Abstract

Laser beam shaping is an important subject for industrial and medical applications since different applications may require different laser intensity distributions. We present an all-fiber beam-shaping device that could transform a Gaussian-shaped laser beam into an intensity uniform beam in the 1.0μm wavelength region using a long-period grating (LPG). The device can be used to shape the beam of a Yb-doped high-power fiber laser. The mode structure of the LPGs made of HI1060 fiber is analyzed. The design parameters that affect the beam shaping are discussed, and the results of the beam shaping using two cladding modes, LP03 and LP04, are presented.

© 2009 Optical Society of America

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References

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  1. A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, J. E. Sipe, and T. E. Ergodan, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58-65(1996).
    [CrossRef]
  2. X. Gu, W. Mohammed, L. Qian, and P. W. E. Smith, “All-fiber dynamic laser beam shaping device using a long-period grating,” IEEE Photon. Technol. Lett. 20, 1130-1132(2008).
    [CrossRef]
  3. D. M. Brown, F. M. Dickey, and L. W. Weichman, “Multi-aperture beam integration systems,” in Laser Beam Shaping, F. M. Dickey and S. C. Holswade, eds. (Marcel Dekker, 2000), pp 273-311.
  4. H. Stolla and A. Yariv, “Coupled-mode analysis of periodic dielectric waveguides,” Opt. Commun. 8, 5-8 (1973).
    [CrossRef]
  5. A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. 9, 919-933 (1973).
    [CrossRef]
  6. Y. Yamamoto, T. Kamiya, and H. Yanai, “Improved coupled mode analysis of corrugated waveguides and lasers,” IEEE J. Quantum Electron. 14, 254-258 (1978).

2008

X. Gu, W. Mohammed, L. Qian, and P. W. E. Smith, “All-fiber dynamic laser beam shaping device using a long-period grating,” IEEE Photon. Technol. Lett. 20, 1130-1132(2008).
[CrossRef]

1996

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, J. E. Sipe, and T. E. Ergodan, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58-65(1996).
[CrossRef]

1978

Y. Yamamoto, T. Kamiya, and H. Yanai, “Improved coupled mode analysis of corrugated waveguides and lasers,” IEEE J. Quantum Electron. 14, 254-258 (1978).

1973

H. Stolla and A. Yariv, “Coupled-mode analysis of periodic dielectric waveguides,” Opt. Commun. 8, 5-8 (1973).
[CrossRef]

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. 9, 919-933 (1973).
[CrossRef]

Bhatia, V.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, J. E. Sipe, and T. E. Ergodan, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58-65(1996).
[CrossRef]

Brown, D. M.

D. M. Brown, F. M. Dickey, and L. W. Weichman, “Multi-aperture beam integration systems,” in Laser Beam Shaping, F. M. Dickey and S. C. Holswade, eds. (Marcel Dekker, 2000), pp 273-311.

Dickey, F. M.

D. M. Brown, F. M. Dickey, and L. W. Weichman, “Multi-aperture beam integration systems,” in Laser Beam Shaping, F. M. Dickey and S. C. Holswade, eds. (Marcel Dekker, 2000), pp 273-311.

Ergodan, T. E.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, J. E. Sipe, and T. E. Ergodan, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58-65(1996).
[CrossRef]

Gu, X.

X. Gu, W. Mohammed, L. Qian, and P. W. E. Smith, “All-fiber dynamic laser beam shaping device using a long-period grating,” IEEE Photon. Technol. Lett. 20, 1130-1132(2008).
[CrossRef]

Judkins, J. B.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, J. E. Sipe, and T. E. Ergodan, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58-65(1996).
[CrossRef]

Kamiya, T.

Y. Yamamoto, T. Kamiya, and H. Yanai, “Improved coupled mode analysis of corrugated waveguides and lasers,” IEEE J. Quantum Electron. 14, 254-258 (1978).

Lemaire, P. J.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, J. E. Sipe, and T. E. Ergodan, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58-65(1996).
[CrossRef]

Mohammed, W.

