Abstract

The beam-quality factor of an amplified spontaneous emission source based on a Yb-doped, large-mode-area (LMA), multimode fiber was found to be optimized when the gain became saturated. A model using spatially resolved gain and transverse-mode decomposition of the optical field showed that transverse spatial-hole burning (TSHB) was responsible for the observed behavior. A simplified model without TSHB failed to predict the observed behavior of beam quality. A comparison of both models shows TSHB is also critical for properly modeling beam quality in LMA fiber amplifiers.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1989).
  2. T. A. Birks, J. C. Knight, and P. St. J. Russell, "Endlessly single-mode photonic crystal fiber," Opt. Lett. 22, 961-963 (1997).
    [CrossRef] [PubMed]
  3. P. Wang, L. J. Cooper, J. K. Sahu, and W. A. Clarkson, "Efficient single-mode operation of a cladding-pumped ytterbium-doped helical-core fiber laser," Opt. Lett. 31, 226-228 (2006).
    [CrossRef] [PubMed]
  4. Z. Jiang and J. R. Marciante, "Mode-area-scaling of helical-core, dual-clad fiber lasers and amplifiers using an improved bend-loss model," J. Opt. Soc. Am. B 23, 2051-2058 (2006).
    [CrossRef]
  5. P. Koplow, D. A. V. Kliner, and L. Goldberg, "Single-mode operation of a coiled multimode fiber amplifier," Opt. Lett. 25, 442-444 (2000).
    [CrossRef]
  6. D. Taverner, D. J. Richardson, L. Dong, J. E. Caplen, K. Williams, and R. V. Penty, "158-μJ pulses from a single-transverse-mode, large-mode-area erbium-doped fiber amplifier," Opt. Lett. 22, 378-380 (1997).
    [CrossRef] [PubMed]
  7. H. L. Offerhaus, N. G. Broderick, D. J. Richardson, R. Sammut, J. Caplen, and L. Dong, "High-energy single-transverse-mode Q-switched fiber laser based on a multimode large-mode-area erbium-doped fiber," Opt. Lett. 23, 1683-1685 (1998).
    [CrossRef]
  8. J. M. Sousa and O. G. Okhotnikov, "Multimode Er-doped fiber for single-transverse-mode amplification," Appl. Phys. Lett. 74, 1528-1530 (1999).
    [CrossRef]
  9. J. R. Marciante, "Effectiveness of radial gain tailoring in large-mode-area fiber lasers and amplifiers," in Advanced Solid-State Photonics, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper WB140 presented at ASSP 2007, Vancouver, Canada, 28-31 January 2007.
  10. A. E. Siegman, G. Nernes, and D. Sema, "How to (maybe) measure laser beam quality," in DPSS (Diode Pumped Solid State) Lasers: Applications and Issues, M.Dowley, ed., Vol. 17 of OSA Trends in Optics and Photonics (Optical Society of America, 1998), paper MQ1.
  11. P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, 1969), pp. 135-155.
  12. C. R. Giles and E. Desurvire, "Modeling erbium-doped fiber amplifiers," J. Lightwave Technol. 9, 271-283 (1991).
    [CrossRef]
  13. J. Y. Law, "Mode-partition noise in vertical-cavity surface-emitting lasers," IEEE Photonics Technol. Lett. 9, 437-439 (1997).
    [CrossRef]
  14. D. Gloge, "Weakly guiding fibers," Appl. Opt. 10, 2252-2258 (1971).
    [CrossRef] [PubMed]
  15. C. R. Pollock, Fundamentals of Optoelectronics (Irwin, 1995).
  16. H. Yoda, P. Polynkin, and M. Mansuripur, "Beam quality factor of higher order modes in a step-index fiber," J. Lightwave Technol. 24, 1350-1355 (2006).
    [CrossRef]
  17. J. R. Marciante and J. D. Zuegel, "High-gain, polarization-preserving, Yb-doped fiber amplifier for low-duty-cycle pulse amplification," Appl. Opt. 45, 6798-6804 (2006).
    [CrossRef] [PubMed]
  18. A. A. Hardy, "Amplified spontaneous emission and Rayleigh backscattering in strongly pumped fiber amplifiers," J. Lightwave Technol. 16, 1865-1873 (1998).
    [CrossRef]

2006

2000

1999

J. M. Sousa and O. G. Okhotnikov, "Multimode Er-doped fiber for single-transverse-mode amplification," Appl. Phys. Lett. 74, 1528-1530 (1999).
[CrossRef]

1998

1997

1991

C. R. Giles and E. Desurvire, "Modeling erbium-doped fiber amplifiers," J. Lightwave Technol. 9, 271-283 (1991).
[CrossRef]

1971

Appl. Opt.

