Abstract

We theoretically analyze gain guiding in large-core Bragg fibers, to be used for large-mode-area laser amplifiers with single-transverse-mode operation. The signal is gain-guided in a low-index core, whereas the pump is guided by the photonic bandgap of the Bragg cladding to achieve good confinement. The high-index layers in the Bragg cladding are half-wave thick at the signal wavelength in order to eliminate Bragg reflection, reducing the Bragg fiber effectively to a step-index fiber for gain guiding.

©2009 Optical Society of America

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References

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  1. A. E. Siegman, “Propagating modes in gain-guided optical fibers,” J. Opt. Soc. Am. B 20(8), 1617 ( 2003).
    [Crossref]
  2. A. E. Siegman, “Gain-guided, index-antiguided fiber lasers,” J. Opt. Soc. Am. B 24(8), 1677 ( 2007).
    [Crossref]
  3. 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(25), 251101 ( 2006).
    [Crossref]
  4. Y. Chen, T. McComb, V. Sudesh, M. Richardson, and M. Bass, “Very large-core, single-mode, gain-guided, index-antiguided fiber lasers,” Opt. Lett. 32(17), 2505–2507 ( 2007).
    [Crossref] [PubMed]
  5. V. Sudesh, T. Mccomb, Y. Chen, M. Bass, M. Richardson, J. Ballato, and A. E. Siegman, “Diode-pumped 200 µm diameter core, gain-guided, index-antiguided single mode fiber laser,” Appl. Phys. B 90(3-4), 369–372 ( 2008).
    [Crossref]
  6. T.-H. Her, “Gain-guiding in transverse grating waveguides for large modal area laser amplifiers,” Opt. Express 16(10), 7197–7202 ( 2008).
    [Crossref] [PubMed]
  7. P. Yeh, A. Yariv, and E. Marom, “Theory of Bragg fiber,” J. Opt. Soc. Am. 68(9), 1196 ( 1978).
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  14. 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 ( 1964).
  15. P. Yeh, A. Yariv, and C. S. Hong, “Electromagnetic propagation in periodic stratified media.I. general theory,” J. Opt. Soc. Am. 67(4), 423 ( 1977).
    [Crossref]
  16. Y. Xu, R. K. Lee, and A. Yariv, “Asymptotic analysis of Bragg fibers,” Opt. Lett. 25(24), 1756–1758 ( 2000).
    [Crossref] [PubMed]
  17. H. A. Macleod, Thin-Film Optical Filters (IOP, Philadelphia, 2001).
  18. T.-H. Her, X. Ao, and L. W. Casperson, “Gain saturation in gain-guided slab waveguides with large-index antiguiding,” Opt. Lett. 34(16), 2411–2413 ( 2009).
    [Crossref] [PubMed]

2009 (1)

2008 (3)

2007 (2)

2006 (3)

2004 (1)

2003 (1)

A. E. Siegman, “Propagating modes in gain-guided optical fibers,” J. Opt. Soc. Am. B 20(8), 1617 ( 2003).
[Crossref]

2002 (1)

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature 420(6916), 650–653 ( 2002).
[Crossref] [PubMed]

2001 (1)

2000 (1)

1978 (1)

1977 (1)

1964 (1)

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 ( 1964).

Ao, X.

Ballato, J.

V. Sudesh, T. Mccomb, Y. Chen, M. Bass, M. Richardson, J. Ballato, and A. E. Siegman, “Diode-pumped 200 µm diameter core, gain-guided, index-antiguided single mode fiber laser,” Appl. Phys. B 90(3-4), 369–372 ( 2008).
[Crossref]

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(25), 251101 ( 2006).
[Crossref]

Bass, M.

V. Sudesh, T. Mccomb, Y. Chen, M. Bass, M. Richardson, J. Ballato, and A. E. Siegman, “Diode-pumped 200 µm diameter core, gain-guided, index-antiguided single mode fiber laser,” Appl. Phys. B 90(3-4), 369–372 ( 2008).
[Crossref]

Y. Chen, T. McComb, V. Sudesh, M. Richardson, and M. Bass, “Very large-core, single-mode, gain-guided, index-antiguided fiber lasers,” Opt. Lett. 32(17), 2505–2507 ( 2007).
[Crossref] [PubMed]

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(25), 251101 ( 2006).
[Crossref]

Benoit, G.

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature 420(6916), 650–653 ( 2002).
[Crossref] [PubMed]

Bjarklev, A.

Blondy, J.-M.

Broeng, J.

Bubnov, M. M.

Casperson, L. W.

Chen, Y.

