Abstract

Superpositions of coherent light waves typically interfere. We present superpositions of up to six plane waves that defy this expectation by having a perfectly homogeneous mean square of the electric field. For many applications in optics, these superpositions can be seen as having a homogeneous intensity. Our superpositions show interesting one-, two-, and three-dimensional patterns in their helicity densities, including several that support bright regions of superchirality. Our superpositions might be used to write chiral patterns in certain materials, and, conversely, such materials might be used as the basis of an “optical helicity camera” capable of recording spatial variations in helicity.

Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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References

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    [Crossref]
  2. G. N. Afanasiev and Y. P. Stepanovski, “The helicity of the free electromagnetic field and its physical meaning,” Nuovo Cim. A 109, 271–279 (1996).
    [Crossref]
  3. R. P. Cameron, S. M. Barnett, and A. M. Yao, “Optical helicity, optical spin and related quantities in electromagnetic theory,” New J. Phys. 14, 053050 (2012).
    [Crossref]
  4. R. P. Cameron and S. M. Barnett, “Electric-magnetic symmetry and Noether’s theorem,” New J. Phys. 14, 123019 (2012).
    [Crossref]
  5. R. P. Cameron, S. M. Barnett, and A. M. Yao, “Optical helicity of interfering waves,” J. Mod. Opt. 61, 25–31 (2013).
    [Crossref]
  6. Y. Tang and A. E. Cohen, “Optical chirality and its interaction with matter,” Phys. Rev. Lett. 104, 163901 (2010).
    [Crossref]
  7. E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Michailovski, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadowala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5, 783–787 (2010).
    [Crossref]
  8. Y. Tang and A. E. Cohen, “Enhanced enantioselectivity in excitation of chiral molecules by superchiral light,” Science 332, 333–336 (2011).
    [Crossref]
  9. C. Rosales-Guzmán, K. Volke-Sepulveda, and J. P. Torres, “Light with enhanced optical chirality,” Opt. Lett. 37, 3486–3488 (2012).
    [Crossref]
  10. M. Schäferling, X. Yin, and H. Giessen, “Formation of chiral fields in a symmetric environment,” Opt. Express 20, 26326–26336 (2012).
    [Crossref]
  11. M. Schäferling, X. Yin, N. Engheta, and H. Giessen, “Helical plasmonic nanostructures as prototypical chiral near-field sources,” ACS Photon. 1, 530–537 (2014).
    [Crossref]
  12. X. Tian, Y. Fang, and M. Sun, “Formation of enhanced uniform chiral fields in symmetric dimer nanostructures,” Sci. Rep. 5, 17534 (2015).
    [Crossref]
  13. M. Schäferling, N. Engheta, H. Giessen, and T. Weiss, “Reducing the complexity: enantioselective chiral near-fields by diagonal slit and mirror configuration,” ACS Photon. 3, 1076–1084 (2016).
    [Crossref]
  14. C. Kramer, M. Schäferling, T. Weiss, H. Giessen, and T. Brixner, “Analytic optimization of near-field optical chirality enhancement,” ACS Photon. 4, 396–406 (2017).
    [Crossref]
  15. L. Woltjer, “A theorem on force-free magnetic fields,” Proc. Natl. Acad. Sci. USA 44, 289–291 (1958).
    [Crossref]
  16. M. G. Calkin, “An invariance property of the electric field,” Am. J. Phys. 33, 958–960 (1965).
    [Crossref]
  17. K. C. van Kruining and J. B. Götte, “The conditions for the preservation of duality symmetry in a linear medium,” J. Opt. 18, 085601 (2016).
    [Crossref]
  18. R. P. Cameron, S. M. Barnett, and A. M. Yao, “Discriminatory optical force for chiral molecules,” New J. Phys. 16, 013020 (2014).
    [Crossref]
  19. A. Canaguier-Durand, J. A. Hutchison, C. Genet, and T. W. Ebbesen, “Mechanical separation of chiral dipoles by chiral light,” New J. Phys. 15, 123037 (2013).
    [Crossref]
  20. S. K. Mohanty, K. D. Rao, and P. K. Gupta, “Optical trap with spatially varying polarization: application in controlled orientation of birefringent microscopic particle(s),” Appl. Phys. B 80, 631–634 (2005).
    [Crossref]
  21. G. Cipparrone, I. Ricardez-Vargas, P. Pagliusi, and C. Provenzano, “Polarization gradient: exploring an original route for optical trapping and manipulation,” Opt. Express 18, 6008–6013 (2010).
    [Crossref]
  22. R. P. Cameron, A. M. Yao, and S. M. Barnett, “Diffraction gratings for chiral molecules and their applications,” J. Phys. Chem. A 118, 3472–3478 (2014).
    [Crossref]
  23. K. Hornberger, S. Gerlich, H. Ulbricht, L. Hackermüller, S. Nimmrichter, I. V. Goldt, O. Botalina, and M. Arndt, “Theory and experimental verification of Kapitza-Dirac-Talbot-Lau interferometry,” New J. Phys. 11, 043032 (2009).
    [Crossref]
  24. S. Eibenberger, S. Gerlich, M. Arndt, M. Mayor, and J. Tüxen, “Matter-wave interference of particles selected from a molecular library with masses exceeding 10,000  amu,” Phys. Chem. Chem. Phys. 15, 14696–14700 (2013).
    [Crossref]
  25. R. P. Cameron, J. B. Götte, S. M. Barnett, and J. P. Cotter, “Matter-wave grating distinguishing conservative and dissipative interactions,” Phys. Rev. A 94, 013604 (2016).
    [Crossref]
  26. L. Nikolova, T. Todorov, M. Ivanov, F. Andruzzi, S. Hvilsted, and P. Ramanujam, “Photoinduced circular anisotropy in side-chain azobenzene polyesters,” Opt. Mater. 8, 255–258 (1997).
    [Crossref]
  27. L. Nikolova, L. Nedelchev, T. Todorov, T. Petrova, N. Tomova, V. Dragostinova, P. S. Ramanujam, and S. Hvilsted, “Self-induced light polarization rotation in azobenzene-containing polymers,” Appl. Phys. Lett. 77, 657–659 (2000).
    [Crossref]
  28. G. Iftime, F. L. Labarthet, A. Natansohn, and P. Rochon, “Control of chirality of an azobenzene liquid crystalline polymer with circularly polarized light,” J. Am. Chem. Soc. 122, 12646–12650 (2000).
    [Crossref]
  29. S.-W. Choi, T. Izumi, Y. Hoshino, Y. Takanishi, K. Ishikawa, J. Watanabe, and H. Takezoe, “Circular-polarization-induced enantiomeric excess in liquid crystals of an achiral, bent-shaped mesogen,” Angew. Chem. 45, 1382–1385 (2006).
    [Crossref]
  30. R. M. Tejedor, L. Oriol, J. L. Serrano, F. Partal Ureña, and J. J. López González, “Photoinduced chiral nematic organization in an achiral glassy nematic azopolymer,” Adv. Funct. Mater. 17, 3486–3492 (2007).
    [Crossref]
  31. F. Vera, R. M. Tejedor, P. Romero, J. Barberá, M. B. Ros, J. L. Serrano, and T. Sierra, “Light-driven supramolecular chirality in propeller-like hydrogen-bonded complexes that show columnar mesomorphism,” Angew. Chem. 46, 1873–1877 (2007).
    [Crossref]
  32. J. D. Barrio, R. M. Tejedor, and L. Oriol, “Thermal and light control of the chiral order of azopolymers,” Eur. Polym. J. 48, 384–390 (2012).
    [Crossref]
  33. L. de Vega, S. van Cleuvenbergen, G. Depotter, E. M. García-Frutos, B. Gómez-Lor, A. Omenat, R. M. Tejedor, J. L. Serrano, G. Hennrich, and K. Clays, “Nonlinear optical thin film device from a chiral octopolar phenylacetylene liquid crystal,” J. Org. Chem. 77, 10891–10896 (2012).
    [Crossref]
  34. J. Kim, J. Lee, W. Y. Kim, H. Kim, S. Lee, H. C. Lee, Y. S. Lee, M. Seo, and S. Y. Kim, “Induction and control of supramolecular chirality by light in self-assembled helical nanostructures,” Nat. Commun. 6, 6959 (2015).
    [Crossref]
  35. G. Martínez-Ponce, C. Solano, R. J. Rodríguez González, L. Larios-López, D. Navarro-Rodríguez, and L. Nikolova, “All-optical switching using supramolecular chiral structures in azopolymers,” J. Opt. A 10, 115006 (2008).
    [Crossref]