Appl. Phys. Lett.

J. M. Sousa and O. G. Okhotnikov, "Multimode Er-doped fiber for single-transverse-mode amplification," Appl. Phys. Lett. 74, 1528-1530 (1999).
[CrossRef]

IEEE Photonics Technol. Lett.

J. Y. Law, "Mode-partition noise in vertical-cavity surface-emitting lasers," IEEE Photonics Technol. Lett. 9, 437-439 (1997).
[CrossRef]

J. Lightwave Technol.

J. Opt. Soc. Am. B

Opt. Lett.

Other

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 1989).

C. R. Pollock, Fundamentals of Optoelectronics (Irwin, 1995).

J. R. Marciante, "Effectiveness of radial gain tailoring in large-mode-area fiber lasers and amplifiers," in Advanced Solid-State Photonics, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper WB140 presented at ASSP 2007, Vancouver, Canada, 28-31 January 2007.

A. E. Siegman, G. Nernes, and D. Sema, "How to (maybe) measure laser beam quality," in DPSS (Diode Pumped Solid State) Lasers: Applications and Issues, M.Dowley, ed., Vol. 17 of OSA Trends in Optics and Photonics (Optical Society of America, 1998), paper MQ1.

P. R. Bevington, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, 1969), pp. 135-155.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (12)

Fig. 1
Fig. 1

Experimental configuration of the multimode fiber ASE source.

Fig. 2
Fig. 2

Output power versus input pump power from the ASE source. The dashed vertical line is the pump threshold for saturation.

Fig. 3
Fig. 3

Optical spectrum of ASE output power.

Fig. 4
Fig. 4

Beam-quality factor of the ASE source versus input pump power in the x (upper) and y (lower) directions. The dashed vertical line is the pump threshold for saturation.

Fig. 5
Fig. 5

ASE output power versus input pump power from localized model (solid) and experiment (dotted). The dashed vertical line is the pump threshold for saturation.

Fig. 6
Fig. 6

Output-fraction factors of LP fiber modes versus input pump power from the localized model. The dashed vertical line is the pump threshold for saturation.

Fig. 7
Fig. 7

Beam-quality factor versus input pump power from the localized model. The dashed vertical line is the pump threshold for saturation.

Fig. 8
Fig. 8

Upper-level dopant distributions with different input pump powers across the injection fiber end.

Fig. 9
Fig. 9

Output-fraction factors of LP fiber modes versus input pump power from the localized (solid) and simplified (dashed) models. The dashed vertical line is the pump threshold for saturation.

Fig. 10
Fig. 10

Beam-quality factor versus input pump power from localized (solid) and simplified (dashed) models. The dashed vertical line is the pump threshold for saturation.

Fig. 11
Fig. 11

Output-fraction factors of the fundamental mode versus input-fraction factors of the fundamental mode from localized (solid) and simplified (dashed) models.

Fig. 12
Fig. 12

Beam-quality factors versus input pump power from localized (solid) and simplified (dashed) models.

Tables (3)

Tables Icon

Table 1 Parameters Used in Simulations

Tables Icon

Table 2 Ratio of the Gain Seen by Other Transverse Modes to the Gain Seen by the Fundamental Mode with 5 W Pump Power

Tables Icon

Table 3 New and Changed Parameters Used in Simulations

Equations (38)

Equations on this page are rendered with MathJax. Learn more.