V. Sudesh, T. Mccomb, Y. Chen, M. Bass, M. Richardson, J. Ballato, and A. E. Siegman, “Diode-pumped 200 µm diameter core, gain-guided, index-antiguided single mode fiber laser,” Appl. Phys. B 90(3-4), 369–372 ( 2008).
[Crossref]

Y. Chen, T. McComb, V. Sudesh, M. Richardson, and M. Bass, “Very large-core, single-mode, gain-guided, index-antiguided fiber lasers,” Opt. Lett. 32(17), 2505–2507 ( 2007).
[Crossref] [PubMed]

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(25), 251101 ( 2006).
[Crossref]

Deyerl, H.-J.

Dianov, E. M.

Engeness, T.

Février, S.

Fink, Y.

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature 420(6916), 650–653 ( 2002).
[Crossref] [PubMed]

S. G. Johnson, M. Ibanescu, M. Skorobogatiy, O. Weisberg, T. Engeness, M. Soljacic, S. Jacobs, J. Joannopoulos, and Y. Fink, “Low-loss asymptotically single-mode propagation in large-core OmniGuide fibers,” Opt. Express 9(13), 748–779 ( 2001).
[Crossref] [PubMed]

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(25), 251101 ( 2006).
[Crossref]

Gaponov, D. D.

Guryanov, A. N.

Hansen, T. P.

Hart, S. D.

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature 420(6916), 650–653 ( 2002).
[Crossref] [PubMed]

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(25), 251101 ( 2006).
[Crossref]

Her, T.-H.

Hong, C. S.

Huang, Y.

Ibanescu, M.

Jacobs, S.

Jakobsen, C.

Jamier, R.

Jensen, J.

Joannopoulos, J.

Joannopoulos, J. D.

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature 420(6916), 650–653 ( 2002).
[Crossref] [PubMed]

Johnson, S. G.

Katagiri, T.

Khopin, V. F.

Lee, R. K.

Likhachev, M. E.

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 ( 1964).

Marom, E.

Matsuura, Y.

Mccomb, T.

V. Sudesh, T. Mccomb, Y. Chen, M. Bass, M. Richardson, J. Ballato, and A. E. Siegman, “Diode-pumped 200 µm diameter core, gain-guided, index-antiguided single mode fiber laser,” Appl. Phys. B 90(3-4), 369–372 ( 2008).
[Crossref]

Y. Chen, T. McComb, V. Sudesh, M. Richardson, and M. Bass, “Very large-core, single-mode, gain-guided, index-antiguided fiber lasers,” Opt. Lett. 32(17), 2505–2507 ( 2007).
[Crossref] [PubMed]

Miyagi, M.

Mortensen, N. A.

Richardson, M.

V. Sudesh, T. Mccomb, Y. Chen, M. Bass, M. Richardson, J. Ballato, and A. E. Siegman, “Diode-pumped 200 µm diameter core, gain-guided, index-antiguided single mode fiber laser,” Appl. Phys. B 90(3-4), 369–372 ( 2008).
[Crossref]

Y. Chen, T. McComb, V. Sudesh, M. Richardson, and M. Bass, “Very large-core, single-mode, gain-guided, index-antiguided fiber lasers,” Opt. Lett. 32(17), 2505–2507 ( 2007).
[Crossref] [PubMed]

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(25), 251101 ( 2006).
[Crossref]

Roy, P.

Salganskii, M. Y.

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 ( 1964).

Semjonov, S. L.

Siegman, A. E.

V. Sudesh, T. Mccomb, Y. Chen, M. Bass, M. Richardson, J. Ballato, and A. E. Siegman, “Diode-pumped 200 µm diameter core, gain-guided, index-antiguided single mode fiber laser,” Appl. Phys. B 90(3-4), 369–372 ( 2008).
[Crossref]

A. E. Siegman, “Gain-guided, index-antiguided fiber lasers,” J. Opt. Soc. Am. B 24(8), 1677 ( 2007).
[Crossref]

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(25), 251101 ( 2006).
[Crossref]

A. E. Siegman, “Propagating modes in gain-guided optical fibers,” J. Opt. Soc. Am. B 20(8), 1617 ( 2003).
[Crossref]

Simonsen, H.

Skorobogatiy, M.

Soljacic, M.

Sorensen, T.

Sudesh, V.

V. Sudesh, T. Mccomb, Y. Chen, M. Bass, M. Richardson, J. Ballato, and A. E. Siegman, “Diode-pumped 200 µm diameter core, gain-guided, index-antiguided single mode fiber laser,” Appl. Phys. B 90(3-4), 369–372 ( 2008).
[Crossref]

Y. Chen, T. McComb, V. Sudesh, M. Richardson, and M. Bass, “Very large-core, single-mode, gain-guided, index-antiguided fiber lasers,” Opt. Lett. 32(17), 2505–2507 ( 2007).
[Crossref] [PubMed]

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(25), 251101 ( 2006).
[Crossref]

Temelkuran, B.

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature 420(6916), 650–653 ( 2002).
[Crossref] [PubMed]

Terrel, M.

Vienne, G.

Weisberg, O.

Xu, Y.

Yariv, A.

Yashkov, M. Y.

Yeh, P.

