42
S. Droulias and L. Bougas
emphasize here that this is a realistic value for the chirality parameter, corresponding, for example, to the case of aqueous solutions of monosaccharides [23, 24] or
biomolecules [34–36]. For such a realistic value of κ, therefore, we observe ρ DR
signals of the order of ∼10
−4 and φ DR signals of the order of a few ∼mdegs, both
within the sensitivity range of SPR instruments [60–62]. As a comparison, we note
that the optical rotation signal from a transmission measurement of a 100 nm chiral layer with κ = +10
−5 at 633 nm, is ϕ 6 × 10
−4 deg (2.1). Furthermore, we
observe that ρ DR (−κ) = −ρ DR (κ) and φ DR (−κ) = −φ DR (κ). Thus, using the DRdependent signals, we are able to quantify Re(κ) (magnitude and sign) with increased
sensitivity compared to measurements of the angular split, θ [61, 63, 64].
Another important feature of the differential signals, ρ DR and φ DR , is that these
decrease in amplitude as the plasmon resonance moves away from the critical angle,
contrary to θ//κ which we observe to increase (Fig. 2.8). This decrease is related
to the broadening of the SPR feature due to increased losses for higher k SPP , and
to the reduction of the R s /R p ratio, which expresses the strength of the p- to swave conversion. In particular, in Fig. 2.11 we show the change in the R s /R p ratio
with increasing SPR angle (due to increasing n c ). We observe that the R s /R p ratio
decreases while simultaneously broadening, which yields, thus, reduced differential
signals. Moreover, the peak-to-peak values of ρ DR and φ DR [ρ DR and φ DR , respectively; Fig. 2.11b], qualitatively follow a similar trend indicating a strong connection
with the strength of R s /R p . Furthermore, we observe that the variation of R s /R p
(and consequently of ρ DR and φ DR ) is non-monotonic and it generally depends
on the properties of the particular metal. Despite these, it is apparent that regardless
of the exact variation, the differential signals of ρ DR and φ DR allow for unambiguous
determination of κ.
Fig. 2.11 Effect of coupling strength between s− and p−waves due to chirality on differential
reflection measurements. a R s /R p ratio as function of n c for κ = ±10 −5 . b Peak-to-peak values
of the differential signals ρ DR and φ DR [ρ DR (top) and φ DR (bottom), respectively]. The solid
black lines represent a multitude of individual calculations, on which the cases for n c shown in a
are marked with dots of the same colour. In addition, the marked cases in a, b correspond to the
cases shown in Fig. 2.8 using the same colour-code
S. Droulias and L. Bougas
emphasize here that this is a realistic value for the chirality parameter, corresponding, for example, to the case of aqueous solutions of monosaccharides [23, 24] or
biomolecules [34–36]. For such a realistic value of κ, therefore, we observe ρ DR
signals of the order of ∼10
−4 and φ DR signals of the order of a few ∼mdegs, both
within the sensitivity range of SPR instruments [60–62]. As a comparison, we note
that the optical rotation signal from a transmission measurement of a 100 nm chiral layer with κ = +10
−5 at 633 nm, is ϕ 6 × 10
−4 deg (2.1). Furthermore, we
observe that ρ DR (−κ) = −ρ DR (κ) and φ DR (−κ) = −φ DR (κ). Thus, using the DRdependent signals, we are able to quantify Re(κ) (magnitude and sign) with increased
sensitivity compared to measurements of the angular split, θ [61, 63, 64].
Another important feature of the differential signals, ρ DR and φ DR , is that these
decrease in amplitude as the plasmon resonance moves away from the critical angle,
contrary to θ//κ which we observe to increase (Fig. 2.8). This decrease is related
to the broadening of the SPR feature due to increased losses for higher k SPP , and
to the reduction of the R s /R p ratio, which expresses the strength of the p- to swave conversion. In particular, in Fig. 2.11 we show the change in the R s /R p ratio
with increasing SPR angle (due to increasing n c ). We observe that the R s /R p ratio
decreases while simultaneously broadening, which yields, thus, reduced differential
signals. Moreover, the peak-to-peak values of ρ DR and φ DR [ρ DR and φ DR , respectively; Fig. 2.11b], qualitatively follow a similar trend indicating a strong connection
with the strength of R s /R p . Furthermore, we observe that the variation of R s /R p
(and consequently of ρ DR and φ DR ) is non-monotonic and it generally depends
on the properties of the particular metal. Despite these, it is apparent that regardless
of the exact variation, the differential signals of ρ DR and φ DR allow for unambiguous
determination of κ.
Fig. 2.11 Effect of coupling strength between s− and p−waves due to chirality on differential
reflection measurements. a R s /R p ratio as function of n c for κ = ±10 −5 . b Peak-to-peak values
of the differential signals ρ DR and φ DR [ρ DR (top) and φ DR (bottom), respectively]. The solid
black lines represent a multitude of individual calculations, on which the cases for n c shown in a
are marked with dots of the same colour. In addition, the marked cases in a, b correspond to the
cases shown in Fig. 2.8 using the same colour-code