2017 (1)

C. Kramer, M. Schäferling, T. Weiss, H. Giessen, and T. Brixner, “Analytic optimization of near-field optical chirality enhancement,” ACS Photon. 4, 396–406 (2017).
[Crossref]

2016 (3)

R. P. Cameron, J. B. Götte, S. M. Barnett, and J. P. Cotter, “Matter-wave grating distinguishing conservative and dissipative interactions,” Phys. Rev. A 94, 013604 (2016).
[Crossref]

M. Schäferling, N. Engheta, H. Giessen, and T. Weiss, “Reducing the complexity: enantioselective chiral near-fields by diagonal slit and mirror configuration,” ACS Photon. 3, 1076–1084 (2016).
[Crossref]

K. C. van Kruining and J. B. Götte, “The conditions for the preservation of duality symmetry in a linear medium,” J. Opt. 18, 085601 (2016).
[Crossref]

2015 (2)

X. Tian, Y. Fang, and M. Sun, “Formation of enhanced uniform chiral fields in symmetric dimer nanostructures,” Sci. Rep. 5, 17534 (2015).
[Crossref]

J. Kim, J. Lee, W. Y. Kim, H. Kim, S. Lee, H. C. Lee, Y. S. Lee, M. Seo, and S. Y. Kim, “Induction and control of supramolecular chirality by light in self-assembled helical nanostructures,” Nat. Commun. 6, 6959 (2015).
[Crossref]

2014 (3)

