Abstract

We investigate the properties of an interfering optical coherence lattice, which is generated by passing an optical coherence lattice through a wavefront-folding interferometer. Two symmetrical lattices are formed in the far-field. Changing the phase difference between the two optical paths causes the interference pattern, and thus the far-field intensity profile to change. In addition, we have shown that in the non-uniform case, the intensity pattern can also be changed by varying the weight distribution parameter. Our results may be applied in free-space communications and periodic trapping of micro-particles.

© 2017 Optical Society of America

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References

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2016 (4)

2015 (4)

2014 (3)

M. Kumar and J. Joseph, “Optical generation of a spatially variant two-dimensional lattice structure by using a phase only spatial light modulator,” Appl. Phys. Lett. 105(5), 051102 (2014).
[Crossref]

B. C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[Crossref] [PubMed]

L. Ma and S. A. Ponomarenko, “Optical coherence gratings and lattices,” Opt. Lett. 39(23), 6656–6659 (2014).
[Crossref] [PubMed]

2010 (1)

S. López-Aguayo, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Method to Generate Complex Quasinondiffracting Optical Lattices,” Phys. Rev. Lett. 105(1), 013902 (2010).
[Crossref] [PubMed]

2007 (1)

2005 (4)

2004 (1)

S. A. Ponomarenko and G. P. Agrawal, “Asymmetric incoherent vector solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(3), 036604 (2004).
[Crossref] [PubMed]

2003 (1)

M. P. MacDonald, G. C. Spalding, and K. Dholakia, “Microfluidic sorting in an optical lattice,” Nature 426(6965), 421–424 (2003).
[Crossref] [PubMed]

2002 (1)

2000 (1)

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404(6773), 53–56 (2000).
[Crossref] [PubMed]

1997 (1)

V. Berger, O. Gauthler-Lafaye, and E. Costard, “Photonic band gaps and holography,” J. Appl. Phys. 82(1), 60–64 (1997).
[Crossref]

1994 (2)

K. I. Petsas, A. B. Coates, and G. Grynberg, “Crystallography of optical lattices,” Phys. Rev. A 50(6), 5173–5189 (1994).
[Crossref] [PubMed]

P. Senthilkumaran and R. S. Sirohi, “Michelson interferometers in tandem for array generation,” Opt. Commun. 105(3–4), 158–160 (1994).
[Crossref]

1988 (2)

Q. He, J. Turunen, and A. T. Friberg, “Propagation and imaging experiments with Gausian Schell-model sources,” Opt. Commun. 67(4), 245–250 (1988).
[Crossref]

F. Gori, G. Guattari, C. Palma, and C. Padovani, “Specular cross-spectral density functions,” Opt. Commun. 68(4), 239–243 (1988).
[Crossref]

1987 (2)

P. DeSantis, F. Gori, G. Guattari, and C. Palma, “A space-time modulated field with specular coherence function,” Opt. Commun. 64(1), 9–14 (1987).
[Crossref]

A. S. Marathay, “Noncoherent-object hologram: its reconstruction and optical processing,” J. Opt. Soc. Am. A 4(10), 1861–1868 (1987).
[Crossref]

Agrawal, G. P.

S. A. Ponomarenko and G. P. Agrawal, “Asymmetric incoherent vector solitons,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 69(3), 036604 (2004).
[Crossref] [PubMed]

Bembenek, J. N.

B. C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[Crossref] [PubMed]

Berger, V.

V. Berger, O. Gauthler-Lafaye, and E. Costard, “Photonic band gaps and holography,” J. Appl. Phys. 82(1), 60–64 (1997).
[Crossref]

Betzig, E.

B. C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[Crossref] [PubMed]

E. Betzig, “Sparse and composite coherent lattices,” Phys. Rev. A 71(6), 063406 (2005).
[Crossref]

Bloch, I.

I. Bloch, “Ultracold quantum gases in optical lattices,” Nat. Phys. 1(1), 23–30 (2005).
[Crossref]

Böhme, R.

B. C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[Crossref] [PubMed]

Cai, Y.

