Abstract

The use of diffractive optical elements (DOEs) in broadband optical systems can often significantly reduce their size or enhance their performance but is mostly prevented by stray light in unwanted diffraction orders. This is because dispersion causes the diffraction efficiency to decrease as a function of the wavelength. Here we introduce nanocomposites as a material platform that allows for the design of dispersion-engineered materials. We show that these materials enable the design of almost dispersion-free, i.e., achromatic, echelette-type gratings with diffraction efficiencies of close to 100% in the entire visible spectral range. Using numerical simulations, we demonstrate that such high efficiencies are maintained across the range of incidence angles and grating periods required for most optical systems. This concept of dispersion-engineered nanocomposites can also be applied to other applications, and nanocomposite-enabled DOEs have the potential to be an enabling technology for a new generation of better and more compact optical systems.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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2019 (1)

M. Decker, W. T. Chen, T. Nobis, A. Y. Zhu, M. Khorasaninejad, Z. Bharwani, F. Capasso, and J. Petschulat, “Imaging performance of polarization-insensitive metalenses,” ACS Photon. 6, 1493–1499 (2019).
[Crossref]

2018 (4)

D. Werdehausen, T. Scharf, J. Petschulat, S. Burger, T. Pertsch, I. Staude, and M. Decker, “Using effective medium theories to design tailored nanocomposite materials for optical systems,” Proc. SPIE 10745, 107450H (2018).
[Crossref]

D. Werdehausen, I. Staude, S. Burger, J. Petschulat, T. Scharf, T. Pertsch, and M. Decker, “Design rules for customizable optical materials based on nanocomposites,” Opt. Mater. Express 8, 3456–3469 (2018).
[Crossref]

W. T. Chen, A. Y. Zhu, V. Sanjeev, M. Khorasaninejad, Z. Shi, E. Lee, and F. Capasso, “A broadband achromatic metalens for focusing and imaging in the visible,” Nat. Nanotechnol. 13, 220–226 (2018).
[Crossref]

S. Wang, P. C. Wu, V. C. Su, Y. C. Lai, M. K. Chen, H. Y. Kuo, B. H. Chen, Y. H. Chen, T. T. Huang, J. H. Wang, R. M. Lin, C. H. Kuan, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13, 227–232 (2018).
[Crossref]

2017 (3)

P. Lalanne and P. Chavel, “Metalenses at visible wavelengths: past, present, perspectives,” Laser Photon. Rev. 11, 1600295 (2017).
[Crossref]

P. Genevet, F. Capasso, F. Aieta, M. Khorasaninejad, and R. Devlin, “Recent advances in planar optics: from plasmonic to dielectric metasurfaces,” Optica 4, 139–152 (2017).
[Crossref]

M. Khorasaninejad and F. Capasso, “Metalenses: versatile multifunctional photonic components,” Science 358, eaam8100 (2017).
[Crossref]

2016 (2)

M. Decker and I. Staude, “Resonant dielectric nanostructures: a low-loss platform for functional nanophotonics,” J. Opt. 18, 103001 (2016).
[Crossref]

T. Gissibl, S. Thiele, A. Herkommer, and H. Giessen, “Two-photon direct laser writing of ultracompact multi-lens objectives,” Nat. Photonics 10, 554–560 (2016).
[Crossref]

2015 (1)

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High‐efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mater. 3, 813–820 (2015).
[Crossref]

2013 (1)

A. A. Kazemi, B. Kress, T. Starner, B. C. Kress, and S. Thibault, “A review of head-mounted displays (HMD) technologies and applications for consumer electronics,” Proc. SPIE 8720, 87200A (2013).
[Crossref]

2012 (4)

S. Larouche and D. R. Smith, “Reconciliation of generalized refraction with diffraction theory,” Opt. Lett. 37, 2391–2393 (2012).
[Crossref]

G. I. Greisukh, E. G. Ezhov, A. V. Kalashnikov, and S. A. Stepanov, “Diffractive-refractive correction units for plastic compact zoom lenses,” Appl. Opt. 51, 4597–4604 (2012).
[Crossref]

