Tunable and free-form planar optics

Article metrics


The advent of spatial control over the phase and amplitude of light waves has profoundly transformed photonics, enabling major advances in fields from imaging and information technology to biomedical optics. Here we propose a method of deterministic phase-front shaping using a planar thermo-optical module and designed microheaters to locally shape the refractive index distribution. When combined with a genetic algorithm optimization, this SmartLens can produce free-form optical wavefront modifications. Individually, or in arrays, it can generate complex functions based on either pure or combined Zernike polynomials, including lenses or aberration correctors of electrically tunable magnitude. This simple and compact concept complements the existing optical shaping toolbox by offering low-chromatic-aberration, polarization-insensitive and transmission-mode components that can readily be integrated into existing optical systems.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Principle of the electrically tunable micro-optic device.
Fig. 2: Modelling and wavefront engineering procedure.
Fig. 3: Wavefront engineering.
Fig. 4: Generation of tunable annular and Bessel–Gaussian beams.
Fig. 5: Tunability ranges and response times for four different spiral sizes.
Fig. 6: Broadband multiplane imaging with a SmartLens array.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.


  1. 1.

    Rbinsztein-Dunlop, H. et al. Roadmap on structured light. J. Opt. 19, 013001 (2017).

  2. 2.

    Maurer, C., Jesacher, A., Bernet, S. & Ritsch-Marte, M. What spatial light modulators can do for optical microscopy. Laser Photon. Rev. 5, 81–101 (2011).

  3. 3.

    Hornbeck, L. J. Deformable-mirror spatial light modulators. Proc. SPIE 1150, 1–17 (1989).

  4. 4.

    Berge, B. & Peseux, J. Variable focal lens controlled by an external voltage: an application of electrowetting. Eur. Phys. J. E 3, 159–163 (2000).

  5. 5.

    Kuiper, S. & Hendriks, B. H. W. Variable-focus liquid lens for miniature cameras. Appl. Phys. Lett. 85, 1128–1130 (2004).

  6. 6.

    Ren, H., Fox, D., Anderson, P. A., Wu, B. & Wu, S.-T. Tunable-focus liquid lens controlled using a servo motor. Opt. Express 14, 8031 (2006).

  7. 7.

    Liebetraut, P., Petsch, S., Liebeskind, J. & Zappe, H. Elastomeric lenses with tunable astigmatism. Light Sci. Appl. 2, e98 (2013).

  8. 8.

    Beadie, G. et al. Tunable polymer lens. Opt. Express 16, 11847 (2008).

  9. 9.

    Carpi, F., Frediani, G., Turco, S. & De, R. D. Bioinspired tunable lens with muscle-like electroactive elastomers. Adv. Funct. Mater. 21, 4152–4158 (2011).

  10. 10.

    Zhang, W., Zappe, H. & Seifert, A. Wafer-scale fabricated thermo-pneumatically tunable microlenses. Light Sci. Appl. 3, e145 (2014).

  11. 11.

    Zhang, D. Y., Lien, V., Berdichevsky, Y., Choi, J. & Lo, Y. H. Fluidic adaptive lens with high focal length tunability. Appl. Phys. Lett. 82, 3171–3172 (2003).

  12. 12.

    Liebetraut, P., Petsch, S., Mönch, W. & Zappe, H. Tunable solid-body elastomer lenses with electromagnetic actuation. Appl. Opt. 50, 3268 (2011).

  13. 13.

    Yu, H., Zhou, G., Chau, F. S. & Sinha, S. K. Tunable electromagnetically actuated liquid-filled lens. Sens. Actuat. A 167, 602–607 (2011).

  14. 14.

    Xu, S. et al. Adaptive liquid lens actuated by photo-polymer. Opt. Express 17, 17590 (2009).

  15. 15.

    Glebov, A. L., Huang, L., Aoki, S., Lee, M. & Yokouchi, K. Planar hybrid polymer–silica microlenses with tunable beamwidth and focal length. IEEE Photon. Technol. Lett. 16, 1107–1109 (2004).

