# Nanopillar Diffraction Gratings by Two-Photon Lithography

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## Abstract

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## 1. Introduction

## 2. Experimental

#### 2.1. Two-Photon Lithography (TPL)

#### 2.2. Scanning Electron Microscopy (SEM)

#### 2.3. Optical Microscopy

## 3. Numerical Simulations

#### 3.1. Voxel Sizes

^{5}contributions per pixel) were averaged into one field vector approximating the electrical field with full phase information at the center of each pixel. The square of the above field vector, $I={\overrightarrow{E}}^{2}$, is a relative intensity proportional to the physical intensity; the factor of proportionality arising from all the constants explicitly or implicitly omitted above. To calculate voxel sizes as a function of the laser power, this intensity distribution needs to be correlated to the laser power. We start by expressing the latter as a factor $f$ times the threshold laser power (determined to be 9.3 mW by the analysis of the observed pillar diameters according to Equation (1); see Figure 1b). On the other hand, the above intensity distribution has a maximum ${I}_{max}$ at the focal spot. At the threshold laser power ($f=1$), this maximum is equivalent to the polymerization threshold ${I}_{th}$, ${I}_{max}={I}_{th}$. At a higher laser power, the whole intensity distribution is multiplied by $f$, and polymerization is initiated wherever the scaled intensity exceeds the threshold. The theoretical height of a voxel is thus determined as the size of the interval in a longitudinal section through the intensity map where $f\xb7I>{I}_{th}$. To derive the width of the voxel, the same analysis is applied to the cross-section.

