Abstract

We found that by opportune functionalization of a polar dielectric substrate, a self-arrangement of hemi cylindrical or toroidal-shaped liquid droplets can be obtained. The process takes place when a thermal stimulus is provided to a poled substrate whose surface is covered by an oily substance layer. Liquid droplet self-arrangement is due to the pyroelectric effect, and interferometric characterization of the droplets is also reported. We investigated this open microfluidic system for exploring the possibility to obtain liquid cylindrical microlens with variable focal length. Liquid microtoroidal structures arrays are also realized. They could find application as resonant liquid microcavities for whispering gallery modes.

© 2009 Optical Society of America

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2009

J. Heikenfeld, N. Smith, M. Dhindsa, K. Zhou, M. Kilaru, L. Hou, J. Zhang, E. Kreit, and B. Raj, Opt. Photonics News 20(1), 20 (2009).
[CrossRef]

L. Miccio, A. Finizio, S. Grilli, V. Vespini, M. Paturzo, S. De Nicola, and P. Ferraro, Opt. Express 17, 2487 (2009).
[CrossRef] [PubMed]

2008

S. Grilli, M. Paturzo, L. Miccio, and P. Ferraro, Meas. Sci. Technol. 19, 074008 (2008).
[CrossRef]

G. Milne, G. D. M. Jeffries, and D. T. Chiu, Appl. Phys. Lett. 92, 261101 (2008).
[CrossRef]

P. Ferraro, L. Miccio, S. Grilli, A. Finizio, S. De Nicola, and V. Vespini, Opt. Photonics News 19(12), 34 (2008).
[CrossRef]

J. H. Lee, Y. H. Ho, K. Y. Chen, H. Y. Lin, J. H. Fang, S. C. Hsu, J. R. Lin, and M. K. Wei, Opt. Express 16, 21184 (2008).
[CrossRef] [PubMed]

D. Xia and S. R. J. Brueck, Nano Lett. 8, 2819 (2008).
[CrossRef] [PubMed]

A. Kiraz, Y. Karadag, and A. F. Coskun, Appl. Phys. Lett. 92, 191104 (2008).
[CrossRef]

P.-H. Huang, T. C. Huang, Y.-T. Sun, and S. Y. Yang, Opt. Express 16, 3041 (2008).
[CrossRef] [PubMed]

H. Ren and S.-T. Wu, Opt. Express 16, 2646 (2008).
[CrossRef] [PubMed]

X. Huang, C. M. Cheng, L. Wang, C. C. Su, M. S. Ho, P. R. LeDuc, and Q. Lin, Appl. Phys. Lett. 92, 251904 (2008).
[CrossRef]

2007

C. C. Cheng and J. A. Yeh, Opt. Express 15, 7140 (2007).
[CrossRef] [PubMed]

S. I. Shopova, H. Zhou, X. Fan, and P. Zhang, Appl. Phys. Lett. 90, 221101 (2007).
[CrossRef]

X. Mao, J. R. Waldeisen, B. K. Juluri, and T. J. Huang, Lab Chip 7, 1303 (2007).
[CrossRef] [PubMed]

2006

S. Y. Lee, H. W. Tung, W. C. Chen, and W. Fang, IEEE Photon. Technol. Lett. 18, 2191 (2006).
[CrossRef]

L. Lin Jr., G. B. Lee, Y. H. Chang, and K. Y. Lien, Langmuir 22, 484 (2006).
[CrossRef]

P. M. Moran, S. Dharmatilleke, A. H. Khaw, K. W. Tan, M. L. Chan, and I. Rodriguez, Appl. Phys. Lett. 88, 041120 (2006).
[CrossRef]

2005

L. PangU. Levy, K. Campbell, A. Groisman, and Y. Fainman, Opt. Express 13, 9003 (2005).
[CrossRef] [PubMed]

H. Ren, Y. H. Fan, S. Gauza, and S. T. Wu, Jpn. J. Appl. Phys. 44, 243 (2005).
[CrossRef]

2004

S. Kuiper and B. H. W. Hendriks, Appl. Phys. Lett. 85, 1128 (2004).
[CrossRef]

2003

2000

B. Berge and J. Peseux, Eur. Phys. J. E 3, 159 (2000).
[CrossRef]

L. G. Commander, S. E. Day, and D. R. Selviah, Opt. Commun. 177, 157 (2000).
[CrossRef]

Berge, B.