X. Gu, W. Mohammed, L. Qian, and P. W. E. Smith, “All-fiber dynamic laser beam shaping device using a long-period grating,” IEEE Photon. Technol. Lett. 20, 1130-1132(2008).
[CrossRef]

Qian, L.

X. Gu, W. Mohammed, L. Qian, and P. W. E. Smith, “All-fiber dynamic laser beam shaping device using a long-period grating,” IEEE Photon. Technol. Lett. 20, 1130-1132(2008).
[CrossRef]

Sipe, J. E.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, J. E. Sipe, and T. E. Ergodan, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58-65(1996).
[CrossRef]

Smith, P. W. E.

X. Gu, W. Mohammed, L. Qian, and P. W. E. Smith, “All-fiber dynamic laser beam shaping device using a long-period grating,” IEEE Photon. Technol. Lett. 20, 1130-1132(2008).
[CrossRef]

Stolla, H.

H. Stolla and A. Yariv, “Coupled-mode analysis of periodic dielectric waveguides,” Opt. Commun. 8, 5-8 (1973).
[CrossRef]

Vengsarkar, A. M.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, J. E. Sipe, and T. E. Ergodan, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58-65(1996).
[CrossRef]

Weichman, L. W.

D. M. Brown, F. M. Dickey, and L. W. Weichman, “Multi-aperture beam integration systems,” in Laser Beam Shaping, F. M. Dickey and S. C. Holswade, eds. (Marcel Dekker, 2000), pp 273-311.

Yamamoto, Y.

Y. Yamamoto, T. Kamiya, and H. Yanai, “Improved coupled mode analysis of corrugated waveguides and lasers,” IEEE J. Quantum Electron. 14, 254-258 (1978).

Yanai, H.

Y. Yamamoto, T. Kamiya, and H. Yanai, “Improved coupled mode analysis of corrugated waveguides and lasers,” IEEE J. Quantum Electron. 14, 254-258 (1978).

Yariv, A.

H. Stolla and A. Yariv, “Coupled-mode analysis of periodic dielectric waveguides,” Opt. Commun. 8, 5-8 (1973).
[CrossRef]

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. 9, 919-933 (1973).
[CrossRef]

IEEE J. Quantum Electron.

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. 9, 919-933 (1973).
[CrossRef]

Y. Yamamoto, T. Kamiya, and H. Yanai, “Improved coupled mode analysis of corrugated waveguides and lasers,” IEEE J. Quantum Electron. 14, 254-258 (1978).

IEEE Photon. Technol. Lett.

X. Gu, W. Mohammed, L. Qian, and P. W. E. Smith, “All-fiber dynamic laser beam shaping device using a long-period grating,” IEEE Photon. Technol. Lett. 20, 1130-1132(2008).
[CrossRef]

J. Lightwave Technol.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, J. E. Sipe, and T. E. Ergodan, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58-65(1996).
[CrossRef]

Opt. Commun.

H. Stolla and A. Yariv, “Coupled-mode analysis of periodic dielectric waveguides,” Opt. Commun. 8, 5-8 (1973).
[CrossRef]

Other

D. M. Brown, F. M. Dickey, and L. W. Weichman, “Multi-aperture beam integration systems,” in Laser Beam Shaping, F. M. Dickey and S. C. Holswade, eds. (Marcel Dekker, 2000), pp 273-311.

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Figures (7)

Fig. 1
Fig. 1

Schematic diagram of the laser beam shaping device in a SMF using a LPG.

Fig. 2
Fig. 2

Transmission spectra of LPGs with four different periods: 580, 590, 610, and 620 μm . The three plots are shifted to improve clarity.

Fig. 3
Fig. 3

Resonant wavelengths of the LPGs plotted as the function of the LPG periods.

Fig. 4
Fig. 4

Transmission spectrum of the LPG with a period 580 μm showing three low-order cladding modes.

Fig. 5
Fig. 5

Change of the transmittance of the core mode (dashed curve) and the relative phase between the core and the LP 03 cladding mode (solid curve).

Fig. 6
Fig. 6

Two-dimensional beam intensity profiles measured at 13 mm from the fiber facet as the result of core mode and LP 03 mode interference.

