## Active aberration- and point-spread-function control in direct laser writing |

Optics Express, Vol. 20, Issue 22, pp. 24949-24956 (2012)

http://dx.doi.org/10.1364/OE.20.024949

Acrobat PDF (1895 KB)

### Abstract

We control the point-spread-function of high numerical aperture objectives used for direct laser writing with a spatial light modulator. Combining aberration correction with different types of amplitude filters to reduce the aspect ratio of the point-spread-function enhances the structural and optical quality of woodpile photonic crystals. Here, aberration correction is crucial to ensure the functionality of the filters. Measured point-spread-functions compare well with numerical calculations and with structures generated by direct laser writing. The shaped point-spread-function not only influences the maximum achievable three-dimensional resolution but also proximity effect and optical performance of woodpile photonic crystals.

© 2012 OSA

## 1. Introduction

2. M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. **3**, 444–447 (2004). [CrossRef] [PubMed]

3. F. Klein, T. Striebel, J. Fischer, Z. Jiang, C. M. Franz, G. von Freymann, M. Wegener, and M. Bastmeyer, “Elastic fully three-dimensional microstructure scaffolds for cell force measurements,” Adv. Mater. **22**, 868–871 (2010). [CrossRef] [PubMed]

4. T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science **328**, 337–339 (2010). [CrossRef] [PubMed]

5. N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nat. Mater. **7**, 31–37 (2008). [CrossRef]

6. J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science **325**, 1513–1515 (2009). [CrossRef] [PubMed]

7. M. Thiel, M. S. Rill, G. von Freymann, and M. Wegener, “Three-dimensional bi-chiral photonic crystals,” Adv. Mater. **21**, 4680–4682 (2009). [CrossRef]

8. T. Bückmann, N. Stenger, M. Kadic, J. Kaschke, A. Frölich, T. Kennerknecht, C. Eberl, M. Thiel, and M. Wegener, “Tailored 3D mechanical metamaterials made by dip-in direct-laser-writing optical lithography,” Adv. Mater. **24**, 2710–2714 (2012). [CrossRef] [PubMed]

9. G. von Freymann, A. Ledermann, M. Thiel, I. Staude, S. Essig, K. Busch, and M. Wegener, “Three-dimensional nanostructures for photonics,” Adv. Funct. Mater. **20**, 1038–1052 (2010). [CrossRef]

10. Here, as in many other publication, we refer to the iso-intensity surface. However, the actual shape is determined be the distribution of the electric-field (∝ |**E**|^{2} for one-photon absorption; ∝ |**E**|^{4} for two-photon absorption), as it is this field interacting with the photoinitiator molecules.

12. V. Schmidt, L. Kuna, V. Satzinger, G. Jakopic, and G. Leising, “Two-photon 3D lithography: a versatile fabrication method for complex 3D shapes and optical interconnects within the scope of innovative industrial applications,” JLMN **2**, 170–177 (2007). [CrossRef]

13. A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Mater. **5**, 942 (2006). [CrossRef] [PubMed]

14. M. Hermatschweiler, A. Ledermann, G. A. Ozin, M. Wegener, and G. von Freymann, “Fabrication of silicon inverse woodpile photonic crystals,” Adv. Funct. Mater. **17**, 2273–2277 (2007). [CrossRef]

15. M. A. A. Neil, R. Juškaitis, T. Wilson, Z. J. Laczik, and V. Sarafis, “Optimized pupil-plane filters for confocal microscope point-spread function engineering,” Opt. Lett. **25**, 245–247 (2000). [CrossRef]

16. P. S. Salter, A. Jesacher, J. B. Spring, B. J. Metcalf, N. Thomas-Peter, R. D. Simmonds, N. K. Langford, I. A. Walmsley, and M. J. Booth, “Adaptive slit beam shaping for direct laser written waveguides,” Opt. Lett. **37**, 470–472 (2012). [CrossRef] [PubMed]

17. M. Ams, G. D. Marshall, D. J. Spence, and M. J. Withford, “Slit beam shaping method for femtosecond laser direct-write fabrication of symmetric waveguides in bulk glasses,” Opt. Express **13**, 5676–5681 (2005). [CrossRef] [PubMed]

18. B. P. Cumming, A. Jesacher, M. J. Booth, T. Wilson, and M. Gu, “Adaptive aberration compensation for three-dimensional micro-fabrication of photonic crystals in lithium niobate,” Opt. Express **19**, 9419–9425 (2011). [CrossRef] [PubMed]

19. A. Jesacher and M. J. Booth, “Parallel direct laser writing in three dimensions with spatially dependent aberration correction,” Opt. Express **18**, 21091–21099 (2010). [CrossRef]

## 2. Experimental setup

20. J. A. Davis, J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, and I. Moreno, “Encoding amplitude information onto phase-only filters,” Appl. Optics **38**, 5004–5013 (1999). [CrossRef]

