Abstract

A configuration of N coated mirrors or mirror pairs is described that has the potential to coherently combine 2N single-frequency phase-locked diffraction-limited polarized optical beams to form a single diffraction-limited beam. The application to beam combination of fiber amplifiers is discussed.

© 2002 Optical Society of America

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References

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  1. L. Bartelt-Berger, U. Brauch, A. Giesen, H. Huegel, H. Opower, “Power-scalable system of phase-locked single-mode diode lasers,” Appl. Opt. 38, 5752–5760 (1999).
    [CrossRef]
  2. A. E. Siegman, “New developments in laser resonators,” in Optical Resonators, D. A. Holmes, ed., Proc. SPIE1224, 2–14 (1990).
  3. J. R. Leger, M. L. Scott, W. B. Veldkamp, “Coherent addition of AlGaAs lasers using microlenses and diffractive coupling,” Appl. Phys. Lett. 52, 1771–1773 (1988).
    [CrossRef]
  4. G. T. Moore, “A model for diffraction-limited high-power multimode fiber amplifiers using seeded stimulated Brillouin scattering phase conjugation,” IEEE J. Quantum Electron. 37, 781–789 (2001).
    [CrossRef]
  5. H. J. Eichler, J. Kunde, B. Liu, “Quartz fibre phase conjugators with high fidelity and reflectivity,” Opt. Commun. 139, 327–334 (1997).
    [CrossRef]
  6. R. G. Harrison, V. I. Kovalev, W. Lu, D. Yu, “SBS self-phase conjugation of CW Nd:YAG laser radiation in an optical fibre,” Opt. Commun. 163, 208–211 (1999).
    [CrossRef]
  7. V. I. Kovalev, R. G. Harrison, “Diffraction limited output from a CW Nd:YAG master oscillator/power amplifier with fibre phase conjugate SBS mirror,” Opt. Commun. 166, 89–93 (1999).
    [CrossRef]
  8. C. V. Cryan, “Two-dimensional multimode fibre array for optical interconnects,” Electron. Lett. 34, 586–587 (1998).
    [CrossRef]
  9. G. T. Moore, “Crystal stack for coherent optical beam combination,” U.S. patent6,310,715 (30October2001).
  10. W. Stoner, Alpine Research Optics Corporation, 3180 Sterling Circle, Suite 101, Boulder, Colo. 80301 (personal communication, 2001).
  11. H. Kogelnik, T. Li, “Laser beams and resonators,” Appl. Opt. 5, 1550–1567 (1966).
    [CrossRef] [PubMed]
  12. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vettering, Numerical Recipes in FORTRAN, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).
  13. T. B. Simpson, A. Gavrielides, P. Peterson, “Coherent intracavity coupling of fiber lasers,” in IEEE Lasers and Electro-Optics Society Annual Meeting (Institute of Electrical and Electronics Engineers, New York, 2001), pp. 62–63.
  14. M. Auerbach, D. Wandt, C. Fallnich, H. Welling, S. Unger, “High-power tunable narrow line width ytterbium-doped double-clad fiber laser,” Opt. Commun. 195, 437–441 (2001).
    [CrossRef]

2001

G. T. Moore, “A model for diffraction-limited high-power multimode fiber amplifiers using seeded stimulated Brillouin scattering phase conjugation,” IEEE J. Quantum Electron. 37, 781–789 (2001).
[CrossRef]

M. Auerbach, D. Wandt, C. Fallnich, H. Welling, S. Unger, “High-power tunable narrow line width ytterbium-doped double-clad fiber laser,” Opt. Commun. 195, 437–441 (2001).
[CrossRef]

1999

L. Bartelt-Berger, U. Brauch, A. Giesen, H. Huegel, H. Opower, “Power-scalable system of phase-locked single-mode diode lasers,” Appl. Opt. 38, 5752–5760 (1999).
[CrossRef]

R. G. Harrison, V. I. Kovalev, W. Lu, D. Yu, “SBS self-phase conjugation of CW Nd:YAG laser radiation in an optical fibre,” Opt. Commun. 163, 208–211 (1999).
[CrossRef]

V. I. Kovalev, R. G. Harrison, “Diffraction limited output from a CW Nd:YAG master oscillator/power amplifier with fibre phase conjugate SBS mirror,” Opt. Commun. 166, 89–93 (1999).
[CrossRef]

1998

C. V. Cryan, “Two-dimensional multimode fibre array for optical interconnects,” Electron. Lett. 34, 586–587 (1998).
[CrossRef]

1997

H. J. Eichler, J. Kunde, B. Liu, “Quartz fibre phase conjugators with high fidelity and reflectivity,” Opt. Commun. 139, 327–334 (1997).
[CrossRef]

1988

J. R. Leger, M. L. Scott, W. B. Veldkamp, “Coherent addition of AlGaAs lasers using microlenses and diffractive coupling,” Appl. Phys. Lett. 52, 1771–1773 (1988).
[CrossRef]

1966

Auerbach, M.