B. Berge and J. Peseux, Eur. Phys. J. E 3, 159 (2000).
[CrossRef]

Brueck, S. R. J.

D. Xia and S. R. J. Brueck, Nano Lett. 8, 2819 (2008).
[CrossRef] [PubMed]

Campbell, K.

Chan, M. L.

P. M. Moran, S. Dharmatilleke, A. H. Khaw, K. W. Tan, M. L. Chan, and I. Rodriguez, Appl. Phys. Lett. 88, 041120 (2006).
[CrossRef]

Chang, Y. H.

L. Lin Jr., G. B. Lee, Y. H. Chang, and K. Y. Lien, Langmuir 22, 484 (2006).
[CrossRef]

Chen, K. Y.

Chen, W. C.

S. Y. Lee, H. W. Tung, W. C. Chen, and W. Fang, IEEE Photon. Technol. Lett. 18, 2191 (2006).
[CrossRef]

Cheng, C. C.

Cheng, C. M.

X. Huang, C. M. Cheng, L. Wang, C. C. Su, M. S. Ho, P. R. LeDuc, and Q. Lin, Appl. Phys. Lett. 92, 251904 (2008).
[CrossRef]

Chiu, D. T.

G. Milne, G. D. M. Jeffries, and D. T. Chiu, Appl. Phys. Lett. 92, 261101 (2008).
[CrossRef]

Chronis, N.

Commander, L. G.

L. G. Commander, S. E. Day, and D. R. Selviah, Opt. Commun. 177, 157 (2000).
[CrossRef]

Coskun, A. F.

A. Kiraz, Y. Karadag, and A. F. Coskun, Appl. Phys. Lett. 92, 191104 (2008).
[CrossRef]

Day, S. E.

L. G. Commander, S. E. Day, and D. R. Selviah, Opt. Commun. 177, 157 (2000).
[CrossRef]

De Nicola, S.

L. Miccio, A. Finizio, S. Grilli, V. Vespini, M. Paturzo, S. De Nicola, and P. Ferraro, Opt. Express 17, 2487 (2009).
[CrossRef] [PubMed]

P. Ferraro, L. Miccio, S. Grilli, A. Finizio, S. De Nicola, and V. Vespini, Opt. Photonics News 19(12), 34 (2008).
[CrossRef]

DeVore, S. L.

D. Malacara and S. L. DeVore, in Optical Shop Testing, D.Malacara, ed. (Wiley, 1992), pp. 455-480.

Dharmatilleke, S.

P. M. Moran, S. Dharmatilleke, A. H. Khaw, K. W. Tan, M. L. Chan, and I. Rodriguez, Appl. Phys. Lett. 88, 041120 (2006).
[CrossRef]

Dhindsa, M.

J. Heikenfeld, N. Smith, M. Dhindsa, K. Zhou, M. Kilaru, L. Hou, J. Zhang, E. Kreit, and B. Raj, Opt. Photonics News 20(1), 20 (2009).
[CrossRef]

Fainman, Y.

Fan, X.

S. I. Shopova, H. Zhou, X. Fan, and P. Zhang, Appl. Phys. Lett. 90, 221101 (2007).
[CrossRef]

Fan, Y. H.

H. Ren, Y. H. Fan, S. Gauza, and S. T. Wu, Jpn. J. Appl. Phys. 44, 243 (2005).
[CrossRef]

Fang, J. H.

Fang, W.

S. Y. Lee, H. W. Tung, W. C. Chen, and W. Fang, IEEE Photon. Technol. Lett. 18, 2191 (2006).
[CrossRef]

Ferraro, P.

L. Miccio, A. Finizio, S. Grilli, V. Vespini, M. Paturzo, S. De Nicola, and P. Ferraro, Opt. Express 17, 2487 (2009).
[CrossRef] [PubMed]

P. Ferraro, L. Miccio, S. Grilli, A. Finizio, S. De Nicola, and V. Vespini, Opt. Photonics News 19(12), 34 (2008).
[CrossRef]

S. Grilli, M. Paturzo, L. Miccio, and P. Ferraro, Meas. Sci. Technol. 19, 074008 (2008).
[CrossRef]

P. Ferraro, S. Grilli, M. Paturzo, and S. Nicola, in Ferroelectric Crystals for Photonic Applications, P.Ferraro, S.Grilli, and P.De Natale, eds. (Springer, 2008), pp. 165-208.

