## Modeling focusing characteristics of low F-number diffractive optical elements with continuous relief fabricated by laser direct writing

Optics Express, Vol. 15, Issue 25, pp. 17032-17037 (2007)

http://dx.doi.org/10.1364/OE.15.017032

Acrobat PDF (239 KB)

### Abstract

A theoretical model is established using Rayleigh-Sommerfeld diffraction theory to describe the diffraction focusing characteristics of low F-number diffractive optical elements with continuous relief fabricated by laser direct writing, and continuous-relief diffractive optical elements with a design wavelength of 441.6nm and a F-number of F/4 are fabricated and measured to verify the validity of the diffraction focusing model. The measurements made indicate that the spot size is 1.75µm and the diffraction efficiency is 70.7% at the design wavelength, which coincide well with the theoretical results: a spot size of 1.66µm and a diffraction efficiency of 71.2%.

© 2007 Optical Society of America

## 1. Introduction

1. P. Ehbets, M. Rossi, and H. P. Herzig, “Continuous-relief fan-out elements with optimized fabrication tolerance,” Opt. Eng. **34**, 3456–3464 (1995). [CrossRef]

3. D. Feng, Y. Yan, G. Jin, and S. Fan, “Design and fabrication of continuous-profile diffractive micro-optical elements as a beam splitter,” Appl. Opt. **43**, 5476–5480 (2004). [CrossRef] [PubMed]

4. R. Yang, K.F. Chan, Z. Feng, I. Akihito, and W. Mei, “Design and fabrication of microlens and spatial filter array by self-alignment for maskless lithography systems,” J. Microlith. Microfab. Microsyst. **2**, 210–219 (2003). [CrossRef]

6. J. B. Tan, M.G. Shan, J. Liu, H. Zhang, and C.G. Zhao. “Model analysis of effect of diffraction focus characteristics of microlens arrays on parallel laser direct writing quality,” Opt. Commun. **277**, 237–240(2007). [CrossRef]

9. V. P. Korolkov, R. K. Nasyrov, and R. V. Shimansky, “Zone-boundary optimization for direct laser writing of continuous-relief diffractive optical elements,” Appl. Opt. **45**, 53–62 (2006). [CrossRef] [PubMed]

10. M. Okano, H. Kikuta, Y. Hirai, K. Yamamoto, and T. Yotsuya, “Optimization of diffraction grating profiles in fabrication by electron-beam lithography,” Appl. Opt. **43**, 5137–5142 (2004). [CrossRef] [PubMed]

2. F. Yong-Qi, N. Kok Ann Bryan, and O. Shing, “Diffractive optical elements with continuous relief fabricated by focused ion beam for monomode fiber coupling,” Opt. Express **7**, 141–147 (2000). [CrossRef] [PubMed]

9. V. P. Korolkov, R. K. Nasyrov, and R. V. Shimansky, “Zone-boundary optimization for direct laser writing of continuous-relief diffractive optical elements,” Appl. Opt. **45**, 53–62 (2006). [CrossRef] [PubMed]

11. M. Kuittinen, H. P. Herzig, and P. Ehbets, “Improvements in diffraction efficiency of gratings and microlenses with continuous relief structures,” Opt. Commun. **120**, 230–234 (1995). [CrossRef]

14. I. Kallioniemi, T. Ammer, and M. Rossi, “Optimization of continuous-profile blazed gratings using rigorous diffraction theory,” Opt. Commun. **177**, 15–24 (2000). [CrossRef]

9. V. P. Korolkov, R. K. Nasyrov, and R. V. Shimansky, “Zone-boundary optimization for direct laser writing of continuous-relief diffractive optical elements,” Appl. Opt. **45**, 53–62 (2006). [CrossRef] [PubMed]

11. M. Kuittinen, H. P. Herzig, and P. Ehbets, “Improvements in diffraction efficiency of gratings and microlenses with continuous relief structures,” Opt. Commun. **120**, 230–234 (1995). [CrossRef]

14. I. Kallioniemi, T. Ammer, and M. Rossi, “Optimization of continuous-profile blazed gratings using rigorous diffraction theory,” Opt. Commun. **177**, 15–24 (2000). [CrossRef]

*F*/#) array is usually utilized to enhance the writing resolution. It is therefore of great significance to accurately characterize the focusing characteristics of each DOE in the array to improve the pattern fidelity through exposure dose modulation [5

5. R. Menon, D. Gil, and H. I. Smith, “Experimental characterization of focusing by high-numerical-aperture zone plates,” J. Opt. Soc. Am. A **23**, 567–571 (2006). [CrossRef]

## 2. Diffraction focusing model of DOEs with continuous relief

2. F. Yong-Qi, N. Kok Ann Bryan, and O. Shing, “Diffractive optical elements with continuous relief fabricated by focused ion beam for monomode fiber coupling,” Opt. Express **7**, 141–147 (2000). [CrossRef] [PubMed]

13. T. Hessler, M. Rossi, R. E. Kunz, and M. T. Gale, “Analysis and optimization of fabrication of continuous-relief diffractive optical elements,” Appl. Opt. **37**, 4069–4079 (1998). [CrossRef]