M. Auerbach, D. Wandt, C. Fallnich, H. Welling, S. Unger, “High-power tunable narrow line width ytterbium-doped double-clad fiber laser,” Opt. Commun. 195, 437–441 (2001).
[CrossRef]

Bartelt-Berger, L.

Brauch, U.

Cryan, C. V.

C. V. Cryan, “Two-dimensional multimode fibre array for optical interconnects,” Electron. Lett. 34, 586–587 (1998).
[CrossRef]

Eichler, H. J.

H. J. Eichler, J. Kunde, B. Liu, “Quartz fibre phase conjugators with high fidelity and reflectivity,” Opt. Commun. 139, 327–334 (1997).
[CrossRef]

Fallnich, C.

M. Auerbach, D. Wandt, C. Fallnich, H. Welling, S. Unger, “High-power tunable narrow line width ytterbium-doped double-clad fiber laser,” Opt. Commun. 195, 437–441 (2001).
[CrossRef]

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vettering, Numerical Recipes in FORTRAN, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).

Gavrielides, A.

T. B. Simpson, A. Gavrielides, P. Peterson, “Coherent intracavity coupling of fiber lasers,” in IEEE Lasers and Electro-Optics Society Annual Meeting (Institute of Electrical and Electronics Engineers, New York, 2001), pp. 62–63.

Giesen, A.

Harrison, R. G.

R. G. Harrison, V. I. Kovalev, W. Lu, D. Yu, “SBS self-phase conjugation of CW Nd:YAG laser radiation in an optical fibre,” Opt. Commun. 163, 208–211 (1999).
[CrossRef]

V. I. Kovalev, R. G. Harrison, “Diffraction limited output from a CW Nd:YAG master oscillator/power amplifier with fibre phase conjugate SBS mirror,” Opt. Commun. 166, 89–93 (1999).
[CrossRef]

Huegel, H.

Kogelnik, H.

Kovalev, V. I.

V. I. Kovalev, R. G. Harrison, “Diffraction limited output from a CW Nd:YAG master oscillator/power amplifier with fibre phase conjugate SBS mirror,” Opt. Commun. 166, 89–93 (1999).
[CrossRef]

R. G. Harrison, V. I. Kovalev, W. Lu, D. Yu, “SBS self-phase conjugation of CW Nd:YAG laser radiation in an optical fibre,” Opt. Commun. 163, 208–211 (1999).
[CrossRef]

Kunde, J.

H. J. Eichler, J. Kunde, B. Liu, “Quartz fibre phase conjugators with high fidelity and reflectivity,” Opt. Commun. 139, 327–334 (1997).
[CrossRef]

Leger, J. R.

J. R. Leger, M. L. Scott, W. B. Veldkamp, “Coherent addition of AlGaAs lasers using microlenses and diffractive coupling,” Appl. Phys. Lett. 52, 1771–1773 (1988).
[CrossRef]

Li, T.

Liu, B.

H. J. Eichler, J. Kunde, B. Liu, “Quartz fibre phase conjugators with high fidelity and reflectivity,” Opt. Commun. 139, 327–334 (1997).
[CrossRef]

Lu, W.

R. G. Harrison, V. I. Kovalev, W. Lu, D. Yu, “SBS self-phase conjugation of CW Nd:YAG laser radiation in an optical fibre,” Opt. Commun. 163, 208–211 (1999).
[CrossRef]

Moore, G. T.

G. T. Moore, “A model for diffraction-limited high-power multimode fiber amplifiers using seeded stimulated Brillouin scattering phase conjugation,” IEEE J. Quantum Electron. 37, 781–789 (2001).
[CrossRef]

G. T. Moore, “Crystal stack for coherent optical beam combination,” U.S. patent6,310,715 (30October2001).

Opower, H.

Peterson, P.

T. B. Simpson, A. Gavrielides, P. Peterson, “Coherent intracavity coupling of fiber lasers,” in IEEE Lasers and Electro-Optics Society Annual Meeting (Institute of Electrical and Electronics Engineers, New York, 2001), pp. 62–63.

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vettering, Numerical Recipes in FORTRAN, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).

Scott, M. L.

J. R. Leger, M. L. Scott, W. B. Veldkamp, “Coherent addition of AlGaAs lasers using microlenses and diffractive coupling,” Appl. Phys. Lett. 52, 1771–1773 (1988).
[CrossRef]

Siegman, A. E.

A. E. Siegman, “New developments in laser resonators,” in Optical Resonators, D. A. Holmes, ed., Proc. SPIE1224, 2–14 (1990).

Simpson, T. B.

