Abstract

The capability of binary gray scale masks in generating beams with a desired lateral intensity profile is extensively studied in order to fabricate large-angle microprisms. Using a recently introduced technique, some samples based on pulsewidth modulation are designed, so that the pulsewidth is changed with different linear rates from a completely clear to a fully dark slit, which results in a different number of gray steps. Then, the influence of the rate on turning an incident plane wave into beams with different specially linear lateral intensity distributions was studied by simulation, experiment, and fabrication of a large-angle microprism. Further, it was shown that the width of the first slit and the increment of gray level have an effective impact on the slope and smoothness of the generated linear intensity profile across the beam. Simulation results are completely verified by experimental data and the fabricated linear gray scale element.

© 2014 Optical Society of America

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References

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  1. S. Bhattacharya, “Simplified mesh techniques for design of beam-shaping diffractive optical elements,” Optik 119, 321–328 (2008).
    [CrossRef]
  2. S. Lu, Y. Yan, D. Yi, G. Jin, and M. Wu, “Semiconductor laser diode to single-mode fiber coupling using diffractive optical elements,” Opt. Commun. 220, 345–351 (2003).
    [CrossRef]
  3. T. J. Suleski and D. C. O’Shea, “Gray scale masks for diffractive-optics fabrication. I. Commercial slide imager,” Appl. Opt. 34, 7518–7526 (1995).
    [CrossRef]
  4. A. Sabatyan and A. Hemmat, “Study of a novel and simple method of generating binary mask for microprism fabrication,” Appl. Opt 51, 525–530 (2012).
    [CrossRef]
  5. A. Sabatyan and M. R. Fasihanifard, “Generating of quadratic gray scale beam profile using binary gray scale masks,” Optik 124, 5604–5606 (2013).
    [CrossRef]

2013 (1)

A. Sabatyan and M. R. Fasihanifard, “Generating of quadratic gray scale beam profile using binary gray scale masks,” Optik 124, 5604–5606 (2013).
[CrossRef]

2012 (1)

A. Sabatyan and A. Hemmat, “Study of a novel and simple method of generating binary mask for microprism fabrication,” Appl. Opt 51, 525–530 (2012).
[CrossRef]

2008 (1)

S. Bhattacharya, “Simplified mesh techniques for design of beam-shaping diffractive optical elements,” Optik 119, 321–328 (2008).
[CrossRef]

2003 (1)

S. Lu, Y. Yan, D. Yi, G. Jin, and M. Wu, “Semiconductor laser diode to single-mode fiber coupling using diffractive optical elements,” Opt. Commun. 220, 345–351 (2003).
[CrossRef]

1995 (1)

Bhattacharya, S.

S. Bhattacharya, “Simplified mesh techniques for design of beam-shaping diffractive optical elements,” Optik 119, 321–328 (2008).
[CrossRef]

Fasihanifard, M. R.

A. Sabatyan and M. R. Fasihanifard, “Generating of quadratic gray scale beam profile using binary gray scale masks,” Optik 124, 5604–5606 (2013).
[CrossRef]

Hemmat, A.

A. Sabatyan and A. Hemmat, “Study of a novel and simple method of generating binary mask for microprism fabrication,” Appl. Opt 51, 525–530 (2012).
[CrossRef]

Jin, G.

S. Lu, Y. Yan, D. Yi, G. Jin, and M. Wu, “Semiconductor laser diode to single-mode fiber coupling using diffractive optical elements,” Opt. Commun. 220, 345–351 (2003).
[CrossRef]

Lu, S.

S. Lu, Y. Yan, D. Yi, G. Jin, and M. Wu, “Semiconductor laser diode to single-mode fiber coupling using diffractive optical elements,” Opt. Commun. 220, 345–351 (2003).
[CrossRef]

O’Shea, D. C.

Sabatyan, A.

A. Sabatyan and M. R. Fasihanifard, “Generating of quadratic gray scale beam profile using binary gray scale masks,” Optik 124, 5604–5606 (2013).
[CrossRef]

A. Sabatyan and A. Hemmat, “Study of a novel and simple method of generating binary mask for microprism fabrication,” Appl. Opt 51, 525–530 (2012).
[CrossRef]

Suleski, T. J.

Wu, M.

S. Lu, Y. Yan, D. Yi, G. Jin, and M. Wu, “Semiconductor laser diode to single-mode fiber coupling using diffractive optical elements,” Opt. Commun. 220, 345–351 (2003).
[CrossRef]

Yan, Y.

S. Lu, Y. Yan, D. Yi, G. Jin, and M. Wu, “Semiconductor laser diode to single-mode fiber coupling using diffractive optical elements,” Opt. Commun. 220, 345–351 (2003).
[CrossRef]

Yi, D.

