Abstract

Many applications of diffractive phase elements involve the calculation of a continuous phase profile that is subsequently quantized for fabrication. The quantization process maps the continuous range of phase values to a limited number of discrete steps. We report our observation of the influence of this quantization process on the performance of mode-selecting diffractive elements and show that the quantization process produces significantly better results by use of an optimized bias phase. In principle this process can be employed to a greater or lesser extent in any quantization process.

© 1999 Optical Society of America

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  1. I. M. Barton, P. Blair, A. J. Waddie, K. Ballüder, M. R. Taghizadeh, H. McInnes, and T. H. Bett, Proc. SPIE 3492, 437 (1999).
    [CrossRef]
  2. 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) (Optical Society of America, Washington, D.C., 1998), p. 363.
  3. K. Ballüder and M. R. Taghizadeh, in Postgraduate Research in Electronics and Photonics—PREP99 Proceedings (Institute of Physics, London, 1999), p. 17.
  4. K. Ballüder and M. R. Taghizadeh, in Conference on Lasers and Electro-Optics (CLEO/US) (Optical Society of America, Washington, D. C., 1999), p. 482.
  5. J. W. Goodman and A. M. Silvestri, IBM J. Res. Dev. 14, 478 (1970).
    [CrossRef]
  6. Y. J. Guo and S. K. Barton, IEEE Trans. Antennas Propag. 142, 115 (1995).
  7. K. Ballüder, M. R. Taghizadeh, H. R. McInnes, and T. Bett, Appl. Opt. 38, 5768 (1999).
    [CrossRef]
  8. I. M. Barton and M. R. Taghizadeh, Opt. Lett. 23, 198 (1998).
    [CrossRef]

1999

I. M. Barton, P. Blair, A. J. Waddie, K. Ballüder, M. R. Taghizadeh, H. McInnes, and T. H. Bett, Proc. SPIE 3492, 437 (1999).
[CrossRef]

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

1998

1995

Y. J. Guo and S. K. Barton, IEEE Trans. Antennas Propag. 142, 115 (1995).

1970

J. W. Goodman and A. M. Silvestri, IBM J. Res. Dev. 14, 478 (1970).
[CrossRef]

Ballüder, K.

I. M. Barton, P. Blair, A. J. Waddie, K. Ballüder, M. R. Taghizadeh, H. McInnes, and T. H. Bett, Proc. SPIE 3492, 437 (1999).
[CrossRef]

K. Ballüder, M. R. Taghizadeh, H. R. McInnes, and T. Bett, Appl. Opt. 38, 5768 (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) (Optical Society of America, Washington, D.C., 1998), p. 363.

K. Ballüder and M. R. Taghizadeh, in Postgraduate Research in Electronics and Photonics—PREP99 Proceedings (Institute of Physics, London, 1999), p. 17.

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

Barton, I. M.

I. M. Barton, P. Blair, A. J. Waddie, K. Ballüder, M. R. Taghizadeh, H. McInnes, and T. H. Bett, Proc. SPIE 3492, 437 (1999).
[CrossRef]

I. M. Barton and M. R. Taghizadeh, Opt. Lett. 23, 198 (1998).
[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) (Optical Society of America, Washington, D.C., 1998), p. 363.

Barton, S. K.

Y. J. Guo and S. K. Barton, IEEE Trans. Antennas Propag. 142, 115 (1995).

Bett, T.

Bett, T. H.

I. M. Barton, P. Blair, A. J. Waddie, K. Ballüder, M. R. Taghizadeh, H. McInnes, and T. H. Bett, Proc. SPIE 3492, 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) (Optical Society of America, Washington, D.C., 1998), p. 363.

Blair, P.

I. M. Barton, P. Blair, A. J. Waddie, K. Ballüder, M. R. Taghizadeh, H. McInnes, and T. H. Bett, Proc. SPIE 3492, 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) (Optical Society of America, Washington, D.C., 1998), p. 363.

Goodman, J. W.

J. W. Goodman and A. M. Silvestri, IBM J. Res. Dev. 14, 478 (1970).
[CrossRef]

Guo, Y. J.

Y. J. Guo and S. K. Barton, IEEE Trans. Antennas Propag. 142, 115 (1995).

McInnes, H.

I. M. Barton, P. Blair, A. J. Waddie, K. Ballüder, M. R. Taghizadeh, H. McInnes, and T. H. Bett, Proc. SPIE 3492, 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) (Optical Society of America, Washington, D.C., 1998), p. 363.

McInnes, H. R.

Silvestri, A. M.

J. W. Goodman and A. M. Silvestri, IBM J. Res. Dev. 14, 478 (1970).
[CrossRef]

Taghizadeh, M. R.

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

I. M. Barton, P. Blair, A. J. Waddie, K. Ballüder, M. R. Taghizadeh, H. McInnes, and T. H. Bett, Proc. SPIE 3492, 437 (1999).
[CrossRef]

I. M. Barton and M. R. Taghizadeh, Opt. Lett. 23, 198 (1998).
[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) (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) (Optical Society of America, Washington, D. C., 1999), p. 482.

K. Ballüder and M. R. Taghizadeh, in Postgraduate Research in Electronics and Photonics—PREP99 Proceedings (Institute of Physics, London, 1999), p. 17.

Waddie, A. J.

I. M. Barton, P. Blair, A. J. Waddie, K. Ballüder, M. R. Taghizadeh, H. McInnes, and T. H. Bett, Proc. SPIE 3492, 437 (1999).
[CrossRef]

Appl. Opt.

IBM J. Res. Dev.

J. W. Goodman and A. M. Silvestri, IBM J. Res. Dev. 14, 478 (1970).
[CrossRef]

IEEE Trans. Antennas Propag.

Y. J. Guo and S. K. Barton, IEEE Trans. Antennas Propag. 142, 115 (1995).

Opt. Lett.

Proc. SPIE

I. M. Barton, P. Blair, A. J. Waddie, K. Ballüder, M. R. Taghizadeh, H. McInnes, and T. H. Bett, Proc. SPIE 3492, 437 (1999).
[CrossRef]

Other

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) (Optical Society of America, Washington, D.C., 1998), p. 363.

K. Ballüder and M. R. Taghizadeh, in Postgraduate Research in Electronics and Photonics—PREP99 Proceedings (Institute of Physics, London, 1999), p. 17.

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

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Figures (5)

Fig. 1
Fig. 1

Scan through the required phase profile (solid curve) for forming a flat-topped output beam from a Fabry–Perot laser resonator. The ideal continuous profile cannot be fabricated directly; it needs to be quantized first. Dotted curve, the quantized eight-level MSE that can be used to approximate this profile. Dashed curve, the phase profile of a combination of a MSE and a lens that is better approximation to the required profile.

Fig. 2
Fig. 2

Commonly used quantization scheme, simply mapping the total range 02π onto N evenly spaced discrete values.

Fig. 3
Fig. 3

The effect of the additional bias phase on the quantization process is equivalent to a rotation of the discrete phase levels relative to the original phase value.

Fig. 4
Fig. 4

Improvement in beam quality of a MSE combined with a lens. Variations in the focal length f of the lens lead to different phase profiles for the MSE. Small changes in f produce large variations in the beam quality. This variation can be reduced by as much as 1 order of magnitude by use of an optimized bias phase in the quantization.

Fig. 5
Fig. 5

Beam profiles obtained with a particularly bad choice of bias phase, leading to a MSE design that produces a large deviation from the desired beam profile, and a bias phase chosen by our optimization algorithm, compared with the ideal beam profile as produced by the unquantized MSE.

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