Abstract

A method for coherent addition of lasers is presented that uses binary phase-only gratings. It is shown that a grating that splits a single beam into N equal orders with high efficiency can be used in reverse to convert N laser beams into a single beam with the same efficiency. Experiments to demonstrate the conversion of seven beams to one beam are performed with a resulting conversion efficiency of 75%. An experimental apparatus is described that adds the power from both two and three He–Ne lasers (wavelength, 3.39 μm) with efficiencies as high as 83%.

© 1986 Optical Society of America

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References

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  1. H. Dammann, K. Goertler, Opt. Commun. 3, 312 (1971).
    [CrossRef]
  2. U. Killat, G. Rabe, W. Rave, Fiber Integ. Opt. 4, 159 (1982).
    [CrossRef]

1982 (1)

U. Killat, G. Rabe, W. Rave, Fiber Integ. Opt. 4, 159 (1982).
[CrossRef]

1971 (1)

H. Dammann, K. Goertler, Opt. Commun. 3, 312 (1971).
[CrossRef]

Dammann, H.

H. Dammann, K. Goertler, Opt. Commun. 3, 312 (1971).
[CrossRef]

Goertler, K.

H. Dammann, K. Goertler, Opt. Commun. 3, 312 (1971).
[CrossRef]

Killat, U.

U. Killat, G. Rabe, W. Rave, Fiber Integ. Opt. 4, 159 (1982).
[CrossRef]

Rabe, G.

U. Killat, G. Rabe, W. Rave, Fiber Integ. Opt. 4, 159 (1982).
[CrossRef]

Rave, W.

U. Killat, G. Rabe, W. Rave, Fiber Integ. Opt. 4, 159 (1982).
[CrossRef]

Fiber Integ. Opt. (1)

U. Killat, G. Rabe, W. Rave, Fiber Integ. Opt. 4, 159 (1982).
[CrossRef]

Opt. Commun. (1)

H. Dammann, K. Goertler, Opt. Commun. 3, 312 (1971).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

(a) Single period of the grating for adding seven lasers. The grating consisted of a replication of this pattern. (b) Diffraction pattern produced by grating in (a).

Fig. 2
Fig. 2

Angular plane-wave spectrum of light field as it leaves the combining grating. The coupling efficiency can be calculated by computing the ratio of power in the central order to the total power in all the orders.

Fig. 3
Fig. 3

Two configurations to achieve coherent beam addition. (a) A master oscillator is used to injection lock the slave lasers. The grating is used in reverse to split the master oscillator beam into N locking beams. (b) A common-cavity configuration is used, and the grating is placed inside the cavity.

Fig. 4
Fig. 4

(a) Impulse response of the grating designed to combine two He–Ne lasers. The orders to the left of −1 are all evanescent. The splitting efficiency was measured to be 90%. (b) The angular plane-wave spectrum of the combined He–Ne laser beams. 83% of the power is contained in the zero-order Gaussian beam.

Equations (7)

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t ( x ) = n = - a n exp ( j ϕ n ) exp ( j n α x ) ,
ζ = n = - N / 2 N / 2 a n 2 ( N + 1 ) a 0 2 .
E ( x ) = m = - N / 2 N / 2 exp ( - j ϕ m ) exp ( - j m a x ) ,
I 0 = | n = - N / 2 N / 2 a n | 2 ( N + 1 ) 2 a 0 2 ,
η = ( N + 1 ) 2 a 0 2 ( N + 1 ) = ( N + 1 ) a 0 2 .
I 0 | n = - N / 2 n 1 , 2 , , L N / 2 a n | 2 ( N + 1 - L ) 2 a 0 2 ,
η = ( N + 1 - L ) a 0 2 .

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