Abstract

As design algorithms for diffractive optical elements improve, the limiting factor becomes the fabrication process. It is hoped a better understanding of fabrication errors will allow elements with greater tolerance to be designed. This is important for high-power laser fiber coupling, where hot spots lead to failure. We model seven different fan-out gratings applying misetch, misalignment, and feature rounding. Our main findings are that misetch can lead to improved results, misalignment is strongly asymmetric, and both the π and π/2 masks can dominate misalignment. Rounding has a r2 dependence and potentially can be incorporated into the design stage. Finally we present some experimental data for misalignment.

© 2007 Optical Society of America

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  1. M. J. Thomson and M. R. Taghizadeh, "Diffractive elements for high-power fibre coupling applications," J. Mod. Opt. 50, 1691-1699 (2003).
  2. K. Ballüder and M. R. Taghizadeh, "Regenerative ring-laser design by use of an intracavity diffractive mode-selecting element," Appl. Opt. 38, 5768-5774 (1999).
    [CrossRef]
  3. M. R. Taghizadeh and A. J. Waddie, "Micro-optical and optoelectronic components for optical interconnection applications," Acta Phys. Pol. A 101, 175-188 (2002).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  7. J. S. Liu, A. J. Caley, and M. R. Taghizadeh, "Symmetrical iterative Fourier-transform algorithm using both phase and amplitude freedoms," Opt. Commun. 267, 347-355 (2006).
    [CrossRef]
  8. S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, "Optimization by simulated annealing," Science 220, 671-679 (1983).
    [CrossRef] [PubMed]
  9. M. R. Taghizadeh, P. Blair, B. Layet, I. M. Barton, A. J. Waddie, and N. Ross, "Design and fabrication of diffractive optical elements," Microelectron. Eng. 34, 219-242 (1997).
    [CrossRef]
  10. J. Bengtsson and M. Johansson, "Fan-out diffractive optical elements designed for increased fabrication tolerence to linear relief depth errors," Appl. Opt. 41, 281-289 (2002).
    [CrossRef] [PubMed]
  11. V. Kettunen, K. Jefimovs, J. Simonen, O. Ripoll, M. Kuittinen, and H. P. Herzig, "Diffractive elements designed to suppress unwanted zeroth order due to surface depth error," J. Mod. Opt. 51, 2111-2123 (2004).
    [CrossRef]
  12. J. M. Miller, M. R. Taghizadeh, J. Turunen, and N. Ross, "Multilevel-grating array generators: fabrication error analysis and experiments," Appl. Opt. 32, 2519-2525 (1993).
    [CrossRef] [PubMed]
  13. U. D. Zeitner and P. Dannberg, "On-axis diffractive elements with improved signal quality in the presence of fabrication errors and wavelength tolerances," J. Mod. Opt. 52, 2051-2057 (2005).
    [CrossRef]
  14. A. J. Waddie and M. R. Taghizadeh, "Interference effects in far-field diffractive optical elements," Appl. Opt. 34, 5915-5919 (1999).
    [CrossRef]
  15. K. Ballüder and M. R. Taghizadeh, "Optimized quantization for diffractive phase elements by use of uneven phase levels," Opt. Lett. 26, 417-419 (2001).
    [CrossRef]

2006 (1)

J. S. Liu, A. J. Caley, and M. R. Taghizadeh, "Symmetrical iterative Fourier-transform algorithm using both phase and amplitude freedoms," Opt. Commun. 267, 347-355 (2006).
[CrossRef]

2005 (1)

U. D. Zeitner and P. Dannberg, "On-axis diffractive elements with improved signal quality in the presence of fabrication errors and wavelength tolerances," J. Mod. Opt. 52, 2051-2057 (2005).
[CrossRef]

2004 (1)

V. Kettunen, K. Jefimovs, J. Simonen, O. Ripoll, M. Kuittinen, and H. P. Herzig, "Diffractive elements designed to suppress unwanted zeroth order due to surface depth error," J. Mod. Opt. 51, 2111-2123 (2004).
[CrossRef]

2003 (2)

Y. Ha, H. Hua, and J. P. Rolland, "Design of an ultralight and compact projection lens," Appl. Opt. 42, 97-107 (2003).
[CrossRef] [PubMed]

M. J. Thomson and M. R. Taghizadeh, "Diffractive elements for high-power fibre coupling applications," J. Mod. Opt. 50, 1691-1699 (2003).

