Abstract
We suggest that the force F exerted upon a chiral molecule by light assumes the form 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 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 vanishes but 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.
Highlights
It was Kelvin who introduced the word chiral [1, 2] to refer to any geometrical figure or group of points that cannot be brought into coincidence with its image as seen in a plane mirror, possessing a sense of handedness
The separate and seemingly stable existence of mirror-image forms, or enantiomers, of certain chiral molecules is a remarkable example of symmetry breaking [7]: see figure 1
We suggest that the centre-of-mass motion of a chiral molecule is, under appropriate circumstances, sensitive to gradients in the helicity of an optical field and observe that the force associated with these gradients points in opposite directions for the molecule’s enantiomers
Summary
It was Kelvin who introduced the word chiral [1, 2] to refer to any geometrical figure or group of points that cannot be brought into coincidence with its image as seen in a plane mirror, possessing a sense of handedness. We present a simple optical field for which this phenomenon is brought to prominence (section 3) and propose two potential applications, namely a Stern–Gerlachtype deflector capable of spatially separating the enantiomers of a chiral molecule (section 4) and a diffraction grating to which chiral molecules alone are sensitive, the resulting diffraction patterns encoding information about their chiral geometry (section 5). Our approach differs, it seems, from others that have been presented in the literature [16,17,18,19,20] in that we make no critical assumptions regarding the energy-level structure of our molecule but rather, rely upon the sign of a certain polarizability. We consider ourselves to be in an inertial frame of reference and adopt a right-handed Cartesian coordinate system (x, y and z), employing SI units
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