Abstract

A diffractive optical element is used to relay complex laser beam profiles by phase conjugation. It has the advantage over a conventional afocal system of avoiding light concentration at the intermediate focal point. Theoretical and experimental results show that the image quality is a function of alignment errors and mode-size changes. When the optical system is within the calculated tolerances, the diffractive optic reproduces images of high quality.

© 1997 Optical Society of America

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References

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  1. D. M. Pepper, D. Fekete, A. Yariv, “Observation of amplified phase-conjugate reflection and optical parametric oscillation by degenerate four-wave mixing in a transparent medium,” Appl. Phys. Lett. 33, 41–44 (1978).
    [CrossRef]
  2. J. R. Leger, D. Chen, Z. Wang, “Diffractive optical element for mode shaping of a Nd:YAG laser,” Opt. Lett. 19, 108–110 (1994).
    [CrossRef] [PubMed]

1994 (1)

1978 (1)

D. M. Pepper, D. Fekete, A. Yariv, “Observation of amplified phase-conjugate reflection and optical parametric oscillation by degenerate four-wave mixing in a transparent medium,” Appl. Phys. Lett. 33, 41–44 (1978).
[CrossRef]

Chen, D.

Fekete, D.

D. M. Pepper, D. Fekete, A. Yariv, “Observation of amplified phase-conjugate reflection and optical parametric oscillation by degenerate four-wave mixing in a transparent medium,” Appl. Phys. Lett. 33, 41–44 (1978).
[CrossRef]

Leger, J. R.

Pepper, D. M.

D. M. Pepper, D. Fekete, A. Yariv, “Observation of amplified phase-conjugate reflection and optical parametric oscillation by degenerate four-wave mixing in a transparent medium,” Appl. Phys. Lett. 33, 41–44 (1978).
[CrossRef]

Wang, Z.

Yariv, A.

D. M. Pepper, D. Fekete, A. Yariv, “Observation of amplified phase-conjugate reflection and optical parametric oscillation by degenerate four-wave mixing in a transparent medium,” Appl. Phys. Lett. 33, 41–44 (1978).
[CrossRef]

Appl. Phys. Lett. (1)

D. M. Pepper, D. Fekete, A. Yariv, “Observation of amplified phase-conjugate reflection and optical parametric oscillation by degenerate four-wave mixing in a transparent medium,” Appl. Phys. Lett. 33, 41–44 (1978).
[CrossRef]

Opt. Lett. (1)

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Figures (10)

Fig. 1
Fig. 1

Propagation of a flattop square laser beam along the optical axis of (a) an afocal imaging system, and (b) a phase-conjugate system.

Fig. 2
Fig. 2

On-axis relative intensity of a flattop square laser beam along the optical axis of an afocal imaging system.

Fig. 3
Fig. 3

Experimental measurements of intensity patterns before and after the diffractive phase plate.

Fig. 4
Fig. 4

Resulting image intensity of a shifted object profile (shift is 10% of width): (a) computer simulation, and (b) experiment.

Fig. 5
Fig. 5

One-dimensional image profile for various amounts of object shift in a system with a Fresnel number of 1/π.

Fig. 6
Fig. 6

(a) Normalized power within the desired aperture; (b) peak relative intensity versus percentage of shift of the object beam profile.

Fig. 7
Fig. 7

Resulting image intensities from different-sized object modes: (a) 10% smaller (simulation), (b) 10% larger (simulation), (c) 10% smaller (experiment), and (d) 10% larger (experiment).

Fig. 8
Fig. 8

One-dimensional image profile for different-sized modes in a system with a Fresnel number of 1.

Fig. 9
Fig. 9

(a) Normalized power in the aperture and, (b) peak relative intensity versus percentage of size of the object mode.

Fig. 10
Fig. 10

(a) Normalized power in the aperture versus the image distance (normalized to the designed image distance, N = 1/π); (b) location of the best image (normalized to the designed image distance) versus the percentage of size of the object beam profile (N = 1/π).

Equations (7)

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I10, 0, z=4 sin2πr122λz.
I2r2, z=2f=πr12λf22J12πr1r2/λz2πr1r2/λz2.
I1x1, y1, z=14Cξ2-Cξ12+Sξ2-Sξ12×Cη2-Cη12+Sη2-Sη12,
ξ1=-2λz1/2d2+x1,  ξ2=2λz1/2d2-x1,  η1=-2λz1/2d2+y1,  η2=2λz1/2d2-y1,
Cα=0α cosπt2/2dt,  Sα=0α sinπt2/2dt.
I10, 0, z=4C2ξ1+S2ξ12.
I2x2, y2, z=2f=d4λ2f2 sinc2dx2λfsinc2dy2λf.

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