Abstract

We demonstrate high aperture (up to NA0.64) three-dimensional focusing in free space based on wavefront-engineered diffraction gratings. The grating lens’ optical response is tailored by spatially varying the grating ridge and groove width in two dimensions to achieve focal lengths of order 100 μm that are crucial for micro-optical applications. The phase profile of the lens includes multiple 2π phase jumps and was obtained by applying an algorithm for finding the optimal path for both phase and amplitude. Experimental measurements reveal a lateral spot size of 5 μm that is close to the size of a corresponding Airy disk.

© 2013 Optical Society of America

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Corrections

Annett B. Klemm, Daan Stellinga, Emiliano R. Martins, Liam Lewis, Guillaume Huyet, Liam O’Faolain, and Thomas F. Krauss, "Experimental high numerical aperture focusing with high contrast gratings: publisher’s note," Opt. Lett. 39, 825-825 (2014)
https://www.osapublishing.org/ol/abstract.cfm?uri=ol-39-4-825

References

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A. Ricciardi, S. Campopiano, A. Cusano, T. F. Krauss, and L. O’Faolain, IEEE Photon. J. 2, 696 (2010).
[CrossRef]

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, Nat. Photonics 4, 466 (2010).
[CrossRef]

F. Lu, F. G. Sedgwick, V. Karagodsky, C. Chase, and C. J. Chang-Hasnain, Opt. Express 18, 12606 (2010).
[CrossRef]

2008 (2)

2006 (1)

H. Ottevaere, R. Cox, H. P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. J. Woo, and H. Thienpont, J. Opt. A 8, S407 (2006).
[CrossRef]

2004 (1)

C. F. R. Mateus, M. C. Y. Huang, D. Yunfei, A. R. Neureuther, and C. J. Chang-Hasnain, IEEE Photon. Technol. Lett. 16, 518 (2004).
[CrossRef]

2002 (2)

S. Fan and J. D. Joannopoulos, Phys. Rev. B 65, 235112 (2002).
[CrossRef]

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, Phys. Rev. E 66, 066608 (2002).
[CrossRef]

1981 (1)

1959 (1)

E. W. Dijkstra, Numer. Math. 1, 269 (1959).
[CrossRef]

Beausoleil, R. G.

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, Nat. Photonics 4, 466 (2010).
[CrossRef]

Bienstman, P.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, Phys. Rev. E 66, 066608 (2002).
[CrossRef]

Campopiano, S.

A. Ricciardi, S. Campopiano, A. Cusano, T. F. Krauss, and L. O’Faolain, IEEE Photon. J. 2, 696 (2010).
[CrossRef]

Chang-Hasnain, C. J.

Chase, C.

Chen, Y.

Cox, R.

H. Ottevaere, R. Cox, H. P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. J. Woo, and H. Thienpont, J. Opt. A 8, S407 (2006).
[CrossRef]

Cusano, A.

A. Ricciardi, S. Campopiano, A. Cusano, T. F. Krauss, and L. O’Faolain, IEEE Photon. J. 2, 696 (2010).
[CrossRef]

Dijkstra, E. W.

E. W. Dijkstra, Numer. Math. 1, 269 (1959).
[CrossRef]

Du, C.

Fan, S.

S. Fan and J. D. Joannopoulos, Phys. Rev. B 65, 235112 (2002).
[CrossRef]

Fattal, D.

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, Nat. Photonics 4, 466 (2010).
[CrossRef]

Fiorentino, M.

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, Nat. Photonics 4, 466 (2010).
[CrossRef]

Gaylord, T. K.

Herzig, H. P.

H. Ottevaere, R. Cox, H. P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. J. Woo, and H. Thienpont, J. Opt. A 8, S407 (2006).
[CrossRef]

Huang, M. C. Y.

Y. Zhou, M. C. Y. Huang, and C. J. Chang-Hasnain, Opt. Express 16, 14221 (2008).
[CrossRef]

C. F. R. Mateus, M. C. Y. Huang, D. Yunfei, A. R. Neureuther, and C. J. Chang-Hasnain, IEEE Photon. Technol. Lett. 16, 518 (2004).
[CrossRef]

Ibanescu, M.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, Phys. Rev. E 66, 066608 (2002).
[CrossRef]

Joannopoulos, J. D.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, Phys. Rev. E 66, 066608 (2002).
[CrossRef]

S. Fan and J. D. Joannopoulos, Phys. Rev. B 65, 235112 (2002).
[CrossRef]

Johnson, S. G.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, Phys. Rev. E 66, 066608 (2002).
[CrossRef]

Karagodsky, V.

Krauss, T. F.

A. Ricciardi, S. Campopiano, A. Cusano, T. F. Krauss, and L. O’Faolain, IEEE Photon. J. 2, 696 (2010).
[CrossRef]

Li, J.

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, Nat. Photonics 4, 466 (2010).
[CrossRef]

Lidorikis, E.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, Phys. Rev. E 66, 066608 (2002).
[CrossRef]

Lu, F.

Luo, X.

Mateus, C. F. R.

C. F. R. Mateus, M. C. Y. Huang, D. Yunfei, A. R. Neureuther, and C. J. Chang-Hasnain, IEEE Photon. Technol. Lett. 16, 518 (2004).
[CrossRef]

Miyashita, T.

