2 Surface Plasmons for Chiral Sensing
37
chirality using SPR measurements [55, 56], but it is effectively insensitive to the
sign of the chiral parameter κ.
When we now analyze the reflected wave in terms of RCP/LCP (+/−) components, we observe that the minima of the R + , R − reflectances do not coincide, but
are separated by an angle θ ≡ θ + − θ − , where θ + (θ − ) denotes the angle of the R +
(R − ) minimum [Fig. 2.6b, c]. Moreover, we observe that for κ > 0 (κ < 0), θ > 0
( < 0). Thus, the presence of a thin chiral layer results in a chiral-dependent angular split θ between the measured reflectances of R + and R − , which has a distinct
behaviour depending on the sign and magnitude of κ. We wish to note here that our
polarimetric measurement scheme, where the reflected wave is analyzed in terms of
+/− components, is sensitive only to chiral effects and not to general spectral shifts
(possible if variations to the host refractive index are present), and moreover it is
equivalent to the chirality flux spectroscopy used to probe the chiral near-fields of
chiral nanosystems, as presented in [57].
2.3.1 Mechanism of Chiral-Dependent SPR-Reflectance
Angular Split
To understand the mechanism behind the chiral-dependent SPR-reflectance angular
split, we examine how the near-field properties of the SPP wave are associated with
the properties of the reflected wave in the far-field. We start by analyzing the SPP wave
along its propagation direction (x) into +/− components, i.e. A SPP = A y ˆ
y + A z ˆ
z =
A
+
SPP ( ˆ
y + i ˆ
z) + A
−
SPP ( ˆ
y − i ˆ
z), where A
±
SPP = (A y ∓ A z )/2 and A is any of the
electromagnetic field quantities E, H, B, D; then, we calculate the electric and
magnetic energy densities w
±
e = (1/4)E
±
SPP (D
±
SPP )
∗ and w
±
m = (1/4)B
±
SPP (H
±
SPP )
∗ ,
respectively, which we integrate to find the total energy stored in each of the two
(+/−) components, namely W ± =
V (w
±
e + w
±
m ) d
3 x [Fig. 2.7a]. Here, the integration volume V is the entire SPP volume extending above the metal (where the chiral
layer is to be probed). For κ = 0 we obtain W + = W − , as the SPP wave has only an
E z -component on the yz-plane, which is equally distributed between the two +/−
components (typical nonchiral SPR case). This is shown in Fig. 2.7b, where the
energy difference W + − W − is normalized to the incident energy S inc /2ω (ω is the
angular frequency and S inc is the magnitude of the time-averaged Poynting vector).
However, the onset of chirality causes the emergence of an E y -component [51] and,
hence, an unbalanced storage of the optical energy between the +/− components of
the SPP. In fact, for κ > 0 (κ < 0), RCP (LCP) components are favoured and, therefore, W + > W − (W + < W − ) [Fig. 2.7b]. This stored energy excess between +/−
SPP components in the near-field results in nonzero R s reflectance in the far-field;
this is apparent in the fact that the peak of R s coincides with the peak of W + − W −
at 59.5 deg which differs from the R p minimum at 60.3 deg [Figs. 2.6a and 2.7b].
In other words, the E y -component that emerges in the near-field due to chirality,
is identified in the far-field as well, as power transfer from the outgoing p-wave
37
chirality using SPR measurements [55, 56], but it is effectively insensitive to the
sign of the chiral parameter κ.
When we now analyze the reflected wave in terms of RCP/LCP (+/−) components, we observe that the minima of the R + , R − reflectances do not coincide, but
are separated by an angle θ ≡ θ + − θ − , where θ + (θ − ) denotes the angle of the R +
(R − ) minimum [Fig. 2.6b, c]. Moreover, we observe that for κ > 0 (κ < 0), θ > 0
( < 0). Thus, the presence of a thin chiral layer results in a chiral-dependent angular split θ between the measured reflectances of R + and R − , which has a distinct
behaviour depending on the sign and magnitude of κ. We wish to note here that our
polarimetric measurement scheme, where the reflected wave is analyzed in terms of
+/− components, is sensitive only to chiral effects and not to general spectral shifts
(possible if variations to the host refractive index are present), and moreover it is
equivalent to the chirality flux spectroscopy used to probe the chiral near-fields of
chiral nanosystems, as presented in [57].
2.3.1 Mechanism of Chiral-Dependent SPR-Reflectance
Angular Split
To understand the mechanism behind the chiral-dependent SPR-reflectance angular
split, we examine how the near-field properties of the SPP wave are associated with
the properties of the reflected wave in the far-field. We start by analyzing the SPP wave
along its propagation direction (x) into +/− components, i.e. A SPP = A y ˆ
y + A z ˆ
z =
A
+
SPP ( ˆ
y + i ˆ
z) + A
−
SPP ( ˆ
y − i ˆ
z), where A
±
SPP = (A y ∓ A z )/2 and A is any of the
electromagnetic field quantities E, H, B, D; then, we calculate the electric and
magnetic energy densities w
±
e = (1/4)E
±
SPP (D
±
SPP )
∗ and w
±
m = (1/4)B
±
SPP (H
±
SPP )
∗ ,
respectively, which we integrate to find the total energy stored in each of the two
(+/−) components, namely W ± =
V (w
±
e + w
±
m ) d
3 x [Fig. 2.7a]. Here, the integration volume V is the entire SPP volume extending above the metal (where the chiral
layer is to be probed). For κ = 0 we obtain W + = W − , as the SPP wave has only an
E z -component on the yz-plane, which is equally distributed between the two +/−
components (typical nonchiral SPR case). This is shown in Fig. 2.7b, where the
energy difference W + − W − is normalized to the incident energy S inc /2ω (ω is the
angular frequency and S inc is the magnitude of the time-averaged Poynting vector).
However, the onset of chirality causes the emergence of an E y -component [51] and,
hence, an unbalanced storage of the optical energy between the +/− components of
the SPP. In fact, for κ > 0 (κ < 0), RCP (LCP) components are favoured and, therefore, W + > W − (W + < W − ) [Fig. 2.7b]. This stored energy excess between +/−
SPP components in the near-field results in nonzero R s reflectance in the far-field;
this is apparent in the fact that the peak of R s coincides with the peak of W + − W −
at 59.5 deg which differs from the R p minimum at 60.3 deg [Figs. 2.6a and 2.7b].
In other words, the E y -component that emerges in the near-field due to chirality,
is identified in the far-field as well, as power transfer from the outgoing p-wave