2 Surface Plasmons for Chiral Sensing
39
an excess of either RCP or LCP waves below or above the SPR angle and, hence,
a reflectance split between R + and R − waves. As for the magnitude of κ, it does
not significantly affect the arg(E y /E x ) (it induces a slight angular shift), however, it
notably changes the amplitude of E y /E x , which increases with increasing κ. Changing the sign of κ induces a π -shift of the E y phase, without affecting E x [Fig. 2.7c].
Hence, the sign of κ does not affect the amplitude of the ratio E y /E x but causes the
interchange between RCP/LCP components.
2.3.2 Sensitivity of Chiral-Dependent SPR-reflectance
Angular Split
Because the resonance of the SPP wave depends strongly on the material parameters
at the metal-chiral interface, it is expected that the strength of the SPR reflectance
angular split θ will depend, besides the chirality parameter κ, also on the chiral
substance’s refractive index, n c .
In Fig. 2.8 we show this dependence for the case of real κ (we discuss the case
of imaginary κ in a following section). Overall, we observe (a) a linear dependence
between the magnitudes of θ and κ, (b) a distinct correspondence between the
signs of θ and κ, and (c) a non-monotonic dependence of θ on n c . This nonmonotonic dependence is related to the interplay between the coupling strength of
the incident wave to the SPP wave and the interaction strength of the SPP wave with
the chiral layer. In particular, as n c increases, the SPR dispersion changes and the
reflection-dip is shifted to higher angles due to higher k SPP [Fig. 2.8a]. In turn, the
coupling of the incident wave to the SPP becomes stronger, leading to higher θ and,
hence, in increased sensitivity [Fig. 2.8b]. Eventually, for very high incident angles
the coupling of the incident wave to the SPP becomes weaker, leading to weaker
accordingly. In addition, for angles close to the critical angle the effect
becomes the weakest. In reflection-based polarimetric measurements, the optical
rotation signals scale as ∼
√
Re(κ) when approaching the critical angle (see [23, 24,
58, 59]), which is not the case here [Fig. 2.8b]. This is a consequence of the fact that
the measurement is mediated entirely by the SPP wave and is not associated with
direct polarimetric signals from the chiral layer. Thus, by measuring the magnitude
and sign of this chiral-dependent angular split, we obtain information about the
magnitude and sign of κ.
Furthermore, because the thickness of the chiral film is finite, the SPP interacts
both with the chiral film and the dielectric region above (air). In essence, the SPP
experiences an effective index in the chiral-air region, which depends on the chiral film thickness; with increasing film thickness, the evanescent tails of the SPP
interact less and less with the air above, until this effective index converges to n c .
In our simulations so far we considered a chiral layer of 100 nm thickness, which is
in the order of the calculated field penetration depth [see Fig. 2.3b]. For this reason,
in Fig. 2.9 we repeat the calculations of the measurement sensitivity (θ//κ) pre-
39
an excess of either RCP or LCP waves below or above the SPR angle and, hence,
a reflectance split between R + and R − waves. As for the magnitude of κ, it does
not significantly affect the arg(E y /E x ) (it induces a slight angular shift), however, it
notably changes the amplitude of E y /E x , which increases with increasing κ. Changing the sign of κ induces a π -shift of the E y phase, without affecting E x [Fig. 2.7c].
Hence, the sign of κ does not affect the amplitude of the ratio E y /E x but causes the
interchange between RCP/LCP components.
2.3.2 Sensitivity of Chiral-Dependent SPR-reflectance
Angular Split
Because the resonance of the SPP wave depends strongly on the material parameters
at the metal-chiral interface, it is expected that the strength of the SPR reflectance
angular split θ will depend, besides the chirality parameter κ, also on the chiral
substance’s refractive index, n c .
In Fig. 2.8 we show this dependence for the case of real κ (we discuss the case
of imaginary κ in a following section). Overall, we observe (a) a linear dependence
between the magnitudes of θ and κ, (b) a distinct correspondence between the
signs of θ and κ, and (c) a non-monotonic dependence of θ on n c . This nonmonotonic dependence is related to the interplay between the coupling strength of
the incident wave to the SPP wave and the interaction strength of the SPP wave with
the chiral layer. In particular, as n c increases, the SPR dispersion changes and the
reflection-dip is shifted to higher angles due to higher k SPP [Fig. 2.8a]. In turn, the
coupling of the incident wave to the SPP becomes stronger, leading to higher θ and,
hence, in increased sensitivity [Fig. 2.8b]. Eventually, for very high incident angles
the coupling of the incident wave to the SPP becomes weaker, leading to weaker
accordingly. In addition, for angles close to the critical angle the effect
becomes the weakest. In reflection-based polarimetric measurements, the optical
rotation signals scale as ∼
√
Re(κ) when approaching the critical angle (see [23, 24,
58, 59]), which is not the case here [Fig. 2.8b]. This is a consequence of the fact that
the measurement is mediated entirely by the SPP wave and is not associated with
direct polarimetric signals from the chiral layer. Thus, by measuring the magnitude
and sign of this chiral-dependent angular split, we obtain information about the
magnitude and sign of κ.
Furthermore, because the thickness of the chiral film is finite, the SPP interacts
both with the chiral film and the dielectric region above (air). In essence, the SPP
experiences an effective index in the chiral-air region, which depends on the chiral film thickness; with increasing film thickness, the evanescent tails of the SPP
interact less and less with the air above, until this effective index converges to n c .
In our simulations so far we considered a chiral layer of 100 nm thickness, which is
in the order of the calculated field penetration depth [see Fig. 2.3b]. For this reason,
in Fig. 2.9 we repeat the calculations of the measurement sensitivity (θ//κ) pre-