M. Schäferling, X. Yin, N. Engheta, and H. Giessen, “Helical plasmonic nanostructures as prototypical chiral near-field sources,” ACS Photon. 1, 530–537 (2014).
[Crossref]

R. P. Cameron, S. M. Barnett, and A. M. Yao, “Discriminatory optical force for chiral molecules,” New J. Phys. 16, 013020 (2014).
[Crossref]

R. P. Cameron, A. M. Yao, and S. M. Barnett, “Diffraction gratings for chiral molecules and their applications,” J. Phys. Chem. A 118, 3472–3478 (2014).
[Crossref]

2013 (3)

S. Eibenberger, S. Gerlich, M. Arndt, M. Mayor, and J. Tüxen, “Matter-wave interference of particles selected from a molecular library with masses exceeding 10,000  amu,” Phys. Chem. Chem. Phys. 15, 14696–14700 (2013).
[Crossref]

A. Canaguier-Durand, J. A. Hutchison, C. Genet, and T. W. Ebbesen, “Mechanical separation of chiral dipoles by chiral light,” New J. Phys. 15, 123037 (2013).
[Crossref]

R. P. Cameron, S. M. Barnett, and A. M. Yao, “Optical helicity of interfering waves,” J. Mod. Opt. 61, 25–31 (2013).
[Crossref]

2012 (6)

C. Rosales-Guzmán, K. Volke-Sepulveda, and J. P. Torres, “Light with enhanced optical chirality,” Opt. Lett. 37, 3486–3488 (2012).
[Crossref]

M. Schäferling, X. Yin, and H. Giessen, “Formation of chiral fields in a symmetric environment,” Opt. Express 20, 26326–26336 (2012).
[Crossref]

R. P. Cameron, S. M. Barnett, and A. M. Yao, “Optical helicity, optical spin and related quantities in electromagnetic theory,” New J. Phys. 14, 053050 (2012).
[Crossref]

R. P. Cameron and S. M. Barnett, “Electric-magnetic symmetry and Noether’s theorem,” New J. Phys. 14, 123019 (2012).
[Crossref]

J. D. Barrio, R. M. Tejedor, and L. Oriol, “Thermal and light control of the chiral order of azopolymers,” Eur. Polym. J. 48, 384–390 (2012).
[Crossref]

L. de Vega, S. van Cleuvenbergen, G. Depotter, E. M. García-Frutos, B. Gómez-Lor, A. Omenat, R. M. Tejedor, J. L. Serrano, G. Hennrich, and K. Clays, “Nonlinear optical thin film device from a chiral octopolar phenylacetylene liquid crystal,” J. Org. Chem. 77, 10891–10896 (2012).
[Crossref]

2011 (1)

Y. Tang and A. E. Cohen, “Enhanced enantioselectivity in excitation of chiral molecules by superchiral light,” Science 332, 333–336 (2011).
[Crossref]

2010 (3)

Y. Tang and A. E. Cohen, “Optical chirality and its interaction with matter,” Phys. Rev. Lett. 104, 163901 (2010).
[Crossref]

E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Michailovski, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadowala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5, 783–787 (2010).
[Crossref]

G. Cipparrone, I. Ricardez-Vargas, P. Pagliusi, and C. Provenzano, “Polarization gradient: exploring an original route for optical trapping and manipulation,” Opt. Express 18, 6008–6013 (2010).
[Crossref]

2009 (1)

K. Hornberger, S. Gerlich, H. Ulbricht, L. Hackermüller, S. Nimmrichter, I. V. Goldt, O. Botalina, and M. Arndt, “Theory and experimental verification of Kapitza-Dirac-Talbot-Lau interferometry,” New J. Phys. 11, 043032 (2009).
[Crossref]

2008 (1)

G. Martínez-Ponce, C. Solano, R. J. Rodríguez González, L. Larios-López, D. Navarro-Rodríguez, and L. Nikolova, “All-optical switching using supramolecular chiral structures in azopolymers,” J. Opt. A 10, 115006 (2008).
[Crossref]

2007 (2)

R. M. Tejedor, L. Oriol, J. L. Serrano, F. Partal Ureña, and J. J. López González, “Photoinduced chiral nematic organization in an achiral glassy nematic azopolymer,” Adv. Funct. Mater. 17, 3486–3492 (2007).
[Crossref]

F. Vera, R. M. Tejedor, P. Romero, J. Barberá, M. B. Ros, J. L. Serrano, and T. Sierra, “Light-driven supramolecular chirality in propeller-like hydrogen-bonded complexes that show columnar mesomorphism,” Angew. Chem. 46, 1873–1877 (2007).
[Crossref]

2006 (1)

S.-W. Choi, T. Izumi, Y. Hoshino, Y. Takanishi, K. Ishikawa, J. Watanabe, and H. Takezoe, “Circular-polarization-induced enantiomeric excess in liquid crystals of an achiral, bent-shaped mesogen,” Angew. Chem. 45, 1382–1385 (2006).
[Crossref]

2005 (1)

S. K. Mohanty, K. D. Rao, and P. K. Gupta, “Optical trap with spatially varying polarization: application in controlled orientation of birefringent microscopic particle(s),” Appl. Phys. B 80, 631–634 (2005).
[Crossref]