H. Liu, X. Zeng, X. Kong, S. Bian, and J. Chen, “A simple two-step method to fabricate highly transparent ITO/polymer nanocomposite films,” Appl. Surf. Sci. 258, 8564–8569 (2012).
[Crossref]

T. Ogata, R. Yagi, N. Nakamura, Y. Kuwahara, and S. Kurihara, “Modulation of polymer refractive indices with diamond nanoparticles for metal-free multilayer film mirrors,” ACS Appl. Mater. Interfaces 4, 3769–3772 (2012).
[Crossref]

2011 (2)

P. Tao, Y. Li, A. Rungta, A. Viswanath, J. Gao, B. C. Benicewicz, R. W. Siegel, and L. S. Schadler, “TiO2 nanocomposites with high refractive index and transparency,” J. Mater. Chem. A 21, 18623–18629 (2011).
[Crossref]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref]

2010 (1)

2009 (2)

N. Sultanova, S. Kasarova, and I. Nikolov, “Dispersion properties of optical polymers,” Acta Phys. Pol. A 116, 585–587 (2009).
[Crossref]

C. Lü and B. Yang, “High refractive index organic-inorganic nanocomposites: design, synthesis and application,” J. Mater. Chem. A 19, 2884–2901 (2009).
[Crossref]

2008 (2)

B. H. Kleemann, M. Seesselberg, and J. Ruoff, “Design concepts for broadband high-efficiency DOEs,” J. Eur. Opt. Soc. 3, 08015 (2008).
[Crossref]

M. S. Rill, C. Plet, M. Thiel, I. Staude, G. von Freymann, S. Linden, and M. Wegener, “Photonic metamaterials by direct laser writing and silver chemical vapour deposition,” Nat. Mater. 7, 543–546 (2008).
[Crossref]

2007 (3)

E. Ōsawa, “Recent progress and perspectives in single-digit nanodiamond,” Diamond Relat. Mater. 16, 2018–2022 (2007).
[Crossref]

S. Kubo, A. Diaz, Y. Tang, T. S. Mayer, I. C. Khoo, and T. E. Mallouk, “Tunability of the refractive index of gold nanoparticle dispersions,” Nano Lett. 7, 3418–3423 (2007).
[Crossref]

J. L. H. Chau, Y.-M. Lin, A.-K. Li, W.-F. Su, K.-S. Chang, S. L.-C. Hsu, and T.-L. Li, “Transparent high refractive index nanocomposite thin films,” Mater. Lett. 61, 2908–2910 (2007).
[Crossref]

2006 (2)

O. Sandfuchs, R. Brunner, D. Pätz, S. Sinzinger, and J. Ruoff, “Rigorous analysis of shadowing effects in blazed transmission gratings,” Opt. Lett. 31, 3638–3640 (2006).
[Crossref]

J. A. Davison and M. J. Simpson, “History and development of the apodized diffractive intraocular lens,” J. Cataract Refractive Surg. 32, 849–858 (2006).
[Crossref]

2003 (1)

R. J. Nussbaumer, W. R. Caseri, P. Smith, and T. Tervoort, “Polymer‐TiO2 nanocomposites: a route towards visually transparent broadband UV Filters and high refractive index materials,” Macromol. Mater. Eng. 288, 44–49 (2003).
[Crossref]

2000 (1)

1992 (2)

1988 (1)

Achtner, B.

H. Gross, W. Singer, M. Totzeck, F. Blechinger, and B. Achtner, Handbook of Optical Systems (Wiley-VCH, 2005).

Aieta, F.

P. Genevet, F. Capasso, F. Aieta, M. Khorasaninejad, and R. Devlin, “Recent advances in planar optics: from plasmonic to dielectric metasurfaces,” Optica 4, 139–152 (2017).
[Crossref]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref]

Benicewicz, B. C.

