) ) e t ( HE ) = 1 , m , cos , x ̂ - 1 , m , sin , y ̂ ,
1 , m , sin , x ̂ + 1 , m , cos , y ̂ .
n gr 2 x t z r cos ( θ θ 0 ) cos ( 2 π Λ z )
da 0 dz = iK 0,1 e iαz a 1
da 1 dz = iK 1,0 e iαz a 0 ,
K i , j = κ rdrdθ e t ( i ) r cos ( θ θ 0 ) e t ( j ) .
a 1 ( L ) 2 = ( 1 + x ) 1 sin 2 ( π 2 ( 1 + x ) 1 2 )
x = L 2 π 2 ( β 01 β Λ ) 2 .
δλ ( ε ) π L β ˙ 01 ( 0 ) ε ,
β ˙ 01 ( 0 ) = 01 λ = λ 0 .

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