Abstract

Binary phase diffraction gratings are shown to couple light coherently from a laser array into a single on-axis beam. The diffraction grating, designed to split a single beam into a specific number of equal intensity diffraction orders, is placed inside the cavity formed by the laser array and a common output mirror. The grating superimposes the light beams from the lasers in the array and produces a far-field pattern with the same divergence as that of a single laser. Six GaAlAs lasers from an antireflection-coated linear array were combined with a coupling efficiency of 68.4%. The far field of the combined GaAlAs lasers consisted of a single on-axis Gaussian beam.

© 1987 Optical Society of America

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  1. D. R. Scifres, W. Streifer, R. D. Burnham, “Experimental and Analytic Studies of Coupled Multiple Stripe Diode Lasers,” IEEE J. Quantum Electron. QE-15, 917 (1979).
    [CrossRef]
  2. G. L. Hafnagel, P. S. Cross, D. R. Scifres, D. F. Welch, C. R. Lennon, D. P. Worland, R. D. Burnham, “High-Power Quasi-cw Monolithic Laser Diode Linear Arrays,” Appl. Phys. Lett. 49, 1418 (1986).
    [CrossRef]
  3. J. N. Walpole, Z. L. Liau, “Monolithic Two-Dimensional Arrays of High-Power GalnAsP/InP Surface-Emitting Diode Lasers,” Appl. Phys. Lett. 48, 1636 (1986).
    [CrossRef]
  4. L. A. Newman, R. A. Hart, J. T. Kennedy, A. J. Canter, A. J. DeMaria, W. B. Bridges, “High Power Coupled CO2 Waveguide Laser Array,” Appl. Phys. Lett. 48, 1701 (1986).
    [CrossRef]
  5. E. M. Philipp-Rutz, “Spatially Coherent Radiation from an Array of GaAs Lasers,” Appl. Phys. Lett. 26, 475 (1975).
    [CrossRef]
  6. R. H. Rediker, R. P. Schloss, L. J. VanRuyven, “Operation of Individual Diode Lasers as a Coherent Ensemble Controlled by a Spatial Filter within an External Cavity,” Appl. Phys. Lett. 46, 133 (1985).
    [CrossRef]
  7. J. R. Leger, G. J. Swanson, W. B. Veldkamp, “Coherent Beam Addition of GaAlAs Lasers by Binary Phase Gratings,” Appl. Phys. Lett. 48, 888 (1986).
    [CrossRef]
  8. R. C. Dixon, Spread Spectrum Systems (Wiley, New York, 1976).
  9. R. H. Barker, Communication Theory, W. Jackson, Ed. (Butterworths, London, 1953), pp. 273–287.
  10. H. Dammann, K. Goertler, “High-Efficiency In-Line Multiple Imaging by Means of Multiple Phase Holograms,” Opt. Commun. 3, 312 (1971).
    [CrossRef]
  11. U. Killat, G. Rabe, W. Rave, “Binary Phase Gratings for Star Couplers with High Splitting Ratio,” Fiber Integr. Opt. 4, 159 (1982).
    [CrossRef]
  12. W. H. Lee, “High Efficiency Multiple Beam Gratings,” Appl. Opt. 18, 2152 (1979).
    [CrossRef] [PubMed]
  13. W. B. Veldkamp, J. R. Leger, G. J. Swanson, “Coherent Summation of Laser Beams Using Binary Phase Gratings,” Opt. Lett. 11, 303 (1986).
    [CrossRef] [PubMed]

1986

G. L. Hafnagel, P. S. Cross, D. R. Scifres, D. F. Welch, C. R. Lennon, D. P. Worland, R. D. Burnham, “High-Power Quasi-cw Monolithic Laser Diode Linear Arrays,” Appl. Phys. Lett. 49, 1418 (1986).
[CrossRef]

J. N. Walpole, Z. L. Liau, “Monolithic Two-Dimensional Arrays of High-Power GalnAsP/InP Surface-Emitting Diode Lasers,” Appl. Phys. Lett. 48, 1636 (1986).
[CrossRef]

