Abstract

Many applications of diffractive phase elements involve the calculation of a continuous phase profile, which is subsequently quantized for fabrication. The quantization process maps the continuous range of phase values to a limited number of discrete steps. We present a new scheme with unevenly spaced levels for the design of diffractive elements and apply it to the design of intracavity mode-selecting elements. We show that this modified quantization can produce significantly better results than are possible with a regular or even the bias-phase-optimized quantization scheme that we reported here earlier. In principle this process can be employed to a greater or lesser extent in any quantization process, allowing the fabrication of diffractive elements with much improved performance.

© 2001 Optical Society of America

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References

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  1. J. R. Leger, D. Chen, and Z. Wang, Opt. Lett. 19, 108 (1994).
    [CrossRef]
  2. J. R. Leger, D. Chen, and G. Mowry, Appl. Opt. 34, 2498 (1995).
    [CrossRef] [PubMed]
  3. J. R. Leger in Diffractive Optics for Industrial and Commercial Applications, J. Turunen and F. Wyrowski, eds. (Akademie Verlag, Berlin, 1997), pp. 189–215.
  4. S. Makki, Z. Wang, and J. R. Leger, Appl. Opt. 36, 4749 (1997).
    [CrossRef] [PubMed]
  5. I. M. Barton, P. Blair, A. J. Waddie, K. Ballüder, M. R. Taghizadeh, H. McInnes, and T. H. Bett, in Third International Conference on Solid State Lasers for Application to Inertial Confinement Fusion, W. H. Lowdermilk, ed., Proc. SPIE3492, 437 (1999).
    [CrossRef]
  6. K. Ballüder, I. M. Barton, P. Blair, M. R. Taghizadeh, H. McInnes, and T. H. Bett, in European Conference on Lasers and Electro-Optics (CLEO Europe), 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. 363.
  7. K. Ballüder and M. R. Taghizadeh, in Conference on Lasers and Electro-Optics (CLEO US), 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), p. 482.
  8. K. Ballüder and M. R. Taghizadeh, Appl. Opt. 38, 5768 (1999).
    [CrossRef]
  9. K. Ballüder, P. Blair, P. Rudman, A. Waddie, and M. R. Taghizadeh, “Design and fabrication of diffractive optics for material processing applications,” Opt. Laser Eng. (to be published).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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  16. A. G. Fox and T. Li, Bell Syst. Tech. J. 40, 453 (1961).
    [CrossRef]

2000 (1)

K. Ballüder, M. R. Taghizadeh, H. A. McInnes, and T. H. Bett, J. Mod. Opt. 47, 2421 (2000).
[CrossRef]

1999 (2)

K. Ballüder and M. R. Taghizadeh, Opt. Lett. 24, 1576 (1999).
[CrossRef]

K. Ballüder and M. R. Taghizadeh, Appl. Opt. 38, 5768 (1999).
[CrossRef]

1997 (1)

1995 (2)

1994 (2)

1993 (1)

1988 (1)

1961 (1)

A. G. Fox and T. Li, Bell Syst. Tech. J. 40, 453 (1961).
[CrossRef]

Ballüder, K.

K. Ballüder, M. R. Taghizadeh, H. A. McInnes, and T. H. Bett, J. Mod. Opt. 47, 2421 (2000).
[CrossRef]

K. Ballüder and M. R. Taghizadeh, Appl. Opt. 38, 5768 (1999).
[CrossRef]

K. Ballüder and M. R. Taghizadeh, Opt. Lett. 24, 1576 (1999).
[CrossRef]

K. Ballüder and M. R. Taghizadeh, in Conference on Lasers and Electro-Optics (CLEO US), 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), p. 482.

K. Ballüder, P. Blair, P. Rudman, A. Waddie, and M. R. Taghizadeh, “Design and fabrication of diffractive optics for material processing applications,” Opt. Laser Eng. (to be published).

I. M. Barton, P. Blair, A. J. Waddie, K. Ballüder, M. R. Taghizadeh, H. McInnes, and T. H. Bett, in Third International Conference on Solid State Lasers for Application to Inertial Confinement Fusion, W. H. Lowdermilk, ed., Proc. SPIE3492, 437 (1999).
[CrossRef]

K. Ballüder, I. M. Barton, P. Blair, M. R. Taghizadeh, H. McInnes, and T. H. Bett, in European Conference on Lasers and Electro-Optics (CLEO Europe), 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. 363.

Barton, I. M.