T. B. Simpson, A. Gavrielides, P. Peterson, “Coherent intracavity coupling of fiber lasers,” in IEEE Lasers and Electro-Optics Society Annual Meeting (Institute of Electrical and Electronics Engineers, New York, 2001), pp. 62–63.

Stoner, W.

W. Stoner, Alpine Research Optics Corporation, 3180 Sterling Circle, Suite 101, Boulder, Colo. 80301 (personal communication, 2001).

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vettering, Numerical Recipes in FORTRAN, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).

Unger, S.

M. Auerbach, D. Wandt, C. Fallnich, H. Welling, S. Unger, “High-power tunable narrow line width ytterbium-doped double-clad fiber laser,” Opt. Commun. 195, 437–441 (2001).
[CrossRef]

Veldkamp, W. B.

J. R. Leger, M. L. Scott, W. B. Veldkamp, “Coherent addition of AlGaAs lasers using microlenses and diffractive coupling,” Appl. Phys. Lett. 52, 1771–1773 (1988).
[CrossRef]

Vettering, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vettering, Numerical Recipes in FORTRAN, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).

Wandt, D.

M. Auerbach, D. Wandt, C. Fallnich, H. Welling, S. Unger, “High-power tunable narrow line width ytterbium-doped double-clad fiber laser,” Opt. Commun. 195, 437–441 (2001).
[CrossRef]

Welling, H.

M. Auerbach, D. Wandt, C. Fallnich, H. Welling, S. Unger, “High-power tunable narrow line width ytterbium-doped double-clad fiber laser,” Opt. Commun. 195, 437–441 (2001).
[CrossRef]

Yu, D.

R. G. Harrison, V. I. Kovalev, W. Lu, D. Yu, “SBS self-phase conjugation of CW Nd:YAG laser radiation in an optical fibre,” Opt. Commun. 163, 208–211 (1999).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

J. R. Leger, M. L. Scott, W. B. Veldkamp, “Coherent addition of AlGaAs lasers using microlenses and diffractive coupling,” Appl. Phys. Lett. 52, 1771–1773 (1988).
[CrossRef]

Electron. Lett.

C. V. Cryan, “Two-dimensional multimode fibre array for optical interconnects,” Electron. Lett. 34, 586–587 (1998).
[CrossRef]

IEEE J. Quantum Electron.

G. T. Moore, “A model for diffraction-limited high-power multimode fiber amplifiers using seeded stimulated Brillouin scattering phase conjugation,” IEEE J. Quantum Electron. 37, 781–789 (2001).
[CrossRef]

Opt. Commun.

H. J. Eichler, J. Kunde, B. Liu, “Quartz fibre phase conjugators with high fidelity and reflectivity,” Opt. Commun. 139, 327–334 (1997).
[CrossRef]

R. G. Harrison, V. I. Kovalev, W. Lu, D. Yu, “SBS self-phase conjugation of CW Nd:YAG laser radiation in an optical fibre,” Opt. Commun. 163, 208–211 (1999).
[CrossRef]

V. I. Kovalev, R. G. Harrison, “Diffraction limited output from a CW Nd:YAG master oscillator/power amplifier with fibre phase conjugate SBS mirror,” Opt. Commun. 166, 89–93 (1999).
[CrossRef]

M. Auerbach, D. Wandt, C. Fallnich, H. Welling, S. Unger, “High-power tunable narrow line width ytterbium-doped double-clad fiber laser,” Opt. Commun. 195, 437–441 (2001).
[CrossRef]

Other

A. E. Siegman, “New developments in laser resonators,” in Optical Resonators, D. A. Holmes, ed., Proc. SPIE1224, 2–14 (1990).

G. T. Moore, “Crystal stack for coherent optical beam combination,” U.S. patent6,310,715 (30October2001).

W. Stoner, Alpine Research Optics Corporation, 3180 Sterling Circle, Suite 101, Boulder, Colo. 80301 (personal communication, 2001).

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vettering, Numerical Recipes in FORTRAN, 2nd ed. (Cambridge U. Press, Cambridge, UK, 1992).

T. B. Simpson, A. Gavrielides, P. Peterson, “Coherent intracavity coupling of fiber lasers,” in IEEE Lasers and Electro-Optics Society Annual Meeting (Institute of Electrical and Electronics Engineers, New York, 2001), pp. 62–63.

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Figures (12)

Fig. 1
Fig. 1

Reflection from a mirror pair. AR, antireflection coated; HR, high-reflection coated.

Fig. 2
Fig. 2

Walk-off and effective diffraction distances for n = 1.45 and D = 0.

Fig. 3
Fig. 3

Cut-and-fold template for a nonplanar beam path.

Fig. 4
Fig. 4

Relation between incidence angle θ and azimuthal angle ϕ. Solid curve is for loose folding; dashed curve is for tight folding.