*r*is the radius of the

_{m}*m*-th zone of DOEs, which can be given by

*p*is the phase depth factor used to optimize the relief depth and the radius of zone to make the fabrication easy;

*f*

_{0}is the focal length of the DOEs for design wavelength λ

_{0};

*n*

_{0}is the refractive index of DOEs material for design wavelength λ

_{0};

*c*and

*K*are the factors used to determine the relief curvature which can be given by

*φ*(

_{s}*r*) with Gaussian intensity distribution

*I*(

*r*) in the writing spot [9

**45**, 53–62 (2006). [CrossRef] [PubMed]

11. M. Kuittinen, H. P. Herzig, and P. Ehbets, “Improvements in diffraction efficiency of gratings and microlenses with continuous relief structures,” Opt. Commun. **120**, 230–234 (1995). [CrossRef]

14. I. Kallioniemi, T. Ammer, and M. Rossi, “Optimization of continuous-profile blazed gratings using rigorous diffraction theory,” Opt. Commun. **177**, 15–24 (2000). [CrossRef]

*φ*(

_{c}*r*) is the phase function of the DOEs with continuous relief fabricated;

*φ*(

_{s}*r*) is the phase function

*φ*

_{0}(

*r*) sampled by the interscan distance rs, which can be given by

*I*(

*r*) in the writing spot can be expressed as

*ω*is the radius of

*I*(

*r*) at maximum intensity level

*e*

^{-2}of the writing spot.

15. N. Delen and B. Hooker, “Free-space beam propagation between arbitrarily oriented planes based on full diffraction theory: a fast Fourier transform approach,” J. Opt. Soc. Am. A **15**, 857–867 (1998). [CrossRef]

*U*

_{1}(

*x*

_{1},

*y*

_{1}) in the back focal plane of DOEs.

*U*

_{1}(

*x*

_{1},

*y*

_{1}) can then be given by

*F*and

*F*

^{-1}denote the forward and inverse Fourier transforms, respectively;

*U*

_{0}(

*x, y*) is the complex amplitude distribution of the incident plane wave;

*H*(

*v*) is the transform function of free-space propagation from DOEs to the focal plane;

_{x}, v_{y}*z*

_{12}is the distance of propagation from DOEs to the back focal plane;

*v*=sin

_{x}*θ*/λ and

_{x}*v*=sin

_{y}*θ*/λ are spatial frequencies.

_{y}## 3. Analysis

**45**, 53–62 (2006). [CrossRef] [PubMed]

*p*=3 [16

16. M. Rossi, R. E. Kunz, and H. P. Herzig, “Refractive and diffractive properties of planar micro-optical elements,” Appl. Opt. **34**, 5996–6007 (1995). [CrossRef] [PubMed]

_{E}=1.75µm) is slightly larger than the theoretical spot size (FWHM

_{T}=1.66µm).

## 4. Conclusion

## Acknowledgments

## References and links

1. | P. Ehbets, M. Rossi, and H. P. Herzig, “Continuous-relief fan-out elements with optimized fabrication tolerance,” Opt. Eng. |

2. | F. Yong-Qi, N. Kok Ann Bryan, and O. Shing, “Diffractive optical elements with continuous relief fabricated by focused ion beam for monomode fiber coupling,” Opt. Express |

3. | D. Feng, Y. Yan, G. Jin, and S. Fan, “Design and fabrication of continuous-profile diffractive micro-optical elements as a beam splitter,” Appl. Opt. |

4. | R. Yang, K.F. Chan, Z. Feng, I. Akihito, and W. Mei, “Design and fabrication of microlens and spatial filter array by self-alignment for maskless lithography systems,” J. Microlith. Microfab. Microsyst. |

5. | R. Menon, D. Gil, and H. I. Smith, “Experimental characterization of focusing by high-numerical-aperture zone plates,” J. Opt. Soc. Am. A |

6. | J. B. Tan, M.G. Shan, J. Liu, H. Zhang, and C.G. Zhao. “Model analysis of effect of diffraction focus characteristics of microlens arrays on parallel laser direct writing quality,” Opt. Commun. |

7. | M. T. Gale , “Direct writing of continuous-relief elements,” in Micro-Optics-Elements, Systems, and Applications, H. P. Herzig, ed. (Taylor & Francis, London, 1997). |

8. | M.T. Gale, M. Rossi, J. Pedersen, and H. Schutz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists,” Opt. Eng. |

9. | V. P. Korolkov, R. K. Nasyrov, and R. V. Shimansky, “Zone-boundary optimization for direct laser writing of continuous-relief diffractive optical elements,” Appl. Opt. |

10. | M. Okano, H. Kikuta, Y. Hirai, K. Yamamoto, and T. Yotsuya, “Optimization of diffraction grating profiles in fabrication by electron-beam lithography,” Appl. Opt. |

11. | M. Kuittinen, H. P. Herzig, and P. Ehbets, “Improvements in diffraction efficiency of gratings and microlenses with continuous relief structures,” Opt. Commun. |

12. | T. Hessler and R. E. Kunz, “Relaxed fabrication tolerances for low-Fresnel-number lenses,” J. Opt. Soc. Am. A |