2000 (2)

L. Nikolova, L. Nedelchev, T. Todorov, T. Petrova, N. Tomova, V. Dragostinova, P. S. Ramanujam, and S. Hvilsted, “Self-induced light polarization rotation in azobenzene-containing polymers,” Appl. Phys. Lett. 77, 657–659 (2000).
[Crossref]

G. Iftime, F. L. Labarthet, A. Natansohn, and P. Rochon, “Control of chirality of an azobenzene liquid crystalline polymer with circularly polarized light,” J. Am. Chem. Soc. 122, 12646–12650 (2000).
[Crossref]

1997 (1)

L. Nikolova, T. Todorov, M. Ivanov, F. Andruzzi, S. Hvilsted, and P. Ramanujam, “Photoinduced circular anisotropy in side-chain azobenzene polyesters,” Opt. Mater. 8, 255–258 (1997).
[Crossref]

1996 (2)

J. L. Trueba and A. F. Rañada, “The electromagnetic helicity,” Eur. J. Phys. 17, 141–144 (1996).
[Crossref]

G. N. Afanasiev and Y. P. Stepanovski, “The helicity of the free electromagnetic field and its physical meaning,” Nuovo Cim. A 109, 271–279 (1996).
[Crossref]

1965 (1)

M. G. Calkin, “An invariance property of the electric field,” Am. J. Phys. 33, 958–960 (1965).
[Crossref]

1958 (1)

L. Woltjer, “A theorem on force-free magnetic fields,” Proc. Natl. Acad. Sci. USA 44, 289–291 (1958).
[Crossref]

Afanasiev, G. N.

G. N. Afanasiev and Y. P. Stepanovski, “The helicity of the free electromagnetic field and its physical meaning,” Nuovo Cim. A 109, 271–279 (1996).
[Crossref]

Andruzzi, F.

L. Nikolova, T. Todorov, M. Ivanov, F. Andruzzi, S. Hvilsted, and P. Ramanujam, “Photoinduced circular anisotropy in side-chain azobenzene polyesters,” Opt. Mater. 8, 255–258 (1997).
[Crossref]

Arndt, M.

S. Eibenberger, S. Gerlich, M. Arndt, M. Mayor, and J. Tüxen, “Matter-wave interference of particles selected from a molecular library with masses exceeding 10,000  amu,” Phys. Chem. Chem. Phys. 15, 14696–14700 (2013).
[Crossref]

K. Hornberger, S. Gerlich, H. Ulbricht, L. Hackermüller, S. Nimmrichter, I. V. Goldt, O. Botalina, and M. Arndt, “Theory and experimental verification of Kapitza-Dirac-Talbot-Lau interferometry,” New J. Phys. 11, 043032 (2009).
[Crossref]

Barberá, J.

F. Vera, R. M. Tejedor, P. Romero, J. Barberá, M. B. Ros, J. L. Serrano, and T. Sierra, “Light-driven supramolecular chirality in propeller-like hydrogen-bonded complexes that show columnar mesomorphism,” Angew. Chem. 46, 1873–1877 (2007).
[Crossref]

Barnett, S. M.

R. P. Cameron, J. B. Götte, S. M. Barnett, and J. P. Cotter, “Matter-wave grating distinguishing conservative and dissipative interactions,” Phys. Rev. A 94, 013604 (2016).
[Crossref]

R. P. Cameron, A. M. Yao, and S. M. Barnett, “Diffraction gratings for chiral molecules and their applications,” J. Phys. Chem. A 118, 3472–3478 (2014).
[Crossref]

R. P. Cameron, S. M. Barnett, and A. M. Yao, “Discriminatory optical force for chiral molecules,” New J. Phys. 16, 013020 (2014).
[Crossref]

R. P. Cameron, S. M. Barnett, and A. M. Yao, “Optical helicity of interfering waves,” J. Mod. Opt. 61, 25–31 (2013).
[Crossref]

R. P. Cameron and S. M. Barnett, “Electric-magnetic symmetry and Noether’s theorem,” New J. Phys. 14, 123019 (2012).
[Crossref]

R. P. Cameron, S. M. Barnett, and A. M. Yao, “Optical helicity, optical spin and related quantities in electromagnetic theory,” New J. Phys. 14, 053050 (2012).
[Crossref]

Barrio, J. D.

J. D. Barrio, R. M. Tejedor, and L. Oriol, “Thermal and light control of the chiral order of azopolymers,” Eur. Polym. J. 48, 384–390 (2012).
[Crossref]

Barron, L. D.

E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Michailovski, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadowala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5, 783–787 (2010).
[Crossref]

Botalina, O.

K. Hornberger, S. Gerlich, H. Ulbricht, L. Hackermüller, S. Nimmrichter, I. V. Goldt, O. Botalina, and M. Arndt, “Theory and experimental verification of Kapitza-Dirac-Talbot-Lau interferometry,” New J. Phys. 11, 043032 (2009).
[Crossref]

Brixner, T.