2002 (2)

M. R. Taghizadeh and A. J. Waddie, "Micro-optical and optoelectronic components for optical interconnection applications," Acta Phys. Pol. A 101, 175-188 (2002).

J. Bengtsson and M. Johansson, "Fan-out diffractive optical elements designed for increased fabrication tolerence to linear relief depth errors," Appl. Opt. 41, 281-289 (2002).
[CrossRef] [PubMed]

2001 (1)

1999 (2)

K. Ballüder and M. R. Taghizadeh, "Regenerative ring-laser design by use of an intracavity diffractive mode-selecting element," Appl. Opt. 38, 5768-5774 (1999).
[CrossRef]

A. J. Waddie and M. R. Taghizadeh, "Interference effects in far-field diffractive optical elements," Appl. Opt. 34, 5915-5919 (1999).
[CrossRef]

1997 (1)

M. R. Taghizadeh, P. Blair, B. Layet, I. M. Barton, A. J. Waddie, and N. Ross, "Design and fabrication of diffractive optical elements," Microelectron. Eng. 34, 219-242 (1997).
[CrossRef]

1993 (2)

1983 (1)

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, "Optimization by simulated annealing," Science 220, 671-679 (1983).
[CrossRef] [PubMed]

1967 (1)

Ballüder, K.

Barton, I. M.

M. R. Taghizadeh, P. Blair, B. Layet, I. M. Barton, A. J. Waddie, and N. Ross, "Design and fabrication of diffractive optical elements," Microelectron. Eng. 34, 219-242 (1997).
[CrossRef]

Bengtsson, J.

Blair, P.

M. R. Taghizadeh, P. Blair, B. Layet, I. M. Barton, A. J. Waddie, and N. Ross, "Design and fabrication of diffractive optical elements," Microelectron. Eng. 34, 219-242 (1997).
[CrossRef]

Caley, A. J.

J. S. Liu, A. J. Caley, and M. R. Taghizadeh, "Symmetrical iterative Fourier-transform algorithm using both phase and amplitude freedoms," Opt. Commun. 267, 347-355 (2006).
[CrossRef]

Dannberg, P.

U. D. Zeitner and P. Dannberg, "On-axis diffractive elements with improved signal quality in the presence of fabrication errors and wavelength tolerances," J. Mod. Opt. 52, 2051-2057 (2005).
[CrossRef]

Farn, M. W.

Gelatt, C. D.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, "Optimization by simulated annealing," Science 220, 671-679 (1983).
[CrossRef] [PubMed]

Ha, Y.

Herzig, H. P.

V. Kettunen, K. Jefimovs, J. Simonen, O. Ripoll, M. Kuittinen, and H. P. Herzig, "Diffractive elements designed to suppress unwanted zeroth order due to surface depth error," J. Mod. Opt. 51, 2111-2123 (2004).
[CrossRef]

Hua, H.

Jefimovs, K.

V. Kettunen, K. Jefimovs, J. Simonen, O. Ripoll, M. Kuittinen, and H. P. Herzig, "Diffractive elements designed to suppress unwanted zeroth order due to surface depth error," J. Mod. Opt. 51, 2111-2123 (2004).
[CrossRef]

Johansson, M.

Kettunen, V.

V. Kettunen, K. Jefimovs, J. Simonen, O. Ripoll, M. Kuittinen, and H. P. Herzig, "Diffractive elements designed to suppress unwanted zeroth order due to surface depth error," J. Mod. Opt. 51, 2111-2123 (2004).
[CrossRef]

Kirkpatrick, S.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, "Optimization by simulated annealing," Science 220, 671-679 (1983).
[CrossRef] [PubMed]

Kuittinen, M.

V. Kettunen, K. Jefimovs, J. Simonen, O. Ripoll, M. Kuittinen, and H. P. Herzig, "Diffractive elements designed to suppress unwanted zeroth order due to surface depth error," J. Mod. Opt. 51, 2111-2123 (2004).
[CrossRef]

Layet, B.