#### 3.2. Optical Spectra

## 4. Results and Discussion

#### 4.1. Nanopillar Sizes

#### 4.2. Optical Properties

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Catchpole, K.R.; Green, M.A. A conceptual model of light coupling by pillar diffraction gratings. J. Appl. Phys.
**2007**, 101, 063105. [Google Scholar] [CrossRef] - Chong, T.K.; Wilson, J.; Mokkapati, S.; Catchpole, K.R. Optimal wavelength scale diffraction gratings for light trapping in solar cells. J. Opt.
**2012**, 14, 024012. [Google Scholar] [CrossRef] - Yan, H.; Huang, L.; Xu, X.; Chakravarty, S.; Tang, N.; Tian, H.; Chen, R.T. Unique surface sensing property and enhanced sensitivity in microring resonator biosensors based on subwavelength grating waveguides. Opt. Express
**2016**, 24, 29724–29733. [Google Scholar] [CrossRef] [PubMed] - Mao, X.; Zeng, L. Design and fabrication of crossed gratings with multiple zero-reference marks for planar encoders. Meas. Sci. Technol.
**2018**, 29, 025204. [Google Scholar] [CrossRef] - Kim, D.Y.; Tripathy, S.K.; Li, L.; Kumar, J. Laser-induced holographic surface relief gratings on nonlinear optical polymer films. Appl. Phys. Lett.
**1995**, 66, 1166–1168. [Google Scholar] [CrossRef] - Gale, M.T.; Knop, K.; Morf, R.H. Zero-Order Diffractive Microstructures for Security Applications; SPIE: Bellingham, WA, USA, 1990; Volume 1210. [Google Scholar]
- Wang, Y.; Lu, N.; Xu, H.; Shi, G.; Xu, M.; Lin, X.; Li, H.; Wang, W.; Qi, D.; Lu, Y.; et al. Biomimetic corrugated silicon nanocone arrays for self-cleaning antireflection coatings. Nano Res.
**2010**, 3, 520–527. [Google Scholar] [CrossRef][Green Version] - Dewan, R.; Fischer, S.; Meyer-Rochow, V.B.; Özdemir, Y.; Hamraz, S.; Knipp, D. Studying nanostructured nipple arrays of moth eye facets helps to design better thin film solar cells. Bioinspiration Biomim.
**2011**, 7, 016003. [Google Scholar] [CrossRef] - Ji, S.; Park, J.; Lim, H. Improved antireflection properties of moth eye mimicking nanopillars on transparent glass: Flat antireflection and color tuning. Nanoscale
**2012**, 4, 4603–4610. [Google Scholar] [CrossRef] - Lora Gonzalez, F.; Chan, L.; Berry, A.; Morse, D.E.; Gordon, M.J. Simple colloidal lithography method to fabricate large-area moth-eye antireflective structures on Si, Ge, and GaAs for IR applications. J. Vac. Sci. Technol. B
**2014**, 32, 051213. [Google Scholar] [CrossRef] - Chigrin, D.N.; Lavrinenko, A.V. Nanopillar Coupled Periodic Waveguides: From Basic Properties to Applications; SPIE: Bellingham, WA, USA, 2006; Volume 6393. [Google Scholar]
- Farsari, M.; Chichkov, B.N. Materials processing: Two-photon fabrication. Nat. Photonics
**2009**, 3, 450–452. [Google Scholar] [CrossRef] - Gissibl, T.; Thiele, S.; Herkommer, A.; Giessen, H. Two-photon direct laser writing of ultracompact multi-lens objectives. Nat. Photonics
**2016**, 10, 554–560. [Google Scholar] [CrossRef] - Hohmann, J.K.; Renner, M.; Waller, E.H.; von Freymann, G. Three-Dimensional μ-Printing: An Enabling Technology. Adv. Opt. Mater.
**2015**, 3, 1488–1507. [Google Scholar] [CrossRef] - Kawata, S.; Sun, H.B.; Tanaka, T.; Takada, K. Finer features for functional microdevices. Nature
**2001**, 412, 697. [Google Scholar] [CrossRef] [PubMed] - Waheed, S.; Cabot, J.M.; Macdonald, N.P.; Lewis, T.; Guijt, R.M.; Paull, B.; Breadmore, M.C. 3D printed microfluidic devices: Enablers and barriers. Lab Chip
**2016**, 16, 1993–2013. [Google Scholar] [CrossRef] [PubMed] - Fischer, S.C.L.; Groß, K.; Torrents Abad, O.; Becker, M.M.; Park, E.; Hensel, R.; Arzt, E. Funnel-Shaped Microstructures for Strong Reversible Adhesion. Adv. Mater. Interfaces
**2017**, 4, 1700292. [Google Scholar] [CrossRef] - Hensel, R.; Moh, K.; Arzt, E. Engineering Micropatterned Dry Adhesives: From Contact Theory to Handling Applications. Adv. Funct. Mater.
**2018**, 28, 1800865. [Google Scholar] [CrossRef] - Marino, A.; Filippeschi, C.; Mattoli, V.; Mazzolai, B.; Ciofani, G. Biomimicry at the nanoscale: Current research and perspectives of two-photon polymerization. Nanoscale
**2015**, 7, 2841–2850. [Google Scholar] [CrossRef] - Wolfenson, H.; Meacci, G.; Liu, S.; Stachowiak, M.R.; Iskratsch, T.; Ghassemi, S.; Roca-Cusachs, P.; O’Shaughnessy, B.; Hone, J.; Sheetz, M.P. Tropomyosin controls sarcomere-like contractions for rigidity sensing and suppressing growth on soft matrices. Nat. Cell Biol.
**2015**, 18, 33. [Google Scholar] [CrossRef] - Marino, A.; Ciofani, G.; Filippeschi, C.; Pellegrino, M.; Pellegrini, M.; Orsini, P.; Pasqualetti, M.; Mattoli, V.; Mazzolai, B. Two-Photon Polymerization of Sub-micrometric Patterned Surfaces: Investigation of Cell-Substrate Interactions and Improved Differentiation of Neuron-like Cells. ACS Appl. Mater. Interfaces
**2013**, 5, 13012–13021. [Google Scholar] [CrossRef] - Klein, F.; Striebel, T.; Fischer, J.; Jiang, Z.; Franz, C.M.; von Freymann, G.; Wegener, M.; Bastmeyer, M. Elastic Fully Three-dimensional Microstructure Scaffolds for Cell Force Measurements. Adv. Mater.