C. Kramer, M. Schäferling, T. Weiss, H. Giessen, and T. Brixner, “Analytic optimization of near-field optical chirality enhancement,” ACS Photon. 4, 396–406 (2017).
[Crossref]

Calkin, M. G.

M. G. Calkin, “An invariance property of the electric field,” Am. J. Phys. 33, 958–960 (1965).
[Crossref]

Cameron, R. P.

R. P. Cameron, J. B. Götte, S. M. Barnett, and J. P. Cotter, “Matter-wave grating distinguishing conservative and dissipative interactions,” Phys. Rev. A 94, 013604 (2016).
[Crossref]

R. P. Cameron, S. M. Barnett, and A. M. Yao, “Discriminatory optical force for chiral molecules,” New J. Phys. 16, 013020 (2014).
[Crossref]

R. P. Cameron, A. M. Yao, and S. M. Barnett, “Diffraction gratings for chiral molecules and their applications,” J. Phys. Chem. A 118, 3472–3478 (2014).
[Crossref]

R. P. Cameron, S. M. Barnett, and A. M. Yao, “Optical helicity of interfering waves,” J. Mod. Opt. 61, 25–31 (2013).
[Crossref]

R. P. Cameron, S. M. Barnett, and A. M. Yao, “Optical helicity, optical spin and related quantities in electromagnetic theory,” New J. Phys. 14, 053050 (2012).
[Crossref]

R. P. Cameron and S. M. Barnett, “Electric-magnetic symmetry and Noether’s theorem,” New J. Phys. 14, 123019 (2012).
[Crossref]

Canaguier-Durand, A.

A. Canaguier-Durand, J. A. Hutchison, C. Genet, and T. W. Ebbesen, “Mechanical separation of chiral dipoles by chiral light,” New J. Phys. 15, 123037 (2013).
[Crossref]

Carpy, T.

E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Michailovski, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadowala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5, 783–787 (2010).
[Crossref]

Choi, S.-W.

S.-W. Choi, T. Izumi, Y. Hoshino, Y. Takanishi, K. Ishikawa, J. Watanabe, and H. Takezoe, “Circular-polarization-induced enantiomeric excess in liquid crystals of an achiral, bent-shaped mesogen,” Angew. Chem. 45, 1382–1385 (2006).
[Crossref]

Cipparrone, G.

Clays, K.

L. de Vega, S. van Cleuvenbergen, G. Depotter, E. M. García-Frutos, B. Gómez-Lor, A. Omenat, R. M. Tejedor, J. L. Serrano, G. Hennrich, and K. Clays, “Nonlinear optical thin film device from a chiral octopolar phenylacetylene liquid crystal,” J. Org. Chem. 77, 10891–10896 (2012).
[Crossref]

Cohen, A. E.

Y. Tang and A. E. Cohen, “Enhanced enantioselectivity in excitation of chiral molecules by superchiral light,” Science 332, 333–336 (2011).
[Crossref]

Y. Tang and A. E. Cohen, “Optical chirality and its interaction with matter,” Phys. Rev. Lett. 104, 163901 (2010).
[Crossref]

Cotter, J. P.

R. P. Cameron, J. B. Götte, S. M. Barnett, and J. P. Cotter, “Matter-wave grating distinguishing conservative and dissipative interactions,” Phys. Rev. A 94, 013604 (2016).
[Crossref]

de Vega, L.

L. de Vega, S. van Cleuvenbergen, G. Depotter, E. M. García-Frutos, B. Gómez-Lor, A. Omenat, R. M. Tejedor, J. L. Serrano, G. Hennrich, and K. Clays, “Nonlinear optical thin film device from a chiral octopolar phenylacetylene liquid crystal,” J. Org. Chem. 77, 10891–10896 (2012).
[Crossref]

Depotter, G.

L. de Vega, S. van Cleuvenbergen, G. Depotter, E. M. García-Frutos, B. Gómez-Lor, A. Omenat, R. M. Tejedor, J. L. Serrano, G. Hennrich, and K. Clays, “Nonlinear optical thin film device from a chiral octopolar phenylacetylene liquid crystal,” J. Org. Chem. 77, 10891–10896 (2012).
[Crossref]

Dragostinova, V.

L. Nikolova, L. Nedelchev, T. Todorov, T. Petrova, N. Tomova, V. Dragostinova, P. S. Ramanujam, and S. Hvilsted, “Self-induced light polarization rotation in azobenzene-containing polymers,” Appl. Phys. Lett. 77, 657–659 (2000).
[Crossref]

Ebbesen, T. W.

A. Canaguier-Durand, J. A. Hutchison, C. Genet, and T. W. Ebbesen, “Mechanical separation of chiral dipoles by chiral light,” New J. Phys. 15, 123037 (2013).
[Crossref]

Eibenberger, S.

S. Eibenberger, S. Gerlich, M. Arndt, M. Mayor, and J. Tüxen, “Matter-wave interference of particles selected from a molecular library with masses exceeding 10,000  amu,” Phys. Chem. Chem. Phys. 15, 14696–14700 (2013).
[Crossref]

Engheta, N.