P. Tao, Y. Li, A. Rungta, A. Viswanath, J. Gao, B. C. Benicewicz, R. W. Siegel, and L. S. Schadler, “TiO2 nanocomposites with high refractive index and transparency,” J. Mater. Chem. A 21, 18623–18629 (2011).
[Crossref]

Bharwani, Z.

M. Decker, W. T. Chen, T. Nobis, A. Y. Zhu, M. Khorasaninejad, Z. Bharwani, F. Capasso, and J. Petschulat, “Imaging performance of polarization-insensitive metalenses,” ACS Photon. 6, 1493–1499 (2019).
[Crossref]

Bian, S.

H. Liu, X. Zeng, X. Kong, S. Bian, and J. Chen, “A simple two-step method to fabricate highly transparent ITO/polymer nanocomposite films,” Appl. Surf. Sci. 258, 8564–8569 (2012).
[Crossref]

Blechinger, F.

H. Gross, W. Singer, M. Totzeck, F. Blechinger, and B. Achtner, Handbook of Optical Systems (Wiley-VCH, 2005).

Brener, I.

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High‐efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mater. 3, 813–820 (2015).
[Crossref]

Brunner, R.

Buralli, D. A.

Burger, S.

D. Werdehausen, T. Scharf, J. Petschulat, S. Burger, T. Pertsch, I. Staude, and M. Decker, “Using effective medium theories to design tailored nanocomposite materials for optical systems,” Proc. SPIE 10745, 107450H (2018).
[Crossref]

D. Werdehausen, I. Staude, S. Burger, J. Petschulat, T. Scharf, T. Pertsch, and M. Decker, “Design rules for customizable optical materials based on nanocomposites,” Opt. Mater. Express 8, 3456–3469 (2018).
[Crossref]

Cambril, E.

Capasso, F.

M. Decker, W. T. Chen, T. Nobis, A. Y. Zhu, M. Khorasaninejad, Z. Bharwani, F. Capasso, and J. Petschulat, “Imaging performance of polarization-insensitive metalenses,” ACS Photon. 6, 1493–1499 (2019).
[Crossref]

W. T. Chen, A. Y. Zhu, V. Sanjeev, M. Khorasaninejad, Z. Shi, E. Lee, and F. Capasso, “A broadband achromatic metalens for focusing and imaging in the visible,” Nat. Nanotechnol. 13, 220–226 (2018).
[Crossref]

M. Khorasaninejad and F. Capasso, “Metalenses: versatile multifunctional photonic components,” Science 358, eaam8100 (2017).
[Crossref]

P. Genevet, F. Capasso, F. Aieta, M. Khorasaninejad, and R. Devlin, “Recent advances in planar optics: from plasmonic to dielectric metasurfaces,” Optica 4, 139–152 (2017).
[Crossref]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref]

Caseri, W. R.

R. J. Nussbaumer, W. R. Caseri, P. Smith, and T. Tervoort, “Polymer‐TiO2 nanocomposites: a route towards visually transparent broadband UV Filters and high refractive index materials,” Macromol. Mater. Eng. 288, 44–49 (2003).
[Crossref]

Chang, K.-S.

J. L. H. Chau, Y.-M. Lin, A.-K. Li, W.-F. Su, K.-S. Chang, S. L.-C. Hsu, and T.-L. Li, “Transparent high refractive index nanocomposite thin films,” Mater. Lett. 61, 2908–2910 (2007).
[Crossref]

Chau, J. L. H.

J. L. H. Chau, Y.-M. Lin, A.-K. Li, W.-F. Su, K.-S. Chang, S. L.-C. Hsu, and T.-L. Li, “Transparent high refractive index nanocomposite thin films,” Mater. Lett. 61, 2908–2910 (2007).
[Crossref]

Chavel, P.

P. Lalanne and P. Chavel, “Metalenses at visible wavelengths: past, present, perspectives,” Laser Photon. Rev. 11, 1600295 (2017).
[Crossref]

Chen, B. H.

S. Wang, P. C. Wu, V. C. Su, Y. C. Lai, M. K. Chen, H. Y. Kuo, B. H. Chen, Y. H. Chen, T. T. Huang, J. H. Wang, R. M. Lin, C. H. Kuan, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13, 227–232 (2018).
[Crossref]

Chen, J.