L. A. Newman, R. A. Hart, J. T. Kennedy, A. J. Canter, A. J. DeMaria, W. B. Bridges, “High Power Coupled CO2 Waveguide Laser Array,” Appl. Phys. Lett. 48, 1701 (1986).
[CrossRef]

J. R. Leger, G. J. Swanson, W. B. Veldkamp, “Coherent Beam Addition of GaAlAs Lasers by Binary Phase Gratings,” Appl. Phys. Lett. 48, 888 (1986).
[CrossRef]

W. B. Veldkamp, J. R. Leger, G. J. Swanson, “Coherent Summation of Laser Beams Using Binary Phase Gratings,” Opt. Lett. 11, 303 (1986).
[CrossRef] [PubMed]

1985

R. H. Rediker, R. P. Schloss, L. J. VanRuyven, “Operation of Individual Diode Lasers as a Coherent Ensemble Controlled by a Spatial Filter within an External Cavity,” Appl. Phys. Lett. 46, 133 (1985).
[CrossRef]

1982

U. Killat, G. Rabe, W. Rave, “Binary Phase Gratings for Star Couplers with High Splitting Ratio,” Fiber Integr. Opt. 4, 159 (1982).
[CrossRef]

1979

W. H. Lee, “High Efficiency Multiple Beam Gratings,” Appl. Opt. 18, 2152 (1979).
[CrossRef] [PubMed]

D. R. Scifres, W. Streifer, R. D. Burnham, “Experimental and Analytic Studies of Coupled Multiple Stripe Diode Lasers,” IEEE J. Quantum Electron. QE-15, 917 (1979).
[CrossRef]

1975

E. M. Philipp-Rutz, “Spatially Coherent Radiation from an Array of GaAs Lasers,” Appl. Phys. Lett. 26, 475 (1975).
[CrossRef]

1971

H. Dammann, K. Goertler, “High-Efficiency In-Line Multiple Imaging by Means of Multiple Phase Holograms,” Opt. Commun. 3, 312 (1971).
[CrossRef]

Barker, R. H.

R. H. Barker, Communication Theory, W. Jackson, Ed. (Butterworths, London, 1953), pp. 273–287.

Bridges, W. B.

L. A. Newman, R. A. Hart, J. T. Kennedy, A. J. Canter, A. J. DeMaria, W. B. Bridges, “High Power Coupled CO2 Waveguide Laser Array,” Appl. Phys. Lett. 48, 1701 (1986).
[CrossRef]

Burnham, R. D.

G. L. Hafnagel, P. S. Cross, D. R. Scifres, D. F. Welch, C. R. Lennon, D. P. Worland, R. D. Burnham, “High-Power Quasi-cw Monolithic Laser Diode Linear Arrays,” Appl. Phys. Lett. 49, 1418 (1986).
[CrossRef]

D. R. Scifres, W. Streifer, R. D. Burnham, “Experimental and Analytic Studies of Coupled Multiple Stripe Diode Lasers,” IEEE J. Quantum Electron. QE-15, 917 (1979).
[CrossRef]

Canter, A. J.

L. A. Newman, R. A. Hart, J. T. Kennedy, A. J. Canter, A. J. DeMaria, W. B. Bridges, “High Power Coupled CO2 Waveguide Laser Array,” Appl. Phys. Lett. 48, 1701 (1986).
[CrossRef]

Cross, P. S.

G. L. Hafnagel, P. S. Cross, D. R. Scifres, D. F. Welch, C. R. Lennon, D. P. Worland, R. D. Burnham, “High-Power Quasi-cw Monolithic Laser Diode Linear Arrays,” Appl. Phys. Lett. 49, 1418 (1986).
[CrossRef]

Dammann, H.

H. Dammann, K. Goertler, “High-Efficiency In-Line Multiple Imaging by Means of Multiple Phase Holograms,” Opt. Commun. 3, 312 (1971).
[CrossRef]

DeMaria, A. J.

L. A. Newman, R. A. Hart, J. T. Kennedy, A. J. Canter, A. J. DeMaria, W. B. Bridges, “High Power Coupled CO2 Waveguide Laser Array,” Appl. Phys. Lett. 48, 1701 (1986).
[CrossRef]

Dixon, R. C.

