Abstract

A zigzag array structure is proposed for passive coherent beam combining. Modal analysis was conducted via a transfer matrix method to demonstrate the support of a single supermode in this structure with a large modal discrimination. The performance of the proposed structure against the phase variation is also investigated by calculating the modal loss with different strengths of phase variation. The scalability of this structure is estimated from the perspective of brightness in two situations: the fully correlated one and the adjacent-correlated one. A brightness saturation behavior is observed for the latter with a sufficiency of available emitters in an array.

© 2012 Optical Society of America

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  1. T. Y. Fan, “Laser beam combining for high-power, high-radiance sources,” IEEE J. Sel. Top. Quantum Electron. 11, 567–577 (2005).
    [CrossRef]
  2. A. Tünnermann, S. Hüfer, A. Liem, J. Limpert, M. Reich, F. Rüser, and T. Schreiber, “Power scaling of high-power fiber lasers and amplifiers,” Laser Physics 15, 107–117 (2005).
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    [CrossRef]
  4. C. Wirth, O. Schmidt, I. Tsybin, T. Schreiber, R. Eberhardt, J. Limpert, A. Tünnermann, K. Ludewigt, M. Gowin, E. Have, and M. Jung, “High average power spectral beam combining of four fiber amplifiers to 8.2 kW,” Opt. Lett. 36, 3118–3120 (2011).
    [CrossRef]
  5. O. Andrusyak, V. Smirnov, G. Venus, and L. Glebov, “Beam combining of lasers with high spectral density using volume Bragg gratings,” Opt. Commun. 282, 2560–2563 (2009).
    [CrossRef]
  6. T. M. Shay, S. Member, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron. 13, 480–486 (2007).
    [CrossRef]
  7. E. C. Cheung, J. G. Ho, G. D. Goodno, R. R. Rice, J. Rothenberg, P. Thielen, M. Weber, and M. Wickham, “Diffractive-optics-based beam combination of a phase-locked fiber laser array,” Opt. Lett. 33, 354–356 (2008).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  11. D. F. Welch, D. Scifres, P. Cross, H. Kung, W. Streifer, R. D. Burnham, and J. Yaeli, “High-power (575 mW) singled-lobed emission from a phased-laser laser,” Electron. Lett. 21, 603–604(1985).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  19. K. L. Chen and S. Wang, “Single-lobe symmetric coupled laser arrays,” Electron. Lett. 21, 347–349 (1985).
    [CrossRef]
  20. K. Chen and S. Wang, “Analysis of symmetric Y junction laser arrays with uniform near field distribution,” Electron. Lett. 22, 644–645 (1986).
    [CrossRef]
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    [CrossRef]

2011 (1)

2010 (4)

2009 (3)

2008 (2)

2007 (1)

T. M. Shay, S. Member, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron. 13, 480–486 (2007).
[CrossRef]

2005 (4)

C. J. Corcoran and F. Durville, “Experimental demonstration of a phase-locked laser array using a self-Fourier cavity,” Appl. Phys. Lett. 86, 201118 (2005).
[CrossRef]

C. J. Corcoran and K. A. Pasch, “Modal analysis of a self-Fourier laser,” J. Opt. A 7, L1–L7 (2005).
[CrossRef]

T. Y. Fan, “Laser beam combining for high-power, high-radiance sources,” IEEE J. Sel. Top. Quantum Electron. 11, 567–577 (2005).
[CrossRef]

A. Tünnermann, S. Hüfer, A. Liem, J. Limpert, M. Reich, F. Rüser, and T. Schreiber, “Power scaling of high-power fiber lasers and amplifiers,” Laser Physics 15, 107–117 (2005).

1994 (1)

1991 (1)

1986 (1)

K. Chen and S. Wang, “Analysis of symmetric Y junction laser arrays with uniform near field distribution,” Electron. Lett. 22, 644–645 (1986).
[CrossRef]

1985 (2)

D. F. Welch, D. Scifres, P. Cross, H. Kung, W. Streifer, R. D. Burnham, and J. Yaeli, “High-power (575 mW) singled-lobed emission from a phased-laser laser,” Electron. Lett. 21, 603–604(1985).
[CrossRef]

K. L. Chen and S. Wang, “Single-lobe symmetric coupled laser arrays,” Electron. Lett. 21, 347–349 (1985).
[CrossRef]

Alley, T. G.