H. Ottevaere, R. Cox, H. P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. J. Woo, and H. Thienpont, J. Opt. A 8, S407 (2006).
[CrossRef]

Moharam, M. G.

Naessens, K.

H. Ottevaere, R. Cox, H. P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. J. Woo, and H. Thienpont, J. Opt. A 8, S407 (2006).
[CrossRef]

Neureuther, A. R.

C. F. R. Mateus, M. C. Y. Huang, D. Yunfei, A. R. Neureuther, and C. J. Chang-Hasnain, IEEE Photon. Technol. Lett. 16, 518 (2004).
[CrossRef]

O’Faolain, L.

A. Ricciardi, S. Campopiano, A. Cusano, T. F. Krauss, and L. O’Faolain, IEEE Photon. J. 2, 696 (2010).
[CrossRef]

Ottevaere, H.

H. Ottevaere, R. Cox, H. P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. J. Woo, and H. Thienpont, J. Opt. A 8, S407 (2006).
[CrossRef]

Peng, Z.

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, Nat. Photonics 4, 466 (2010).
[CrossRef]

Ricciardi, A.

A. Ricciardi, S. Campopiano, A. Cusano, T. F. Krauss, and L. O’Faolain, IEEE Photon. J. 2, 696 (2010).
[CrossRef]

Sedgwick, F. G.

Skorobogatiy, M. A.

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, Phys. Rev. E 66, 066608 (2002).
[CrossRef]

Taghizadeh, M.

H. Ottevaere, R. Cox, H. P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. J. Woo, and H. Thienpont, J. Opt. A 8, S407 (2006).
[CrossRef]

Thienpont, H.

H. Ottevaere, R. Cox, H. P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. J. Woo, and H. Thienpont, J. Opt. A 8, S407 (2006).
[CrossRef]

Völkel, R.

H. Ottevaere, R. Cox, H. P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. J. Woo, and H. Thienpont, J. Opt. A 8, S407 (2006).
[CrossRef]

Woo, H. J.

H. Ottevaere, R. Cox, H. P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. J. Woo, and H. Thienpont, J. Opt. A 8, S407 (2006).
[CrossRef]

Yunfei, D.

C. F. R. Mateus, M. C. Y. Huang, D. Yunfei, A. R. Neureuther, and C. J. Chang-Hasnain, IEEE Photon. Technol. Lett. 16, 518 (2004).
[CrossRef]

Zhou, C.

Zhou, Y.

IEEE Photon. J. (1)

A. Ricciardi, S. Campopiano, A. Cusano, T. F. Krauss, and L. O’Faolain, IEEE Photon. J. 2, 696 (2010).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

C. F. R. Mateus, M. C. Y. Huang, D. Yunfei, A. R. Neureuther, and C. J. Chang-Hasnain, IEEE Photon. Technol. Lett. 16, 518 (2004).
[CrossRef]

J. Opt. A (1)

H. Ottevaere, R. Cox, H. P. Herzig, T. Miyashita, K. Naessens, M. Taghizadeh, R. Völkel, H. J. Woo, and H. Thienpont, J. Opt. A 8, S407 (2006).
[CrossRef]

J. Opt. Soc. Am. (1)

Nat. Photonics (1)

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, Nat. Photonics 4, 466 (2010).
[CrossRef]

Numer. Math. (1)

E. W. Dijkstra, Numer. Math. 1, 269 (1959).
[CrossRef]

Opt. Express (2)

Opt. Lett. (1)

Phys. Rev. B (1)

S. Fan and J. D. Joannopoulos, Phys. Rev. B 65, 235112 (2002).
[CrossRef]

Phys. Rev. E (1)

S. G. Johnson, P. Bienstman, M. A. Skorobogatiy, M. Ibanescu, E. Lidorikis, and J. D. Joannopoulos, Phys. Rev. E 66, 066608 (2002).
[CrossRef]

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Figures (4)

Fig. 1.
Fig. 1.

RCWA plots with highlighted paths found for reflected (a) phase (path in black) and (b) amplitude (path in white) as a function of the period and duty cycle of the grating. The plots are optimized for TM polarization and normal incidence. (c) Simulated top view of a quarter of the grating lens with f = 100 μm showing several phase jump regions. Grating ridges are visualized in black and grooves in white.

Fig. 2.
Fig. 2.

(a) Quarter of the simulated grating geometry with a plane wave incident from the top. (b) 3D simulated averaged power flow for the 2D grating design exhibiting a focal spot around 4 μm above the grating plane. The plots are optimized for TM polarization and normal incidence. Numbers denote spatial dimensions in micrometers.

Fig. 3.
Fig. 3.

Scanning micrograph of the entire fabricated grating lens for f = 100 μm (top view). The inset emphasizes the region with two phase jumps (taken at 70° viewing angle).

Fig. 4.
Fig. 4.

Lateral intensity profiles of the reflected focal spot for TM (solid black line) and TE polarization (dashed grey line) together with the respective images. The first-order rings of the Airy diffraction pattern are clearly visible in the intensity plots.

Equations (1)

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ϕ ( r ) = ( 2 π λ ) * ( r 2 + f 2 f )

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