13. | T. Hessler, M. Rossi, R. E. Kunz, and M. T. Gale, “Analysis and optimization of fabrication of continuous-relief diffractive optical elements,” Appl. Opt. |

14. | I. Kallioniemi, T. Ammer, and M. Rossi, “Optimization of continuous-profile blazed gratings using rigorous diffraction theory,” Opt. Commun. |

15. | N. Delen and B. Hooker, “Free-space beam propagation between arbitrarily oriented planes based on full diffraction theory: a fast Fourier transform approach,” J. Opt. Soc. Am. A |

16. | M. Rossi, R. E. Kunz, and H. P. Herzig, “Refractive and diffractive properties of planar micro-optical elements,” Appl. Opt. |

**OCIS Codes**

(050.1970) Diffraction and gratings : Diffractive optics

(220.4000) Optical design and fabrication : Microstructure fabrication

(260.1960) Physical optics : Diffraction theory

**ToC Category:**

Diffraction and Gratings

**History**

Original Manuscript: September 28, 2007

Revised Manuscript: November 13, 2007

Manuscript Accepted: November 23, 2007

Published: December 5, 2007

**Citation**

Mingguang Shan and Jiubin Tan, "Modeling focusing characteristics of low Fnumber diffractive optical elements with continuous relief fabricated by laser direct writing," Opt. Express **15**, 17032-17037 (2007)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-15-25-17032

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### References

- P. Ehbets, M. Rossi, and H. P. Herzig, "Continuous-relief fan-out elements with optimized fabrication tolerance," Opt. Eng. 34, 3456-3464 (1995). [CrossRef]
- F. Yong-Qi, N. Kok Ann Bryan, and O. Shing, "Diffractive optical elements with continuous relief fabricated by focused ion beam for monomode fiber coupling," Opt. Express 7, 141-147 (2000). [CrossRef] [PubMed]
- D. Feng, Y. Yan, G. Jin, and S. Fan, "Design and fabrication of continuous-profile diffractive micro-optical elements as a beam splitter," Appl. Opt. 43, 5476-5480 (2004). [CrossRef] [PubMed]
- R. Yang, K.F. Chan, Z. Feng, I. Akihito, and W. Mei, "Design and fabrication of microlens and spatial filter array by self-alignment for maskless lithography systems," J. Microlithogr. Microfabr. Microsyst. 2, 210-219 (2003). [CrossRef]
- R. Menon, D. Gil, and H. I. Smith, "Experimental characterization of focusing by high-numerical-aperture zone plates," J. Opt. Soc. Am. A 23, 567-571 (2006). [CrossRef]
- J. B. Tan, M.G. Shan, J. Liu, H. Zhang, and C.G. Zhao. "Model analysis of effect of diffraction focus characteristics of microlens arrays on parallel laser direct writing quality," Opt. Commun. 277, 237-240(2007). [CrossRef]
- M. T. Gale, "Direct writing of continuous-relief elements," in Micro-Optics-Elements, Systems, and Applications, H. P. Herzig, ed., (Taylor & Francis, London, 1997).
- M. T. Gale, M. Rossi, J. Pedersen, and H. Schutz, "Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresists," Opt. Eng. 33, 3556-3566 (1994). [CrossRef]
- V. P. Korolkov, R. K. Nasyrov, and R. V. Shimansky, "Zone-boundary optimization for direct laser writing of continuous-relief diffractive optical elements," Appl. Opt. 45, 53-62 (2006). [CrossRef] [PubMed]
- M. Okano, H. Kikuta, Y. Hirai, K. Yamamoto, and T. Yotsuya, "Optimization of diffraction grating profiles in fabrication by electron-beam lithography," Appl. Opt. 43, 5137-5142 (2004). [CrossRef] [PubMed]
- M. Kuittinen, H. P. Herzig, and P. Ehbets, "Improvements in diffraction efficiency of gratings and microlenses with continuous relief structures," Opt. Commun. 120, 230-234 (1995). [CrossRef]
- T. Hessler and R. E. Kunz, "Relaxed fabrication tolerances for low-Fresnel-number lenses," J. Opt. Soc. Am. A 14, 1599- 1606 (1997). [CrossRef]
- T. Hessler, M. Rossi, R. E. Kunz, and M. T. Gale, "Analysis and optimization of fabrication of continuous-relief diffractive optical elements," Appl. Opt. 37, 4069-4079 (1998). [CrossRef]
- I. Kallioniemi, T. Ammer, and M. Rossi, "Optimization of continuous-profile blazed gratings using rigorous diffraction theory," Opt. Commun. 177, 15-24 (2000). [CrossRef]
- N. Delen and B. Hooker, "Free-space beam propagation between arbitrarily oriented planes based on full diffraction theory: a fast Fourier transform approach," J. Opt. Soc. Am. A 15, 857-867 (1998). [CrossRef]
- M. Rossi, R. E. Kunz, and H. P. Herzig, "Refractive and diffractive properties of planar micro-optical elements," Appl. Opt. 34, 5996-6007 (1995). [CrossRef] [PubMed]

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