21. J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, “Vortex knots in light,” New J. Phys. **7**, 1–11 (2005). [CrossRef]

22. T. Wilson, R. Juškaitis, and P. Higdon, “The imaging of dielectric point scatterers in conventional and confocal polarisation microscopes,” Opt. Commun. **141**, 298–213 (1997). [CrossRef]

## 3. Methods and results

*χ*= 2.6, close to the theoretically predicted value of

*χ*= 2.44, by applying the correcting Zernike polynomials, mostly spherical aberration and coma. Additionally, the Strehl intensity increases by 20%. For the numerical calculation [23

23. A. S. van de Nes, L. Billy, S. F. Pereira, and J. J. M. Braat, “Calculation of the vectorial field distribution in a stratified focal region of a high numerical aperture imaging system,” Opt. Express **12**, 1281–1293 (2004). [CrossRef] [PubMed]

*r*

_{1}= 0.179

*r*;

_{p}*r*

_{2}= 0.982

*r*;

_{p}*t*

_{1}= 10.2%; SRFb:

*r*

_{1}= 0.26

*r*;

_{p}*r*

_{2}= 0.95

*r*;

_{p}*t*

_{1}= 10.2%, the definitions of the parameters are depicted in Fig. 1(b)). The corresponding PSFs are shown in column (c) and (d) for SRFa and SRFb. The absolute diffraction efficiencies of the underlying blazed gratings are adjusted to yield approximately the same Strehl intensity for all cases, causing the power on the entrance pupil to differ (around 11 mW on the unobscured pupil, 60 mW for SRFa and 42 mW for SRFb). While the two SRFs do not visually differ much in axial and lateral line widths SRFa results in a measured aspect ratio of

*χ*= 1.9 and SRFb even in

*χ*= 1.7. These values nicely correspond to theory (

*χ*= 1.82 and

*χ*= 1.75 respectively). Compared to the uncorrected objective, the aspect ratio improves by almost 41% (47%), compared to the aberration corrected objective still almost 27% (35%) are reached. However, the sidelobes of SRFa are considerably lower than the sidelobes of SRFb (23% compared to 35% of the peak intensity). Here, the question arises whether the smaller aspect ratio outweighs the increased sidelobe intensity. Without aberration correction the sidelobe intensities reach values above 50%, rendering the filters basically useless.

24. K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. **89**, 413–416 (1994). [CrossRef]

*χ*= 2.6 and

*χ*= 1.9 respectively (visualized by the dashed ellipse, six rods have been analyzed). The correspondence with theoretical expectations (

*χ*= 2.45 and

*χ*= 1.84, [25]) is very good. The samples also show the typical shrinkage on the order of 10%.

26. I. Staude, M. Thiel, S. Essig, C. Wolff, K. Busch, G. von Freymann, and M. Wegener, “Fabrication and characterization of silicon woodpile photonic crystals with a complete bandgap at telecom wavelengths,” Opt. Lett. **35**, 1094–1096 (2010). [CrossRef] [PubMed]

*χ*= 1.6 is reached with rod diameters above 100 nm. This is of great practical importance since rod diameters well below 80 nm tend to loose mechanical stability due to the reduced cross-linking density in direct consequence of reduced laser power. Collapsing or heavily deformed structures without clear spectral response are the result.

## 4. Conclusions

## Acknowledgments

## References and links

1. | S. Maruo and S. Kawata, “Two-photon-absorbed near-infrared photopolymerization for three-dimensional microfabrication,” JMEMS |

2. | M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. |

3. | F. Klein, T. Striebel, J. Fischer, Z. Jiang, C. M. Franz, G. von Freymann, M. Wegener, and M. Bastmeyer, “Elastic fully three-dimensional microstructure scaffolds for cell force measurements,” Adv. Mater. |

4. | T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science |

5. | N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nat. Mater. |

6. | J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science |

7. | M. Thiel, M. S. Rill, G. von Freymann, and M. Wegener, “Three-dimensional bi-chiral photonic crystals,” Adv. Mater. |

8. | T. Bückmann, N. Stenger, M. Kadic, J. Kaschke, A. Frölich, T. Kennerknecht, C. Eberl, M. Thiel, and M. Wegener, “Tailored 3D mechanical metamaterials made by dip-in direct-laser-writing optical lithography,” Adv. Mater. |

9. | G. von Freymann, A. Ledermann, M. Thiel, I. Staude, S. Essig, K. Busch, and M. Wegener, “Three-dimensional nanostructures for photonics,” Adv. Funct. Mater. |

10. | Here, as in many other publication, we refer to the iso-intensity surface. However, the actual shape is determined be the distribution of the electric-field (∝ | |