R. C. Dixon, Spread Spectrum Systems (Wiley, New York, 1976).

Goertler, K.

H. Dammann, K. Goertler, “High-Efficiency In-Line Multiple Imaging by Means of Multiple Phase Holograms,” Opt. Commun. 3, 312 (1971).
[CrossRef]

Hafnagel, G. L.

G. L. Hafnagel, P. S. Cross, D. R. Scifres, D. F. Welch, C. R. Lennon, D. P. Worland, R. D. Burnham, “High-Power Quasi-cw Monolithic Laser Diode Linear Arrays,” Appl. Phys. Lett. 49, 1418 (1986).
[CrossRef]

Hart, R. A.

L. A. Newman, R. A. Hart, J. T. Kennedy, A. J. Canter, A. J. DeMaria, W. B. Bridges, “High Power Coupled CO2 Waveguide Laser Array,” Appl. Phys. Lett. 48, 1701 (1986).
[CrossRef]

Kennedy, J. T.

L. A. Newman, R. A. Hart, J. T. Kennedy, A. J. Canter, A. J. DeMaria, W. B. Bridges, “High Power Coupled CO2 Waveguide Laser Array,” Appl. Phys. Lett. 48, 1701 (1986).
[CrossRef]

Killat, U.

U. Killat, G. Rabe, W. Rave, “Binary Phase Gratings for Star Couplers with High Splitting Ratio,” Fiber Integr. Opt. 4, 159 (1982).
[CrossRef]

Lee, W. H.

Leger, J. R.

J. R. Leger, G. J. Swanson, W. B. Veldkamp, “Coherent Beam Addition of GaAlAs Lasers by Binary Phase Gratings,” Appl. Phys. Lett. 48, 888 (1986).
[CrossRef]

W. B. Veldkamp, J. R. Leger, G. J. Swanson, “Coherent Summation of Laser Beams Using Binary Phase Gratings,” Opt. Lett. 11, 303 (1986).
[CrossRef] [PubMed]

Lennon, C. R.

G. L. Hafnagel, P. S. Cross, D. R. Scifres, D. F. Welch, C. R. Lennon, D. P. Worland, R. D. Burnham, “High-Power Quasi-cw Monolithic Laser Diode Linear Arrays,” Appl. Phys. Lett. 49, 1418 (1986).
[CrossRef]

Liau, Z. L.

J. N. Walpole, Z. L. Liau, “Monolithic Two-Dimensional Arrays of High-Power GalnAsP/InP Surface-Emitting Diode Lasers,” Appl. Phys. Lett. 48, 1636 (1986).
[CrossRef]

Newman, L. A.

L. A. Newman, R. A. Hart, J. T. Kennedy, A. J. Canter, A. J. DeMaria, W. B. Bridges, “High Power Coupled CO2 Waveguide Laser Array,” Appl. Phys. Lett. 48, 1701 (1986).
[CrossRef]

Philipp-Rutz, E. M.

E. M. Philipp-Rutz, “Spatially Coherent Radiation from an Array of GaAs Lasers,” Appl. Phys. Lett. 26, 475 (1975).
[CrossRef]

Rabe, G.

U. Killat, G. Rabe, W. Rave, “Binary Phase Gratings for Star Couplers with High Splitting Ratio,” Fiber Integr. Opt. 4, 159 (1982).
[CrossRef]

Rave, W.

U. Killat, G. Rabe, W. Rave, “Binary Phase Gratings for Star Couplers with High Splitting Ratio,” Fiber Integr. Opt. 4, 159 (1982).
[CrossRef]

Rediker, R. H.

R. H. Rediker, R. P. Schloss, L. J. VanRuyven, “Operation of Individual Diode Lasers as a Coherent Ensemble Controlled by a Spatial Filter within an External Cavity,” Appl. Phys. Lett. 46, 133 (1985).
[CrossRef]

Schloss, R. P.

R. H. Rediker, R. P. Schloss, L. J. VanRuyven, “Operation of Individual Diode Lasers as a Coherent Ensemble Controlled by a Spatial Filter within an External Cavity,” Appl. Phys. Lett. 46, 133 (1985).
[CrossRef]

Scifres, D. R.