Y. Chen, S. A. Ponomarenko, and Y. Cai, “Experimental generation of optical coherence lattices,” Appl. Phys. Lett. 109(6), 061107 (2016).
[Crossref]

X. Liu, J. Yu, Y. Cai, and S. A. Ponomarenko, “Propagation of optical coherence lattices in the turbulent atmosphere,” Opt. Lett. 41(18), 4182–4185 (2016).
[Crossref] [PubMed]

Campbell, M.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404(6773), 53–56 (2000).
[Crossref] [PubMed]

Chen, B. C.

B. C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[Crossref] [PubMed]

Chen, Y.

Y. Chen, S. A. Ponomarenko, and Y. Cai, “Experimental generation of optical coherence lattices,” Appl. Phys. Lett. 109(6), 061107 (2016).
[Crossref]

Chen, Z.

Coates, A. B.

K. I. Petsas, A. B. Coates, and G. Grynberg, “Crystallography of optical lattices,” Phys. Rev. A 50(6), 5173–5189 (1994).
[Crossref] [PubMed]

Cooper, J.

Costard, E.

V. Berger, O. Gauthler-Lafaye, and E. Costard, “Photonic band gaps and holography,” J. Appl. Phys. 82(1), 60–64 (1997).
[Crossref]

Courtial, J.

Daria, V.

Davidson, M. W.

B. C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[Crossref] [PubMed]

Denning, R. G.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404(6773), 53–56 (2000).
[Crossref] [PubMed]

DeSantis, P.

P. DeSantis, F. Gori, G. Guattari, and C. Palma, “A space-time modulated field with specular coherence function,” Opt. Commun. 64(1), 9–14 (1987).
[Crossref]

Dholakia, K.

M. P. MacDonald, G. C. Spalding, and K. Dholakia, “Microfluidic sorting in an optical lattice,” Nature 426(6965), 421–424 (2003).
[Crossref] [PubMed]

English, B. P.

B. C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[Crossref] [PubMed]

Friberg, A. T.

Q. He, J. Turunen, and A. T. Friberg, “Propagation and imaging experiments with Gausian Schell-model sources,” Opt. Commun. 67(4), 245–250 (1988).
[Crossref]

Fritz-Laylin, L.

B. C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[Crossref] [PubMed]

Gauthler-Lafaye, O.

V. Berger, O. Gauthler-Lafaye, and E. Costard, “Photonic band gaps and holography,” J. Appl. Phys. 82(1), 60–64 (1997).
[Crossref]

Glückstad, J.

Gori, F.

F. Gori, G. Guattari, C. Palma, and C. Padovani, “Specular cross-spectral density functions,” Opt. Commun. 68(4), 239–243 (1988).
[Crossref]

P. DeSantis, F. Gori, G. Guattari, and C. Palma, “A space-time modulated field with specular coherence function,” Opt. Commun. 64(1), 9–14 (1987).
[Crossref]

Grill, S. W.

B. C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[Crossref] [PubMed]

Grynberg, G.

K. I. Petsas, A. B. Coates, and G. Grynberg, “Crystallography of optical lattices,” Phys. Rev. A 50(6), 5173–5189 (1994).
[Crossref] [PubMed]

Guattari, G.

F. Gori, G. Guattari, C. Palma, and C. Padovani, “Specular cross-spectral density functions,” Opt. Commun. 68(4), 239–243 (1988).
[Crossref]

P. DeSantis, F. Gori, G. Guattari, and C. Palma, “A space-time modulated field with specular coherence function,” Opt. Commun. 64(1), 9–14 (1987).
[Crossref]

Guo, M.

Hammer, J. A.

B. C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[Crossref] [PubMed]

Harrison, M. T.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404(6773), 53–56 (2000).
[Crossref] [PubMed]

He, Q.

Q. He, J. Turunen, and A. T. Friberg, “Propagation and imaging experiments with Gausian Schell-model sources,” Opt. Commun. 67(4), 245–250 (1988).
[Crossref]

Janetopoulos, C.

B. C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[Crossref] [PubMed]

Jordan, P.

Joseph, J.

M. Kumar and J. Joseph, “Optical generation of a spatially variant two-dimensional lattice structure by using a phase only spatial light modulator,” Appl. Phys. Lett. 105(5), 051102 (2014).
[Crossref]

Kartashov, Y. V.

S. López-Aguayo, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Method to Generate Complex Quasinondiffracting Optical Lattices,” Phys. Rev. Lett. 105(1), 013902 (2010).
[Crossref] [PubMed]

Kiehart, D. P.