**2010**, 22, 868–871. [Google Scholar] [CrossRef] - Thiele, S.; Arzenbacher, K.; Gissibl, T.; Giessen, H.; Herkommer, A.M. 3D-printed eagle eye: Compound microlens system for foveated imaging. Sci. Adv.
**2017**, 3. [Google Scholar] [CrossRef] [PubMed] - von Freymann, G.; Ledermann, A.; Thiel, M.; Staude, I.; Essig, S.; Busch, K.; Wegener, M. Three-Dimensional Nanostructures for Photonics. Adv. Funct. Mater.
**2010**, 20, 1038–1052. [Google Scholar] [CrossRef] - Nawrot, M.; Zinkiewicz, Ł.; Włodarczyk, B.; Wasylczyk, P. Transmission phase gratings fabricated with direct laser writing as color filters in the visible. Opt. Express
**2013**, 21, 31919–31924. [Google Scholar] [CrossRef] [PubMed] - Mueller, J.B.; Fischer, J.; Mayer, F.; Kadic, M.; Wegener, M. Polymerization Kinetics in Three-Dimensional Direct Laser Writing. Adv. Mater.
**2014**, 26, 6566–6571. [Google Scholar] [CrossRef] [PubMed] - Sun, H.B.; Maeda, M.; Takada, K.; Chon, J.W.M.; Gu, M.; Kawata, S. Experimental investigation of single voxels for laser nanofabrication via two-photon photopolymerization. Appl. Phys. Lett.
**2003**, 83, 819–821. [Google Scholar] [CrossRef] - Fischer, J.; Wegener, M. Three-dimensional optical laser lithography beyond the diffraction limit. Laser Photonics Rev.
**2013**, 7, 22–44. [Google Scholar] [CrossRef] - Xing, J.F.; Dong, X.Z.; Chen, W.Q.; Duan, X.M.; Takeyasu, N.; Tanaka, T.; Kawata, S. Improving spatial resolution of two-photon microfabrication by using photoinitiator with high initiating efficiency. Appl. Phys. Lett.
**2007**, 90, 131106. [Google Scholar] [CrossRef] - Tanaka, T.S.; Sun, H.B.; Kawata, S. Rapid sub-diffraction-limit laser micro/nanoprocessing in a threshold material system. Appl. Phys. Lett.
**2002**, 80, 312–314. [Google Scholar] [CrossRef] - Fischer, J.; Mueller, J.B.; Quick, A.S.; Kaschke, J.; Barner-Kowollik, C.; Wegener, M. Exploring the Mechanisms in STED-Enhanced Direct Laser Writing. Adv. Opt. Mater.
**2015**, 3, 221–232. [Google Scholar] [CrossRef] - Sun, H.B.; Takada, K.; Kim, M.S.; Lee, K.S.; Kawata, S. Scaling Laws of Voxels in Two-Photon Photopolymerization Nanofabrication. Appl. Phys. Lett.
**2003**, 83, 1104–1106. [Google Scholar] [CrossRef] - Sun, H.B.; Suwa, T.; Takada, K.; Zaccaria, R.P.; Kim, M.S.; Lee, K.S.; Kawata, S. Shape precompensation in two-photon laser nanowriting of photonic lattices. Appl. Phys. Lett.
**2004**, 85, 3708–3710. [Google Scholar] [CrossRef] - LaFratta, C.; Baldacchini, T. Two-Photon Polymerization Metrology: Characterization Methods of Mechanisms and Microstructures. Micromachines
**2017**, 8, 101. [Google Scholar] [CrossRef] - Hu, Y.; Lao, Z.; Cumming, B.P.; Wu, D.; Li, J.; Liang, H.; Chu, J.; Huang, W.; Gu, M. Laser printing hierarchical structures with the aid of controlled capillary-driven self-assembly. Proc. Natl. Acad. Sci. USA
**2015**, 112, 6876–6881. [Google Scholar] [CrossRef] [PubMed][Green Version] - Purtov, J.; Verch, A.; Rogin, P.; Hensel, R. Improved development procedure to enhance the stability of microstructures created by two-photon polymerization. Microelectron. Eng.
**2018**, 194, 45–50. [Google Scholar] [CrossRef] - Roca-Cusachs, P.; Rico, F.; Martínez, E.; Toset, J.; Farré, R.; Navajas, D. Stability of Microfabricated High Aspect Ratio Structures in Poly(dimethylsiloxane). Langmuir
**2005**, 21, 5542–5548. [Google Scholar] [CrossRef] [PubMed] - Chandra, D.; Yang, S. Capillary-Force-Induced Clustering of Micropillar Arrays: Is It Caused by Isolated Capillary Bridges or by the Lateral Capillary Meniscus Interaction Force? Langmuir
**2009**, 25, 10430–10434. [Google Scholar] [CrossRef] - Liu, V.; Fan, S. S4: A free electromagnetic solver for layered periodic structures. Comput. Phys. Commun.
**2012**, 183, 2233–2244. [Google Scholar] [CrossRef] - Available online: https://web.stanford.edu/group/fan/S4/ (accessed on 24 Nov 2018).
- Lim, T.W.; Son, Y.; Yang, D.Y.; Pham, T.A.; Kim, D.P.; Yang, B.I.; Lee, K.S.; Park, S.H. Net Shape Manufacturing of Three-Dimensional SiCN Ceramic Microstructures Using an Isotropic Shrinkage Method by Introducing Shrinkage Guiders. Int. J. Appl. Ceram. Technol.
**2008**, 5, 258–264. [Google Scholar] [CrossRef] - Kuznetsov, A.I.; Miroshnichenko, A.E.; Brongersma, M.L.; Kivshar, Y.S.; Luk’yanchuk, B. Optically resonant dielectric nanostructures. Science
**2016**, 354, aag2472. [Google Scholar] [CrossRef][Green Version]