  16. 16.

    Angelini, A., Pirani, F., Frascella, F. & Descrovi, E. Reconfigurable elastomeric graded-index optical elements controlled by light. Light Sci. Appl. 7, 7 (2018).

  17. 17.

    Dong, L., Agarwal, A. K., Beebe, D. J. & Jiang, H. Adaptive liquid microlenses activated by stimuli-responsive hydrogels. Nature 442, 551–554 (2006).

  18. 18.

    Ghosh, G. Handbook of Thermo-Optic Coefficients of Optical Materials with Applications (Academic Press, 1998).

  19. 19.

    Rosencwaig, A., Opsal, J., Smith, W. L. & Willenborg, D. L. Detection of thermal waves through optical reflectance. Appl. Phys. Lett. 46, 1013–1015 (1985).

  20. 20.

    Tessier, G., Holé, S. & Fournier, D. Quantitative thermal imaging by synchronous thermoreflectance with optimized illumination wavelengths. Appl. Phys. Lett. 78, 2267–2269 (2001).

  21. 21.

    Boccara, A. C., Fournier, D. & Badoz, J. Thermo-optical spectroscopy: detection by the ‘mirage effect’. Appl. Phys. Lett. 36, 130–132 (1980).

  22. 22.

    Berto, P. et al. Quantitative absorption spectroscopy of nano-objects. Phys. Rev. B 86, 165417 (2012).

  23. 23.

    Boyer, D., Tamarat, P., Maali, A., Lounis, B. & Orrit, M. Photothermal imaging of nanometer-sized metal particles among scatterers. Science 297, 1160 (2002).

  24. 24.

    Gaiduk, A., Yorulmaz, M., Ruijgrok, P. V. & Orrit, M. Room-temperature detection of a single molecule’s absorption by photothermal contrast. Science 330, 353–356 (2010).

  25. 25.

    Donner, J. S., Morales-Dalmau, J., Alda, I., Marty, R. & Quidant, R. Fast and transparent adaptive lens based on plasmonic heating. ACS Photon. 2, 355–360 (2015).

  26. 26.

    Beeckman, J. et al. Multi-electrode tunable liquid crystal lenses with one lithography step. Opt. Lett. 43, 271–274 (2018).

  27. 27.

    Algorri, J. F. et al. Tunable liquid crystal multifocal microlens array. Sci. Rep. 7, 17318 (2017).

  28. 28.

    Li, G. et al. Switchable electro-optic diffractive lens with high efficiency for ophthalmic applications. Proc. Natl Acad. Sci. USA 103, 6100–6104 (2006).

  29. 29.

    Baffou, G. et al. Thermal imaging of nanostructures by quantitative optical phase analysis. ACS Nano 6, 2452–2458 (2012).

  30. 30.

    Bon, P. et al. Three-dimensional temperature imaging around a gold microwire. Appl. Phys. Lett. 102, 3–6 (2013).

  31. 31.

    Radhakrishnan, T. S. Thermal degradation of poly(dimethylsilylene) and poly(tetramethyldisilylene-co-styrene). J. Appl. Polym. Sci. 99, 2679–2686 (2006).

  32. 32.

    Markos, C., Vlachos, K. & Kakarantzas, G. Thermo-optic effect of an index guiding photonic crystal fiber with elastomer inclusions. Proc. SPIE 7753, 775340 (2011).

  33. 33.

    Born, M. & Wolf, E. Principles of Optics (Academic Press, 2000).

  34. 34.

    Lakshminarayanan, V. & Fleck, A. Zernike polynomials: a guide. J. Mod. Opt. 58, 545–561 (2011).

  35. 35.

    Holland, J. H. Adaptation in Natural and Artificial Systems. PhD thesis, Univ. Michigan (1975).

  36. 36.

    Michalewicz, Z. Genetic Algorithms + Data Structures = Evolution Programs (Springer Science & Business Media, 2013).

  37. 37.