Appl. Phys. B (1)

V. Sudesh, T. Mccomb, Y. Chen, M. Bass, M. Richardson, J. Ballato, and A. E. Siegman, “Diode-pumped 200 µm diameter core, gain-guided, index-antiguided single mode fiber laser,” Appl. Phys. B 90(3-4), 369–372 ( 2008).
[Crossref]

Appl. Phys. Lett. (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(25), 251101 ( 2006).
[Crossref]

Bell Syst. Tech. J. (1)

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 ( 1964).

J. Lightwave Technol. (1)

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. B (2)

A. E. Siegman, “Propagating modes in gain-guided optical fibers,” J. Opt. Soc. Am. B 20(8), 1617 ( 2003).
[Crossref]

A. E. Siegman, “Gain-guided, index-antiguided fiber lasers,” J. Opt. Soc. Am. B 24(8), 1677 ( 2007).
[Crossref]

Nature (1)

B. Temelkuran, S. D. Hart, G. Benoit, J. D. Joannopoulos, and Y. Fink, “Wavelength-scalable hollow optical fibres with large photonic bandgaps for CO2 laser transmission,” Nature 420(6916), 650–653 ( 2002).
[Crossref] [PubMed]

Opt. Express (4)

Opt. Lett. (4)

Other (1)

H. A. Macleod, Thin-Film Optical Filters (IOP, Philadelphia, 2001).

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Figures (3)

Fig. 1
Fig. 1 Schematic of a Bragg fiber (a) and the radial index profile (b) (not to scale).

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Fig. 2
Fig. 2 (a) Combinations of n 1 and d 2 for which a complete bandgap exists for the pump at glancing incidence. Other parameters are fixed (see text). (b) Band diagram for n 1 = 2.2, n 2 = 1.57, d 1 = 0.34 µm, and d 2 = 0.575 µm. The shaded areas indicate allowed bands for TE polarization (light gray), TM polarization (dark gray), and overlaps (black). White areas indicate complete bandgaps. (c) Reflectance of a planar structure with the same index profile as in Fig. 1(b).

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Fig. 3
Fig. 3 (a) Radial profile of S z of the HE11 mode in an IAG fiber (open circles) and a Bragg fiber with 6 pairs of Bragg layers (blue solid line) at the signal wavelength. Inset shows the expanded view of S z (left axis; open circles and blue line) and the radial phase profile of the H z field in the Bragg cladding (right axis; green line). (b) Modal gain coefficient of the HE11 mode as a function of the material gain for the IAG fiber (open circles) and a Bragg fiber (solid line).

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Tables (1)

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Table 1 Modal Properties of an IAG Fiber and a Bragg Fiber with 6 pairs of Bragg Layers.

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Equations (11)

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c o s ( K Λ ) = c o s ( k 1 d 1 ) c o s ( k 2 d 2 ) − γ sin ( k 1 d 1 ) sin ( k 2 d 2 ) ,
γ = { 1 2 ( k 1 k 2 + k 2 k 1 ) TE 1 2 ( n 2 2 k 1 n 1 2 k 2 + n 1 2 k 2 n 2 2 k 1 ) TM ,
d 1 = λ s / 2 n 1 2 − n 0 2 .
E z ( r ) = a c J m ( k 0 r ) ,   r ≤ R 0 ,
E z ( r ) = a l ′ exp [ i k 1 ( r − R l ) ] + b l ′ exp [ − i k 1 ( r − R l ) ] k 1 r ,   R l ≤ r ≤ R l + d 1 ,
E z ( r ) = a l exp [ i k 2 ( r − R l − d 1 ) ] + b l exp [ − i k 2 ( r − R l − d 1 ) ] k 2 r ,   R l + d 1 ≤ r ≤ R l + Λ ,
( a l b l ) = [ A TM B TM B TM * A TM * ] ( a l + 1 b l + 1 ) ,
A TM = exp ( − i k 2 d 2 ) [ cos ( k 1 d 1 ) − i 2 ( n 1 2 k 2 n 2 2 k 1 + n 2 2 k 1 k 2 n 1 2 ) sin ( k 1 d 1 ) ] ,
B TM = exp ( − i k 2 d 2 ) [ i 2 ( n 2 2 k 1 k 2 n 1 2 − n 1 2 k 2 n 2 2 k 1 ) sin ( k 1 d 1 ) ] .
( β m λ s 2 π k 0 R 0 n 0 ) 2 ( 1 − k 0 2 k 2 2 ) 2 = [ J ′ m ( k 0 R 0 ) J m ( k 0 R 0 ) − i ε 2 k 0 ε 0 k 2 ] [ J ′ m ( k 0 R 0 ) J m ( k 0 R 0 ) − i k 0 k 2 ] .
| c o s ( φ 1 ) c o s ( φ 2 ) − γ s i n ( φ 1 ) s i n ( φ 2 ) | ≥ 1 ,

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