Fig. 7
Fig. 7

Beam intensity profiles measured at 9.5 mm from the fiber facet at four different wavelengths for LP 03 mode (top) and LP 04 mode (bottom). Profiles b, c, and d are shifted upward to improve visibility.

Equations (20)

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2 E ( r , z ) + ω 2 μ ε c E = 0.
E ( r , z ) = k A k ψ k ( r ) E x p [ i ( ω t β k z ) ] .
E ( r , z ) = k A k ( z ) ψ k ( r ) E x p [ i ( ω t β k z ) ] .
k i 2 β k d A k ( z ) d z ψ k ( z ) E x p [ i ( ω t β k z ) ] = l ω 2 μ Δ ε ( r , z ) A l ( z ) ψ l ( z ) E x p [ i ( ω t β l z ) ] .
d A k ( z ) d z = l i A l ( z ) K k l E x p [ i ( β k β l ) z ] , K k l = ω 2 μ 2 β k r = 0 Δ ε ( r , z ) ψ l ( z ) ψ k * ( z ) r d r .
Δ n ( r , z ) = δ n core [ 1 + m = 1 ν m cos ( 2 π m Λ z ) ] .
K k l = [ σ k l + m = 1 k k l , m cos ( 2 π m Λ z ) ] ,
σ k l = ω 2 μ 2 β k δ ε core r = 0 a ψ l ( z ) ψ k * ( z ) r d r , κ k l , m = ν m σ k l .
i d A 1 , m ( z ) d z = A 1 , m ( z ) σ 11 + A 2 , m ( z ) κ 21 E x p [ i Δ m z ] ,
i d A 2 , m ( z ) d z = A 2 , m ( z ) σ 22 + A 1 , m ( z ) κ 12 E x p [ i Δ m z ] ,
d 2 A 2 , m ( z ) d z 2 i d A 2 , m ( z ) d z ( σ 11 + σ 22 + Δ m ) + A 2 , m ( z ) ( σ 22 Δ m + σ 22 σ 11 κ 21 , m κ 12 , m ) = 0.
d 2 S ( z ) d z 2 i d S ( z ) d z ( 2 a m + σ 11 + σ 22 + Δ m ) + S ( z ) ( a m ( σ 11 + σ 22 + Δ m ) + a m 2 + σ 22 Δ m + σ 22 σ 11 κ 21 , m κ 12 , m ) = 0.
d 2 S ( z ) d z 2 + S ( z ) ( σ ^ m 2 + κ m 2 ) = 0 ,
A 2 , m ( z ) = i κ m σ ^ m 2 + κ m 2 sin ( σ ^ m 2 + κ m 2 z ) × exp ( i σ 11 + σ 22 + Δ m 2 ) .
ψ 1 ( r ) = 1 P 1 { J 0 ( χ 1 r ) r r o J 0 ( χ 1 r o ) K 0 ( γ 1 r o ) K 0 ( γ 1 r ) r > r o ,
ψ 2 ( r ) = 1 P 2 { J 0 ( χ 2 r ) r r o B J 0 ( χ 2 c r ) + C Y 0 ( χ 2 c r ) R r > r o D K 0 ( γ 2 r ) r > R .
χ l = k o 2 n 1 2 β l 2 , l = 1 , 2 , χ 2 c = k o 2 n 2 2 β 2 2 , γ 1 = β 1 2 k o 2 n 2 2 , γ 2 = β 2 2 k o 2 .
σ k 1 = ω n core a 2 4 P k P 1 ( β 1 2 β k 2 ) δ n ¯ core [ χ 2 J 1 ( χ 2 a ) J 0 ( χ 1 a ) χ 1 J 0 ( χ 2 a ) J 1 ( χ 1 a ) ] .
σ k k = ω n core a 2 4 P k δ n ¯ core ( J 0 ( χ k a ) 2 + J 1 ( χ k a ) 2 ) .
E total ( r ) = A 1 ( L g ) ψ 1 ( r ) + A 2 ( L g ) ψ 2 ( r ) exp ( i ( β 2 β 1 ) L f ) exp ( i Δ ϕ 21 ) .

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