H. Liu, X. Zeng, X. Kong, S. Bian, and J. Chen, “A simple two-step method to fabricate highly transparent ITO/polymer nanocomposite films,” Appl. Surf. Sci. 258, 8564–8569 (2012).
[Crossref]

Chen, M. K.

S. Wang, P. C. Wu, V. C. Su, Y. C. Lai, M. K. Chen, H. Y. Kuo, B. H. Chen, Y. H. Chen, T. T. Huang, J. H. Wang, R. M. Lin, C. H. Kuan, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13, 227–232 (2018).
[Crossref]

Chen, W. T.

M. Decker, W. T. Chen, T. Nobis, A. Y. Zhu, M. Khorasaninejad, Z. Bharwani, F. Capasso, and J. Petschulat, “Imaging performance of polarization-insensitive metalenses,” ACS Photon. 6, 1493–1499 (2019).
[Crossref]

W. T. Chen, A. Y. Zhu, V. Sanjeev, M. Khorasaninejad, Z. Shi, E. Lee, and F. Capasso, “A broadband achromatic metalens for focusing and imaging in the visible,” Nat. Nanotechnol. 13, 220–226 (2018).
[Crossref]

Chen, Y. H.

S. Wang, P. C. Wu, V. C. Su, Y. C. Lai, M. K. Chen, H. Y. Kuo, B. H. Chen, Y. H. Chen, T. T. Huang, J. H. Wang, R. M. Lin, C. H. Kuan, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13, 227–232 (2018).
[Crossref]

Clark, P. P.

Davison, J. A.

J. A. Davison and M. J. Simpson, “History and development of the apodized diffractive intraocular lens,” J. Cataract Refractive Surg. 32, 849–858 (2006).
[Crossref]

Decker, M.

M. Decker, W. T. Chen, T. Nobis, A. Y. Zhu, M. Khorasaninejad, Z. Bharwani, F. Capasso, and J. Petschulat, “Imaging performance of polarization-insensitive metalenses,” ACS Photon. 6, 1493–1499 (2019).
[Crossref]

D. Werdehausen, T. Scharf, J. Petschulat, S. Burger, T. Pertsch, I. Staude, and M. Decker, “Using effective medium theories to design tailored nanocomposite materials for optical systems,” Proc. SPIE 10745, 107450H (2018).
[Crossref]

D. Werdehausen, I. Staude, S. Burger, J. Petschulat, T. Scharf, T. Pertsch, and M. Decker, “Design rules for customizable optical materials based on nanocomposites,” Opt. Mater. Express 8, 3456–3469 (2018).
[Crossref]

M. Decker and I. Staude, “Resonant dielectric nanostructures: a low-loss platform for functional nanophotonics,” J. Opt. 18, 103001 (2016).
[Crossref]

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High‐efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mater. 3, 813–820 (2015).
[Crossref]

Devlin, R.

Diaz, A.

S. Kubo, A. Diaz, Y. Tang, T. S. Mayer, I. C. Khoo, and T. E. Mallouk, “Tunability of the refractive index of gold nanoparticle dispersions,” Nano Lett. 7, 3418–3423 (2007).
[Crossref]

Dominguez, J.

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High‐efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mater. 3, 813–820 (2015).
[Crossref]

Ezhov, E. G.

Falkner, M.

M. Decker, I. Staude, M. Falkner, J. Dominguez, D. N. Neshev, I. Brener, T. Pertsch, and Y. S. Kivshar, “High‐efficiency dielectric Huygens’ surfaces,” Adv. Opt. Mater. 3, 813–820 (2015).
[Crossref]

Gaburro, Z.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334, 333–337 (2011).
[Crossref]

Gao, J.

P. Tao, Y. Li, A. Rungta, A. Viswanath, J. Gao, B. C. Benicewicz, R. W. Siegel, and L. S. Schadler, “TiO2 nanocomposites with high refractive index and transparency,” J. Mater. Chem. A 21, 18623–18629 (2011).
[Crossref]

Genevet, P.