B. C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[Crossref] [PubMed]

Korotkova, O.

Kumar, M.

M. Kumar and J. Joseph, “Optical generation of a spatially variant two-dimensional lattice structure by using a phase only spatial light modulator,” Appl. Phys. Lett. 105(5), 051102 (2014).
[Crossref]

Legant, W. R.

B. C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[Crossref] [PubMed]

Lippincott-Schwartz, J.

B. C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[Crossref] [PubMed]

Liu, X.

Liu, Z.

B. C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[Crossref] [PubMed]

López-Aguayo, S.

S. López-Aguayo, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Method to Generate Complex Quasinondiffracting Optical Lattices,” Phys. Rev. Lett. 105(1), 013902 (2010).
[Crossref] [PubMed]

Ma, L.

MacDonald, M. P.

M. P. MacDonald, G. C. Spalding, and K. Dholakia, “Microfluidic sorting in an optical lattice,” Nature 426(6965), 421–424 (2003).
[Crossref] [PubMed]

Mao, Y.

Marathay, A. S.

McCarthy, K.

Mei, Z.

Milkie, D. E.

B. C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[Crossref] [PubMed]

Mimori-Kiyosue, Y.

B. C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[Crossref] [PubMed]

Mitchell, D. M.

B. C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[Crossref] [PubMed]

Mullins, R. D.

B. C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[Crossref] [PubMed]

Padgett, M.

Padovani, C.

F. Gori, G. Guattari, C. Palma, and C. Padovani, “Specular cross-spectral density functions,” Opt. Commun. 68(4), 239–243 (1988).
[Crossref]

Palma, C.

F. Gori, G. Guattari, C. Palma, and C. Padovani, “Specular cross-spectral density functions,” Opt. Commun. 68(4), 239–243 (1988).
[Crossref]

P. DeSantis, F. Gori, G. Guattari, and C. Palma, “A space-time modulated field with specular coherence function,” Opt. Commun. 64(1), 9–14 (1987).
[Crossref]

Partanen, H.

Petsas, K. I.

K. I. Petsas, A. B. Coates, and G. Grynberg, “Crystallography of optical lattices,” Phys. Rev. A 50(6), 5173–5189 (1994).
[Crossref] [PubMed]

Piestun, R.

Ponomarenko, S. A.

Reymann, A. C.

B. C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[Crossref] [PubMed]

Ritter, A. T.

B. C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[Crossref] [PubMed]

Rodrigo, P.

Romero, D. P.

B. C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[Crossref] [PubMed]

Schonbrun, E.

Senthilkumaran, P.

S. Vyas and P. Senthilkumaran, “Interferometric optical vortex array generator,” Appl. Opt. 46(15), 2893–2898 (2007).
[Crossref] [PubMed]

P. Senthilkumaran and R. S. Sirohi, “Michelson interferometers in tandem for array generation,” Opt. Commun. 105(3–4), 158–160 (1994).
[Crossref]

Seydoux, G.

B. C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[Crossref] [PubMed]

Shao, L.

B. C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[Crossref] [PubMed]

Sharmin, N.

Sharp, D. N.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404(6773), 53–56 (2000).
[Crossref] [PubMed]

Sirohi, R. S.

P. Senthilkumaran and R. S. Sirohi, “Michelson interferometers in tandem for array generation,” Opt. Commun. 105(3–4), 158–160 (1994).
[Crossref]

Spalding, G. C.

M. P. MacDonald, G. C. Spalding, and K. Dholakia, “Microfluidic sorting in an optical lattice,” Nature 426(6965), 421–424 (2003).
[Crossref] [PubMed]

Tervo, J.

Torner, L.

S. López-Aguayo, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Method to Generate Complex Quasinondiffracting Optical Lattices,” Phys. Rev. Lett. 105(1), 013902 (2010).
[Crossref] [PubMed]

Tulu, U. S.

B. C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[Crossref] [PubMed]

Turberfield, A. J.

M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404(6773), 53–56 (2000).
[Crossref] [PubMed]

Turunen, J.

