Abstract

An active phase locking of slab laser amplifiers via square wave dithering algorithm is demonstrated experimentally. The MPD technique based on dual-level square wave phase modulation, time division multiplexing, and single detector can achieve the phase error signal of amplifiers, but without coherent demodulation process. The experimental investigation on the 208 W coherent beam combining of two slab amplifiers shows that the whole system in a closed loop performs well over a long time observation. The contrast of the coherent combined beam profile is about 87% and the combining efficiency is nearly 90.4%. The beam steering with three kinds of steering angles based on coherent beam combining using square wave dithering algorithm is demonstrated numerically.

© 2014 Optical Society of America

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2012 (1)

T. J. Wagner, “Fiber laser beam combining and power scaling progress, Air Force Research Laboratory Laser Division,” Proc. SPIE 8237, 823718 (2012).
[Crossref]

2011 (2)

2010 (1)

2006 (2)

2005 (1)

L. Liu and M. A. Vorontsov, “Phase-locking of tiled fiber array using SPGD feedback controller,” Proc. SPIE 5895, 58950P (2005).
[Crossref]

1996 (1)

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268–298 (1996).
[Crossref]

Augst, S. J.

Baker, J. T.

Benham, V.

Cheung, E. C.

Corkum, D. L.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268–298 (1996).
[Crossref]

Culpepper, M. A.

Dong, X.

Dorschner, T. A.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268–298 (1996).
[Crossref]

Du, W.

Epp, P.

Fan, T. Y.

Flores, A.

A. Flores, T. M. Shay, C. A. Lu, C. Robin, B. Pulford, A. D. Sanchez, D. W. Hult, and K. B. Rowland, “Coherent beam combining of fiber amplifiers in a kW regime,” in CLEO, OSA Technical Digest (Optical Society of America, 2011), paper CFE3.

Friedman, L. J.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268–298 (1996).
[Crossref]

Goldizen, K. C.

Goodno, G. D.

Hobbs, D. S.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268–298 (1996).
[Crossref]

Holz, M.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268–298 (1996).
[Crossref]

Howland, D.

Hult, D. W.

A. Flores, T. M. Shay, C. A. Lu, C. Robin, B. Pulford, A. D. Sanchez, D. W. Hult, and K. B. Rowland, “Coherent beam combining of fiber amplifiers in a kW regime,” in CLEO, OSA Technical Digest (Optical Society of America, 2011), paper CFE3.

Injeyan, H.

Komine, H.

Leng, J.

Liberman, S.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268–298 (1996).
[Crossref]

Liu, L.

L. Liu and M. A. Vorontsov, “Phase-locking of tiled fiber array using SPGD feedback controller,” Proc. SPIE 5895, 58950P (2005).
[Crossref]

Liu, Z.

Long, W.

Lu, C. A.

T. M. Shay, V. Benham, J. T. Baker, B. Ward, A. D. Sanchez, M. A. Culpepper, D. Pilkington, J. Spring, D. J. Nelson, and C. A. Lu, “First experimental demonstration of self-synchronous phase locking of an optical array,” Opt. Express 14, 12015–12021 (2006).
[Crossref]

A. Flores, T. M. Shay, C. A. Lu, C. Robin, B. Pulford, A. D. Sanchez, D. W. Hult, and K. B. Rowland, “Coherent beam combining of fiber amplifiers in a kW regime,” in CLEO, OSA Technical Digest (Optical Society of America, 2011), paper CFE3.

Ma, H.

Ma, Y.

McClellan, M.

McManamon, P. F.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268–298 (1996).
[Crossref]

McNaught, S. J.

Murphy, D. V.

Nelson, D. J.

Nguyen, H. Q.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268–298 (1996).
[Crossref]

Pilkington, D.

Pulford, B.

A. Flores, T. M. Shay, C. A. Lu, C. Robin, B. Pulford, A. D. Sanchez, D. W. Hult, and K. B. Rowland, “Coherent beam combining of fiber amplifiers in a kW regime,” in CLEO, OSA Technical Digest (Optical Society of America, 2011), paper CFE3.