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[Crossref]

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Supplementary Material (1)

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Figures (7)

Fig. 1.
Fig. 1. (a) Scheme of a single-layer echelette-type grating (EG). Polychromatic light incident on the grating is split into different diffraction orders: all light at the design wavelength (green) is diffracted into the desired diffraction order (+1), but light at other wavelengths (blue and red) is partly diffracted into spurious orders. The widths of the arrows indicate the relative energy fluxes. (b) Scheme of a nanocomposite-enabled EG, which directs all the light into the desired diffraction order. The two layers have the refractive indices n1(λ) and n2(λ). The diameter of the nanoparticles (dinc) must be smaller than 5 nm to avoid scattering.
Fig. 2.
Fig. 2. Ray-optical illustration of shadowing: rays that hit the boundaries between the periods are diffracted into spurious orders. The amount of shadowing increases with increasing height (h), increasing angle of incidence (AOI), and decreasing period (Λ).
Fig. 3.
Fig. 3. (a) Refractive index (n) over wavelength (λ) for different Abbe numbers (νd) at nd=1.6 (red dot) and Pg,F=0.55. We used Cauchy’s equation to determine n(λ) from the respective nd, νd, and Pg,F values. The red arrow indicates that changing nd shifts the n(λ) curve up and down, whereas lowering the Abbe number increases the total amount of dispersion. (b) Analogous visualization of Pg,F for νd=10. Pg,F characterizes the relative index change on the edges of the spectrum.
Fig. 4.
Fig. 4. (a) Abbe diagram and (b) partial dispersion diagram including commonly used optical polymers (blue stars), possible nanoparticle materials (green stars), and nanocomposites up to volume fractions of 35% (orange lines). The orange area illustrates the region that is accessible by combining multiple nanoparticle materials in the same host. PMMA, poly(methyl methacrylate); COP, cyclic olefin copolymer; PS, polystyrene; PC, polycarbonate; ITO, indium tin oxide; AZO, aluminum-doped zinc oxide.
Fig. 5.
Fig. 5. (a) Efficiency of the single-layer EG 1 (Table 1) from the thin element approximation as a function of the wavelength. The average across the highlighted area defines the polychromatic integral diffraction efficiency (ηPIDE). (b) ηPIDE of EG 1 from FEM simulations (JCMsuite) as a function of the angle of incidence (AOI) and the grating period (Λ). ηPIDE decreases with increasing AOIs and decreasing periods because of shadowing. The dotted line encompasses the regime in which ηPIDE remains within 3% of its theoretical limit.
Fig. 6.
Fig. 6. Maximum phase delay per period (ϕmax) as a function of the wavelength (λ) for EG 1–EG 3. For the single layer, EG 1 ϕmax changes quickly as a function of the wavelength, which leads to a rapid drop of the efficiency. In contrast, EG 2 exhibits almost no dispersion, and EG 3 intersects the ideal ϕmax(λ)=2π line at two wavelengths.
Fig. 7.
Fig. 7. Performance of the nanocomposite-enabled EGs. (a) Efficiency of EG 2 (Table 1) as a function of the wavelength. The efficiency deviates only slightly from 100% throughout the entire visible spectral range. (b) ηPIDE of EG 2 from FEM simulations (JCMsuite) as a function of the angle of incidence (AOI) and the grating period (Λ). The dotted line encompasses the regime in which ηPIDE remains within 3% of its maximum. (c,d) Analogous plots for EG 3 (Table 1), which is only comprised of readily available commercial materials. (c) ηPIDE, as well as the region in which it remains close to its maximum, are slightly decreased.

Tables (1)

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Table 1. Details of all EG Specifications

Equations (3)

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ηq(λ)=sinc2{12[ϕmax(λ)2πq]}.
ϕmax(λ)=2πhλ[n1(λ)n2(λ)]=2πhλΔn(λ),
νd=nd1nFnCandPg,F=ngnFnFnC,