Andrusyak, O.

O. Andrusyak, V. Smirnov, G. Venus, and L. Glebov, “Beam combining of lasers with high spectral density using volume Bragg gratings,” Opt. Commun. 282, 2560–2563 (2009).
[CrossRef]

Bachmann, F.

F. Bachmann, P. Loosen, and R. Poprawe, Springer Series in Optical Science: High Power Diode Lasers (Springer, 2006).

Baker, J. T.

T. M. Shay, S. Member, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron. 13, 480–486 (2007).
[CrossRef]

Barty, C. P. J.

Beach, R. J.

Benham, V.

T. M. Shay, S. Member, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron. 13, 480–486 (2007).
[CrossRef]

Braiman, Y.

Bratcher, A.

Burnham, R. D.

D. F. Welch, D. Scifres, P. Cross, H. Kung, W. Streifer, R. D. Burnham, and J. Yaeli, “High-power (575 mW) singled-lobed emission from a phased-laser laser,” Electron. Lett. 21, 603–604(1985).
[CrossRef]

Chang, W. Z.

Chen, K.

K. Chen and S. Wang, “Analysis of symmetric Y junction laser arrays with uniform near field distribution,” Electron. Lett. 22, 644–645 (1986).
[CrossRef]

Chen, K. L.

K. L. Chen and S. Wang, “Single-lobe symmetric coupled laser arrays,” Electron. Lett. 21, 347–349 (1985).
[CrossRef]

Cheung, E. C.

Corcoran, C. J.

C. J. Corcoran and K. A. Pasch, “Modal analysis of a self-Fourier laser,” J. Opt. A 7, L1–L7 (2005).
[CrossRef]

C. J. Corcoran and F. Durville, “Experimental demonstration of a phase-locked laser array using a self-Fourier cavity,” Appl. Phys. Lett. 86, 201118 (2005).
[CrossRef]

Cross, P.

D. F. Welch, D. Scifres, P. Cross, H. Kung, W. Streifer, R. D. Burnham, and J. Yaeli, “High-power (575 mW) singled-lobed emission from a phased-laser laser,” Electron. Lett. 21, 603–604(1985).
[CrossRef]

Dawson, J. W.

Durville, F.

C. J. Corcoran and F. Durville, “Experimental demonstration of a phase-locked laser array using a self-Fourier cavity,” Appl. Phys. Lett. 86, 201118 (2005).
[CrossRef]

Eberhardt, R.

Fan, T. Y.

T. Y. Fan, “Laser beam combining for high-power, high-radiance sources,” IEEE J. Sel. Top. Quantum Electron. 11, 567–577 (2005).
[CrossRef]

Flores, S.

Galvanauskas, A.

Glebov, L.

O. Andrusyak, V. Smirnov, G. Venus, and L. Glebov, “Beam combining of lasers with high spectral density using volume Bragg gratings,” Opt. Commun. 282, 2560–2563 (2009).
[CrossRef]

Goodno, G. D.

Gowin, M.

Have, E.

Heebner, J. E.

Ho, J. G.

Hüfer, S.

A. Tünnermann, S. Hüfer, A. Liem, J. Limpert, M. Reich, F. Rüser, and T. Schreiber, “Power scaling of high-power fiber lasers and amplifiers,” Laser Physics 15, 107–117 (2005).

Jung, M.

Kung, H.

D. F. Welch, D. Scifres, P. Cross, H. Kung, W. Streifer, R. D. Burnham, and J. Yaeli, “High-power (575 mW) singled-lobed emission from a phased-laser laser,” Electron. Lett. 21, 603–604(1985).
[CrossRef]

Liem, A.

A. Tünnermann, S. Hüfer, A. Liem, J. Limpert, M. Reich, F. Rüser, and T. Schreiber, “Power scaling of high-power fiber lasers and amplifiers,” Laser Physics 15, 107–117 (2005).

Limpert, J.