11. | M. Gu, |

12. | V. Schmidt, L. Kuna, V. Satzinger, G. Jakopic, and G. Leising, “Two-photon 3D lithography: a versatile fabrication method for complex 3D shapes and optical interconnects within the scope of innovative industrial applications,” JLMN |

13. | A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Mater. |

14. | M. Hermatschweiler, A. Ledermann, G. A. Ozin, M. Wegener, and G. von Freymann, “Fabrication of silicon inverse woodpile photonic crystals,” Adv. Funct. Mater. |

15. | M. A. A. Neil, R. Juškaitis, T. Wilson, Z. J. Laczik, and V. Sarafis, “Optimized pupil-plane filters for confocal microscope point-spread function engineering,” Opt. Lett. |

16. | P. S. Salter, A. Jesacher, J. B. Spring, B. J. Metcalf, N. Thomas-Peter, R. D. Simmonds, N. K. Langford, I. A. Walmsley, and M. J. Booth, “Adaptive slit beam shaping for direct laser written waveguides,” Opt. Lett. |

17. | M. Ams, G. D. Marshall, D. J. Spence, and M. J. Withford, “Slit beam shaping method for femtosecond laser direct-write fabrication of symmetric waveguides in bulk glasses,” Opt. Express |

18. | B. P. Cumming, A. Jesacher, M. J. Booth, T. Wilson, and M. Gu, “Adaptive aberration compensation for three-dimensional micro-fabrication of photonic crystals in lithium niobate,” Opt. Express |

19. | A. Jesacher and M. J. Booth, “Parallel direct laser writing in three dimensions with spatially dependent aberration correction,” Opt. Express |

20. | J. A. Davis, J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, and I. Moreno, “Encoding amplitude information onto phase-only filters,” Appl. Optics |

21. | J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, “Vortex knots in light,” New J. Phys. |

22. | T. Wilson, R. Juškaitis, and P. Higdon, “The imaging of dielectric point scatterers in conventional and confocal polarisation microscopes,” Opt. Commun. |

23. | A. S. van de Nes, L. Billy, S. F. Pereira, and J. J. M. Braat, “Calculation of the vectorial field distribution in a stratified focal region of a high numerical aperture imaging system,” Opt. Express |

24. | K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun. |

25. | While PSF measurements are ∝ | |

26. | I. Staude, M. Thiel, S. Essig, C. Wolff, K. Busch, G. von Freymann, and M. Wegener, “Fabrication and characterization of silicon woodpile photonic crystals with a complete bandgap at telecom wavelengths,” Opt. Lett. |

27. | J. Fischer and M. Wegener, “Three-dimensional optical laser lithography beyond the diffraction limit,” Laser Photonics Rev. 1–23 (2012). |

**OCIS Codes**

(050.6624) Diffraction and gratings : Subwavelength structures

(050.6875) Diffraction and gratings : Three-dimensional fabrication

(070.6120) Fourier optics and signal processing : Spatial light modulators

**ToC Category:**

Laser Microfabrication

**History**

Original Manuscript: August 30, 2012

Revised Manuscript: October 11, 2012

Manuscript Accepted: October 11, 2012

Published: October 16, 2012

**Citation**

Erik H. Waller, Michael Renner, and Georg von Freymann, "Active aberration- and point-spread-function control in direct laser writing," Opt. Express **20**, 24949-24956 (2012)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-22-24949

