Abstract

Phased array 1-to-N-way resonators can be relevant in the realization of high output powers from semiconductor laser arrays and have significant advantages over Talbot resonators. However, depending on the number of array elements, the intracavity power density on the output facet can be high, resulting in catastrophic optical mirror damage. We present a variant of the original design that overcomes these power density problems while maintaining the desirable phase-locking and power-combining properties.

© 2005 Optical Society of America

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References

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  1. F. Talbot, “Facts relating to optical science No IV,” Philos. Mag. 9, 401–407 (1836).
  2. D. Mehuys, W. Streifer, R. G. Waarts, D. F. Welch, “Modal analysis of linear Talbot-cavity semiconductor lasers,” Opt. Lett. 16, 823–825 (1991).
    [CrossRef] [PubMed]
  3. R. M. Jenkins, J. Banerji, A. R. Davies, J. M. Heaton, “1-to-N-way phased array resonator,” in Conference on Lasers and Electro Optics, Vol. 8 of 1994OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 228–229.
  4. J. Banerji, A. R. Davies, R. M. Jenkins, “Comparison of Talbot and 1-to-N-way phase locked resonators,” Appl. Opt. 36, 1604–1609 (1997).
    [CrossRef] [PubMed]
  5. L. A. Rivlin, V. S. Shul’dyaev, “Multimode waveguides for coherent light,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 11, 572–578 (1968).
  6. O. Bryngdahl, “Image formation using self-imaging techniques,” J. Opt. Soc. Am. 63, 416–419 (1973).
    [CrossRef]
  7. R. Ulrich, G. Ankele, “Self-imaging in homogeneous planar optical waveguides,” Appl. Phys. Lett. 27, 337–339 (1975).
    [CrossRef]
  8. R. M. Jenkins, R. W. J. Devereux, J. M. Heaton, “Waveguide beam splitters and recombiners based on multimode propagation phenomena,” Opt. Lett. 17, 991–993 (1992).
    [CrossRef] [PubMed]
  9. F. J. Wilson, J. J. Lewandowski, B. K. Nayar, D. J. Robbins, P. J. Williams, N. Carr, F. O. Robson, “9.5W CW output power from high brightness 980 nm InGaAs/AIGaAs tapered laser arrays,” Electron. Lett. 35, 43–44 (1999).
    [CrossRef]
  10. J. P. Donnelly, J. N. Walpole, S. H. Groves, R. J. Bailey, L. J. Missaggia, A. Napoleone, R. E. Reeder, C. C. Cook, “1.5-m tapered-gain-region lasers with high CW output powers,” IEEE Photon. Technol. Lett. 10, 1377–1379 (1998).
    [CrossRef]
  11. E. K. Gorton, R. M. Jenkins, “Theory of 1-N-way phase-locked resonators,” Appl. Opt. 40, 916–920 (2001).
    [CrossRef]
  12. K. D. Laakmann, W. M. Steier, “Waveguides: characteristic modes of hollow rectangular dielectric waveguides,” Appl. Opt. 15, 1334–1340 (1976).
    [CrossRef] [PubMed]

2001 (1)

1999 (1)

F. J. Wilson, J. J. Lewandowski, B. K. Nayar, D. J. Robbins, P. J. Williams, N. Carr, F. O. Robson, “9.5W CW output power from high brightness 980 nm InGaAs/AIGaAs tapered laser arrays,” Electron. Lett. 35, 43–44 (1999).
[CrossRef]

1998 (1)

J. P. Donnelly, J. N. Walpole, S. H. Groves, R. J. Bailey, L. J. Missaggia, A. Napoleone, R. E. Reeder, C. C. Cook, “1.5-m tapered-gain-region lasers with high CW output powers,” IEEE Photon. Technol. Lett. 10, 1377–1379 (1998).
[CrossRef]

1997 (1)

1992 (1)

1991 (1)

1976 (1)

1975 (1)

R. Ulrich, G. Ankele, “Self-imaging in homogeneous planar optical waveguides,” Appl. Phys. Lett. 27, 337–339 (1975).
[CrossRef]

1973 (1)

1968 (1)

L. A. Rivlin, V. S. Shul’dyaev, “Multimode waveguides for coherent light,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 11, 572–578 (1968).

1836 (1)

F. Talbot, “Facts relating to optical science No IV,” Philos. Mag. 9, 401–407 (1836).

Ankele, G.

R. Ulrich, G. Ankele, “Self-imaging in homogeneous planar optical waveguides,” Appl. Phys. Lett. 27, 337–339 (1975).
[CrossRef]

Bailey, R. J.