K. Ballüder, I. M. Barton, P. Blair, M. R. Taghizadeh, H. McInnes, and T. H. Bett, in European Conference on Lasers and Electro-Optics (CLEO Europe), 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. 363.

I. M. Barton, P. Blair, A. J. Waddie, K. Ballüder, M. R. Taghizadeh, H. McInnes, and T. H. Bett, in Third International Conference on Solid State Lasers for Application to Inertial Confinement Fusion, W. H. Lowdermilk, ed., Proc. SPIE3492, 437 (1999).
[CrossRef]

Bett, T. H.

K. Ballüder, M. R. Taghizadeh, H. A. McInnes, and T. H. Bett, J. Mod. Opt. 47, 2421 (2000).
[CrossRef]

K. Ballüder, I. M. Barton, P. Blair, M. R. Taghizadeh, H. McInnes, and T. H. Bett, in European Conference on Lasers and Electro-Optics (CLEO Europe), 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. 363.

I. M. Barton, P. Blair, A. J. Waddie, K. Ballüder, M. R. Taghizadeh, H. McInnes, and T. H. Bett, in Third International Conference on Solid State Lasers for Application to Inertial Confinement Fusion, W. H. Lowdermilk, ed., Proc. SPIE3492, 437 (1999).
[CrossRef]

Blair, P.

K. Ballüder, P. Blair, P. Rudman, A. Waddie, and M. R. Taghizadeh, “Design and fabrication of diffractive optics for material processing applications,” Opt. Laser Eng. (to be published).

I. M. Barton, P. Blair, A. J. Waddie, K. Ballüder, M. R. Taghizadeh, H. McInnes, and T. H. Bett, in Third International Conference on Solid State Lasers for Application to Inertial Confinement Fusion, W. H. Lowdermilk, ed., Proc. SPIE3492, 437 (1999).
[CrossRef]

K. Ballüder, I. M. Barton, P. Blair, M. R. Taghizadeh, H. McInnes, and T. H. Bett, in European Conference on Lasers and Electro-Optics (CLEO Europe), 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. 363.

Chen, D.

Farn, M. W.

Fox, A. G.

A. G. Fox and T. Li, Bell Syst. Tech. J. 40, 453 (1961).
[CrossRef]

Goodman, J. W.

Juday, R. D.

Laude, V.

Leger, J. R.

S. Makki, Z. Wang, and J. R. Leger, Appl. Opt. 36, 4749 (1997).
[CrossRef] [PubMed]

J. R. Leger, D. Chen, and G. Mowry, Appl. Opt. 34, 2498 (1995).
[CrossRef] [PubMed]

J. R. Leger, D. Chen, and Z. Wang, Opt. Lett. 19, 108 (1994).
[CrossRef]

J. R. Leger in Diffractive Optics for Industrial and Commercial Applications, J. Turunen and F. Wyrowski, eds. (Akademie Verlag, Berlin, 1997), pp. 189–215.

Li, T.

A. G. Fox and T. Li, Bell Syst. Tech. J. 40, 453 (1961).
[CrossRef]

Mait, J. N.

Makki, S.

McInnes, H.

I. M. Barton, P. Blair, A. J. Waddie, K. Ballüder, M. R. Taghizadeh, H. McInnes, and T. H. Bett, in Third International Conference on Solid State Lasers for Application to Inertial Confinement Fusion, W. H. Lowdermilk, ed., Proc. SPIE3492, 437 (1999).
[CrossRef]

K. Ballüder, I. M. Barton, P. Blair, M. R. Taghizadeh, H. McInnes, and T. H. Bett, in European Conference on Lasers and Electro-Optics (CLEO Europe), 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. 363.

McInnes, H. A.

K. Ballüder, M. R. Taghizadeh, H. A. McInnes, and T. H. Bett, J. Mod. Opt. 47, 2421 (2000).
[CrossRef]

Mowry, G.

Réfrégier, P.

Rudman, P.

K. Ballüder, P. Blair, P. Rudman, A. Waddie, and M. R. Taghizadeh, “Design and fabrication of diffractive optics for material processing applications,” Opt. Laser Eng. (to be published).

Taghizadeh, M. R.

K. Ballüder, M. R. Taghizadeh, H. A. McInnes, and T. H. Bett, J. Mod. Opt. 47, 2421 (2000).
[CrossRef]

K. Ballüder and M. R. Taghizadeh, Appl. Opt. 38, 5768 (1999).
[CrossRef]

K. Ballüder and M. R. Taghizadeh, Opt. Lett. 24, 1576 (1999).
[CrossRef]

K. Ballüder and M. R. Taghizadeh, in Conference on Lasers and Electro-Optics (CLEO US), 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), p. 482.