S. Lu, Y. Yan, D. Yi, G. Jin, and M. Wu, “Semiconductor laser diode to single-mode fiber coupling using diffractive optical elements,” Opt. Commun. 220, 345–351 (2003).
[CrossRef]

Appl. Opt (1)

A. Sabatyan and A. Hemmat, “Study of a novel and simple method of generating binary mask for microprism fabrication,” Appl. Opt 51, 525–530 (2012).
[CrossRef]

Appl. Opt. (1)

Opt. Commun. (1)

S. Lu, Y. Yan, D. Yi, G. Jin, and M. Wu, “Semiconductor laser diode to single-mode fiber coupling using diffractive optical elements,” Opt. Commun. 220, 345–351 (2003).
[CrossRef]

Optik (2)

S. Bhattacharya, “Simplified mesh techniques for design of beam-shaping diffractive optical elements,” Optik 119, 321–328 (2008).
[CrossRef]

A. Sabatyan and M. R. Fasihanifard, “Generating of quadratic gray scale beam profile using binary gray scale masks,” Optik 124, 5604–5606 (2013).
[CrossRef]

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Figures (10)

Fig. 1.
Fig. 1.

Examples of both linear and quadratic gray level samples generated regarding Eq. (2). (a) Linear gray tone mask, (b) linear gray tone profile, (c) quadratic gray tone mask, and (d) quadratic gray tone profile.

Fig. 2.
Fig. 2.

Computer simulation of deterioration reduction of the intensity profile by increasing the gray level rate in a constant length of samples. (a)–(h) show that increasing the step increment rate effectively smooths the profile. The specification of the implemented samples was as follows: (a) is the principle sample with W1=20μm and totally 50 steps. W1 for samples (b)–(h) was reduced by 2.5 μm steps so the first slit width (W1) for the last sample becomes 2.5 μm.

Fig. 3.
Fig. 3.

Effect of gray scale increment rate on the intensity profile. It is clearly shown that by increasing the number of gray levels and decreasing W1, variation of the output intensity profile gets larger.

Fig. 4.
Fig. 4.

4-f setup used to record the intensity distribution [5].

Fig. 5.
Fig. 5.

First column: linear masks with W1=94μm produced through different gray scale levels, 30, 50, 70, 90, 110, and 130 steps, respectively, from top to the bottom. Second column: intensity distribution at a given distance from the corresponding mask. Third column: simulation and experimental results of intensity profile of the corresponding intensity distribution; dashed and dotted lines, respectively, as well as the solid line, show the best fitted line over the obtained experimental and simulation data. Finally, the fourth column shows the fitted equations.

Fig. 6.
Fig. 6.

First column: linear masks with W1=120μm produced through different gray scale levels, 30, 50, 70, 90, 110, and 130 steps, respectively, from top to the bottom. Second column: intensity distribution at a given distance from the corresponding mask. Third column: simulation and experimental results of intensity profile of the corresponding intensity distribution; dashed and dotted lines, respectively, as well as the solid line, show the best fitted line over the obtained experimental and simulation data. Finally, the fourth column shows the fitted equations.

Fig. 7.
Fig. 7.

First column: linear masks with W1=168μm produced through different gray scale levels, 30, 50, 70, 90, 110, and 130 steps, respectively, from top to the bottom. Second column: intensity distribution at a given distance from the corresponding mask. Third column: simulation and experimental results of intensity profile of the corresponding intensity distribution; dashed and dotted lines, respectively, as well as the solid line, show the best fitted line over the obtained experimental and simulation data. Finally, the fourth column shows the fitted equations.

Fig. 8.
Fig. 8.

Surface profile of the fabricated microprisms using masks with the following specifications. A, W1=56μm and N=40, so the angle of the fabricated microprism was 0.21° by using this mask. B, W1=35μm and N=40, by which the angle of the fabricated microprism was 0.28°. Comparing these figures clearly shows that reduction of W1 reduces the deterioration of the surface. One may note that the lengths of these masks are not the same.

Fig. 9.
Fig. 9.

Surface profile of the fabricated microprisms using masks with the following specifications. C, W1=110μm and N=48, so the angle of the fabricated microprism was 0.21° by using this mask. D, W1=40μm and N=130, by which the angle of the fabricated microprism was 0.26°. Since in this figure the lengths of the masks were kept constant, in this case by increasing the number of steps at the expense of reduction of W1, the surface became much smoother.

Fig. 10.
Fig. 10.

Second mask lithography results. W1 of these masks is chosen to be very small, about the feature size of the fabrication process. Samples labeled A through C were fabricated by masks with the following specifications. A, W1=9μm and N=45, by which the angle of the fabricated microprism is 22.0°. B, W1=10.5μm and N=21, by which the angle of the fabricated microprism is 24.5°. C, W1=13μm and N=26, by which the angle of the fabricated microprism is 21.7°. Apparently, high reduction of W1 around the feature size will abruptly increase the slope of the prism.

Equations (4)

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g(x)=n=1N[WnPn+m=01mπsin(mπWnPn)cos(2mπxPn)].
Wn=W1+α(n1)P,
U(x,y,z)=2πeikziλz[M(x,y)eik2z(x2+y2)],
U(x,y,z)=FT1{FT[M(x,y)]FT[eik2z(x2+y2)]},

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