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### References

- S. Maruo and S. Kawata, “Two-photon-absorbed near-infrared photopolymerization for three-dimensional microfabrication,” JMEMS7, 411–415 (1998).
- M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater.3, 444–447 (2004). [CrossRef] [PubMed]
- F. Klein, T. Striebel, J. Fischer, Z. Jiang, C. M. Franz, G. von Freymann, M. Wegener, and M. Bastmeyer, “Elastic fully three-dimensional microstructure scaffolds for cell force measurements,” Adv. Mater.22, 868–871 (2010). [CrossRef] [PubMed]
- T. Ergin, N. Stenger, P. Brenner, J. B. Pendry, and M. Wegener, “Three-dimensional invisibility cloak at optical wavelengths,” Science328, 337–339 (2010). [CrossRef] [PubMed]
- N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, “Three-dimensional photonic metamaterials at optical frequencies,” Nat. Mater.7, 31–37 (2008). [CrossRef]
- J. K. Gansel, M. Thiel, M. S. Rill, M. Decker, K. Bade, V. Saile, G. von Freymann, S. Linden, and M. Wegener, “Gold helix photonic metamaterial as broadband circular polarizer,” Science325, 1513–1515 (2009). [CrossRef] [PubMed]
- M. Thiel, M. S. Rill, G. von Freymann, and M. Wegener, “Three-dimensional bi-chiral photonic crystals,” Adv. Mater.21, 4680–4682 (2009). [CrossRef]
- T. Bückmann, N. Stenger, M. Kadic, J. Kaschke, A. Frölich, T. Kennerknecht, C. Eberl, M. Thiel, and M. Wegener, “Tailored 3D mechanical metamaterials made by dip-in direct-laser-writing optical lithography,” Adv. Mater.24, 2710–2714 (2012). [CrossRef] [PubMed]
- G. von Freymann, A. Ledermann, M. Thiel, I. Staude, S. Essig, K. Busch, and M. Wegener, “Three-dimensional nanostructures for photonics,” Adv. Funct. Mater.20, 1038–1052 (2010). [CrossRef]
- Here, as in many other publication, we refer to the iso-intensity surface. However, the actual shape is determined be the distribution of the electric-field (∝ |E|2 for one-photon absorption; ∝ |E|4 for two-photon absorption), as it is this field interacting with the photoinitiator molecules.
- M. Gu, Advanced Optical Imaging Theory (Springer, Berlin Heidelberg, 2000)
- V. Schmidt, L. Kuna, V. Satzinger, G. Jakopic, and G. Leising, “Two-photon 3D lithography: a versatile fabrication method for complex 3D shapes and optical interconnects within the scope of innovative industrial applications,” JLMN2, 170–177 (2007). [CrossRef]
- A. Ledermann, L. Cademartiri, M. Hermatschweiler, C. Toninelli, G. A. Ozin, D. S. Wiersma, M. Wegener, and G. von Freymann, “Three-dimensional silicon inverse photonic quasicrystals for infrared wavelengths,” Nat. Mater.5, 942 (2006). [CrossRef] [PubMed]
- M. Hermatschweiler, A. Ledermann, G. A. Ozin, M. Wegener, and G. von Freymann, “Fabrication of silicon inverse woodpile photonic crystals,” Adv. Funct. Mater.17, 2273–2277 (2007). [CrossRef]
- M. A. A. Neil, R. Juškaitis, T. Wilson, Z. J. Laczik, and V. Sarafis, “Optimized pupil-plane filters for confocal microscope point-spread function engineering,” Opt. Lett.25, 245–247 (2000). [CrossRef]
- P. S. Salter, A. Jesacher, J. B. Spring, B. J. Metcalf, N. Thomas-Peter, R. D. Simmonds, N. K. Langford, I. A. Walmsley, and M. J. Booth, “Adaptive slit beam shaping for direct laser written waveguides,” Opt. Lett.37, 470–472 (2012). [CrossRef] [PubMed]
- M. Ams, G. D. Marshall, D. J. Spence, and M. J. Withford, “Slit beam shaping method for femtosecond laser direct-write fabrication of symmetric waveguides in bulk glasses,” Opt. Express13, 5676–5681 (2005). [CrossRef] [PubMed]
- B. P. Cumming, A. Jesacher, M. J. Booth, T. Wilson, and M. Gu, “Adaptive aberration compensation for three-dimensional micro-fabrication of photonic crystals in lithium niobate,” Opt. Express19, 9419–9425 (2011). [CrossRef] [PubMed]
- A. Jesacher and M. J. Booth, “Parallel direct laser writing in three dimensions with spatially dependent aberration correction,” Opt. Express18, 21091–21099 (2010). [CrossRef]
- J. A. Davis, J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, and I. Moreno, “Encoding amplitude information onto phase-only filters,” Appl. Optics38, 5004–5013 (1999). [CrossRef]
- J. Leach, M. R. Dennis, J. Courtial, and M. J. Padgett, “Vortex knots in light,” New J. Phys.7, 1–11 (2005). [CrossRef]
- T. Wilson, R. Juškaitis, and P. Higdon, “The imaging of dielectric point scatterers in conventional and confocal polarisation microscopes,” Opt. Commun.141, 298–213 (1997). [CrossRef]
- A. S. van de Nes, L. Billy, S. F. Pereira, and J. J. M. Braat, “Calculation of the vectorial field distribution in a stratified focal region of a high numerical aperture imaging system,” Opt. Express12, 1281–1293 (2004). [CrossRef] [PubMed]
- K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: new layer-by-layer periodic structures,” Solid State Commun.89, 413–416 (1994). [CrossRef]
- While PSF measurements are ∝ |E|2, the two-photon polymerization is ∝ |E|4. This and the difference between the index of refraction of immersion oil (1.518) and photoresist (1.47) explains the difference in the expected aspect ratios.
- I. Staude, M. Thiel, S. Essig, C. Wolff, K. Busch, G. von Freymann, and M. Wegener, “Fabrication and characterization of silicon woodpile photonic crystals with a complete bandgap at telecom wavelengths,” Opt. Lett.35, 1094–1096 (2010). [CrossRef] [PubMed]
- J. Fischer and M. Wegener, “Three-dimensional optical laser lithography beyond the diffraction limit,” Laser Photonics Rev.1–23 (2012).

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