Finizio, A.

L. Miccio, A. Finizio, S. Grilli, V. Vespini, M. Paturzo, S. De Nicola, and P. Ferraro, Opt. Express 17, 2487 (2009).
[CrossRef] [PubMed]

P. Ferraro, L. Miccio, S. Grilli, A. Finizio, S. De Nicola, and V. Vespini, Opt. Photonics News 19(12), 34 (2008).
[CrossRef]

Gauza, S.

H. Ren, Y. H. Fan, S. Gauza, and S. T. Wu, Jpn. J. Appl. Phys. 44, 243 (2005).
[CrossRef]

Grilli, S.

L. Miccio, A. Finizio, S. Grilli, V. Vespini, M. Paturzo, S. De Nicola, and P. Ferraro, Opt. Express 17, 2487 (2009).
[CrossRef] [PubMed]

P. Ferraro, L. Miccio, S. Grilli, A. Finizio, S. De Nicola, and V. Vespini, Opt. Photonics News 19(12), 34 (2008).
[CrossRef]

S. Grilli, M. Paturzo, L. Miccio, and P. Ferraro, Meas. Sci. Technol. 19, 074008 (2008).
[CrossRef]

P. Ferraro, S. Grilli, M. Paturzo, and S. Nicola, in Ferroelectric Crystals for Photonic Applications, P.Ferraro, S.Grilli, and P.De Natale, eds. (Springer, 2008), pp. 165-208.

Groisman, A.

Heikenfeld, J.

J. Heikenfeld, N. Smith, M. Dhindsa, K. Zhou, M. Kilaru, L. Hou, J. Zhang, E. Kreit, and B. Raj, Opt. Photonics News 20(1), 20 (2009).
[CrossRef]

Hendriks, B. H. W.

S. Kuiper and B. H. W. Hendriks, Appl. Phys. Lett. 85, 1128 (2004).
[CrossRef]

Ho, M. S.

X. Huang, C. M. Cheng, L. Wang, C. C. Su, M. S. Ho, P. R. LeDuc, and Q. Lin, Appl. Phys. Lett. 92, 251904 (2008).
[CrossRef]

Ho, Y. H.

Hou, L.

J. Heikenfeld, N. Smith, M. Dhindsa, K. Zhou, M. Kilaru, L. Hou, J. Zhang, E. Kreit, and B. Raj, Opt. Photonics News 20(1), 20 (2009).
[CrossRef]

Hsu, S. C.

Huang, P.-H.

Huang, T. C.

Huang, T. J.

X. Mao, J. R. Waldeisen, B. K. Juluri, and T. J. Huang, Lab Chip 7, 1303 (2007).
[CrossRef] [PubMed]

Huang, X.

X. Huang, C. M. Cheng, L. Wang, C. C. Su, M. S. Ho, P. R. LeDuc, and Q. Lin, Appl. Phys. Lett. 92, 251904 (2008).
[CrossRef]

Jeffries, G. D. M.

G. Milne, G. D. M. Jeffries, and D. T. Chiu, Appl. Phys. Lett. 92, 261101 (2008).
[CrossRef]

Jeong, K.-H.

Juluri, B. K.

X. Mao, J. R. Waldeisen, B. K. Juluri, and T. J. Huang, Lab Chip 7, 1303 (2007).
[CrossRef] [PubMed]

Karadag, Y.

A. Kiraz, Y. Karadag, and A. F. Coskun, Appl. Phys. Lett. 92, 191104 (2008).
[CrossRef]

Khaw, A. H.

P. M. Moran, S. Dharmatilleke, A. H. Khaw, K. W. Tan, M. L. Chan, and I. Rodriguez, Appl. Phys. Lett. 88, 041120 (2006).
[CrossRef]

Kilaru, M.

J. Heikenfeld, N. Smith, M. Dhindsa, K. Zhou, M. Kilaru, L. Hou, J. Zhang, E. Kreit, and B. Raj, Opt. Photonics News 20(1), 20 (2009).
[CrossRef]

Kiraz, A.

A. Kiraz, Y. Karadag, and A. F. Coskun, Appl. Phys. Lett. 92, 191104 (2008).
[CrossRef]

Kreit, E.