M. Schäferling, N. Engheta, H. Giessen, and T. Weiss, “Reducing the complexity: enantioselective chiral near-fields by diagonal slit and mirror configuration,” ACS Photon. 3, 1076–1084 (2016).
[Crossref]

M. Schäferling, X. Yin, N. Engheta, and H. Giessen, “Helical plasmonic nanostructures as prototypical chiral near-field sources,” ACS Photon. 1, 530–537 (2014).
[Crossref]

Fang, Y.

X. Tian, Y. Fang, and M. Sun, “Formation of enhanced uniform chiral fields in symmetric dimer nanostructures,” Sci. Rep. 5, 17534 (2015).
[Crossref]

Gadegaard, N.

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C. Kramer, M. Schäferling, T. Weiss, H. Giessen, and T. Brixner, “Analytic optimization of near-field optical chirality enhancement,” ACS Photon. 4, 396–406 (2017).
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M. Schäferling, N. Engheta, H. Giessen, and T. Weiss, “Reducing the complexity: enantioselective chiral near-fields by diagonal slit and mirror configuration,” ACS Photon. 3, 1076–1084 (2016).
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M. Schäferling, X. Yin, N. Engheta, and H. Giessen, “Helical plasmonic nanostructures as prototypical chiral near-field sources,” ACS Photon. 1, 530–537 (2014).
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M. Schäferling, X. Yin, and H. Giessen, “Formation of chiral fields in a symmetric environment,” Opt. Express 20, 26326–26336 (2012).
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K. Hornberger, S. Gerlich, H. Ulbricht, L. Hackermüller, S. Nimmrichter, I. V. Goldt, O. Botalina, and M. Arndt, “Theory and experimental verification of Kapitza-Dirac-Talbot-Lau interferometry,” New J. Phys. 11, 043032 (2009).
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E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Michailovski, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadowala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5, 783–787 (2010).
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L. de Vega, S. van Cleuvenbergen, G. Depotter, E. M. García-Frutos, B. Gómez-Lor, A. Omenat, R. M. Tejedor, J. L. Serrano, G. Hennrich, and K. Clays, “Nonlinear optical thin film device from a chiral octopolar phenylacetylene liquid crystal,” J. Org. Chem. 77, 10891–10896 (2012).
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A. Canaguier-Durand, J. A. Hutchison, C. Genet, and T. W. Ebbesen, “Mechanical separation of chiral dipoles by chiral light,” New J. Phys. 15, 123037 (2013).
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L. Nikolova, L. Nedelchev, T. Todorov, T. Petrova, N. Tomova, V. Dragostinova, P. S. Ramanujam, and S. Hvilsted, “Self-induced light polarization rotation in azobenzene-containing polymers,” Appl. Phys. Lett. 77, 657–659 (2000).
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L. Nikolova, T. Todorov, M. Ivanov, F. Andruzzi, S. Hvilsted, and P. Ramanujam, “Photoinduced circular anisotropy in side-chain azobenzene polyesters,” Opt. Mater. 8, 255–258 (1997).
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E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Michailovski, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadowala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5, 783–787 (2010).
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E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Michailovski, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadowala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5, 783–787 (2010).
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J. Kim, J. Lee, W. Y. Kim, H. Kim, S. Lee, H. C. Lee, Y. S. Lee, M. Seo, and S. Y. Kim, “Induction and control of supramolecular chirality by light in self-assembled helical nanostructures,” Nat. Commun. 6, 6959 (2015).
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G. Martínez-Ponce, C. Solano, R. J. Rodríguez González, L. Larios-López, D. Navarro-Rodríguez, and L. Nikolova, “All-optical switching using supramolecular chiral structures in azopolymers,” J. Opt. A 10, 115006 (2008).
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J. Kim, J. Lee, W. Y. Kim, H. Kim, S. Lee, H. C. Lee, Y. S. Lee, M. Seo, and S. Y. Kim, “Induction and control of supramolecular chirality by light in self-assembled helical nanostructures,” Nat. Commun. 6, 6959 (2015).
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J. Kim, J. Lee, W. Y. Kim, H. Kim, S. Lee, H. C. Lee, Y. S. Lee, M. Seo, and S. Y. Kim, “Induction and control of supramolecular chirality by light in self-assembled helical nanostructures,” Nat. Commun. 6, 6959 (2015).
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J. Kim, J. Lee, W. Y. Kim, H. Kim, S. Lee, H. C. Lee, Y. S. Lee, M. Seo, and S. Y. Kim, “Induction and control of supramolecular chirality by light in self-assembled helical nanostructures,” Nat. Commun. 6, 6959 (2015).
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J. Kim, J. Lee, W. Y. Kim, H. Kim, S. Lee, H. C. Lee, Y. S. Lee, M. Seo, and S. Y. Kim, “Induction and control of supramolecular chirality by light in self-assembled helical nanostructures,” Nat. Commun. 6, 6959 (2015).
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R. M. Tejedor, L. Oriol, J. L. Serrano, F. Partal Ureña, and J. J. López González, “Photoinduced chiral nematic organization in an achiral glassy nematic azopolymer,” Adv. Funct. Mater. 17, 3486–3492 (2007).
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S. Eibenberger, S. Gerlich, M. Arndt, M. Mayor, and J. Tüxen, “Matter-wave interference of particles selected from a molecular library with masses exceeding 10,000  amu,” Phys. Chem. Chem. Phys. 15, 14696–14700 (2013).
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S. K. Mohanty, K. D. Rao, and P. K. Gupta, “Optical trap with spatially varying polarization: application in controlled orientation of birefringent microscopic particle(s),” Appl. Phys. B 80, 631–634 (2005).
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G. Martínez-Ponce, C. Solano, R. J. Rodríguez González, L. Larios-López, D. Navarro-Rodríguez, and L. Nikolova, “All-optical switching using supramolecular chiral structures in azopolymers,” J. Opt. A 10, 115006 (2008).
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L. Nikolova, L. Nedelchev, T. Todorov, T. Petrova, N. Tomova, V. Dragostinova, P. S. Ramanujam, and S. Hvilsted, “Self-induced light polarization rotation in azobenzene-containing polymers,” Appl. Phys. Lett. 77, 657–659 (2000).
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K. Hornberger, S. Gerlich, H. Ulbricht, L. Hackermüller, S. Nimmrichter, I. V. Goldt, O. Botalina, and M. Arndt, “Theory and experimental verification of Kapitza-Dirac-Talbot-Lau interferometry,” New J. Phys. 11, 043032 (2009).
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E. Hendry, T. Carpy, J. Johnston, M. Popland, R. V. Michailovski, A. J. Lapthorn, S. M. Kelly, L. D. Barron, N. Gadegaard, and M. Kadowala, “Ultrasensitive detection and characterization of biomolecules using superchiral fields,” Nat. Nanotechnol. 5, 783–787 (2010).
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L. Nikolova, T. Todorov, M. Ivanov, F. Andruzzi, S. Hvilsted, and P. Ramanujam, “Photoinduced circular anisotropy in side-chain azobenzene polyesters,” Opt. Mater. 8, 255–258 (1997).
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L. Nikolova, L. Nedelchev, T. Todorov, T. Petrova, N. Tomova, V. Dragostinova, P. S. Ramanujam, and S. Hvilsted, “Self-induced light polarization rotation in azobenzene-containing polymers,” Appl. Phys. Lett. 77, 657–659 (2000).
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Rochon, P.