C. Wirth, O. Schmidt, I. Tsybin, T. Schreiber, R. Eberhardt, J. Limpert, A. Tünnermann, K. Ludewigt, M. Gowin, E. Have, and M. Jung, “High average power spectral beam combining of four fiber amplifiers to 8.2 kW,” Opt. Lett. 36, 3118–3120 (2011).
[CrossRef]

A. Tünnermann, S. Hüfer, A. Liem, J. Limpert, M. Reich, F. Rüser, and T. Schreiber, “Power scaling of high-power fiber lasers and amplifiers,” Laser Physics 15, 107–117 (2005).

Liu, B.

Liu, Y.

Loosen, P.

F. Bachmann, P. Loosen, and R. Poprawe, Springer Series in Optical Science: High Power Diode Lasers (Springer, 2006).

Lu, C. A.

T. M. Shay, S. Member, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron. 13, 480–486 (2007).
[CrossRef]

Ludewigt, K.

Mccomb, T. S.

McNaught, S. J.

Mehuys, D.

Member, S.

T. M. Shay, S. Member, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron. 13, 480–486 (2007).
[CrossRef]

Messerly, M. J.

Mies, E.

Minden, M.

Nabors, C. D.

Pasch, K. A.

C. J. Corcoran and K. A. Pasch, “Modal analysis of a self-Fourier laser,” J. Opt. A 7, L1–L7 (2005).
[CrossRef]

Pax, P. H.

Pilkington, D.

T. M. Shay, S. Member, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron. 13, 480–486 (2007).
[CrossRef]

Poprawe, R.

F. Bachmann, P. Loosen, and R. Poprawe, Springer Series in Optical Science: High Power Diode Lasers (Springer, 2006).

Pulford, B.

Reich, M.

A. Tünnermann, S. Hüfer, A. Liem, J. Limpert, M. Reich, F. Rüser, and T. Schreiber, “Power scaling of high-power fiber lasers and amplifiers,” Laser Physics 15, 107–117 (2005).

Rice, R. R.

Rothenberg, J.

Rothenberg, J. E.

Rüser, F.

A. Tünnermann, S. Hüfer, A. Liem, J. Limpert, M. Reich, F. Rüser, and T. Schreiber, “Power scaling of high-power fiber lasers and amplifiers,” Laser Physics 15, 107–117 (2005).

Sanchez, A.

Sanchez, A. D.

R. Uberna, A. Bratcher, T. G. Alley, A. D. Sanchez, S. Flores, and B. Pulford, “Coherent combination of high power fiber amplifiers in a two-dimensional re-imaging waveguide,” Opt. Express 18, 13547–13553 (2010).
[CrossRef]

T. M. Shay, S. Member, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron. 13, 480–486 (2007).
[CrossRef]

Schmidt, O.

Schreiber, T.

C. Wirth, O. Schmidt, I. Tsybin, T. Schreiber, R. Eberhardt, J. Limpert, A. Tünnermann, K. Ludewigt, M. Gowin, E. Have, and M. Jung, “High average power spectral beam combining of four fiber amplifiers to 8.2 kW,” Opt. Lett. 36, 3118–3120 (2011).
[CrossRef]

A. Tünnermann, S. Hüfer, A. Liem, J. Limpert, M. Reich, F. Rüser, and T. Schreiber, “Power scaling of high-power fiber lasers and amplifiers,” Laser Physics 15, 107–117 (2005).

Scifres, D.

D. F. Welch, D. Scifres, P. Cross, H. Kung, W. Streifer, R. D. Burnham, and J. Yaeli, “High-power (575 mW) singled-lobed emission from a phased-laser laser,” Electron. Lett. 21, 603–604(1985).
[CrossRef]

Shay, T. M.

T. M. Shay, S. Member, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron. 13, 480–486 (2007).
[CrossRef]

Shverdin, M. Y.

Siders, C. W.

Smirnov, V.

O. Andrusyak, V. Smirnov, G. Venus, and L. Glebov, “Beam combining of lasers with high spectral density using volume Bragg gratings,” Opt. Commun. 282, 2560–2563 (2009).
[CrossRef]

Sridharan, A. K.

Stappaerts, A.

Streifer, W.

D. Mehuys, W. Streifer, R. G. Waarts, and D. F. Welch, “Modal analysis of linear Talbot-cavity semiconductor lasers,” Opt. Lett. 16, 823–825 (1991).
[CrossRef]

D. F. Welch, D. Scifres, P. Cross, H. Kung, W. Streifer, R. D. Burnham, and J. Yaeli, “High-power (575 mW) singled-lobed emission from a phased-laser laser,” Electron. Lett. 21, 603–604(1985).
[CrossRef]

Thielen, P.