J. Heikenfeld, N. Smith, M. Dhindsa, K. Zhou, M. Kilaru, L. Hou, J. Zhang, E. Kreit, and B. Raj, Opt. Photonics News 20(1), 20 (2009).
[CrossRef]

Kuiper, S.

S. Kuiper and B. H. W. Hendriks, Appl. Phys. Lett. 85, 1128 (2004).
[CrossRef]

LeDuc, P. R.

X. Huang, C. M. Cheng, L. Wang, C. C. Su, M. S. Ho, P. R. LeDuc, and Q. Lin, Appl. Phys. Lett. 92, 251904 (2008).
[CrossRef]

Lee, G. B.

L. Lin Jr., G. B. Lee, Y. H. Chang, and K. Y. Lien, Langmuir 22, 484 (2006).
[CrossRef]

Lee, J. H.

Lee, L. P.

Lee, S. Y.

S. Y. Lee, H. W. Tung, W. C. Chen, and W. Fang, IEEE Photon. Technol. Lett. 18, 2191 (2006).
[CrossRef]

Levy, U.

Lien, K. Y.

L. Lin Jr., G. B. Lee, Y. H. Chang, and K. Y. Lien, Langmuir 22, 484 (2006).
[CrossRef]

Lin, H. Y.

Lin, J. R.

Lin, L.

L. Lin Jr., G. B. Lee, Y. H. Chang, and K. Y. Lien, Langmuir 22, 484 (2006).
[CrossRef]

Lin, Q.

X. Huang, C. M. Cheng, L. Wang, C. C. Su, M. S. Ho, P. R. LeDuc, and Q. Lin, Appl. Phys. Lett. 92, 251904 (2008).
[CrossRef]

Liu, G. L.

Malacara, D.

D. Malacara and S. L. DeVore, in Optical Shop Testing, D.Malacara, ed. (Wiley, 1992), pp. 455-480.

Mao, X.

X. Mao, J. R. Waldeisen, B. K. Juluri, and T. J. Huang, Lab Chip 7, 1303 (2007).
[CrossRef] [PubMed]

Miccio, L.

L. Miccio, A. Finizio, S. Grilli, V. Vespini, M. Paturzo, S. De Nicola, and P. Ferraro, Opt. Express 17, 2487 (2009).
[CrossRef] [PubMed]

S. Grilli, M. Paturzo, L. Miccio, and P. Ferraro, Meas. Sci. Technol. 19, 074008 (2008).
[CrossRef]

P. Ferraro, L. Miccio, S. Grilli, A. Finizio, S. De Nicola, and V. Vespini, Opt. Photonics News 19(12), 34 (2008).
[CrossRef]

Milne, G.

G. Milne, G. D. M. Jeffries, and D. T. Chiu, Appl. Phys. Lett. 92, 261101 (2008).
[CrossRef]

Moran, P. M.

P. M. Moran, S. Dharmatilleke, A. H. Khaw, K. W. Tan, M. L. Chan, and I. Rodriguez, Appl. Phys. Lett. 88, 041120 (2006).
[CrossRef]

Nicola, S.

P. Ferraro, S. Grilli, M. Paturzo, and S. Nicola, in Ferroelectric Crystals for Photonic Applications, P.Ferraro, S.Grilli, and P.De Natale, eds. (Springer, 2008), pp. 165-208.

Pang, L.

Paturzo, M.

L. Miccio, A. Finizio, S. Grilli, V. Vespini, M. Paturzo, S. De Nicola, and P. Ferraro, Opt. Express 17, 2487 (2009).
[CrossRef] [PubMed]

S. Grilli, M. Paturzo, L. Miccio, and P. Ferraro, Meas. Sci. Technol. 19, 074008 (2008).
[CrossRef]

P. Ferraro, S. Grilli, M. Paturzo, and S. Nicola, in Ferroelectric Crystals for Photonic Applications, P.Ferraro, S.Grilli, and P.De Natale, eds. (Springer, 2008), pp. 165-208.

Peseux, J.

B. Berge and J. Peseux, Eur. Phys. J. E 3, 159 (2000).
[CrossRef]

Raj, B.

J. Heikenfeld, N. Smith, M. Dhindsa, K. Zhou, M. Kilaru, L. Hou, J. Zhang, E. Kreit, and B. Raj, Opt. Photonics News 20(1), 20 (2009).
[CrossRef]

Ren, H.