G. Iftime, F. L. Labarthet, A. Natansohn, and P. Rochon, “Control of chirality of an azobenzene liquid crystalline polymer with circularly polarized light,” J. Am. Chem. Soc. 122, 12646–12650 (2000).
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G. Martínez-Ponce, C. Solano, R. J. Rodríguez González, L. Larios-López, D. Navarro-Rodríguez, and L. Nikolova, “All-optical switching using supramolecular chiral structures in azopolymers,” J. Opt. A 10, 115006 (2008).
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F. Vera, R. M. Tejedor, P. Romero, J. Barberá, M. B. Ros, J. L. Serrano, and T. Sierra, “Light-driven supramolecular chirality in propeller-like hydrogen-bonded complexes that show columnar mesomorphism,” Angew. Chem. 46, 1873–1877 (2007).
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C. Kramer, M. Schäferling, T. Weiss, H. Giessen, and T. Brixner, “Analytic optimization of near-field optical chirality enhancement,” ACS Photon. 4, 396–406 (2017).
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M. Schäferling, N. Engheta, H. Giessen, and T. Weiss, “Reducing the complexity: enantioselective chiral near-fields by diagonal slit and mirror configuration,” ACS Photon. 3, 1076–1084 (2016).
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M. Schäferling, X. Yin, N. Engheta, and H. Giessen, “Helical plasmonic nanostructures as prototypical chiral near-field sources,” ACS Photon. 1, 530–537 (2014).
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M. Schäferling, X. Yin, and H. Giessen, “Formation of chiral fields in a symmetric environment,” Opt. Express 20, 26326–26336 (2012).
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J. Kim, J. Lee, W. Y. Kim, H. Kim, S. Lee, H. C. Lee, Y. S. Lee, M. Seo, and S. Y. Kim, “Induction and control of supramolecular chirality by light in self-assembled helical nanostructures,” Nat. Commun. 6, 6959 (2015).
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F. Vera, R. M. Tejedor, P. Romero, J. Barberá, M. B. Ros, J. L. Serrano, and T. Sierra, “Light-driven supramolecular chirality in propeller-like hydrogen-bonded complexes that show columnar mesomorphism,” Angew. Chem. 46, 1873–1877 (2007).
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J. D. Barrio, R. M. Tejedor, and L. Oriol, “Thermal and light control of the chiral order of azopolymers,” Eur. Polym. J. 48, 384–390 (2012).
[Crossref]