Pulford, B. N.

B. N. Pulford, “LOCSET phase locking: operation, diagnostics, and applications,” Ph.D. dissertation (University of New Mexico, 2011).

Redmond, S.

Redmond, S. M.

Resler, D. P.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268–298 (1996).
[Crossref]

Robin, C.

A. Flores, T. M. Shay, C. A. Lu, C. Robin, B. Pulford, A. D. Sanchez, D. W. Hult, and K. B. Rowland, “Coherent beam combining of fiber amplifiers in a kW regime,” in CLEO, OSA Technical Digest (Optical Society of America, 2011), paper CFE3.

Rowland, K. B.

A. Flores, T. M. Shay, C. A. Lu, C. Robin, B. Pulford, A. D. Sanchez, D. W. Hult, and K. B. Rowland, “Coherent beam combining of fiber amplifiers in a kW regime,” in CLEO, OSA Technical Digest (Optical Society of America, 2011), paper CFE3.

Sanchez, A.

Sanchez, A. D.

T. M. Shay, V. Benham, J. T. Baker, B. Ward, A. D. Sanchez, M. A. Culpepper, D. Pilkington, J. Spring, D. J. Nelson, and C. A. Lu, “First experimental demonstration of self-synchronous phase locking of an optical array,” Opt. Express 14, 12015–12021 (2006).
[Crossref]

A. Flores, T. M. Shay, C. A. Lu, C. Robin, B. Pulford, A. D. Sanchez, D. W. Hult, and K. B. Rowland, “Coherent beam combining of fiber amplifiers in a kW regime,” in CLEO, OSA Technical Digest (Optical Society of America, 2011), paper CFE3.

Sharp, R. C.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268–298 (1996).
[Crossref]

Shay, T. M.

T. M. Shay, V. Benham, J. T. Baker, B. Ward, A. D. Sanchez, M. A. Culpepper, D. Pilkington, J. Spring, D. J. Nelson, and C. A. Lu, “First experimental demonstration of self-synchronous phase locking of an optical array,” Opt. Express 14, 12015–12021 (2006).
[Crossref]

A. Flores, T. M. Shay, C. A. Lu, C. Robin, B. Pulford, A. D. Sanchez, D. W. Hult, and K. B. Rowland, “Coherent beam combining of fiber amplifiers in a kW regime,” in CLEO, OSA Technical Digest (Optical Society of America, 2011), paper CFE3.

Si, L.

Simpson, R.

Sollee, J.

Spring, J.

Vorontsov, M. A.

L. Liu and M. A. Vorontsov, “Phase-locking of tiled fiber array using SPGD feedback controller,” Proc. SPIE 5895, 58950P (2005).
[Crossref]

Wagner, T. J.

T. J. Wagner, “Fiber laser beam combining and power scaling progress, Air Force Research Laboratory Laser Division,” Proc. SPIE 8237, 823718 (2012).
[Crossref]

Wang, X.

Ward, B.

Watson, E. A.

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268–298 (1996).
[Crossref]

Weber, M.

Weiss, S. B.

Xiao, H.

Xu, X.

Yu, C. X.

Zhao, Y.

Zhou, P.

Zhu, J.

Opt. Express (1)

Opt. Lett. (4)

Proc. IEEE (1)

P. F. McManamon, T. A. Dorschner, D. L. Corkum, L. J. Friedman, D. S. Hobbs, M. Holz, S. Liberman, H. Q. Nguyen, D. P. Resler, R. C. Sharp, and E. A. Watson, “Optical phased array technology,” Proc. IEEE 84, 268–298 (1996).
[Crossref]

Proc. SPIE (2)

T. J. Wagner, “Fiber laser beam combining and power scaling progress, Air Force Research Laboratory Laser Division,” Proc. SPIE 8237, 823718 (2012).
[Crossref]

L. Liu and M. A. Vorontsov, “Phase-locking of tiled fiber array using SPGD feedback controller,” Proc. SPIE 5895, 58950P (2005).
[Crossref]

Other (2)

A. Flores, T. M. Shay, C. A. Lu, C. Robin, B. Pulford, A. D. Sanchez, D. W. Hult, and K. B. Rowland, “Coherent beam combining of fiber amplifiers in a kW regime,” in CLEO, OSA Technical Digest (Optical Society of America, 2011), paper CFE3.

