Discriminatory optical force for chiral molecules

Robert P Cameron, Stephen M Barnett and Alison M Yao

We suggest that the force F exerted upon a chiral molecule by light assumes the form $\mathbf {F}=a\boldsymbol {\nabla } w+b\boldsymbol {\nabla } h$ under appropriate circumstances, where a and b pertain to the molecule whilst w and h are the local densities of electric energy and helicity in the optical field; the gradients $\boldsymbol {\nabla }$ of these quantities thus governing the molecule's centre-of-mass motion. Whereas a is identical for the mirror-image forms or enantiomers of the molecule, b has opposite signs; the associated contribution to F therefore pointing in opposite directions. A simple optical field is presented for which $\boldsymbol {\nabla } w$ vanishes but $\boldsymbol {\nabla }h$ does not, so that F is absolutely discriminatory. We then present two potential applications: a Stern–Gerlach-type deflector capable of spatially separating the enantiomers of a chiral molecule and a diffraction grating to which chiral molecules alone are sensitive; the resulting diffraction patterns thus encoding information about their chiral geometry.

DOI