J. P. Donnelly, J. N. Walpole, S. H. Groves, R. J. Bailey, L. J. Missaggia, A. Napoleone, R. E. Reeder, C. C. Cook, “1.5-m tapered-gain-region lasers with high CW output powers,” IEEE Photon. Technol. Lett. 10, 1377–1379 (1998).
[CrossRef]

Banerji, J.

J. Banerji, A. R. Davies, R. M. Jenkins, “Comparison of Talbot and 1-to-N-way phase locked resonators,” Appl. Opt. 36, 1604–1609 (1997).
[CrossRef] [PubMed]

R. M. Jenkins, J. Banerji, A. R. Davies, J. M. Heaton, “1-to-N-way phased array resonator,” in Conference on Lasers and Electro Optics, Vol. 8 of 1994OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 228–229.

Bryngdahl, O.

Carr, N.

F. J. Wilson, J. J. Lewandowski, B. K. Nayar, D. J. Robbins, P. J. Williams, N. Carr, F. O. Robson, “9.5W CW output power from high brightness 980 nm InGaAs/AIGaAs tapered laser arrays,” Electron. Lett. 35, 43–44 (1999).
[CrossRef]

Cook, C. C.

J. P. Donnelly, J. N. Walpole, S. H. Groves, R. J. Bailey, L. J. Missaggia, A. Napoleone, R. E. Reeder, C. C. Cook, “1.5-m tapered-gain-region lasers with high CW output powers,” IEEE Photon. Technol. Lett. 10, 1377–1379 (1998).
[CrossRef]

Davies, A. R.

J. Banerji, A. R. Davies, R. M. Jenkins, “Comparison of Talbot and 1-to-N-way phase locked resonators,” Appl. Opt. 36, 1604–1609 (1997).
[CrossRef] [PubMed]

R. M. Jenkins, J. Banerji, A. R. Davies, J. M. Heaton, “1-to-N-way phased array resonator,” in Conference on Lasers and Electro Optics, Vol. 8 of 1994OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 228–229.

Devereux, R. W. J.

Donnelly, J. P.

J. P. Donnelly, J. N. Walpole, S. H. Groves, R. J. Bailey, L. J. Missaggia, A. Napoleone, R. E. Reeder, C. C. Cook, “1.5-m tapered-gain-region lasers with high CW output powers,” IEEE Photon. Technol. Lett. 10, 1377–1379 (1998).
[CrossRef]

Gorton, E. K.

Groves, S. H.

J. P. Donnelly, J. N. Walpole, S. H. Groves, R. J. Bailey, L. J. Missaggia, A. Napoleone, R. E. Reeder, C. C. Cook, “1.5-m tapered-gain-region lasers with high CW output powers,” IEEE Photon. Technol. Lett. 10, 1377–1379 (1998).
[CrossRef]

Heaton, J. M.

R. M. Jenkins, R. W. J. Devereux, J. M. Heaton, “Waveguide beam splitters and recombiners based on multimode propagation phenomena,” Opt. Lett. 17, 991–993 (1992).
[CrossRef] [PubMed]

R. M. Jenkins, J. Banerji, A. R. Davies, J. M. Heaton, “1-to-N-way phased array resonator,” in Conference on Lasers and Electro Optics, Vol. 8 of 1994OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 228–229.

Jenkins, R. M.

Laakmann, K. D.

Lewandowski, J. J.

F. J. Wilson, J. J. Lewandowski, B. K. Nayar, D. J. Robbins, P. J. Williams, N. Carr, F. O. Robson, “9.5W CW output power from high brightness 980 nm InGaAs/AIGaAs tapered laser arrays,” Electron. Lett. 35, 43–44 (1999).
[CrossRef]

Mehuys, D.

Missaggia, L. J.

J. P. Donnelly, J. N. Walpole, S. H. Groves, R. J. Bailey, L. J. Missaggia, A. Napoleone, R. E. Reeder, C. C. Cook, “1.5-m tapered-gain-region lasers with high CW output powers,” IEEE Photon. Technol. Lett. 10, 1377–1379 (1998).
[CrossRef]

Napoleone, A.

J. P. Donnelly, J. N. Walpole, S. H. Groves, R. J. Bailey, L. J. Missaggia, A. Napoleone, R. E. Reeder, C. C. Cook, “1.5-m tapered-gain-region lasers with high CW output powers,” IEEE Photon. Technol. Lett. 10, 1377–1379 (1998).
[CrossRef]

Nayar, B. K.

