## Design and analysis of multi-wavelength diffractive optics |

Optics Express, Vol. 20, Issue 3, pp. 2814-2823 (2012)

http://dx.doi.org/10.1364/OE.20.002814

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### Abstract

We present an extension of the direct-binary-search algorithm for designing high-efficiency multi-wavelength diffractive optics that reconstruct in the Fresnel domain. A fast computation method for solving the optimization problem is proposed. Examples of three-wavelength diffractive optics with over 90% diffraction efficiency are presented. These diffractive optical elements reconstruct three distinct image patterns when probed using the design wavelengths. Detailed parametric and sensitivity studies are conducted, which provide insight into the diffractive optic’s performance when subject to different design conditions as well as common systematic and fabrication errors.

© 2012 OSA

## 1. Introduction

2. C. Dankwart, C. Falldorf, R. Gläbe, A. Meier, C. V. Kopylow, and R. B. Bergmann, “Design of diamond-turned holograms incorporating properties of the fabrication process,” Appl. Opt. **49**(20), 3949–3955 (2010). [CrossRef] [PubMed]

3. D. Faklis and G. M. Morris, “Spectral properties of multiorder diffractive lenses,” Appl. Opt. **34**(14), 2462–2468 (1995). [CrossRef] [PubMed]

5. D. Prongué, H. P. Herzig, R. Dändliker, and M. T. Gale, “Optimized kinoform structures for highly efficient fan-out elements,” Appl. Opt. **31**(26), 5706–5711 (1992). [CrossRef] [PubMed]

6. J. A. Domínguez-Caballero, S. Takahashi, G. Barbastathis, and S. J. Lee, “Design and sensitivity analysis of Fresnel domain computer generated holograms,” Int. J. Nanomanufacturing **6**(1/2/3/4), 207 (2010). [CrossRef]

8. H.-Y. Tsai, H. I. Smith, and R. Menon, “Reduction of focal-spot size using dichromats in absorbance modulation,” Opt. Lett. **33**(24), 2916–2918 (2008). [CrossRef] [PubMed]

9. T. Stone and N. George, “Hybrid diffractive-refractive lenses and achromats,” Appl. Opt. **27**(14), 2960–2971 (1988). [CrossRef] [PubMed]

10. Y. Arieli, S. Noach, S. Ozeri, and N. Eisenberg, “Design of diffractive optical elements for multiple wavelengths,” Appl. Opt. **37**(26), 6174–6177 (1998). [CrossRef] [PubMed]

11. D. W. Sweeney and G. E. Sommargren, “Harmonic diffractive lenses,” Appl. Opt. **34**(14), 2469–2475 (1995). [CrossRef] [PubMed]

12. S. Noach, A. Lewis, Y. Arieli, and N. Eisenberg, “Integrated diffractive andrefractive elements for spectrum shaping,” Appl. Opt. **35**(19), 3635–3639 (1996). [CrossRef] [PubMed]

13. M. A. Seldowitz, J. P. Allebach, and D. W. Sweeney, “Synthesis of digital holograms by direct binary search,” Appl. Opt. **26**(14), 2788–2798 (1987). [CrossRef] [PubMed]

14. T. R. M. Sales and D. H. Raguin, “Multiwavelength operation with thin diffractive elements,” Appl. Opt. **38**(14), 3012–3018 (1999). [CrossRef] [PubMed]

## 2. Optimization problem

_{pixels of size Δx}

_{and Δy}, along the

_{x}_{and}

_{y}_{-directions respectively. The DOE’s height profile is given by}and

*d*is the propagation distance, and

^{,}is a complex transmission function; the spatial frequencies are

*H*is the Fresnel transfer function:

6. J. A. Domínguez-Caballero, S. Takahashi, G. Barbastathis, and S. J. Lee, “Design and sensitivity analysis of Fresnel domain computer generated holograms,” Int. J. Nanomanufacturing **6**(1/2/3/4), 207 (2010). [CrossRef]

*B*with rows equal to

## 3. Design example

## 4. Parametric analysis

### 4.1 Number of height quantization levels

### 4.2 Reconstruction distance

### 4.3 Total number of pixels

13. M. A. Seldowitz, J. P. Allebach, and D. W. Sweeney, “Synthesis of digital holograms by direct binary search,” Appl. Opt. **26**(14), 2788–2798 (1987). [CrossRef] [PubMed]

### 4.4 Number of design wavelengths

## 5. Sensitivity analysis

### 5.1 Chromatic effects

### 4.2 Effect of defocus

*u*and

*v*are the spatial frequency coordinates. Hence, fixing the operating wavelength and varying the propagation distance is analogous to fixing the propagation distance and varying the illumination wavelength. Figure 7 shows the resulting average diffraction efficiency as a function of propagation distance,

*d*. The DOE was optimized for

### 4.3 Effect of pixel-height error

## 6. Summary and conclusions

## Acknowledgments

## References and links

1. | B. Kress and P. Meyrueis, |

2. | C. Dankwart, C. Falldorf, R. Gläbe, A. Meier, C. V. Kopylow, and R. B. Bergmann, “Design of diamond-turned holograms incorporating properties of the fabrication process,” Appl. Opt. |

3. | D. Faklis and G. M. Morris, “Spectral properties of multiorder diffractive lenses,” Appl. Opt. |

