Abstract

We discuss the realization of highly efficient fan-out elements. Laser-beam writing lithography is available now for fabricating smooth surface relief microstructures. We develop several methods for optimizing microstructure profiles. Only a small number of parameters in the object plane are necessary for determining the kinoform. This simplifies the calculation of M × N arrays also for large M and N. Experimental results for a 9-beam fan-out element are presented.

© 1992 Optical Society of America

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References

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  1. J. N. Mait, “Design of binary-phase and multiphase Fourier gratings for array generation,” J. Opt. Soc. Am. A 7, 1514–1528 (1990).
    [CrossRef]
  2. J. Turunen, J. Fagerholm, A. Vasara, M. R. Taghizadeh, “Detour-phase kinoform interconnects: the concept and fabrication considerations,” J. Opt. Soc. Am. A 7, 1202–1208 (1990).
    [CrossRef]
  3. M. T. Gale, G. K. Lang, J. M. Raynor, H. Schütz, “Fabrication of micro-optical components by laser writing in photoresist,” in Micro-Optics II, A. M. Scheggi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1506, 65–70 (1991).
  4. M. T. Gale, G. K. Lang, J. M. Raynor, H. Schütz, “Fabrication of kinoform structures for optical computing,” Appl. Opt. 31, 5712–5715 (1992).
    [CrossRef] [PubMed]
  5. H. P. Herzig, R. Dändliker, J. M. Teijido, “Beam shaping for high power laser diode arrays by holographic optical elements,” in Holographic Systems, Components and Applications, Conference Publ. 311 (Institution of Electrical Engineers, London, 1989), pp. 133–137.
  6. H. P. Herzig, D. Prongué, R. Dändliker, “Design and fabrication of highly efficient fan-out element,” Jpn. J. Appl. Phys. 27, L1307–L1309 (1990).
    [CrossRef]
  7. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in Pascal (Cambridge U. Press, Cambridge, 1989)
  8. F. Wyrowski, “Diffractive optical elements: iterative calculation of quantized, blazed phase structures,” J. Opt. Soc. Am. A 7, 961–969 (1990).
    [CrossRef]

1992

1990

Dändliker, R.

H. P. Herzig, D. Prongué, R. Dändliker, “Design and fabrication of highly efficient fan-out element,” Jpn. J. Appl. Phys. 27, L1307–L1309 (1990).
[CrossRef]

H. P. Herzig, R. Dändliker, J. M. Teijido, “Beam shaping for high power laser diode arrays by holographic optical elements,” in Holographic Systems, Components and Applications, Conference Publ. 311 (Institution of Electrical Engineers, London, 1989), pp. 133–137.

Fagerholm, J.

Flannery, B. P.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in Pascal (Cambridge U. Press, Cambridge, 1989)

Gale, M. T.

M. T. Gale, G. K. Lang, J. M. Raynor, H. Schütz, “Fabrication of kinoform structures for optical computing,” Appl. Opt. 31, 5712–5715 (1992).
[CrossRef] [PubMed]

M. T. Gale, G. K. Lang, J. M. Raynor, H. Schütz, “Fabrication of micro-optical components by laser writing in photoresist,” in Micro-Optics II, A. M. Scheggi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1506, 65–70 (1991).

Herzig, H. P.

H. P. Herzig, D. Prongué, R. Dändliker, “Design and fabrication of highly efficient fan-out element,” Jpn. J. Appl. Phys. 27, L1307–L1309 (1990).
[CrossRef]

H. P. Herzig, R. Dändliker, J. M. Teijido, “Beam shaping for high power laser diode arrays by holographic optical elements,” in Holographic Systems, Components and Applications, Conference Publ. 311 (Institution of Electrical Engineers, London, 1989), pp. 133–137.

Lang, G. K.

M. T. Gale, G. K. Lang, J. M. Raynor, H. Schütz, “Fabrication of kinoform structures for optical computing,” Appl. Opt. 31, 5712–5715 (1992).
[CrossRef] [PubMed]

M. T. Gale, G. K. Lang, J. M. Raynor, H. Schütz, “Fabrication of micro-optical components by laser writing in photoresist,” in Micro-Optics II, A. M. Scheggi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1506, 65–70 (1991).

Mait, J. N.

Press, W. H.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in Pascal (Cambridge U. Press, Cambridge, 1989)

Prongué, D.

H. P. Herzig, D. Prongué, R. Dändliker, “Design and fabrication of highly efficient fan-out element,” Jpn. J. Appl. Phys. 27, L1307–L1309 (1990).
[CrossRef]

Raynor, J. M.

M. T. Gale, G. K. Lang, J. M. Raynor, H. Schütz, “Fabrication of kinoform structures for optical computing,” Appl. Opt. 31, 5712–5715 (1992).
[CrossRef] [PubMed]

M. T. Gale, G. K. Lang, J. M. Raynor, H. Schütz, “Fabrication of micro-optical components by laser writing in photoresist,” in Micro-Optics II, A. M. Scheggi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1506, 65–70 (1991).

Schütz, H.

