Abstract

Optical fibers with large diameter cores having a negative index step from cladding to core combined with an adequately large gain coefficient in the core provide near-optimal mode properties for fiber lasers delivering robust single transverse mode operation with very large mode areas. Basic properties and simple design formulas for such fibers are presented.

© 2007 Optical Society of America

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References

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  1. A. E. Siegman, Y. Chen, V. Sudesh, M. C. Richardson, M. Bass, P. Foy, W. Hawkins, and J. Ballato, "Confined propagation and near single mode laser oscillation in a gain guided, index antiguided optical fiber," Appl. Phys. Lett. 89, 251101 (2006).
    [CrossRef]
  2. Y. Chen, V. Sudesh, M. C. Richardson, M. Bass, J. Ballato, and A. E. Siegman, "Experimental demonstration of gain guided lasing in an index antiguiding fiber," presented at the Advanced Solid State Photonics Conference, Vancouver, British Columbia, January 28-31, 2007.
  3. A. E. Siegman, "Propagating modes in gain-guided optical fibers," J. Opt. Soc. Am. A 20, 1617-1628 (2003).
    [CrossRef]
  4. C. J. Koester and E. Snitzer, "Amplification in fiber lasers," Appl. Opt. 3, 1182-1186 (1964).
    [CrossRef]
  5. E. A. J. Marcatili and R. A. Schmeltzer, "Hollow metallic and dielectric waveguides for long distance optical transmission and lasers," Bell Syst. Tech. J. 43, 1783-1809 (1964).
  6. N. S. Kapany and J. J. Burke, Optical Waveguides (Academic, 1972).
  7. K. D. Laakmann and W. H. Steier, "Waveguides: characteristc modes of hollow rectangular dielectric waveguides," Appl. Opt. 15, 1334-1340 (1976).
    [CrossRef] [PubMed]
  8. M. J. Adams, Introduction to Optical Waveguides (Wiley, 1981).

2006

A. E. Siegman, Y. Chen, V. Sudesh, M. C. Richardson, M. Bass, P. Foy, W. Hawkins, and J. Ballato, "Confined propagation and near single mode laser oscillation in a gain guided, index antiguided optical fiber," Appl. Phys. Lett. 89, 251101 (2006).
[CrossRef]

2003

1976

1964

C. J. Koester and E. Snitzer, "Amplification in fiber lasers," Appl. Opt. 3, 1182-1186 (1964).
[CrossRef]

E. A. J. Marcatili and R. A. Schmeltzer, "Hollow metallic and dielectric waveguides for long distance optical transmission and lasers," Bell Syst. Tech. J. 43, 1783-1809 (1964).

Adams, M. J.

M. J. Adams, Introduction to Optical Waveguides (Wiley, 1981).

Ballato, J.

A. E. Siegman, Y. Chen, V. Sudesh, M. C. Richardson, M. Bass, P. Foy, W. Hawkins, and J. Ballato, "Confined propagation and near single mode laser oscillation in a gain guided, index antiguided optical fiber," Appl. Phys. Lett. 89, 251101 (2006).
[CrossRef]

Y. Chen, V. Sudesh, M. C. Richardson, M. Bass, J. Ballato, and A. E. Siegman, "Experimental demonstration of gain guided lasing in an index antiguiding fiber," presented at the Advanced Solid State Photonics Conference, Vancouver, British Columbia, January 28-31, 2007.

Bass, M.

A. E. Siegman, Y. Chen, V. Sudesh, M. C. Richardson, M. Bass, P. Foy, W. Hawkins, and J. Ballato, "Confined propagation and near single mode laser oscillation in a gain guided, index antiguided optical fiber," Appl. Phys. Lett. 89, 251101 (2006).
[CrossRef]

Y. Chen, V. Sudesh, M. C. Richardson, M. Bass, J. Ballato, and A. E. Siegman, "Experimental demonstration of gain guided lasing in an index antiguiding fiber," presented at the Advanced Solid State Photonics Conference, Vancouver, British Columbia, January 28-31, 2007.

Burke, J. J.

N. S. Kapany and J. J. Burke, Optical Waveguides (Academic, 1972).

Chen, Y.