**Figure 1.**Sizes of nanopillars as a function of the applied laser power. (

**a**) Scanning electron micrographs of nanopillars fabricated with different laser powers. The scale bar is 500 nm. (

**b**) Diameters (black symbols) and heights (red symbols) of the nanopillars obtained from two-photon lithography (open circles) compared to numerical simulations (filled stars). The dashed line shows the fit of the pillar diameters using Equation (1) to estimate the threshold laser power of the photo resist. (

**c**) Defect rates of optical gratings expressed as fractions of upright pillars in dependence on the applied laser power. The values were obtained from Scanning Electron Microscopy (SEM)-images as shown for 15 mW in the insert. The scale bar is 10 µm.

**Figure 2.**Optical appearance of the nanopillar gratings in dependence on the laser power. (

**a**) Optical micrographs of 50 × 50 µm nanopillar gratings on a fused silica substrate. Scale bar is 25 µm. (

**b**) Scanning electron micrographs showing the corresponding nanopillars. Scale bar is 1 µm.

**Figure 3.**Optical properties of the nanopillar gratings. Reflectivity in dependence on the wavelength obtained from numerical simulations for structure sizes as measured by SEM (solid line) and pillars assuming 20% smaller diameters (dashed line) (left) compared to optical micrographs of nanopillar gratings fabricated with different laser powers (right). The scale bar is 25 µm.

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**MDPI and ACS Style**

Purtov, J.; Rogin, P.; Verch, A.; Johansen, V.E.; Hensel, R. Nanopillar Diffraction Gratings by Two-Photon Lithography. *Nanomaterials* **2019**, *9*, 1495.
https://doi.org/10.3390/nano9101495

**AMA Style**

Purtov J, Rogin P, Verch A, Johansen VE, Hensel R. Nanopillar Diffraction Gratings by Two-Photon Lithography. *Nanomaterials*. 2019; 9(10):1495.
https://doi.org/10.3390/nano9101495

**Chicago/Turabian Style**

Purtov, Julia, Peter Rogin, Andreas Verch, Villads Egede Johansen, and René Hensel. 2019. "Nanopillar Diffraction Gratings by Two-Photon Lithography" *Nanomaterials* 9, no. 10: 1495.
https://doi.org/10.3390/nano9101495