M. T. Gale, G. K. Lang, J. M. Raynor, H. Schütz, “Fabrication of kinoform structures for optical computing,” Appl. Opt. 31, 5712–5715 (1992).
[CrossRef] [PubMed]

M. T. Gale, G. K. Lang, J. M. Raynor, H. Schütz, “Fabrication of micro-optical components by laser writing in photoresist,” in Micro-Optics II, A. M. Scheggi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1506, 65–70 (1991).

Taghizadeh, M. R.

Teijido, J. M.

H. P. Herzig, R. Dändliker, J. M. Teijido, “Beam shaping for high power laser diode arrays by holographic optical elements,” in Holographic Systems, Components and Applications, Conference Publ. 311 (Institution of Electrical Engineers, London, 1989), pp. 133–137.

Teukolsky, S. A.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in Pascal (Cambridge U. Press, Cambridge, 1989)

Turunen, J.

Vasara, A.

Vetterling, W. T.

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in Pascal (Cambridge U. Press, Cambridge, 1989)

Wyrowski, F.

Appl. Opt.

J. Opt. Soc. Am. A

Jpn. J. Appl. Phys.

H. P. Herzig, D. Prongué, R. Dändliker, “Design and fabrication of highly efficient fan-out element,” Jpn. J. Appl. Phys. 27, L1307–L1309 (1990).
[CrossRef]

Other

W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in Pascal (Cambridge U. Press, Cambridge, 1989)

M. T. Gale, G. K. Lang, J. M. Raynor, H. Schütz, “Fabrication of micro-optical components by laser writing in photoresist,” in Micro-Optics II, A. M. Scheggi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1506, 65–70 (1991).

H. P. Herzig, R. Dändliker, J. M. Teijido, “Beam shaping for high power laser diode arrays by holographic optical elements,” in Holographic Systems, Components and Applications, Conference Publ. 311 (Institution of Electrical Engineers, London, 1989), pp. 133–137.

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Figures (8)

Fig. 1
Fig. 1

Readout of the fan-out element.

Fig. 2
Fig. 2

First optimization process for the phases ϕm to gain high efficiency. The reconstructed object after clipping is nonuniform (Am′ ≠ 1).

Fig. 3
Fig. 3

Numerical optimization of phases for maximum efficiency.

Fig. 4
Fig. 4

Phase transfer function ψ(u, v) of a high-efficiency 9-beam fan-out element.

Fig. 5
Fig. 5

Second optimization step (uniformity): ϕm(0) comes from the first optimization step and (n) counts the number of iterations.

Fig. 6
Fig. 6

Cascading parameter sets.

Fig. 7
Fig. 7

Profile thickness of the fabricated fan-out.

Fig. 8
Fig. 8

Relative intensities of the fabricated fan-out.

Tables (3)

Tables Icon

Table I Highly Efficient 9-Beam Fan-Out Element with Amplitude and Phase of the Virtual Recording Light Sources and the Resulting Light Spots

Tables Icon

Table II Perfectly Uniform 9-Beam Fan-Out Element with Amplitude and Phase of the Virtual Recording Light Sources and the Resulting Light Spots

Tables Icon

Table III Efficiency and Uniformity Issued From First and Second Optimizations

Equations (18)

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U ( x , y ) = m = 1 N A m exp ( i ϕ m ) δ ( x - x m , y ) ,
U ^ ( u , v ) = - U ( x , y ) exp [ 2 π i ( x u + y v ) ] d x d y = m = 1 N A m exp ( i ϕ m ) exp ( 2 π i x m u ) .
U ^ ( u , v ) = U ^ ( u , v ) exp [ i ψ ( u , v ) ] ,
I ( u , v ) = U ^ ( u , v ) 2 = m = 1 N A m 2 + 2 m < n N A m A m cos ( Ω m n ) ,
Ω m n = 2 π u ( x m - x n ) + ϕ m - ϕ n .
Ω m n = 2 π u ( m - n ) s + ϕ m - ϕ n .
I = U ^ 2 = m = 1 N A m 2 .
[ I ( u , v ) - I ] 2 d u d u min .
[ m < n N A m A n cos ( Ω m n ) ] 2 d u d v min ,
m < n N A m A n cos ( Ω m n ) = k = 1 N - 1 m = 1 N - k A m A m + k cos ( 2 π k s u + ϕ m - ϕ m + k ) = k = 1 N - 1 B k cos ( 2 π k s u + Φ k ) .
B k 2 = [ m = 1 N - k A m A m + k cos ( ϕ m - ϕ m + k ) ] 2 + [ m = 1 N - k A m A m + k sin ( ϕ m - ϕ m + k ) ] 2 .
[ k = 1 N - 1 B k cos ( 2 π k s u + Φ k ) ] 2 d u d v min .
k = 1 N - 1 B k 2 min .
B k = m = 1 N - k cos ( ϕ m - ϕ m + k ) .
A m ( n + 1 ) = A m ( n ) A m ( n ) A m ( n ) ,
( U ^ - U ^ ) 2 d u d v min .
U ^ ( u , v ) = exp [ i ψ ( u , v ) ] ,
ψ ( u , v ) = p = 1 P A p cos ( 2 π p u ) .

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