M. R. Taghizadeh, P. Blair, B. Layet, I. M. Barton, A. J. Waddie, and N. Ross, "Design and fabrication of diffractive optical elements," Microelectron. Eng. 34, 219-242 (1997).
[CrossRef]

Liu, J. S.

J. S. Liu, A. J. Caley, and M. R. Taghizadeh, "Symmetrical iterative Fourier-transform algorithm using both phase and amplitude freedoms," Opt. Commun. 267, 347-355 (2006).
[CrossRef]

Lohmann, A. W.

Medeiros, S. S.

Miller, J. M.

Paris, D. P.

Ripoll, O.

V. Kettunen, K. Jefimovs, J. Simonen, O. Ripoll, M. Kuittinen, and H. P. Herzig, "Diffractive elements designed to suppress unwanted zeroth order due to surface depth error," J. Mod. Opt. 51, 2111-2123 (2004).
[CrossRef]

Rolland, J. P.

Ross, N.

M. R. Taghizadeh, P. Blair, B. Layet, I. M. Barton, A. J. Waddie, and N. Ross, "Design and fabrication of diffractive optical elements," Microelectron. Eng. 34, 219-242 (1997).
[CrossRef]

J. M. Miller, M. R. Taghizadeh, J. Turunen, and N. Ross, "Multilevel-grating array generators: fabrication error analysis and experiments," Appl. Opt. 32, 2519-2525 (1993).
[CrossRef] [PubMed]

Simonen, J.

V. Kettunen, K. Jefimovs, J. Simonen, O. Ripoll, M. Kuittinen, and H. P. Herzig, "Diffractive elements designed to suppress unwanted zeroth order due to surface depth error," J. Mod. Opt. 51, 2111-2123 (2004).
[CrossRef]

Stern, M. B.

Taghizadeh, M. R.

J. S. Liu, A. J. Caley, and M. R. Taghizadeh, "Symmetrical iterative Fourier-transform algorithm using both phase and amplitude freedoms," Opt. Commun. 267, 347-355 (2006).
[CrossRef]

M. J. Thomson and M. R. Taghizadeh, "Diffractive elements for high-power fibre coupling applications," J. Mod. Opt. 50, 1691-1699 (2003).

M. R. Taghizadeh and A. J. Waddie, "Micro-optical and optoelectronic components for optical interconnection applications," Acta Phys. Pol. A 101, 175-188 (2002).

K. Ballüder and M. R. Taghizadeh, "Optimized quantization for diffractive phase elements by use of uneven phase levels," Opt. Lett. 26, 417-419 (2001).
[CrossRef]

K. Ballüder and M. R. Taghizadeh, "Regenerative ring-laser design by use of an intracavity diffractive mode-selecting element," Appl. Opt. 38, 5768-5774 (1999).
[CrossRef]

A. J. Waddie and M. R. Taghizadeh, "Interference effects in far-field diffractive optical elements," Appl. Opt. 34, 5915-5919 (1999).
[CrossRef]

M. R. Taghizadeh, P. Blair, B. Layet, I. M. Barton, A. J. Waddie, and N. Ross, "Design and fabrication of diffractive optical elements," Microelectron. Eng. 34, 219-242 (1997).
[CrossRef]

J. M. Miller, M. R. Taghizadeh, J. Turunen, and N. Ross, "Multilevel-grating array generators: fabrication error analysis and experiments," Appl. Opt. 32, 2519-2525 (1993).
[CrossRef] [PubMed]

Thomson, M. J.

M. J. Thomson and M. R. Taghizadeh, "Diffractive elements for high-power fibre coupling applications," J. Mod. Opt. 50, 1691-1699 (2003).

Turunen, J.

Vecchi, M. P.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, "Optimization by simulated annealing," Science 220, 671-679 (1983).
[CrossRef] [PubMed]

Veldkamp, W. B.

Waddie, A. J.

M. R. Taghizadeh and A. J. Waddie, "Micro-optical and optoelectronic components for optical interconnection applications," Acta Phys. Pol. A 101, 175-188 (2002).

A. J. Waddie and M. R. Taghizadeh, "Interference effects in far-field diffractive optical elements," Appl. Opt. 34, 5915-5919 (1999).
[CrossRef]

M. R. Taghizadeh, P. Blair, B. Layet, I. M. Barton, A. J. Waddie, and N. Ross, "Design and fabrication of diffractive optical elements," Microelectron. Eng. 34, 219-242 (1997).
[CrossRef]

Zeitner, U. D.

