Abstract

In an optically active liquid the diffraction angle depends on the circular polarization state of the incident light beam. We report the observation of circular differential diffraction in an isotropic chiral medium, and we demonstrate that double diffraction is an alternate means to determine the handedness (enantiomeric excess) of a solution.

© 2007 Optical Society of America

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References

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  1. A. J. Fresnel, Mémoire sur la double réfraction, in Oeuvres Complètes d'Augustin Fresnel, H.D.Sénarmont, E.Verdet, and L.Fresnel, eds. (Paris, 1822), Vol. 1.
  2. A. Fresnel, Ann. Chim. Phys. 28, 147 (1825).
  3. E. v. Fleischl, Sitz. Ber. Kais. Akad. Wiss. (Math-Nat) 90, 478 (1884).
  4. A. Ghosh and P. Fischer, Phys. Rev. Lett. 97, 173002 (2006).
    [CrossRef] [PubMed]
  5. S. Przezdziecki, Wave Motion 32, 157 (2000).
    [CrossRef]
  6. S. Asghar and A. Lakhtakia, Int. J. Appl. Electromagn. Mater. 5, 181 (1994).
  7. H. Ammari and J.-C. Nedelec, C. R. Acad. Sci., Ser. I: Math. 322, 1087 (1996).
  8. S. B. Panin and A. Y. Poyedinchuk, Telecommun. Radio Eng. (Engl. Transl.) 53, 98 (1999).
  9. S. H. Yueh and J. A. Kong, J. Electromagn. Waves Appl. 5, 701 (1991).
  10. T. Vallius, K. Jefimovs, J. Turunen, P. Vahimaa, and Y. Svirko, Appl. Phys. Lett. 83, 234 (2003).
    [CrossRef]
  11. S. L. Prosvirnin and N. I. Zheludev, Phys. Rev. E 71, 037603 (2005).
    [CrossRef]
  12. J. B. Gedded and A. Lakhtakia, Opt. Commun. 252, 307 (2005).
    [CrossRef]
  13. M. P. Silverman, J. Opt. Soc. Am. A 3, 830 (1986).
    [CrossRef]

2006

A. Ghosh and P. Fischer, Phys. Rev. Lett. 97, 173002 (2006).
[CrossRef] [PubMed]

2005

S. L. Prosvirnin and N. I. Zheludev, Phys. Rev. E 71, 037603 (2005).
[CrossRef]

J. B. Gedded and A. Lakhtakia, Opt. Commun. 252, 307 (2005).
[CrossRef]

2003

T. Vallius, K. Jefimovs, J. Turunen, P. Vahimaa, and Y. Svirko, Appl. Phys. Lett. 83, 234 (2003).
[CrossRef]

2000

S. Przezdziecki, Wave Motion 32, 157 (2000).
[CrossRef]

1999

S. B. Panin and A. Y. Poyedinchuk, Telecommun. Radio Eng. (Engl. Transl.) 53, 98 (1999).

1996

H. Ammari and J.-C. Nedelec, C. R. Acad. Sci., Ser. I: Math. 322, 1087 (1996).

1994

S. Asghar and A. Lakhtakia, Int. J. Appl. Electromagn. Mater. 5, 181 (1994).

1991

S. H. Yueh and J. A. Kong, J. Electromagn. Waves Appl. 5, 701 (1991).

1986

1884

E. v. Fleischl, Sitz. Ber. Kais. Akad. Wiss. (Math-Nat) 90, 478 (1884).

1825

A. Fresnel, Ann. Chim. Phys. 28, 147 (1825).

1822

A. J. Fresnel, Mémoire sur la double réfraction, in Oeuvres Complètes d'Augustin Fresnel, H.D.Sénarmont, E.Verdet, and L.Fresnel, eds. (Paris, 1822), Vol. 1.

Ammari, H.

H. Ammari and J.-C. Nedelec, C. R. Acad. Sci., Ser. I: Math. 322, 1087 (1996).

Asghar, S.

S. Asghar and A. Lakhtakia, Int. J. Appl. Electromagn. Mater. 5, 181 (1994).

Fischer, P.

A. Ghosh and P. Fischer, Phys. Rev. Lett. 97, 173002 (2006).
[CrossRef] [PubMed]

Fleischl, E. v.

E. v. Fleischl, Sitz. Ber. Kais. Akad. Wiss. (Math-Nat) 90, 478 (1884).

Fresnel, A.

A. Fresnel, Ann. Chim. Phys. 28, 147 (1825).

Fresnel, A. J.

A. J. Fresnel, Mémoire sur la double réfraction, in Oeuvres Complètes d'Augustin Fresnel, H.D.Sénarmont, E.Verdet, and L.Fresnel, eds. (Paris, 1822), Vol. 1.

Gedded, J. B.

J. B. Gedded and A. Lakhtakia, Opt. Commun. 252, 307 (2005).
[CrossRef]

Ghosh, A.

A. Ghosh and P. Fischer, Phys. Rev. Lett. 97, 173002 (2006).
[CrossRef] [PubMed]

Jefimovs, K.

T. Vallius, K. Jefimovs, J. Turunen, P. Vahimaa, and Y. Svirko, Appl. Phys. Lett. 83, 234 (2003).
[CrossRef]

Kong, J. A.

S. H. Yueh and J. A. Kong, J. Electromagn. Waves Appl. 5, 701 (1991).

Lakhtakia, A.