    Xu, J. & Zhuang, S. Measurement of lens focal length with Hartmann–Shack wavefront sensor based on 4F system. Optik 126, 1303–1306 (2015).

  38. 38.

    Yang, W. et al. Simultaneous multi-plane imaging of neural circuits. Neuron 89, 269–284 (2016).

  39. 39.

    Hernandez, O. et al. Three-dimensional spatiotemporal focusing of holographic patterns. Nat. Commun. 7, 11928 (2016).

  40. 40.

    Berto, P., Mohamed, M. S. A., Rigneault, H. & Baffou, G. Time-harmonic optical heating of plasmonic nanoparticles. Phys. Rev. B 90, 035439 (2014).

  41. 41.

    Jesacher, A., Bernet, S. & Ritsch-Marte, M. Colour hologram projection with an SLM by exploiting its full phase modulation range. Opt. Express. 22, 20530–20541 (2014).

  42. 42.

    Harm, W., Jesacher, A., Thalhammer, G., Bernet, S. & Ritsch-Marte, M. How to use a phase-only spatial light modulator as a color display. Opt. Lett. 40, 581–584 (2015).

  43. 43.

    Yang, W. & Yuste, R. In vivo imaging of neural activity. Nat. Methods 14, 349–359 (2017).

  44. 44.

    Conchello, J. A. & Lichtman, J. W. Optical sectioning microscopy. Nat. Methods 2, 920–931 (2005).

  45. 45.

    Shack, R. V. & Platt, B. C. Production and use of a lenticular Hartmann screen. J. Opt. Soc. Am. 61, 656 (1971).

  46. 46.

    Levoy, M., Ng, R., Adams, A., Footer, M. & Horowitz, M. Light field microscopy. In Proc. SIGGRAPH 924–934 (ACM, 2006); https://doi.org/10.1145/1179352.1141976.

Download references


The authors acknowledge financial support from the European Research Council programme under grants ERC-CoG QnanoMECA (64790) and ERC-PoC (680898), Fundació Privada Cellex, the CERCA programme and the Spanish Ministry of Economy and Competitiveness, through the ‘Severo Ochoa’ Programme for Centres of Excellence in R&D (SEV-2015-0522), Agence Nationale de la Recherche (ANR Neocastip and ANR BoroGaN) and Région Ile de France (GeneTherm Project–C’Nano IdF–DIM Nano-K 2016-16). The authors also thank J.G. Guirardo, J. Canet-Ferrer, J. Berthelot and A. Reserbat-Plantey for their help with resistor fabrication. The authors thank V. D’Ambrosio for help with data analysis and general discussions on the technology, P. Del Hougne for preliminary COMSOL simulations as well as I. Alda, R. Marty and J. Donner for their preliminary work on SmartLens characterization. The authors also thank P. Bohec for stimulating discussions regarding genetic algorithm implementation and G. Baffou for fruitful discussions on the thermal model.

Author information

R.Q. initiated and supervised the project. R.Q. and P.B. conceived the concept. P.B. developed the electro-thermo-optical model and the genetic algorithm optimization. P.B. and L.P. designed the sample. J.O. and L.P. fabricated the devices. P.B., G.T. and L.P. performed the wavefront sensing experiments and analysed the results. C.L. performed the experiment on Bessel beam generation. P.B., R.Q., L.P., A.A., M.M.M. and B.M.A. designed and performed the imaging experiment. All authors participated in writing the manuscript.

Correspondence to Pascal Berto or Romain Quidant.

Ethics declarations

Competing interests

The authors declare the following competing financial interests: P.B., L.P. and R.Q. of the Institute of Photonic Sciences (ICFO) have filed several patent applications related to SmartLenses.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

This file contains more information about the work, Supplementary Figs. 1–13 and Supplementary Tables 1–2.

Supplementary Video 1

Video showing the simultaneous refocusing of different objects located in different planes

Supplementary Video 2

Video showing simultaneous multiplane imaging in microscopy

Supplementary Video 3

Video showing the genetic algorithm optimization in the case of a conical wavefront (N = 7)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Further reading