U. D. Zeitner and P. Dannberg, "On-axis diffractive elements with improved signal quality in the presence of fabrication errors and wavelength tolerances," J. Mod. Opt. 52, 2051-2057 (2005).
[CrossRef]

Acta Phys. Pol. A (1)

M. R. Taghizadeh and A. J. Waddie, "Micro-optical and optoelectronic components for optical interconnection applications," Acta Phys. Pol. A 101, 175-188 (2002).

Appl. Opt. (6)

J. Mod. Opt. (3)

V. Kettunen, K. Jefimovs, J. Simonen, O. Ripoll, M. Kuittinen, and H. P. Herzig, "Diffractive elements designed to suppress unwanted zeroth order due to surface depth error," J. Mod. Opt. 51, 2111-2123 (2004).
[CrossRef]

U. D. Zeitner and P. Dannberg, "On-axis diffractive elements with improved signal quality in the presence of fabrication errors and wavelength tolerances," J. Mod. Opt. 52, 2051-2057 (2005).
[CrossRef]

M. J. Thomson and M. R. Taghizadeh, "Diffractive elements for high-power fibre coupling applications," J. Mod. Opt. 50, 1691-1699 (2003).

Microelectron. Eng. (1)

M. R. Taghizadeh, P. Blair, B. Layet, I. M. Barton, A. J. Waddie, and N. Ross, "Design and fabrication of diffractive optical elements," Microelectron. Eng. 34, 219-242 (1997).
[CrossRef]

Opt. Commun. (1)

J. S. Liu, A. J. Caley, and M. R. Taghizadeh, "Symmetrical iterative Fourier-transform algorithm using both phase and amplitude freedoms," Opt. Commun. 267, 347-355 (2006).
[CrossRef]

Opt. Lett. (2)

Science (1)

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, "Optimization by simulated annealing," Science 220, 671-679 (1983).
[CrossRef] [PubMed]

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Figures (12)

Fig. 1
Fig. 1

Beam shaping applied to fiber coupling. Example shown contains 512 × 512 pixels and 16 phase levels and is designed for operation with a frequency-doubled Nd:YAG source at 532   nm capable of delivering 20   mJ in 10   ns pulses. For the design shown efficiency is 88% and nonuniformity 1.8%.

Fig. 2
Fig. 2

Steps involved in two mask reactive ion etching of a DOE.

Fig. 3
Fig. 3

Effect of misalignment on the DOE phase profile. (a) Incorrectly aligned mask overlying the photoresist coated substrate. (b) After UV illumination misalignment is transferred to the resist etching, which in turn copies the misalignment to (c) the substrate. (d) The desired profile.

Fig. 4
Fig. 4

Scanning electron microscope image demonstration featuring rounding and misalignment.

Fig. 5
Fig. 5

Effect of misetch on efficiency for (a) 4 × 4 grating and (b) 5 × 5 grating and on nonuniformity for (c) 4 × 4 grating and (d) 5 × 5 grating.

Fig. 6
Fig. 6

Influence of misalignment on efficiency for 6 × 6 grating.

Fig. 7
Fig. 7

Influence of misalignment on nonuniformity for (a) 5 × 5 grating, (b) 7 × 7 grating, and (c) 6 × 6 grating.

Fig. 8
Fig. 8

Influence of feature rounding on efficiency for 6 × 6 grating.

Fig. 9
Fig. 9

Influence of feature rounding on nonuniformity for 6 × 6 grating.

Fig. 10
Fig. 10

Experimental setup.

Fig. 11
Fig. 11

CCD image of the 5 × 5 array used for nonuniformity calculations.

Fig. 12
Fig. 12

Experimentally acquired data. Efficiency shown at the top of each plot, nonuniformity at the bottom.

Tables (2)

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Table 1 Specifications for Modeled, Error-Free Elements

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Table 2 Second Derivative of Parabolic Fit to Misetch Efficiency Plots

Equations (2)

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Δ R = max | F ( X , Y ) G ( X , Y ) G max | ,
η = p F ( X , Y ) ε g ( x , y ) ,

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