L. de Vega, S. van Cleuvenbergen, G. Depotter, E. M. García-Frutos, B. Gómez-Lor, A. Omenat, R. M. Tejedor, J. L. Serrano, G. Hennrich, and K. Clays, “Nonlinear optical thin film device from a chiral octopolar phenylacetylene liquid crystal,” J. Org. Chem. 77, 10891–10896 (2012).
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F. Vera, R. M. Tejedor, P. Romero, J. Barberá, M. B. Ros, J. L. Serrano, and T. Sierra, “Light-driven supramolecular chirality in propeller-like hydrogen-bonded complexes that show columnar mesomorphism,” Angew. Chem. 46, 1873–1877 (2007).
[Crossref]

R. M. Tejedor, L. Oriol, J. L. Serrano, F. Partal Ureña, and J. J. López González, “Photoinduced chiral nematic organization in an achiral glassy nematic azopolymer,” Adv. Funct. Mater. 17, 3486–3492 (2007).
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L. Nikolova, L. Nedelchev, T. Todorov, T. Petrova, N. Tomova, V. Dragostinova, P. S. Ramanujam, and S. Hvilsted, “Self-induced light polarization rotation in azobenzene-containing polymers,” Appl. Phys. Lett. 77, 657–659 (2000).
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Figures (8)

Fig. 1.
Fig. 1. Wave- and polarization vectors for a noninterfering two-wave superposition (top) and its helicity pattern (bottom). For this superposition we chose both amplitudes equal and θ=π/6.
Fig. 2.
Fig. 2. Wave and polarization vectors for three noninterfering orthogonal waves (ϕ1=ϕ2=ϕ3=0), with all amplitudes taken equal (top) and their helicity structure (bottom). For three plane waves, the helicity interference terms always lie in a plane and thus form a two-dimensional helicity lattice. The wavevectors have been rotated to make the helicity lattice lie on the x–y plane.
Fig. 3.
Fig. 3. Construction of a superchiral three-wave superposition (top). We have taken ϕ1=0, ϕ2=7π4, and ϕ3=3π2, rotated to make the helicity lattice vectors parallel to the x and y axes. We took a2 to be 2 times the amplitude of the other waves. The corresponding helicity structure (bottom) has superchiral regions (yellow ellipses), which extend for about half a wavelength in one direction and a quarter of a wavelength in the other.
Fig. 4.
Fig. 4. Four-wave noninterfering superposition with two pairs of cancelling interference terms (top) and its helicity structure (bottom). For this superposition we chose a1=a3, θ=π6, and Δϕ=0. Superchirality is typical for superpositions of this kind and occurs over broad parameter ranges.
Fig. 5.
Fig. 5. Example of a five-wave noninterfering superposition (top) yielding a three-dimensional helicity lattice (bottom). For this superposition we took θ=π6, ϕ=π4, a1=a2=a4=1, and a5=84cosπ/6. The superchiral regions are enclosed by the yellow surfaces. At about half a wavelength in length they are surprisingly large.
Fig. 6.
Fig. 6. Six-wave superposition with θ=2π3 (top). This superposition requires three pairs of interference terms to cancel. For θ=2π3, the helicity forms a triangular lattice. Two examples are shown, one for a1=a2=a3 (center) and one for a1=12a2=12a3 (bottom).
Fig. 7.
Fig. 7. Six-wave superposition for θ=2π30.005 and a1=a2=a3. For this angle, the helicity pattern is aperiodic in the x direction. The size of this plot is 16×16 wavelengths.
Fig. 8.
Fig. 8. Six-wave helicity lattice with θ=arccos35 and a1=a2=a3 (top) and with θ=arccos25 and a1=a2=a3 (bottom). The size of these plots is 8×8 wavelengths.

Tables (7)

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Table 1. Two-Wave Noninterfering Superposition

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Table 2. Three-Wave Noninterfering Superposition

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Table 3. Four-Wave Noninterfering Superposition with All Wavevectors in the Same Planea

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Table 4. Four-Wave Noninterfering Superposition with Two Pairs of Wave Vectors in Perpendicular Planes a

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Table 5. Four-Wave Noninterfering Superposition Which Has Superchiral Helicity Lattices

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Table 6. Five-Wave Noninterfering Superposition

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Table 7. Six-Wave Noninterfering Superpositiona

Equations (10)

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E=ReE˜=Re(j=1NE˜jei(kj·xωt)),
H=ReH˜=Re(1μ0ωj=1Nkj×E˜jei(kj·xωt)).
ω2π02πωE·Edt=12E˜·E˜*=12(l=1NE˜l·E˜l*+j=1NljE˜j·E˜l*ej(kjkl)·x).
H=i4cωi,j=1N(E˜i·H˜j*E˜j*·H˜i)ei(kikj)·x.
H=ε0ω|a1a2*|cos2θsin(k0sin(2θ)x+arg(a1a2*)).
E˜=j=1n(E˜j+δE˜j)eikj·xwithδE˜j·kj=0.
δIk0=14jln(δE˜j*·E˜l+E˜j*·δE˜l)ej(klkj)·x+O(δE˜2).
jlnδE˜j*·E˜l+E˜j*·δE˜ll=1nE˜l*·E˜l=(n1)|δE˜j*·E˜l|jlE˜l*·E˜ll.
2(n1)|δE˜j|j|E˜l|lπE˜l*·E˜ll.
δkj<AmaxLAint,