G. L. Hafnagel, P. S. Cross, D. R. Scifres, D. F. Welch, C. R. Lennon, D. P. Worland, R. D. Burnham, “High-Power Quasi-cw Monolithic Laser Diode Linear Arrays,” Appl. Phys. Lett. 49, 1418 (1986).
[CrossRef]

D. R. Scifres, W. Streifer, R. D. Burnham, “Experimental and Analytic Studies of Coupled Multiple Stripe Diode Lasers,” IEEE J. Quantum Electron. QE-15, 917 (1979).
[CrossRef]

Streifer, W.

D. R. Scifres, W. Streifer, R. D. Burnham, “Experimental and Analytic Studies of Coupled Multiple Stripe Diode Lasers,” IEEE J. Quantum Electron. QE-15, 917 (1979).
[CrossRef]

Swanson, G. J.

W. B. Veldkamp, J. R. Leger, G. J. Swanson, “Coherent Summation of Laser Beams Using Binary Phase Gratings,” Opt. Lett. 11, 303 (1986).
[CrossRef] [PubMed]

J. R. Leger, G. J. Swanson, W. B. Veldkamp, “Coherent Beam Addition of GaAlAs Lasers by Binary Phase Gratings,” Appl. Phys. Lett. 48, 888 (1986).
[CrossRef]

VanRuyven, L. J.

R. H. Rediker, R. P. Schloss, L. J. VanRuyven, “Operation of Individual Diode Lasers as a Coherent Ensemble Controlled by a Spatial Filter within an External Cavity,” Appl. Phys. Lett. 46, 133 (1985).
[CrossRef]

Veldkamp, W. B.

J. R. Leger, G. J. Swanson, W. B. Veldkamp, “Coherent Beam Addition of GaAlAs Lasers by Binary Phase Gratings,” Appl. Phys. Lett. 48, 888 (1986).
[CrossRef]

W. B. Veldkamp, J. R. Leger, G. J. Swanson, “Coherent Summation of Laser Beams Using Binary Phase Gratings,” Opt. Lett. 11, 303 (1986).
[CrossRef] [PubMed]

Walpole, J. N.

J. N. Walpole, Z. L. Liau, “Monolithic Two-Dimensional Arrays of High-Power GalnAsP/InP Surface-Emitting Diode Lasers,” Appl. Phys. Lett. 48, 1636 (1986).
[CrossRef]

Welch, D. F.

G. L. Hafnagel, P. S. Cross, D. R. Scifres, D. F. Welch, C. R. Lennon, D. P. Worland, R. D. Burnham, “High-Power Quasi-cw Monolithic Laser Diode Linear Arrays,” Appl. Phys. Lett. 49, 1418 (1986).
[CrossRef]

Worland, D. P.

G. L. Hafnagel, P. S. Cross, D. R. Scifres, D. F. Welch, C. R. Lennon, D. P. Worland, R. D. Burnham, “High-Power Quasi-cw Monolithic Laser Diode Linear Arrays,” Appl. Phys. Lett. 49, 1418 (1986).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

G. L. Hafnagel, P. S. Cross, D. R. Scifres, D. F. Welch, C. R. Lennon, D. P. Worland, R. D. Burnham, “High-Power Quasi-cw Monolithic Laser Diode Linear Arrays,” Appl. Phys. Lett. 49, 1418 (1986).
[CrossRef]

J. N. Walpole, Z. L. Liau, “Monolithic Two-Dimensional Arrays of High-Power GalnAsP/InP Surface-Emitting Diode Lasers,” Appl. Phys. Lett. 48, 1636 (1986).
[CrossRef]

L. A. Newman, R. A. Hart, J. T. Kennedy, A. J. Canter, A. J. DeMaria, W. B. Bridges, “High Power Coupled CO2 Waveguide Laser Array,” Appl. Phys. Lett. 48, 1701 (1986).
[CrossRef]

E. M. Philipp-Rutz, “Spatially Coherent Radiation from an Array of GaAs Lasers,” Appl. Phys. Lett. 26, 475 (1975).
[CrossRef]

R. H. Rediker, R. P. Schloss, L. J. VanRuyven, “Operation of Individual Diode Lasers as a Coherent Ensemble Controlled by a Spatial Filter within an External Cavity,” Appl. Phys. Lett. 46, 133 (1985).
[CrossRef]

J. R. Leger, G. J. Swanson, W. B. Veldkamp, “Coherent Beam Addition of GaAlAs Lasers by Binary Phase Gratings,” Appl. Phys. Lett. 48, 888 (1986).
[CrossRef]

Fiber Integr. Opt.