H. Ren and S.-T. Wu, Opt. Express 16, 2646 (2008).
[CrossRef] [PubMed]

H. Ren, Y. H. Fan, S. Gauza, and S. T. Wu, Jpn. J. Appl. Phys. 44, 243 (2005).
[CrossRef]

Rodriguez, I.

P. M. Moran, S. Dharmatilleke, A. H. Khaw, K. W. Tan, M. L. Chan, and I. Rodriguez, Appl. Phys. Lett. 88, 041120 (2006).
[CrossRef]

Selviah, D. R.

L. G. Commander, S. E. Day, and D. R. Selviah, Opt. Commun. 177, 157 (2000).
[CrossRef]

Shopova, S. I.

S. I. Shopova, H. Zhou, X. Fan, and P. Zhang, Appl. Phys. Lett. 90, 221101 (2007).
[CrossRef]

Smith, N.

J. Heikenfeld, N. Smith, M. Dhindsa, K. Zhou, M. Kilaru, L. Hou, J. Zhang, E. Kreit, and B. Raj, Opt. Photonics News 20(1), 20 (2009).
[CrossRef]

Su, C. C.

X. Huang, C. M. Cheng, L. Wang, C. C. Su, M. S. Ho, P. R. LeDuc, and Q. Lin, Appl. Phys. Lett. 92, 251904 (2008).
[CrossRef]

Sun, Y.-T.

Tan, K. W.

P. M. Moran, S. Dharmatilleke, A. H. Khaw, K. W. Tan, M. L. Chan, and I. Rodriguez, Appl. Phys. Lett. 88, 041120 (2006).
[CrossRef]

Tung, H. W.

S. Y. Lee, H. W. Tung, W. C. Chen, and W. Fang, IEEE Photon. Technol. Lett. 18, 2191 (2006).
[CrossRef]

Vespini, V.

L. Miccio, A. Finizio, S. Grilli, V. Vespini, M. Paturzo, S. De Nicola, and P. Ferraro, Opt. Express 17, 2487 (2009).
[CrossRef] [PubMed]

P. Ferraro, L. Miccio, S. Grilli, A. Finizio, S. De Nicola, and V. Vespini, Opt. Photonics News 19(12), 34 (2008).
[CrossRef]

Waldeisen, J. R.

X. Mao, J. R. Waldeisen, B. K. Juluri, and T. J. Huang, Lab Chip 7, 1303 (2007).
[CrossRef] [PubMed]

Wang, L.

X. Huang, C. M. Cheng, L. Wang, C. C. Su, M. S. Ho, P. R. LeDuc, and Q. Lin, Appl. Phys. Lett. 92, 251904 (2008).
[CrossRef]

Wei, M. K.

Wu, S. T.

H. Ren, Y. H. Fan, S. Gauza, and S. T. Wu, Jpn. J. Appl. Phys. 44, 243 (2005).
[CrossRef]

Wu, S.-T.

Xia, D.

D. Xia and S. R. J. Brueck, Nano Lett. 8, 2819 (2008).
[CrossRef] [PubMed]

Yang, S. Y.

Yeh, J. A.

Zhang, J.

J. Heikenfeld, N. Smith, M. Dhindsa, K. Zhou, M. Kilaru, L. Hou, J. Zhang, E. Kreit, and B. Raj, Opt. Photonics News 20(1), 20 (2009).
[CrossRef]

Zhang, P.

S. I. Shopova, H. Zhou, X. Fan, and P. Zhang, Appl. Phys. Lett. 90, 221101 (2007).
[CrossRef]

Zhou, H.

S. I. Shopova, H. Zhou, X. Fan, and P. Zhang, Appl. Phys. Lett. 90, 221101 (2007).
[CrossRef]

Zhou, K.

J. Heikenfeld, N. Smith, M. Dhindsa, K. Zhou, M. Kilaru, L. Hou, J. Zhang, E. Kreit, and B. Raj, Opt. Photonics News 20(1), 20 (2009).
[CrossRef]

Appl. Phys. Lett.