H. Partanen, N. Sharmin, J. Tervo, and J. Turunen, “Specular and antispecular light beams,” Opt. Express 23(22), 28718–28727 (2015).
[Crossref] [PubMed]

Q. He, J. Turunen, and A. T. Friberg, “Propagation and imaging experiments with Gausian Schell-model sources,” Opt. Commun. 67(4), 245–250 (1988).
[Crossref]

Vyas, S.

Vysloukh, V. A.

S. López-Aguayo, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Method to Generate Complex Quasinondiffracting Optical Lattices,” Phys. Rev. Lett. 105(1), 013902 (2010).
[Crossref] [PubMed]

Wang, J. T.

B. C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[Crossref] [PubMed]

Wang, K.

B. C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[Crossref] [PubMed]

Wu, X. S.

B. C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[Crossref] [PubMed]

Wulff, K.

Yu, J.

Zhao, D.

Zhou, Z.

Appl. Opt. (2)

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M. Kumar and J. Joseph, “Optical generation of a spatially variant two-dimensional lattice structure by using a phase only spatial light modulator,” Appl. Phys. Lett. 105(5), 051102 (2014).
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Y. Chen, S. A. Ponomarenko, and Y. Cai, “Experimental generation of optical coherence lattices,” Appl. Phys. Lett. 109(6), 061107 (2016).
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V. Berger, O. Gauthler-Lafaye, and E. Costard, “Photonic band gaps and holography,” J. Appl. Phys. 82(1), 60–64 (1997).
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M. Campbell, D. N. Sharp, M. T. Harrison, R. G. Denning, and A. J. Turberfield, “Fabrication of photonic crystals for the visible spectrum by holographic lithography,” Nature 404(6773), 53–56 (2000).
[Crossref] [PubMed]

M. P. MacDonald, G. C. Spalding, and K. Dholakia, “Microfluidic sorting in an optical lattice,” Nature 426(6965), 421–424 (2003).
[Crossref] [PubMed]

Opt. Commun. (4)

P. Senthilkumaran and R. S. Sirohi, “Michelson interferometers in tandem for array generation,” Opt. Commun. 105(3–4), 158–160 (1994).
[Crossref]

P. DeSantis, F. Gori, G. Guattari, and C. Palma, “A space-time modulated field with specular coherence function,” Opt. Commun. 64(1), 9–14 (1987).
[Crossref]

F. Gori, G. Guattari, C. Palma, and C. Padovani, “Specular cross-spectral density functions,” Opt. Commun. 68(4), 239–243 (1988).
[Crossref]

Q. He, J. Turunen, and A. T. Friberg, “Propagation and imaging experiments with Gausian Schell-model sources,” Opt. Commun. 67(4), 245–250 (1988).
[Crossref]

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K. I. Petsas, A. B. Coates, and G. Grynberg, “Crystallography of optical lattices,” Phys. Rev. A 50(6), 5173–5189 (1994).
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S. López-Aguayo, Y. V. Kartashov, V. A. Vysloukh, and L. Torner, “Method to Generate Complex Quasinondiffracting Optical Lattices,” Phys. Rev. Lett. 105(1), 013902 (2010).
[Crossref] [PubMed]

Science (1)

B. C. Chen, W. R. Legant, K. Wang, L. Shao, D. E. Milkie, M. W. Davidson, C. Janetopoulos, X. S. Wu, J. A. Hammer, Z. Liu, B. P. English, Y. Mimori-Kiyosue, D. P. Romero, A. T. Ritter, J. Lippincott-Schwartz, L. Fritz-Laylin, R. D. Mullins, D. M. Mitchell, J. N. Bembenek, A. C. Reymann, R. Böhme, S. W. Grill, J. T. Wang, G. Seydoux, U. S. Tulu, D. P. Kiehart, and E. Betzig, “Lattice light-sheet microscopy: Imaging molecules to embryos at high spatiotemporal resolution,” Science 346(6208), 1257998 (2014).
[Crossref] [PubMed]

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E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge University, 2007).