U. Killat, G. Rabe, W. Rave, “Binary Phase Gratings for Star Couplers with High Splitting Ratio,” Fiber Integr. Opt. 4, 159 (1982).
[CrossRef]

IEEE J. Quantum Electron.

D. R. Scifres, W. Streifer, R. D. Burnham, “Experimental and Analytic Studies of Coupled Multiple Stripe Diode Lasers,” IEEE J. Quantum Electron. QE-15, 917 (1979).
[CrossRef]

Opt. Commun.

H. Dammann, K. Goertler, “High-Efficiency In-Line Multiple Imaging by Means of Multiple Phase Holograms,” Opt. Commun. 3, 312 (1971).
[CrossRef]

Opt. Lett.

Other

R. C. Dixon, Spread Spectrum Systems (Wiley, New York, 1976).

R. H. Barker, Communication Theory, W. Jackson, Ed. (Butterworths, London, 1953), pp. 273–287.

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Figures (11)

Fig. 1
Fig. 1

Binary phase grating is placed inside a common cavity resonator. The grating both combines the light from the array and splits the feedback light from the common output mirror.

Fig. 2
Fig. 2

Complex angular plane wave spectra resulting from coupling laser arrays with two different phase states. (a) All the lasers are in phase; the resulting coupling efficiency is only 45%. (b) A Barker code phase state is used with a resulting coupling efficiency of 95%.

Fig. 3
Fig. 3

(a) Profile of binary diffraction grating designed to combine six lasers. (b) Theoretical diffraction pattern of the binary grating in (a), where 81% of the light is in the six central diffraction orders.

Fig. 4
Fig. 4

Error in the grating diffraction pattern as a function of transition points. The binary profile consists of four symmetrically spaced transition points. The two peaks correspond to two shifted versions of the same grating profile.

Fig. 5
Fig. 5

SEM photograph of a binary grating etched in quartz. Space between lines is 1.0 μm (magnification = 15,000×).

Fig. 6
Fig. 6

Experimental diffraction pattern of the binary grating in Fig. 3(a). The pattern was measured by illuminating the grating with a single collimated GaAlAs laser and scanning the far field. Compare with Fig. 3(b).

Fig. 7
Fig. 7

Experimental setup for laser beam addition from a GaAlAs array. The beam splitter before the grating is used to measure the phase state of the array. The beam splitter after the grating is used to calculate the grating coupling efficiency. The beam splitter in the output measures the far-field pattern of the combined beams.

Fig. 8
Fig. 8

Results of coherence measurement performed on lasers spaced 60 μm apart. Visibility and stability of interference pattern on the right indicate mutual coherence between sources.

Fig. 9
Fig. 9

Phase state measurement of the first four lasers from a six-laser addition experiment. An on-axis null indicates that the first and second lasers are out of phase. On-axis peaks indicate that the second, third, and fourth lasers are all in phase.

Fig. 10
Fig. 10

Angular plane wave spectrum of six laser beams after passing through the binary diffraction grating; 68.4% of the total power is contained in the on-axis beam.

Fig. 11
Fig. 11

Far-field pattern of the output resulting from the summation of six laser beams (solid line) compared to a single laser beam (dotted line). The two curves have been scaled in intensity to compare their shapes.