F. J. Wilson, J. J. Lewandowski, B. K. Nayar, D. J. Robbins, P. J. Williams, N. Carr, F. O. Robson, “9.5W CW output power from high brightness 980 nm InGaAs/AIGaAs tapered laser arrays,” Electron. Lett. 35, 43–44 (1999).
[CrossRef]

Reeder, R. E.

J. P. Donnelly, J. N. Walpole, S. H. Groves, R. J. Bailey, L. J. Missaggia, A. Napoleone, R. E. Reeder, C. C. Cook, “1.5-m tapered-gain-region lasers with high CW output powers,” IEEE Photon. Technol. Lett. 10, 1377–1379 (1998).
[CrossRef]

Rivlin, L. A.

L. A. Rivlin, V. S. Shul’dyaev, “Multimode waveguides for coherent light,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 11, 572–578 (1968).

Robbins, D. J.

F. J. Wilson, J. J. Lewandowski, B. K. Nayar, D. J. Robbins, P. J. Williams, N. Carr, F. O. Robson, “9.5W CW output power from high brightness 980 nm InGaAs/AIGaAs tapered laser arrays,” Electron. Lett. 35, 43–44 (1999).
[CrossRef]

Robson, F. O.

F. J. Wilson, J. J. Lewandowski, B. K. Nayar, D. J. Robbins, P. J. Williams, N. Carr, F. O. Robson, “9.5W CW output power from high brightness 980 nm InGaAs/AIGaAs tapered laser arrays,” Electron. Lett. 35, 43–44 (1999).
[CrossRef]

Shul’dyaev, V. S.

L. A. Rivlin, V. S. Shul’dyaev, “Multimode waveguides for coherent light,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 11, 572–578 (1968).

Steier, W. M.

Streifer, W.

Talbot, F.

F. Talbot, “Facts relating to optical science No IV,” Philos. Mag. 9, 401–407 (1836).

Ulrich, R.

R. Ulrich, G. Ankele, “Self-imaging in homogeneous planar optical waveguides,” Appl. Phys. Lett. 27, 337–339 (1975).
[CrossRef]

Waarts, R. G.

Walpole, J. N.

J. P. Donnelly, J. N. Walpole, S. H. Groves, R. J. Bailey, L. J. Missaggia, A. Napoleone, R. E. Reeder, C. C. Cook, “1.5-m tapered-gain-region lasers with high CW output powers,” IEEE Photon. Technol. Lett. 10, 1377–1379 (1998).
[CrossRef]

Welch, D. F.

Williams, P. J.

F. J. Wilson, J. J. Lewandowski, B. K. Nayar, D. J. Robbins, P. J. Williams, N. Carr, F. O. Robson, “9.5W CW output power from high brightness 980 nm InGaAs/AIGaAs tapered laser arrays,” Electron. Lett. 35, 43–44 (1999).
[CrossRef]

Wilson, F. J.

F. J. Wilson, J. J. Lewandowski, B. K. Nayar, D. J. Robbins, P. J. Williams, N. Carr, F. O. Robson, “9.5W CW output power from high brightness 980 nm InGaAs/AIGaAs tapered laser arrays,” Electron. Lett. 35, 43–44 (1999).
[CrossRef]

Appl. Opt. (3)

Appl. Phys. Lett. (1)

R. Ulrich, G. Ankele, “Self-imaging in homogeneous planar optical waveguides,” Appl. Phys. Lett. 27, 337–339 (1975).
[CrossRef]

Electron. Lett. (1)

F. J. Wilson, J. J. Lewandowski, B. K. Nayar, D. J. Robbins, P. J. Williams, N. Carr, F. O. Robson, “9.5W CW output power from high brightness 980 nm InGaAs/AIGaAs tapered laser arrays,” Electron. Lett. 35, 43–44 (1999).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

J. P. Donnelly, J. N. Walpole, S. H. Groves, R. J. Bailey, L. J. Missaggia, A. Napoleone, R. E. Reeder, C. C. Cook, “1.5-m tapered-gain-region lasers with high CW output powers,” IEEE Photon. Technol. Lett. 10, 1377–1379 (1998).
[CrossRef]

Izv. Vyssh. Uchebn. Zaved. Radiofiz. (1)

L. A. Rivlin, V. S. Shul’dyaev, “Multimode waveguides for coherent light,” Izv. Vyssh. Uchebn. Zaved. Radiofiz. 11, 572–578 (1968).

