Nonlinear laser lithography for indefinitely large-area nanostructuring with femtosecond pulses


Dynamical systems based on the interplay of nonlinear feedback mechanisms are ubiquitous in nature1,2,3,4,5. Well-understood examples from photonics include mode locking6 and a broad class of fractal optics7, including self-similarity8. In addition to the fundamental interest in such systems, fascinating technical functionalities that are difficult or even impossible to achieve with linear systems can emerge naturally from them7 if the right control tools can be applied. Here, we demonstrate a method that exploits positive nonlocal feedback to initiate, and negative local feedback to regulate, the growth of ultrafast laser-induced metal–oxide nanostructures with unprecedented uniformity, at high speed, low cost and on non-planar or flexible surfaces. The nonlocal nature of the feedback allows us to stitch the nanostructures seamlessly, enabling coverage of indefinitely large areas with subnanometre uniformity in periodicity. We demonstrate our approach through the fabrication of titanium dioxide and tungsten oxide nanostructures, but it can also be extended to a large variety of other materials.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Conceptual model.
Figure 2: Experimental set-up.
Figure 3: Nanostructure formation dynamics.
Figure 4: Examples of fabricated nanostructures.


  1. 1

    Bhalla, U. S. & Iyengar, R. Emergent properties of networks of biological signaling pathways. Science 283, 381–387 (1999).

  2. 2

    Hopfield, J. J. Neural networks and physical systems with emergent collective computational abilities. Proc. Natl Acad. Sci. USA 79, 2554–2558 (1982).

  3. 3

    Ferrell, J. E. Jr. Self-perpetuating states in signal transduction: positive feedback, double-negative feedback and bistability. Curr. Opin. Cell Biol. 14, 140–148 (2002).

  4. 4

    Mandelbrot, B. How long is the coast of Britain? Statistical self-similarity and fractional dimension. Science 156, 636–638 (1967).

  5. 5

    Kitano, H. Biological robustness. Nature Rev. Genet. 5, 826–837 (2004).

  6. 6

    Haus, H. A. Theory of mode locking with a fast saturable absorber. J. Appl. Phys. 46, 3049–3058 (1975).

  7. 7

    Segev, M., Soljačić, M. & Dudley, J. M. Fractal optics and beyond. Nature Photon. 6, 209–210 (2012).

  8. 8

    Dudley, J. M., Finot, C., Richardson, D. J. & Millot, G. Self-similarity in ultrafast nonlinear optics. Nature Phys. 3, 597–603 (2007).

  9. 9

    Barth, J. V., Costantini, G. & Kern, K. Engineering atomic and molecular nanostructures at surfaces. Nature 437, 671–679 (2005).

  10. 10

    Ito, T. & Okazaki, S. Pushing the limits of lithography. Nature 406, 1027–1031 (2000).

  11. 11

    Sreekanth, K. V., Chua, J. K. & Murukeshan, V. M. Interferometric lithography for nanoscale feature patterning: a comparative analysis between laser interference, evanescent wave interference, and surface plasmon interference. Appl. Opt. 49, 6710–6717 (2010).

  12. 12

    Whitesides, G. M. Self-assembly at all scales. Science 295, 2418–2421 (2002).

  13. 13

    Gattass, R. R. & Mazur, E. Femtosecond laser micromachining in transparent materials. Nature Photon. 2, 219–225 (2008).

  14. 14

    Birnbaum, M. Semiconductor surface damage produced by ruby lasers. J. Appl. Phys. 36, 3688–3689 (1965).

  15. 15

    Temple, P. & Soileau, M. Polarization charge model for laser-induced ripple patterns in dielectric materials. IEEE J. Quantum Electron. 17, 2067–2072 (1981).

  16. 16

    Sipe, J. E., Young, J. F., Preston, J. S. & van Driel, H. M. Laser-induced periodic surface structure I: theory. Phys. Rev. B 27, 1141–1154 (1983).