B. N. Pulford, “LOCSET phase locking: operation, diagnostics, and applications,” Ph.D. dissertation (University of New Mexico, 2011).

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Figures (13)

Fig. 1.
Fig. 1.

Phase modulation diagram of dual-level phase dithering method.

Fig. 2.
Fig. 2.

Distribution of near-field intensity: (a) beam-let A only and (b) both beam-lets A and B.

Fig. 3.
Fig. 3.

Distribution of far-field intensity: (a) beam A only, (b) two beams of θ=0°, δ=0, and (c) two beams of θ=0°, δ=π.

Fig. 4.
Fig. 4.

Schematic of system architecture for coherent combining of two slab laser beams.

Fig. 5.
Fig. 5.

Average output power as pump power of two slab laser beams.

Fig. 6.
Fig. 6.

Coherent combining of two slab laser beams and prism combination system.

Fig. 7.
Fig. 7.

Near-field (top) and far-field (bottom) intensity profiles. (a) Beam-let A only and (b) beam-let B only.

Fig. 8.
Fig. 8.

Near-field intensity profile of beam-lets A and B.

Fig. 9.
Fig. 9.

Long-exposure interference patterns in (a) open and (b) closed loops. (c) Cross section of the interference fringe image.

Fig. 10.
Fig. 10.

Energy in the pinhole in open loop and closed loop.

Fig. 11.
Fig. 11.

Frequency spectrum in open loop and closed loop.

Fig. 12.
Fig. 12.

Square distributed laser beam array.

Fig. 13.
Fig. 13.

Simulation of electronic beam steering of an N=9 element laser array by steering angles of 5, 10, and 15 μrad in both horizontal and vertical steering using the square wave dithering algorithm. (a) Convergence curve for steering angle of 5 μrad. (b) Convergence curve for steering angle of 10 μrad. (c) Convergence curve for steering angle of 15 μrad. (d) Far-field intensity pattern of 5 μrad steering. (e) Far-field intensity pattern of 10 μrad steering. (f) Far-field intensity pattern of 15 μrad steering.

Equations (11)

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iPD(ϕ1,,ϕN)=12RPDAε0μ0i=1Nj=1NE0iE0jcos(ϕiϕj).
Pi=iPD(ϕ1,,ϕi+ψi+,,ϕN),Ni=iPD(ϕ1,,ϕi+ψi,,ϕN),Zi=iPD(ϕ1,,ϕi+ψi,,ϕN),
Si=RPDAε0μ0j=1NE0iE0jsin(ϕjϕi).
Si=cosψi(PiZi)+cosψi+(ZiNi)+cosψi(NiPi)sin(ψiψi)+sin(ψi+ψi)+sin(ψiψi+).
Si=RPDA(ε0/μ0)1/2j=1NE0iE0jsin(ϕjϕi)=PiNi2sinψ.
E1(x0,y0,0)=rect(x0b/2Δd/2b)rect(y0a)exp(iφ1),E2(x0,y0,0)=rect(x0+b/2+Δd/2b)rect(y0a)exp[i(φ2+δ)],
φ(x0,y0)=random(1,1)*exp{[(x0σx)2+(y0σy)2]},
E1,2(x,y)=A1,2exp(iα1,2)=iλfexp[ik(f+x2+y22f)]·F{E1,2(x0,y0)exp[ik2f(x02+y02)]},
I(x,y)=[E1(x,y)+E2(x,y)]·[E1(x,y)+E2(x,y)]*=A12+A22+2A1A2[ei(α1α2)+ei(α1α2)]=A12+A22+2A1A2cosδcosθ.
ai=fλDi,i=x,y,
η=Preal/Pideal=Preal/(NPincoherent).

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