J. Opt. Soc. Am. (1)

Opt. Lett. (2)

Philos. Mag. (1)

F. Talbot, “Facts relating to optical science No IV,” Philos. Mag. 9, 401–407 (1836).

Other (1)

R. M. Jenkins, J. Banerji, A. R. Davies, J. M. Heaton, “1-to-N-way phased array resonator,” in Conference on Lasers and Electro Optics, Vol. 8 of 1994OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), pp. 228–229.

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Figures (6)

Fig. 1
Fig. 1

Schematic of a 1-to-N-way array resonator. Here M1 and M2 are fully and partially reflecting plane mirrors, respectively; G is a multimode guide of cross section 2a × 2b and length L/N(L = 4b2/λ); gi are elements of an array of N single-mode guides of cross section 2a × 2b and length l placed on a pitch p = 2b/N; Pi are elements of an array of phase plates; and g0 is a single-mode guide of cross section 2a × 2b and length l. The output from g0 is reimaged onto itself because of the self-imaging property of the multimode guide.

Fig. 2
Fig. 2

Schematic of a new design for the 1-to-N-way resonator in which the on-axis output guide g0 and the plane mirror M2 (see Fig. 1) are replaced by a convex mirror C of curvature Rz [see Eq. (6)]. In addition, the length of the multimode guide G is reduced by an amount z. All other details are as in Fig. 1.

Fig. 3
Fig. 3

Round-trip loss of the resonator supermodes as functions of z, the reduction in multimode guide length. The solid curve corresponds to the lowest-loss resonator supermode. Note that low loss and good mode discrimination are achievable in the range 0.005 ≤ z/L ≤ 0.025.

Fig. 4
Fig. 4

Axial power density (shown as a percentage of the value obtained in our earlier design) of the lowest-loss resonator supermode as a function of z (the reduction in multimode guide length) for small values of z.

Fig. 5
Fig. 5

Far-field intensity profile of the lowest-loss resonator supermode for various values of z (the reduction in multimode guide length).

Fig. 6
Fig. 6

Contour plots of the intensity profile for the lowest-loss resonator mode inside the multimode guide G. (a) Corresponds to what would be obtained in the original 1-to-N-way design. The next four plots are obtained with the new design for various values of z (the reduction in multimode guide length): (b) z/L = 0.01, (c) z/L = 0.02, (d) z/L = 0.03, (e) z/L = 0.04.

Equations (21)

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y j ( N ) = b ( 2 j 1 N ) b .
E ( y , L / N ) = 1 N j = 1 N E [ y y j ( N ) , 0 ] exp [ i π ϕ j ( N ) ] ,
ϕ j ( N ) = 1 2 N + N + 1 4 + j ( j N 1 ) N .
E ( y , z ) ~ w z 1 / 2 exp ( y 2 w z 2 + i π y 2 λ R z )
w z = w 0 ( 1 + z 2 z 0 2 ) ,
R z = z + z 0 2 z .
z 0 = π w 0 2 λ = ( π w 0 2 4 b 2 ) L .
E ( y , z ) ~ w z 1 / 2 exp ( y 2 w z 2 i π y 2 λ R z ) .
E q ( y , b ) | y | b = { cos ( π q y 2 b ) , q odd ; sin ( π q y 2 b ) , q even .
E 1 ( y , a ) = 1 a cos ( π y 2 a ) , | y | a .
F ( 0 ) ( y , 0 ) = n = 1 N a n E 1 [ y y n ( N ) , a ] .
E 1 [ y y n ( N ) , a ] = q C n q E q ( y , b ) .
n = 1 N a n q C n q E q ( y , b ) exp [ i β q ( L / N z ) ] , β q = π q 2 4 L .
E q ( y , b ) exp ( 2 π i y 2 / λ R ) = q M q q E q ( y , b )
r 2 n = 1 N a n q C n q exp [ i β q ( L / N z ) ] q M q q E q ( y , b ) .
r 2 n = 1 N a n q C n q exp [ i β q ( L / N z ) ] × q M q q E q ( y , b ) exp [ i β q ( L / N z ) ] .
r 2 n = 1 N a n n = 1 N D n m E 1 [ y y m ( N ) , a ] ,
D n m = q C n q exp [ i β q ( L / N z ) ] × q M q q C m q exp [ i β q ( L / N z ) ] .
F ( 1 ) ( y , 0 ) = r 1 r 2 n = 1 N a n m = 1 N D n m exp { 2 i [ l β 1 b 2 / a 2 + π ϕ m ( N ) ] } E 1 [ y y m ( N ) , a ] ,
n = 1 N D n m exp [ 2 i π ϕ m ( N ) ] a n = g a m ,
g = σ r 1 r 2 exp [ 2 i ( l β 1 b 2 / a 2 ) ] .

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