Fig. 5
Fig. 5

Projection onto the (x, y) plane of a ray undergoing s reflections from mirrors lying on a pentagonal cylinder. Dashed circle is a guide for the eye.

Fig. 6
Fig. 6

Beam positions transverse to the direction of propagation when 32 beams are multiplexed and five mirror pairs are used to produce a single beam. Filled circles indicate the beams that are present when optimal phase constraints are maintained. Open circles indicate additional unwanted beams generated in the absence of phase constraints. Coordinates shown for the corner beams are values of (k x , k y ). The left 16 beams (four in each row) of the incident array constitute one of the two frequency subarrays.

Fig. 7
Fig. 7

Intersections of beams with eight equally spaced planes of constant z when 32 beams are multiplexed to produce a single beam by the pentagonal configuration with N = 5 and D = 0.4a. Axial separation between the first and last z slices is 16a. Red symbols indicate beam positions with optimal phase constraints (beam positions for demultiplexing). Blue symbols indicate additional unwanted beams produced in the absence of optimal phase constraints. The unpaired s mirror 5, which polarization combines the two incident subarrays, is not present at the axial position where the multiplexed beam leaves the device. Likewise, mirror pair 1 is not present where the incident beams enter, heading for mirror 5.

Fig. 8
Fig. 8

Birefringent crystal stack for beam multiplexing or demultiplexing. Top: end view of crystal plates (here cut as octagonal cylinders) before stacking. Bottom: side view after stacking. Demultiplexing occurs during propagation from left to right at normal incidence. Walk-off is in the plane of the crystal axis, indicated by arrows.

Fig. 9
Fig. 9

Confocal imaging of two Gaussian beams, followed by reflection from a mirror pair, results in one to three Gaussian beams resolved at their waists.

Fig. 10
Fig. 10

Geometry of the subsidiary coordinates. Dashed lines indicate typical incident and reflected rays.

Fig. 11
Fig. 11

Transparency template illustrating the multiplexing of 32 beams to produce a single beam. To assemble, photocopy onto a transparency, cut along the solid lines, fold along the dashed lines with the creases protruding, align the arrows, and tape the opposite edges to form a pentagonal cylinder. The ellipses indicate the intersections of the beams with the s reflectors, as described in the text.

Fig. 12
Fig. 12

Schematic diagram of how multiplexing and demultiplexing might be used in a device to coherently combine beams from an array of multimode fiber amplifiers with SBS phase conjugation of a demultiplexed beam from a FMO and seeding the Stokes field with a BMO. PBS, polarization beam splitter; BS, beam splitter.

Equations (35)

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

tn=tn-1,
bn=An-tn cosϕ/2/sinϕ/2,
zn=zn-1+Bbn-bn-1,
tn=tn cosϕ+bn sinϕ,
bn=bn cosϕ-tn sinϕ,
xn=tn cosn-1/2ϕ-bn sinn-1/2ϕ,
yn=bn cosn-1/2ϕ+tn sinn-1/2ϕ.
B=±C-cos ϕ/1-C1/2
t0=X cosϕ/2+Y sinϕ/2,
b0=-X-t0 cosϕ/2/sinϕ/2
tf=tN,
bf=bN+zf-zN/B,
tf=tf cos ϕ+bf sin ϕ,
bf=bf cos ϕ-tf sin ϕ.
tf=tN,
bf=bN+zf-zN/B.
xf=tf cosN-1/2ϕ-bf sinN-1/2ϕ,
yf=bf cosN-1/2ϕ+tf sinN-1/2ϕ.
x=-b sinn-3/2ϕ+tn cosn-3/2ϕ,
y=b cosn-3/2ϕ+tn sinn-3/2ϕ,
z=Bb-δn,
x=-b sinn-1/2ϕ+tn cosn-1/2ϕ,
y=b cosn-1/2ϕ+tn sinn-1/2ϕ,
z=Bb-δn.
cos γ=cosϕ21-C1+C1/2.
dkx, ky, 1, n=ckx, ky, 1, n+1+ckx, ky, 2, n+1/2,
dkx, ky, 2, n=-ckx, ky, 1, n+1+ckx, ky, 2, n+1/2
ckx, ky, 1, n=dkx, ky, 1, n,
ckx, ky+jn, 2, n=dkx, ky, 2, n, ky1,
ckx, ky, 2, n=0, 1kyjn
dkx, ky, 1, n=ckx, ky, 1, n+1-ckx, ky, 2, n+1/2,
dkx, ky, 2, n=ckx, ky, 1, n+1+ckx, ky, 2, n+1/2
ckx, ky, 1, n=dkx, ky, 1, n,
ckx+jn, ky+jn, 2, n=dkx, ky, 2, n, ky1,
ckx, ky, 2, n=0, 1kxjn or 1kyjn

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