Thielen, P. A.

Tsybin, I.

Tünnermann, A.

C. Wirth, O. Schmidt, I. Tsybin, T. Schreiber, R. Eberhardt, J. Limpert, A. Tünnermann, K. Ludewigt, M. Gowin, E. Have, and M. Jung, “High average power spectral beam combining of four fiber amplifiers to 8.2 kW,” Opt. Lett. 36, 3118–3120 (2011).
[CrossRef]

A. Tünnermann, S. Hüfer, A. Liem, J. Limpert, M. Reich, F. Rüser, and T. Schreiber, “Power scaling of high-power fiber lasers and amplifiers,” Laser Physics 15, 107–117 (2005).

Uberna, R.

Venus, G.

O. Andrusyak, V. Smirnov, G. Venus, and L. Glebov, “Beam combining of lasers with high spectral density using volume Bragg gratings,” Opt. Commun. 282, 2560–2563 (2009).
[CrossRef]

Waarts, R. G.

Wang, B.

Wang, S.

K. Chen and S. Wang, “Analysis of symmetric Y junction laser arrays with uniform near field distribution,” Electron. Lett. 22, 644–645 (1986).
[CrossRef]

K. L. Chen and S. Wang, “Single-lobe symmetric coupled laser arrays,” Electron. Lett. 21, 347–349 (1985).
[CrossRef]

Weber, M.

Weber, M. E.

Welch, D. F.

D. Mehuys, W. Streifer, R. G. Waarts, and D. F. Welch, “Modal analysis of linear Talbot-cavity semiconductor lasers,” Opt. Lett. 16, 823–825 (1991).
[CrossRef]

D. F. Welch, D. Scifres, P. Cross, H. Kung, W. Streifer, R. D. Burnham, and J. Yaeli, “High-power (575 mW) singled-lobed emission from a phased-laser laser,” Electron. Lett. 21, 603–604(1985).
[CrossRef]

Wickham, M.

E. C. Cheung, J. G. Ho, G. D. Goodno, R. R. Rice, J. Rothenberg, P. Thielen, M. Weber, and M. Wickham, “Diffractive-optics-based beam combination of a phase-locked fiber laser array,” Opt. Lett. 33, 354–356 (2008).
[CrossRef]

M. Wickham, “Coherent beam combining of fiber amplifiers and solid-state lasers including the use of diffractive optical elements,” in Conference on Lasers and Electro-Optics, Technical Digest (CD) (Optical Society of America, 2010), paper CThG2.

Wickham, M. G.

Winful, H. G.

Wirth, C.

Wu, T. Z.

Yaeli, J.

D. F. Welch, D. Scifres, P. Cross, H. Kung, W. Streifer, R. D. Burnham, and J. Yaeli, “High-power (575 mW) singled-lobed emission from a phased-laser laser,” Electron. Lett. 21, 603–604(1985).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

C. J. Corcoran and F. Durville, “Experimental demonstration of a phase-locked laser array using a self-Fourier cavity,” Appl. Phys. Lett. 86, 201118 (2005).
[CrossRef]

Electron. Lett. (3)

K. L. Chen and S. Wang, “Single-lobe symmetric coupled laser arrays,” Electron. Lett. 21, 347–349 (1985).
[CrossRef]

K. Chen and S. Wang, “Analysis of symmetric Y junction laser arrays with uniform near field distribution,” Electron. Lett. 22, 644–645 (1986).
[CrossRef]

D. F. Welch, D. Scifres, P. Cross, H. Kung, W. Streifer, R. D. Burnham, and J. Yaeli, “High-power (575 mW) singled-lobed emission from a phased-laser laser,” Electron. Lett. 21, 603–604(1985).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (2)

T. Y. Fan, “Laser beam combining for high-power, high-radiance sources,” IEEE J. Sel. Top. Quantum Electron. 11, 567–577 (2005).
[CrossRef]

T. M. Shay, S. Member, V. Benham, J. T. Baker, A. D. Sanchez, D. Pilkington, and C. A. Lu, “Self-synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron. 13, 480–486 (2007).
[CrossRef]

J. Opt. A (1)

C. J. Corcoran and K. A. Pasch, “Modal analysis of a self-Fourier laser,” J. Opt. A 7, L1–L7 (2005).
[CrossRef]

Laser Physics (1)

A. Tünnermann, S. Hüfer, A. Liem, J. Limpert, M. Reich, F. Rüser, and T. Schreiber, “Power scaling of high-power fiber lasers and amplifiers,” Laser Physics 15, 107–117 (2005).

