Biomedical Engineering Reference
In-Depth Information
paradoxically challenged Lorentz principle of reciprocity [1] (which
is known to hold for any linear non magneto-optical media) and
stirred up considerable debate [21, 22, 24, 41] which came to the
conclusion that optical activity cannot be a purely 2D effect and
always requires a small dissymmetry between the two sides of the
system [24, 28-30].
This point becomes more clear from the previous definitions
and discussion concerning chirality and reciprocity. Indeed, a
gammadion being rotationally invariant its optical properties must
becharacterized by a Jones matrix belongingto
E
o.a.
that is,
A
0
0
B
,
J
o.a.
=
(2.58)
with
A
=
B
However, since geometrically the 2D gammadion
change its sense of twist when watched from the other side, the
discussion concerning reciprocity and change of twist developed
between Eqs. (2.35, 2.40) imposes that the Jones matrix should also
belong to
E
2D
, that is,
αβ
γα
J
2D
=
(2.59)
with
|
β
| =
γ
|
. The only possibility for having
J
2D
=
J
o.a.
is to
impose
γ
=
β
=
0aswellas
A
=
B
=
α
and consequently to
havenoopticalchiralsignaturewhatsoever.Thissolvestheparadox
and shows that if gammadion generate nevertheless optical activity
with giant gyrotropic factors [24, 28-30] then the system cannot be
purely 2D. The third dimension (such as the presence of substrate
for example) is enough to break the symmetry between the two
directions of transmission through the structure and there is no
violation of reciprocity, as the matrix has no anymore reason to
satisfy Eq. (2.35) or Eq. (2.37), that is, to belong to
E
2D
.
We also point out that Bunn [53] and later L. Barron [40, 41]
already remarked that optical chirality in 3D and also in 2D (see the
next section) characterizes not only the structure itself but also the
complete illumination protocol including the specific orientation of
the incident light relatively to the structure. This idea was recently
applied in the context of metamaterials by Zheludev and coworkers
by demonstrating specific forms of extrinsic optical chirality in
