Biomedical Engineering Reference
In-Depth Information
In addition for an optically chiral system, the application of
amirrorsymmetry
ϑ
provides new chiral optical structures
ca
lled enantiomers, which are characterized by their Jones matrices
J
enant
(
ϑ
). By definition, wehave
·
ϑ
−
1
J
enant
(
ϑ
=
ϑ
·
=
)
J
J
.
(2.22)
In general, the lack of rotational invariance of
J
implies that
these ena
ntio
morphic matrices depend specifically on the mirror
reflection
ϑ
choseninthedefinitiongivenbyEq.(2.21).Thus,there
are actually infinitenumbers of such enantiomers.
Three important classes of chiral systems can be derived from
the truth table associated with the theorem:
i) Afirstclasssatisfying
J
ll
=
J
rr
butwith
|
J
lr
|=|
J
rl
|
.Forreasons
presented below, this class will be named the “optical activity
class” or
E
o.a.
. This class is, until recently, the class essentially
discussed in the literature.
ii) A second class corresponding to
J
ll
=
J
rr
but satisfying the
constraint
|
J
lr
| =|
J
rl
|
. This class will be named in the following
the “(genuine) planar chirality class”
E
2D
, for reasons also to be
givenfurther down.
iii) A third class associated with
J
ll
=
J
rr
and
|
J
lr
| =|
J
rl
|
. This is
the most general class of optically chiral system coined as the
“optical chirality class” and which will be described below in
details.
Our point is that these chiral classes correspond to specific spatial
relations of chiral systems with respect to 3D space. Such relations
are fundamental to the characterization of chiral objects, which
depends on the shape of the objects and the dimension of the
space within which the objects are probed [51]. In optics, these
relations can be unveiled through reciprocity: as light propagates
in 3D space, the effect of optical path reversal through any chiral
object will reveal its relation with surrounding space. Analyzing the
behavior of the objects concerning reciprocity allow characterizing
the relation of any chiral objects with respect to 3D space, from
which a classification ofthe chirality type can bedrawn.