S. Kuiper and B. H. W. Hendriks, Appl. Phys. Lett. 85, 1128 (2004).
[CrossRef]

X. Huang, C. M. Cheng, L. Wang, C. C. Su, M. S. Ho, P. R. LeDuc, and Q. Lin, Appl. Phys. Lett. 92, 251904 (2008).
[CrossRef]

P. M. Moran, S. Dharmatilleke, A. H. Khaw, K. W. Tan, M. L. Chan, and I. Rodriguez, Appl. Phys. Lett. 88, 041120 (2006).
[CrossRef]

G. Milne, G. D. M. Jeffries, and D. T. Chiu, Appl. Phys. Lett. 92, 261101 (2008).
[CrossRef]

A. Kiraz, Y. Karadag, and A. F. Coskun, Appl. Phys. Lett. 92, 191104 (2008).
[CrossRef]

S. I. Shopova, H. Zhou, X. Fan, and P. Zhang, Appl. Phys. Lett. 90, 221101 (2007).
[CrossRef]

Eur. Phys. J. E

B. Berge and J. Peseux, Eur. Phys. J. E 3, 159 (2000).
[CrossRef]

IEEE Photon. Technol. Lett.

S. Y. Lee, H. W. Tung, W. C. Chen, and W. Fang, IEEE Photon. Technol. Lett. 18, 2191 (2006).
[CrossRef]

Jpn. J. Appl. Phys.

H. Ren, Y. H. Fan, S. Gauza, and S. T. Wu, Jpn. J. Appl. Phys. 44, 243 (2005).
[CrossRef]

Lab Chip

X. Mao, J. R. Waldeisen, B. K. Juluri, and T. J. Huang, Lab Chip 7, 1303 (2007).
[CrossRef] [PubMed]

Langmuir

L. Lin Jr., G. B. Lee, Y. H. Chang, and K. Y. Lien, Langmuir 22, 484 (2006).
[CrossRef]

Meas. Sci. Technol.

S. Grilli, M. Paturzo, L. Miccio, and P. Ferraro, Meas. Sci. Technol. 19, 074008 (2008).
[CrossRef]

Nano Lett.

D. Xia and S. R. J. Brueck, Nano Lett. 8, 2819 (2008).
[CrossRef] [PubMed]

Opt. Commun.

L. G. Commander, S. E. Day, and D. R. Selviah, Opt. Commun. 177, 157 (2000).
[CrossRef]

Opt. Express

Opt. Photonics News

P. Ferraro, L. Miccio, S. Grilli, A. Finizio, S. De Nicola, and V. Vespini, Opt. Photonics News 19(12), 34 (2008).
[CrossRef]

J. Heikenfeld, N. Smith, M. Dhindsa, K. Zhou, M. Kilaru, L. Hou, J. Zhang, E. Kreit, and B. Raj, Opt. Photonics News 20(1), 20 (2009).
[CrossRef]

Other

P. Ferraro, S. Grilli, M. Paturzo, and S. Nicola, in Ferroelectric Crystals for Photonic Applications, P.Ferraro, S.Grilli, and P.De Natale, eds. (Springer, 2008), pp. 165-208.

D. Malacara and S. L. DeVore, in Optical Shop Testing, D.Malacara, ed. (Wiley, 1992), pp. 455-480.

Supplementary Material (3)

» Media 1: AVI (1593 KB)     
» Media 2: AVI (1611 KB)     
» Media 3: AVI (1337 KB)     

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Figures (4)

Fig. 1
Fig. 1

(a) Image of the PPLN sample used for the cylindrical lens. (b) Image of a part of the domain wall used for single toroidal lens. (c) Typical periodic hexagonal structures used to form a microarray of toroidal lenses. Due to the strong refractive index variation along the domain walls, these are clearly visible with an optical microscope.

Fig. 2
Fig. 2

Schematic pictures of the poled region for (a) the PPLN sample and (c) the single domain wall. Optical microscope image of [(b), Media 1] cylindrical liquid lens and (d) toroidal lens.

Fig. 3
Fig. 3

Liquid microarray of liquid toroidal structures. The liquid follows the nonuniform geometry of each hexagon. (b) DH setup based on a Mach–Zehnder interferometer

Fig. 4
Fig. 4

(a) Wrapped phase distribution (Media 2) and (b) unwrapped phase distribution of the optical wavefront of the final frame at 30° (Media 3). (c) Fitted surface obtained by the two-dimensional fitting procedure, (d) focal length measurement at the stationary condition.

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