Tables (5)

Tables Icon

Table I Phase States for Addition of Eight Lasers (N = 8) Using A Real Symmetric Grating

Tables Icon

Table II Optimum Phase State Using a Real Symmetric Grating

Tables Icon

Table III Binary Phase Grating Parameters

Tables Icon

Table IV Phase State Measurements (N = 6)

Tables Icon

Table V Coupling Efficiency Measurements (N = 3–6)

Equations (18)

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t ( x , y ) = a ( x , y ) exp [ j ϕ ( x , y ) ] ,
t ( x , y ) = m = n = A ( m , n ) [ exp { j Φ ( m , n ) ] exp [ j 2 π ( m α x + n β y ) ] ,
ζ = m = M M n = N N A 2 ( m , n ) .
E ( x , y ) = b ( x , y ) exp [ j θ ( x , y ) ] = m = M M n = N N B ( m , n ) exp [ j θ ( m , n ) ] × exp [ j 2 π ( m α x + n β y ) ] ,
P 0 = 1 s | s E ( x , y ) t ( x , y ) dxdy | 2 = 1 s | s m = n = m = M M n = N N A ( m , n ) B ( m , n ) × exp [ j Φ ( m , n ) ] × exp [ j θ ( m , n ) ] exp { j 2 π [ ( m + m ) α x + ( n + n ) β y ] } dxdy | 2 ,
P 0 = | m = M M n = N N A ( m , n ) B ( m , n ) × exp [ j Φ ( m , n ) ] exp [ j θ ( m , n ) ] | 2 s .
P t = s | E ( x , y ) | 2 dxdy = s | m = M M n = N N B ( m , n ) exp [ j θ ( m , n ) ] × exp [ j 2 π ( m α x + n β y ) ] | 2 dxdy = m = M M n = N N B 2 ( m , n ) s .
η = P 0 P t = 1 s | s E ( x , y ) t ( x , y ) dxdy | 2 s | E ( x , y ) | 2 dxdy = | m = M M n = N N A ( m , n ) B ( m , n ) exp [ j Φ ( m , n ) ] exp [ j θ ( m , n ) ] | 2 m = M M n = N N B 2 ( m , n ) .
B ( m , n ) exp [ j θ ( m , n ) ] = A ( m , n ) exp [ j Φ ( m , n ) ] ,
η = | m = M M n = N N A 2 ( m , n ) | 2 m = M M n = N N A 2 ( m , n ) = n = M M n = N N A 2 ( m , n ) = ζ ,
η = 1 s | s a ( x , y ) b ( x , y ) exp { j [ ϕ ( x , y ) + θ ( x , y ) ] } dxdy | 2 s | b ( x , y ) exp [ j θ ( x , y ) ] | 2 dxdy .
η = 1 s | s b ( x , y ) dxdy | 2 s | b ( x , y ) | 2 dxdy .
b ( x , y ) = | m = M M n = N N B ( m , n ) exp [ j θ ( m , n ) ] × exp [ j 2 π ( m α x + n β y ) ] | .
b 2 ( x , y ) = m = M M m = M M n = N N n = N N B ( m , n ) × exp [ j θ ( m , n ) ] B ( m , n ) exp [ j θ ( m , n ) ] × exp { j 2 π [ ( m m ) α x + ( n n ) β y ] } C ,
[ b 2 ( x , y ) ] = m = M M m = M M n = N N n = N N B ( m , n ) exp [ j θ ( m , n ) ] × B ( m , n ) exp [ j θ ( m , n ) ] δ [ u ( m m ) α , υ ( n n ) β ] C δ ( u , υ ) .
[ b 2 ( x , y ) ] = m = M M n = N N B 2 ( m , n ) δ ( u , υ ) + p = 1 2 M m = M M P q = 1 2 N n = N N q B ( m , n ) × exp [ j θ ( m , n ) ] B ( m + p , n + q ) × exp [ j θ ( m + p , n + q ) ] δ ( u + p α , υ + q β ) + p = 1 2 M m = M M P q = 1 2 N n = N N q B ( m , n ) × exp [ j θ ( m , n ) ] B ( m + p , n + q ) × exp [ j θ ( m + p , n + q ) ] δ ( u p α , υ + q β ) C δ ( u , υ ) .
t ( x , y ) = exp [ j d 2 squ ( x ) ] ,
d = 2 arccot [ | P | 2 squ ( x ) 2 ] ,

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