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Figures (6)

Fig. 1
Fig. 1 Wavefront-folding interferometer. S is the source, BS is a non-polarizing beam splitter, PRx and PRy are right-angle prisms.
Fig. 2
Fig. 2 Intensity distributions of the input and output beams of the WFI in the uniform case. Row 1, evolution of intensity profile of a uniformly distributed OCL (input). The rows are from 2 to 4 the intensity distributions of the corresponding interfering OCL (output) with the phase difference ϕ = 0 , π / 2 , π , respectively. The first images are calculated immediately behind the interferometer.
Fig. 3
Fig. 3 The modulus of the spectral degree of coherence between two symmetrical points P 1 = ( X / 2 , Y / 2 ) and P 2 = ( X / 2 , Y / 2 ) . Rows 1 and 2 correspond to the coherence distributions of a uniformly distributed OCL and a uniformly distributed interfering OCL (with ϕ = π / 2 ), respectively.
Fig. 4
Fig. 4 The modulus of the spectral degree of coherence between two axial points P 1 = ( X 1 , 0 ) and P 2 = ( X 2 , 0 ) . Rows 1 and 2 correspond to the coherence distributions of a uniformly distributed interfering OCL with the phase differences ϕ = 0 and ϕ = π , respectively.
Fig. 5
Fig. 5 Intensity distributions of the input and output beams of the WFI in the non-uniform case. Row 1, evolution of intensity profile of a non-uniformly distributed OCL. The rows are from 2 to 4 the intensity distributions of the corresponding interfering OCL with the phase difference ϕ = 0 , π / 2 , π , respectively. The weight distribution parameter γ = 1 .
Fig. 6
Fig. 6 Intensity profiles of non-uniformly distributed OCLs (column 1) and the corresponding interfering OCLs (columns 2 to 4) in the far zone ( Z = 5 ). Rows 1 and 2 correspond to γ =2 and γ =3 , respectively.

Equations (10)

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E ( x , y ) = 1 2 [ E 0 ( x , y ) + E 0 ( x , y ) exp ( i ϕ ) ] ,
W ( x 1 , y 1 , x 2 , y 2 ) = 1 2 [ W 0 ( x 1 , y 1 , x 2 , y 2 ) + W 0 ( x 1 , y 1 , x 2 , y 2 ) ] + 1 2 [ W 0 ( x 1 , y 1 , x 2 , y 2 ) exp ( i ϕ ) + W 0 ( x 1 , y 1 , x 2 , y 2 ) exp ( i ϕ ) ] ,
W 0 ( X 1 , Y 1 , X 2 , Y 2 ) = s = X , Y n s v n s π exp [ s 1 2 + s 2 2 2 i π n s ( s 1 s 2 ) a ] ,
W ( X 1 , Y 1 , X 2 , Y 2 ) = exp ( X 1 2 + Y 1 2 + X 2 2 + Y 2 2 2 ) n X n Y v n X v n Y π × { cos [ π n X a ( X 1 X 2 ) π n Y a ( Y 1 Y 2 ) ] + cos [ π n X a ( X 1 + X 2 ) π n Y a ( Y 1 + Y 2 ) ϕ ] } .
I ( X , Y ) = exp [ ( X 2 + Y 2 ) ] n X n Y v n X v n Y π { 1 + cos [ 2 π a ( n X X n Y Y ) ϕ ] } .
W ( P 1 , P 2 , Z ) = 1 π σ 2 ( Z ) exp [ i σ 0 2 R ( Z ) ( P 1 2 P 2 2 ) 1 2 σ 2 ( Z ) ( P 1 2 + P 2 2 ) ] n X n Y v n X v n Y × exp [ π 2 Z a 2 R ( Z ) ( n X 2 + n Y 2 ) ] { cos h [ H 1 ( P 1 , P 2 , Z ) ] + cos h [ H 2 ( P 1 , P 2 , Z ) + i ϕ ] } ,
H 1 ( P 1 , P 2 , Z ) = π a R ( Z ) [ n X ( X 1 + X 2 ) i n X Z ( X 1 X 2 ) n Y ( Y 1 + Y 2 ) + i n Y Z ( Y 1 Y 2 ) ] ,
H 2 ( P 1 , P 2 , Z ) = π a R ( Z ) [ n X ( X 1 X 2 ) i n X Z ( X 1 + X 2 ) n Y ( Y 1 Y 2 ) + i n Y Z ( Y 1 + Y 2 ) ] .
I ( P , Z ) = W ( P , P , Z ) ,
μ ( P 1 , P 2 , Z ) = W ( P 1 , P 2 , Z ) I ( P 1 , Z ) I ( P 2 , Z ) .

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