A. E. Siegman, Y. Chen, V. Sudesh, M. C. Richardson, M. Bass, P. Foy, W. Hawkins, and J. Ballato, "Confined propagation and near single mode laser oscillation in a gain guided, index antiguided optical fiber," Appl. Phys. Lett. 89, 251101 (2006).
[CrossRef]

Y. Chen, V. Sudesh, M. C. Richardson, M. Bass, J. Ballato, and A. E. Siegman, "Experimental demonstration of gain guided lasing in an index antiguiding fiber," presented at the Advanced Solid State Photonics Conference, Vancouver, British Columbia, January 28-31, 2007.

Foy, P.

A. E. Siegman, Y. Chen, V. Sudesh, M. C. Richardson, M. Bass, P. Foy, W. Hawkins, and J. Ballato, "Confined propagation and near single mode laser oscillation in a gain guided, index antiguided optical fiber," Appl. Phys. Lett. 89, 251101 (2006).
[CrossRef]

Hawkins, W.

A. E. Siegman, Y. Chen, V. Sudesh, M. C. Richardson, M. Bass, P. Foy, W. Hawkins, and J. Ballato, "Confined propagation and near single mode laser oscillation in a gain guided, index antiguided optical fiber," Appl. Phys. Lett. 89, 251101 (2006).
[CrossRef]

Kapany, N. S.

N. S. Kapany and J. J. Burke, Optical Waveguides (Academic, 1972).

Koester, C. J.

Laakmann, K. D.

Marcatili, E. A. J.

E. A. J. Marcatili and R. A. Schmeltzer, "Hollow metallic and dielectric waveguides for long distance optical transmission and lasers," Bell Syst. Tech. J. 43, 1783-1809 (1964).

Richardson, M. C.

A. E. Siegman, Y. Chen, V. Sudesh, M. C. Richardson, M. Bass, P. Foy, W. Hawkins, and J. Ballato, "Confined propagation and near single mode laser oscillation in a gain guided, index antiguided optical fiber," Appl. Phys. Lett. 89, 251101 (2006).
[CrossRef]

Y. Chen, V. Sudesh, M. C. Richardson, M. Bass, J. Ballato, and A. E. Siegman, "Experimental demonstration of gain guided lasing in an index antiguiding fiber," presented at the Advanced Solid State Photonics Conference, Vancouver, British Columbia, January 28-31, 2007.

Schmeltzer, R. A.

E. A. J. Marcatili and R. A. Schmeltzer, "Hollow metallic and dielectric waveguides for long distance optical transmission and lasers," Bell Syst. Tech. J. 43, 1783-1809 (1964).

Siegman, A. E.

A. E. Siegman, Y. Chen, V. Sudesh, M. C. Richardson, M. Bass, P. Foy, W. Hawkins, and J. Ballato, "Confined propagation and near single mode laser oscillation in a gain guided, index antiguided optical fiber," Appl. Phys. Lett. 89, 251101 (2006).
[CrossRef]

A. E. Siegman, "Propagating modes in gain-guided optical fibers," J. Opt. Soc. Am. A 20, 1617-1628 (2003).
[CrossRef]

Y. Chen, V. Sudesh, M. C. Richardson, M. Bass, J. Ballato, and A. E. Siegman, "Experimental demonstration of gain guided lasing in an index antiguiding fiber," presented at the Advanced Solid State Photonics Conference, Vancouver, British Columbia, January 28-31, 2007.

Snitzer, E.

Steier, W. H.

Sudesh, V.

A. E. Siegman, Y. Chen, V. Sudesh, M. C. Richardson, M. Bass, P. Foy, W. Hawkins, and J. Ballato, "Confined propagation and near single mode laser oscillation in a gain guided, index antiguided optical fiber," Appl. Phys. Lett. 89, 251101 (2006).
[CrossRef]

Y. Chen, V. Sudesh, M. C. Richardson, M. Bass, J. Ballato, and A. E. Siegman, "Experimental demonstration of gain guided lasing in an index antiguiding fiber," presented at the Advanced Solid State Photonics Conference, Vancouver, British Columbia, January 28-31, 2007.

Appl. Opt.

Appl. Phys. Lett.