4. | D. Faklis and G. M. Morris, “Polychromatic diffractive lenses,” U.S. patent 5,589,982 (31 December 1996). |

5. | D. Prongué, H. P. Herzig, R. Dändliker, and M. T. Gale, “Optimized kinoform structures for highly efficient fan-out elements,” Appl. Opt. |

6. | J. A. Domínguez-Caballero, S. Takahashi, G. Barbastathis, and S. J. Lee, “Design and sensitivity analysis of Fresnel domain computer generated holograms,” Int. J. Nanomanufacturing |

7. | R. Menon, P. Rogge, and H.-Y. Tsai, “Design of diffractive lenses that generate optical nulls without phase singularities,” J. Opt. Soc. Am. A |

8. | H.-Y. Tsai, H. I. Smith, and R. Menon, “Reduction of focal-spot size using dichromats in absorbance modulation,” Opt. Lett. |

9. | T. Stone and N. George, “Hybrid diffractive-refractive lenses and achromats,” Appl. Opt. |

10. | Y. Arieli, S. Noach, S. Ozeri, and N. Eisenberg, “Design of diffractive optical elements for multiple wavelengths,” Appl. Opt. |

11. | D. W. Sweeney and G. E. Sommargren, “Harmonic diffractive lenses,” Appl. Opt. |

12. | S. Noach, A. Lewis, Y. Arieli, and N. Eisenberg, “Integrated diffractive andrefractive elements for spectrum shaping,” Appl. Opt. |

13. | M. A. Seldowitz, J. P. Allebach, and D. W. Sweeney, “Synthesis of digital holograms by direct binary search,” Appl. Opt. |

14. | T. R. M. Sales and D. H. Raguin, “Multiwavelength operation with thin diffractive elements,” Appl. Opt. |

**OCIS Codes**

(050.1970) Diffraction and gratings : Diffractive optics

(090.1995) Holography : Digital holography

**History**

Original Manuscript: November 23, 2011

Revised Manuscript: January 11, 2012

Manuscript Accepted: January 12, 2012

Published: January 23, 2012

**Citation**

Ganghun Kim, José A. Domínguez-Caballero, and Rajesh Menon, "Design and analysis of multi-wavelength diffractive optics," Opt. Express **20**, 2814-2823 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-3-2814

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### References

- B. Kress and P. Meyrueis, Digital Diffractive Optics: An Introduction to Planar Diffractive Optics and Related Technology (John Wiley, 2000).
- C. Dankwart, C. Falldorf, R. Gläbe, A. Meier, C. V. Kopylow, and R. B. Bergmann, “Design of diamond-turned holograms incorporating properties of the fabrication process,” Appl. Opt.49(20), 3949–3955 (2010). [CrossRef] [PubMed]
- D. Faklis and G. M. Morris, “Spectral properties of multiorder diffractive lenses,” Appl. Opt.34(14), 2462–2468 (1995). [CrossRef] [PubMed]
- D. Faklis and G. M. Morris, “Polychromatic diffractive lenses,” U.S. patent 5,589,982 (31 December 1996).
- D. Prongué, H. P. Herzig, R. Dändliker, and M. T. Gale, “Optimized kinoform structures for highly efficient fan-out elements,” Appl. Opt.31(26), 5706–5711 (1992). [CrossRef] [PubMed]
- J. A. Domínguez-Caballero, S. Takahashi, G. Barbastathis, and S. J. Lee, “Design and sensitivity analysis of Fresnel domain computer generated holograms,” Int. J. Nanomanufacturing6(1/2/3/4), 207 (2010). [CrossRef]
- R. Menon, P. Rogge, and H.-Y. Tsai, “Design of diffractive lenses that generate optical nulls without phase singularities,” J. Opt. Soc. Am. A26(2), 297–304 (2009). [CrossRef] [PubMed]
- H.-Y. Tsai, H. I. Smith, and R. Menon, “Reduction of focal-spot size using dichromats in absorbance modulation,” Opt. Lett.33(24), 2916–2918 (2008). [CrossRef] [PubMed]
- T. Stone and N. George, “Hybrid diffractive-refractive lenses and achromats,” Appl. Opt.27(14), 2960–2971 (1988). [CrossRef] [PubMed]
- Y. Arieli, S. Noach, S. Ozeri, and N. Eisenberg, “Design of diffractive optical elements for multiple wavelengths,” Appl. Opt.37(26), 6174–6177 (1998). [CrossRef] [PubMed]
- D. W. Sweeney and G. E. Sommargren, “Harmonic diffractive lenses,” Appl. Opt.34(14), 2469–2475 (1995). [CrossRef] [PubMed]
- S. Noach, A. Lewis, Y. Arieli, and N. Eisenberg, “Integrated diffractive andrefractive elements for spectrum shaping,” Appl. Opt.35(19), 3635–3639 (1996). [CrossRef] [PubMed]
- M. A. Seldowitz, J. P. Allebach, and D. W. Sweeney, “Synthesis of digital holograms by direct binary search,” Appl. Opt.26(14), 2788–2798 (1987). [CrossRef] [PubMed]
- T. R. M. Sales and D. H. Raguin, “Multiwavelength operation with thin diffractive elements,” Appl. Opt.38(14), 3012–3018 (1999). [CrossRef] [PubMed]

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