W 2 ( z ) = W 0 2 + M 4 ( λ π W 0 ) 2 ( z z 0 ) 2 ,
d n 2 ( r , ϕ , z ) d t = k P k ( z ) i k ( r , ϕ ) σ a k h ν k n 1 ( r , ϕ , z ) k P k ( z ) i k ( r , ϕ ) σ e k h ν k n 2 ( r , ϕ , z ) n 2 ( r , ϕ , z ) τ ,
n t ( r , ϕ , z ) = n 1 ( r , ϕ , z ) + n 2 ( r , ϕ , z ) ,
P k ( z ) = 0 2 π 0 I k ( r , ϕ , z ) r d r d ϕ .
i k ( r , ϕ ) = I k ( r , ϕ , z ) P k ( z ) ,
n 2 ( r , ϕ , z ) = n t k P k ( z ) i k ( r , ϕ ) σ a k h ν k 1 τ + k P k ( z ) i k ( r , ϕ ) ( σ a k + σ e k ) h ν k .
d P k ( z ) d z = u k σ e k [ P k ( z ) + m h c 2 λ k 3 Δ λ k ] 0 2 π 0 a i k ( r , ϕ ) n 2 ( r , ϕ , z ) r d r d ϕ u k σ a k P k ( z ) 0 2 π 0 a i k ( r , ϕ ) n 1 ( r , ϕ , z ) r d r d ϕ u k α P k ( z ) ,
i ν m ( r , ϕ ) = E ν m 2 ( r , ϕ ) ,
E ν m ( r , ϕ ) = { b J ν ( κ ν m r ) f ν ( ϕ ) , r < a core b J ν ( κ ν m a core ) K ν ( γ ν m r ) f ν ( ϕ ) K ν ( γ ν m a core ) , r a core } ,
κ ν m J ν 1 ( κ ν m a core ) J ν ( κ ν m a core ) = γ ν m K ν 1 ( γ ν m a core ) K ν ( γ ν m a core ) ,
κ ν m 2 + γ ν m 2 = V 2 a core 2 .
V = 2 π λ a core NA ,
NA = n core 2 n clad 2 ,
f ν ( ϕ ) = { cos ( ν ϕ ) , even sin ( ν ϕ ) , odd } ,
i pump = 1 π a clad 2 ,
P output = ν , m P ν m ( 0 ) .
α ν m = P ν m ( 0 ) P output .
M x 2 = 2 [ ν , m α ν m E ν m ( r , ϕ ) x 2 r d r d ϕ ] [ x 2 ν , m α ν m E ν m ( r , ϕ ) 2 r d r d ϕ ] ,
M y 2 = 2 [ ν , m α ν m E ν m ( r , ϕ ) y 2 r d r d ϕ ] [ y 2 ν , m α ν m E ν m ( r , ϕ ) 2 r d r d ϕ ] .
P pump + ( 0 ) = P 0 ,
P pump ( L ) = 0 ,
P ν m + ( 0 ) = 0 ,
P ν m ( L ) = 0 ,
d n 2 ( z ) d t = k P k ( z ) Γ k σ a k h ν k A n 1 ( z ) k P k ( z ) Γ k σ e k h ν k A n 2 ( z ) n 2 ( z ) τ ,
n t ( z ) = n 1 ( z ) + n 2 ( z ) ,
Γ ν m = 0 2 π 0 i ν m ( r , ϕ ) n t ( r , ϕ , z ) r d r d ϕ 0 2 π 0 n t ( r , ϕ , z ) r d r d ϕ .
Γ ν m = 0 2 π 0 a core i ν m ( r , ϕ ) r d r d ϕ .
Γ pump = a core 2 a clad 2 .
n 2 ( z ) = n t k P k ( z ) Γ k σ a k h ν k A 1 τ + k P k ( z ) Γ k ( σ a k + σ e k ) h ν k A .
d P k ( z ) d z = u k σ e k [ P k ( z ) + m h c 2 λ k 3 Δ λ k ] Γ k n 2 ( z ) u k σ a k P k ( z ) Γ k n 1 ( z ) u k α P k ( z ) .
P pump + ( 0 ) = P 0 ,
P pump ( L ) = 0 ,
P 01 + ( 0 ) = P s χ ,
P 11 + ( 0 ) = P s ( 1 χ ) ,
P ν m + ( 0 ) = 0 ,
P ν m ( L ) = 0 ,
E ( r , ϕ ) = ν , m α ν m E ν m ( r , ϕ ) e i β ν m L ,
β ν m 2 = ( 2 π λ ) 2 n core 2 κ ν m 2 .

Metrics