J. B. Gedded and A. Lakhtakia, Opt. Commun. 252, 307 (2005).
[CrossRef]

S. Asghar and A. Lakhtakia, Int. J. Appl. Electromagn. Mater. 5, 181 (1994).

Nedelec, J.-C.

H. Ammari and J.-C. Nedelec, C. R. Acad. Sci., Ser. I: Math. 322, 1087 (1996).

Panin, S. B.

S. B. Panin and A. Y. Poyedinchuk, Telecommun. Radio Eng. (Engl. Transl.) 53, 98 (1999).

Poyedinchuk, A. Y.

S. B. Panin and A. Y. Poyedinchuk, Telecommun. Radio Eng. (Engl. Transl.) 53, 98 (1999).

Prosvirnin, S. L.

S. L. Prosvirnin and N. I. Zheludev, Phys. Rev. E 71, 037603 (2005).
[CrossRef]

Przezdziecki, S.

S. Przezdziecki, Wave Motion 32, 157 (2000).
[CrossRef]

Silverman, M. P.

Svirko, Y.

T. Vallius, K. Jefimovs, J. Turunen, P. Vahimaa, and Y. Svirko, Appl. Phys. Lett. 83, 234 (2003).
[CrossRef]

Turunen, J.

T. Vallius, K. Jefimovs, J. Turunen, P. Vahimaa, and Y. Svirko, Appl. Phys. Lett. 83, 234 (2003).
[CrossRef]

Vahimaa, P.

T. Vallius, K. Jefimovs, J. Turunen, P. Vahimaa, and Y. Svirko, Appl. Phys. Lett. 83, 234 (2003).
[CrossRef]

Vallius, T.

T. Vallius, K. Jefimovs, J. Turunen, P. Vahimaa, and Y. Svirko, Appl. Phys. Lett. 83, 234 (2003).
[CrossRef]

Yueh, S. H.

S. H. Yueh and J. A. Kong, J. Electromagn. Waves Appl. 5, 701 (1991).

Zheludev, N. I.

S. L. Prosvirnin and N. I. Zheludev, Phys. Rev. E 71, 037603 (2005).
[CrossRef]

Ann. Chim. Phys.

A. Fresnel, Ann. Chim. Phys. 28, 147 (1825).

Appl. Phys. Lett.

T. Vallius, K. Jefimovs, J. Turunen, P. Vahimaa, and Y. Svirko, Appl. Phys. Lett. 83, 234 (2003).
[CrossRef]

C. R. Acad. Sci., Ser. I: Math.

H. Ammari and J.-C. Nedelec, C. R. Acad. Sci., Ser. I: Math. 322, 1087 (1996).

Int. J. Appl. Electromagn. Mater.

S. Asghar and A. Lakhtakia, Int. J. Appl. Electromagn. Mater. 5, 181 (1994).

J. Electromagn. Waves Appl.

S. H. Yueh and J. A. Kong, J. Electromagn. Waves Appl. 5, 701 (1991).

J. Opt. Soc. Am. A

Opt. Commun.

J. B. Gedded and A. Lakhtakia, Opt. Commun. 252, 307 (2005).
[CrossRef]

Phys. Rev. E

S. L. Prosvirnin and N. I. Zheludev, Phys. Rev. E 71, 037603 (2005).
[CrossRef]

Phys. Rev. Lett.

A. Ghosh and P. Fischer, Phys. Rev. Lett. 97, 173002 (2006).
[CrossRef] [PubMed]

Sitz. Ber. Kais. Akad. Wiss. (Math-Nat)

E. v. Fleischl, Sitz. Ber. Kais. Akad. Wiss. (Math-Nat) 90, 478 (1884).

Telecommun. Radio Eng. (Engl. Transl.)

S. B. Panin and A. Y. Poyedinchuk, Telecommun. Radio Eng. (Engl. Transl.) 53, 98 (1999).

Wave Motion

S. Przezdziecki, Wave Motion 32, 157 (2000).
[CrossRef]

Other

A. J. Fresnel, Mémoire sur la double réfraction, in Oeuvres Complètes d'Augustin Fresnel, H.D.Sénarmont, E.Verdet, and L.Fresnel, eds. (Paris, 1822), Vol. 1.

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Figures (2)

Fig. 1
Fig. 1

Diffraction at a reflection grating immersed in a chiral liquid. (a) Linear or unpolarized incident beam is shown to split into its two circular polarization components at each diffraction order. The splitting is of opposite sign for the mirror-image liquid (enantiomer) and vanishes in an achiral system. (b) Experimental arrangement used for the diffraction measurements. A rectangular liquid cuvette holds a reflection grating.

Fig. 2
Fig. 2

Difference in the diffraction angles for left- and right-circularly polarized light. The angular deviation is recorded for each diffraction order in carvone and limonene as a function of the liquid’s enantiomeric excess, which is defined as the percent concentration difference between the two mirror-image forms of the liquid, denoted as R and S, respectively. The straight lines are from a fit to the experimental data, and the dotted lines are from theory.

Equations (4)

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n ( ) sin ( α ) n ( ± ) sin ( β m ( ± ) ) = m λ D .
sin ( β m ± δ m 2 ) sin β m ± δ m 2 cos β m ,
δ m = n ( ) n ( + ) n ( sin α cos β m + tan β m ) .
δ m n ( ) n ( + ) n ( 1 + tan β m ) .

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