Opt. Commun. (1)

O. Andrusyak, V. Smirnov, G. Venus, and L. Glebov, “Beam combining of lasers with high spectral density using volume Bragg gratings,” Opt. Commun. 282, 2560–2563 (2009).
[CrossRef]

Opt. Express (5)

Opt. Lett. (5)

Other (2)

M. Wickham, “Coherent beam combining of fiber amplifiers and solid-state lasers including the use of diffractive optical elements,” in Conference on Lasers and Electro-Optics, Technical Digest (CD) (Optical Society of America, 2010), paper CThG2.

F. Bachmann, P. Loosen, and R. Poprawe, Springer Series in Optical Science: High Power Diode Lasers (Springer, 2006).

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Figures (4)

Fig. 1.
Fig. 1.

Topographic structures of different passive beam combining systems. Adjacent laser beams are connected by a 2×2 coupler. (a) The proposed zigzag-like structure. Each laser beam is directly coupled with adjacent neighbors. The system has N/2 output ports. (b) The treelike structure. The system has only one output port.

Fig. 2.
Fig. 2.

Dependence of eigenvalues on phase variation ΔΦ and total beam number N in the zigzag array structure

Fig. 3.
Fig. 3.

Normalized IG versus θdλ. The solid line shows the ideal case. The dash line shows the fully correlated case. The dot-dash line shows the adjacent-correlated case. In the simulation, σϕ is set to be π/5 [22].

Fig. 4.
Fig. 4.

(a) Brightness with respect to the standard variation of phase noise σϕ. N is set to be 30 in the calculation. (b) Brightness with respect to the number of emitters N. σϕ is set to be π/8 in the calculation. The solid line shows the ideal case. The dashed line shows the fully correlated case, and the dot-dashed line shows the adjacent-correlated case.

Equations (18)

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

[jtssjt],
X=R1A*SB*R2BSA,
XE=μE,
A=[0jtssjt0],S=[ejΦ1ejΦ2ejΦ3ejΦ4],B=[jtssjtjtssjt],R1=[1101],R2=[0R0R].
Xa=0.99,|Ea|=[0.5,0.7071,0,0.5],Xb=0.495,|Eb|=[0.5,0,0.7071,0.5].
X=[0.990.9520.8450.6840.4950.3060.1450.038],|E|=[0.250.35400.35400.35400.35400.35400.35400.35400.250.3540.46200.35400.1910000.19100.35400.46200.3540.3540.3540000.35400.500.3540000.35400.3540.3540.19100.35400.4620000.46200.35400.19100.3540.354000.50000.50000.50000.3540.3540.19100.35400.4620000.46200.35400.19100.3540.3540.3540000.35400.500.3540000.35400.3540.3540.46200.35400.1910000.19100.35400.46200.354].
B=PAΩ,
B0=P0A0Ω0.
BB0=PP0A0Ω0AΩ.
Ω=Sr2πrθxrθyr2=πθxθy,
BB0=1NPP0θx,0θx,tot.
u(x)=u0(x)j=1Nδ(xjd)exp(iϕj)=u0(x)g(x),
U(sx)=U0(sx)j=1Nexp(2πijsxd+iϕj)=U0(sx)G(sx).
I(sx)=|U(sx)|2=|U0(sx)|2|G(sx)|2=I0IG,
IG=j=1Nl=1Nexp(2πisxd(jl))exp(i(ϕjϕl)).
IGideal=sin2(πNsxd)sin2(πsxd),
IGful_corr=exp(δϕ22)IGideal+N(1exp(δϕ22)),
IGadj_corr=1[12αcos(β)+α2]2(4α2+N(1α4)+2αcos(β)[α2(N1)N1]+2αN+1{α2cos[(N1)β]2αcos(Nβ)+cos[(N+1)β]}),

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