  17. 17

    Bonch-Bruevich, A. M., Libenson, M. N., Makin, V. S. & Trubaev, V. V. Surface electromagnetic waves in optics. Opt. Eng. 31, 718–730 (1991).

  18. 18

    Sun, Q., Liang, F., Vallée, R. & Chin, S. L. Nanograting formation on the surface of silica glass by scanning focused femtosecond laser pulses. Opt. Lett. 33, 2713–2715 (2008).

  19. 19

    Bonse, J., Krüger, J., Höhm, S. & Rosenfeld, A. Femtosecond laser-induced periodic surface structures. J. Laser Appl. 24, 042006 (2012).

  20. 20

    Kalaycioglu, H., Oktem, B., Şenel, Ç., Paltani, P. P. & Ilday, F. Ö. Microjoule-energy, 1 MHz repetition rate pulses from all-fiber-integrated nonlinear chirped-pulse amplifier. Opt. Lett. 35, 959–961 (2010).

  21. 21

    Atwater, H. A. & Polman, A. Plasmonics for improved photovoltaic devices. Nature Mater. 9, 205–213 (2010).

  22. 22

    Srituravanich, W., Fang, N., Sun, C., Luo, Q. & Zhang, X. Plasmonic nanolithography. Nano Lett. 4, 1085–1088 (2004).

  23. 23

    Konstantatos, G. & Sargent, E. H. Nanostructured materials for photon detection. Nature Nanotech. 5, 391–400 (2010).

  24. 24

    Juan, M. L., Righini, M. & Quidant, R. Plasmon nano-optical tweezers. Nature Photon. 5, 349–356 (2011).

  25. 25

    Strukov, D. B., Snider, G. S., Stewart, D. R. & Williams, R. S. The missing memristor found. Nature 453, 80–83 (2008).

  26. 26

    Didiot, C., Pons, S., Kierren, B., Fagot-Revurat, Y. & Malterre, D. Nanopatterning the electronic properties of gold surfaces with self-organized superlattices of metallic nanostructures. Nature Nanotech. 2, 617–621 (2007).

  27. 27

    Flemming, R. G., Murphy, C. J., Abrams, G. A., Goodman, S. L. & Nealey, P. F. Effects of synthetic micro- and nano-structured surfaces on cell behavior. Biomaterials 20, 573–588 (1999).

  28. 28

    Kang, T.-S., Smith, A. P., Taylor, B. E. & Durstock, M. F. Fabrication of highly-ordered TiO2 nanotube arrays and their use in dye-sensitized solar cells. Nano Lett. 9, 601–606 (2009).

Download references


The authors acknowledge support from the Scientific and Technological Research Council of Turkey (TÜBİTAK; grant nos 106G089 and 209T058) and a Distinguished Young Scientist award from the Turkish Academy of Sciences (TÜBA). The authors thank G. Ertaş for help with Raman spectroscopy.

Author information




B.Ö. and I.P. conducted the experiments and analysed the data. I.P., S.I. and F.Ö.I. developed the theoretical model and I.P. performed the simulations. I.P., B.Ö., A.R., S.Y. and M.E. constructed the laser microscope set-up. H.K., B.Ö. and A.R. constructed the laser system.

Corresponding author

Correspondence to F. Ömer Ilday.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary information (PDF 4789 kb)

Supplementary movie (MOV 1239 kb)

Supplementary movie

Supplementary movie (MOV 1239 kb)

Supplementary movie (MOV 4686 kb)

Supplementary movie

Supplementary movie (MOV 4686 kb)

Supplementary movie (MOV 1761 kb)

Supplementary movie

Supplementary movie (MOV 1761 kb)

Supplementary movie (MOV 4107 kb)

Supplementary movie

Supplementary movie (MOV 4107 kb)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Öktem, B., Pavlov, I., Ilday, S. et al. Nonlinear laser lithography for indefinitely large-area nanostructuring with femtosecond pulses. Nature Photon 7, 897–901 (2013).

Download citation

Further reading