K. Ballüder, P. Blair, P. Rudman, A. Waddie, and M. R. Taghizadeh, “Design and fabrication of diffractive optics for material processing applications,” Opt. Laser Eng. (to be published).

K. Ballüder, I. M. Barton, P. Blair, M. R. Taghizadeh, H. McInnes, and T. H. Bett, in European Conference on Lasers and Electro-Optics (CLEO Europe), 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. 363.

I. M. Barton, P. Blair, A. J. Waddie, K. Ballüder, M. R. Taghizadeh, H. McInnes, and T. H. Bett, in Third International Conference on Solid State Lasers for Application to Inertial Confinement Fusion, W. H. Lowdermilk, ed., Proc. SPIE3492, 437 (1999).
[CrossRef]

Waddie, A.

K. Ballüder, P. Blair, P. Rudman, A. Waddie, and M. R. Taghizadeh, “Design and fabrication of diffractive optics for material processing applications,” Opt. Laser Eng. (to be published).

Waddie, A. J.

I. M. Barton, P. Blair, A. J. Waddie, K. Ballüder, M. R. Taghizadeh, H. McInnes, and T. H. Bett, in Third International Conference on Solid State Lasers for Application to Inertial Confinement Fusion, W. H. Lowdermilk, ed., Proc. SPIE3492, 437 (1999).
[CrossRef]

Wang, Z.

Appl. Opt. (6)

Bell Syst. Tech. J. (1)

A. G. Fox and T. Li, Bell Syst. Tech. J. 40, 453 (1961).
[CrossRef]

J. Mod. Opt. (1)

K. Ballüder, M. R. Taghizadeh, H. A. McInnes, and T. H. Bett, J. Mod. Opt. 47, 2421 (2000).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Lett. (2)

K. Ballüder and M. R. Taghizadeh, Opt. Lett. 24, 1576 (1999).
[CrossRef]

J. R. Leger, D. Chen, and Z. Wang, Opt. Lett. 19, 108 (1994).
[CrossRef]

Other (5)

K. Ballüder, P. Blair, P. Rudman, A. Waddie, and M. R. Taghizadeh, “Design and fabrication of diffractive optics for material processing applications,” Opt. Laser Eng. (to be published).

J. R. Leger in Diffractive Optics for Industrial and Commercial Applications, J. Turunen and F. Wyrowski, eds. (Akademie Verlag, Berlin, 1997), pp. 189–215.

I. M. Barton, P. Blair, A. J. Waddie, K. Ballüder, M. R. Taghizadeh, H. McInnes, and T. H. Bett, in Third International Conference on Solid State Lasers for Application to Inertial Confinement Fusion, W. H. Lowdermilk, ed., Proc. SPIE3492, 437 (1999).
[CrossRef]

K. Ballüder, I. M. Barton, P. Blair, M. R. Taghizadeh, H. McInnes, and T. H. Bett, in European Conference on Lasers and Electro-Optics (CLEO Europe), 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), p. 363.

K. Ballüder and M. R. Taghizadeh, in Conference on Lasers and Electro-Optics (CLEO US), 1999 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1999), p. 482.

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Figures (4)

Fig. 1
Fig. 1

(c) Irregularly spaced quantization scheme compared with (a) the standard 8-level quantization and (b) the regular quantization with bias phase.

Fig. 2
Fig. 2

Difference between two 16-level quantization schemes. Top, the standard equidistant quantization in which each level is twice the size of the next-smaller one. Bottom, a particular irregularly sized quantization. Right, the respective resultant phase levels.

Fig. 3
Fig. 3

Central sections of three MSE profiles: the ideal, continuous phase profile, a 16-level DOE quantized with a regular quantization with bias phase ΦBπ, and a DOE quantized to 16 irregularly spaced levels with bias phase. The irregularly quantized MSE reproduces the small variations in the central profile section much better than does the standard quantization.

Fig. 4
Fig. 4

Resultant beam shapes from the two quantized MSE profiles in Fig.  3. Both profiles use the same bias phase value and 16  phase levels. As it uses an irregular spacing for the phase levels, the MSE exhibits a significantly improved performance. The total squared deviation from the desired profile has been reduced by 84.3%.

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