A. E. Siegman, Y. Chen, V. Sudesh, M. C. Richardson, M. Bass, P. Foy, W. Hawkins, and J. Ballato, "Confined propagation and near single mode laser oscillation in a gain guided, index antiguided optical fiber," Appl. Phys. Lett. 89, 251101 (2006).
[CrossRef]

Bell Syst. Tech. J.

E. A. J. Marcatili and R. A. Schmeltzer, "Hollow metallic and dielectric waveguides for long distance optical transmission and lasers," Bell Syst. Tech. J. 43, 1783-1809 (1964).

J. Opt. Soc. Am. A

Other

M. J. Adams, Introduction to Optical Waveguides (Wiley, 1981).

N. S. Kapany and J. J. Burke, Optical Waveguides (Academic, 1972).

Y. Chen, V. Sudesh, M. C. Richardson, M. Bass, J. Ballato, and A. E. Siegman, "Experimental demonstration of gain guided lasing in an index antiguiding fiber," presented at the Advanced Solid State Photonics Conference, Vancouver, British Columbia, January 28-31, 2007.

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Figures (4)

Fig. 1
Fig. 1

Propagating modes that are generalized extensions of the LP01 and LP11 modes of a conventional index-guided optical fiber can exist everywhere in the “modal regions” above and to the right of the solid boundary lines in the dimensionless Δ N , G or complex- V 2 plane shown in this diagram. The modes of primary interest in this paper are located along the negative real axis and in the upper left quadrant of this plane.

Fig. 2
Fig. 2

Threshold values of the dimensionless gain parameter G required to produce confined and amplifying LP01 and LP11 modes in a gain-guided, index-antiguided fiber plotted versus increasingly large negative values of the dimensionless index parameter Δ N .

Fig. 3
Fig. 3

Threshold value of the dimensionless gain parameter G for the LP01 mode in a gain-guided, index-antiguided fiber plotted versus negative values of the index step parameter Δ N on expanded logarithmic scales. The corresponding curve for the LP11 mode has a similar variation but is shifted upward by a factor of 2.54.

Fig. 4
Fig. 4

Field amplitude and phase profiles for the propagating modes of gain-guided, index-antiguided optical fibers plotted versus radius with, from the top down, Δ N = 2.0 , 5 , 10 , and 100 . Each plot shows the mode profiles for three values of the dimensionless gain parameter, namely G = 0 (dashed curves), G = G th (light curves), and G = 2 G th (dark curves). Note that the three profiles for the Δ N = 100 case are indistinguishable over the radial range shown.

Equations (15)

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Δ N ( 2 π a λ ) 2 × 2 n 0 × Δ n
G ( 2 π a λ ) 2 × ( n 0 λ 2 π ) × g ,
V ̃ 2 Δ N + j G .
G th 4 j 01 4 Δ N 133.8 Δ N [ LP 01 mode ] ,
G th 4 j 11 4 Δ N 862.2 Δ N [ LP 11 mode ] ,
w r ( j 01 2 Δ N ) × [ G G th 1 ] ,
w i Δ N ,
G m ( 2 π a λ ) 2 × ( n 0 λ 2 π ) × g m = 2 w r w i .
G m G G th ( p 1 ) × G th ,
E ̃ 01 ( r ) = { J 0 ( u ̃ r a ) , r a [ J 0 ( u ̃ ) K 0 ( w ̃ ) ] × K 0 ( w ̃ r a ) , r a } ,
E ̃ 11 ( r ) = { J 1 ( u ̃ r a ) , r a [ J 1 ( u ̃ ) K 1 ( w ̃ ) ] × K 1 ( w ̃ r a ) , r a }
u ̃ J 1 ( u ̃ ) J 0 ( u ̃ ) = w ̃ K 1 ( w ̃ ) K 0 ( w ̃ ) ( LP 01 modes ) ,
u ̃ J 1 ( u ̃ ) J 1 ( u ̃ ) = w ̃ K 0 ( w ̃ ) K 1 ( w ̃ ) ( LP 11 modes )
u ̃ 2 + w ̃ 2 = V ̃ 2 = Δ N + j G .
j 01 j 01 u ̃ w ̃ .

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